Blood Clotting Modeling and Simulation

Blood circulates through the vascular system under pressure and puncture or transection of a blood vessel would lead to rapid outpouring of blood if there were no system to plug the opening and stanch the bleeding. Blood clotting is the physiological process through which the body tries to accomplish this. Because transmural pressure differences vary greatly in the circulatory system and because blood flowing at different speeds through vessels of widely varying diameter leads to great variation in shear stress, the challenges of forming a blood clot to stop the outflow of blood differ substantially in different vascular beds. The system that has evolved to cope with these disparate challenges involves the aggregation of cells (platelets) and the formation of fibrous protein gel (fibrin). In addition, there is a complex, powerful, and tightly regulated enzyme network (the coagulation system) involving reactions on the surfaces of activated platelets, that leads to production of an enzyme, thrombin, that is key both in activating platelets so they can cohere to one another and in forming the protein fibrin from which the fibrin mesh is constructed. Hence, fluid dynamic forces, fluid-mediated transport of cells and proteins, the kinetics and mechanics of inter-platelet bond formation and breaking, the biochemical reactions of the coagulation enzyme network, and the polymerization of fibrin all play roles in blood clot formation to greater or lesser extents in different parts of the vasculature. Other processes, including fibrinolysis, work to break down a blood clot, not only after it has served its purpose, but also during its initial formation. Failure of the combined blood clot formation and breakdown systems to produce a clot sufficient to stop blood leakage leads to hemorrhage and can cause serious, even life-threatening, problems, while excessive clot formation, and insuffficient clot breakdown, within blood vessels can occlude those vessels and also cause life-threatening problems including heart attacks and strokes.

My research group has been developing models of many of the disparate aspects of blood clotting for close to 40 years. We have built and analyzed models based on PDEs, ODEs, or SDEs, and, as needed, we have developed novel numerical methods with which to study the PDE-based models.

Projects of current interest include:

1) Developing ODE-based compartment models of platelet deposition and coagulation under flow that treat developing thrombi as porous materials and which can track resulting flow, the growth of aggregates, and the biochemistry of platelet signaling and coagulation from the initiation of clot formation through vessel occlusion. The goal is a high-throughput simulation tool that will allow extensive investigation of model behavior as model parameters and other inputs are varied to reflect different physiological situations and disease states. This work builds on our earlier work described in:

Kathryn G. Link, Michael T. Stobb, Matthew G. Sorrells, Maria Bortot, Katherine Ruegg, Marilyn J. Manco-Johnson, Jorge A. Di Paola, Suzanne S. Sindi, Aaron L. Fogelson, Karin Leiderman, Keith B. Neeves, A mathematical model of coagulation under flow identifies factor V as a modifier of thrombin generation in hemophilia A, Journal of Thrombosis and Hemostasis, 2020, 18, 306-317.

Kathryn Link, Matthew Sorrells, Nicholas Danes, Keith Neeves, Karin Leiderman, and Aaron Fogelson A mathematical model of platelet aggregation in an extravascular injury under flow, SIAM Multiscale Modeling and Simulation, 2020, 18, 1489-1524.

Kathryn G. Link, Michael T. Stobb, Dougald M. Monroe, Aaron L. Fogelson, Keith B. Neeves, Suzanne S. Sindi, Karin Leiderman, Computationally Driven Discovery in Coagulation, Arteriosclerosis, Thrombosis, and Vascular Biology, 2021 41:79-86.

This work is in collaboration with Katie Link (UC, Davis), Karin Leiderman (Colorado School of Mines), Keith Neeves (CU Medical Center, Denver) and others, and is supported in part by NHLBI Grant 1 R01 HL151984-01.

2) Integrating our models of fibrin polymerization with our models of platelet deposition and coagulation under flow during arterial thrombosis, to produce a more comprehensive model of the clot formation process. This work builds on:

Aaron L. Fogelson, Anna C. Nelson, Cheryl Zapata-Allegro, James P. Keener, Development of Fibrin Branch Structure Before and After Gelation, SIAM Journal on Applied Mathematics, 2021, accepted.

Aaron L. Fogelson, Yasmeen H. Hussain, and Karin M. Leiderman, Blood Clot Formation Under Flow: The Importance of Factor XI on Thrombin Production Depends Strongly on Platelet Count, Biophysical Journal, 2012, 102, 10-18.

This work is in collaboration with Anna Nelson (Duke) and was supported in part by NHLBI Grant R01HL120728.

