Abstract
We describe a mathematical/computational model for thrombin concentration gradients generated by procoagulant circulating tumor cells (CTCs) in flow. We examine how CTCs enhance blood coagulation as they diffuse tissue factor-dependent coagulation enzymes in a flow environment with vessel walls. Concentration fields of various enzymes, such as prothrombin and thrombin, diffuse, to, and from CTCs, respectively, as they propagate through the bloodstream. The diffusion-dependent generation of these enzymes sets up complex time-dependent concentration fields. The CTCs are modeled as diffusing point particles in an incompressible fluid, and we exploit exact analytical solutions based on three-dimensional Green’s functions for unbounded domains with one wall for high resolution numerical simulations. Time-dependent gradient trackers are used to highlight that concentration fields build-up (i) near boundaries (vessel walls), (ii) in regions surrounding the diffusing particles, and (iii) in complex time-dependent regions of the flow where fields associated with different particles overlap. Two flow conditions are modeled: no flow, and unidirectional constant flow. Our results indicate that the CTC-generated thrombin diffuses to and persists at the blood vessel wall, and that the spatial distribution of CTCs in flow determines local thrombin concentration. The magnitude of the diffusion gradient and local thrombin concentration is dependent upon bulk solution concentrations of coagulation factors within normal reported concentration ranges. Therefore, our model highlights the potential to determine patient-specific risks for CTC-induced hypercoagulability as a function of CTC number and individual patient concentration of coagulation factors.
Highlights
Metastatic cancer accounts for the majority of deaths caused by cancer
Metastasis is believed to result from tumor cells from a primary site, migrating toward and intravasating into a blood vessel, navigating the blood circulation to arrive at a distant site whereby it arrests from the blood flow, extravasates, and establishes a metastatic tumor site
Very near the vessel wall where viscous flow boundary conditions dominate, blood velocity magnitudes are small, so should have minimal effects on disturbing the concentration fields that buildup there, we do not expect the inviscid fluid boundary conditions used in this study to qualitatively alter this main finding
Summary
Metastatic cancer accounts for the majority of deaths caused by cancer. Metastasis is believed to result from tumor cells from a primary site, migrating toward and intravasating into a blood vessel, navigating the blood circulation to arrive at a distant site whereby it arrests from the blood flow, extravasates, and establishes a metastatic tumor site. Procoagulant circulating tumor cells incidence of thrombosis is known to correlate with cancer type and tissue of origin, suggesting that the cancerous cells themselves have a role in the formation of pathological thrombi (Blom et al, 2005). The ability of TF to activate blood coagulation is dependent upon the presence of phospholipids, suggesting that only cell surface-expressed TF or cell membrane-derived TF bearing microvesicles are capable of activating coagulation (Nemerson, 1968). A CTC would experience different flow regimes if it were circulating on the arterial side versus the venous side or if it were free-flowing or adherent to the cell wall, and the effects that these different conditions have on coagulation kinetics have not been established In this manuscript, we model the concentration of thrombin generated by dispersed CTCs under constant laminar flow. Modeling and simulation of coagulation processes has been performed (Fogelson and Tania, 2005; Fogelson, 2007; Bodnar and Sequeira, 2008; Chatterjee et al, 2010; Gregg, 2010; Leiderman and Fogelson, 2011), but to our knowledge, our work is the first to model the physiologically relevant scenario of a TF-expressing cell entering into and circulating within the bloodstream and simulate its effects on coagulation processes
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