TY - JOUR
T1 - The buckling of capillaries in solid tumours
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
M3 - 10.1098/rspa.2012.0418
AU - MacLaurin, James
AU - Chapman, Jon
AU - Jones, Gareth Wyn
AU - Roose, Tiina
Y1 - 2012/10/10
UR - http://rspa.royalsocietypublishing.org/content/early/2012/10/09/rspa.2012.0418.abstract
N2 - We develop a model of the buckling (both planar and axial) of capillaries in cancer tumours, using nonlinear solid mechanics. The compressive stress in the tumour interstitium is modelled as a consequence of the rapid proliferation of the tumour cells, using a multiplicative decomposition of the deformation gradient. In turn, the tumour cell proliferation is determined by the oxygen concentration (which is governed by the diffusion equation) and the solid stress. We apply a linear stability analysis to determine the onset of mechanical instability, and the Liapunovâ€“Schmidt reduction to determine the postbuckling behaviour. We find that planar modes usually go unstable before axial modes, so that our model can explain the buckling of capillaries, but not as easily their tortuosity. We also find that the inclusion of anisotropic growth in our model can substantially affect the onset of buckling. Anisotropic growth also results in a feedback effect that substantially affects the magnitude of the buckle.
ER -