
635 F.3d 1074 (2011)
UNITED STATES of America, Appellee,
v.
Lisa M. MONTGOMERY, Appellant.
No. 08-1780.
United States Court of Appeals, Eighth Circuit.
Submitted: September 22, 2010.
Filed: April 5, 2011.
*1078 Frederick A. Duchardt, Jr., Trimble, MO, argued (John G. Gromowsky, Kansas City, MO, on the brief), for appellant.
Roseann A. Ketchmark, Cynthia L. Cordes, Asst. U.S. Attys., Kansas City, MO, argued (Matt J. Whitworth, U.S. Atty., Philip M. Koppe, Asst. U.S. Atty., on the brief), for appellee.
Before WOLLMAN, MURPHY, and SHEPHERD, Circuit Judges.
WOLLMAN, Circuit Judge.
A federal jury convicted Lisa Montgomery of kidnapping resulting in death, in violation of 18 U.S.C. § 1201(a), and recommended that she be sentenced to death. *1079 The district court[1] imposed the death sentence, and Montgomery appeals. With respect to the guilt phase of her trial, Montgomery argues that the government failed to prove that death resulted from kidnapping and that the district court erred in excluding certain evidence. Montgomery also alleges that a number of errors infected the penalty phase, including the exclusion of expert evidence, prosecutorial misconduct, failure to properly instruct the jury, and submission to the jury of an unproven aggravating factor. We affirm.

I. Background

A. The Crime
Montgomery and Bobbie Jo Stinnett met at a dog show in April 2004. Both women were involved in the breeding of rat terriers and were acquainted through online message boards dedicated to their mutual interest. Stinnett maintained a website to promote Happy Haven Farms, her dog breeding business located in her home in Skidmore, Missouri. The website included pictures of Stinnett and her dogs. After she became pregnant in spring 2004, Stinnett shared the news with her online community, which included Montgomery. Stinnett was eight months pregnant in December 2004.
In spring 2004, Montgomery began telling her friends, family, and online community that she was pregnant. More than a decade earlier, however, she had undergone tubal fulguration, a sterilization procedure that involved occluding her fallopian tubes by cauterization. Montgomery was thus incapable of becoming pregnant. Nonetheless, Montgomery reported testing positive for pregnancy, began wearing maternity clothes, and began behaving as if she were pregnant. Unaware of the permanent sterilization, Montgomery's husband, Kevin Montgomery (Kevin), and her children believed that she was expecting. Some of Montgomery's acquaintances believed that she was pregnant and showed signs of pregnancy, but others did not. Those who knew that Montgomery had been sterilizedincluding her former husband and his wifeaccused Montgomery of deceiving her family. She responded that she would prove them wrong.
Using the alias Darlene Fischer, Montgomery contacted Stinnett on December 15, 2004, via instant message. Stinnett had a litter of puppies for sale, and Montgomery expressed interest in purchasing one. The women agreed to meet the next day. Although Montgomery lived in Melvern, Kansas, she told Stinnett that she was from Fairfax, Missouri, a town near Skidmore. That night, Stinnett told her husband and her mother, Becky Harper, that a woman from Fairfax was going to stop by and look at the puppies.
On December 16, Montgomery drove from Melvern to Skidmore and arrived at Stinnett's home around 12:30 p.m. Montgomery carried a sharp kitchen knife and a white cord in her jacket pocket. The women brought the puppies outside and played with them. At 2:30 p.m., Stinnett received a phone call from Harper and confirmed that she would give Harper a ride home from work at 3:30 p.m.
Some time after the phone call ended, Montgomery attacked Stinnett and used the cord to strangle her until she was unconscious. Montgomery then used the kitchen knife to cut into Stinnett's abdomen, causing Stinnett to regain consciousness. A struggle ensued, and Montgomery strangled Stinnett a second *1080 time, killing her. Montgomery extracted the fetus from Stinnett's body, cut the umbilical cord, and left with the baby. Montgomery entered her car and drove away from the Stinnett home, holding the baby in her arms and pinching the umbilical cord.
Harper called Stinnett shortly after 3:30 p.m. When no one answered, Harper walked the two blocks to Stinnett's home. The front door was open, and Harper went inside, calling for her daughter. She reached the dining room and found Stinnett's body lying there, covered in blood. Harper called 911 and told the operator that her daughter was eight months pregnant and in need of medical assistance. Harper said that it looked like Stinnett's stomach had exploded.
Meanwhile, after driving a short distance from Stinnett's home, Montgomery stopped to clamp the umbilical cord and to suction any mucus from the baby's mouth. The baby cried, but other than a cut above her eye, she was uninjured. After cleaning the baby with wipes, Montgomery retrieved the car seat she had stored in the trunk of her car and placed the baby in the seat. She drove to Topeka, Kansas, and called her husband, telling him that she had gone into labor while Christmas shopping and that she had given birth at a women's clinic in Topeka. She asked him to meet her at a parking lot near the clinic, which he did. They returned to Melvern together, with Montgomery's daughter and son driving her car home.
The Montgomery's called friends and relatives to announce the birth of their daughter, Abigail. They slept in the living room, next to the baby's bassinet. The next day, they ran errands and went out for breakfast, introducing Abigail to the people they met. Shortly after they returned home, law enforcement officials knocked on their door. Kevin answered the door and invited the officers into the home. Montgomery was sitting on the couch, holding the baby.
Sergeant Investigator Randy Strong explained that they were investigating the murder of Bobbie Jo Stinnett. He asked about the baby, and Montgomery said that she had given birth at a women's clinic in Topeka. She asked Kevin to retrieve the discharge papers from his truck. Kevin searched the truck, but he could not find the papers.
Strong then asked to speak to Montgomery outside the home. Montgomery allowed a law enforcement officer to hold the baby and accompanied Strong. Montgomery explained that her family was having some financial problems, so, unbeknownst to her husband, she had given birth at home, with the help of two friends. When asked the names of the friends, Montgomery responded that they had not been with her at the house but were available by phone in case she had trouble delivering the baby. Montgomery said that she had given birth in the kitchen and had disposed of the placenta in a nearby creek. At Montgomery's request, the officers moved their questioning to the sheriff's office. Shortly thereafter, Montgomery confessed to killing Stinnett, removing the fetus from Stinnett's womb, and abducting the child.
After the baby was returned to her father, she was named Victoria Jo Stinnett.

B. Montgomery's Personal History
For years, Montgomery was physically and sexually abused by her stepfather. When she was sixteen, her mother and stepfather divorced. Some family members believed that Montgomery's mother blamed her for the abuse and for the divorce, but her mother denied ever doing so. From childhood on, Montgomery had *1081 endured a tumultuous relationship with her mother.
Montgomery married Carl Boman, her step-brother, when she turned eighteen in August 1986. She had her first child in January 1987, and three more in the three years that followed. In 1990, Montgomery underwent the sterilization procedure described above. The procedure was successful, and a pretrial hysterosalpingogram confirmed that the sterilization rendered Montgomery unable to become pregnant. Montgomery claimed that her mother and Boman forced her to undergo the sterilization procedure.
In the years following the sterilization procedure, Montgomery claimed that she had four more pregnancies. In 1994, while separated from Boman, Montgomery had an affair and claimed that she was pregnant. Montgomery and Boman later reconciled, and she ceased making the claim. She and Boman divorced in 1998. In 2000, before she and Kevin were married, she told him that she was pregnant and intended to have an abortion. Kevin gave her forty dollars, and the pregnancy was not mentioned again. In 2002, Montgomery told her friends and family that she was pregnant again. Although she said that she was receiving prenatal care from her physician, she would not allow Kevin to attend the appointments. Her physician testified that he had treated Montgomery for ankle pain and a cold, but he did not provide her any prenatal care, despite Montgomery's claims to the contrary. When the alleged due date passed, Montgomery told Kevin that the baby had died and that she had donated its body to science. As described above, Montgomery claimed in spring 2004 that she was pregnant and that she was due in December.
Throughout the fall of 2004, Montgomery was involved in a custody dispute with Boman. He knew that Montgomery was unable to become pregnant and that she was again claiming that she was pregnant. He and his wife sent emails to Montgomery, telling her that they planned to expose her deception and use it against her in the custody proceedings. Montgomery said that she would prove them wrong. On December 10, 2004, days before the kidnapping, Boman filed a motion for change of custody of the two minor children who lived with Montgomery.

