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Medicine & Biophysics

From neural action potentials to epidemic spread — biophysics at the boundary of life and mathematics. Model the body with differential equations.

3 simulations Canvas 2D · WebGL ODE · Epidemiology · Agent-Based

Category Simulations

Biological and medical systems modelled in real time

Biophysics treats living systems as physical machines obeying the same differential equations as circuits and fluids. A neuron fires exactly like an RC circuit. Blood flows like a Newtonian fluid. Epidemic spread follows the SIR logistic curve. The same mathematics — radically different phenomena.

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★☆☆ Beginner
SIR Epidemic Model
Susceptible → Infected → Recovered. Adjust infection rate β and recovery rate γ to watch epidemic waves grow, peak and die out in real time.
Canvas 2D SIR/SEIR ODE
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★★☆ Moderate
Neural Network
Build and train a multilayer perceptron in the browser. Visualise activations, weights, backpropagation and decision boundaries live.
Canvas 2D Backprop Perceptron
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★☆☆ Beginner
Prey-Predator (Lotka-Volterra)
Two species coupled ODEs: rabbits grow exponentially, foxes hunt them. Watch population oscillations and phase-space orbits in real time.
Canvas 2D Lotka-Volterra Phase Space
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★★★ Advanced
Cardiac Action Potential
FitzHugh-Nagumo excitable-media model. Click to stimulate cardiac tissue — watch action potential waves and spiral reentry arrhythmia emerge from two coupled ODEs.
Canvas 2D FitzHugh-Nagumo Excitable Media
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★★☆ Moderate
Drug Diffusion
Two-compartment pharmacokinetics model. Compare IV bolus and oral dosing, visualise plasma & tissue concentration curves, and compute Cmax, AUC and half-life.
Canvas 2D Pharmacokinetics Two-Compartment
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★★★ Advanced
Blood Flow & Vessels
Poiseuille parabolic velocity profile with pulsatile animation. Model stenosis effects on wall shear stress, flow rate and Reynolds number.
Canvas 2D Poiseuille Hemodynamics
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★★☆ Moderate New
Pharmacokinetics
One-compartment PK model: plasma concentration vs time for IV bolus or oral dosing. See Cmax, Tmax, t½ and AUC in real time.
Half-life ADME AUC Bioavailability

Key Concepts

The mathematics behind living systems

SIR Model
Compartmental ODE: dS/dt = −βSI, dI/dt = βSI − γI, dR/dt = γI. Basic reproduction number R₀ = β/γ. Epidemic grows when R₀ > 1. Herd immunity requires vaccinating a fraction 1 − 1/R₀ of the population.
Hodgkin-Huxley
Four-ODE model of the neuron: membrane capacitance, Na⁺ activation/inactivation gates m and h, and K⁺ gate n. The coupled equations produce the stereotyped all-or-nothing action potential spike (≈ 1 ms).
Lotka-Volterra
Prey: ẋ = αx − βxy; Predator: ẏ = δxy − γy. Solutions are closed orbits in phase space — populations oscillate indefinitely. Adding logistic prey growth (x(1−x/K)) adds a stable spiral equilibrium.
Excitable Media
Cells with threshold dynamics: rest → excited → refractory → rest. Local coupling via diffusion enables travelling waves, spiral waves, and re-entry. Unifying framework for heart tissue, neurons, and slime moulds.

Learning Resources

Articles and tutorials about the algorithms in this category

Article SIR & SEIR Epidemic Models Compartmental ODE models. Basic reproduction number R₀. Herd immunity threshold. Spatial extensions on graphs. → Article Hodgkin-Huxley Neuron Four-variable model of action potential. Ion channel gating. Numerical integration with RK4. 2D excitable tissue and spiral waves. →
All articles →

About Medicine & Physiology Simulations

Epidemics, cardiovascular flow, pharmacokinetics, and physiology — simulated

Medicine and physiology simulations model biological systems at the whole-organ and whole-body scale. Epidemic simulations implement SIR/SEIR compartmental models and network-based transmission to show how vaccination coverage, incubation period, and contact rate interact to determine outbreak size and herd-immunity thresholds. Cardiovascular fluid-dynamics simulations model pulsatile blood flow in vessel bifurcations using Navier–Stokes.

Pharmacokinetics simulations plot drug concentration curves in multi-compartment absorption-distribution-metabolism-excretion (ADME) models. Population health simulations track chronic disease prevalence under different screening and treatment coverage scenarios. These models are the same computational tools used in clinical trial design, public-health policy planning, and medical device regulatory submissions.

Each simulation in this category is built with accuracy and interactivity in mind. The underlying mathematical models are the same ones used in academic research and professional engineering — just made accessible through a web browser. Changing parameters in real time and observing the results is one of the most effective ways to build intuition for complex scientific and engineering concepts.

Key Concepts

Topics and algorithms you'll explore in this category

Interactive ModelReal-time browser simulation with live parameter controls
WebGL / Canvas 2DHardware-accelerated rendering in the browser
Mathematical FoundationDifferential equations and numerical integration
Open SourceMIT-licensed code — inspect, fork, and learn
No Install RequiredRuns directly in Chrome, Firefox, Safari, Edge
Educational FocusBuilt to explain the underlying science clearly

Frequently Asked Questions

Common questions about this simulation category

Do these simulations require installation?
No. Every simulation runs entirely in your web browser using WebGL and Canvas 2D. Nothing to install or download — open the page and the simulation starts immediately.
Can I use these simulations for teaching?
Yes — all simulations are designed to be educational and run without an account or login. They are widely used in university lectures, high-school science classes, and self-directed learning. Embed them via iframe or link directly.
What devices do the simulations support?
All simulations work on desktop browsers (Chrome, Firefox, Edge, Safari). Many work on mobile and tablets too, though some physics-heavy simulations benefit from the GPU performance of a desktop or laptop.

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