Cancer recurrence times from a branching process model
Fig 1
Sample realisation of the model obtained by simulations.
The primary tumor grows according to a deterministic exponential function n(t)—depicted by the blue line. It initiates distant metastases at rate νn(t), and each of them grows as an independent branching process (only the first five are plotted). The first time τ that any of these metastases reaches a minimal detectable size M is defined as the time to cancer relapse. Also, the primary tumor is surgically removed at a given time T, when it is made of N = n(T) cells. In the realisation shown, the third established metastases (green curve) is the first to reach detectable size, and hence determines the time to cancer relapse τ. Based on clinical data (summarized in Table 1), we estimated model parameters (summarized in Table 2), and here we use those for colorectal cancer, with N = 2 × 1011. Note that a similar illustration for metastasis formation appears in [30].