Post-surgical passive response of local environment to primary tumor removal

Prompted by recent clinical observations on the phenomenon of metastasis inhibition by an angiogenesis inhibitor, a mathematical model is developed to describe the post-surgical response of the local environment to the “surgical” removal of a spherical tumor in an infinite homogeneous domain. The primary tumor is postulated to be a source of growth inhibitor prior to its removal at t = 0; the resulting relaxation wave arriving from the disturbed (previously steady) state is studied, closed form analytic solutions are derived, and the asymptotic speed of the pulse is estimated to be about 2 × 10−4 cm/sec for the parameters chosen. In general, the asymptotic speed is found to be 2√Dγ, where D is the diffusion coefficient and γ is the inhibitor depletion or decay rate.