
831 F.Supp. 1354 (1993)
In the Matter of MAHURKAR DOUBLE LUMEN HEMODIALYSIS CATHETER PATENT LITIGATION.
No. MDL 853.
United States District Court, N.D. Illinois, E.D.
August 18, 1993.
*1355 *1356 Joseph N. Hosteny, Raymond P. Niro, John C. Janka, Michael P. Mazza, Niro, Scavone, Haller & Niro, Chicago, IL, for Sakharam D. Mahurkar.
Marvin A. Glazer, Janelle F. Raupp, Cahill, Sutton & Thomas, Phoenix, AZ, for IMPRA, Inc.
Granger Cook, Jr., Mark J. Murphy, Cook, Egan, McFarron & Manzo, Ltd., Chicago, IL, for IMPRA, Inc. Local Counsel.

OPINION
EASTERBROOK, Circuit Judge.[*]
Kidneys remove toxins from the blood. Kidney failure is fatal unless a way can be found to replace their function. Hemodialysis does this. Blood is removed from the body, toxins are removed from the blood, and the blood is then returned to the body. Sometimes a few days or weeks of hemodialysis is enough; in the interim the kidneys, having suffered an acute failure because of trauma or disease, return to normal functioning. Chronic kidney failure requires long-term hemodialysis, with the blood being cleansed several times a week. In either event, physicians need access to the blood stream without doing excessive damage to the circulatory system and the blood itself.
This patent litigation arises out of a duallumen catheter developed to provide that access. Earlier opinions describe the litigation. See Vas-Cath Inc. v. Mahurkar, 745 F.Supp. 517 (N.D.Ill.1990), reversed in part, 935 F.2d 1555 (Fed.Cir.1991); In re Mahurkar Double Lumen Hemodialysis Catheter Patent Litigation, 750 F.Supp. 330 (N.D.Ill. 1990), 781 F.Supp. 1295 (1991), 140 B.R. 969 (1992). After a bench trial in the last of these consolidated actions, the others having been resolved by settlement, I now make the required findings of fact and conclusions of law.
Sakharam D. Mahurkar, a nephrologist, developed his first dual-lumen catheter in his kitchen in 1980, finishing the assembly on January 1, 1981. He has obtained a series of *1357 patents for that catheter and several variations, but the litigation has come to focus on No. 4,583,968, which issued on April 22, 1986. At the conclusion of the first phase of the bench trial, I informed the parties that in my view independent claims 1 and 19 of the '968 patent are valid and infringed by the devices IMPRA, Inc., has sold, and that dependent claims 2, 3, 6, 7, 8, 11, 20, 21, 22, and 23 also are valid and infringed by those catheters. Only one other patent, No. 4,692,141, issued on September 8, 1987, figures in Mahurkar's claims against IMPRA, and I concluded that I did not need to resolve certain issues concerning this patent in order either to decide liability or calculate damages. IMPRA informed me that it had taken its infringing dual-lumen catheters out of production, so I did not issue an injunction at the time. We proceeded to a trial on damages. This opinion elaborates on the oral decision on liability, addresses a few subjects that were not covered at trial, and reaches a conclusion on damages.
This litigation has been complex and extended, with disputes on hundreds of questions, central and tangential. In order to simplify this opinion, I confine my findings and conclusions to the issues that ultimately shape the decisions on the merits and relief. I assume familiarity with the earlier published opinions and do not recapitulate the nature of the devices and the background of the dispute. If the parties believe that some important factual or legal dispute still requires resolution, they should draw that issue to my attention promptly after receiving this opinion.

I
Mahurkar charges IMPRA with infringing his patents. On this question Mahurkar bears the burden of persuasion, In re Hayes Microcomputer Products, Inc., Patent Litigation, 982 F.2d 1527, 1541 (Fed.Cir. 1992), so I start here. The trial was structured in much the same fashion. See Howard T. Markey, On Simplifying Patent Trials, 116 F.R.D. 369 (1987); Rita Mankovich Irani, The New Skirmish in Patent Cases: Who Goes First at Trial and With What Evidence? 17 AIPLA Q.J. 364 (1989).
The '968 patent covers a smooth bore, dual-lumen catheter, and there is no doubt that IMPRA made such a catheter, all but identical to the one described in the '968 patent. Figures 1 and 2 (Figures 6 and 7 from the '968 patent) show the cross-section and tip of Mahurkar's device, and Figure 3 shows IMPRA's.

*1358 
Changes were made to IMPRA's catheter through the years, but none of these changes is material to IMPRA's liability. For example, IMPRA added a bevel to the D-plug sealing off the intake lumen; this change made it more like the '968 design.
After the extended pretrial proceedings, and the admissions of the parties, resolved many disputes, the essential question concerning infringement came down to a disagreement about the meaning of language in the '968 patent concerning the septum. The septum is the divider between the lumens (that is, the tubes) of the catheter.
Claim 1 of the '968 patent describes a device including a "longitudinal planar septum ... said first lumen and the internal wall thereof formed by said septum extending continuously through said conical tapered tip". Claim 19 uses this variation: "integral septum extending axially along the entire length of the tube". IMPRA contends that its catheter does not have such a septum, for reasons related to the manner of its construction.
IMPRA made its catheters by extruding plastic tubing in a double-D configuration and inserting one end of the tube into a heated die. The die was shaped like an inverted cone, so that the catheter acquired a taper, and the die had a protrusion called a mandrel. The mandrel kept a circular hole open in the return lumen of the tube so that the catheter could be inserted into the patient's circulatory system over a guidewire (the Seldinger technique) and so that blood would pass through this opening while the catheter was in use. Using a die with mandrel to form the conic, tapered tip meant that the dividing wall between the double-D tubing was melted and pushed to the outer wall. This simultaneously closed off the intake lumen and produced a thickening of one side of the wall of the tip.
The parties have had some dispute about the precise construction and shape of IMPRA's device. To tie up loose ends, I find that Figure 3 (MMDL 327) is an accurate rendering of IMPRA's device. It is taken from a diagram attached to the narrative statement of Gary Smith, one of IMPRA's experts. Figure 3 shows two deflections of the septum: one drawn by IMPRA's inhouse staff, and another closer to the tip penciled in by Smith. Glen Harding, IMPRA's current engineering supervisor, confirmed that the Smith alterations to this drawing are accurate. Tr. 736-37. I find that Smith's correction depicts the tip. The hand-drawn nature of this drawing makes it hard to say exactly where the deflection begins, but it is less than 0.188 inch, the location of the deflection in the drawing before Smith made his correction. A photograph in the record (MMDL 441) shows the deflection at the very tip. Variations attributable to differing methods of construction do not affect my conclusions, so I do not include other figures.
The upshot: for the last fraction of an inch of the IMPRA catheter there is only one lumen, the material constituting the divider having been deflected to the sidewall by the mandrel. According to IMPRA, its catheter does not infringe claims 1 and 19 because the septum in its device is not continuous through the tip. A "septum" is something dividing two lumens; because at the tip IMPRA's device has only one lumen, it has no septum there. Moreover, the material from the wall between the D-shaped lumens acquires a curve at the very end. The mandrel that melts and deflects it has a circular cross-section, so the material from the dividing wall acquires a curve that at the tip approaches *1359 a semi-circle. Yet claim 1 speaks of a "planar" septum, which to IMPRA means an uncurved septum. Thus IMPRA's argument: its catheter does not have a "continuous" septum (claim 1) extending "along the entire length of the tube" (claim 19), but even if it does it still wins because the septum is not "planar".
Although IMPRA's arguments have some semantic attraction, they are ultimately inconsistent with the terms of the patent. Both the full text of claims 1 and 19, and the diagrams illustrating the invention, call for a conversion to a conic section at the tip. The preferred embodiment of the invention has the apex of this cone on the axis of the tube, and the opening in the conic tip is in the shape of a circle rather than a D, in order to facilitate insertion by the Seldinger technique. The apex of the cone can be on the axis of the tube only if the septum is moved out of the way at the tip, and the transformation from D-shape to O-shape is possible only if at least some portion of the septum (or what used to be the septum) is curved. In other words, the invention claimed and described in the patent has exactly the deflection that IMPRA's device does. "Continuous" and "planar" thus describe the construction of the septum until the tip, but not at the tip. IMPRA's device literally infringes.
A second set of considerations supports the same conclusion. Figure 2 (Fig. 7 of the '968 patent) shows that the intake lumen of the Mahurkar catheter is sealed off below the intake ports and replaced with a plug of plastic, which the claims of the patent call a "relative concentration of material". (This both stiffens the tip and eliminates space in which blood may pool and clot.) Below the intake ports in the '968 device there is only one "lumen" through which blood flows. Yet the claims speak without embarrassment of a septum extending through the tip. If there cannot be a "septum" without two lumens, then the septum in the catheter described by claims 1 and 19 of the '968 patent must end at the intake ports. That would make the patent internally contradictory. Far better, I believe, to read the claim language so that the word "septum" as used in the patent refers both to the divider between lumens (when there are two lumens) and the wall formed by the extension of that divider along the longer (return) lumen after the intake lumen ends. This is precisely how claim 1 puts it: "the internal wall thereof formed by said septum". The septum forms an internal wall at the tip in the patent claims and in IMPRA's catheter, so again IMPRA's device literally infringes. A device need not be identical to trigger literal infringement. In patent law, as in horseshoes, close enough counts. Read Corp. v. Portec, Inc., 970 F.2d 816, 823 (Fed.Cir.1992).
Interpretation of language in patent claims is an issue of law, Read, 970 F.2d at 822, and the question whether a device literally infringes the claim as construed is one of fact. Hayes Microcomputer Products, 982 F.2d at 1541. Claim construction plays the leading role in today's case, but judges should not pretend that all nominally "legal" issues may be resolved without reference to facts. It would be folly to suppose that the two prior paragraphs capture the only possible understanding of the language in the '968 patent. Claims 1 and 19 are not self-defining. What seems clear to a judge may read otherwise to a skilled designer. That is why we had a trial. Mahurkar offered three principal expert witnesses: himself, Dr. Stephen R. Ash, and Ronald B. Luther. All three have designed catheters and hold patents for several designs; Drs. Mahurkar and Ash have used these catheters in their patients. All three of these skilled designers accorded the language in claims 1 and 19 the meaning I have ascribed to it. IMPRA also offered experts: principally its president Harold Green plus Gary P. Smith, a chemical engineer. Neither Green nor Smith is a physician or catheter designer. As it turned out, Smith essentially conceded that IMPRA's device literally infringes claim 1 of the '968 patent. Tr. 922-26. To the extent the testimony of Mahurkar's experts disagrees with that of IMPRA's, I have generally accepted Mahurkar's  not so much because of a difference in credibility as because of a difference in expertise. Mahurkar's experts know the relevant field better, making their views more reliable even after the generous discount I have applied on account of their *1360 status as hired guns (and, in Mahurkar's case, as a party).
Mahurkar, Ash, and Luther testified that no functional difference is attributable to the last-centimeter deflection of the septum into the outer wall of IMPRA's catheter. Smith agreed. Tr. 961-62. I accept these conclusions, which means that IMPRA's device also infringes the '968 patent by the doctrine of equivalents. IMPRA tries to avoid this conclusion by pointing to the prosecution history of the patent, but that effort is unavailing. Claim 19 was not amended in any way material to this case in the course of prosecution, so it cannot be narrowed by its prosecution history. Claim 1 was amended by adding the language about the continuous planar septum, but for reasons I have already given this does not matter to our case.
What IMPRA principally relies on to avoid infringement by equivalents is a single sentence in a letter Mahurkar's lawyer sent to the patent examiner distinguishing the Martin patent No. 4,451,252 on the basis of its tip construction. Richard Auchterlonie, then representing Mahurkar, wrote: "In Martin 4,451,252 the septum is deformed at its proximal end and joins the outer wall to close off the second lumen." Having avoided Martin by distinguishing the '252 tip, IMPRA insists, Mahurkar may not contend that IMPRA's catheter infringes by equivalents. Not so, and for two reasons:
First, what ultimately persuaded Examiner Truluck that Mahurkar's catheter was patentable over Martin was that Mahurkar's invention predated Martin's application. Mahurkar filed a Rule 131 affidavit, with photographs, showing the devices cobbled together in his kitchen. Martin's application after the date Mahurkar reduced his invention to practice became of no further moment, and accordingly cannot be used to restrict the scope of the claims in the '968 patent. Sun Studs, Inc. v. ATA Equipment Leasing, Inc., 872 F.2d 978, 983-84 (Fed.Cir.1989).
Second, the tip of the Martin '252 device is so completely different from the tip of the Mahurkar '968 device and the IMPRA device that the sentence distinguishing Martin on the basis of tip construction does not narrow claims 1 and 19 in any way material to IMPRA's device. Distinguishing a prior reference does not estop the applicant on each element, but only on the distinguished elements in combination. Read, 970 F.2d at 824. Both the '968 catheter and IMPRA's catheter close the intake lumen at or near the intake ports, have a long portion of the return lumen downstream of the intake ports, have a taper with a conic section, and come to a circular return port at the tip. The Martin '252 patent shows a mandrel and die being used to pinch off the intake lumen at the tip, a method utterly different from Mahurkar's, and IMPRA's. See Figure 4.
*1361 
Saying, as Mahurkar did, that the Martin '252 device is materially different is true, and of no aid to IMPRA, whose device is almost exactly like Mahurkar's and has much less in common with Martin's. "Depending on the nature and purpose of an amendment, it may have a limiting effect within a spectrum ranging from great to small to zero." Hughes Aircraft Co. v. United States, 717 F.2d 1351, 1363 (Fed.Cir.1983). In a suit against Martin, the effect of this prosecution history would be small; in a suit against IMPRA, it is zero.
For all of these reasons, I conclude that IMPRA's catheter infringes independent claims 1 and 19 of the '968 patent, and given this conclusion IMPRA cannot successfully deny that it infringes the dependent claims I mentioned at the outset. I move to the question whether the '968 patent is valid.

II
From here on IMPRA bears the burden of persuasion, 35 U.S.C. § 282, and by clear and convincing evidence. Mumm v. Decker & Sons, 301 U.S. 168, 171, 57 S.Ct. 675, 676-77, 81 L.Ed. 983 (1937); Jones v. Hardy, 727 F.2d 1524, 1528 (Fed.Cir.1984). It is a burden IMPRA has not carried, and I find independent claims 1 and 19 valid. (The validity of the dependent claims has not been separately attacked.)
The first four of IMPRA's arguments are designed to show that Mahurkar waited too long before seeking his utility patents. His first applications sought design patents. Design Serial No. 538,671, filed October 3, 1983, was converted on August 15, 1984, to an application for a utility patent, which issued as the '968 patent. A separate design application, Serial No. 356,081, filed on March 8, 1982, was the parent of the utility application filed on October 1, 1984, that led to the '141 patent. In August 1982 Mahurkar obtained a Canadian design patent on the '081 drawings. This event, more than a year before the conversions of the U.S. design applications to requests for utility patents, means that unless the utility applications are treated as continuations of the design applications, the filings come too late. See 35 U.S.C. §§ 102(b), 120. Earlier published opinions lay out the background of this timing problem, so I turn directly to the three ways in which IMPRA seeks to knock out the use of the design applications. Following that is a fourth timing argument: that Mahurkar's invention was "on sale" more than a year before the filing of design patent application '671, so that the utility application is untimely even if it takes that design application's date. Only after resolving these timing *1362 issues do I turn to obviousness, anticipation, and the like. For simplicity, and because I largely avoid questions about the '141 patent, I concentrate on timing questions concerning the '968 patent.

