Conceptual illustration of radiating lines

His and Her Mathematical Models

Anita Layton, UWaterloo,  March 8, 2020


Imagine someone having a heart attack. Do you see the “classic heart attack”, in which a man collapses, grabbing his chest in agony? What you have just imagined is the typical dramatic Hollywood portrayal of a heart attack, and that is almost always depicted for a man. In fact, even though heart disease is the leading killer of women worldwide, the misconception that heart disease is a men’s disease has persisted. This misconception is dangerous and risks women ignoring their own symptoms


Gender biases and false impressions are by no means limited to heart attack symptoms. Such prejudices exist throughout our healthcare system, from scientific research to disease diagnosis and treatment strategies. If we are to address this gender equity, we must make sure that the broader public are aware of this dangerous gap in knowledge and pay more attention. Those of us who conduct research in mathematical biomedicine have the additional responsibility of addressing both sexes in our studies.


You might be amazed by the extent to which women have historically been neglected in clinical research studies. The Physicians’ Health Study—a landmark Harvard Medical School analysis founded in 1982 to examine aspirin’s effect on heart disease—initially enrolled over 22,000 participants. How many of these participants were female? Zero. The Harvard study was by no means an anomaly. In the 1970s, the U.S. Food and Drug Administration (FDA) banned women of childbearing age from participating in phase I clinical trials. The ban remained in effect for 20 years and was only lifted in 1993.


This bias is not limited to clinical trials. Historically, scientists conduct biological studies primarily in male animals. Mathematical models that base their parameters on these studies would then be more applicable to the male population. Why would researchers choose to exclude half of the population? Female menstrual cycles and fluctuating hormones, which scientists fear may limit the reliability and reproducibility of their findings, might be to blame. Cost is another likely deterrent, as replicating experiments in both sexes requires double the resources. For these reasons, researchers often conduct experiments in men and male animals, and assume that the findings apply to women as well.


Does this mentality pose a problem? Consider a scenario in which the FDA approved a drug that was tested exclusively in chimpanzees. Given that chimpanzees share about 96% of our genes, would you be comfortable taking the drug without human data? Of course not; biological differences between people and animals could lead to unexpected, undesirable drug reactions. In 2006, a German biotech company TeGenero tested a drug called TGN1412 on human volunteers. The result was one of the most disastrous clinical trials in history. Although TGN1412 is harmless to other primates at high doses, it sent the immune systems of six people into near-deadly overdrive, causing widespread inflammation and multiple-organ failure.


Granted, the physiological differences between males and females are undoubtedly much smaller than those between humans and chimpanzees, important—albeit subtle—variations nonetheless exist. For example, men are generally larger than women. As a result, a recommended dosage calculated for an average-sized man may cause an overdose in small women. Major differences also exist in the kidneys, which can affect how the body excretes some drugs.


Sex as a Biological and Mathematical Variable


Because of these gender disparities, many diseases affect men and women in dissimilar ways and elicit different responses to treatment.


Hypertension. One notable example of gender bias in medicine is in the treatment of high-blood pressure, also known as hypertension. Hypertension affects one in five Canadian adults, based on a survey from Statistics Canada and is the leading cause of premature death in the developed world. Scientists have long shown that men generally have higher blood pressure and are at greater risk for heart and kidney diseases. Despite these well-known differences, men and women suffering from high-blood pressure are often prescribed the same medication. This one-size-fits-all approach is problematic: even though women with hypertension are more likely than men to be treated and take their medication, incredibly, only 45% of treated women achieve blood-pressure control, compared to 51% of treated men.


What can mathematicians do about this inequity? Those of us who applies mathematical modeling techniques to study hypertension and its treatments should develop and use sex-specific models as much as possible. Blood pressure regulation involves multiple systems; as such, it can benefit from studies related to systems biology. In 1972, Arthur Guyton, Thomas Coleman, and Harris Granger pioneered computational modeling of the circulatory system for blood pressure regulation in their seminal work, often referred to as the Guyton model [Guyton et al. 1972]. The model consists of a large set of coupled ordinary differential and algebraic equations that describe how different regulators operate synergistically in the circulatory system. Model components include cardiovascular function, circulatory dynamics, renal hemodynamics, kidney function, respiratory function, neurohormonal feedback, autonomic nervous system activity, and electrolyte balance. For instance, the kidneys effectively regulate blood pressure by decreasing reabsorption and thus increasing sodium and water excretion in response to elevated blood pressure. This causes extracellular fluid volume to go down, which in turn lowers blood pressure.


