Modeling thrombosis in silico: Frontiers, challenges, unresolved problems and milestones

Abstract

Hemostasis is a complex physiological mechanism that functions to maintain vascular integrity under any conditions. Its primary components are blood platelets and a coagulation network that interact to form the hemostatic plug, a combination of cell aggregate and gelatinous fibrin clot that stops bleeding upon vascular injury. Disorders of hemostasis result in bleeding or thrombosis, and are the major immediate cause of mortality and morbidity in the world. Regulation of hemostasis and thrombosis is immensely complex, as it depends on blood cell adhesion and mechanics, hydrodynamics and mass transport of various species, huge signal transduction networks in platelets, as well as spatiotemporal regulation of the blood coagulation network. Mathematical and computational modeling has been increasingly used to gain insight into this complexity over the last 30 years, but the limitations of the existing models remain profound. Here we review state-of-the-art-methods for computational modeling of thrombosis with the specific focus on the analysis of unresolved challenges. They include: a) fundamental issues related to physics of platelet aggregates and fibrin gels; b) computational challenges and limitations for solution of the models that combine cell adhesion, hydrodynamics and chemistry; c) biological mysteries and unknown parameters of processes; d) biophysical complexities of the spatiotemporal networks' regulation. Both relatively classical approaches and innovative computational techniques for their solution are considered; the subjects discussed with relation to thrombosis modeling include coarse-graining, continuum versus particle-based modeling, multiscale models, hybrid models, parameter estimation and others. Fundamental understanding gained from theoretical models are highlighted and a description of future prospects in the field and the nearest possible aims are given.

Mathematical modelling of atherosclerosis

“…Detached pieces of the damaged plaque can block blood vessels downstream. Furthermore, plaque rupture can initiate blood coagulation, thrombus formation and vessel occlusion [15,131]. Both cases can lead to dangerous cardio-vascular events.…”

Review of quantitative systems pharmacological modeling in thrombosis

“…Thrombotic models that employ molecular, cellular/tissue, fluid, microfluidic and physiological descriptions have rarely been used in practical QSP for pharmacokinetic and pharmacodynamic computation. 61 Models of signal transduction 14,15,62 and blood coagulation in vitro 63,64 are used to provide limited mechanism-driven molecular-level insights. As a result, simpler models with fewer parameters, rather than complex QSP physiological models, are more often utilized to explore fundamental hypotheses about thrombus generation and drug discovery/development.…”

“…Moreover, the granules' contents activate a Gq-linked protein receptor cascade, resulting in increased calcium concentration in the platelets' cytosol. 7 Calcium signaling modulated microtubule/actin filament reorganization in the presence of ATP gives rise to platelet morphological changes required to adapt to the fluid dynamic and structural conditions within the blood vessel and thrombus. 13 Calcium also activates protein kinase C, which, in turn, activates the membrane enzyme phospholipase A2 (PLA2).…”

Shape effects in biological adhesion of ellipsoidal cells

“…Blood platelets play a key role in arterial and microvascular thrombosis, where the intensive hemodynamic flows and near-wall viscous stresses hinder the clotting of blood plasma [1,2]. Physiological functions of platelets rely on their ability to adhere to a wound (or to a thrombus) and to withstand relatively mechanical stresses in the flowing blood [3].…”