
627 F.3d 1336 (2010)
James PAVATT, Plaintiff, and
Jeffrey Matthews, Plaintiff-Intervenor-Appellant, and
John David Duty, Plaintiff-Intervenor,
v.
Justin JONES, Director, Department of Corrections, Randall G. Workman, Warden, Oklahoma State Penitentiary; John Doe, 1-50 Unknown Executioners, Defendants-Appellees.
No. 10-6268.
United States Court of Appeals, Tenth Circuit.
December 14, 2010.
*1337 Timothy R. Payne, Assistant Federal Public Defender, Western District of Oklahoma, Oklahoma City, OK, for Plaintiff-Intervenor-Appellant.
Seth S. Branham, Assistant Attorney General, W.A. Drew Edmondson, Attorney General of Oklahoma, Oklahoma City, OK, for the Defendants-Appellees.
Before BRISCOE, Chief Judge, GORSUCH, and HOLMES, Circuit Judges.
BRISCOE, Chief Judge.
Plaintiff Jeffrey Matthews, an Oklahoma state prisoner sentenced to death by lethal injection, appeals from the district court's denial of his motion for a preliminary injunction of the execution. Exercising jurisdiction pursuant to 28 U.S.C. § 1292(a)(1), we affirm.[*]

I
Matthews was convicted in Oklahoma state court of first degree murder and sentenced to death. See Matthews v. Workman, 577 F.3d 1175, 1178-79 (10th Cir.2009) (outlining factual and state procedural history of Matthews' case). After Matthews exhausted the available state and federal court remedies, the Oklahoma Court of Criminal Appeals (OCCA), at the request of the Oklahoma Department of Corrections (ODC), scheduled Matthews to be executed on August 17, 2010.
On the eve of his execution, Matthews was informed by ODC officials that the anesthetic drug traditionally employed in ODC's three-drug lethal injection protocol, sodium thiopental, was unavailable and that ODC officials planned to substitute an alternative barbiturate, pentobarbital, during Matthews' execution.[1] Matthews responded *1338 by simultaneously moving to stay his execution and to intervene in Pavatt v. Jones, Case No. 10-141-F (W.D.Okla. 2010), an ongoing 42 U.S.C. § 1983 action filed by another Oklahoma prisoner asserting an Eighth Amendment challenge to Oklahoma's lethal injection protocol. The district court granted Matthews' motions, allowed him to file a complaint, and authorized Matthews to conduct discovery and obtain and file an expert report. On November 19, 2010, the district court held an evidentiary hearing on Matthews' motion for preliminary injunction. During that hearing, Matthews presented testimony from his expert witness, and defendants presented the videotaped deposition testimony of their expert. At the conclusion of the hearing, the district court ruled from the bench, denying Matthews' motion for preliminary injunction. On November 22, 2010, the district court issued a memorandum and order memorializing its findings and conclusions. On that same date, the Oklahoma Attorney General's Office requested the OCCA to set January 4, 2011, as the execution date for Matthews.[2]
Matthews now appeals from the district court's denial of his motion for preliminary injunction seeking to stay his execution.