Mathematical biologists often fail to account for sex differences. Indeed, the Guyton model and its many variants—published over the last four and a half decades—are all gender neutral. To investigate sexual dimorphism and its implications in antihypertensive therapy, our group recently published the first and only set of sex-specific computational models for blood pressure regulation [Leete & Layton 2019]. These models represent sex differences in the renin-angiotensin system [Leete et al. 2018], a signaling pathway that interacts with the kidneys and plays a crucial role in blood pressure regulation, as well as the less excitable and more easily repressed female renal sympathetic nervous activity. Sex-specific models such as ours can be useful for contrasting male and female responses to various hypertensive stimuli, and for understanding the mechanisms underlying sex differences in the effectiveness of some anti-hypertensive therapies. Given that sex differences in blood pressure control and hypertension have been widely recognized for decades, it is somewhat surprising that modelling efforts in unraveling the mechanisms and functional implications of those sex differences remain limited.


Coronavirus. The coronavirus that originated in China has spread fear and anxiety around the world. But while the novel virus has largely spared one vulnerable group — children — it appears to pose a particular threat to middle-aged and older adults, particularly men. A large analysis of coronavirus cases, published by the Chinese Center for Disease Control and Prevention, has revealed sex disparity in the disease. Although men and women have been infected in roughly equal numbers, researchers found, the death rate among men was 2.8%, compared with 1.7% among women. The figures were drawn from patient medical records, and the sample may not fully reflect the scope of the outbreak. But the disparity has been seen in the past. Men also were disproportionately affected during the SARS and Middle East Respiratory Syndrome (MERS) outbreaks, which were caused by coronaviruses. More women than men were infected by SARS in Hong Kong in 2003, but the death rate among men was 50% higher, according to a study published in the Annals of Internal Medicine.

Some 32% of men infected with MERS died, compared with 25.8% of women. Young adult men also died at higher rates than female peers during the influenza epidemic of 1918.


Mathematical biologists have developed epidemiological models to predict the spread of coronavirus. These models contain various degrees of details; populations are typically divided in geography, age, and health. Given the sexual disparity in mortality rates, sex should be considered a key model parameter, to yield accurate prediction of casualty.


What else? Sex and gender differences exist in many other ailments. Heart disease is a classic example, as men and women have disparate prevalence, symptoms, comorbidities, and treatment responses. For instance, women are more likely to report pain associated with heart attack somewhere other than the chest. Multiple sclerosis is another example: females are more susceptible to the condition, but it progresses more severely in males. Pain can also affect men and women differently. Failure to properly account for these gender discrepancies often leads to misdiagnosis and inappropriate treatment in women. Mathematical modeling can play an important role in identifying the most suitable treatment for each sex or gender.


Science is better with Sex and Gender


Policymakers have begun the effort of closing the gender gap in medical research. In recent years, the Canadian Institutes of Health Research (CIHR) has been promoting the use of SGBA+ (sex- and gender-based analysis plus) in health research, acknowledging that both biology (sex) and society (gender) influence our health and wellbeing in distinct yet interrelated ways. CIHR’s SGBA+ policy aligns with the Government of Canada’s commitment to the integration of sex and gender throughout its policies and programs—including the way government-funded research is conducted.


While modeling has seen similar progress, the overall number of sex-specific computational models remains low. A search for “sex-specific computational model kidney” on PubMed yields only four publications, all of which belong to our group [Ahmed & Layton 2020; Chen et al. 2017; Leete & Layton 2019; Li et al. 2018].


A comprehensive understanding of sex and gender’s impact on health and disease is key to the ultimate development of effective sex-based therapies, and mathematical modeling has rich potential of being a major contributor. Model analysis that include if not highlights sex and gender differences will facilitate the larger effort of precision medicine.




Ahmed S and Layton AT. Sex-Specific Computational Models for Blood Pressure Regulation in the Rat. Am J Physiol Renal Physiol. 2020 Feb 10. doi: 10.1152/ajprenal.00376.2019.


Chen Y, Sullivan JC, Edwards A, Layton AT. Sex-specific computational models of the spontaneously hypertensive rat kidneys: factors affecting nitric oxide bioavailability. Am J Physiol Renal Physiol. 2017 Aug 1;313(2):F174-F183.


Guyton AC, Coleman TG, and Granger HJ. Circulation: overall regulation. Ann Rev Physiol 34.1 (1972): 13-44


Leete J, Gurley S, and Layton AT. Modeling sex differences in the renin angiotensin system and the efficacy of antihypertensive therapies. Comput Chem Eng 112 (2018): 253-264


Leete J, Layton AT. Sex-specific long-term blood pressure regulation: Modeling and analysis.

Comput Biol Med. 2019 Jan;104:139-148.


Li Q, McDonough AA, Layton HE, Layton AT. Functional implications of sexual dimorphism of transporter patterns along the rat proximal tubule: modeling and analysis. Am J Physiol Renal Physiol. 2018 Sep 1;315(3):F692-F700.