Understanding the uptake of a drug by diseased tissue, and the drug's subsequent spatiotemporal distribution, are central factors in the development of effective targeted therapies. However, the interaction between the pathophysiology of diseased tissue and individual therapeutic agents can be complex, and can vary across tissue types and across subjects. Here, we show that the combination of mathematical modelling, of high-resolution optical imaging of intact and optically cleared tumour tissue from animal models, and of in vivo imaging of vascular perfusion predicts the heterogeneous uptake, by large tissue samples, of specific therapeutic agents, as well as their spatiotemporal distribution. In particular, by using murine models of colorectal cancer and glioma, we report and validate predictions of steady-state blood flow and intravascular and interstitial fluid pressure in tumours, of the spatially heterogeneous uptake of chelated gadolinium by tumours, and of the effect of a vascular disrupting agent on tumour vasculature.

The neurovascular mechanisms underpinning the local regulation of cerebral blood flow (CBF) and oxygen transport remain elusive. In this study we have combined novel in vivo imaging of cortical microvascular and mural cell architecture with mathematical modelling of blood flow and oxygen transport, to provide new insights into CBF regulation that would be inaccessible in a conventional experimental context. Our study indicates that vasoconstriction of smooth muscle actin-covered vessels, rather than pericyte-covered capillaries, induces stable reductions in downstream intravascular capillary and tissue oxygenation. We also propose that seemingly paradoxical observations in the literature around reduced blood velocity in response to arteriolar constrictions might be caused by a propagation of constrictions to upstream penetrating arterioles. We provide support for pericytes acting as signalling conduits for upstream smooth muscle activation, and erythrocyte deformation as a complementary regulatory mechanism. Finally, we caution against the use of blood velocity as a proxy measurement for flow. Our combined imaging-modelling platform complements conventional experimentation allowing cerebrovascular physiology to be probed in unprecedented detail.

In recent years, biological imaging techniques have advanced significantly and it is now possible to digitally reconstruct microvascular network structures in detail, identifying the smallest capillaries at sub-micron resolution and generating large three-dimensional structural data sets of size > 10 6 vessel segments. However, this relies on ex vivo imaging; corresponding in vivo measures of microvascular structure and flow are limited to larger branching vessels and are not achievable in three dimensions for the smallest vessels. This suggests the use of computational modelling to combine in vivo measures of branching vessel architecture and flows with ex vivo data on complete microvascular structures to predict effective flow and pressures distributions. In this paper, a hybrid discrete-continuum model to predict microcirculatory blood flow based on structural information is developed and compared with existing models for flow and pressure in individual vessels. A continuum-based Darcy model for transport in the capillary bed is coupled via point sources of flux to flows in individual arteriolar vessels, which are described explicitly using Poiseuille's law. The venular drainage is represented as a spatially uniform flow sink. The resulting discrete-continuum framework is parameterised using structural data from the capillary network and compared with a fully discrete flow and pressure solution in three networks derived from observations of the rat mesentery. The discrete-continuum approach is feasible and effective, providing a promising tool for extracting functional transport properties in situations where vascular branching structures are well defined.

It is critically important to understand and predict fluid transport within both physiological and pathological tissues in order to develop effective treatment strategies.Recent advances in high-resolution optical imaging allow the acquisition of whole tumour vascular networks which can be used to parameterise computational models to predict the fluid dynamics at all length scales across the tissue. This enables hypothesis testing around the role of the tumour microenvironment in determining transport characteristics, which would otherwise be unavailable using traditional experiments.In this study, we present a novel computational framework for the efficient simulation of vascular blood flow and interstitial fluid transport based on complete three-dimensional, whole tumour vasculature obtained using high-resolution optical imaging. This framework comprises a Poiseuille flow model which simulates vascular blood flow within the vessel network, coupled via point sources of flux to a porous medium model describing interstitial fluid transport. We develop a computational algorithm for prescription of network boundary conditions and validation of tissue-scale fluid transport against measured in vivo perfusion data acquired using biomedical imaging tools. We present simulations of the model on orthoptic murine glioma and December 24, 2018 1/36 human colorectal carcinoma xenograft data (GL261 and LS147T, respectively), and perform sensitivity analysis on key unknown parameters relating to the tissue microenvironment, to understand their impact in predicting vascular and interstitial flow. Finally, we simulate radially varying vascular normalisation in a LS147T tumour and hypothesise that uniform normalisation is required to lower tumour interstitial fluid pressure.Our computational framework permits predictions of whole tumour fluid dynamics which incorporate the inherent architectural heterogeneities appearing at the micron-scale, and outputs three-dimensional spatial maps detailing these flow properties from micro to macro length scales. This provides vital information on the tumour microenvironment which could enable the design and delivery of future anti-cancer therapies. Author summaryThe structure of tumours varies widely, with dense and chaotically-formed networks of blood vessels that differ between each individual tumour and even between different regions of the same tumour. This atypical environment can inhibit the delivery of anti-cancer therapies. Computational tools are urgently required which incorporate micron-scale tumour biomechanics to predict tissue-scale fluid dynamics, and consequently the efficacy of cancer therapies.We have developed a computational framework which integrates the complex tumour vascular architecture to predict fluid transport across all lengths scales in whole tumours. This enables computationally efficient hypothesis testing of cancer therapies which manipulate the tumour microenvironment in order to improve drug delivery to tumours. Introduction 1 Architectural heterogeneities in...

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