A
Section 112 of the patent code calls for the application to contain "a written description of the invention, and of the manner and process of making and using it". 35 U.S.C. § 112. The design application did not contain any pertinent words. It just had drawings, leading to IMPRA's contention that it flunks § 112, and that the utility application therefore must be treated as a new application rather than a continuation.
Resolving a tension in its own cases, the Federal Circuit concluded on an earlier appeal that diagrams may satisfy the "written description" requirement of § 112 when they "clearly allow persons of ordinary skill in the art to recognize that [he or she] invented what is claimed." 935 F.2d at 1563, quoting from In re Gosteli, 872 F.2d 1008, 1012 (Fed. Cir.1989) (bracketed material added by Vas-Cath opinion). "[T]he test for sufficiency of support in a parent application is whether the disclosure of the application relied upon reasonably conveys to the artisan that the inventor had possession at that time of the later claimed subject matter." 935 F.2d at 1563 (internal quotations and attributions omitted). This approach has been reiterated in later opinions. Wang Laboratories, Inc. v. Toshiba Corp., 993 F.2d 858, 865 (Fed.Cir. 1993); Hayes Microcomputer Products, 982 F.2d at 1533. And the panel in Vas-Cath added still another expression of the thought: "the applicant must ... convey with reasonable clarity to those skilled in the art that, as of the filing date sought, he or she was in possession of the invention. The invention is, for purposes of the `written description' inquiry, whatever is now claimed." 935 F.2d at 1563-64 (emphasis in original). Another variation: "[T]he proper test is whether the drawings conveyed with reasonable clarity to those of ordinary skill that Mahurkar had in fact invented the catheter recited in those claims". Id. at 1566.
Because a "specification is directed to one skilled in the art", Hayes Microcomputer Products, 982 F.2d at 1533, I must decide whether such a person would understand the drawings of the design application as showing that Mahurkar was in possession, when he filed the design application, of the features claimed in the utility application. The answer to that question must be "yes." The drawings accompanying the design and utility applications are identical (except for the addition of arrows and numbers to the utility drawings). The utility application simply lays out the details of what the design drawings show  to be precise, the utility claims narrate what features of the drawings are important, without adding anything. I find that Mahurkar was in possession of the whole invention when he filed the design applications, and the drawings in the design application would have enabled a person of ordinary skill in the art to draft the written claims that appeared in the design application.
What the drawings show to a person skilled in the art is a question of fact, on which there was extensive testimony at trial. Mahurkar testified that any fool could see the import of the drawings  they are so clear that even a judge can tell what is going on. Tr. 127-28. In my first published opinion I wrote that Mahurkar plainly had possession of the invention and showed that invention in the drawings  "what Mahurkar eventually patented is exactly what the pictures in [the design applications] show", 745 F.Supp. at 523  but I did not think them legally sufficient.
But of course judges and other amateurs in this technical field are not the right audience. During the trial each of Mahurkar's three experts in catheter design stepped through each of the elements in each claim of the '968 and '141 patents. Each expert was asked whether the claim could be seen in the design drawings. Each answered yes. Mahurkar's lawyers produced charts relating each element of each independent claim to a specific part of the drawings. The experts stated that this correspondence was accurate. I credit those answers, which when combined with the Federal Circuit's legal standard *1363 means that the design applications satisfy the written description requirement of § 112. Examiner Truluck, a person of ordinary skill in the art of catheter design, Bausch & Lomb, Inc. v. Barnes-Hind/Hydrocurve, Inc., 796 F.2d 443, 447 (Fed.Cir.1986), must have seen it too, for he allowed the utility application as a continuation of the design application.
IMPRA replies that Mahurkar, Ash, and Luther are not persons of ordinary skill in the art. They are persons of extraordinary skill. (Luther, for example, holds more patents on catheter technology than any other person in the world.) Mahurkar must have felt honored to be flattered by his opponent, and to hear a concession that buttresses his position on other aspects of the case by building up his witnesses' credentials. Let us suppose IMPRA is right, that Mahurkar, Ash, and Luther stand head and shoulders above ordinary catheter designers and nephrologists. Still, the leaders of a field understand something about how the median members of the discipline think, and each of the three witnesses testified that not only he but also a "normal" catheter designer could see the correspondence. I credit those statements, too  especially given what happened when IMPRA's expert Smith took the stand. Mahurkar's lawyer took Mr. Smith through exactly the same charts and questions. Could Smith see the correspondence between the design drawings and the claims of the utility patents? Yes, Smith answered, he could, at least for the '141 patent (in which the link between the drawings and the utility claims is harder to establish). For the '968 patent he was silent; IMPRA effectively offered no evidence on the '968 patent to rebut the testimony of Mahurkar, Ash, and Luther, and the inference to be drawn from Examiner Truluck's decision.
In sum, I answer the questions posed by the Federal Circuit with the finding of fact that the design drawings clearly show that Mahurkar possessed the invention claimed in the '968 patent as of the date of the design filing and that the drawings conveyed with reasonable clarity to those of ordinary skill in the art that Mahurkar in fact invented the catheter recited in the utility claims.

B
Section 112 also requires an application to "set forth the best mode contemplated by the inventor of carrying out his invention". IMPRA observes that the design applications do not show a catheter with a separately molded tip. To the contrary, they imply that the tube and tip belong to a single piece of plastic. Yet Quinton Instruments Company, Mahurkar's licensee and his confederate in arms in this litigation, makes its catheters in two pieces. The tube is cut at a right angle to its length, while it still has a double-D cross-section, and a separately molded tip is glued on. Figure 5 shows the construction of the Quinton-Mahurkar catheter.
*1364 
If Quinton, with Mahurkar's blessing, makes the tube and tip out of different pieces (and, it turns out, different materials), does it not follow that the design drawings fail to disclose the best mode?
No, it does not follow. IMPRA's argument depends on the premise that Quinton is today using the best mode contemplated by the inventor in 1982 and 1983, when Mahurkar filed the design applications. Section 112 calls on the inventor to disclose the best mode that he contemplates at the time; it does not impose requirements on licensees and other manufacturers, who make their own decisions at a later time. "A best mode analysis has two components. The first inquiry focuses on whether the inventor knew of a mode of practicing his invention at the time he filed his patent application which he considered to be better than any other. This determination is subjective, focusing on the inventor's state of mind at the time he filed his application. If he did have a best mode, the next question is whether he disclosed it and did so adequately to enable one of ordinary skill in the art to practice the best mode. This is an objective determination. There must be no concealment of a mode known by the inventor to be better than that which he disclosed." Hayes Microcomputer Products, 982 F.2d at 1536 (citations omitted). See also, e.g., Brooktree Corp. v. Advanced Micro Devices, Inc., 977 F.2d 1555, 1575 (Fed.Cir.1992).
Mahurkar dealt directly with the subjective portion of this test. He testified that when he filed the design applications he believed single-piece molding to be the best way to form the catheter. Separately molded tips can break off, and Mahurkar prefers to avoid that risk. IMPRA, too, sees a separate tip as undesirable and does not use one. I credit Mahurkar's testimony, which means that the drawings disclosed the inventor's preference. As for the objective component: there can be no question that the design drawings adequately disclose single-piece construction of tube and tip. IMPRA's argument starts from the premise that they convey this message to anyone skilled in the art.
Lest there be any doubt, I add that the utility application also discloses the best mode known to the inventor. The drawings are materially identical, and lines 31-37 of column 4 of the patent (part of the "detailed description of the preferred embodiment") read: "The tip 20 including the relative concentration of material 23 is easily molded and bonded or is integrally formed from the cylindrical *1365 tube 11 by the use of internal and external mandrels and the application of heat by any number of conventional means such as RF forming, thermal forming, or infrared forming." So the utility patent itself mentions both unitary and separate-tip construction.
By the time Mahurkar sought his patents, Quinton had decided to use a separate tip produced by injection molding. Testimony at trial revealed why. Although Quinton, like Mahurkar, preferred unitary construction, Quinton had trouble finding a vendor that could supply a properly shaped tip molded from the double-D tubing. It tried several suppliers and rejected the products of each. Rather than accept defective catheters, or delay their introduction until it could improve its thermal forming methods, Quinton decided to make the tip separately. To put this differently, the manufacturer compromised on one aspect of the product (the probability of tip separation) to improve other aspects, such as the smoothness of the intake and return ports and the stiffness of the tip. The use of the separate tip helped Quinton to meet another of Mahurkar's specifications, the absence of "dead space" below the intake port that causes clotting. And by getting the product to market faster Quinton produced benefits for persons in need of hemodialysis. Compromises in construction, as in a design itself, are common, and this particular compromise does nothing to undermine the fact that both the design drawings and the utility patent reveal Mahurkar's preference for single-piece construction.

C
IMPRA believes that the design drawings would not have enabled a person skilled in the art to practice the invention. This is essentially a replay of an argument that failed to persuade the Federal Circuit, and it does not persuade me. Mahurkar, Ash, and Luther testified that the drawings would have enabled a person skilled in the art to make and use the invention, and I accept this testimony.
The current variation of the enabling-disclosure argument is that the drawings in the design applications lack arrows showing the direction in which blood flows. If you can't tell which way the blood is flowing, the argument goes, how can you tell how to connect the catheter to the machine that purifies the blood? Other shadings of this "how can you ...?" question are possible, but they assume that the diagrams are addressed to children rather than persons skilled in the art. Any catheter designer, any dialysis technician, any nephrologist, indeed any general practitioner of medicine, would understand that the shorter lumen takes in the blood (or whatever other fluid passes through the catheter) and the longer lumen returns that fluid. Otherwise recirculation would defeat the purpose for which the catheter was being used. Catheters of this kind go into large veins. Blood comes out of the vein "upstream" (through the intake ports in the shorter lumen), is processed, and is returned downstream. If the blood were returned upstream via the shorter lumen, it would be sucked back out as it continued down the vein. Clean blood would be re-cleansed; other blood would be untreated. Anyone with an inkling of what the diagrams depict would understand this in a flash.
Parts II.A, II.B, and II.C of this opinion, taken together, lead me to find that the '968 utility patent application must be deemed to have been filed on October 3, 1983, when the '671 design application was filed. 35 U.S.C. § 120; Racing Strollers, Inc. v. TRI Industries, Inc., 878 F.2d 1418, 1421 (Fed. Cir.1989); KangaROOS U.S.A., Inc. v. Caldor, Inc., 778 F.2d 1571 (Fed.Cir.1985).

D
On August 31, 1982, Quinton delivered two prototype Mahurkar catheters to the Northwest Kidney Center in Seattle (Quinton's home base). This occurred thirteen months before Mahurkar filed design application '671, parent to the '968 patent. Section 102(b) of the patent code gives an inventor only one year to apply, once his invention is "in public use or on sale in this country". 35 U.S.C. § 102(b). IMPRA contends that the transfer to the Northwest Kidney Center activates the "on sale" bar and invalidates the '968 patent. Note that this argument does not affect the '141 patent, *1366 whose parent design application was filed in March 1982. The difference may account for the presence of the '141 patent in this litigation, and my resolution of the on-sale question in Mahurkar's favor makes irrelevant to the parties' entitlements a knotty problem about that patent, discussed in Part III.

1
Mahurkar gave Quinton an exclusive license to produce his dual-lumen catheters. One condition on exclusivity was the sale of the first catheter within a year, that is, by September 30, 1982. Paragraph 2.8 of the Quinton-Mahurkar license. As the time approached, Quinton had not made a sale, because it had not been able to make catheters according to Mahurkar's specifications. Vendors could not form the double-D tubing correctly. Quinton could not form a tip out of the tubing it had received or create smooth holes; the list of difficulties was extensive, although similar difficulties accompany the introduction of many novel devices. At all events, Quinton had nothing for sale  at least, not for commercial sale.
Which is not to say that Quinton could not make double-D catheters bearing some of the hallmarks of Mahurkar's designs. Its staff made a few prototypes by hand to test the rates of flow and the pressure changes. Finding them satisfactory, it furnished prototypes to Dr. Carlos Flombaum at the Memorial-Sloan Kettering Cancer Center for tests. Dr. Flombaum performed the tests and reported favorable flow rates but unacceptable flow resistance readings and recirculation rates. Flombaum Dep. 38-39. He also reported that the catheters were of poor construction and recommended that further testing be conducted on dogs. MMDL 176 at 4.
Wayne Quinton, the CEO of Quinton Instruments, decided to sell similar prototypes in order to retain the exclusive license. Being no ghoul, Quinton structured this transaction to ensure that the prototypes would not be implanted in human subjects. He paid a call on Christopher Blagg, the executive director of Northwest Kidney Center and a long-standing acquaintance. Quinton asked Blagg for what Blagg characterized as a personal favor: to buy some of his new catheters. (Blagg testified by deposition, as did most of the other participants in the events of August 1982. The depositions were introduced into evidence at trial.) Blagg called both the visit and the request unusual, but he accommodated Quinton and agreed to buy the devices. Northwest received an invoice for 20 catheters at $20 apiece. It did not pay this bill, and it received only two catheters. The minutes of Quinton's Renal Projects Team include this observation: "Shipped two catheters to N.W. Kidney Center August 31, to satisfy marketing requirement." Whether the Kidney Center paid even for the two is unclear; I shall assume it did, although I do not think the answer matters. Mahurkar protested that this was a sham and threatened to terminate Quinton's exclusivity; the parties eventually worked out their differences and Quinton kept its exclusive rights.
The two catheters were never used. They were delivered directly to Dr. Tom Sawyer, chief staff physician of the Center (products usually were delivered to the shipping department), who put them not in the Center's medical stores but in a closed cabinet over a sink, where they remained until patent litigation erupted. It was clear from the outset that they would not be used, and this for two reasons.
First, Northwest Kidney Center's principal business is dialysis of persons with chronic kidney failure. Patients receiving long-term dialysis rarely use catheters of the kind Mahurkar designed. Instead blood is exchanged through a fistula, a knot of tissue arranged as a receptacle for connections to the dialysis machine. Fistulas sometimes fail, or do not form properly, and in these cases chronic dialysis patients need catheters or some alternative means of access. Northwest sends these patients to hospitals for the insertion of the necessary catheters. Northwest was not going to use the catheters Quinton supplied, because it does not install any subclavian catheters. Blagg Dep. 50-51, 61-62.
Second, the technicians who fabricated the catheters by hand at Quinton made sure that they would never be used, at least not if the recipients followed the instructions typed on *1367 the packages. The catheters were not sterilized at Quinton, and the instructions directed the user to sterilize them in an autoclave at 250° F for 30 minutes before insertion in a patient. An autoclave uses superheated water (that is, above 212° F) under high pressure. Yet the catheters were made of plastic. Spending 30 minutes or more at 250° F or higher would have melted the devices, or at least deformed them. Browne Declaration ¶ 8; Sommercorn Declaration ¶ 7. The sterilization instructions were equivalent to "melt before using"  thus ensuring no use. Of course a physician could have ignored the instructions and implanted a non-sterile device, or sterilized the devices in a cold chemical bath, but no one following the instructions could have used these devices.
In finding that use was not contemplated by either Quinton or Northwest, I have not overlooked Blagg's testimony that he did not buy things that he did not plan to use, and that he wanted to put the catheters "into some patients and see how they worked." Blagg Dep. 23. Blagg confessed to substantial difficulties in remembering what had happened in 1982, and one of the things he seems to have forgotten is that the Quinton-Mahurkar catheter is a product of a class that the Northwest Kidney Center did not insert; it sent patients to hospitals for that procedure. Blagg testified that the whole procedure was out of the ordinary  that vendors usually give away samples of new products, but that Wayne Quinton had asked him as a favor to buy these, and that he accommodated his long-time vendor. Blagg Dep. 18-20; Blagg Declaration ¶ 3. That Blagg does not "recall" any restrictions on the use of the devices does not mean that there were none, either by agreement or by practical necessity.
The hand-made devices that Quinton put in Dr. Sawyer's hands were better than the catheters Mahurkar made in his kitchen, and were of approximately the same construction as those that Dr. Flombaum had used with human patients. Accordingly they could have been used as catheters, notwithstanding the many shortcomings in their design that made them unsuitable as commercial products. (I reject Mr. Green's testimony that these devices were merchantable in the trade in 1982; they were prototypes, not saleable devices, and were so crude that Quinton would not even have given them away, except for testing or a desire to retain its exclusive license. Instead I accept the testimony of Dr. Mahurkar and Mr. Harding, and the implication of the depositions of Quinton's staff, that these were not functional as therapeutic catheters.) The catheters were crudely formed, and the holes for the passage of blood were drilled by hand. For one of these catheters the drill slipped, creating a hole in the septum that would lead to recirculation. The edges of the drilled holes were rough, creating a risk of hemolysis (rupture of red blood cells and the release of hemoglobin directly into the blood, with potentially fatal effects), and there were dead spots where blood would stagnate, creating a risk of clotting. They were not radiopaque. The tip was not stiff enough for normal insertion using the Seldinger technique. These flaws prevented commercial sale. Yet they did not make the devices killers, as Mahurkar would have it. Quinton told the FDA, when applying for approval to sell catheters of Mahurkar's design, that the devices it furnished to Northwest Kidney Center were safe. Careful monitoring during hemodialysis would have enabled a physician to remove these catheters if the risks came to pass. A need for full-time monitoring is another reason, however, why these devices could not have been sold commercially: an important objective of the Mahurkar catheter is to permit patients to go weeks or even months at a time without clotting and with only occasional supervision.