C. Procedural History and Trial
Montgomery was charged with kidnapping resulting in death, in violation of 18 U.S.C. § 1201(a)(1). The superseding indictment alleged:
[Montgomery] willfully and unlawfully kidnapped, abducted, carried away, and held Victoria Jo Stinnett, for the purpose and benefit of claiming Victoria Jo Stinnett as her child, and willfully transported Victoria Jo Stinnett in interstate commerce from Skidmore, Missouri, across the state line to Melvern, Kansas, the actions of the defendant resulting in the death of Bobbie Jo Stinnett.
The superseding indictment further alleged statutory aggravating factors, including that Montgomery killed Stinnett in an especially heinous, cruel, and depraved manner, in that it involved serious physical abuse to Stinnett. See § 3592(c)(6).[2] Thereafter, the government filed its notice of intent to seek the death penalty. See § 3593.
Montgomery moved to prohibit the government from seeking the death penalty, contending that the government could not prove that the kidnapping of a person resulted in Stinnett's death. A magistrate *1082 judge[3] recommended that Montgomery's motion be denied. The district court adopted the report and denied the motion.
Montgomery filed her notice of intent to assert the defense of insanity and to present expert evidence relating to mental disease or defect. See Fed.R.Crim.P. 12.2. Defense counsel engaged Vilayanur Ramachandran, M.D., and William Logan, M.D., to evaluate Montgomery. Both Drs. Ramachandran and Logan diagnosed Montgomery with depression, borderline personality disorder, post-traumatic stress disorder, and pseudocyesis. The government's expert, Park Dietz, M.D., agreed that Montgomery suffered from depression, borderline personality disorder, and post-traumatic stress disorder but did not diagnose her as suffering from pseudocyesis.
The Diagnostic and Statistical Manual of Mental Disorders (DSM-IV) defines pseudocyesis as "a false belief of being pregnant that is associated with objective signs of pregnancy, which may include abdominal enlargement, . . . reduced menstrual flow, amenorrhea, subjective sensation of fetal movement, nausea, breast engorgement and secretions, and labor pains at the expected date of delivery." Am. Psychiatric Ass'n, Diagnostic and Statistical Manual of Mental Disorders, 511 (4th ed. text revision 2000). The DSM-IV classifies pseudocyesis as a somatoform disorder. Id. "The common feature of Somatoform Disorders is the presence of physical symptoms that suggest a general medical condition, . . . and are not fully explained by a general medical condition, by the direct effects of a substance, or by another mental disorder." Id. at 485.
Before trial, defense counsel asked Ruben Gur, Ph.D., to opine whether Montgomery suffered from any mental abnormality, injury, or illness. Dr. Gur was prepared to testify that Montgomery's brain had structural and functional abnormalities consistent with the diagnosis of pseudocyesis. To reach this conclusion, Dr. Gur relied upon neuropsychological testing, magnetic resonance imaging (MRI), and positron emission tomography (PET).[4] The government challenged Dr. Gur's proffered testimony in a pretrial motion pursuant to Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993), and Federal Rules of Evidence 702 and 403, arguing that Dr. Gur's principles and methods were unreliable. The government sought to exclude Dr. Gur's analysis of Montgomery's MRI and PET scan. The government also asserted that its experts could not properly examine the underlying data because Dr. Gur had failed to produce the data from which his conclusions were drawn.
After hearing two days of expert testimony, the district court concluded that Montgomery's MRI results were not abnormal and thus did not show "any mental condition or circumstance that would be relevant to matters at issue in this case." The court indicated that it would allow some PET evidence. Although concerned about the reliability of Dr. Gur's PET analysis, the court determined that it would permit Dr. Gur to testify (1) that Montgomery's PET scan showed abnormalities in the somatomotor region of the *1083 brain and (2) that abnormalities in the somatomotor region are consistent with a diagnosis of pseudocyesis. The government requested that certain data be produced so that its experts could reproduce Dr. Gur's analysis, and the district court ordered that Montgomery produce the data.
During Montgomery's interviews with defense and government experts, she claimed that her brother, Tommy Kleiner, had accompanied her to Stinnett's home on December 16, 2004. Defense counsel arranged for Montgomery to undergo a polygraph examination. The polygraph examiner opined that Montgomery's statements that Kleiner had been with her at Stinnett's home "were not indicative of deception." The district court granted the government's motion to exclude any evidence regarding the polygraph examination.
After the jury had been selected and before opening statements, the district court ruled that Dr. Gur's testimony regarding his PET scan analysis would be excluded, finding that the evidence had minimal probative value because the abnormalities were consistent with many disorders, including pseudocyesis. The district court noted that the government's experts were unable to replicate Dr. Gur's calculations and that although Dr. Gur had produced the data that formed the basis of his opinion, he had failed to produce the original data from the PET scan centers. The district court concluded that the dispute over Dr. Gur's calculations would confuse the jury and distract it from the relevant and significant issues.
The jury heard eleven days of testimony related to the offense charged in the indictment and Montgomery's insanity plea. Dr. Ramachandran testified that pseudocyesis is a somatoform disorder in which the patient develops the delusion that she is pregnant. To be diagnosed with pseudocyesis, an individual must have an intense desire to become pregnant. Dr. Ramachandran explained that the desire gives rise to hormonal changes that result in physical changes consistent with pregnancy, including abdominal enlargement, breast enlargement, nipple pigmentation, and the cessation of menstruation. A person suffering from pseudocyesis might also crave strange foods, have nausea, feel fetal quickening, and have contractions.
Dr. Ramachandran testified that Montgomery suffered from severe pseudocyesis delusion and that she was in a dissociative state when she murdered Stinnett and delivered the baby. According to Dr. Ramachandran, Montgomery's childhood sexual abuse and post-traumatic stress disorder predisposed her to pseudocyesis. He testified that Montgomery sustained her pregnancy delusion with Internet research on cesarean sections, home birth, and hormones to assist in delivery. Montgomery's purchases of maternity clothes, a home birthing kit, and items for a baby nursery were consistent with pseudocyesis.
Dr. Ramachandran further testified that inconsistent stories were not evidence of malingering,[5] but of Montgomery's delusional state. He explained that malingering involves a consistent story because "it's a planned volition and a lie" and that a delusional state involves "constantly chang[ing] the story to accommodate the delusion and then forgetting what you said earlier." Because Montgomery's delusional state fluctuated, her story also fluctuated. Dr. Ramachandran stated *1084 that Montgomery's symptoms of pregnancy, her extensive internet research on home birthing, and her minimal research on cesarean-section delivery supported his opinion that she was not malingering. Dr. Ramachandran opined that Montgomery was suffering from a severe mental disease or defect when she committed the crime and that she was unable to appreciate the nature and quality of her acts.
The government's expert, Dr. Dietz, testified that there are two different phenomena that have been called pseudocyesis. The first is a condition in which a woman sincerely believes that she is pregnant, but she is not mentally ill and does not have delusions. The belief usually ends when the woman is confronted with evidence that she is not pregnant. The second involves mental illnessusually schizophreniaand the delusion of pregnancy. Dr. Dietz testified that the delusion is a firmly held conviction and that patients continue to believe they are pregnant, even after being confronted with evidence that they are not. Dr. Dietz explained that pseudocyesis is a psychosomatic condition that is classified as a somatoform disorder to "reflect its historical origin as hysterical conversion,. . . in which conflicts in the mind are converted into a bodily symptom."
Dr. Dietz opined that Montgomery did not suffer from pseudocyesis at the time of the offense because she did not hold a sincere belief that she was pregnant. When asked what evidence indicated that Montgomery did not believe she was pregnant, Dr. Dietz replied that Montgomery was well aware that she had undergone permanent sterilization, despite her statements that the procedure had been reversed. With her previous pregnancies, she sought prenatal care, had her husband attend the appointments, and gave birth in the hospital. But with this alleged pregnancy, Montgomery did not seek medical confirmation of the pregnancy or prenatal care. After Kevin made arrangements to attend an appointment with her, Montgomery told him that she had cancelled the appointment. She also reported that she had tested positive for pregnancy and had shown the test to Kevin, while Kevin maintained that he had not seen the test results. When she filled out an insurance application in September 2004, she indicated that she was not pregnant. Finally, Dr. Dietz took into account Montgomery's previous false claims of pregnancy, including one in which she said that she had donated a stillborn infant to science and forged a letter from the purported research institution.
Dr. Dietz further opined that Montgomery was not delusional. He testified that "[a] delusion of pregnancy would be consistent, she would tell the same story, she would happily reveal it. . . . No one could talk her out of it." Montgomery, however, gave contradictory accounts regarding the sex of the fetus, whether she was carrying twins or a single fetus, and the manner in which she would deliver. Before admitting that she had killed Stinnett and abducted the baby, Montgomery gave multiple narratives for the birth, first stating that she had given birth in a women's clinic, then at home with the help of two friends, and, finally, alone. After she had confessed and was in custody, she changed her story again, this time claiming that her brother was with her at Stinnett's home. And after it was determined that Kleiner could not have been with her at the time of the kidnapping, Montgomery claimed to have amnesia before and during Stinnett's murder. She also gave inconsistent reports on how many pregnancies she had experienced. In two Bureau of Prison medical forms, she claimed four, but during psychological exams she was vague, sometimes reporting three additional pregnancies. Dr. Dietz concluded that Montgomery *1085 malingered the 2004 pregnancy: "In other words, . . . she knew she was not pregnant but told people that she was."
Dr. Dietz ultimately testified that:
[I]t's my opinion, with reasonable medical certainty, that at the time of the charged offenses the defendant did not suffer from any mental disease or defect, that affected her ability to appreciate the nature and quality of wrongfulness of her acts.
. . .
[I]t is my opinion with reasonable medical certainty that the defendant was entirely capable of appreciating that she was engaged in a lengthy and elaborate plan designed to kill Bobbie Jo Stinnett at a stage of advanced pregnancy, to successfully conduct a Cesarean section on her first attempt and to kidnap a healthy [i]nfant she could present to the world as her own.
The jury found Montgomery guilty beyond a reasonable doubt of kidnapping resulting in death, and the case proceeded to the penalty phase. Over the course of two days, the jury heard testimony from Montgomery's friends, family, coworkers, Dr. Logan, and Ruth Kuncel, Ph.D.
Montgomery asserted the following mitigating factors, among others, to support her case for life imprisonment: her capacity to appreciate the wrongfulness of her conduct or to conform her conduct to the requirements of the law was significantly impaired; she committed the offense under severe mental and emotional disturbance; she had reared and supported four good children, to whom she had offered advice, nurturance, and emotional support and would continue to do so if she was sentenced to life imprisonment. Drs. Logan and Kuncel opined that, at the time of the offense, Montgomery's ability to appreciate the wrongfulness of her actions was substantially impaired and that she suffered from a severe mental or emotional disturbance. Throughout both phases of trial, various witnesses had testified that Montgomery was a good and loving mother, that she and her children got along well, and that they had a harmonious relationship. Over defense counsel's objections, the prosecutor asked Montgomery's daughter whether Montgomery had ever apologized for the suffering she caused the family. During closing arguments, the prosecutor expounded on the theme that Montgomery was not a good mother and that a good mother would not force her children to testify in this high profile trial.
Montgomery requested that the jury be instructed that it is never required to return a sentence of death. As discussed more fully below, the district court rejected Montgomery's proposed language and instructed the jury that if it unanimously concluded that the death penalty was the appropriate sentence, it must record its "determination that a sentence of death shall be imposed."
The jury returned a death-penalty verdict. It unanimously found that the government had proved beyond a reasonable doubt all statutory and non-statutory aggravating factors, including that Montgomery committed the offense "in an especially heinous or depraved manner in that the killing involved serious physical abuse to Bobbie Jo Stinnett." Thereafter, the district court sentenced Montgomery to death.

