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This is a simple model of tumour growth, and response to radiotherapy. It uses a model called "logistic growth" to describe the size of a tumour over time. When the tumour is small it grows quickly, but as it becomes larger the model assumes that the tumour reaches a "carrying capacity" - this can be understood as describing the point at which there are no longer available resources to sustain the growth of new cells, causing growth to slow and ultimately stop.

Move the sliders to adjust the simulation and change the equation - for more details of the model used here, please see below!

 Growth Rate: Carrying capacity: Initial size: RT strength: Number of RT doses:

${V}^{\prime }\left(t\right)=V\left(1-\frac{V}{}\right)-V\delta \left(t-{t}_{i}\right)$

To simulate this, we solve the equation ${V}^{\prime }\left(t\right)=\mathrm{\alpha V}\left(1-\frac{V}{K}\right)-\mathrm{\gamma V}\delta \left(t-{t}_{i}\right)$ . In this equation, we have:

• $\mathrm{V =}$ Tumour volume
• $\mathrm{t =}$ Time
• $\mathrm{\alpha =}$ Growth rate
• $\mathrm{K =}$ Carrying capacity
• $\mathrm{\gamma =}$ Strength of radiotherapy
and $\delta$ is the delta function, which describes instantaneous application of radiotherapy at time ${t}_{i}$.