2
What is one to make of these events? Do they show that the Mahurkar invention was "on sale in this country" in August 1982? IMPRA contends that it does, because (i) the devices constitute a "reduction to practice" and would have worked as well as those Dr. Flombaum implanted, and (ii) the transaction was a bona fide sale under the Uniform Commercial Code and not for experimental purposes. Mahurkar replies that the devices were so unsafe that they could not properly be called "catheters," that they do not embody his invention because they lack elements *1368 such as axially separated intake and exit ports and a relative concentration of material in the tip, and that the transaction was a sham.
I find that the devices furnished to the Northwest Kidney Center were "catheters" and constituted a reduction to practice of the Mahurkar invention, to the extent it was possible to do this by hand. If IMPRA were to make and sell identical devices today, Mahurkar could contend, successfully, that they infringed claims 1 and 19 of the '968 patent. Although the hand-made devices of August 1982 were far from the polished commercial products of today, they either embodied the invention or came close enough to satisfy the standard of Atlantic Thermoplastics Co. v. Faytex Corp., 970 F.2d 834, 836 (Fed.Cir. 1992) (whether the complete invention was "embodied in or obvious in view of the thing sold or offered for sale").
The transaction was a "sale" for purposes of contract law. Northwest Kidney Center got good title to the catheters and was free to do with them what it pleased. If it did not pay, this does not undo the quality of the transaction as a sale; Quinton could have filed suit for the $40 price. Yet the transaction was also a sham, from the perspective of the Quinton-Mahurkar license. The pertinent clause of that license was designed to induce Quinton to get the product into commercial sale and use, and Quinton failed in that task. What it furnished to Northwest Kidney Center was not a marketable product, could not have been used in compliance with the package directions, and could not have been used therapeutically even by persons willing to ignore those instructions.
Many years ago the Second Circuit adopted a mechanical rule: any transaction that is a "sale" for purposes of the law of contracts starts the clock under § 102(b), even if the "sale" is a sham or a device to bamboozle the inventor (or one of the inventor's creditors). Mayer v. A & H.G. Mutschler, 248 F. 911, 915-16 (2d Cir.1918). See also Timely Products Corp. v. Arron, 523 F.2d 288, 302 (2d Cir.1975). If this were the prevailing law, IMPRA would win. But it is not the law in the Federal Circuit, which has disparaged any mechanical equation between "sale" for the purpose of commercial law and "on sale" for the purpose of § 102(b). See UMC Electronics Co. v. United States, 816 F.2d 647, 654-57 (Fed.Cir.1987).
UMC Electronics abolished all mechanical tests and substituted an approach under which triers of fact must consider all facts and circumstances in light of the purposes of the patent laws in general and § 102(b) in specific. Until UMC it was widely thought that to determine whether the invention was "on sale," one asked whether the inventor offered or sold an item constituting a "reduction to practice." UMC Electronics holds that reduction to practice not dispositive, although it is a consideration. Other cases wipe away other simple tests. Barmag Barmer Maschinenfabrik AG v. Murata Machinery, Ltd., 731 F.2d 831, 838-39 (Fed.Cir. 1984), holds that whether the item sold is of commercial quality is important but not dispositive. A sale (or offer for sale) may satisfy § 102(b) even though the product is not ready for commercial marketing. But whether the item is merchantable still matters. See Shatterproof Glass Corp. v. Libby-Owens Ford Co., 758 F.2d 613, 621-23 (Fed. Cir.1985). I agree with IMPRA that Shatterproof Glass does not embrace every word of the jury instruction that includes "commercially useful" language. The key to that decision was that the apparatus and method were not even "functional" on the bar date. 758 F.2d at 623. Still, Shatterproof Glass implies that the trier of fact must consider the extent to which the product works properly. Cases such as UMC Electronics require the trier of fact to consider all of the circumstances.
What circumstances matter? That depends on the policies § 102(b) serves. According to IMPRA, "the principal policy underlying the `on sale' bar is to discourage the removal of inventions from the public domain that the public justifiably comes to believe are freely available." Memorandum in Support of IMPRA's Position That No Injunction Should Issue 3 (emphasis in original). If that is indeed the function of the on-sale bar, then Mahurkar wins this case hands down. No member of the public, or even of the *1369 trade, would have believed that the Quinton-Mahurkar catheter was "freely available" in August 1982. The circumstances of the transaction show that this was a put-up job, a favor Blagg did for a friend in order to satisfy a licensing condition, without any prospect that the catheters would be used. It was not a sale on ordinary commercial terms. No one else relied, or could have relied, on any belief that the Quinton-Mahurkar catheter would be available on any terms. The language in IMPRA's memorandum is similar to one of the considerations listed in UMC Electronics; in the original version, that language is even less favorable to IMPRA, because the Federal Circuit added after "freely available": "to all as a consequence of prolonged sales activity." 816 F.2d at 652, quoting from General Electric Co. v. United States, 654 F.2d 55, 61, 228 Ct.Cl. 192 (1981) (in banc). Whatever phrases might be used to describe the transaction between Quinton and Northwest Kidney Center, "prolonged sales activity" is not among them.
The Federal Circuit's cases suggest several other roles for § 102(b). UMC Electronics offers two of salience here: preventing the inventor from commercially exploiting his exclusive position before obtaining the patent (in other words, preventing the inventor from increasing by more than one year the effective length of exclusivity), and giving the inventor time to test the commercial market so that he may determine whether it is worth incurring the costs of pursuing a patent. Id. at 652-53. The latter consideration again counsels against treating the Northwest Kidney Center transaction as putting the catheter "on sale." It was not a means of sticking one's toe into the commercial waters; information about the commercial demand for a catheter of this design did not come in until Quinton began to advertise and sell the catheter in May or June of 1983  and Mahurkar filed his patent application less than a year later.
Cases since UMC Electronics imply that commercial exploitation and the potential extension of the exclusivity period are the most important considerations. Paragon Podiatry Laboratory, Inc. v. KLM Laboratories, Inc., 984 F.2d 1182, 1185 (Fed.Cir.1993), the most recent case, equates "on sale" with "commercialization outside of the grace period." "[T]he thrust of the on-sale inquiry is whether the inventor thought he had a product which could be and was offered to customers". Id. at 1187 n. 5. "When sales are made in an ordinary commercial environment" the product is on sale. Id. at 1187, quoting from LaBounty Manufacturing, Inc. v. ITC, 958 F.2d 1066, 1072 (Fed.Cir.1992). In Paragon Podiatry the invention was publicly advertised, and 300 items were sold without restriction. In this case, by contrast, the product was not advertised, was not offered to anyone other than Blagg, and that offer was arranged as a non-commercial special deal. It was not done for profit; $40 does not come close to covering the costs of having one's technical staff make two unique medical devices by hand. Keeping exclusivity might have produced profit for Quinton later, but this is not the sense in which Paragon Podiatry used "commercialization". And a search for commercial profits from the invention has deep roots. McClurg v. Kingsland, 42 U.S. (1 How.) 202, 208-09, 11 L.Ed. 102 (1843), and Kendall v. Winsor, 62 U.S. (21 How.) 322, 16 L.Ed. 165 (1859), pose exactly this question when looking for sales under a predecessor to § 102(b).
Judges sometimes say that the function of a rule such as § 102(b) is preventing the "extension" of the patent monopoly. Ordinary sales in competition do not yield monopoly profits, and the longer an inventor sells his product without seeking a patent, the more competition there is likely to be. Yet the threat of a patent application in the background may stifle the power of competition. A potential rival deciding whether to invest in equipment to make the product must consider the possibility that after the costs have been sunk, the inventor will apply for a patent. Fear of losing their investment may discourage rivals and enable the inventor to collect supra-competitive profits before obtaining a patent. Section 102(b) limits to *1370 one year the duration of this in terrorem effect. From this perspective, however, the policy of § 102(b) is not even activated unless the inventor makes commercial use of the product in a way that is simultaneously capable of generating profits while discouraging competition.
Consider the need for functional and merchantable products from this perspective. Most of the time it is impossible to make a profit without having a merchantable article. Non-functional items usually cannot be sold commercially. But sometimes the ordinary course of commerce entails genuine sales of prototypes or even of concepts. In many industries  military aviation being a prime example  commercial sales occur while the items are still being developed. The vendor sells the germ of an idea and works out the bugs later, often in cooperation with the principal customer. Revenues flow in, and knowledge that the developer will seek a patent discourages rivals from investing in what may be expensive work along the same lines. Treating such sales as "real" sales for purposes of § 102(b) is sensible, for that is the way the market works.
The less a "sale" looks like ordinary commerce in search of profit, however, the more complete the invention must be. UMC Electronics, 816 F.2d at 656, emphasizes this sliding scale. Recent decisions reiterate it. E.g., Paragon Podiatry, 984 F.2d at 1185-88. And throughout the process of this weighing, the burden is on the infringer, by clear and convincing evidence. Atlantic Thermoplastics, 970 F.2d at 836. (Loose language to the contrary in Hycor Corp. v. Schlueter Co., 740 F.2d 1529, 1535 (Fed.Cir.1984), suggesting that the burden is on the patent holder, is no longer authoritative, if it ever was.)
The catheters furnished to Northwest Kidney Center do not establish commercialization. "[T]he inventor [did not think] he had a product which could be and was offered to customers". Paragon Podiatry, 984 F.2d at 1187 n. 5. Mahurkar knew that Quinton lacked a marketable product and protested the "sale" to Northwest Kidney Center. Northwest bought outside the usual channels, as a favor to Wayne Quinton rather than as an ordinary customer. As I have emphasized, the articles it received could not have been used by anyone who followed the instructions. No rival would have been discouraged from developing, investing in, or producing potentially competing catheters; indeed, no rival knew anything about the transaction.
One more purpose of patent law requires consideration: the dominant purpose of them all, the purpose of encouraging innovation by rewarding it. Advances in technology are not born market-ready. While ideas are being translated from the drawing board to production, manufacturers will consult with their customers in order to find out which lines of development will be most useful. They will make samples and prototypes. Many such endeavors can be characterized as offers or sales, just as IMPRA has done here. But reading "on sale" to cover these exploratory discussions and transactions would either reduce the incentive to invent (by increasing the risk that persons who make valuable discoveries will not obtain valid patents) or discourage inventors from engaging in the very discussions with customers that may increase the commercial and hence social value of their work. Neither outcome is desirable.
I conclude that the Northwest Kidney transaction did not put Mahurkar's device "on sale" within the meaning of § 102(b).

E
The basic requirement of patentability appears in 35 U.S.C. § 101: "Whoever invents or discovers any new and useful ... machine ... or any new and useful improvement thereof, may obtain a patent therefor". Mahurkar's dual-lumen catheter is unquestionably new and useful.

1
Until well into this century, people who suffered renal failure died quickly. The development of a means to remove toxins from *1371 the blood made treatment possible, but it was still necessary to link the dialysis machine to the patient's circulatory system, which was no easy matter. Between approximately 1930 and 1960 the standard means of obtaining access was the "cut down"  a surgical incision that connected a vein or artery to a tube, and hence to a dialysis machine. The procedure meant a permanent loss of the vein or artery, and the connection thus established would last only ten days or so. The patient would be hospitalized. If the patient's kidneys did not recover during this time, dialysis would be discontinued, and the patient would die. (This history comes from William Drukker, Hæmodialysis: A Historical Review, in Replacement of Renal Function by Dialysis 38-41, 49, 58-59 (John F. Maher 3d ed. 1989); Raymond Vanholder, Nicholas A. Hoenich & Severin Ringoir, Single Needle Hæmodialysis, id. at 382-99; and Dr. Mahurkar's testimony, which was not challenged in this respect.) The longest survival on record was approximately half a year.
In 1960 Wayne Quinton and Belding H. Scribner devised a shunt that could extend the time of treatment. An artery and vein in the arm would be cut down, and a tube called a shunt would be inserted to connect them. The shunt could be removed periodically, routing the blood from the artery through a dialyzer before being returned to the vein. After dialysis, the shunt could be replaced. Clotting and hemolysis, two of the principal dangers of dialysis, were greatly reduced. For the first time, victims of renal failure could be kept alive for significant periods. But walking around with a loop of tubing sticking out of your lower arm is hazardous. The shunt might pull out, or the places where it entered the body could become infected. Some clots might form. And the procedure severely reduced circulation to the hand.
"It became obvious that the arterio-veinous shunt was the Achilles heel of chronic dialysis. Patients, doctors and nurses were plagued by episodes of clotting, infections and subsequent loss of shunts." Drukker, Hæmodialysis: A Historical Review at 49. Efforts to find a better way led to two innovations during the 1960s. One was the femoral catheter. Catheters with circular cross-sections would be inserted in the femoral veins in the legs. Blood could be removed from one vein, cleansed, and returned to the other. Femoral catheters did not result in permanent loss of the veins or any limb, and they could remain in the patient for weeks at a time  but the patient was effectively immobilized. Walking with the catheters in the legs was possible but not practical. The location of the insertion also increased the risk of infection.
The second innovation, from 1966, was the fistula. It is an internal shunt constructed of the body's own tissues. A surgical procedure rearranges the body's plumbing so that blood crosses from artery to vein in an area where a buildup of scar tissue makes it possible to insert a needle repeatedly, withdrawing blood for cleansing, without collapsing the vessel. Because the fistula is internal, it cannot pull out and is unlikely to become infected or clot. Fistulas are the method of choice to this day for long-term access to the circulatory system. But fistulas take six to eight weeks to form (so that other means of access are essential in the interim), and in some cases they do not form successfully, or form but fail later.
One thing missing after the development of femoral catheters and shunts in the 1960s was a means of immediate access to the circulatory system (while the fistula was forming, or if the patient was unable to form one) that required only one puncture and left the patient ambulatory. Such a device would entail two tubes (lumens) joined so that they could be inserted into a single blood vessel. The subclavian vein near the neck is large and readily accessible; an outpatient procedure may suffice to implant a catheter in this vein. A patient remains mobile and may return to the dialysis center for tri-weekly treatments while his fistula forms.
Putting two tubes into one vessel implies a small cross-section for each lumen  yet a *1372 small cross-section may mean low rates of blood flow (with correspondingly long times connected to the dialysis machine) or high pressures and velocities to move more blood through the smaller tubes. High pressures increase the risk of hemolysis, and sucking the blood into the tube at high pressure also increases recirculation (that is, removing and cleansing the blood that has just been returned to the patient), reducing the efficiency of dialysis and again increasing the time. Any device left in the body for extended periods, to avoid multiple surgical insertions, poses a serious risk of clotting.
The challenge was to obtain the best compromise along the attributes. Lumens with large cross-sections would mean fast flow of blood at low pressures, but the larger the cross-section the more difficult the insertion and the shorter the time the device may be left without doing damage. Lumens with circular cross-sections can carry the most blood for a given diameter, but putting two such lumens side-by-side requires a very large puncture  it effectively makes the catheter rectangular, which is not desirable. A soft device is more tolerable to ambulatory patients, but a stiff one is more readily inserted. The list of variable attributes may be extended. Some others are discussed below.
Robert Uldall developed a coaxial catheter as one solution. His device holds U.S. Patent No. 4,493,696 (issued in 1985, and cited by Examiner Truluck in the '968 patent). A coaxial catheter has two tubes, each with a circular cross-section, one inside the other. Because the two lumens have different shapes and areas, it is difficult to ensure that they operate at the same pressure when withdrawing and returning the same amount of blood. The donut-shaped intake lumen, which has both inner and outer walls, is more resistant to blood flow than is the inner lumen, with only an outer wall. (Each wall is a source of resistance, and the rate of flow approaches zero at the wall itself. The details of fluid dynamics do not matter to this opinion, but they matter a great deal to the design of efficient catheters.) The presence of two tubes also contributes to clotting. To avoid infection, technicians remove the inner tube (the return lumen) after each treatment, and replace it before the next. This procedure is often painful and creates a potential for complications.
Another approach to a single-entry catheter is a single-lumen device used both to withdraw and return blood. Such a catheter may be built with a circular cross-section, for maximum flow at a given diameter and pressure. It thus minimizes the trauma caused by insertion and minimizes the risk of clotting. Yet this procedure, too, is far from ideal. A machine designed to use a single-lumen catheter with alternating flow is more expensive than an ordinary dialysis machine. Removing blood without returning any during one cycle requires higher pressures (with risk of hemolysis); the blood returned on the next cycle may be removed once again when the flow alternates. High recirculation rates imply longer treatment, with greater expense and inconvenience to the patient.
Mahurkar's solution to the problem abandons the circular cross-section for each lumen while maintaining the circle for the catheter as a whole. Each lumen in his devices is a semi-circle. There is only one wall, so blood flows more freely than it does in a donut-shaped coaxial lumen of equal area. A double-D configuration has a higher wall-to-diameter ratio and thus more resistance to flow than does a circular cross-section, but it avoids the need for two insertions or for the side-by-side tubes that have a very large effective puncture area, with extra trauma and risk of infection. The following data, from one of Mahurkar's publications, show the differences.


*1373
     THE COMPARISON OF PERFORMANCE OF THREE GEOMETRIES
           Cross-Sectional Geometry of Catheter
Hydrodynamic                                                                            Equation
Parameters              Circular             Semicircular              Annular          Reference
--------------------------------------------------------------------------------------------------
Diameter (cm)           0.197923                0.3                  0.3581758         (2.2), (2.19)
        % of           34.0256%                                     19.391933%             (2.12)
Semicircular             Less                                          More
Cross-Sectional         0.0307668               0.0353429            0.0699918
Area (cm2)             13.437564%                                   98.036381%
         %                Less                                         More
Puncture                0.615336                0.706858             0.1007586       (2.1)
Area (cm2)             12.947712%                                   42.54433%       (2.11)
         %                Less                                         More         (2.18)
Reynolds Number        87.135352               80.699527            70.55100
Total Drag            153.24528               176.03826            348.61992
(dynes)                12.947742%                                   98.03645%       (2.2)
         %                Less                                         More
Mean Shear             16.43048                14.963061            13.303291       (2.9)
(dynes/cm2)             9.8069439                                   11.09245%       (2.16)
         %               % More                                        Less
Pressure Gradient      4980.864                4980.864             4980.864
(dynes/cm3)
Flux                    8.9545637               8.9545637            8.9545637

Sakharam D. Mahurkar, The Fluid Dynamics of Hemodialysis Catheters, 31 Trans.Am. Soc. Artificial Internal Organs 124, 129 (1985). Mahurkar's catheter has two lumens, so the costs and difficulties of alternating-flow machines are avoided. Other features of his catheters are designed to produce smooth (laminar) flow; reducing turbulence increases the amount of blood that can be moved per second at a given pressure; and the possibility of reduced pressure lowers the risk of hemolysis and clotting. Dividing the flow axially (left and right lumens drawing in and returning on opposite sides) cuts down recirculation. His catheters also are designed to eliminate spots where blood stagnates and clots. And catheters of this general design can be made of fairly stiff plastic and be inserted via the Seldinger technique without surgery, without being so stiff that the patient is uncomfortable.
A compromise, to be sure. Yet many of the most important medical advances lie in finding the best compromise among available devices. Circles and semi-circles have been around for a long time. Single and dual-lumen catheters have been, too. Arranging the shape and placement of the lumens, and arranging the shape and placement of the intake and return ports, to maximize flow while reducing pressure and recirculation, is what this invention is about. It has been a great success. Since its introduction to the trade in mid-1983, the Quinton-Mahurkar catheter (or infringing designs modeled after it) has swept the market. It is the catheter of choice for hemodialysis until a fistula forms, and in some cases even thereafter.
That the device is "new and useful" is beyond question. (I speak of "the" device even though Mahurkar holds patents for several variations. I come later to the question *1374 whether one of his initial variations anticipates the variation claimed in the '968 patent.) There was nothing like it when Mahurkar invented it. The device addressed a long-felt need, and it displaced alternative means of achieving the same objectives. Its success surprised many other students of the subject, who believed that a double-D configuration would not produce flow rates high enough, and recirculation low enough, to be useful. These same considerations show that the device is novel. In reaching this conclusion I have relied on the testimony of Mahurkar, Ash, and Luther, which I find persuasive.