II. Discussion

A. Prosecution under 18 U.S.C. § 1201(a)
In her motion to prohibit the government from seeking the death penalty, Montgomery argued that, under federal criminal law, Victoria Jo Stinnett was not considered a person until removed from *1086 her mother's womb. Accordingly, because Stinnett died before Victoria Jo attained legal personhood by being born, the kidnapping of a person could not be the cause of Stinnett's death.
On appeal, Montgomery renews her argument that Stinnett's death did not result from kidnapping. She argues that the crime was not a kidnapping resulting in death, but a death resulting in kidnapping. Although she frames her argument as a challenge to the sufficiency of the evidence, it presents the following question: whether death results from kidnapping if the death precedes the completion of the kidnapping of a person.
Title 18 of United States Code § 1201(a) provides that "[w]hoever unlawfully seizes, confines, inveigles, decoys, kidnaps, abducts, or carries away and holds for ransom or reward or otherwise any person" and willfully transports the person in interstate commerce shall be punished by imprisonment, "and if the death of any person results, shall be punished by death or life imprisonment." Montgomery concedes that she had completed the crime of kidnapping after she removed the infant from the womb, held Victoria Jo for purposes of claiming the infant as her own, and transported the infant from Missouri to Kansas. But she argues that because Stinnett died with her fetus in utero, there was no kidnapping of a person resulting in death.

1. Definition of Person Under 18 U.S.C. § 1201(a)
In Roe v. Wade, the Supreme Court held that the word "person" as used in the Fourteenth Amendment did not include fetuses. 410 U.S. 113, 158, 93 S.Ct. 705, 35 L.Ed.2d 147 (1973). The Court reviewed the use of the word throughout the Constitution and concluded that "in nearly all [such] instances, the use of the word is such that it has application only postnatally. None indicates, with any assurance, that it has any possible pre-natal application." Id. at 157, 93 S.Ct. 705. The government argues that Roe is limited to its context and that Congress has enacted legislation defining person to include the unborn.
Congress has defined the word "person" to include any infant who is born alive. In 2002, Congress enacted 1 U.S.C. § 8, which states that "[i]n determining the meaning of any Act of Congress, . . . the word[ ] `person' . . . shall include every infant member of the species homo sapiens who is born alive at any stage of development." § 8(a). The statute states that an infant is "born alive" after "complete expulsion or extraction from his or her mother. . . [and] who after such expulsion or extraction breathes or has a beating heart, pulsation of the umbilical cord, or definite movement of voluntary muscles." § 8(b). Under a literal reading of the statute, the term "person" does not include fetuses.
Congress did not, as the government suggests, expand the term "person" to include the unborn in its enactment of the Unborn Victims of Violence Act of 2004. 18 U.S.C. § 1841. The statute recognizes unborn children as a class of victims not previously protected under federal law and criminalizes the killing or injuring of unborn children during the commission of certain federal offenses. See H.R. 108-420, 108th Cong. (2004). The statute defines unborn child as "a child in utero" and defines that term as "a member of the species homo sapiens, at any stage of development, who is carried in the womb." § 1841(d). The statute thus defines the term "unborn child" and limits its definition to § 1841. See id. The term "person" is not defined in the statute.


