HOWARD, Chief Judge.
Defendant-Appellant Rosalind Herman was convicted, after a jury trial, of conspiracy, willful violation of the Investment Advisers Act, wire fraud, and corruptly impeding the administration of internal revenue laws. These charges arose from a scheme in which Herman and a co-eonspir-ator solicited funds for purported investment in a hedge fund management company. Rather than investing the money they obtained, totaling more than $1.3 million, Herman and her confederate used it for personal expenses. Herman also allegedly defrauded the Internal Revenue Service by claiming false business deductions and failing to file tax returns in some years, resulting in almost $1.85 million in unreported income. After the jury returned its guilty verdict, the district court sentenced Herman to eighty-four months’ imprison
ment. On appeal, Herman raises two narrow claims, one relating to her convictions and a second challenging her sentence. Because we find each of these claims unavailing, we affirm.
I.
We begin with Herman’s challenge to her convictions, which is predicated entirely upon purported deficiencies in the district court’s instructions on the reasonable doubt standard. Because Herman failed to object to the instructions below, we review only for plain error. See United States v. Van Anh, 523 F.3d 43, 57 (1st Cir. 2008). In order to satisfy this demanding standard, Herman must establish that “(1) [ ] an error occurred (2) which was clear or obvious and which not only (3) affected [her] substantial rights, but also (4) seriously impaired the fairness, integrity, or public reputation of judicial proceedings.” Id. at 55 (first alteration in original) (citation omitted). Herman’s claim falters on the first element. We perceive no error, much less plain error, in the district court’s reasonable doubt instructions.
As an initial matter, we have repeatedly noted “that reasonable doubt does not require definition.” United States v. Rodríguez-Cardona, 924 F.2d 1148, 1160 (1st Cir. 1991). Thus, “an instruction which uses the words reasonable doubt without further definition adequately apprises the jury of the proper burden of proof.” United States v. Ademaj, 170 F.3d 58, 66 (1st Cir. 1999) (citation omitted); see also Victor v. Nebraska, 511 U.S. 1, 5, 114 S.Ct. 1239, 127 L.Ed.2d 583 (1994) (“[T]he Constitution neither prohibits trial courts from defining reasonable doubt nor requires them to do so as a matter of course.”). Where, however, the court does undertake to define the term, it cannot employ a definition that creates “a reasonable likelihood of leading the jury to believe that it can convict on some lesser standard of proof.” Van Anh, 523 F.3d at 57 (citation omitted). With that said, “the Constitution does not require ... any particular form of words.” Victor, 511 U.S. at 5, 114 S.Ct. 1239. The district court, thus, retains significant discretion in formulating its instructions, so long as it “correctly conveys] the concept of reasonable doubt to the jury.” M. (citation omitted).
Here, Herman takes issue with the following passage from the court’s instructions:
[T]he burden of proof here is not common sense, of course you can use your common sense, the burden of proof here is proof beyond a reasonable doubt, and there must be no guesswork, no speculation, no “maybe this happened,” “perhaps,” “possibly,” “it could have,” not even that it’s likely that this or that happened, it has to be proved beyond a reasonable doubt.
Herman makes five specific arguments as to why the reasonable doubt instructions were deficient. Four are easily disposed of. First, while Herman correctly notes that the court was not required to define reasonable doubt, neither was it prohibited from doing so. See Victor, 511 U.S. at 5, 114 S.Ct. 1239. Second, once it decided to provide a definition, the court was not bound to use one of the specific formulations that Herman now proposes. See id. Third, the mere fact that the district court gave a “negative” definition, explaining reasonable doubt by reference to what it is not, does not, in itself, require reversal. United States v. DeVincent, 632 F.2d 147, 152-53 (1st Cir. 1980). Fourth, the court’s allusion to the jury’s use of “common sense,” while perhaps unnecessary, did not constitute error. United States v. Munson, 819 F.2d 337, 346 (1st Cir. 1987).
Herman’s fifth claim of instructional error is the most substantial, but it too
ultimately fails. Herman posits that, by presenting “a choice between guesswork and speculation on the one hand, and reasonable doubt on the other,” the court “effectively reduced the government’s burden of proof.” This is because the instructions could have led the jury to believe that “it could return a guilty verdict so long as it found the government’s proof was non-speculative.” Unfortunately for Herman, we have previously upheld the use of language very similar to that at issue here. See United States v. Burnette, 375 F.3d 10, 20 (1st Cir. 2004) (“The jury must never find the defendant guilty on mere suspicion, conjecture or guess.”), vacated on other grounds, 543 U.S. 1181, 125 S.Ct. 1406, 161 L.Ed.2d 176 (2005); United States v. Whiting, 28 F.3d 1296, 1304 (1st Cir. 1994) (“[A] defendant is never to be convicted ‘on the basis of mere conjecture, surmise or guesswork.’ ”).