II
"We review the district court's order for an abuse of discretion." Hamilton v. Jones, 472 F.3d 814, 815 (10th Cir. 2007). The principles that apply to our review were outlined by the Supreme Court in Hill v. McDonough, 547 U.S. 573, 126 S.Ct. 2096, 165 L.Ed.2d 44 (2006). "[A] stay of execution is an equitable remedy" that "is not available as a matter of right, and equity must be sensitive to the State's strong interest in enforcing its criminal judgments without undue interference from the federal courts." 547 U.S. at 584, 126 S.Ct. 2096. Consequently, "like other stay applicants, inmates seeking time to challenge the manner in which the State plans to execute them must satisfy all of the requirements for a stay, including a showing of a significant possibility of success on the merits." Id.
As the district court aptly noted, Matthews' challenge to the ODC's planned lethal injection procedure, i.e., its planned substitution of pentobarbital for sodium thiopental, is governed by the Supreme Court's decision in Baze v. Rees, 553 U.S. 35, 128 S.Ct. 1520, 170 L.Ed.2d 420 (2008). In Baze, the Court acknowledged "that subjecting individuals to a risk of future harmnot simply actually inflicting pain can qualify as cruel and unusual punishment." Id. at 49, 128 S.Ct. 1520. However, the Court emphasized, "[t]o establish that such exposure violates the Eighth Amendment, ... the conditions presenting the risk must be `sure or very likely to cause serious illness and needless suffering,' and give rise to `sufficiently imminent dangers.'" Id. at 49-50, 128 S.Ct. 1520 (quoting Helling v. McKinney, 509 U.S. 25, 33, 34-35, 113 S.Ct. 2475, 125 L.Ed.2d 22 (1993) (emphasis added)). Thus, the Court held, "[s]imply because an execution method may result in pain, either by accident or as an inescapable consequence of death, does not establish the sort of `objectively *1339 intolerable risk of harm' that qualifies as cruel and unusual." Id. at 50, 128 S.Ct. 1520. Lastly, the Court held that "[a] stay of execution may not be granted on [such] grounds ... unless the condemned prisoner establishes that the State's lethal injection protocol creates a demonstrated risk of severe pain ... [and] that the risk is substantial when compared to the known and available alternatives." Id. at 61, 128 S.Ct. 1520.
The district court, applying the Baze principles, concluded that Matthews failed to demonstrate such a risk in connection with his impending execution. In reaching this conclusion, the district court found:
 that the first step of the ODC's lethal injection protocol mandates the intravenous administration to the subject inmate of 5,000 milligrams of pentobarbital (2,500 milligrams in each arm);
 that the ODC's protocol requires the attending physician to "ensure that the [inmate] is sufficiently unconscious [as a result of the pentobarbital] prior to the administration of the [second drug and paralytic agent,] vecuronium bromide," Aplt. Br., Att. A at 153;
 that the administration of a sufficient dose of pentobarbital will render an individual unconscious and that the administration of a sufficient dose of pentobarbital will be lethal;
 that defendant's expert witness, Dr. Mark Dershwitz, an anesthesiologist with a Ph.D. in pharmacology, "persuasively characterized a 5,000 milligram dose of pentobarbital as `an enormous overdose'" that "would cause a flat line of the EEG, which is the deepest measurable effect of a central nervous system depressant," and "would be lethal as a result of two physiological responses": the cessation of respiration and the drop in blood pressure "to an unsurvivable level," id. at 154;
 that Dershwitz "very persuasively explained" that "pentobarbital is highly likely to cause death in five minutes or within a short time thereafter," id.;