*1087 2. Death Resulted from the Kidnapping
That the term "person" does not necessarily include fetuses does not preclude a finding that Stinnett's death resulted from the kidnapping. The plain language of the statute reflects congressional judgment that the punishment for committing the crime of kidnapping should be more severe if the crime, as actually perpetrated, includes conduct that results in the death of any person. We have interpreted the term "results" broadly, stating that the statute requires "only that `the death of any person results' in the course of the kidnapping." United States v. Barraza, 576 F.3d 798, 807 (8th Cir.2009) (quoting 18 U.S.C. § 1201(a)).
A comparison to felony murder is instructive. Felony murder is the unlawful killing of a human being "committed in the perpetration of, or attempt to perpetrate, any arson, escape, murder, kidnapping, treason, espionage, sabotage, aggravated sexual abuse or sexual abuse, child abuse, burglary, or robbery." 18 U.S.C. § 1111(a). The federal statute is similar to the common law felony-murder rule, which requires that a killing occur "in the commission or attempted commission of" certain felonies. See 2 Wayne R. Lafave, Substantive Criminal Law § 14.5 (2d ed. 2003). Common law felony murder requires a temporal and causal connection between the death and the felony, but the death and the felony need not occur in a particular sequence. Id. Accordingly, the death may precede the felony and nonetheless constitute a killing that occurred "in the commission or attempted commission of" the felony. See, e.g., State v. Jacques, 270 Kan. 173, 14 P.3d 409, 422 (2000) ("When applying the felony-murder rule, . . . the felony and the victim's death do not need to occur simultaneously, nor does the felony need to occur before the death."); People v. Jones, 86 Ill.App.3d 253, 41 Ill.Dec. 733, 408 N.E.2d 79, 83 (1980) (The acts causing death "need not coincide with the felony as to time of occurrence but may occur before or after the felony."), rev'd in part, 85 Ill.2d 559, 62 Ill.Dec. 171, 435 N.E.2d 1143 (1981). Similarly, we conclude that a death may precede the completion of the crime of kidnapping, but nonetheless result from the kidnapping.
Stinnett's death occurred during the kidnapping and resulted from the acts required to complete the kidnapping. Montgomery asks us to view Stinnett's death and Victoria Jo's kidnapping as entirely distinct crimes, with the death preceding the kidnapping. To do so, we would have to disregard that the death and kidnapping occurred almost simultaneously and that Montgomery incapacitated a pregnant woman so that she could extract the fetus and complete the kidnapping of a person. Montgomery could not deliver the infant without subduing Stinnett, and thus she rendered Stinnett unconscious by strangulation. When Montgomery began the cesarean-section delivery of the infant, her incising of Stinnett's abdomen caused Stinnett to rouse and Montgomery to strangle her a second time. Stinnett's death resulted from the second strangulation and allowed Montgomery to deliver the baby and complete the crime of kidnapping. Montgomery was thus properly charged with kidnapping resulting in death.

B. Brain Imaging Evidence
Montgomery intended to introduce expert evidence that a PET scan and MRI showed that her brain had structural and functional abnormalities consistent with the diagnosis of pseudocyesis. Montgomery contends that the district court erred in excluding the evidence at both the guilt and the penalty phases of the trial. She *1088 argues that the evidence met the admissibility standards set forth in Federal Rule of Evidence 702 and the Federal Death Penalty Act. She contends that the evidence was highly probative because it provided support for the pseudocyesis diagnosis, bolstered Dr. Ramachandran's opinion, and rebutted Dr. Dietz's contrary opinion. Montgomery argues that the error cannot be deemed harmless, given the critical nature of the evidence. Moreover, she says, the PET evidence should not have been excluded because of her failure to timely comply with the district court's order to produce certain data from the PET scan centers.