Any suggestion that the jury may have been misled is further undermined by the court’s repeated emphasis that proof beyond a reasonable doubt was required for conviction. Indeed, the court mentioned the reasonable doubt standard no fewer than nine times in its instructions to the jury. And it introduced the concept on the very first day of trial, when it made clear that Herman sat before the jury as “an innocent woman” who could only be convicted based on proof “beyond a reasonable doubt.” In this context, we perceive no reasonable likelihood that the language cited by Herman led the jury to apply a lesser standard of proof. See Van Anh, 523 F.3d at 58 (holding that instruction “adequately communicated the government’s burden” where the court mentioned that burden ten times and “stressed the presumption of innocence”).
II.
We turn now to Herman’s claim of sentencing error. The parties do not contest the district court’s calculation of the guideline sentencing range (“GSR”) as 108 to 135 months. After arriving at this GSR, the court proceeded to vary downward to “avoid unwarranted sentencing disparities among defendants.”
It ultimately imposed an incarcerative sentence of' eighty-four months, a full two years below the bottom of the GSR.
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HOWARD, Chief Judge.
Defendant-Appellant Rosalind Herman was convicted, after a jury trial, of conspiracy, willful violation of the Investment Advisers Act, wire fraud, and corruptly impeding the administration of internal revenue laws. These charges arose from a scheme in which Herman and a co-eonspir-ator solicited funds for purported investment in a hedge fund management company. Rather than investing the money they obtained, totaling more than $1.3 million, Herman and her confederate used it for personal expenses. Herman also allegedly defrauded the Internal Revenue Service by claiming false business deductions and failing to file tax returns in some years, resulting in almost $1.85 million in unreported income. After the jury returned its guilty verdict, the district court sentenced Herman to eighty-four months’ imprison
ment. On appeal, Herman raises two narrow claims, one relating to her convictions and a second challenging her sentence. Because we find each of these claims unavailing, we affirm.
I.
We begin with Herman’s challenge to her convictions, which is predicated entirely upon purported deficiencies in the district court’s instructions on the reasonable doubt standard. Because Herman failed to object to the instructions below, we review only for plain error. See United States v. Van Anh, 523 F.3d 43, 57 (1st Cir. 2008). In order to satisfy this demanding standard, Herman must establish that “(1) [ ] an error occurred (2) which was clear or obvious and which not only (3) affected [her] substantial rights, but also (4) seriously impaired the fairness, integrity, or public reputation of judicial proceedings.” Id. at 55 (first alteration in original) (citation omitted). Herman’s claim falters on the first element. We perceive no error, much less plain error, in the district court’s reasonable doubt instructions.
As an initial matter, we have repeatedly noted “that reasonable doubt does not require definition.” United States v. Rodríguez-Cardona, 924 F.2d 1148, 1160 (1st Cir. 1991). Thus, “an instruction which uses the words reasonable doubt without further definition adequately apprises the jury of the proper burden of proof.” United States v. Ademaj, 170 F.3d 58, 66 (1st Cir. 1999) (citation omitted); see also Victor v. Nebraska, 511 U.S. 1, 5, 114 S.Ct. 1239, 127 L.Ed.2d 583 (1994) (“[T]he Constitution neither prohibits trial courts from defining reasonable doubt nor requires them to do so as a matter of course.”). Where, however, the court does undertake to define the term, it cannot employ a definition that creates “a reasonable likelihood of leading the jury to believe that it can convict on some lesser standard of proof.” Van Anh, 523 F.3d at 57 (citation omitted). With that said, “the Constitution does not require ... any particular form of words.” Victor, 511 U.S. at 5, 114 S.Ct. 1239. The district court, thus, retains significant discretion in formulating its instructions, so long as it “correctly conveys] the concept of reasonable doubt to the jury.” M. (citation omitted).
Here, Herman takes issue with the following passage from the court’s instructions:
[T]he burden of proof here is not common sense, of course you can use your common sense, the burden of proof here is proof beyond a reasonable doubt, and there must be no guesswork, no speculation, no “maybe this happened,” “perhaps,” “possibly,” “it could have,” not even that it’s likely that this or that happened, it has to be proved beyond a reasonable doubt.