2
IMPRA does not really challenge any of this. It does, however, contend that the Mahurkar designs are "obvious" or "anticipated." 35 U.S.C. §§ 102(a), 103. Its strategy has been to show that each feature of the '968 catheter exists in some other medical device. Catheter # 1 has two lumens; catheter # 2 has multiple lumens with a circular outside cross-section; catheter # 3 has a planar septum; catheter # 4 has a conically tapered tip. So it goes. I grant that each of these statements is true, but they are individually and collectively irrelevant.
Whether a device is obvious or anticipated depends on whether "the differences between the subject matter sought to be patented and the prior art are such that the subject matter as a whole would have been obvious at the time the invention was made to a person having ordinary skill in the art to which said subject matter pertains." 35 U.S.C. § 103 (emphasis added); see also Graham v. John Deere Co., 383 U.S. 1, 86 S.Ct. 684, 15 L.Ed.2d 545 (1966). Mahurkar does not claim to have invented the dual-lumen catheter, or anything of the kind. He claims a particular arrangement of elements. The invention is in how these are put together  in the nature of the compromises struck and problems overcome  and not in the elements themselves.
A person having ordinary skill in this art is one who understands both catheter technology and the demands of hemodialysis. Ordinary skill means at least the ability to understand the technology and make modest adaptations or advances. That is impossible without first understanding both goals of hemodialysis (or some other use of catheters) and fluid dynamics  the needs of medicine, the tolerances of the bodily fluid to be exchanged, and how geometry affects pressures, shears, and turbulence. The "art" does not lie in seeing circles and semicircles, or in understanding that a catheter with a tapered tip is easier to insert than is a catheter with a blunt nose. Advances made in this art lie in the details, the relation among surfaces, sections, and features, and not their existence. Understanding is achieved, and intellectual advances made, by seeing the objectives and choosing among ways to achieve them  figuring out what features to keep and which to discard, knowing that one choice may interfere with others and producing the optimal compromise.
Consider an analogy in linear programming. An airline that serves 50 airports wants to choose routes for its planes that maximize the time they can be in the air (and the number of passengers per flight) while minimizing waste motion. Back-and-forth between city pairs will not do; sometimes the plane goes on to a third city. What route will best bring it back full of customers? This is a variation of the "salesman's tour" problem of finding the shortest path that takes the salesman to 50 cities without retracing his ground. Anyone can choose the shortest path to two or three or five, or can schedule stops for a fleet with only two airplanes; but it takes a genius to design an algorithm that can complete the whole tour in less computing time than the age of the universe. As the number of variables increases, and the number of possible combinations increases by the factorial of the number of elements, greater skill is needed. Back to catheters: there are 10! permutations of 10 elements, assuming that each element can take only one configuration. An ability to see cities and trace paths, or to see elements that might be combined, is of no utility.
All of this is just another way of making a staple proposition in patent law: decomposing an invention into its constituent elements, finding each element in the prior *1375 art, and then claiming that it is easy to reassemble these elements into the invention, is a forbidden ex post analysis. E.g., In re Fritch, 972 F.2d 1260, 1265-66 (Fed.Cir. 1992). With hindsight the transistor is obvious; but devising the transistor was still a work of genius. An invention lies in a combination of elements that are themselves mundane. "Virtually all inventions are combinations and virtually all are combinations of old elements." Environmental Designs, Ltd. v. Union Oil Co., 713 F.2d 693, 698 (Fed.Cir. 1983). Unless the prior art itself suggests the particular combination, it does not show that the actual invention was obvious or anticipated. See also, e.g., Minnesota Mining & Manufacturing Co. v. Johnson & Johnson Orthopædics, Inc., 976 F.2d 1559, 1565 (Fed. Cir.1992) (the party challenging the patent must show "that each element of the claim in issue is found, either expressly or under principles of inherency, in a single prior art reference, or that the claimed invention was previously known or embodied in a single prior art device or practice.") (citation omitted); Panduit Corp. v. Dennison Manufacturing Co., 810 F.2d 1561, 1568 (Fed.Cir. 1987) (improper to use the patent as an instruction manual to lead to elements of prior art); In re Donohue, 766 F.2d 531, 534 (Fed.Cir.1985).
Three persons skilled in the art of catheter design  Mahurkar, Ash, and Luther  testified at trial. Mahurkar described the process by which he made the invention and showed why it was a substantial advance over the existing state of the art. Ash and Luther agreed that Mahurkar's design was a big advance and, analyzing other designs, showed why none anticipates Mahurkar's or makes it obvious. Luther is not an expert at hemodialysis, but against this stands the fact that he has designed and patented more catheters than anyone else, and that this is the first time he has ever testified as an expert witness; he is not a mouthpiece. I agree with the conclusions Mahurkar, Ash, and Luther offered about the state of the art in either 1981 or 1983.
Certainly IMPRA has not established anticipation or obviousness by clear and convincing evidence. Its technical witness, Gary Smith, is not an expert in either kidney disease or catheter design. His job is managing quality control at a firm making arterial catheters (which carry wires to pacemakers); he did not design any of these devices. He knows nothing of the objectives of the designs he analyzed for purposes of this case, and although he can see the menu of options he cannot enlighten on how a person skilled in the art in 1981-83 would have chosen among them for optimal results. He explicitly followed the forbidden strategy of decomposing the patented device into elements and seeing whether he could find each in some other catheter. He found 25 such elements, and testified that each of the 25 appears in some other device. Smith added that he thought it obvious how to reassemble them to get the '968 catheter. This is much like testifying that because Shakespeare used only 26 letters, each of which had been used many times before, his plays are obvious. Only Mahurkar, Ash, and Luther assessed the design as a whole, in light of the state of knowledge in 1981 to 1983. They concluded that the design is not obvious or anticipated. I credit their testimony and disbelieve Smith's. (I mention 1981 and 1983 because, given the holdings of Part II.A through C, prior art means items made, or descriptions published, by October 1983, or inventions before January 1981.)
At this point I could move to the next issue. Still, the parties have invested so much energy in analyzing particular prior art (even though IMPRA and Smith went about that task in a flawed way) that it may be best to tie up loose ends by a brief discussion of the principal items of prior art on which IMPRA relies.
1. One patent that received substantial attention at trial is No. 3,634,924, awarded to Lawrence W. Blake and four colleagues in 1972. This patent covers a "Method of Making Multilumen Balloon Catheter". The caption on the patent is enough to show how far afield IMPRA has gone. Blake invented a method of making a certain kind of catheter. The catheter described in this patent is a balloon catheter  that is, a device inserted into the body and filled with some fluid, which expands a balloon covering the catheter. *1376 Such devices are used in angioplasty to enlarge a vein or artery, and in other procedures to test the body's internal pressure (the physician measures resistance to the pressure applied to the fluid). Their objective is not to deliver the fluid (air, water, or oil) passed through the lumens, but to deliver pressure via the balloon. The catheter is then promptly withdrawn.
IMPRA highlighted the Blake catheter because it shows two lumens inside a device whose outer cross-section is circular, and has an integral (albeit not planar) septum. Well and good, but what has this to do with optimizing the exchange of fluids via a device that can be left in the patient for extended periods, which is the function of the Mahurkar invention? As I have said, two lumens inside a catheter is no news, yet this is all Blake shows. The lumens are not of equal size, are not D-shaped, there is no axial separation to improve flow (Blake was uninterested in flow), no details to prevent clotting. In a nice touch, Clement K. Lieber, one of the coinventors on the Blake patent, was shown a catheter covered by Mahurkar's '968 patent. Lieber could not identify what such a device was for! Lieber Dep. 110. Balloon catheters and hemodialysis catheters are utterly different beasts; finding one or two particular elements of the '968 device in the Blake diagrams would have provided no information of value to someone trying to improve the palliation of renal failure.
2. Much the same can be said about the Edslab Model 93-136-6F Thermodilution Catheter, on which IMPRA also concentrated a great deal of fire. This unpatented device, described in MMDL 3100, has a circular cross-section and an integral planar septum. I should say, septa. It has three, dividing a tube of circular cross-section into three pie-shaped lumens. (This is "planar" only in the sense that the septum joins three planes at 120° angles.) One lumen contains a thermistor, for measuring temperature deep inside the body. It is a diagnostic device; the other two lumens pass fluids for use in the process of measuring the rate of change of temperature, as the literature says, "for determination of cardiac output using a non-balloon catheter."
Edslab's device is not designed to remove and return large volumes of bodily fluids. The lumens are tiny, the better to achieve access deep inside the circulatory system, and are not of uniform diameter. Low volumes of fluid move at high pressure, the opposite of the high-volume, low-pressure design appropriate for hemodialysis. It is not designed to stay in the body without infection or clotting or hemolysis. Shear and recirculation are irrelevant to its design. It cannot be inserted by the Seldinger technique; it is flexible to the point of being droopy. The pie-shaped lumens have three corners that constrict flow. Mahurkar, Ash, and Luther all said that they would have learned nothing from such a device about a good way to make hemodialysis catheters, and that testimony is not only credible but also obviously correct.
Again I emphasize that the art of hemodialysis catheter design lies in combining a knowledge of flows, pressures, turbulence, edges, capacity, recirculation, puncture area, durability, manner of insertion, risk of infection, and so on. The Edslab thermodilution catheter is of no use in optimizing devices to achieve these objectives. Simple inspection of a catheter's features doesn't offer a clue about the right combination for a particular job (or range of jobs), which is why Mahurkar's employment of features observable in other designs does not make his arrangement obvious. IMPRA might as well say that the '968 device is made out of plastic, and as plastic is well known ...
3. Richard H. McFarlane received U.S. Design Patent No. 250,349 in 1978. His design shows a catheter with a circular cross-section and a conically tapered tip. It has only one lumen. This device might have been useful in the design of catheters for alternating-flow machines, but the information in McFarlane's drawings would not have helped a person skilled in the art to develop a dual-lumen catheter for hemodialysis. Mahurkar does not claim to have invented the cone or the use of a cone on the tip of a catheter. If that were his claim, IMPRA could show that the invention was obvious by observing that prehistoric man tapered the tips of arrows to facilitate insertion. Cf. Sakraida v. Ag Pro, Inc., 425 U.S. 273, 275 n. *1377 1, 282, 96 S.Ct. 1532, 1534 n. 1, 1537-38, 47 L.Ed.2d 784 (1976) (system of cleaning barns by flooding them with water obvious in light of method Hercules used to clean the Augean Stables).
4. United States Patent No. 4,403,983, issued in 1983, shows a genuine dual-lumen catheter for the withdrawal and return of blood. IMPRA has spent some time on this device, invented by Edelman et al., but what it principally shows to me is how much of an advance Mahurkar's catheters were over the state of the art at the time. One of the lumens has been sawed off short of the tip, so that insertion of the half-tapered, half-blunt tip is bound to cause trauma. The intake and return ports are close together, and not axially separated, so that recirculation is a problem. The lumens change size and shape several times, creating turbulence in the flow of blood and offering not only sharp edges (risk of hemolysis) but also nooks and crannies where stagnant blood will pool (risk of clotting). This device, in other words, not only does not show all of the elements of the '968 patent in combination, or suggest such a combination to a person skilled in the art, but actually would lead a practitioner in the wrong direction.
5. Mahurkar's first patent for a dual-lumen hemodialysis catheter is No. 4,134,402, issued in 1979. Throughout this litigation the accused infringers have suggested that the '402 patent anticipates the '968 device or makes it obvious. An earlier opinion shows the basic design of the '402 catheter. 781 F.Supp. at 1297. That opinion also holds that IMPRA's devices do not infringe the '402 patent, and the considerations supporting that conclusion also show that the '402 patent does not anticipate the '968 device. The '402 catheter uses a double-D configuration but is a rigid tube whose configuration does not permit laminar flow of blood. Instead of having a conical tip that slides along a vein, it has a beveled tip that punctures the vessel wall. (Similarly the Consalvo device covered by Patent No. 4,098,275 is rigid and lacks a conical tip; it also lacks a continuous septum.) The '402 design did not suggest the '968 design even to its inventor, who did substantial additional work on the problem before developing the superior approach in 1980.
By the way, the McFarlane, Edelman, Consalvo, and Mahurkar '402 catheters were all cited to, and by, Examiner Truluck, who obviously believed that these devices did not anticipate the Mahurkar '968 catheter or make it obvious.
6. Finally I consider a category of catheters that includes side-by-side tubes with circular cross-sections. IMPRA has emphasized several such devices, including one that may or may not have been built to special order of the Brooklyn Hospital in 1960. Catheters of this general design require larger punctures through the skin and must be inserted surgically. The sketch the Brooklyn Hospital sent to its manufacturer (MMDL 1244) called for two tubes to be tightly wrapped in dacron, with one tube terminated five centimeters short of the other. Tight wrapping would deform the tubes toward semi-circular cross-sections, but the resulting device would have been quite cumbersome. Most of the blood would have flowed in and out at the end of each lumen, promoting recirculation, rather than through side ports farther apart as in the '968 design. The tubing included a right-angle bend, which would have played havoc with the flow of blood. The Cropp catheter to which the parties have referred incorporates two circular lumens into a single piece of plastic, for an even greater puncture area, and lacks a planar septum, tapered tip (again one lumen has simply been cut off at right angles to the tube), and side ports, among other things. Once again, these devices show how crude the state of the art was before Mahurkar invented his catheters. They do not anticipate his work or make his design obvious.
Enough additional devices to line a wall with binders were introduced at trial. The binders have subjected the foundations of this courthouse to undue stress. I will spare the reader any additional stress, as these devices are even less relevant than those I have discussed.

3
Perhaps turning to the secondary evidence is an occasion for a 15-yard piling-on penalty. *1378 Doing so, however, removes the last vestiges of doubt.
The existence of an enduring, unmet need is strong evidence that the invention is novel, not obvious, and not anticipated. If people are clamoring for a solution, and the best minds do not find it for years, that is practical evidence  the kind that can't be bought from a hired expert, the kind that does not depend on fallible memories or doubtful inferences  of the state of knowledge. See Minnesota Mining, 976 F.2d at 1574-75. See generally Environmental Designs, 713 F.2d at 697; Stratoflex, Inc. v. Aeroquip Corp., 713 F.2d 1530, 1538-39 (Fed.Cir.1983); Connell v. Sears, Roebuck & Co., 722 F.2d 1542, 1549 (Fed.Cir.1983).
There was such an enduring, unmet need in the treatment of renal disease. Cutdowns are damaging to the patient. Shunts pull out, clot, and become infected. Fistulas take time to form and do not work for all patients. Single-needle systems take a long time to dialyze and have 20% or higher recirculation. Coaxial catheters have high pressure in the return lumen, clotting, and high recirculation. Femoral catheters immobilize the patient. Hundreds of thousands of patients were and are treated yearly, yet until 1983 there was no satisfactory solution. If Mahurkar's device were obvious, other persons skilled in the art would have made it.
Mahurkar's device replaced its predecessors for acute use and swept the market. Quinton's sales took off, and everyone else in the industry promptly copied it. According to IMPRA's own market assessment (MMDL 55), in 1990 the Quinton-Mahurkar catheter and the infringing copies captured 91% of the unit sales for chronic and acute hemodialysis catheters. By any measure, that is spectacular success. IMPRA says that this is not so  that the Quinton catheter does not practice the '968 patent and therefore does not establish that the '968 invention filled any need. I disagree. The only ground IMPRA gives for believing that the Quinton-Mahurkar product is not covered by the '968 patent is the separately molded and bonded tip. The patent refers to integral septums  that is, septums integral with the tube  and one-piece catheters. As I have already discussed, however, the "best mode" revelation in the '968 patent mentions separate tips. The septum is integral with the tube. Nothing in the '968 patent implies that the whole device is made from a single piece of plastic. The words and diagrams depict many pieces: sleeves, Y-connectors, luer locks, and so on. It is enough that the septum is integral with the walls in both the tube and the tip of the Quinton-Mahurkar catheter. And the tube itself is of one-piece construction.
If because of the bonded tip the Quinton-Mahurkar catheter did not practice the '968 patent, then its success would understate the value of Mahurkar's invention! Bonded tips, Mahurkar and IMPRA agree, make a catheter less attractive for patient care. If the Quinton-Mahurkar device, which apart from the bonded tip is unquestionably covered by the '968 patent, boomed despite this undesirable feature, a "pure" '968 device would have done better.
I think it significant as well that other manufacturers have taken licenses or settled litigation with Mahurkar and have paid $7.4 million in damages for infringement. I ruled before trial that this evidence is admissible and reiterate that conclusion. Many cases say that settlements and settlement offers are inadmissible under Fed.R.Evid. 408 when used to show substantive liability (i.e., that the manufacturer was negligent or could have built a better product). The final sentence of Rule 408 says that the evidence may be used for other purposes: "This rule also does not require exclusion when the evidence is offered for another purpose, such as proving bias or prejudice of a witness, negativing a contention of undue delay, or proving an effort to obstruct a criminal investigation or prosecution."
The settlement of patent litigation may be functionally identical to a license  indeed, often includes an explicit license  and the willingness of other firms to take licenses is one secondary indicator of validity. If licenses are admissible, and if secondary evidence must be employed, Stratoflex, 713 F.2d at 1539, then it follows that the consent judgments are admissible. See Creative Pioneer Products Corp. v. K Mart Corp., 5 U.S.P.Q.2d 1841, 1843, 1986 WL 84403 *1379 (S.D.Tex.1986); American Standard Inc. v. Pfizer Inc., 722 F.Supp. 86, 136 n. 55 (D.Del. 1989); American Standard Inc. v. Pfizer Inc., 8 U.S.P.Q.2d 2019, 2020-21, 1988 WL 156152 (S.D.Ind.1988) (dictum; actually about discovery). But cf. Alpex Computer Corp. v. Nintendo Co., 770 F.Supp. 161, 166-68 (S.D.N.Y.1991). I recognize that people may settle patent litigation to reduce the costs of the legal process. The terms of a settlement reflect these costs as well as the parties' estimates about the probable outcome on the merits if the case proceeds. It is risky to use the parties' predictions as a reason to decide some other case on the merits. Yet deciding whether to take a license entails a similar assessment of the risks posed by litigation  prediction and avoidance of costs before suit begins  and it is settled that licenses are admissible as secondary evidence of validity.
There is of course a risk of undue prejudice in a jury trial; but as this was a bench trial, I admitted the evidence for its limited relevance. Such use of the consent decrees won't discourage settlements. To the contrary, the worst fear of early settlers is that others will go to trial and win. Vas-Cath's nightmare was victory for IMPRA, leaving Vas-Cath out of the market and IMPRA in it. Evidentiary uses tending to uniform treatment of similarly situated parties promotes settlement and justice too.

