24 research outputs found
Cancer recurrence times from a branching process model
As cancer advances, cells often spread from the primary tumor to other parts
of the body and form metastases. This is the main cause of cancer related
mortality. Here we investigate a conceptually simple model of metastasis
formation where metastatic lesions are initiated at a rate which depends on the
size of the primary tumor. The evolution of each metastasis is described as an
independent branching process. We assume that the primary tumor is resected at
a given size and study the earliest time at which any metastasis reaches a
minimal detectable size. The parameters of our model are estimated
independently for breast, colorectal, headneck, lung and prostate cancers. We
use these estimates to compare predictions from our model with values reported
in clinical literature. For some cancer types, we find a remarkably wide range
of resection sizes such that metastases are very likely to be present, but none
of them are detectable. Our model predicts that only very early resections can
prevent recurrence, and that small delays in the time of surgery can
significantly increase the recurrence probability.Comment: 26 pages, 9 figures, 4 table