Computational study of cellular adhesion in metastasis: Implications for Circulating Tumor Cell Arrest, Extravasation, and Thrombosis Formation

Abstract

Cancer metastasis is the process by which cancer cells spread from the primary tumor to distant sites in the body, forming secondary tumors. This process is responsible for the majority of cancer-related deaths, despite significant advancements in treating primary tumors. This thesis aims to enhance the understanding of metastasis mechanisms by exploring the roles of circulating tumor cells (CTCs), ultra-large Von Willebrand Factor (UL-VWF) multimers, and blood vessel configurations. This study focuses on the mechanical, biochemical, and hemodynamic factors that drive metastatic processes and cancer-associated coagulopathies, providing insights into the interactions between CTCs, VWF, and endothelial cells. Through computational modeling and simulations, first, we investigate the role of UL-VWF multimers in cancer-associated thrombosis. The computational model integrates the lattice Boltzmann method for simulating blood flow, a coarse-grained model for deformable cells to capture their mechanical behavior, and the immersed boundary method to handle fluid-structure interactions. Additionally, an adhesion model was developed to simulate the binding dynamics between cells. This multi-scale approach allows for a detailed analysis of how UL-VWF multimers interact with blood cells to initiate microthrombus formation and progression. The findings reveal that UL-VWF plays a dual role in thrombosis and metastasis, enhancing platelet adhesion and trapping red blood cells, which can lead to significant changes in blood flow dynamics, such as reduced velocity and increased shear stress near thrombus sites, leading to a pressure drop of up to six times compared to healthy conditions. The study also explores the impact of blood vessel architecture on CTC dynamics, focusing on how vessel tortuosity influences CTC adhesion and extravasation. The same computational methodology has been utilized to analyze CTC interactions with the vessel wall, incorporating adhesion dynamics between the CTCs and the endothelial surface while considering the effect of shear rate on adhesion strength. The results indicate that curved vessels create asymmetrical flow patterns, resulting in variable shear stress, a 25% decrease in the wall shear stress in low-shear regions and a 58.5% increase in the high-shear region, that significantly affects CTC behavior. Specifically, high-shear regions in curved vessels show a threefold rise in adhesion bond formation compared to straight vessels, enhancing the likelihood of CTC extravasation. Increasing the tortuosity index of the vessel led to a 50% increase in maximum wall shear stress ratio and a 15.3% decrease in minimum wall shear stress ratio, as well as a 58% increase in the transit time of CTCs through the vessel curvature. The adhesion force in these high-shear regions increased by about 171%, indicating a significantly higher risk of CTC adhesion and extravasation in vessels with higher curvature. Additionally, while softer CTCs in low-shear regions showed a higher likelihood of detachment, stiffer cells in high-shear regions exhibited a reduction of approximately 12% in adhesion force compared to their behavior in straight vessels. This study identified an optimal range of cellular stiffness for successful CTC extravasation, challenging the assumption that softer cells always extravasate more efficiently. In this thesis, we also employed a stochastic model to analyze the dynamics of CTC adhesion, a crucial factor driving metastasis, incorporating parameter uncertainties in cell mechanical properties and adhesion characteristics. This probabilistic approach realistically captures the biological variability inherent in CTC behavior by accounting for a wide range of possible cell adhesion scenarios. Our analysis revealed that incorporating parameter variability, with a coefficient of variation of 20%, led to a maximum uncertainty of 12% in cell velocity. This variability manifested in two distinct CTC behaviors: either the cells detached from the vessel wall or continued to roll in a semi-stable manner, emphasizing the non-linear and complex nature of the adhesion dynamics. To efficiently manage computational demands, we developed a Random Forest surrogate model, achieving a high level of accuracy with a maximum error of 4.36% for velocity and 0.63% for stretch ratio. This model enabled comprehensive sensitivity analysis using Sobol' and E-FAST methods, which identified the bond spring constant and rupture strength as the most influential parameters following the initial adhesion phase, while cell membrane elasticity played a critical role during the initial adhesion. We also observed significant interdependencies between bond formation and rupture properties, underscoring their combined impact on CTC dynamics. Furthermore, machine learning techniques, particularly XGBoost, validated the model's predictive capabilities by achieving a classification accuracy of 95.62% and an area under the curve (AUC) value of 0.99 in distinguishing between 'rolling' and 'detached' CTC states. These findings highlight the importance of focusing on key parameter interactions to refine predictive models for metastasis. This comprehensive approach builds on the computational frameworks developed in this thesis, enhancing our understanding of metastasis by offering predictive insights into CTC behavior under different conditions. By integrating these findings into a cohesive framework, the thesis supports the development of more targeted therapeutic strategies to prevent or disrupt cancer progression.