F
IMPRA believes that Mahurkar should lose even if the '968 patent is valid and infringed. This is so, it asserts, for two reasons: laches and inequitable conduct before the Patent Office. Neither of these contentions is persuasive.
Start with laches. The '968 patent issued in April 1986, and Mahurkar commenced this suit in 1990. That is a significant delay, enough to initiate inquiry under A.C. Aukerman Co. v. R.L. Chaides Construction Co., 960 F.2d 1020 (Fed.Cir.1992) (in banc). To succeed under the standards of Aukerman, however, IMPRA must establish that the delay in filing suit led it to change its position to its detriment. "It is not enough that the alleged infringer changed his position  i.e., invested in production of the allegedly infringing device. The change must be because of and as a result of the delay, not simply a business decision to capitalize on a market opportunity." Hemstreet v. Computer Entry Systems Corp., 972 F.2d 1290, 1294 (Fed.Cir.1992). That requirement is almost impossible to meet when the accused infringer knew about the patent and received notice that it would face litigation if it persisted. Ibid. See also Myers v. Asics Corp., 974 F.2d 1304 (Fed.Cir.1992).
On May 12, 1986, only three weeks after the '968 patent issued, Mahurkar sent IMPRA a letter stating that IMPRA's product "appears to infringe" that patent. Harold Green passed this letter to IMPRA's patent counsel, who obtained a copy of the patent and its prosecution history. IMPRA decided to continue selling the product, which it was acquiring from Kendall Med-West and rebranding. IMPRA knew not only about the patent and Mahurkar's belief that its product "appears" to infringe the patent, but also that Mahurkar was pursuing other infringers (albeit firms with larger sales volumes than IMPRA's). Mahurkar and Quinton had sued Shiley, Inc., for infringement. Green knew about this litigation no later than May 1986 (Green Dep. 244). IMPRA was deposed in Quinton v. Shiley in September 1987; it sent Mr. Green as its witness. Tr. 568. IMPRA's counsel followed the litigation and expressed a belief that Shiley had the stronger case. In fact Shiley capitulated, consenting to withdraw its catheter from the market and to pay damages. IMPRA learned of this outcome. IMPRA knew that Mahurkar had sued Vas-Cath in Canada and learned that Mahurkar had prevailed. In May 1988 IMPRA received a stronger letter from Mahurkar's lawyer, stating that its catheter infringed his patents and threatening litigation.
Green believed that the May 1986 letter was not enough to notify him about the risk of litigation because it says "appears to infringe" rather than "infringes". He concedes that the May 1988 letter gave good notice and faulted it for being too aggressive. IMPRA's patent counsel, however, thought the 1986 letter a notice of infringement. A letter from counsel dated October 6, 1986, states: *1380 "Earlier this year, Mahurkar directed a letter to you noticing IMPRA for infringement of this ['968] patent." A letter dated February 25, 1988, reads: "IMPRA received a letter dated May 12, 1986 from Mr. Mahurkar noticing IMPRA for infringement of both U.S. Patent Nos. 4,134,402 and 4,583,968."
After receiving the 1986 and 1988 letters IMPRA continued selling infringing catheters. Indeed, IMPRA did not change course even after Mahurkar commenced this suit, and to this day it insists that it is entitled to make and sell the accused catheters. The timing of notice and suit cannot have played much role. Mid-way between the 1986 and 1988 letters IMPRA began to make its own catheters in order to increase its profit margin and improve quality control. Approximately 90% of the expenditures for this production were incurred after receipt of the 1988 letter. IMPRA copied the design of the Kendall product, even though it knew that Mahurkar believed that this product infringed the '968 patent. An internal IMPRA memorandum dated November 7, 1986, reads: "Over two months ago ... it was outlined that Harold [Green] had given instructions to duplicate the Dual-Lumen catheter which we are currently purchasing from [Kendall] MedWest." MMDL 264 (emphasis in original). And so IMPRA did. Its drawings were based on the Kendall catheter, and it neither made changes nor saw any possibility of doing do. It did not change the design of the product in response to the notices, the Shiley litigation, or this suit. The market (that is, the design that worked best and that physicians therefore demanded), rather than notices and suits, determined the attributes of IMPRA's products.
In sum, nothing about the timing of this suit affected IMPRA's conduct, let alone caused it to make expenditures in detrimental reliance on delay. IMPRA knew about the patent, knew Mahurkar's position, knew the risks, and took them. It sought profit, and if it had been right in believing that Mahurkar's patents were invalid, it would have been entitled to the rewards of entrepreneurship. But IMPRA turned out to be wrong, so Mahurkar is entitled to damages. IMPRA gambled and lost. Its risk-taking does not prevent Mahurkar from enforcing his statutory rights.
Next comes the claim of inequitable conduct. To demonstrate that a patent is unenforceable because of inequitable conduct before the Patent Office, the accused infringer must establish by clear and convincing evidence that the applicant withheld prior art or other information material to the application. There are also two state-of-mind elements: the applicant must know that the withheld information is material, and must intend to deceive the examiner. Paragon Podiatry, 984 F.2d at 1188-93; Western Electric Co. v. Piezo Technology, Inc., 860 F.2d 428, 433 (Fed.Cir.1988); Under Sea Industries, Inc. v. Dacor Corp., 833 F.2d 1551, 1559 (Fed.Cir.1987).
IMPRA's argument fails on the subjective component, so I need not discuss the objective component. Mahurkar testified that he submitted to the examiner every bit of prior art known to him, and the evidence at trial backs up this assertion. Many of the items IMPRA submitted as prior art were not discussed in published literature. For example, the Edslab thermodilution catheter is from a field other than nephrology, and Mahurkar had no reason to know about its existence. The Brooklyn Hospital catheter of 1960 was made to order, in response to drawings given to a manufacturer but never published. The closest predecessors to the '968 design were Mahurkar's '402 device and the Edelman '982 device. These were cited to (and by) the examiner. In an ideal world it would be nice to provide the examiner even with unpublished designs, such as the Brooklyn Hospital catheter, but failure to cite a design you do not know about is not "inequitable conduct." What is more, Examiner Truluck was the examiner on most of the other catheter patents during the relevant period and likely had a better view of the literature than did Mahurkar. He was not deceived.
Only two items that Mahurkar knew about, and which might therefore support a decision for IMPRA on the subjective component, have come to light. One is an affidavit stating that the Northwest Kidney Center catheters had not been "reduced to practice." I *1381 have found that these devices were a "reduction to practice," setting up IMPRA's argument that Mahurkar acted inequitably in saying otherwise to Examiner Truluck. Again this is hindsight. "Reduction to practice" is a plastic phrase, and Mahurkar had a solid argument that the Northwest Kidney devices did not reduce to practice the '968 invention. Mahurkar testified that he used this phrase only at his lawyer's insistence; he had wanted to explain to Examiner Truluck exactly how the Northwest Kidney catheters departed from his specifications. They were crude; the hand-drilled holes did not achieve the axial separation specified by the patent claims, and the devices had other shortcomings. Mahurkar acted in good faith when taking his position before the Patent Office. It would be bizarre to say that a patent is unenforceable whenever the applicant loses on any issue in the litigation, even an issue, such as the reduction-to-practice dispute, that does not affect the validity of the patent. Yet that is what IMPRA's argument implies. Unless the applicant tells the examiner whatever the trier of fact later determines to be the best assessment of ambiguous circumstances, the patent is unenforceable. Obtaining a patent is not such a game of chance. If it were, the incentive to invent would be seriously eroded.
The other item within Mahurkar's knowledge was a change in the diagrams. My earlier statement that the '671 design application and the '968 utility application contain the same drawings is a simplification. One element in addition to numbers and other identifying marks was added to the original design drawings: a dashed line to show the septum in elevations depicting the outer parts of the tube. While prosecuting the application for a design patent, Mahurkar added these dashed lines. Examiner Word rejected the amendment, on the ground that the septum "would not be visible in said views." A design patent covers only ornamental appearance, so that the internal structure of a device is irrelevant and should not be depicted. Mahurkar replied that the device would be translucent, so that its internal structure could be seen. Examiner Word observed that the original drawings do not distinguish between translucent and opaque materials. Rather than extend the colloquy concerning the right way to depict the design, Mahurkar converted the application to one for a utility patent. The inequitable conduct, according to IMPRA, lies in Mahurkar's failure to tell Examiner Truluck that the dotted lines were latecomers.
This is a tempest in a teapot, because the original '671 design application shows the septum even without the dotted lines. Figure 6 of the original design application is a section at right angles to the length of the tube, showing the integral septum that creates the double-D design. Figure 7 of the original design application shows a cut-away of the tip in which the septum again appears. These figures carried over to the utility application and appear, with the additional identifying marks, as Figures 1 and 2 of this opinion. Mahurkar therefore was not trying to (and did not) put anything over on Examiner Truluck. So far as Examiner Word was concerned, the dotted lines were new matter because their significance depended on translucency, which would indeed have been new matter. Come the application for a utility patent, translucency is unimportant, and any dispute about whether a claim implying translucency is new falls away. The dotted line was relevant to the utility patent, but irrelevant to the design application. Nothing changed, so nothing was withheld from Examiner Truluck (who anyway had full access to the design application file), and there is no basis for an argument that he was deceived. Recasting this as a "new matter" argument under 35 U.S.C. § 112 rather than an "inequitable conduct" argument adds nothing, and I therefore do not address § 112 separately.
True, it is possible to say that only the dotted lines show a unitary, planar, full-length septum. But only a dunderhead looking at Figures 6 and 7 of the original design application would have supposed that the septum is discontinuous, or curved in places not depicted. As I emphasized in Parts II.A and II.C of this opinion, persons skilled in the art looking at the design drawings would have understood that this was a catheter, which could not function with gaps in the septum. IMPRA's expert, Gary Smith, all but conceded this. The design drawings *1382 alone therefore imply a unitary, planar, full-length septum. The conclusions reached in those portions of the opinion dispose of both objective and subjective components of the "inequitable conduct" inquiry as applied to the dashed lines.

III
Mahurkar contended at the outset of this suit that IMPRA infringed not only independent claims 1 and 19 of the '968 patent (and the several dependent claims) but also independent claims 12 and 25 of that patent, plus claims 8 and 10 of the '141 patent.
Claims 12 and 25 of the '968 patent are valid under the approach I have taken, but there is a question whether IMPRA's device infringes them. These two claims include a "relative concentration of material extending axially" through the tip of the catheter, and IMPRA says that its devices lack this feature. IMPRA's catheters have a plug immediately below the intake port, and a thickening of the tip where the mandrel melts and deflects the septum, but do not have solid plastic running continuously from the intake port through the tip.
The plug and the thickening of the wall at the tip are a "concentration of material", but can one say that this "extend[s] axially" from intake port through tip? Mahurkar argues that one can and should, because the septum itself counts as a "relative concentration of material", because even the air between the plug and the tip is "material" that becomes "concentrated" (i.e., compressed) when the tube bends inside a patient's body, and because the IMPRA design is equivalent in stiffness to the one described in claims 12 and 25. So Mahurkar's experts testified. Yet one would suppose that a highway "extending" from Chicago to Milwaukee goes all the way; just so a relative concentration "extending" from intake through outlet. The "extending" language in claims 12 and 25 differs from, for example, claim 3, which speaks of a tip that "comprises a concentration of material" in the tip itself. The difference between extending and in suggests that IMPRA's device does not infringe claims 12 and 25 (and dependent claims containing or incorporating the "extending axially" language). Because Mahurkar and Quinton would not be entitled to any relief under claims 12 and 25 that they do not obtain under claims 1 and 19, it is unnecessary for me to decide who is right.
As for the '141 patent: Here the problem is whether the design drawings adequately conveyed, to one skilled in the art, a smooth bore catheter of the kind described in claims 8 and 10 of the '141 patent. This has become known as the "bend in the bore" issue. The drawings submitted with the application for the design patent show what IMPRA calls a "bend in the bore", while claims 8 and 10 of the '141 utility patent call for a smooth bore. (To be precise, claims 8 and 10 lack any language limiting their scope to catheters having a "bend in the bore".) IMPRA's catheter has a smooth bore. But the '141 patent issued after the '968 patent. Finding the '141 patent valid and infringed would not add one penny to the damages. Although it has a potential effect on injunctive relief  it could extend the injunction from April 22, 2003, when the '968 patent expires, to September 8, 2004, when the '141 patent expires  this effect is hypothetical. It would matter only if, in mid-2003, IMPRA would want to offer a catheter that has features covered by the '141 patent, but no other patent. Ongoing developments in catheter technology make this unlikely. It is a non-zero chance, but an injunction is an equitable remedy, and one important consideration is the avoidance of advisory opinions. Issuing an opinion on validity and infringement on account of a product IMPRA made in the 1980s, when the stakes are an unknown product IMPRA might want to make in the next century, depends on altogether too many contingencies. I appreciate that after Cardinal Chemical Co. v. Morton International, Inc., ___ U.S. ___, 113 S.Ct. 1967, 124 L.Ed.2d 1 (1993), one could not say that such an act exceeds the judicial power under Article III. Still, Cardinal Chemical did not forbid a court to exercise sound discretion to determine which issues in a case ought appropriately to be decided. ___ U.S. at ___ - ___, 113 S.Ct. at 1976-78.
IMPRA has not told me that it plans to commence making smooth bore double-D *1383 catheters with conical tapered tips in April 2003, and that delay until September 2004 would be deleterious. Instead it argues that I should decide the issues just because they have been raised. Yet arguments about the '141 patent occupied the parties largely because the validity of that patent is unaffected by the on-sale question arising out of the Northwest Kidney Center sales. With that subject behind us, the '141 patent loses salience. Of course, if the Federal Circuit disagrees with my decision about the '968 patent, it may be necessary to come to closure on the '141 patent. But a record adequate to permit a decision on that subject has been assembled, and a decision can be made, if necessary. One will not be made unless it is necessary.
Indeed, it is not so clear whether such a decision would resolve a current dispute. After dismissing the suit that it had filed in Arizona, IMPRA did not file a counterclaim asking for a declaratory judgment that the '141 patent is invalid or not infringed. Instead it simply offered a defense to Mahurkar's claims under that patent. Mahurkar is satisfied with the decision on the '968 patent, and his post-trial memoranda imply that he no longer seeks any relief under the '141 patent. E.g., Dr. Mahurkar's and Quinton's Response in Support of Their Request for Immediate Injunction 3-4. I do not think it appropriate to press forward to a decision on a claim that the plaintiffs in this case no longer pursue.

IV
"Upon finding for the claimant the court shall award the claimant damages adequate to compensate for the infringement, but in no event less than a reasonable royalty for the use made of the invention by the infringer, together with interest and costs as fixed by the court." 35 U.S.C. § 284. This brief statutory formula sets the stage for the parties' dispute about money damages.

