Multi-Constituent Simulation of Thrombus Deposition

📝 Abstract

In this paper, we present a spatio-temporal mathematical model for simulating the formation and growth of a thrombus. Blood is treated as a multi-constituent mixture comprised of a linear fluid phase and a thrombus (solid) phase. The transport and reactions of 10 chemical and biological species are incorporated using a system of coupled convection-reaction-diffusion (CRD) equations to represent three processes in thrombus formation: initiation, propagation and stabilization. Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: in vivo thrombus growth in an injured blood vessel and in vitro thrombus deposition in micro-channels (1.5mm x 1.6mm x 0.1mm) with small crevices (125{\mu}m x 75{\mu}m and 125{\mu}m x 137{\mu}m). For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally. Based on the success with these two benchmark problems, which have very different flow conditions and biological environments, we believe that the current model will provide useful insight into the genesis of thrombosis in blood-wetted devices, and provide a tool for the design of less thrombogenic devices.

💡 Analysis

In this paper, we present a spatio-temporal mathematical model for simulating the formation and growth of a thrombus. Blood is treated as a multi-constituent mixture comprised of a linear fluid phase and a thrombus (solid) phase. The transport and reactions of 10 chemical and biological species are incorporated using a system of coupled convection-reaction-diffusion (CRD) equations to represent three processes in thrombus formation: initiation, propagation and stabilization. Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: in vivo thrombus growth in an injured blood vessel and in vitro thrombus deposition in micro-channels (1.5mm x 1.6mm x 0.1mm) with small crevices (125{\mu}m x 75{\mu}m and 125{\mu}m x 137{\mu}m). For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally. Based on the success with these two benchmark problems, which have very different flow conditions and biological environments, we believe that the current model will provide useful insight into the genesis of thrombosis in blood-wetted devices, and provide a tool for the design of less thrombogenic devices.

📄 Content

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Multi-Constituent Simulation of Thrombus Deposition Wei-Tao Wu1, Megan A. Jamiolkowski2.3, William R. Wagner2,3,4,5, Nadine Aubry6, Mehrdad Massoudi7, James F. Antaki1*

1. Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA
2. McGowan Institute for Regenerative Medicine, Pittsburgh, PA, USA
3. Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA, USA
4. Department of Surgery, University of Pittsburgh, Pittsburgh, PA, USA
5. Department of Chemical Engineering, University of Pittsburgh, Pittsburgh, PA, USA
6. Department of Mechanical Engineering, Northeastern University, Boston, MA, 02115, USA
7. U. S. Department of Energy, National Energy Technology Laboratory (NETL), PA, 15236, USA

Address for correspondence: James F. Antaki, PhD,
Scott Hall 4N209, Department of Biomedical Engineering Carnegie Mellon University, Pittsburgh, PA 15213.
Phone: 412-268-9857.
Email: antaki@cmu.edu

2 Abstract In this paper, we present a spatio-temporal mathematical model for simulating the formation and growth of a thrombus. Blood is treated as a multi-constituent mixture comprised of a linear fluid phase and a thrombus (solid) phase. The transport and reactions of 10 chemical and biological species are incorporated using a system of coupled convection-reaction-diffusion (CRD) equations to represent three processes in thrombus formation: initiation, propagation and stabilization. Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: in vivo thrombus growth in an injured blood vessel and in vitro thrombus deposition in micro-channels (1.5mm × 1.6mm × 0.1mm) with small crevices (125m × 75m and 125m × 137m). For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally. Based on the success with these two benchmark problems, which have very different flow conditions and biological environments, we believe that the current model will provide useful insight into the genesis of thrombosis in blood-wetted devices, and provide a tool for the design of less thrombogenic devices. Introduction The hemostatic response at the site of vascular injury prevents the loss of blood, but excessive thrombosis may impede or interrupt blood flow to vital organs and tissues. The development of a thrombus in the vasculature is associated with myocardial infarction and stroke, as well as venous thromboembolic disorders.1,2 Thrombus formation in blood-contacting medical devices is a common cause of failure, and one of the most significant sources of morbidity and mortality.3,4 For instance, thrombosis in patients receiving ventricular assist devices (VADs) is one of the leading adverse events associated with this therapy, and has raised concerns in the medical community5–8 and with regulatory bodies such as the FDA9. Therefore, there is a critical need for improved understanding of the conditions under which hemostatic pathways may proceed to an excessive and undesirable thrombotic response. Thrombosis is a complex phenomenon in which a combination of interrelated biochemical and hemodynamic factors result in several cascade reactions causing platelet activation, deposition, aggregation, and stabilization10–12. The complexity is accentuated by several feed-forward and feedback mechanisms promoting and inhibiting coagulation reactions. Therefore a comprehensive description of thrombus generation requires a model which can account for interrelated reactions involving platelet activation and aggregation, transport of platelets and chemical species in flow, and the interaction between the formed thrombus and the flow field 10,13–17. The large number of chemical species and the complexity of cascade reactions make it very 3 difficult to synthesize a comprehensive picture of coagulation dynamics using traditional laboratory approaches 16. This motivates the pursuit of mathematical models 13,17–23.
For practical objective of predicting thrombosis in blood-wetted medical devices there is inevitably a tradeoff between complexity and utility. An overly simplistic model may fail to account for the essential mechanisms listed above. However, an overly complex model that includes the numerous biochemical species and pathways of coagulation may contain many unidentified parameters, and therefore be intractable or indeterminate to compute. A reasonable compromise was formulated by Sorensen et al. in which a set of convection-reaction-diffusion equations were employed to simulate platelet activation. This model featured a weighted linear combination of agonist concentrations, agonist release and synthesis by activated platelets, platelet-phospholipid-dependent generation of thrombin, and thrombin inhibition by heparin 13,14. All of the parameters employed in Sorensen’s model were availabl

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