Mathematical Models

Simulate tumor proliferation using validated mathematical models from literature

FPGA Acceleration

~50x Faster

Based on peer-reviewed research

Models implemented from: Jarrett et al. "Mathematical Models of Tumor Cell Proliferation: A Review of the Literature" Expert Rev Anticancer Ther. 2018;18(12):1271-1286

Growth Model Parameters

Configure tumor proliferation model

Growth Model

$\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right)$

Density-dependent growth. Accounts for resource limitation.

Initial Cell Count (N₀)

Growth Rate (r) [day⁻¹]: 0.3

Carrying Capacity (K)

Time Span (days)

Simulation Results

Configure parameters and run simulation

Mathematical Model Reference

Summary of implemented models from peer-reviewed literature

Model	Equation	Parameters	Application
Exponential	$\frac{dN}{dt} = rN$	$r$: growth rate	Early tumor growth
Logistic	$\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right)$	$r$, $K$: carrying capacity	Resource-limited growth
Gompertz	$\frac{dN}{dt} = \lambda e^{-\alpha t} N$	$\lambda$, $\alpha$	Clinical tumor progression
Linear-Quadratic	$S = e^{-\alpha D - \beta D^2}$	$\alpha$, $\beta$, $D$	Radiation response
Eichholtz-Wirth	$SF = e^{-k \cdot t \cdot C}$	$k$, $t$, $C$	Chemotherapy cytotoxicity
de Pillis-Radunskaya	$\frac{dT}{dt} = rT\left(1 - \frac{T}{K}\right) - kET$	$r$, $K$, $k$, $s$, $d$	Immune-tumor interaction
Reaction-Diffusion	$\frac{\partial N}{\partial t} = D\nabla^2 N + rN\left(1 - \frac{N}{K}\right)$	$D$, $r$, $K$	Spatial tumor invasion
Mendoza-Juez	$\frac{dP_o}{dt}, \frac{dP_g}{dt}$ with phenotype switching	$\tau_o$, $\tau_g$, thresholds	Metabolic phenotype (Warburg)
Bellomo-Delitala (Kinetic)	$\frac{\partial f_i}{\partial t} = \int \eta(u,u^)f_i(u)f_j(u^) - \mu_i(u)f_i \, du^*$	$\eta$, $\mu$, activity states	Tumor-immune with activity states
Kolev CTL Differentiation	$\frac{\partial n}{\partial t} + \frac{\partial}{\partial u}(G(u)n) = P(u) - D(u)n$	$G$, $P$, $D$	CTL differentiation dynamics

Command Palette

Mathematical Models