(193ak) Modeling of Fluid Flow and Oxygen Distribution in Solid Tumors

Most types of human cancer develop into solid tumors whereby cancer cells multiply uncontrollably to form neoplastic lesions embedded in tissues. In tumors, the interactions between cancer and normal cells causes abnormal physiological and biological changes to the tissue that leads to the development of the tumor microenvironment which inhibits the effectiveness of therapy and promotes tumor growth and heterogeneity. Some features of the tumor microenvironment include heterogeneous vascular structure and distribution, high interstitial fluid pressures, dense extracellular matrix and the presence of hypoxic regions. These properties are quite dynamic, vary from patient to patient and can influence each other. Currently, most forms of treatment used for tumors involve of the use of drugs that pass through systemic circulation whereby the drug must transport through the blood vessels of the tissue, across the vessel walls and make their way through the interstitial fluid and extracellular matrix in the interstitium to reach cancer cells in concentrations significant enough to induce cell death. Alternative treatments include the use of radiotherapy however this requires oxygen to be present in the target region to be effective. This highlights the need for a deeper understanding of the tumor microenvironment and its influence on transport so that the performance of treatments may be enhanced.

In this work, we employ computational mathematical modelling tools to allow us to understand the influence of various properties of the tumor microenvironment on fluid flow and oxygen distribution. Previous studies have attempted this however the tumor models considered were usually oversimplified where the heterogeneous vascular properties were not explicitly represented. In this study, we address this issue by building a model that can describe fluid flow and oxygen distribution in vasculature formed by tumor induced angiogenesis. Anderson and Chaplain’s mathematical model for tumor induced angiogenesis is used as a basis to construct 3D tumor vasculature and geometry [1]. The vessels are segmented into straight cylindrical pipes and Poiseuilles law is used to describe flow through the vessels. Transvascular and interstitial flows are described by starlings and Darcy’s equation respectively and are together coupled with vascular flow. A greens functions formulation developed by Pozrikidis (2010) and Secomb et al. (2004) is used to describe fluid and oxygen flux as a set of source points along a vessel [2][3]. Doing this allows interstitial fluid pressure, flow and oxygen distribution to be represented as function of vascular structure and density. To validate the model, morphological and hemodynamic analyses were performed and the data was found to correspond quite well with experimental values found in literature [4]. Fluid flow results from the model predicted elevated interstitial fluid pressure values between 1000-2000 pa which were corroborated by values determined experimentally. So far, our results show how interstitial fluid flow and pressure are affected by changes in properties such as vascular structure, heterogeneity, vessel permeability and ECM density. Spatial distributions of interstitial fluid pressure indicate that the discrete nature of the tumor vasculature can affect interstitial fluid pressure in some regions of the tumor which can in turn influence the penetration of drugs into these regions and allow cancer cells to survive treatment cycles. We present further results describing the effect of different vascular properties on the spatial distribution of oxygen in the tumor model.

[1] A. R. A. Anderson and M. A. J. Chaplain, "Continuous and Discrete Mathematical Models of Tumor-induced Angiogenesis," Bulletin of Mathematical Biology, vol. 60, pp. 857-900, 1998.

[2] C. Pozrikidis, "Numerical simulation of blood and interstitial flow through a solid tumor," Journal of Mathematical Biology, vol. 60, pp. 75-94, 2010.

[3] T. W. Secomb, R. Hsu, E. Y. H. Park and M. W. Dewhirst, "Green’s Function Methods for Analysis of Oxygen Delivery to Tissue Microvascular Networks," Annals of Biomedical Engineering, vol. 32, pp. 1519-1529, 2004.

[4] S. K. Stamatelos, E. Kim, A. P. Pathak and A. S. Popel, "A bioimage informatics based reconstruction of breast tumor microvasculature with computational blood flow predictions," Microvascular Research, vol. 91, pp. 8-21, 2014.