A four‐compartment multiscale model of fluid and drug distribution in vascular tumours

Abstract

The subtle relationship between vascular network structure and mass transport is vital to predict and improve the efficacy of anticancer treatments. Here, mathematical homogenisation is used to derive a new multiscale continuum model of blood and chemotherapy transport in the vasculature and interstitium of a vascular tumour. This framework enables information at a range of vascular hierarchies to be fed into an effective description on the length scale of the tumour. The model behaviour is explored through a demonstrative case study of a simplified representation of a dorsal skinfold chamber, to examine the role of vascular network architecture in influencing fluid and drug perfusion on the length scale of the chamber. A single parameter, P, is identified that relates tumour‐scale fluid perfusion to the permeability and density of the capillary bed. By fixing the topological and physiological properties of the arteriole and venule networks, an optimal value for P is identified, which maximises tumour fluid transport and is thus hypothesised to benefit chemotherapy delivery. We calculate the values for P for eight explicit network structures; in each case, vascular intervention by either decreasing the permeability or increasing the density of the capillary network would increase fluid perfusion through the cancerous tissue. Chemotherapeutic strategies are compared and indicate that single injection is consistently more successful compared with constant perfusion, and the model predicts optimal timing of a second dose. These results highlight the potential of computational modelling to elucidate the link between vascular architecture and fluid, drug distribution in tumours.

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

“…Additionally, while signaling pathways and TEC motion may feature fast mechanisms on the order of milliseconds to seconds, the formation of fully functioning new vessels may take days and the vascular-induced changes in tumor growth may occur over weeks [ 150 ]. Thus, to fully characterize the complexity of angiogenesis, multiscale mathematical models that combine the description of biological processes underlying the formation of tumor-induced neovasculature at multiple scales are needed [ 24 , 76 , 141 , 147 , 148 , 149 , 150 , 151 , 152 , 153 , 154 , 155 ]. Some models of angiogenesis already include a multiscale component.…”

Computational model of silica nanoparticle penetration into tumor spheroids: Effects of methoxy and carboxy PEG surface functionalization and hyperthermia

“…For example, detailed analysis of nanoparticle transport through solid tumors in vivo with particular attention to the orientation and characteristics of the tumor‐associated vasculature will shed light on this problem. Recent efforts by Cattaneo and Zunino 103 and Shipley et al 104 aimed to solve this issue through multiscale modeling of fluid and drug distribution in vascular tumors.…”

Macro-scale models for fluid flow in tumour tissues: impact of microstructure properties

“…A generalization of homogenized modelling for vascularized poroelastic materials has also been presented [37,38]. More recently, higher complexity has been added to the homogenized models [49] considering three length scales for the vessel network (i.e., arteriole, venule and capillary scales). Roughly speaking, 2 type of models have been proposed be used to describe fluid flow in tumors.…”