 that Dershwitz "credibly testified ... that the 5,000-milligram dosage will give rise ... to a virtually nil likelihood that the inmate will feel the effects of the subsequently administered vecuronium bromide and potassium chloride," id. at 155; and
 that Dershwitz "persuasively responded to Dr. [David] Waisel's testimony that clinicians do not know what dosage of pentobarbital would be required to achieve anesthesia by pointing out that the use of pentobarbital to induce a barbiturate coma, which at least in Dr. Dershwitz's practice is a common use of pentobarbital, takes the patient to a state of unconsciousness beyond a normal clinical level of anesthesia," id. at 155-56.
Based upon these factual findings, the district court concluded that Matthews failed to establish "that the use of pentobarbital in Oklahoma's lethal injection protocol presents a constitutionally unacceptable risk of harm to the inmate." Id. at 156. "To the contrary," the district court concluded, "the evidence in this case clearly establishe[d] under the standards established... in Baze ... that any risk associated with the use of pentobarbital in Oklahoma's lethal injection protocol falls short of the level of risk that must be shown as a prerequisite to establishing an Eighth Amendment claim." Id. Thus, the district court concluded that Matthews "failed to establish ... a significant possibility of success on the merits...." Id. Lastly, the district court concluded that the likelihood that Matthews "w[ould] suffer ... injury... [w]as ... virtually nil." Id.
After conducting our own review of the record, we conclude the district court *1340 did not abuse its discretion in denying Matthews' motion. Each of the district court's factual findings are well-supported by the testimony of defendant's expert, Dr. Dershwitz. Although Matthews' expert witness, Dr. Waisel, expressed concern that there was insufficient data to allow the ODC to determine the proper amount of pentobarbital to use as part of its protocol, it was by no means clear error for the district court to find that Dr. Dershwitz, who has substantially more clinical experience with the use of pentobarbital than Dr. Waisel, persuasively rejected those concerns as unfounded. The district court likewise committed no clear error in finding that the amount of pentobarbital selected for use by the ODC as part of its protocol was sufficient to induce unconsciousness in an inmate, and indeed would likely be lethal in most, if not all, instances. Those findings, combined with the portion of the ODC's protocol that requires the attending physician to confirm that an inmate is unconscious prior to the administration of the final two drugs in the ODC's protocol, support the district court's legal conclusion that Matthews failed to establish a substantial likelihood of success on the merits of his Eighth Amendment challenge to the ODC's revised protocol.

III
Matthews also contended below, albeit in summary fashion, that the use of pentobarbital, which Dr. Dershwitz classified as an intermediate-acting barbiturate, would violate Oklahoma state law, which expressly requires the use of an "ultrashort-acting barbiturate"[3] in executions.[4] Okla. Stat. tit. 22, § 1014(A).[5] In turn, Matthews contended that the ODC's proposed execution protocol threatened to violate what he characterized as his "state-created life interest under the Fifth and Fourteenth Amendments." Aplt. Br. at 6. More specifically, Matthews contended he could not "be deprived of this Constitutional right *1341 through the arbitrary and capricious actions of persons acting under the color of State law." Id.
"A violation of state law does not by itself constitute a violation of the Federal Constitution." Nordlinger v. Hahn, 505 U.S. 1, 26, 112 S.Ct. 2326, 120 L.Ed.2d 1 (1992). To the extent, however, that state law creates an interest substantial enough to rise to the level of a "legitimate claim of entitlement," that interest is protected by the Due Process Clause of the Fifth Amendment. Bd. of Regents of State Colls. v. Roth, 408 U.S. 564, 577, 92 S.Ct. 2701, 33 L.Ed.2d 548 (1972). The Due Process Clause provides that "[n]o State shall ... deprive any person of life, liberty, or property, without due process of law," U.S. Const. amdt. XIV, § 1; accord amdt. V, and thus "imposes procedural limitations on a State's power to take away protected entitlements." Dist. Attorney's Office for Third Judicial Dist. v. Osborne, ___ U.S. ___, 129 S.Ct. 2308, 2319, 174 L.Ed.2d 38 (2009).
Here, as noted, Matthews asserts that he has a protected, "state-created life interest" in being executed in accordance with the precise protocol set forth in Okla. Stat. tit. 22, § 1014(A), and that defendants are threatening to violate that right. However, there is no indication in the record that defendants have denied Matthews the opportunity to challenge the protocol either administratively or in the Oklahoma state courts.[6] Indeed, the record indicates that Matthews has, in opposition to the State's request for the OCCA to set an execution date, filed an objection specifically arguing that the ODC's newly revised execution protocol is contrary to state law.[7] Consequently, we conclude, as did the district court, that Matthews has failed to establish a substantial likelihood of prevailing on his due process challenge to the ODC's newly revised execution protocol.
AFFIRMED.
NOTES
[*]  After examining the briefs and appellate record, this panel has determined unanimously that oral argument would not materially assist in the determination of this appeal. See Fed. R.App. P. 34(a)(2); 10th Cir. R. 34.1(G). The case is, therefore, submitted without oral argument.

