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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

What this category covers

Medicine and biophysics treat the living body as a physical system you can describe with equations and watch unfold in real time. This category covers the core models of physiology and public health: epidemic dynamics (SIR and SEIR), cardiac action potentials and excitable tissue, pharmacokinetics and drug diffusion, blood flow and vessel mechanics, antibiotic resistance and predator-prey ecology. Through each interactive Medicine model you learn how parameters such as the basic reproduction number, infection and recovery rates, dosing schedules, vessel geometry and ion-channel gating shape the outcomes that clinicians and researchers care about. It matters because the same mathematics behind these browser simulations powers real clinical trial design, vaccination policy, medical-device modelling and the everyday reasoning of evidence-based medicine.

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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★★★ Advanced New
Antibiotic Resistance
Bacteria evolve resistance under antibiotic selection: susceptible cells die above their MIC, resistant survive at a fitness cost, and under-dosing breeds resistance while a full course clears the colony.
Antibiotic ResistanceNatural SelectionMICCanvas 2D
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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
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★★☆ Moderate New
Epidemic Model — SIR & Vaccination Thresholds
SIR compartmental ODE with vaccination: adjust R0, recovery rate and vaccine coverage to find the herd immunity threshold. Watch S/I/R curves update in real time.
SIR ModelVaccinationHerd ImmunityR0Disease Spread
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★★★ Advanced
SEIR Epidemic Model — Exposed & Intervention Dynamics
Extended SIR model with Exposed compartment for incubation period. Simulate COVID-19-like epidemics with vaccination, social distancing and mask interventions. Track R₀ and herd immunity threshold.
SEIR Incubation COVID-19 Intervention
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★★☆ Moderate New
Wound Healing — Cell Migration
Collective cell migration closes a wound. Leading edge cells extend lamellipodia driven by actin pol...
Cell Migration Wound Healing Actin Canvas 2D

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

How does the SIR epidemic model predict outbreak size?
The SIR model uses three coupled ODEs: dS/dt = −βSI, dI/dt = βSI − γI, dR/dt = γI. The basic reproduction number R₀ = β/γ determines outbreak size. If R₀ > 1, an epidemic grows; if R₀ < 1, it fades. The herd immunity threshold — the fraction of the population that must be immune to prevent spread — is 1 − 1/R₀. Adjust β and γ sliders live in the simulation to see how interventions change the epidemic curve.
What does the cardiac action potential simulation model?
The simulation uses the FitzHugh-Nagumo excitable-media model — a two-variable simplification of the Hodgkin-Huxley equations — to model how electrical excitation propagates through cardiac tissue. Clicking the canvas stimulates a region; the wavefront spreads through coupled cells and can form spiral reentry arrhythmias, the mechanism behind some dangerous heart rhythms.
How does the drug diffusion simulation model pharmacokinetics?
The two-compartment pharmacokinetics model tracks drug concentration in plasma and tissue over time. IV bolus dosing gives an immediate peak followed by bi-exponential decay; oral dosing adds an absorption phase with a delayed Cmax. Key metrics — Cmax, AUC, and half-life — are computed in real time. The model uses the same mathematical framework as clinical trial PK analysis.
What is the Lotka-Volterra model and what does it explain?
The Lotka-Volterra predator-prey model is a pair of coupled ODEs: prey grow exponentially (ẋ = αx) and are eaten by predators (−βxy); predators grow by eating prey (δxy) and die at rate γy. Solutions are closed orbits in phase space — prey and predator populations oscillate indefinitely out of phase. The Fox & Rabbits simulation shows these coupled oscillations with live population charts.

Other Categories

Explore Medicine simulations online

Every Medicine simulation here runs free in your browser, so you can learn Medicine online without any installation or sign-up. Each interactive Medicine model lets you adjust live parameters — infection rates, drug doses, vessel stenosis or ion-channel gating — and see the physiology respond instantly. The same compartmental and biophysical models drive a real-world application like vaccination policy and herd immunity planning, where epidemiologists tune R₀ and coverage to forecast outbreaks. Whether you are a student, teacher or curious learner, these interactive Medicine simulations turn abstract equations into intuition you can see, test and remember.