1. PET Evidence
Dr. Gur supervised a PET scan of Montgomery's brain. PET scanners measure the level of activity in different areas of the brain. The results of Montgomery's scan revealed elevated activity throughout the limbic system, particularly in the right limbic regions, which are "important for emotion processing and memory formation." The limbic system also detects danger and regulates aggression. Montgomery's PET results also showed increased activity in the somatomotor region, including the hypothalamus. According to Dr. Gur, the somatomotor region "collects the body sensation. It tells the brain whether you are hot or cold, whether you are hungry or thirsty. It informs the brain of your sex drive, all those sensations that come from the body." Moreover, heightened activity in the hypothalamus has been shown to produce pseudopregnancy in rats. When asked whether it was significant that pseudocyesis "is what is called a somatoform disorder," Dr. Gur replied, "That's exactly what my thought was when I saw these findings."
Based on the PET results, Dr. Gur opined that Montgomery suffered from functional abnormalities consistent with the diagnosis of pseudocyesis. Dr. Gur testified that the purpose of the PET scan was not to diagnose Montgomery with pseudocyesis or any other condition, but to identify any brain abnormalities that might underlie her extreme behavior. Dr. Gur hesitated to say that Montgomery's brain abnormalities caused her to commit the crime. He testified that her brain abnormalities contributed to her actions and that "the brain she has may explain at least part of what happened."
Alan Evans, Ph.D., conceded that Montgomery's PET results were "not inconsistent with" the diagnosis of pseudocyesis, but he testified that no causal connection existed between Montgomery's brain functioning and the diagnosis. According to Dr. Evans, Montgomery's PET profile could be consistent with numerous neurological states, both normal and pathological, and thus "it is not particularly relevant or important to say it's consistent with pseudocyesis. It's consistent with many, many, many things." Likewise, Helen Mayberg, Ph.D., explained that a treating physician would not request a PET scan to determine whether the patient had pseudocyesis because its results would not be helpful in making the diagnosis. Although the PET scan indicates brain activity, no PET scan pattern indicates pseudocyesis, and PET results cannot be used to predict behavior. Dr. Mayberg testified that the reliance on the study of hypothalamic activity in rats was misguided. When asked whether PET results could be used to identify or diagnose psychiatric disorders, Dr. Mayberg replied unequivocally, "no."
Drs. Evans and Mayberg also took issue with Dr. Gur's methodology. They claimed that Dr. Gur had calculated the data from the normative population differently than he had calculated Montgomery's data. They were able to duplicate Dr. *1089 Gur's calculations only if they employed one method for Montgomery and a different method for the control group. They also expressed concerns over testing conditions and scanner resolution.
Following the Daubert hearing, the district court indicated that it would admit PET evidence regarding abnormalities in the somatomotor region of Montgomery's brain. Although skeptical of its reliability, it found that the PET evidence was relevant to the extent that Drs. Ramachandran and Logan would testify that the results showed abnormalities in the area of the brain where they would expect to find abnormalities in a person suffering from pseudocyesis. It found baseless "Dr. Gur's opinions about impulse control or aggression and what he identifies as abnormalities in the brain having any causal effect." It also found that Montgomery had failed to show that the results from a PET scan administered in 2007 would reveal the brain's condition in 2004.
As set forth earlier, prior to opening statements the district court decided to exclude the PET evidence regarding somatomotor abnormalities. It stated that the evidence had minimal probative value, that the dispute over Dr. Gur's calculations would confuse the jury, that the government's experts were able to duplicate Dr. Gur's results only when they used an invalid methodology, and that the original data from the PET scan center for the control group was unavailable and thus not produced to the government's experts. At the close of the guilt phase evidence and again at the close of the penalty phase evidence, the district court denied Montgomery's renewed requests to present evidence related to the PET scan.[6]
We review the district court's interpretation and application of the Federal Rules of Evidence de novo and its evidentiary rulings for abuse of discretion. United States v. Street, 531 F.3d 703, 708 (8th Cir.2008). "We may affirm on any ground supported by the record, even if that ground was not relied on by the district court." United States v. Purkey, 428 F.3d 738, 752 (8th Cir.2005). Moreover, even if the evidence was erroneously excluded, the defendant is not entitled to a new trial if its exclusion was harmless. United States v. Bistrup, 449 F.3d 873, 882 (8th Cir. 2006). "An error is harmless if it does not affect substantial rights of the defendant. . . and did not influence or had only a slight influence on the verdict." Id. (internal citations omitted).
During the guilt phase of trial, Federal Rule of Evidence 702 governs the admission of expert testimony and requires the district court to serve as a gatekeeper to "ensure that any and all scientific testimony or evidence admitted is not only relevant, but reliable." Daubert, 509 U.S. at 589, 113 S.Ct. 2786. Accordingly, an expert may testify in the form of an opinion or otherwise "if scientific, technical, or other specialized knowledge will assist the trier of fact to understand the *1090 evidence or to determine a fact in issue" and "if (1) the testimony is based upon sufficient facts or data, (2) the testimony is the product of reliable principles and methods, and (3) the witness has applied the principles and methods reliably to the facts of the case." Fed.R.Evid. 702.
Dr. Gur's testimony that Montgomery's PET scan showed abnormalities in the limbic and somatomotor regions of her brain was sufficiently reliable to be admitted. The experts agreed that PET scanners reliably measure brain activity, and we have previously noted that "[t]here is also no question that the PET scan is scientifically reliable for measuring brain function." Hose v. Chi. Nw. Transp. Co., 70 F.3d 968, 973 (8th Cir.1995). The government experts did not dispute Dr. Gur's testimony that the limbic system regulates emotion processing and that the midbrain, including the hypothalamus, regulates core functions like sleep and sex drive.[7]
That Montgomery's PET scan showed abnormalities in areas regulating emotion processing and core functions had minimal probative value. The abnormalities would have been significant only if they had assisted Montgomery in establishing her insanity defense, which was based on Dr. Ramachandran's opinion that Montgomery suffered from pseudocyesis, that pseudocyesis involves the delusion that one is pregnant, and that she was in a delusional or dissociative state when she kidnapped Victoria Jo and killed Stinnett. The PET scan was not used as a diagnostic aid for pseudocyesis, and as conceded by Dr. Gur, the abnormalities do not predict behavior and they did not cause Montgomery to commit the crime. Accordingly, any error in excluding the evidence that Montgomery's PET scan showed abnormalities in the limbic and somatomotor regions of the brain was harmless.
Dr. Gur's opinion that Montgomery's PET results showed abnormalities consistent with a diagnosis of pseudocyesis is another matter. Dr. Gur's opinion does not meet Rule 702's reliability requirement because it was "at most a working hypothesis, not admissible scientific `knowledge.'" See Tamraz v. Lincoln Elec. Co., 620 F.3d 665, 670 (6th Cir. 2010) (citing Fed.R.Evid. 702). Although Rule 702's inquiry is "a flexible one," it requires that the principles underlying the proposed submission be scientifically valid. Daubert, 509 U.S. at 594-95, 113 S.Ct. 2786. Scientific knowledge requires "more than subjective belief or unsupported speculation." Id. at 590, 113 S.Ct. 2786.
Montgomery failed to show that Dr. Gur's opinion was based on scientifically valid principles. Dr. Gur opined that Montgomery's "increased hypothalamic and related activation is potentially a source of vulnerability to pseudocyesis (by history)." At the Daubert hearing, he cited the scientific study involving rats as evidence of the correlation between increased activity in the hypothalamus and pseudocyesis. Dr. Mayberg, however, described that study in detail. When rats copulate, their hypothalamus gives a pulse of hormone that causes the pituitary to release other hormones, setting the stage for fertilization. The rats may experience a state of pseudopregnancy within two weeks of copulation. Dr. Mayberg explained that the increased hypothalamic *1091 activity is temporary and that the hypothalamus does not have a persistent state of activity in the rat experiments. Accordingly, Dr. Mayberg concluded that, even assuming a correlation between a rat and a human hypothalamus, the study was not applicable because (1) Montgomery had been incarcerated for more than two years and thus had not engaged in sexual intercourse and (2) she was not in a state of pseudopregnancy at the time of her PET scan. Dr. Gur made only a passing reference to the study and did not rebut Dr. Mayberg's testimony, other than stating that PET results remain constant unless the patient suffers a major illness or brain injury.
The remaining support offered for Dr. Gur's opinion was the fact that the hypothalamus is located in the somatomotor area of the brain and that pseudocyesis is a somatoform disorder. That similarity, however, is irrelevant in the absence of a showing that somatoform disorders are accompanied by abnormalities in the somatomotor region of the brain. Dr. Gur testified that certain areas of the brain affect certain functions, but he was unable to substantiate the opinion that Montgomery's abnormalities were consistent with the diagnosis of pseudocyesis. The district court expected that the defense psychiatrists would testify that Montgomery's PET results revealed abnormalities consistent with her diagnosis of pseudocyesis, but their expert reports did not clearly state or substantiate that opinion.
Pseudocyesis is an extremely rare disorder. As such, it is unlikely that individuals with the disorder will undergo PET scans or that scientists will be able to discern a signature PET scan pattern to diagnose the disorder. Other than his mention of the study on rats, there was no evidence offered to show the scientific reliability of Dr. Gur's opinion. Similarly, no evidence was offered that individuals suffering from other somatoform disorders have somatomotor abnormalities similar to Montgomery's. As stated above, the PET evidence that showed increased activity in the limbic and somatomotor regions of Montgomery's brain and the evidence that those areas are associated with certain functions was reliable and should have been admitted. The opinion that the abnormalities were consistent with pseudocyesis, however, did not rise to the level of scientific knowledge.
A hypothesis without support, like the one posited here, is no more than a subjective belief or an exercise in speculation. "[I]t thus is not knowledge, nor is it based upon sufficient facts or data or the product of reliable principles and methods applied reliably to the facts of the case." Tamraz, 620 F.3d at 670 (quoting Fed.R.Evid. 702) (internal quotations and alterations omitted). The district court thus did not abuse its discretion in excluding Dr. Gur's opinion during the guilt phase of trial.
Montgomery also contends that the exclusion of Dr. Gur's opinion at the penalty phase of the trial amounted to reversible error. We review the district court's evidentiary rulings for an abuse of discretion, and we determine de novo the question of whether Montgomery's constitutional rights have been violated. Purkey, 428 F.3d at 756-57. "Even if we conclude that the district court erred, we cannot reverse or vacate a federal death sentence on account of an error that is harmless beyond a reasonable doubt." Id. at 757.
During the penalty phase of a capital trial, "[i]nformation is admissible regardless of its admissibility under the rules governing admission of evidence at criminal trials except that information may be excluded if its probative value is outweighed by the danger of creating unfair *1092 prejudice, confusing the issues, or misleading the jury." 18 U.S.C. § 3593(c). "Since the need to regulate the scope of testimony is less at the penalty phase than at the guilt phase of trial, parties may present evidence `as to any matter relevant to the sentence.'" United States v. Lee, 274 F.3d 485, 494 (8th Cir.2001) (quoting 18 U.S.C. § 3593(c)); see also Williams v. New York, 337 U.S. 241, 247, 69 S.Ct. 1079, 93 L.Ed. 1337 (1949) (The factfinder at the penalty phase should "not be denied an opportunity to obtain pertinent information by a requirement of rigid adherence to restrictive rules of evidence properly applicable to the trial."); Gregg v. Georgia, 428 U.S. 153, 204, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976) (At the penalty phase, "it [is] desirable for the jury to have as much information before it as possible when it makes the sentencing decision.").
Under the Federal Death Penalty Act's low threshold for admissibility, Dr. Gur's interpretation of the PET scan was arguably admissible.[8] Whether its exclusion constituted reversible error is another question. We conclude that any error in excluding the proposed testimony was harmless beyond a reasonable doubt. The jury heard extensive testimony from Drs. Ramachandran, Logan, and Kuncel, as well as from Montgomery's treating psychiatrist, about Montgomery's background and psychiatric diagnoses. Dr. Gur's testimony would have informed the jury that Montgomery's brain had certain functional abnormalities, would have offered his minimally probative and scientifically unreliable opinion that the abnormalities were consistent with the pseudocyesis diagnosis, and would have expressed his opinion that "the brain she has may explain at least part of what happened" and that the abnormalities contributed to her actions. Nevertheless, we conclude that what we said in Purkey is of equal force in this case: "[A]lthough we recognize that a jury may be more likely to believe that someone suffers from a problem if its cause is explained, we nevertheless harbor no doubt that considering the minimal probative value of the evidence and the overwhelming evidence and jury findings of serious aggravating factors, its exclusion was harmless." 428 F.3d at 758.

