Biochemomechanical modeling of vascular collapse in growing tumors

Abstract

The collapse of blood vessels are widely observed in solid tumors, but the mechanisms underpinning this abnormal behavior remain unclear. In this paper, we investigate the stability of blood vessels embedded in a growing solid tumor by using a chemomechanical poroelastic theory. Linear stability analysis is first made to give the critical condition of vascular buckling. Thereby, pattern diagrams are provided to predict the collapsed shape of a blood vessel from the mechanical and geometric parameters of the system. Due to the mechano-chemo-biological coupling effect in tumors which involve both fluid transport and tissue growth, the buckling of blood vessels exhibits distinctly different features from such previously reported tubular tissues as airways and esophagi. We show that interstitial fluid pressure tends to drive blood vessels to buckle with a lower buckling mode, while perivascular cell proliferation favors a higher mode. Furthermore, a nonlinear biochemomechanical finite element method is formulated to track the morphological evolution of blood vessels during postbuckling. It is found that the blood vessels with the second mode of buckling may readily evolve into a crack-like shape. This method can reproduce the essential features of vascular collapse observed in in vivo tumors and provide clues for vascular normalization and stress alleviation in cancer treatments.