Morpho-elastic model of the tortuous tumour vessels

Abstract

Solid tumours have the ability to assemble their own vascular network for optimizing their access to the vital nutrients. These new capillaries are morphologically different from normal physiological vessels. In particular, they have a much higher spatial tortuosity forcing an impaired flow within the peritumoral area. This is a major obstacle for the efficient delivery of antitumoral drugs. This work proposes a morpho-elastic model of the tumour vessels. A tumour capillary is considered as a growing hyperelastic tube that is spatially constrained by a linear elastic environment, representing the interstitial matter. We assume that the capillary is an incompressible neo-Hookean material, whose growth is modeled using a multiplicative decomposition of the deformation gradient. We study the morphological stability of the capillary by means of the method of incremental deformations superposed on finite strains, solving the corresponding incremental problem using the Stroh formulation and the impedance matrix method. The incompatible axial growth of the straight capillary is found to control the onset of a bifurcation towards a tortuous shape. The post-buckling morphology is studied using a mixed finite element formulation in the fully nonlinear regime. The proposed model highlights how the geometrical and the elastic properties of the capillary and the surrounding medium concur to trigger the loss of marginal stability of the straight capillary and the nonlinear development of its spatial tortuosity.

Differentiation of Brain Tumor Microvasculature From Normal Vessels Using Optical Coherence Angiography

“…This change in vessel structure may be associated with the production of VegF [39] as a cause of tortuosity, introducing many smaller bends with a larger bend [40]. Tortuosity of the tumor vascular network might be due to the elastic confinement of embedded interstitial matter [41]. Our findings show that many of the vessels immediately surrounding the tumor show directional migration towards the tumor.…”