Math as the New Microscope

A presentation at the 2024 Eye Data and AI Summit

By Professor Anita Layton
Canada 150 Research Chair in Mathematical Biology and Medicine
Professor of Applied Mathematics, University of Waterloo

Future Medicine

  • The future of medicine is personalized. 

  • Every patient is shaped by a unique combination of sex, age, lifestyle, environment, and genetics. These factors influence how diseases develop, how symptoms present, and how treatments work — but they’re often invisible to traditional diagnostic tools. To truly personalize care, we need a new kind of lens. That’s where mathematics comes in. Like a microscope, mathematical models allow us to zoom in on the hidden mechanisms that drive health outcomes. They help us simulate, predict, and understand — not just what’s happening, but why.”

Future Medicine is Personalized

Personalized medicine shaped by a unique combination of sex, age, demographics, lifestyle and environment to drive better health outcomes.

A diagram titled "Future Medicine More Personalized Diagnostics" illustrating the process of personalized medicine. It shows a diverse group of "Cancer patients with e.g. colon cancer" undergoing "Blood, DNA, Urine and Tissue Analysis." The analysis leads to different "Therapy" options tailored to patient groups (represented by different colored figures with corresponding colored pills), resulting in a positive "Effect" shown as an upward-trending graph.

Sex differences in health

Heart attack symptoms differ between men and women

Male

Male patient holding hand to his chest.
  • Squeezing chest pressure or pain
  • Jaw, neck or back pain
  • Nausea or vomiting
  • Shortness of breath

Female

Female patient taking her own pulse at neck.
  • Chest pain, but not always
  • Pain or pressure in the lower chest or upper abdomen
  • Jaw, neck or upper back pain
  • Nausea or vomiting
  • Shortness of breath
  • Fainting
  • Indigestion
  • Extreme fatigue
A bar chart showing two sets of data across different age groups: 35-44, 45-54, 55-64, 65-74, 75-84, and 85+. Each age group has two bars, one blue and one red, with numerical values indicated above each bar. For example, the 35-44 age group shows values of 25 (blue) and 10 (red), while the 55-64 age group shows 125 (blue) and 60 (red)

Sex Differences in Physiology

Four images illustrating sex differences in physiology: Over The Counter Pain Relievers, End-stage human autosomal dominant polycystic kidney (right) compared with a healthy kidney, A shield to block virus from human, and A healthy liver vs a liver with disease

Sex Differences in Drug Processing

Females

Body composition

Males

Slower processing of most drugs

More accumulation of lipophilic drugs

Different concentrations of hydrophilic drugs (also dependent on stages of menstrual cycle)

Fat mass

Lean mass

Free water

Faster processing of most drugs

Less accumulation of lipophilic drugs

Different concentrations of hydrophilic drugs

Higher resting heart rate

Longer QT intervals

Higher risk of arrhythmias

Variation in heart rate

Lower resting heart rate

Shorter QT intervals

Lower risk of arrhythmias

Slower absorption of drugs

Gastric motility

Faster absorption of drugs

Different expression of cytochrome P450 (more CYP3A4 in women)

Stomach PH

Different expression of cytochrome P450 (more CYP2D6 and CYP2E1 in men)

Oestrogen and progesterone compete with drugs for degradation by CYP450

Liver enzymes

Slower excretion of drugs

Kidney excretion

Faster excretion of drugs

Sex As a Risk Factor for Glaucoma and Diabetic Retinopathy

Box-and-whisker plot displaying age-standardized DALYs per 100,000 population across four HDI categories (Low, Medium, High, Very high), stratified by sex (Male and Female). The plot shows differences in DALYs between sexes within each HDI category, with significant differences indicated by asterisks (**, *)
Prevalence of diabetic retinopathy according to age and gender." The x-axis represents age groups: "<45 yrs," "45-55 yrs," "56-65 yrs," and ">65 yrs." The y-axis represents the "percentage" from 0 to 60. Two sets of bars are shown for each age group, representing "Men" (white bars) and "Women" (black bars).

Hypertension Prevalence: Ethnicity, Sex

Two sets of bar graphs detailing the prevalence of hypertension among adults aged 18 and over, categorized by gender. The left panel shows the prevalence of hypertension by race/ethnicity for both men and women: Men: Prevalence among Non-Hispanic white (29.7%), Non-Hispanic black (40.6%), Non-Hispanic Asian (28.7%), and Hispanic (27.3%). Women: Prevalence among Non-Hispanic white (25.6%), Non-Hispanic black (39.9%), Non-Hispanic Asian (21.9%), and Hispanic (28.0%). The right panel shows the prevalence of hy

Math as the New Microscope in Medicine

Heart graphic surrounded by four questions: What is the best medication for my patient? (Why?); What (combinations of) drugs are best for patients with diabetes?; Will my patient respond to this medication? (Why?); Is my patient at risk for complications? How can complications be avoided?

Blood Pressure Regulation

Blood pressure impacts on different body functions: Vaculature, Adrenal (kidney), Brain, Pituitary gland, and the Heart itself.

Sex-specific Blood Pressure Regulation Models

Flow chart representation of two models published by Leete and Layton, Comput Biol Med 2019.

Leete and Layton, Comput Biol Med 2019

Drug Testing Using Virtual Patient Cohort

Diagram illustrating a virtual patient (VP) model for simulating interventions and their effect on blood pressure.
Six bar graphs (A-F) showing the frequency distribution of various physiological parameters in males (blue) and females (purple). Graph A shows arterial resistance, B shows venous resistance, C shows afferent arteriolar resistance, D shows renin secretion rate, E shows aldosterone secretion rate, and F shows renal sympathetic nerve activity.

Simulated Response to Different Classes of Anti-hypertensive Drugs

  • At high dosages, BP drops more in women.
  • Women respond better to ARB than ACEi.
  • Women respond better to thiazide diuretic than men.
The image displays four graphs, labeled A, B, A, and A (top left, top right, bottom left, bottom right respectively), each showing the percentage change in Mean Arterial Pressure (% ΔMAP) on the y-axis against a percentage of a substance on the x-axis.

Using Underlying Pathophysiology to Predict Optimal Drug Class

A flowchart illustrating sex-specific decision trees for antihypertensive drug choice based on physiological parameters. Published by Ahmed et al, Science 2021.

Each model has strengths and limitations

Mechanistic Models: Pros

  • Hypothesis testing
  • Predictions
  • Biological insights

Mechanistic Models: Cons

  • Extensive biological knowledge required
  • Model parameters may be unknown or difficult to determine

Data-driven Models: Pros

  • Pattern recognition
  • Predictions
  • Biological insights

Data-driven Models: Cons

  • Overfitting
  • Data volume requirements
  • Lack of transparency

Integration of Mechanistic and Data-driven Models

  • Translation of data à information à knowledge à wisdom
  • Research may generate both data (1) and knowledge (3)
  • ‘Big data” interpreted by ML may generate information (2)
  • MM may yield knowledge (3), which can be used to derive wisdom (4)
  • Hybridization of ML and MM may close the loop between prediction accuracy and causality
Diagram illustrating the transformation of Data into Information, Knowledge, and Wisdom, showing the flow from customer to solution in a data-driven model.

In Conclusion: Math as the new microscope in medicine

Math, like a microscope, allows us to see what’s hidden: the underlying mechanisms, the subtle differences, the personalized pathways. In medicine, math is helping us move from generalized treatment to personalized care.