The Art and Science of Building a Computational Model to Understand Hemostasis

Abstract

Computational models of various facets of hemostasis and thrombosis have increased substantially in the last decade. These models have the potential to make predictions that can uncover new mechanisms within the complex dynamics of thrombus formation. However, these predictions are only as good as the data and assumptions they are built upon, and therefore model building requires intimate coupling with experiments. The objective of this article is to guide the reader through how a computational model is built and how it can inform and be refined by experiments. This is accomplished by answering six questions facing the model builder: (1) Why make a model? (2) What kind of model should be built? (3) How is the model built? (4) Is the model a "good" model? (5) Do we believe the model? (6) Is the model useful? These questions are answered in the context of a model of thrombus formation that has been successfully applied to understanding the interplay between blood flow, platelet deposition, and coagulation and in identifying potential modifiers of thrombin generation in hemophilia A.

Fig. 1

Mathematizing biological schematics. The reaction scheme describing the binding and unbinding of activated factor VII (FVIIa) with tissue factor (TF) and the corresponding translation into mathematical equations. These equations here take the form of ordinary differential equations, meaning that they track variations in time and not in space.

Fig. 2

(Color online) Schematic of coagulation reactions included in our model. Schematic ( A ) of the reaction zone where platelet deposition and coagulation reactions are tracked, and ( B ) of the endothelial zone into which thrombin can diffuse from the reaction zone, and in which thrombin binds to thrombomodulin and produces activated protein C (APC) which can diffuse into the reaction zone. ( C ) Dashed magenta arrows show cellular or chemical activation processes. Blue arrows show chemical transport in the fluid or on a surface. Green segments with two arrowheads depict binding and unbinding from a surface. Rectangular boxes denote surface-bound species. Solid black lines with open arrows show enzyme action in a forward direction, while dashed black lines with open arrows show feedback action of enzymes. Red disks show chemical inhibitors. APC, activated protein C; AT, antithrombin; EC, endothelial cell; PC, protein C; TF, tissue factor; TM, thrombomodulin. Image Courtesy: Link et al.

Fig. 3.

(Color online) Thrombin concentration dynamics under flow generated by varying plasma zymogen and anticoagulant levels under normal ( A ) and severe factor VIII (FVIII) deficiency ( B ) conditions. Data represents 110,000 simulations where levels were uniformly varied from 50% to 150% of the population mean values. The mean (solid black line) and boundaries that encompass 50% of the data (pink), and 90% of the data (orange), and the maximum/minimum of all solutions (gray-dashed). The surface tissue factor concentration in ( A ) is 15 and in ( B ) is 5 fmol/cm ² . Image Courtesy: Link et al.