Herman makes five specific arguments as to why the reasonable doubt instructions were deficient. Four are easily disposed of. First, while Herman correctly notes that the court was not required to define reasonable doubt, neither was it prohibited from doing so. See Victor, 511 U.S. at 5, 114 S.Ct. 1239. Second, once it decided to provide a definition, the court was not bound to use one of the specific formulations that Herman now proposes. See id. Third, the mere fact that the district court gave a “negative” definition, explaining reasonable doubt by reference to what it is not, does not, in itself, require reversal. United States v. DeVincent, 632 F.2d 147, 152-53 (1st Cir. 1980). Fourth, the court’s allusion to the jury’s use of “common sense,” while perhaps unnecessary, did not constitute error. United States v. Munson, 819 F.2d 337, 346 (1st Cir. 1987).
Herman’s fifth claim of instructional error is the most substantial, but it too
ultimately fails. Herman posits that, by presenting “a choice between guesswork and speculation on the one hand, and reasonable doubt on the other,” the court “effectively reduced the government’s burden of proof.” This is because the instructions could have led the jury to believe that “it could return a guilty verdict so long as it found the government’s proof was non-speculative.” Unfortunately for Herman, we have previously upheld the use of language very similar to that at issue here. See United States v. Burnette, 375 F.3d 10, 20 (1st Cir. 2004) (“The jury must never find the defendant guilty on mere suspicion, conjecture or guess.”), vacated on other grounds, 543 U.S. 1181, 125 S.Ct. 1406, 161 L.Ed.2d 176 (2005); United States v. Whiting, 28 F.3d 1296, 1304 (1st Cir. 1994) (“[A] defendant is never to be convicted ‘on the basis of mere conjecture, surmise or guesswork.’ ”).
Any suggestion that the jury may have been misled is further undermined by the court’s repeated emphasis that proof beyond a reasonable doubt was required for conviction. Indeed, the court mentioned the reasonable doubt standard no fewer than nine times in its instructions to the jury. And it introduced the concept on the very first day of trial, when it made clear that Herman sat before the jury as “an innocent woman” who could only be convicted based on proof “beyond a reasonable doubt.” In this context, we perceive no reasonable likelihood that the language cited by Herman led the jury to apply a lesser standard of proof. See Van Anh, 523 F.3d at 58 (holding that instruction “adequately communicated the government’s burden” where the court mentioned that burden ten times and “stressed the presumption of innocence”).
II.
We turn now to Herman’s claim of sentencing error. The parties do not contest the district court’s calculation of the guideline sentencing range (“GSR”) as 108 to 135 months. After arriving at this GSR, the court proceeded to vary downward to “avoid unwarranted sentencing disparities among defendants.”
It ultimately imposed an incarcerative sentence of' eighty-four months, a full two years below the bottom of the GSR.
Herman now argues that, notwithstanding this below-guidelines sentence, the court erred by refusing to grant, in addition, a downward departure on two alternative bases: (1) Herman’s own physical impairments, see U.S.S.G. § 5H1.4; and (2) her responsibilities caring for family members, see id. § 5H1.6. Herman characterizes her claim as a challenge to the substantive reasonableness of the sentence. See United States v. Del Valle-Rodríguez, 761 F.3d 171, 176 (1st Cir. 2014) (“The substantive dimension [of our sentencing review] focuses on the duration of the sentence in light of the totality of the circumstances.”). In any event, whether the issue is framed as substantive or procedural, we review the district court’s “discretionary refusal to depart” from the GSR for “reasonableness.” United States v. Anonymous Defendant, 629 F.3d 68, 74 (1st Cir. 2010); see also United States v. Maguire, 752 F.3d 1, 7 (1st Cir. 2014) (“[Discretionary refusals to vary or depart are open to reasonableness review in accordance with an abuse of discretion standard.”). And Herman faces an even steeper climb than most defendants seeking to establish sentencing error. This is because “[i]t is a rare below-the-range sentence
that will prove vulnerable to a defendant’s claim of substantive unreasonableness.” United States v. King, 741 F.3d 305, 310 (1st Cir. 2014). We apply these principles in turn to each of Herman’s purported grounds for departure.
The guidelines provide that “[a]n extraordinary physical impairment may be a reason to depart downward” from the GSR. U.S.S.G. § 5H1.4. We have, however, clarified that “[djepartures based upon health problems are discouraged and can only be justified if the medical problems are present in unusual kind or degree.” United States v. LeBIanc, 24 F.3d 340, 348 (1st Cir. 1994) (citation omitted). Thus, in order to be entitled to a departure, a defendant must establish that her “life would be threatened or shortened by virtue of being incarcerated” or that “the Bureau of Prisons would be unable to adequately accommodate [her] medical needs.” Id. at 349.