2. MRI Evidence
According to Dr. Gur's report, Montgomery's MRI revealed structural abnormalities, including reduced brain volume in the right parietal lobes and right medial gray matter. Right parietal dysfunction, according to the report, "manifests itself behaviorally in loss of sense of self, difficulties in emotion processing, attentional neglect and depressed or flat affect."
At the Daubert hearing, the experts interpreted a graph in Dr. Gur's report that charted the deviation of Montgomery's MRI results from normal. Montgomery's parietal and medial gray matter regions were less than one standard deviation from normal. Dr. Evans explained that Montgomery's results were within the normal range and that approximately fifty percent of the population would have comparable results. Montgomery's ventrical measurements were one standard deviation from normal, and Dr. Evans stated that approximately thirty percent of the population would have similar results. Drs. Evans *1093 and Mayberg testified that Montgomery's deviations were not statistically significant because none of her measurements deviated more than one standard deviation from the mean. Dr. Mayberg also testified that to infer statistical analysis from numbers within the normal range "and extrapolate about complex behavior that doesn't have a known brain organization is basically having an opinion that far exceeds both the data we have here and what is known in the literature."
Dr. Gur testified that, even if the deviations were not statistically significant, they were nonetheless clinically significant. Dr. Gur compared Montgomery's right parietal and medial gray matter to her left-side counterparts. Based on his "eyeball" comparison, he determined that Montgomery's right parietal and medial gray matter appeared abnormally low. Dr. Evans testified, however, that Dr. Gur had failed to show that Montgomery's left-right difference was abnormal.
The district court did not abuse its discretion in excluding the MRI evidence from both the guilt and the penalty phases of the trial. It found unreliable the methodology underlying Dr. Gur's opinion that the results were clinically significant. Moreover, it found that the MRI results had no scientifically recognized significance. Accordingly, the district court concluded that the results were irrelevant to Montgomery's insanity defense and the mitigating factors she pleaded. The district court thus exercised its authority "to exclude, as irrelevant, evidence not bearing on the defendant's character, prior record, or the circumstances of [her] offense." Lockett v. Ohio, 438 U.S. 586, 604 n. 12, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978) (plurality opinion).

C. Polygraph Examination Evidence
As set forth above, Montgomery confessed that she acted alone in killing Stinnett and in kidnapping the infant. In early 2007, however, Montgomery claimed that her brother, Tommy Kleiner, had accompanied her on December 16, 2004. She reiterated the allegations during interviews with psychiatrists for the government and for the defense. Accordingly, her attorneys commissioned a polygraph examination to test the veracity of the allegations.
According to the polygraph report, the purpose of the examination was to determine the truthfulness of Montgomery's assertions that her brother accompanied her to Skidmore and that he was present when Stinnett was killed. During the examination, Montgomery was asked the following questions: (1) "On that day, was Tommy with you at the house?" (2) "Was Tommy present in the house on that day?" Montgomery answered "yes" to both questions. The polygraph examiner opined that Montgomery did not show a "consistent and strong physiological reaction when responding" to the relevant questions and concluded that her answers were "not indicative of deception." The government was not notified of the polygraph examination and did not take part in it.
After Montgomery's allegations regarding her brother came to light, the government investigated whether Kleiner was involved in the crime. It discovered that Kleiner had been meeting with his probation officer in Lyndon, Kansas, at the time of Stinnett's murder. Kleiner's probation officer and probation records confirmed the meeting. Lyndon is approximately three hours away from Skidmore.
Montgomery's counsel shared the results of the polygraph examination with the government. Thereafter, the government moved to exclude any testimony related to the examination or its results, *1094 arguing that the questions were flawed, that the results were unreliable, and that any evidence related to the polygraph examination should be excluded under Federal Rules of Evidence 702 and 403. Montgomery sought to use the evidence to impeach the government's expert's opinion that Montgomery's allegations against Kleiner were "intentional and knowing fabrications and not the product of an unsound mind." The district court granted the motion to exclude.
Montgomery contends that the exclusion of the polygraph evidence amounted to reversible error. We review evidentiary rulings for abuse of discretion. United States v. Gianakos, 415 F.3d 912, 924 (8th Cir.2005); United States v. Jordan, 150 F.3d 895, 899 (8th Cir.1998). Although there is no per se ban on the use of polygraph evidence in this circuit, "[o]ur cases make clear that polygraph evidence is disfavored." United States v. Gill, 513 F.3d 836, 846 (8th Cir.2008) (gathering cases). To be admissible, polygraph evidence must be relevant, and its probative value must not be "substantially outweighed by the danger of unfair prejudice, confusion of the issues, or misleading the jury."[9] Fed.R.Evid. 403; see also Fed. R.Evid. 401.
Results from a unilateral polygraph examinations have little probative value. See United States v. Sherlin, 67 F.3d 1208, 1217 (6th Cir.1995) (concluding that the defendant's "privately commissioned polygraph test, which was unknown to the government until after its completion, is of extremely dubious probative value"). The defendant has no adverse interest at stake because a polygraph examination administered without notice to and participation by the government "carries no negative consequences, and probably won't see the light of day if a defendant flunks." United States v. Ross, 412 F.3d 771, 773 (7th Cir.2005). Applying the balancing test set forth in Federal Rule of Evidence 403, courts have routinely deemed inadmissible evidence related to unilateral polygraph examinations. See, e.g., id.; United States v. Thomas, 167 F.3d 299, 308-09 (6th Cir. 1999); United States v. Gilliard, 133 F.3d 809, 815-16 (11th Cir.1998); Sherlin, 67 F.3d at 1217; see also United States v. Williams, 95 F.3d 723, 729-30 (8th Cir. 1996) (affirming the district court's exclusion of polygraph evidence on the basis that the evidence would be more prejudicial than probative).
The district court did not abuse its discretion in excluding the polygraph evidence under Federal Rule of Evidence 403. Montgomery's polygraph evidence had minimal probative value. The test was administered without the government's knowledge and without the possibility that Montgomery might suffer negative consequences from a failed examination. The questions were vague, with the results establishing only that Montgomery did not show a "consistent and strong physiological reaction" when responding to questions regarding whether Kleiner was "with [her] at the house" and "present in the house on that day." Moreover, the admission of the proposed evidence would have necessitated collateral proceedings regarding the validity of a unilateral polygraph examination. Accordingly, the polygraph evidence was properly excluded.
*1095 For the same reasons, we conclude that the district court did not abuse its discretion in excluding the polygraph test results at the penalty phase of the trial.

