Automated reduction of blood coagulation models

Abstract

Mathematical modeling of thrombosis typically involves modeling the coagulation cascade. Models of coagulation generally involve the reaction kinetics for dozens of proteins. The resulting system of equations is difficult to parameterize, and its numerical solution is challenging when coupled to blood flow or other physics important to clotting. Prior research suggests that essential aspects of coagulation may be reproduced by simpler models. This evidence motivates a systematic approach to model reduction. We herein introduce an automated framework to generate reduced‐order models of blood coagulation. The framework consists of nested optimizations, where an outer optimization selects the optimal species for the reduced‐order model and an inner optimization selects the optimal reaction rates for the new coagulation network. The framework was tested on an established 34‐species coagulation model to rigorously consider what level of model fidelity is necessary to capture essential coagulation dynamics. The results indicate that a nine‐species reduced‐order model is sufficient to reproduce the thrombin dynamics of the benchmark 34‐species model for a range of tissue factor concentrations, including those not included in the optimization process. Further model reduction begins to compromise the ability to capture the thrombin generation process. The framework proposed herein enables automated development of reduced‐order models of coagulation that maintain essential dynamics used to model thrombosis.

Uncertainty quantification of a thrombosis model considering the clotting assay PFA‐100®

“…When considering the closure percentage and the thrombus volume QoIs, a series of PCE meta-models were constructed, one for each time step at which the QoI was saved during the simulations (for more information in timedependent generalized polynomial chaos the reader is referred to the work of Gerritsma et al 67 ). For the closure percentage the non-zero PCE coefficients range from , on the other hand, for the thrombus volume QoI the range is [13][14][15][16][17][18][19][20][21][22][23]. To cross-validate the model for each time step, 125 points were sampled using the quasi-random Sobol' sequence, of which 120 points were used for the training set to build the surrogate model and five points used as the test set.…”

“…These models span several degrees of complexity, from simple flow characteristic indices to complicated, coupled biochemical interactions. Mechanistic models, for example, may contain equations that describe shear dependent platelet activity including adhesion, aggregation, and activation 13–15 ; hemodynamics that regulate the transport of biochemical species 16,17 ; and/or coagulation reactions that lead to the formation of fibrin 18–20 . Increasing modeling complexity improves the fidelity and versatility of the model, but the computational cost of the simulation escalates.…”

“…Mechanistic models, for example, may contain equations that describe shear dependent platelet activity including adhesion, aggregation, and activation [13][14][15] ; hemodynamics that regulate the transport of biochemical species 16,17 ; and/or coagulation reactions that lead to the formation of fibrin. [18][19][20] Increasing modeling complexity improves the fidelity and versatility of the model, but the computational cost of the simulation escalates. In addition, increasing detail introduces additional uncertainties that can have a great impact on its accuracy.…”

Data-driven cardiovascular flow modelling: examples and opportunities

“…Finally, the governing equations for the dynamical system could be written for each state x k as _ x k (t) ¼ Q(X)z k : (9:5) Modelling the fluid mechanics of thrombosis (blood clot formation) requires solving large systems of advectiondiffusion-reaction equations. It is highly desirable to identify reduced-order thrombosis models from data to simplify thrombosis simulations [109]. Given the temporal evolution of the prominent biochemicals involved in thrombosis, is it possible to identify the governing equations for the reaction kinetics?…”

Data-driven cardiovascular flow modeling: examples and opportunities

“…Problem statement: Modeling the fluid mechanics of thrombosis (blood clot formation) requires solving large systems of advection-diffusion-reaction equations. It is highly desirable to identify reduced-order thrombosis models from data to simplify thrombosis simulations [99]. Given the temporal evolution of the prominent biochemicals involved in thrombosis, is it possible to identify the governing equations for the reaction kinetics?…”