Computational Model for Tumor Oxygenation Applied to Clinical Data on Breast Tumor Hemoglobin Concentrations Suggests Vascular Dilatation and Compression

Abstract

We present a computational model for trans-vascular oxygen transport in synthetic tumor and host tissue blood vessel networks, aiming at qualitatively explaining published data of optical mammography, which were obtained from 87 breast cancer patients. The data generally show average hemoglobin concentration to be higher in tumors versus host tissue whereas average oxy-to total hemoglobin concentration (vascular segment RBC-volume-weighted blood oxygenation) can be above or below normal. Starting from a synthetic arterio-venous initial network the tumor vasculature was generated by processes involving cooption, angiogenesis, and vessel regression. Calculations of spatially resolved blood flow, hematocrit, oxy- and total hemoglobin concentrations, blood and tissue oxygenation were carried out for ninety tumor and associated normal vessel networks starting from various assumed geometries of feeding arteries and draining veins. Spatial heterogeneity in the extra-vascular partial oxygen pressure distribution can be related to various tumor compartments characterized by varying capillary densities and blood flow characteristics. The reported higher average hemoglobin concentration of tumors is explained by growth and dilatation of tumor blood vessels. Even assuming sixfold metabolic rate of oxygen consumption in tumorous versus host tissue, the predicted oxygen hemoglobin concentrations are above normal. Such tumors are likely associated with high tumor blood flow caused by high-caliber blood vessels crossing the tumor volume and hence oxygen supply exceeding oxygen demand. Tumor oxy- to total hemoglobin concentration below normal could only be achieved by reducing tumor vessel radii during growth by a randomly selected factor, simulating compression caused by intra-tumoral solid stress due to proliferation of cells and extracellular matrix. Since compression of blood vessels will impede chemotherapy we conclude that tumors with oxy- to total hemoglobin concentration below normal are less likely to respond to chemotherapy. Such behavior was recently reported for neo-adjuvant chemotherapy of locally advanced breast tumors.

Tumorcode - A framework to simulate vascularized tumors

“…In [15] we showed that the equation for the vascular oxygen distribution together with 104 the diffusion equation for the tissue form a complicated nonlinear system of equations 105 with the partial pressure values of oxygen as unknowns. For the longitudinal transport a 106 bisection search is used to gather the partial oxygen pressure values within each vessel.…”

“…Secondly, an elaborated model of blood and tissue oxygenation was developed [15]. 181 Similarly to 'submitIff', 'submitDetailedO2' needs a parameter set, a tumor simulation 182 and a specified time point as input.…”

Towards personalized computational oncology: from spatial models of tumour spheroids, to organoids, to tissues

“…The authors investigated the structural adaptation of tumour vasculature and its pruning in response to haemodynamic and metabolic stimuli as well as spatial patterns and frequency distributions of both oxygen and VEGF concentrations around vascular networks of distinct topologies (figure 2c). Welter and co-workers [87,97] modelled the complex hierarchical tree-like vascular structures via a hybrid model combining a discrete triangular grid-based vascular network and a continuous description of a homogeneous medium representing host or tumour cells. The authors investigated the relation between the morphology of tumour vasculature and the intra-and extravascular transport characteristics of blood flow, oxygen distribution, interstitial fluid pressure and drug delivery efficiency.…”

Adaption of artificial microvascular networks

“…Second, the position of the capillaries within the volume is optimized towards a homogeneous capillary volume density using a hierarchical iteration scheme. For the scope of this paper, we consider only a root node configuration (RC) where one artery is opposite to one vein on the same axis (figure 2, compare also RC5 in figure 4 75 of [24]) and a single hierarchical iteration. Since the construction algorithm in the Tumorcode fixes the radii of all capillaries ( 2.5 µm in presented case) and determines the radii of all intermittent vessels between root nodes and capillaries by Murray's law, all radii at the intersections fulfill Murray's law by construction.…”

“…In solid tumors, topological 240 modifications are an essential part of the growth procedure and therefore considered in our simulation framework [21]. In [24], we simulated the oxygen distribution in breast carcinoma and found that an additional vessel dilation is required to obtain oxygen distributions in agreement with the clinical measurements. We conjectured that the adaptation algorithm could possibly 245 provide a physiological mechanism for this vessel dilation.…”