D. Sufficiency of Evidence To Support Aggravating Factor
At the close of the penalty phase evidence, Montgomery moved to dismiss the statutory aggravating factor that she "committed the offense in an especially heinous or depraved manner in that it involved serious physical abuse to the victim, Bobbie Jo Stinnett." Montgomery argued that the evidence showed that she used only the force necessary to commit the offense and thus the evidence was insufficient to submit the factor to the jury. The motion was denied, and the jury returned a unanimous verdict that the aggravating factor had been proved.
Montgomery renews her challenge on appeal, arguing that she could not complete the kidnapping resulting in death without strangling Stinnett and performing a cesarean-section delivery of the infant.[10] Montgomery claims that she did not cause or intend to cause more suffering than required to complete the offense and that the government thus failed to prove that she committed the offense in a heinous or depraved manner in that it involved serious physical abuse to Stinnett.
Montgomery's claim of error is based on her offense conduct, but the statute focuses on the harm inflicted on the victim. The aggravating factor is met if "[t]he defendant committed the offense in an especially heinous, cruel, or depraved manner in that it involved torture or serious physical abuse to the victim." 18 U.S.C. § 3592(c)(6). Most federal offenses that carry the death-penalty punishment could be fairly characterized as heinous, cruel, or depraved. See Godfrey v. Georgia, 446 U.S. 420, 428-29, 100 S.Ct. 1759, 64 L.Ed.2d 398 (1980) ("A person of ordinary sensibility could fairly characterize almost every murder as `outrageously or wantonly vile, horrible and inhuman.'"). Accordingly, the statute limits the application of the aggravating factor to offenses that involve "torture or serious physical abuse to the victim." § 3592(c)(6). The limiting construction, along with the jury instructions defining the statute's terms, provides "a meaningful basis for distinguishing the few cases in which [the death penalty] is imposed from the many cases in which it is not." Godfrey, 446 U.S. at 428, 100 S.Ct. 1759 (quoting Furman v. Georgia, 408 U.S. 238, 313, 92 S.Ct. 2726, 33 L.Ed.2d 346 (1972) (White, J. concurring)).
We conclude that the evidence was sufficient to submit the aggravating factor to the jury and that a rational trier of fact could have found the aggravating circumstance to exist beyond a reasonable doubt. See United States v. Ortiz, 315 F.3d 873, 902 (8th Cir.2002) (standard of review). To constitute serious physical abuse for purposes of § 3592(c)(6), the defendant *1096 must have inflicted "suffering or mutilation above and beyond that necessary to cause death." United States v. Agofsky, 458 F.3d 369, 374 (5th Cir.2006). The jury instruction stated as much, defining serious physical abuse as "significant or considerable amount of injury or damage to the victim's body" and requiring that the defendant "intended the abuse in addition to the killing."
Overwhelming evidence supported the jury's verdict. Montgomery mutilated Stinnett's body to remove the infant from Stinnett's womb. Montgomery confessed to using a rope to strangle Stinnett until she was unconscious. Montgomery then punctured Stinnett's abdomen with a kitchen knife. The medical examiner testified that this likely caused Stinnett to rouse and that the two women struggled after Stinnett regained consciousness. The blood caked between Stinnett's toes indicated that she had lost a significant amount of blood before and during the struggle. The autopsy revealed that there were two ligature strangulations, and the medical examiner opined that it was the second strangulation that resulted in Stinnett's death. Montgomery confessed to using a kitchen knife to make an incision along Stinnett's abdomen. The autopsy revealed that the incision was jagged. After reaching into Stinnett's body and removing the fetus, Montgomery left Stinnett's mutilated body on the floor. The dining room was covered in blood, and Harper described her daughter's body as looking like her stomach had exploded. The evidence thus supported the determination that Montgomery committed the offense in an especially heinous or depraved manner in that it involved serious physical abuse to Stinnett.

E. Prosecutorial Misconduct
During the penalty phase of the trial, the government asked Montgomery's oldest daughter whether Montgomery had "ever apologized for what she did to Bobbie Jo Stinnett and Victoria Jo Stinnett as she counseled you and emotionally support[ed] you." After defense counsel's objection was overruled, the prosecutor rephrased the question to ask whether Montgomery "ever apologize[d] for what she put you and your siblings through." The daughter responded that her mother did not remember committing the crime.
During penalty phase closing argument, the prosecutor argued, "Deception, manipulation is a way of life and they want you to give her credit and say she's a good wife, a good mother. She never apologized for her actions." Defense counsel's objection to the argument was overruled, and the prosecutor set forth the following argument in rebuttal:
And then after all of that she drags those kids into court here to testify in this high profile case in front of all these people and puts them through this again and victimizes them again in front of the whole world.
. . .
She drug these kids in here to testify on her behalf. Don't you think that's painful for them. She's a good mom? Most of us, if we had children [and] we were involved in a situation we would want them a thousand miles away from this. We wouldn't make them come to court and testify.
Montgomery alleges that the government's questions and closing remarks constituted prosecutorial misconduct. "To obtain a reversal based on prosecutorial misconduct to which there was proper objection, a defendant must show that (1) the prosecutor's remarks or conduct were improper, and (2) the remarks or conduct affected the defendant's substantial rights so as to deprive him of a *1097 fair trial." United States v. New, 491 F.3d 369, 377 (8th Cir.2007). If the remarks were improper, we examine the cumulative effect of the misconduct, the strength of the properly admitted evidence, and any curative actions taken by the district court. Id.
The government contends that the questions and closing remarks were proper rebuttal to certain mitigating factors and to defense evidence that Montgomery was a good mother. The Federal Death Penalty Act provides that "[t]he government and the defendant shall be permitted to rebut any information received at the hearing, and shall be given fair opportunity to present argument as to the adequacy of the information to establish the existence of any aggravating or mitigating factor." 18 U.S.C. § 3593(c); see also United States v. Allen, 247 F.3d 741, 773 (8th Cir.2001) ("The government must be able to put on a fair rebuttal to a defendant's mitigation evidence during sentencing."), vacated on other grounds, 536 U.S. 953, 122 S.Ct. 2653, 153 L.Ed.2d 830 (2002). We have defined rebuttal evidence as that which is "offered to explain, repel, counteract, or disprove evidence of the adverse party." United States v. Harris, 557 F.3d 938, 942 (8th Cir.2009) (quoting Sterkel v. Fruehauf Corp., 975 F.2d 528, 532 (8th Cir.1992)). Accordingly, "rebuttal evidence must be reasonably tailored to the evidence it seeks to refute." United States v. Jackson, 327 F.3d 273, 306 (4th Cir.2003) (quoting United States v. Stitt, 250 F.3d 878, 897 (4th Cir.2001)). We conclude that the questions and general remarks about Montgomery's parenting were proper rebuttal, but that the prosecutor's argument that Montgomery victimized her children by calling them as witnesses went beyond the pale.
It was not improper for the prosecutor to ask Montgomery's daughter whether Montgomery had "ever apologize[d] for what she put you and your siblings through." As stated above, Montgomery pleaded that she offered advice, nurturance, and emotional support to her children and that she would continue to do so if she was sentenced to life imprisonment. The question posed to Montgomery's daughter called for an answer that would explain the emotional support Montgomery had offered to her children since her incarceration. The daughter responded that Montgomery did not remember what she had done, and thus the jury learned that whatever support Montgomery provided did not include an apology for the pain caused to her family. This evidence tended to disprove and rebut Montgomery's mitigating factors and mitigating evidence. Similarly, the prosecutor's remark in closing argument that Montgomery "never apologized [to her family] for her actions" was permissible.
The prosecutor's general remarks regarding whether Montgomery was a good mother were proper rebuttal argument. Montgomery contends that she never claimed that she was a good mother, but rather that she had reared good children. The record, however, shows that defense counsel elicited testimony about Montgomery's relationship with her children and that some witnesses testified that she was a good mother. Moreover, although the mitigating factors, testimony and exhibits, and defense counsel's arguments focused on evidence that the children were well behaved and lovable, the plain import of the evidence and argument was that Montgomery was a good mother because she reared good children, whom she had supported financially and emotionally.
The prosecutor's remarks criticizing the decision to have Montgomery's *1098 children testify is another matter. The Sixth Amendment confers the right of the accused "to have compulsory process for obtaining witnesses in his favor." U.S. Const. amend. VI. Although its terms grant only the right to compel witnesses to appear through the use of subpoena power, the compulsory process clause has been interpreted to include the right to offer testimony. "The right to compel a witness' presence in the courtroom could not protect the integrity of the adversary process if it did not embrace the right to have the witness' testimony heard by the trier of fact." Taylor v. Illinois, 484 U.S. 400, 409, 108 S.Ct. 646, 98 L.Ed.2d 798 (1988). The Supreme Court has described the Sixth Amendment right to offer testimony and compel witness attendance as, "in plain terms the right to present a defense." Id. (quoting Washington v. Texas, 388 U.S. 14, 19, 87 S.Ct. 1920, 18 L.Ed.2d 1019 (1967)).
"The prosecution cannot use the defendant's exercise of specific fundamental constitutional guarantees against him at trial." Burns v. Gammon, 260 F.3d 892, 896 (8th Cir.2001) (citing Griffin v. California, 380 U.S. 609, 615, 85 S.Ct. 1229, 14 L.Ed.2d 106 (1965) (prosecutor is prohibited from using defendant's exercise of the constitutional right to remain silent against defendant in case-in-chief) and comparing Portuondo v. Agard, 529 U.S. 61, 73, 120 S.Ct. 1119, 146 L.Ed.2d 47 (2000) (prosecutor's closing argument that defendant had the opportunity to hear other witnesses testify and tailor his testimony accordingly did not unlawfully burden his right to be present at trial, to confront witnesses against him, or to testify on his own behalf because comments were directed at defendant's status as witness whose credibility was subject to attack)). Montgomery had the right to have her children testify at her trial. It was thus improper for the prosecutor to argue that Montgomery forced her children to testify and "victimize[d] them again in front of the whole world."
We conclude that, however improper they may have been, the remarks did not deprive Montgomery of a fair trial. They were made in support of the argument that Montgomery was not a good mother and that she had failed to establish that she had supported and nurtured her children. The cumulative effect of the argument was marginal, particularly in light of the substantial evidence supporting the aggravating factors. Moreover, the offending remarks were brief and were made in the context of an otherwise proper argument. We therefore reject Montgomery's contention that they warrant reversal.