Here, the evidence of Herman’s physical impairment falls well short of this bar. Herman cites portions of the Presen-tence Investigation Report (“PSR”) indicating that: (1) she is five-foot-two-inches tall but weighs only seventy-two pounds; (2) she claimed to have been diagnosed with “malnourishment and dehydration” during her spring 2016 trial; and (3) she reported suffering from tachycardia (an elevated heart rate), resulting in blood pressure fluctuations and difficulty breathing. Herman, who was sixty-one years old at the time of sentencing, conclusorily asserts that, in light of these conditions, she “is unlikely to survive 84-months’ imprisonment.” But the PSR also indicated that Herman “does not regularly see any doctors and does not take any prescription medications.” And, before the district court, defense counsel expressly acknowledged the lack of medical records substantiating Herman’s health issues. In these circumstances, we “discern no hint of unreasonableness” in the district court’s conclusion “that there was no evidence that the federal prison system could not deal appropriately with [Herman’s] medical problems.” Maguire, 752 F.3d at 7. We note also that the court recommended that the Bureau of Prisons initially house Herman in a “medical facility for a complete evaluation of [her] medical situation.”
Herman’s second proposed ground for departure, her family responsibilities, is “not ordinarily relevant” to the sentencing determination. U.S.S.G. § 5H1.6. Accordingly, this too is a “discouraged” basis for departure. United States v. Pereira, 272 F.3d 76, 80 (1st Cir. 2001). Indeed, as we have explained, “[a] defendant’s incarceration will invariably cause hardship to [her] family.” United States v. Louis, 300 F.3d 78, 82 (1st Cir. 2002). Departure is only warranted in “exceptional” cases. Id. Exceptional circumstances may exist where the defendant’s caretaking is “irreplaceable” to her family. U.S.S.G. § 5H1.6 cmt. n.1(B)(iii). By contrast, courts should not grant a departure where “there are feasible alternatives of care that are relatively comparable to what the defendant provides.” Pereira, 272 F.3d at 83.
In the present case, while Herman cites evidence that she provided care to her family prior to her incarceration, she fails to demonstrate that such care is irreplaceable. First, she points to the fact that one of her sons “suffers from a minor learning disability” and that the second has “brain damage” resulting from a traffic accident. With respect to the former, Herman does not explain how any care that she provided for her son’s “minor learning disability” is irreplaceable. Herman’s other son, who was thirty-two years old at the time of sentencing, sustained a brain injury in a 2000 car accident. He is employed as a “concrete/cement worker.” He has also graduated from high school
and taken some college courses since the accident. Herman provides no information about the seriousness of her son’s injuries or the extent of any care that she provided for him.
Herman’s most substantial contention on this issue relates to care that she provided for her husband, but, even in this context, she fails to demonstrate that her care is irreplaceable. Herman’s husband has been largely incapacitated since 2012. He suffers from a variety of medical conditions, which Herman details in her briefing. The PSR recounts a number of tasks that Herman performed for her husband prior to her incarceration. But Herman fails to dispute the government’s assertion that, during part of the time her husband was experiencing these health issues, Herman lived in Las Vegas, while her husband remained in Massachusetts. Moreover, the record reflects multiple alternative sources of care for Herman’s husband. Both of the couple’s sons live in Woburn, Massachusetts, the same town as their father. Herman also has three sisters who live in that state. Moreover, after Herman was ordered detained, the family hired a visiting nurse to care for her husband. Nowhere in her briefing does Herman explain why any of these alternative care options are not feasible. Accordingly, the district court’s decision not to depart downward was reasonable.
While the foregoing is sufficient to dispatch with Herman’s claim of sentencing error, we pause for a moment to note other factors that the district court was permitted to consider in exercising its broad discretion. See United States v. Politano, 522 F.3d 69, 73 (1st Cir. 2008). Herman stole more than $1.3 million from several victims, some of whom were unsophisticated investors who entrusted Herman with their life savings. And, even after the jury returned its guilty verdict, Herman refused to take responsibility for abusing that trust. Instead, she placed the blame squarely at the feet of her co-conspirator. The district court, however, did not find Herman’s denials credible. These facts relating to Herman’s offense conduct and her subsequent refusal to accept responsibility were plainly relevant to the court’s sentencing determination. See 18 U.S.C. § 3553(a). The fact that the district court may have weighed these considerations more heavily than Herman would have preferred, especially in relation to her proffered physical impairments and family responsibilities, does not render the sentence unreasonable. See United States v. Clogston, 662 F.3d 588, 593 (1st Cir. 2011).
III.
For the foregoing reasons, we AFFIRM Herman’s convictions and sentence.