3) Adding new TPFI- and antithrombin-mediated inhibition mechanisms to the model used in our previous arterial thrombosis models. This work builds on our previous work in:

Karin Leiderman, William Chang, Mikhail Ovanesov, Aaron L. Fogelson, Synergy Between Tissue Factor and Factor XIa in Initiating Coagulation, Arteriosclerosis, Thrombosis, and Vascular Biology, 2016, 36, 2334-2345.

Andrew L. Kuharsky and Aaron L. Fogelson, Surface-mediated Control of Blood Coagulation: The Role of Binding Site Densities and Platelet Deposition, Biophysical Journal, 80, (2001), 1050-1074.

This work is in collaboration with Karin Leiderman and Kenji Miyazawa and is funded in part by NHLBI Grant R01HL151984-01.

4) Developing PDE-based models of thrombus formation on moving cardiac structures including the walls of the left-atrial appendage (for studying clot formation during atrial fibrillation) and on bio-prosthetic aortic valve replacements for studying thrombus formation on valve leaflets. This atrial fibrillation work is in collaboration with Boyce Griffith (UNC), Craig Henriquez (Duke), Aaron Barrett (Utah) and others, supported by NHLBI Grant 1U01HL143336, and the aortic valve replacement work is in collaboration with Boyce Griffith (UNC), Arash Kheradvar (UCI), Aaron Barrett (Utah) and others. Initial work on these projects is described in:

Aaron Barrett, Aaron L. Fogelson, Boyce E. Griffith, A Hybrid Semi-Lagrangian Cut Cell Method for Advection-Diffusion Problems with Robin Boundary Conditions in Moving Domains', Journal of Computational Physics, 2022, 449, 110805.

Aaron Barrett, Jordan Brown, Aaron L. Fogelson, Boyce E. Griffith, An Immersed Boundary Model of Aortic Stenosis with Biochemical Interactions, 2021, submitted.

5) Developing two-phase continuum PDE models of platelet deposition in arteries to study clot development under high shear conditions in coronary arteries and elsewhere as described in:

Jian Du, Elise Aspray, Aaron L. Fogelson, Computational Investigation of Platelet Thrombus Mechanics and Stability in Stenotic Channels, Journal of Biomechanics, 2021, 222, 110398.

Jian Du, Dongjune Kim, Ghadah Alhawael, David N. Ku, Aaron L. Fogelson, Clot Permeability, Agonist Transport, and Platelet Binding Kinetics in Arterial Thrombosis, Biophysical Journal, 2020,119:2102-2115.

Jian Du and Aaron L. Fogelson, A two-phase mixture model of platelet aggregation, Mathematical Biology and Medicine, 2018, 35, 225-256. doi: 10.1093/imammb/dqx001.

This work is in collaboration with Jian Du (Florida Tech) and David N. Ku (Georgia Tech) and is supported by NSF Grant DMS-1716898.

6). Developing models of platelet interactions with biomaterial surfaces to study the effects of upstream priming on downstream adhesion and using the models to analyze experiments from the Hlady lab.

Shekh Rahman, Aaron L. Fogelson, Vladimir Hlady, Effects of elapsed time on downstream platelet adhesion following transient exposure to elevated upstream shear forces, 2020, Colloids and Surfaces B: Biointerfaces, 193:111118.

Colin D. Eichinger, Aaron L. Fogelson, Vladimir Hlady, Functional assay of antiplatelet drugs based on margination of platelets in flowing blood, Biointerphases, 2016, 11, 029805.

This work is in collaboration with Vladimir Hlady (Utah), Shekh Rahman (Utah), and Andrew Watson (Utah) and has been supported by NHLBI Grant R01HL126864.

7). Developing models of the intracellular regulation of ADP-receptor-mediated platelet integrin receptor activation.

This work is in collaboration with Wolfgang Bergmeier (UNC) and Keshav Patel (Utah).

8). Developing three-dimensional immersed-boundary based fluid-structure interaction models of platelet interactions with red blood cells and with the topography of the vascular wall. This work is described in:

Andrew Kassen, Aaron Barrett, Varun Shankar, Aaron L. Fogelson, Immersed boundary simulations of cell-cell interactions in whole blood, Journal of Computational Physics, 2021, submitted.

Andrew Kassen, Varun Shankar, Aaron L. Fogelson, A fine-grained parallelization of the immersed boundary method, 2020, International Journal of High-Performance Computing Applications, accepted.

This is in collaboration with Andy Kassen (Utah), Aaron Barrett (Utah), and Varun Shankar (Utah) and has been supported in part by NSF Grant DMS-1521748 and NHLBI Grant 1U01HL143336.

Prior Work on Blood Clotting Modeling