A
The owner of the patent receives the greater of compensatory damages and a reasonable royalty. Bio-Rad Laboratories, Inc. v. Nicolet Instrument Corp., 739 F.2d 604, 617 (Fed.Cir.1984); Hanson v. Alpine Valley Ski Area, Inc., 718 F.2d 1075, 1081 (Fed.Cir. 1983). Quinton Instruments, as the holder of an exclusive license for use of the '968 catheter in hemodialysis, is the "owner" for this purpose. The reasonable royalty charged by a party, such as Quinton, that manufactures the patented item would not be greater than the compensatory award when the authorized manufacturer and the infringer have the same costs. Therefore, I do not attempt to compute a royalty separately from compensatory damages.
A patent owner who does not manufacture the invention expects to make money principally if not exclusively from the royalty. Then it is necessary to enter into the complex counterfactual process of approximating the royalty that would have been agreed on by parties that did not agree on anything at all. See Panduit Corp. v. Stahlin Bros. Fibre Works, 575 F.2d 1152, 1157-58 (6th Cir. 1978) (Markey, J.); TWM Manufacturing Co. v. Dura Corp., 789 F.2d 895, 898-99 (Fed.Cir.1986). But when the patent's owner (or, here, his exclusive licensee) also makes the patented article, the profitability of the owner's manufacture and sale also determines the royalty that would be charged. To see this, consider a simple example. Firm # 1 can make a patented article for $7, a cost that includes goods, machinery, labor, sales, and the competitive return on invested capital. If there were no competition, the profit-maximizing price would be, let us suppose, $10. At a higher price, so many sales would be lost to less effective, but cheaper, competing products, that total profits would decline. The $3 difference between cost and profit-maximizing price is a return to the patent, an implicit royalty. I state the royalty in dollars rather than a percentage of the price, but the two are equivalent. Here, where the price is $10, it would be easy to restate the $3 return as a 30% royalty.
How much would Firm # 1 charge to allow some other manufacturer into the business? Not less than $3, because it can earn that much by making the article itself. Whether it can get more depends on the costs someone else would incur in making the article. Suppose Firm # 2 would incur costs of $8 in *1384 manufacturing and selling the patented article. Firm # 2 would not pay more than $2 in royalty for the privilege, and Firm # 1 would not take less than $3. If Firm # 2 would incur costs of $7 in manufacture and sale, it would pay a royalty up to $3, but not more. (It is important to remember that the "cost" of $7 includes the competitive rate of return on the capital invested in the process. An accountant would call this a profit. Thus Firm # 2 "makes a profit" on this transaction even with a royalty of $3 per item, but no more of a profit than it would earn from some other use of its time and resources.) Finally, suppose Firm # 2 would incur costs of only $6 in making and selling the article, indicating that Firm # 2 is more efficient than Firm # 1. Now what royalty would be charged? Firm # 2 would be willing to pay as much as $4 per item; Firm # 1 would accept as little as $3; how they divide the difference will depend on their bargaining strategies and the elasticity of demand. Lower costs of production reduce the profit-maximizing price, and the two firms would share the higher profits associated with the greater output. The royalty per item might even fall, although Firm # 1's total return would rise. The point here is that Firm # 1 (which I am treating as the patentee and manufacturer combined) would be able to collect a royalty exceeding the difference between its cost and the market price only if Firm # 2 has lower costs. This is a standard conclusion of the economic literature, which the parties have given me no reason to doubt. See Roger D. Blair & David L. Kaserman, Law and Economics of Vertical Integration and Control 58-68 (1983).
None of the evidence introduced in this case suggests that IMPRA was more efficient than Quinton. The technology of making the Mahurkar catheter is well established. Evidence during the damages phase of the trial shows that both IMPRA and Quinton could expand their output without increasing unit costs. Each firm also has an established sales force that visits most if not all potential users of hemodialysis catheters, so that an increase in output does not lead to a marked increase in selling expenses per unit (or to any difference between the firms in the rate of increase). That is to say, the marginal cost of each firm appears to be flat in the relevant range of production. Either could double its output by adding a second production line, and so on. Because Quinton and IMPRA have stable average and variable costs of production, and because Quinton appears to be the more efficient producer, Quinton would not be able to collect from IMPRA, as a royalty, any sum greater than the difference between its cost and the price customers are willing to pay.
Although the royalty cannot be greater than compensatory damages in a case such as this, compensatory damages easily can exceed the reasonable royalty. An infringer's activities do more than divert sales to the infringer. They also depress the price. Competition drives price toward marginal cost. In a fully competitive market, the item in my hypothetical would be available for $7. Consumers, although willing to pay more, need not do so; customers willing to pay $10 would enjoy the extra $3 as a consumer surplus, and customers willing to pay less than $10 but more than $7 would begin to buy, and they too would reap some consumer surplus. Thus the loss to Firm # 1 in the hypothetical could be as large as $3 multiplied by the entire volume it could sell at a price of $10. Damages thus exceed the reasonable royalty, which would be measured by $3 multiplied by Firm # 2's sales. Notice, however, that the damages are not as large as $3 times the actual sales of Firm # 1 and Firm # 2 put together. Customers will buy more at a price of $7 than they will at a price of $10. The correct way to compensate Firm # 1 is to award it $3 times the number of units it would have sold had there been no infringement  or, to put it differently, the monopoly output times the monopoly profit, a profit made lawful by the patent. The patent holder does not receive the monopoly price times the competitive output. See generally John W. Schlicher, Patent Law: Legal and Economic Principles, § 9.05 (1992).
Although it is easy to conclude that compensatory damages are the proper measure in this case, it is not at all easy to decide what those damages are. For markets cannot be dropped into bins marked "competition" and "monopoly." There are degrees of *1385 competition. It is easy to award Mahurkar and Quinton damages on the number of units IMPRA actually sold. Just multiply IMPRA's sales by Quinton's profits per sale  being careful to subtract that portion of the accountant's understanding of "profit" that reflects only the competitive rate of return on Quinton's investment. (Recall that I have held that the Quinton-Mahurkar catheter is covered by the '968 patent. That Quinton's license to use the '968 patent was implied until made express on January 1, 1988, is not relevant.) But IMPRA's sales drove down the price of all catheters using the Mahurkar design. How much could Quinton have charged had there been no competition from IMPRA? From all infringers combined? We need to know how fast price falls with an increase in output attributable to infringers' sales. To use the technical term, what is the elasticity of demand facing a sole manufacturer of hemodialysis catheters using the '968 design? The record does not point to an inevitable conclusion on this question. It is a counterfactual. During the entire time Quinton has made and sold the Quinton-Mahurkar catheter, it has faced competition from firms that have copied its product  most of which have now conceded infringement and stopped.

B
What all of this implies is that Quinton and Mahurkar are entitled to damages measured by the profit they lost as a result of the infringement, and that the lost profit has two components: sales diverted to IMPRA, and a reduction in the price Quinton realized for the catheters it sold itself. "In patent cases, as in other commercial torts, damages are measured by inquiring: had the tortfeasor not committed the wrong, what would have been the financial position of the person wronged?" Brooktree Corp. v. Advanced Micro Devices, Inc., 977 F.2d 1555, 1579 (Fed.Cir.1992), citing Aro Manufacturing Co. v. Convertible Top Replacement Co., 377 U.S. 476, 507, 84 S.Ct. 1526, 1543, 12 L.Ed.2d 457 (1964). I proceed in three steps: determining Quinton's cost per catheter; determining the price Quinton would have realized had there been no competition from the copycats; and determining IMPRA's appropriate share of this diminution. In the course of this I consider each of the elements that the Federal Circuit has said is relevant to a lost-profit analysis: demand for the patented product, capacity to make the volume of sales that the infringer had diverted; effect of non-infringing substitutes; and the incremental profit lost. See Kaufman Co. v. Lantech, Inc., 926 F.2d 1136, 1140-41 (Fed.Cir.1991). The demand for catheters of the '968 design is high and requires no further comment. The other elements are disputed.

1
Mahurkar and Quinton offered Paul J. Duggan and Carol Kone as accounting experts to establish its costs of production and the volume of business diverted to IMPRA. Both prepared written narrative statements, something I required of all expert witnesses. Kone did not testify at trial, but her narratives are in the record.
During the years in question, the Quinton-Mahurkar catheter sold for prices ranging from a low of $32.81 in 1986 (this is the average price realized during the year) to a high of $35.89 in 1991. Duggan concluded that Quinton's variable costs of manufacturing and selling these catheters were approximately 28% of its selling price (an average of about $9.50 per catheter on an average price of $34). Duggan excluded what he called "variable overhead" costs, such as the expenses of the sales force, on the ground that the same salesmen could handle higher volumes of sales: their salaries and related costs, while incremental costs of Quinton's actual production, would not be incremental costs of an expansion in output. Other witnesses for Quinton testified that when IMPRA withdrew its catheters from the market because of production difficulties, Quinton was able to expand its output at only the marginal costs of materials and labor.
Kone allocated more of Quinton's costs to the variable category and computed its costs separately for catheters, kits, and trays. (Kits and trays include other products that medical professionals use in inserting the catheters. Sterile kits and trays are a convenience *1386 for these customers, and plaintiffs are entitled to damages for the profits they could have made in selling these assemblies of products. For reasons that will become clear, however, the "price erosion" approach does not apply to the non-catheter components of the kits and trays.) She determined that in 1991 (to use one year as an example) Quinton's costs of materials, labor, and overhead were 15.7% of the costs of catheters, 22.8% of the costs of kits, and 28.7% of the costs of trays. (I refer here to her second narrative, dated August 10, 1992.) There remained costs of marketing and sales, storage, packaging, and the administrative expenses of products in general. Costs of this kind Duggan excluded because he believed that they do not increase with output. Kone made the opposite assumption and included them. She determined that Quinton's firm-wide expenses in these categories were about 38% of sales, took out costs that were fixed over the long term or unrelated to catheter sales, and allocated such expenses to catheter products accordingly, arriving at figures between 9.7% and 30.6% of sales in particular years. For example, this process produced for 1991 sales a conclusion that if Quinton had expanded its output of catheters, kits, and trays, then selling at $35.89, $54.17, and $74.19, it would have incurred additional costs of 36.2% ($12.99) for catheters, 43.3% ($23.46) for kits, and 49.2% ($36.50) for trays.
I find Kone's methodology superior to Duggan's and adopt it. Although costs of sales, general overhead, and the like, are not variable for small changes in output over the short run, they are most assuredly variable for larger changes over the long run. And to determine damages, I must ascertain what Quinton's costs and prices would have been had it had the market to itself beginning in 1986. Nothing in the record supports a conclusion that Quinton's costs per unit would have been higher had it produced twice as many units. I credit Mr. Perri's testimony that it could have added a second production line at the same cost experienced in building the first. It was not running into a region of increasing marginal costs. Materials were readily available. Had the infringers ceased their production earlier, Quinton could have purchased the supplies of double-D tubing and other inputs that were going to these rivals. And I am not persuaded that Quinton could have avoided any of these costs as it expanded output. This conclusion accords not only with Kone's but also with those of IMPRA's witnesses Green and Rhulette Mounia, who testified that these kinds of expenses would have been variable costs had IMPRA itself expanded production. (I deny Mahurkar's post-trial motion to strike this testimony. It may be that Mahurkar had, and did not use at trial, ways to impeach this testimony, but foregone impeachment is not a reason to strike. At all events, I find the testimony credible.)
In determining Quinton's cost per unit, I shall adopt Kone's approach and calculations. When submitting their final proposals on damages (see Part VII of this opinion), the parties should use the methods and data in Kone's second report to determine a dollar cost per catheter, kit, and tray that Quinton sold (or could have sold had the copycats been out of the market) for each year from 1986 forward.

