Full title: Asymptotic homogenization for fluid and drug transport in malignant vessels and the impact of microvascular tortuosity on tumor blood flow
Abastract: We present a new system of partial differential equations for fluid and drug transport in the malignant microvasculature and its practical application to determine the role of the microvascular network geometry on transport phenomena in solid tumors. Our starting point is the asymptotic homogenization model developed in [2], which is derived via asymptotic (locally periodic) homogenization, exploiting the sharp length scale separation that exists between the characteristic vessels and tumor tissue spatial scales, referred to as the microscale and the macroscale, respectively. After the upscaling process, the macroscale coupling between the interstitial and capillary compartment is described by a double Darcy model (fluid transport), as in the previous work [1], while drug transport is described by an advection-diffusion-reaction-type system of PDEs both in the vessels and in the tumor interstitial space.
The geometric information on the microvascular structure is encoded in the model coefficients (such as effective hydraulic conductivities and diffusivities) which are to be (numerically) computed solving classical differential problems on the microscale representative emph{cell}. We then apply our findings focusing on the role of microvascular tortuosity in tumor transport pheomena [5]. Microscale information obtained from the solution of the fluid transport (Stokes’-type) cell problems derived in [2] is injected into the fluid transport macroscopic model, which is analytically solved in a prototypical geometry and compared with previous experimentally validated, phenomenological models, [3], [4]. In this way, we are able to capture the role of the standard blood flow determinants in the tumor, such as the tumor radius, tissue hydraulic conductivity and vessels permeability, as well as the influence of the vascular tortuosity on fluid convection. The results quantitatively confirm that transport of blood (and, as a consequence, of any advected anti-cancer drug) can be dramatically impaired by increasing
the geometrical complexity of the microvasculature. Hence, our quantitative analysis supports the argument that geometric regularization of the capillary network improve blood transport and drug delivery in the tumor mass.
Bibliography
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