The role of the microvascular network structure on diffusion and consumption of anticancer drugs

Abstract

SUMMARYWe investigate the impact of the tumor microvascular geometry on transport of drugs in solid tumors, in particular focusing on the diffusion and consumption phenomena. We embrace recent advances in the asymptotic homogenization literature starting from a double Darcy, double advection-diffusion-reaction system of partial differential equations which is obtained exploiting the sharp length separation between the intercapillary distance and the average tumor size. The geometric information on the microvascular network is encoded into effective hydraulic conductivities and diffusivities, which are numerically computed by solving periodic cell problems on appropriate microscale representative cells. The coefficients are then injected into the macroscale equations, which are solved for an isolated, vascularized spherical tumor. We consider the effect of vascular tortuosity on the transport of anti-cancer molecules, focusing on the Vinblastine and Doxorubicin dynamics, which can be considered a tracer and a highly interacting molecule, respectively. The computational model is able to quantify the performance of the treatment through the analysis of the interstitial drug concentration and the quantity of drug metabolized in the tumor. Our results show that both drug advection and diffusion are dramatically impaired by increasing geometrical complexity of the microvasculature, leading to non-optimal absorption and delivery of therapeutic agents. However, this effect apparently has a minor role whenever the dynamics are mostly driven by metabolic reactions in the tumor interstitium, i.e. for highly interacting molecules. In the latter case, anti-cancer therapies that aim at regularizing the microvasculature might not play a major role and different strategies are to be developed.

Effective balance equations for elastic composites subject to inhomogeneous potentials

“…(26)); the latter requires the solution of the arising elastic cell problem (58-61), which is solely driven by microscale variations of the scalar and vector potentials, namely f y (cf. (27)). Our result reduces to the standard case, where only the body force itself or its cell average appears in the homogenized balance equations, when microscale variations of the potentials can be neglected.…”

“…This particular case is achieved considering an additive decomposition of the potentials into purely macroscopically and microscopically varying components, cf. (26)(27).…”

“…The cell problem (82) corresponds to the one solved by the auxiliary variable w in [52] when identifying f y with the local component of the force F given in [52]. In our case, we do not need to assume the compatibility condition (49) (as done in [52] for F ), as this is automatically satisfied by means of its definition in terms of the local Helmholtz decomposition (27), see Remark 3. Enforcing (73) and (81), the effective elasticity tensor (64) and body force (66) readC…”

“…We then apply the asymptotic homogenization technique via formal expansions and by adopting a strong form formulation approach (see [43,44]), which has been recently enforced also to investigate various problems of practical interest such as bone modeling [46], filter efficiency [14], cardiac electrical activity [48], transport, growth, and heat exchange in tumors ( [27,40,41,42,45,47,54]). We admit both macroscale and microscale variations of the elastic coefficients of the individual phases of the composite, as well as possible discontinuities of the elastic moduli across the interface between two different phases.…”

Homogenized modeling for vascularized poroelastic materials

“…Exploiting the representation (46) and the spatial scale decoupling (45), equations (30-40) read (after multiplying each of them by a suitable power of )…”