F. Penalty Phase Jury Instructions
Montgomery argues that the district court erred in failing to instruct the jury that it is never required to impose a sentence of death. Montgomery recognizes that her argument is foreclosed by our prior panel decision in United States v. Allen, 247 F.3d 741, 780-82 (8th Cir.2001), vacated on other grounds, 536 U.S. 953, 122 S.Ct. 2653, 153 L.Ed.2d 830 (2002), but seeks to preserve her argument for en banc or Supreme Court review.
Over Montgomery's objection, the district court instructed the jury as follows. Penalty Phase Instruction No. 1 stated:
This decision is left exclusively to you, the jury. If you determine that the defendant should be sentenced to death, or to life imprisonment without possibility of release, the court is required to impose that sentence.
. . .
If you unanimously find that the aggravating factor or factors, which you all found to exist, sufficiently outweigh any mitigating factor or factors, which any *1099 one of you found to exist to justify imposition of a sentence of death, . . . and that death is therefore the appropriate sentence in this case, the law provides that the defendant must be sentenced to death.
Penalty Phase Instruction No. 11 stated:
If you unanimously conclude that the aggravating factor or factors found to exist sufficiently outweigh any mitigating factor or factors which any of you found to exist to justify a sentence of death, and that therefore death is the appropriate sentence in this case, you must record your determination that a sentence of death shall be imposed [on the special verdict form].
Montgomery argues that it was error for the instruction to use the mandatory language, "must be sentenced to death," and that the district court should have used her proposed permissive language, "may be sentenced to death." She also argues that the jury should have been instructed that it is never required to return a sentence of death.
The Federal Death Penalty Act states that a defendant who has been found guilty of an enumerated offense for which a sentence of death is provided "shall be sentenced to death if, after consideration of the factors set forth in section 3592 [delineating possible aggravating and mitigating factors] in the course of a hearing held pursuant to section 3593, it is determined that imposition of a sentence of death is justified." 18 U.S.C. § 3591(a). Section 3593(e) requires the jury to consider whether the aggravating factors outweigh the mitigating factors to justify a sentence of death. Based upon that consideration, the jury by unanimous vote "shall recommend whether the defendant should be sentenced to death, to life imprisonment without possibility of release or some other lesser sentence." § 3593(e). We have interpreted the statutory language to mean that "once a jury makes a final, unanimous determination that a sentence of death is justified, then the FDPA requires its imposition." Allen, 247 F.3d at 780. Because Montgomery's requested instructions were contrary to our case law interpreting the Federal Death Penalty Act, the district court did not err in giving to the jury the penalty phase instructions recited above. E.g., United States v. Rodriguez, 581 F.3d 775, 812-14 (8th Cir.2009); Purkey, 428 F.3d at 762-63; United States v. Nelson, 347 F.3d 701, 712 (8th Cir.2003); Ortiz, 315 F.3d at 900-01.

III. Conclusion
Montgomery argues that the cumulative effect of the alleged errors warrant a new trial. "We may reverse where the case as a whole presents an image of unfairness that has resulted in the deprivation of a defendant's constitutional rights, even though none of the claimed errors is itself sufficient to require reversal." United States v. Samples, 456 F.3d 875, 887 (8th Cir.2006) (quoting United States v. Riddle, 193 F.3d 995, 998 (8th Cir.1999)). Having determined that any error was harmless, we conclude that Montgomery suffered no substantial prejudice and that the cumulative effect of the alleged errors did not deprive her of her constitutional rights.
The conviction and sentence are affirmed.
NOTES
[1]  The Honorable Gary A. Fenner, United States District Judge for the Western District of Missouri.
[2]  The Federal Death Penalty Act is found at 18 U.S.C. §§ 3591, et seq.
[3]  The Honorable John T. Maughmer, United States Magistrate Judge for the Western District of Missouri.
[4]  The government's expert explained that MRI "provides quantitative analysis on brain anatomy, brain structure," while "PET provides quantitative results on brain physiology, brain function."
[5]  DSM-IV states that the essential feature of malingering is "the intentional production of false or grossly exaggerated physical or psychological symptoms, motivated by external incentives such as . . . evading criminal prosecution." Diagnostic and Statistical Manual of Mental Disorders at 739.
[6]  In its post-trial order denying Montgomery's motion for a new trial, the district court addressed the PET evidence:

[T]he government's experts showed conclusively that Dr. Gur's principles and methods were not subjected to adequate peer review or publication and that Dr. Gur's application of his principles and methods to the facts was unreliable, and thus would have misled and confused the jury rather than assisted it. Finally, the evidence was of extremely low probative value as it provided only minimal support for the sweeping conclusion that PET scans of Defendant's brain showed patterns consistent with the rare diagnosis of pseudocyesis without ruling out compatibility with a multitude of other more common conditions and circumstances.
D. Ct. Order of Mar. 12, 2008, at 2-3.
[7]  The district court did not determine whether Dr. Gur used a valid normalization method or an invalid one, as Dr. Mayberg and Dr. Evans claimed. We decline to do so here. Suffice it to say that had the evidence been admitted, the jury could have considered the dispute, as well as the concerns over testing conditions and scanner resolution, and weighed the evidence accordingly.
[8]  Montgomery complied with the expert disclosure requirements under the Federal Rules of Criminal Procedure. See Fed.R.Crim.P. 16(b)(1)(C) (requiring the defendant to provide a description of any expert "witness's opinions, the bases and reasons for those opinions, and the witness's qualifications"). Accordingly, to the extent the district court based its decision to exclude the PET evidence on Montgomery's alleged discovery violation, the sanction was unwarranted.
[9]  Polygraph evidence must also be reliable. Fed.R.Evid. 702; Daubert, 509 U.S. 579, 113 S.Ct. 2786. As the Supreme Court has noted, "there is simply no consensus that polygraph evidence is reliable." United States v. Scheffer, 523 U.S. 303, 309, 118 S.Ct. 1261, 140 L.Ed.2d 413 (1998). Because we affirm the district court's evidentiary ruling on the basis of Rule 403, we need not engage in the Rule 702 analysis.
[10]  Montgomery's reply brief argues that the cesarean-section removal of the infant from Stinnett's womb is irrelevant to whether the offense involved serious physical abuse to Stinnett. She contends that our review is limited to the evidence regarding Stinnett's strangulation. This argument is contrary to the argument in her opening brief, and it fails on the merits. In determining whether the offense involved serious physical abuse to the victim, the jury must consider the physical abuse the victim endured. The physical abuse inflicted here included ligature strangulation, the puncturing of Stinnett's abdomen with a kitchen knife, the subsequent struggle, the cutting of Stinnett's abdomen, and the removal of her eight-month-old fetus. As stated above, the kidnapping is inextricably intertwined with Stinnett's death. The jury properly considered the physical abuse Stinnett endured throughout the offense conduct.