For purposes of expediency, we previously issued a substantially similar order and judgment in this case. The clerk of the court has been now been directed to reissue the decision for publication nunc pro tunc to the original filing date.
[1]  According to the record, sodium thiopental is now effectively unobtainable anywhere in the United States, thus requiring Oklahoma and other death-penalty states to revise their lethal injection protocols. Two of those states, Ohio and Washington, have purportedly now replaced their three-drug protocols with a one-drug protocol based upon pentobarbital. Other states, in particular Oklahoma, have simply revised their existing three-drug protocols by substituting pentobarbital for sodium thiopental.
[2]  On December 14, 2010, the OCCA granted the request and established January 11, 2011 as Matthews' execution date.
[3]  The record on appeal establishes that Dr. Dershwitz used the terms "intermediate-acting" and "ultrashort-acting" to refer to the length of the barbiturate's effect, not on how quickly the barbiturate takes effect. Although it is not entirely clear, Oklahoma's statute appears to use the term "ultrashort-acting" in a different sense, to refer to how quickly the barbiturate takes effect. And on that score, as Dr. Dershwitz testified and the district court found, a 5,000 milligram dose of pentobarbital will quickly induce an unconscious state.
[4]  Matthews did not assert a separate due process claim in his intervenor complaint. Instead, he waited until filing his amended motion for preliminary injunction to assert, for the first time, that the use of pentobarbital would violate Oklahoma state law and, in turn, violate his federal due process rights. Although Matthews continued to mention the claim thereafter, including at the hearing on his motion for preliminary injunction, he presented no evidence, and few legal authorities, in support of the claim. In turn, the district court summarily rejected the claim as meritless at the preliminary injunction hearing, and did not expressly address it in its subsequent written order memorializing its oral rulings.
[5]  The statute provides, in its entirety:

A. The punishment of death must be inflicted by continuous, intravenous administration of a lethal quantity of an ultrashort-acting barbiturate in combination with a chemical paralytic agent until death is pronounced by a licensed physician according to accepted standards of medical practice.
B. If the execution of the sentence of death as provided in subsection A of this section is held unconstitutional by an appellate court of competent jurisdiction, then the sentence of death shall be carried out by electrocution.
C. If the execution of the sentence of death as provided in subsections A and B of this section is held unconstitutional by an appellate court of competent jurisdiction, then the sentence of death shall be carried out by firing squad.
Okla. Stat. tit. 22, § 1014.
[6]  There was no indication in any of Matthews' district court pleadings, or in his opening appellate brief, that he was seeking to assert a substantive due process violation. More specifically, at no point in any of those pleadings did Matthews mention the concept of substantive due process, or the associated "`fundamental right' or ... `shocks the conscience' standards...." Seegmiller v. LaVerkin City, 528 F.3d 762, 767 (10th Cir.2008).

In his appellate reply brief, Matthews mentioned the concept of substantive due process for the first time, stating in a footnote: "Mr. Matthews' asserted due process claim is as much, if not more, a substantive due process violation as it is a procedural due process violation." Aplt. Reply Br. at 15 n. 5. We conclude, however, that any such claim has been waived. See United States v. Smith, 606 F.3d 1270, 1284 n. 5 (10th Cir.2010) (explaining that "issues raised by an appellant for the first time on appeal in a reply brief are generally deemed waived" (quotations omitted)).
[7]  In its December 14, 2010 order setting Matthews' execution date, the OCCA declined, given the narrow context of the proceeding before it, to address the merits of Matthews' argument. However, the OCCA noted that Matthews could "present any appropriate issues challenging his conviction or sentence in a second or subsequent [state] post-conviction application." Matthews v. State, No. D-1999-1139, slip op. at 2 n. 2 (Okla.Crim.App. Dec. 14, 2010).