2
IMPRA would like me to stop here. IMPRA believes that I should determine the lost profit per unit using actual transactions prices for 1986 to 1991, multiply that lost-profit-per-unit by the number of units IMPRA sold to private customers excluding samples and sales to the federal government, and award that sum. (Actually IMPRA says that the damages should be even lower based on a hypothetical percentage royalty, but, as I have already explained, plaintiffs receive the greater of lost profits or a reasonable royalty.) Quinton and Mahurkar ask me to press on, awarding as damages the difference between actual costs of goods and potential price  the price they could have realized had there been no competition from the infringers. This is the "price erosion" theory of damages, one with substantial support in the cases. E.g., Yale Lock Manufacturing Co. v. Sargent, 117 U.S. 536, 552, 6 S.Ct. 934, 942-43, 29 L.Ed. 954 (1886); TWM Manufacturing, 789 F.2d at 902; Brooktree, 977 F.2d at 1579-81; Minnesota Mining & Manufacturing, 976 F.2d at 1578-79 (also reducing award because of reduction in output); Kalman *1387 v. Berlyn Corp., 914 F.2d 1473, 1485 (Fed.Cir.1990); Lam, Inc. v. Johns-Manville Corp., 718 F.2d 1056, 1067 (Fed.Cir.1983).
As IMPRA sees things Quinton and Mahurkar surrendered any entitlement to use a price erosion approach. They did not plead it in their complaint, and the narrative statements of Duggan and Kone do not attempt to estimate either the price Quinton could have realized had there been less competition or the reduction in sales that a higher price would have caused. I agree with IMPRA that the Duggan and Kone narratives are silent on this score. But I required narratives only from expert witnesses, and plaintiffs sought to establish the price erosion theory through witnesses testifying from personal knowledge. For example, Mr. Perri, Quinton's president, testified about customers' resistance (or lack of resistance) to higher prices. Several other witnesses, including Ash and Mounia, testified from personal knowledge about the prices of competing products and the costs of treatment using these alternatives. They provided facts from personal knowledge, not an expert analysis of facts. None of these witnesses was required by any of my orders to file a pretrial narrative about price erosion.
If IMPRA chose not to pursue the subject in discovery it has only itself to blame. Plaintiffs dropped hints by propounding interrogatories relevant to price effects. Price erosion is an almost inevitable issue in a patent case. (The case from 1886 cited in the first paragraph of this part should have been warning enough!) Patents create a lawful ability to exclude competition, and thus some ability to increase price. That competition undercuts price is not such an esoteric theory that an accused infringer needs express notice, as if lower prices were an item of special damages that had to be pleaded under Fed.R.Civ.P. 9(g). Litigants in federal court do not need to plead their theories of damages. Instead they may ask generally for whatever relief the court deems appropriate. "Except as to a party against whom a judgment is entered by default, every final judgment shall grant the relief to which the party in whose favor it is rendered is entitled, even if the party has not demanded such relief in the party's pleadings." Fed. R.Civ.P. 54(c). See Williamson v. Handy Button Machine Co., 817 F.2d 1290, 1298 (7th Cir.1987).
Quinton and Mahurkar sent signals strong enough to convey to Kendall, another of the accused infringers, the need to meet a price erosion theory. Kendall engaged as its expert Jerry A. Hausman, Professor of Economics at MIT, whose specialties include industrial organization and intellectual property. Professor Hausman prepared a narrative statement devoting substantial attention to the possibility that Quinton's rivals depressed the price of the Quinton-Mahurkar catheter. Instead of hiring Professor Hausman jointly with Kendall, or engaging another expert to study the problem, IMPRA proffered as its sole expert one Gary Freed, an accountant, whose narrative statement ran less than two pages and did not include one word about Quinton's lost profits. I struck that statement and barred Freed from testifying because IMPRA did not comply with my requirement that experts disclose their conclusions and reasoning by narrative declarations before trial. That order cost IMPRA nothing, because the only subject on which Freed was prepared to testify was IMPRA's costs and output  which might have been relevant if damages were based on the profits IMPRA made, but irrelevant when damages are based on the profits Quinton lost. As it turned out, Freed and Duggan came within one catheter in counting the number of units IMPRA shipped between 1986 and 1991, so he had nothing of value to contribute to the case. IMPRA's position on damages has been that it owes none. It has not been very interested in the details. A litigant may take such a view, but it should not express shock when its rival offers a surprising theory.
Having failed to prepare before trial, IMPRA swung into action afterward. It hired F.M. Scherer, one of the nation's foremost students of patents and the author of a leading textbook on industrial organization. See F.M. Scherer & David Ross, Industrial Market Structure and Economic Performance (3d ed. 1990). See also, e.g., F.M. Scherer, International High-Technology Competition (1992); F.M. Scherer, The Economic Effects *1388 of Compulsory Patent Licensing (1977). Nine days after the completion of the damages portion of the trial, IMPRA tendered Professor Scherer's narrative declaration, which analyzed price and output effects under a variety of assumptions about market structure, elasticity of demand, and the behavior of Quinton's rivals. Professor Scherer is, according to the narrative, "well-acquainted with IMPRA and its attorneys from a litigation in the vascular grafts field." One wonders why IMPRA did not introduce its acquaintance to dual-lumen catheters earlier. By the time they asked for his views, discovery was closed, the trial had been held, and Prof. Scherer could not immerse himself in the subject: "The pressures of time have not permitted me to read materials from the Quinton litigation or to familiarize myself with the economics of the renal catheter business." That did not prevent him, however, from offering an economic analysis complete with empirical assessments of price and quantity under several assumptions about what the economics of the renal catheter business might be.
Unsurprisingly, Mahurkar has asked me to strike this statement and to close the record as of the end of trial. By all rights, he is entitled to this relief. Professor Scherer was not amenable to discovery or cross-examination. Yet I shall nonetheless indulge all doubts in favor of IMPRA, deny the motion, and receive the narrative for what it is worth  very little, alas. What Professor Scherer describes is what every student of economics knows: conclusions depend on models and data. You need data to test models in order to decide which best describes actual behavior. Scherer lacked essential data, so he was confined to theory and simulations. That is much the state of this record, too. Witnesses were guessing about price effects. (Professor Hausman, who had more time and data, also was unable to produce empirical estimates.) Scherer adds that trial-and-error may be the only way to understand price movements in this market. After using the few data available to him to tease an elasticity (1.33) out of Quinton's prices and marginal costs in competition with the infringers, Prof. Scherer observed that a price of $50 would imply an elasticity of 1.21. If indeed the elasticity is 1.21, then Quinton could have raised the price to $50 in the absence of competition from IMPRA and the other infringers. He continued: "The difference between elasticities of 1.33 and 1.21 is so small that it would be quite difficult to ascertain with confidence econometrically. In order to find out whether such a price increase would be profitable, Quinton would have to experiment with higher prices and see how they affected its revenues." This is how markets work. Managers try out a strategy; if profits rise they do more in the same vein, and if profits fall they try something else. Competition strongly affects which strategies work and which flop, but armchair observers (including judges) have great difficulty knowing how things that were not tried would have worked had they been tried.
It is tempting to throw up one's hands. IMPRA doubtless wants me to do just this, to discard as "speculative" any particular hypothesis about price and output effects in a world without the imitators. Surrender would reward infringement, however. Having got this far, Quinton and Mahurkar are entitled to an award best approximating their actual loss, and the infringers must bear the burden of uncertainty. Story Parchment Co. v. Paterson Parchment Paper Co., 282 U.S. 555, 562-66, 51 S.Ct. 248, 250-52, 75 L.Ed. 544 (1931); Del Mar Avionics, Inc. v. Quinton Instrument Co., 836 F.2d 1320, 1327 (Fed.Cir.1987); Gyromat Corp. v. Champion Spark Plug Co., 735 F.2d 549, 554-55 (Fed. Cir.1984). Professor Scherer correctly warns about the risks of speculation, and his analysis cautions against adopting the view of Dr. Ash that hospitals would have been willing to pay $100, $200, even more for the Quinton-Mahurkar catheter. Ash estimated the labor cost savings of using a Quinton-Mahurkar catheter at $490 per patient, compared with femoral catheters, over a two week dialysis treatment. Surely hospitals and dialysis centers would have paid through the nose if there were no catheters in the world other than femoral, but there are many  single-lumen subclavian catheters for use with an alternating-flow machine, dual-lumen catheters such as the Cook catheter *1389 and Quinton's PermCath that do not infringe Mahurkar's patents. These constrain the price Quinton could charge for the Mahurkar product. (At least, the catheters other than the PermCath do. Quinton would not use this device, which it markets, to undercut its profits from the Mahurkar design. In considering the power of substitutes to constrain price, then, I disregard the PermCath.)
The best one can do in the absence of a sophisticated (or any!) study of elasticities is to ask whether modest changes in the price of catheters with the Mahurkar design would have led to substantial declines in output, enough to make the increase unprofitable. Modest changes for this purpose are 10% per year, the figure Mr. Perri suggested, so that the price of the Quinton-Mahurkar catheter would have progressed in increments from $32.81 in 1986 to $52.84 in 1991, instead of the $35.89 it actually reached in that year. Some rough estimation is involved here, but it is not "speculation" by any means. Getting to $50 is quite plausible; Prof. Scherer noted that it does not require any dramatic inelasticity in the market demand for the product. See also, e.g., Dennis W. Carlton & Jeffrey Perloff, Modern Industrial Organization 332-42 (1990); William M. Landes & Richard A. Posner, Market Power in Antitrust Cases, 94 Harv.L.Rev. 937, 939-52 (1981); Landes and Posner on Market Power: Four Responses, 95 Harv.L.Rev. 1787-1874 (1982), for descriptions of the relation among elasticity of demand, market share, marginal cost, and price. The figure of $52 for a Quinton-Mahurkar product is one that IMPRA's witness Mounia, who for years worked in the dialysis section of a leading hospital, testified would not send buyers scampering to alternatives. Tr. 1840.
Indeed, Mounia explained that until being displaced by products of Mahurkar's design, the Cook and PermCath catheters were his hospital's products of choice. Each is more expensive than $53 (Cook's dual-lumen subclavian catheter sold for about $65 in 1991, and PermCath fetched $90, see MMDL 49). The Cook product, being relatively soft and having a larger cross-section than the Mahurkar catheter, is harder to implant; it requires an introducer sheath, the use of which calls for additional time from a hematologist or another skilled professional. Its different-sized lumens produce unequal pressures. The PermCath catheter is designed for placement in the jugular vein, which requires special skills, and must be surgically removed. No surprise that Mahurkar's design displaced its rivals as the catheter of choice and today holds 91% of the market, compared with Cook's sales of less than 1%. MMDL 49, 55, 56. If the Quinton-Mahurkar design is both superior in use to the others and slightly cheaper to implant, it could be sold for at least as high a price. Perri's suggestion for a slow increase to $53 is modest. I conclude that plaintiffs are entitled to the benefit of this 10% per annum increase, which, if an estimate, is more likely to be off by being too low than by being too high. During the same time, the cost of medical care was rising steeply. The consumer price index for medical care rose between 6.5% and 9% per year during 1986 to 1991. Statistical Abstract of the United States Table 739 (1992). Even small savings in the time of medical professionals would translate to substantially higher prices. Yet competition from IMPRA, Vas-Cath, and other infringers prevented Quinton and Mahurkar from taking advantage of this market opportunity.
Notice that in this discussion I assume that not only IMPRA but also Vas-Cath, Shiley, Kendall, and the other admitted infringers departed the market in 1986. The departure of one of these firms, while the others continued to compete, would have left Quinton without ability to increase its price significantly. Professor Hausman, when opining that Quinton had not established any price erosion attributable to Kendall's sales, assumed that if Kendall had departed Vas-Cath would have remained. To understand what would have happened but for the infringement I must ask what the state of the market would have been if there had been no infringers. My answer differs from Prof. Hausman's only because he made an assumption inappropriate to this litigation.
In reaching the conclusion that Quinton could have raised its prices I am quite conscious that there are other catheters in the market. Competition is not an all-or-none *1390 process. There are degrees of substitutability. "[I]t is not necessary for the patent holder to negate all possibilities that a purchaser might have bought a different product or might have foregone the purchase altogether." Minnesota Mining & Manufacturing, 976 F.2d at 1577. Piston planes can get people from one place to another, but the holder of a patent on the jet engine would have a gold mine. Other products can do the job of vascular access. I described several in Part II.E. They just have higher unit prices and entail greater professional time or less convenience for patients, which gives Quinton an opportunity to capitalize on the virtues of the Mahurkar design. See Kaufman, 926 F.2d at 1142-43. Perhaps this is why, when it discontinued sales during 1990 in order to improve the reliability of its manufacturing processes, IMPRA referred its customers to Quinton and Vas-Cath. It did not suggest that they try Cook or any of the other devices that it now paints as perfect substitutes. When making real decisions in the marketplace, IMPRA treated these devices as inferior; I credit market behavior over testimony.
Ironically, one nice piece of evidence supporting this conclusion was offered by IMPRA after trial. It asked me to reopen the record to receive an article published in August 1992 about which IMPRA did not learn until after trial. I grant this motion  if indeed it was necessary, given that litigants may draw a court's attention to published literature by letter. The article describes a study of 134 patients who received the Cook catheter for acute hemodialysis. Howard Silberman, Thomas V. Berne & Richard Escandon, Prospective Evaluation of a Double-Lumen Subclavian Dialysis Catheter for Acute Vascular Access, 58 Am. Surgeon 443 (1992). The study described the need for a dual-sheath introducer to implant the Cook catheter. The authors found that 62% of these catheters functioned properly for the required duration of the treatment. Twenty-six (16%) of the 162 catheters used in the study never functioned properly; 18 (11%) had to be replaced by another catheter after a period of functioning; 75% had to be adjusted from time to time to preserve satisfactory flow. These data suggest that there are substantial competitive opportunities for catheters such as Mahurkar's design that are easier to insert and have lower probabilities of clotting, even if the differences are small.
How much would the total sales of catheters of Mahurkar's design have fallen at a price of $53? An elasticity of demand expresses a percentage change in sales for a given percentage change in price. What Perri calls a "10% increase" in price is not in fact that large an increase, because Perri was speaking in nominal dollars. An average change of 10% per year would have exceeded only slightly the average change in the cost of medical care. Adjusting instead for general changes in the value of money would deduct between 3.09% and 4.34% per year during 1986 to 1991. Statistical Abstract Table 753. Thus what Perri called a 10% increase would be a small price increase using the price of medical care as a benchmark, or a 5.6% to 7% annual increase using the price level in the whole economy as a benchmark. The economy as a whole is the preferable benchmark for this purpose because price changes in medical care are linked to labor in addition to inputs of supplies. Next we need to know the elasticity. I determined above that Quinton was experiencing a roughly stable variable cost of $13 for catheters. Professor Scherer provides this standard formula relating price, marginal cost, and elasticity at the profit-maximizing price:
P - MC       1
     ________   =  ___
         P         ξ
In this equation P is price, MC is marginal cost, and ξ is the elasticity of demand. This simplification may appear to ignore the role of fringe suppliers such as Cook, but their influence is reflected in the elasticity derived from actual prices in the industry. If P = $53, MC = $13, then ξ = 1.33. For every 1% increase in price, total sales fall by 1.33%.
This still does not entirely capture quantity effects. The formula gives the elasticity at the monopoly price. A monopolist continues to increase price past the point where its gross revenues begin to fall (this is what it means to say that the elasticity exceeds 1). Its profits continue to increase for some time *1391 after revenue begins to fall because it saves money by producing fewer units. Perri thought that $52 or so was the monopoly price and proposed 10% annual increases to get there only because Quinton did not want to aggravate its customers, on whose goodwill it depends to sell other products. I cannot treat the movement from $32 to $52 as if the elasticity were 1.33 in the entire area. For much of this range the elasticity is apt to be less than 1. The best I can do is to assume that the average elasticity, throughout the range of potential movement, is 1  which turns out to be a working assumption of many economists.
For current purposes, recall, we are assuming that Quinton has cornered the market in devices covered by the '968 patent. So to determine what Quinton's sales would be in a given year, it is necessary to take the actual total sales of Mahurkar catheters  that is, sales of Quinton, Vas-Cath, Kendall, IMPRA, and other infringers combined  and reduce them by 1% times the amount by which the imputed monopoly price exceeds the actual selling price in that year. This is a question on which the parties should submit their calculations under the procedure established in Part VII of this opinion.
This should not be difficult. Here is an example. According to Kone's data, the net price of Quinton's catheters increased from $32.81 in 1986 to $33.15 in 1987, a change of approximately 1%. The 10% figure I have accepted implies an increase to $36.09. The value of the dollar fell by 3% in 1987, so the "real" increase Quinton would have achieved had it been freed of the infringers, net of the actual change and the change in the value of money, was 6%. That implies a reduction in unit sales of 6% compared with what Quinton and the infringers, put together, actually delivered in 1987. To arrive at lost profits for catheters in 1987, then, it is necessary to multiply that number of units by $36.09 (because, had there been no competition from the infringers, Quinton would have sold them all) and subtract the variable cost of $13 per catheter. It is also necessary to subtract Quinton's profit of $32.81 - 13 = $19.81 on the units it actually sold. The resulting number is lost profits.
The procedure should be much the same for kits and trays, except that the record does not support a conclusion that the price of kits and trays would have gone up at 10% per year. Much of the price of these items reflects the cost of staple products plus labor. To determine Quinton's lost profits on kits and trays, it is necessary to use the actual selling price for the year, increased by the change in the catheter's price. For example, in 1991 Quinton actually sold catheters for $35.89 and trays for $74.19. I have concluded that, but for the infringers' competition, Quinton could have sold the Mahurkar catheter in that year for $52.84, a difference of $16.95. Quinton would have had market power in catheters but not the other components of kits and trays. Thus to determine the price for which trays would have sold in 1991, it is necessary to add $74.19 and $16.95, for a total of $91.14. A similar process yields the adjusted price of kits and trays for the other years and permits a computation of lost profit per kit and tray.
Before we move on, one final reality check. IMPRA says that these numbers are off the wall because they exceed by a great deal what it views as a "reasonable royalty" for the Mahurkar catheter. A few percent of the selling price, according to Mr. Green, is all he would pay; yet 10% per year compounded for five or six years is a significant multiplier. IMPRA's unwillingness to pay significant royalties might well be justified  in competition. With competition reduced to that offered by femoral, alternating-flow, and soft dual-lumen catheters such as Cook's, however, the value of Mahurkar's intellectual property would increase. Even during a time of rampant infringement Quinton has been paying Mahurkar a hefty royalty. As of January 1, 1988, Quinton was paying Mahurkar a royalty of 9% on its sales of all products containing his catheters. This is a lot more than 9% on the value of the catheter itself. Trays sold for more than twice the price of the catheter, so a 9% royalty on a tray is more like a 20% royalty on the catheter it contains. If Mahurkar's contribution was worth this much even while Quinton faced competition from firms that were selling his invention without paying for his contribution, *1392 it is a very valuable piece of intellectual property indeed. And of course Quinton's own contribution, including development of a workable product and entrepreneurial risk-taking, is significant. The price implied by the method I have used is not out of line with this recognition.

3
Quinton and Mahurkar would like to collect from IMPRA their whole lost profit, but IMPRA was only one of the many infringers in the market. Determining IMPRA's appropriate share of the lost profits requires additional adjustments.
First, there is the question whether IMPRA is entitled to "credit," as it were, for the price erosion caused by the other infringers' sales. For reasons explored in the previous part of this opinion, the answer is no. Let us suppose Quinton and Mahurkar had brought all of the infringers into court at once and that none had settled. At the conclusion of the trial they would have been entitled to a fully compensatory award. A judge would not let the infringers play a game of whipsaw, in which each argued that it should pay less of the damages than its share of the sales, because the price would have been depressed anyway even had it never infringed. That approach would lead to a less than compensatory award. Indeed it might lead to no damages at all, even though by hypothesis the patent holder and his licensee have been injured.
Full compensation is possible only if each infringer pays damages computed by multiplying the total lost profit by each infringer's share of the infringing sales. For example, suppose the patent holder's lost profit (including price erosion) is $10 million and that there are four infringers. Infringer A sold 50,000 units, B sold 100,000 units, C sold 150,000 units, and D sold 200,000 units, for total infringing sales of 500,000 units. A's share of the infringing products is 10%, B's is 20%, C's is 30%, and D's is 40%. At the close of trial, A should be required to pay $1 million, and so on. This procedure fully compensates the patent holder. It is the mirror image of the damages model used in antitrust cases, appropriate for the same reasons: it compensates victims fully while giving each offender the correct incentives. Suppose A, B, C, and D form a cartel, increasing the price of widgets. When customer X files suit, A will not be permitted to defend by saying that, had it not joined the cartel, B, C, and D still would have raised prices, so that X still would have paid too much. A, as a member of the cartel, is liable for the whole overcharge  but any given customer recovers only for its actual purchases, so a member of the cartel is liable only on the units it sold. In the patent case each infringer is liable for the whole price erosion, but only in proportion to the units it actually sold.
Quinton and Mahurkar therefore can proceed in one of two ways, which at least in principle ought to produce the same damages. First, they can determine (using the method described in Parts IV.B.1 and 2 above) their lost profits attributable to all infringing sales in 1986-92, determine IMPRA's share of those sales, and multiply the two. Second, they can determine the profits per transaction lost on IMPRA's precise sales using actual costs and prices (e.g., ($32.81 - 13) × IMPRA's sales of catheters in 1986, repeated for each product and year) and then determine separately the profits lost because of price erosion, and allocate these among the infringers according to market share. The first method looks simpler, but performing both calculations to see whether they tally (as they should) has something to recommend it.
Requiring IMPRA to compensate Quinton and Mahurkar in proportion to "IMPRA's share" of the infringing sales poses still a further problem, because some of these sales were resales of infringing catheters IMPRA purchased from Kendall Med-West. IMPRA started making its own devices in 1987 but did not wean itself fully from Kendall until late 1988. Shortly before the trial began, Kendall settled with Mahurkar and Quinton, paying $870,000 in damages (about 18% of its gross sales) and withdrawing from the hemodialysis market. IMPRA contends that Kendall's settlement and payment releases it from any liability on the catheters it purchased from Kendall. Plaintiffs were satisfied with what they received from Kendall *1393 and cannot ask for more, IMPRA insists. It characterizes the Kendall settlement as creating a retroactive license; how can it be liable for selling catheters that Kendall produced under license from Mahurkar?, IMPRA asks. It contends, finally, that if it must pay damages on the catheters it bought from Kendall and resold, it should receive as a credit against the judgment the whole $870,000 plaintiffs accepted from Kendall.
Let us suppose Kendall had an implied, retroactive license to make catheters covered by the '968 patent. IMPRA still needed a license to sell those catheters. Making and selling are independently forbidden unless the owner of the patent consents. 35 U.S.C. § 271(a). Kendall's settlement therefore does not automatically release Kendall's customers. Such a settlement could release the customers, but no language in this particular agreement does so. Thus this case is within the domain of the usual rule that, as all infringers are jointly and severally liable, a settlement by one infringer reduces the recovery from the others dollar-for-dollar. Aro Manufacturing, 377 U.S. at 503, 84 S.Ct. at 1541. See also, e.g., Zenith Radio Corp. v. Hazeltine Research, Inc., 401 U.S. 321, 348, 91 S.Ct. 795, 811, 28 L.Ed.2d 77 (1971); Birdsell v. Shaliol, 112 U.S. 485, 489, 5 S.Ct. 244, 246, 28 L.Ed. 768 (1884). Kendall sold 16% of its output to IMPRA (this figure is not disputed); 16% of $870,000 is $139,200, which is the full credit IMPRA receives from the Kendall settlement. IMPRA also gets a credit of $40,000 from a settlement between Mahurkar and Med-Comp, another of IMPRA's suppliers. Total credit: $179,200.
Another feature of the Kendall settlement has a potential effect on Mahurkar's net recovery from IMPRA. Kendall wanted assurance that $870,000 and an injunction against further infringement would be the limit of its liability. It feared that, if held liable, IMPRA would turn around and attempt to obtain contribution or indemnity. (Which IMPRA is trying to do. It has filed a suit against Kendall in the Maricopa County Superior Court. Prosecution of IMPRA's action, No. CV 92-16190, has been stayed pending the disposition of this case.) Quinton and Mahurkar promised to indemnify Kendall for any recoveries against it on account of the sales covered by the settlement. Both IMPRA and Kendall have filed memoranda asking me to preclude any award against IMPRA on account of the Kendall catheters, in order to avoid triangular litigation: Mahurkar collects from IMPRA, which collects from Kendall, which collects from Mahurkar.
I deny Mahurkar's motion to strike these filings but also decline to reduce the damages IMPRA must pay Mahurkar and Quinton. I have no idea whether the contractual arrangements between IMPRA and Kendall permit IMPRA to obtain contribution or indemnity. Unless they do, there will be no triangular exchange of money: Quinton and Mahurkar will keep what they recover from IMPRA. This is a patent infringement case, and I shall award damages reflecting plaintiffs' lost profits. If as IMPRA contends a chain of indemnities means that Quinton and Mahurkar are not going to be able to retain their full recovery, the parties undoubtedly can work that out without two additional rounds of litigation. This is neither the time nor the place to decide what, if anything, IMPRA is entitled to collect from Kendall, and whether Mahurkar is required to defend Kendall in IMPRA's pending action in Arizona.
The approach to determining damages that I have laid out depends, in part, on IMPRA's infringing sales. The record contains good data on IMPRA's shipments, but there is a dispute about its sales. The first step is to exclude all catheters sold to the United States; under 28 U.S.C. § 1498(a) the patent holder must go to the Court of Federal Claims to collect for these sales. Patti Capps, IMPRA's accounting manager, testified that from 1986 through 1991 IMPRA shipped a total of 87,038 catheters, kits, and trays, of which 4,787 were furnished to the federal government, for a total of 82,251 private-market shipments. Duggan, on behalf of Mahurkar, found private shipments of 82,250. Close enough for government work. The parties should use Duggan's figures when making the submissions called for by Part VII.
*1394 Still we are not done, because IMPRA denies that shipments equate to sales. Some of the products went to salesmen, who used them to demonstrate the catheters' attributes to potential customers. Quinton and Mahurkar reply that IMPRA sent sterile catheters to its sales force. Capps testified that in less than 1% of IMPRA's samples was sterility destroyed before the samples were delivered to the customer. "Samples" in condition to be used may be a disguised discount. Quinton's demonstration models were not sterile. IMPRA's list price exceeded Quinton's; but if IMPRA used the "samples" as a discount (buy ten, get a "free sample," equates to a 9% discount) its price would have been very close to Quinton's, and the "samples" should be treated just like any other sales. IMPRA sends many of its sterile "samples" direct to customers, increasing the likelihood that they will be used in treatment.
Nothing in the record enables me to determine which of IMPRA's shipments were genuine demonstration models and which competed with Quinton's products for implantation in patients. The record does, however, contain a breakdown by size of shipment. That is, it shows that IMPRA shipped X many catheters in units of 10, Y many catheters in units of 2, and so on. Genuine demonstrators would have been sent to salesmen in small numbers, one or two at a time. As a rough compromise  and mindful that doubts are to be resolved against the infringer  I conclude that one-third of the catheters in one-unit shipments should be treated as demonstrators; the rest count as sales.

C
Plaintiffs are entitled to prejudgment interest on the lost profits they suffered. General Motors Corp. v. Devex Corp., 461 U.S. 648, 103 S.Ct. 2058, 76 L.Ed.2d 211 (1983); Gyromat, 735 F.2d at 555-56. Although Devex leaves some room for a discretionary denial of interest, this case does not justify exercising in IMPRA's favor whatever discretion I possess.
Mahurkar's delay in instituting this suit does not counsel against interest. It means instead that IMPRA has had the proceeds of the infringement (and the plaintiffs have lacked them) for a longer time. Interest is not a "penalty" of any kind; it simply represents the time value of money and is an element of complete compensation, putting the victim in the position it would have occupied had there been no wrong. Interest cancels the effects of delay. If delay does not establish laches (and I have held that it does not), it does not warrant a denial of interest. In re Oil Spill by the Amoco Cadiz, 954 F.2d 1279, 1331-35 (7th Cir.1992). Similarly, that some issues in this case were close does not justify the withholding of interest. Partington v. Broyhill Furniture Industries, Inc., 999 F.2d 269, 274 (7th Cir. 1993).
As a fallback, IMPRA asks me to award interest at the rate the United States pays to borrow money, the rate that by statute is used for post-judgment interest. Both the Federal Circuit and the Seventh Circuit have held that such a rate is inappropriate. Amoco Cadiz, 954 F.2d at 1332; Uniroyal, Inc. v. Rudkin-Wiley Corp., 939 F.2d 1540, 1545 (Fed.Cir.1991). Professor Hausman contended that the appropriate rate for prejudgment interest "is the rate over the relevant period on U.S. three-month Treasury Bills. Any lower rate would not properly compensate Dr. Mahurkar or Quinton for the time value of the money. Any higher rate would be improper, since a higher rate would serve to compensate Dr. Mahurkar and Quinton for financial risks associated with investing the alleged lost royalties/profits that Dr. Mahurkar and Quinton did not actually undertake." This passage recognizes that interest compensates not only for the time value of money (deferred consumption or other use of money) but also for the risk of nonpayment. Yet Quinton and Mahurkar have had their funds at risk. Winners in litigation are not called "judgment creditors" for nothing. They have made a large, involuntary, unsecured loan to a debtor of uncertain credit-worthiness that is doing its utmost to avoid paying. In the market the rate of interest on such loans greatly exceeds the rate the United States Government has to pay  a rate that economists usually call the "riskfree rate." Plaintiffs did not make a riskfree loan.
*1395 Plaintiffs are entitled to the market rate their debtor pays for money. What did IMPRA pay to its creditors during this time? Duggan testified that IMPRA borrowed at prime plus ½%. The source of this statement is unclear. When the record is inconclusive, courts commonly supply the prime rate that banks charge for unsecured loans to credit-worthy customers. Gyromat, 735 F.2d at 557; Uniroyal, 939 F.2d at 1545; Gorenstein Enterprises, Inc. v. Quality Care-U.S.A., Inc., 874 F.2d 431, 436-37 (7th Cir.1989). This rate is favorable to judgment debtors, because the prime rate applies to short-term credit that is highly likely to be repaid. When calculating damages in accordance with Part VII, the parties should use the prime rate during the relevant times, compounded monthly.

V
I informed the parties before the start of the damages trial that I would not enhance the award under the second paragraph of 35 U.S.C. § 284. This part of the opinion elaborates on my reasons.
The statute authorizes an award of up to three times actual damages but does not say when enhancement is appropriate. The Federal Circuit believes that enhancement is appropriate when the infringement was "wilful" and not otherwise. IMPRA infringed intentionally in the sense that it knew about Mahurkar's patents and knew that its catheters contained many of the elements covered by those patents. Ordinarily this leads to a finding of wilfulness, but IMPRA contends that reliance on an opinion of counsel negates this conclusion.
Read, 970 F.2d at 826-31, contains a thorough discussion of the criteria that a trier of fact should employ when deciding whether to award enhanced damages. After listing a large number of factors bearing on wilfulness and telling triers of fact that they should consider all circumstances, the court added that "wilfulness is ... a state of mind", id. at 828, which makes it particularly difficult to infer wilfulness when a layman receives and acts on legal advice. The court continued:
Those cases where willful infringement is found despite the presence of an opinion of counsel generally involve situations where opinion of counsel was either ignored or found to be incompetent.... That an opinion is "incompetent" must be shown by objective evidence. For example, an attorney may not have looked into the necessary facts, and, thus, there would be no foundation for his opinion. A written opinion may be incompetent on its face by reason of its containing merely conclusory statements without discussion of facts or obviously presenting only a superficial or off-the-cuff analysis.
Id. at 828-29 (citations omitted). Read added two considerations that help to verify or refute an inference of incompetence. One, which I find particularly appealing, is hindsight  the proof of a pudding is in the eating. The court observed: "A good test that the advice given is genuine and not merely self-serving is whether the asserted defenses are backed up with viable proof during trial which raises substantial questions". Id. at 829 n. 9. It added that the "most important consideration" is whether anything in the attorney's letter "would alert a client to reject the letter as an obviously bad opinion." Id. at 830.
One circumstance strongly suggests wilful infringement. IMPRA's product is a knock-off of a catheter that IMPRA had been buying from Kendall Med-West. Kendall had derived its product from the Quinton-Mahurkar catheter, and Kendall has since agreed to cease its infringement and pay damages. Outright copying implies wilfulness, State Industries, Inc. v. Mor-Flo Industries, Inc., 883 F.2d 1573, 1581-82 (Fed.Cir.1989), but circumstances are complicated because IMPRA copied Kendall's product, and Kendall made a variation rather than a precise copy of the Quinton-Mahurkar catheter.
Against this must be set the fact that before IMPRA started to make and sell its own device, Mr. Green asked Marvin A. Glazer of Cahill, Sutton & Thomas, IMPRA's patent counsel, whether such a course of action would infringe anyone's intellectual property rights. Mr. Glazer concluded that it would not. When Mahurkar sent letters to IMPRA questioning its sale of catheters that appeared to practice his patents, Green *1396 promptly sent them to Glazer and requested advice. This occurred even though, at the time, IMPRA was still selling Kendall's product, and it would have been easy (though incorrect) to fob off the inquiry as Kendall's problem.
By the time it went into production with its own device, IMPRA had four comfort letters from Mr. Glazer, three addressing a variety of patents and a fourth dealing exclusively with Mahurkar's '141 patent. These are careful, reasoned letters. Mr. Green testified that he relied on them in fact, and I credit that testimony.
The letters are competently prepared, at least on the surface. Mr. Glazer assessed the devices factually and legally. Before rendering a final opinion, Mr. Glazer obtained the prosecution history of the patents. On reviewing this history, he found and discussed the design-to-utility conversion, which created the possibility that Mahurkar's Canadian patent disabled him from obtaining valid United States patents. The letters discuss some of the prior art. The letter of May 28, 1986, suggests that the deflection of the septum at the very tip of IMPRA's catheter distinguishes the '968 patent. A reasonable business manager could rely on such advice and would not find it, in the language of Read, an "obviously bad opinion." I conclude that Mr. Green did rely on these letters.
Notice that I have relied on the qualifying language of Read: "obviously" bad opinion. The letters are notable, at least in retrospect, for what they omit as well as for what they say. Nowhere in any of the letters does Mr. Glazer expressly state that the IMPRA devices would not literally infringe all of Mahurkar's patents. In one of the letters, for example, Glazer concludes that "IMPRA has avoided infringement of Claims 1-6 of the '141 patent." What about the other claims? Similarly, the letters did not discuss the doctrine of equivalents, although the circumstances cried out for it  especially after Mr. Glazer himself concluded that IMPRA's device avoided literal infringement only barely, by a last millimeter deflection of the septum. The lack of a firm conclusion that IMPRA's products would not infringe Mahurkar's patents might have served as a warning, perhaps fortified by oral exchanges. Intentional infringement of a patent in the hope that the patent will be overturned is wilful infringement if the court ultimately sustains the validity of the patents.
The letters have another interesting omission. By the time IMPRA started making double-D catheters, other manufacturers were leaving that part of the business, many after concluding that Mahurkar's patents gave them no alternative. Either Glazer did not ask these manufacturers why they had quit, or he asked and left the answers out of his letters.
Nonetheless, these weaknesses do not make the letters incompetent. As the Federal Circuit said in Read, the acid test is what happens in the litigation. The accused infringers (Vas-Cath and Kendall as well as IMPRA) put on a good defense, strong enough to lead me to invalidate two of Mahurkar's many patents because of the design-to-utility dating problem. The Federal Circuit concluded that factual issues prevented summary judgment but left untouched the conclusion that Vas-Cath (and hence IMPRA) had substantial defenses to Mahurkar's claims. The validity of the '968 patent remained in question through the trial because of the Northwest Kidney sales. With a good faith defense on validity, and the advice of counsel, even a deliberate decision to make the article exactly as described in the patent is not wilful infringement.
Mahurkar bears the burden of proof on wilfulness and has not carried it. I believe that Mr. Glazer's letters were the sort of communications on which manufacturers are entitled to rely, and that the competence of Mr. Glazer's advice has been borne out by the existence of substantial issues in this litigation. An enhancement of damages is therefore inappropriate.

VI
Quinton and Mahurkar are entitled to an injunction in addition to damages. "It is the general rule that an injunction will issue when infringement has been adjudged, absent a sound reason for denying it." Richardson *1397 v. Suzuki Motor Co., 868 F.2d 1226, 1247 (Fed.Cir.1989). A patent conveys the right to exclude others from making, using, or selling the invention, and this right implies the propriety of an injunction enforcing exclusivity. The injunction creates a property right and leads to negotiations between the parties. A private outcome of these negotiations  whether they end in a license at a particular royalty or in the exclusion of an infringer from the market  is much preferable to a judicial guesstimate about what a royalty should be. The actual market beats judicial attempts to mimic the market every time, making injunctions the normal and preferred remedy. See Schlicher, Patent Law: Legal and Economic Principles §§ 1.14, 9.03[1]. No "sound reason" counsels against injunctive relief in this case. The burdens an injunction will impose on IMPRA do not differ from those other infringers experience when told that they must change or abandon a product. Windsurfing International, Inc. v. AMF, Inc., 782 F.2d 995, 1003 n. 12 (Fed. Cir.1986); Polaroid Corp. v. Eastman Kodak Co., 641 F.Supp. 828, 228 U.S.P.Q. 305, 344 (D.Mass.1985), affirmed, 789 F.2d 1556 (Fed. Cir.1986).
IMPRA contends that I should not issue an injunction (or should stay enforcement of any injunction) because the Federal Circuit is going to reverse my decision concerning the on-sale question. Every unsuccessful litigant has hopes of triumph in the next tribunal, but this line of reasoning would keep the victors from savoring the fruits. I have adjudged this case to the best of my ability and do not believe that IMPRA has unusually high prospects of success on appeal. Accordingly, I shall enter the injunction, and I will not stay that injunction pending appeal. I will, however, refrain from formally entering the injunction until the final decision on damages, so that the Federal Circuit need not hear multiple appeals, and the injunction will include a two-week delay to give IMPRA time to seek a stay from the Federal Circuit.
IMPRA also argues that Mahurkar's delay in seeking injunctive relief disentitles him to that remedy. Although this contention might have some force if Mahurkar were seeking a preliminary injunction, it has none now that the trial is over. (All of the cases IMPRA cites dealt with delay in seeking interlocutory relief.) Delay short of laches is irrelevant, and IMPRA cannot establish either that Mahurkar's delay was excessive or that it suffered prejudice attributable to this delay.
One subject lies outside the injunction. By virtue of 28 U.S.C. § 1498(a), IMPRA is entitled to continue selling infringing catheters to the United States and its agencies (principally the Veterans Administration). See also W.L. Gore & Associates, Inc. v. Garlock, Inc., 842 F.2d 1275, 1282 (Fed.Cir.1988); Trojan, Inc. v. Shat-R-Shield, 885 F.2d 854, 856 (Fed.Cir.1989). The privilege of selling existing inventory to the government (recall that IMPRA already has stopped manufacturing infringing catheters) also means that IMPRA is not likely to suffer irreparable harm while the appeal is under consideration.
I have considered the parties' submissions about the form of appropriate equitable relief. Contemporaneously with the final calculation of damages, I will enter the following combined declaratory judgment and injunction:
1. United States Patent No. 4,583,968, owned by Sakharam D. Mahurkar, is valid and enforceable.
2. IMPRA Inc. has infringed Claims 1, 2, 3, 6, 7, 8, 11, 19, 20, 21, 22, and 23 of that patent by its sale of its Model DL hemodialysis catheters, kits, and trays. The infringing IMPRA catheters are identified in this litigation as exhibits MMDL 9, 11, 202, 249, 255, 256, 288, 302, 331, and 1296, and drawings MMDL 66, 70, 327, and 3002.
3. No later than two weeks from today, IMPRA, its officers, agents, servants, employees, and attorneys, and those persons in active concert or participation with them who receive actual notice of this order by personal service or otherwise, shall cease making, using, or selling devices covered by Claims 1, 2, 3, 6, 7, 8, 11, 19, 20, 21, 22, and 23 of United States Patent No. 4,583,968, except to the extent sales to, and manufacture for the benefit of, the federal government are permitted by 28 U.S.C. § 1498(a).

*1398 4. The prohibition of paragraph 3 covers all of the catheters and catheter designs identified by paragraph 2 of this order, and any other design that literally satisfies the language of Claims 1, 2, 3, 6, 7, 8, 11, 19, 20, 21, 22, or 23 of United States Patent No. 4,583,968 or that has the same or substantially equivalent combination of elements. This includes any catheter with an elongated unitary tube, at least one septum or wall extending axially along the length of the tube and dividing the tube into at least two lumens, and ending in a conically tapered tip, and, where required by an applicable claim, having: (i) lumens that are axially spaced, (ii) a concentration of material in the conically tapered tip, (iii) a tip whose apex is substantially aligned with the cylindrical tube, (iv) semi-circular lumens, (v) scaphoid openings in the outer circumference of the lumens, (vi) a planar septum, (vii) a tip with a length at least two diameters that of the tube, (viii) the opening at the distal end is eccentric with respect to the axis of the tube, and (ix) a longer lumen having a uniform diameter along its length.

VII
This opinion resolves every subject remaining in dispute between the parties, except for the precise computation of damages. At the close of the damages trial, I informed the parties that I would establish a framework  a set of ground rules  and then invite submissions applying the rules to the facts established at trial. I assume that the parties will want their accountants to have another go at the subject in light of this opinion. Mr. Freed, although excluded as an expert at trial in light of the deficiencies, in his narrative, is not disqualified from participating in this final set of calculations.
Quinton and Mahurkar should submit a calculation of damages (including prejudgment interest), using the framework established in Part IV, within three weeks of this opinion. IMPRA has ten days to respond to that submission, and plaintiffs have seven days to file a reply. All parties are free to include additional experts' reports and tables to support their computations. No additional documents will be accepted except by leave of court, which is not apt to be forthcoming.
NOTES
[*]   Of the Seventh Circuit, sitting by designation.
