The Quick Machine – A Mathematical Model for the Extrinsic Activation of Coagulation

Abstract

The present paper describes a mathematical model of the kinetics of the extrinsic coagulation cascade in vitro. The coagulation factors FI, FII, FV, FVII, FX, heparin and antithrombin III (ATIII) as well as soluble fibrin polymers are considered. The effect of single-factor deficiencies of the factors II, V, VII and X, diseases like hypo- and dysfibrinogenaemia, hepatic insufficiency, inhibited polymerisation by degradation products, heparin therapy with and without ATIII deficiency and coumarin therapy on prothrombin time can be portrayed. Physiology of coagulation is represented in a dynamic mathematical model as a differential equation system. The model is based on three reaction types: enzymatic cleavage, complex formation and polymerisation. The model was implemented in a continuous simulation program on a personal computer using the Pascal programming language. Unknown rate constants were estimated by χ² fit. Prothrombin time calculated by the model was compared to the training set of 20 plasma samples. In most but not all cases the model harmonized quite well with the coagulometric data.

A Model Incorporating Some of the Mechanical and Biochemical Factors Underlying Clot Formation and Dissolution in Flowing Blood

“…Models of greater complexity, which brought together the kinetics of various sets of reactions and included feed back loops and inhibitors under different reaction conditions (like flow, extent of stimulus, etc. ), emerged towards the late 1980s (Khanin and Semenov, 1989;Willems et al, 1991;Jesty et al, 1993;Baldwin and Basmadjian, 1994;Jones and Mann, 1994;Pohl et al, 1994). This trend has continued with the emergence of models characterized by extremely large systems of equations (ODEs or reaction-diffusion equations) with inclusion of a greater number of aspects (flow rates, membrane binding site densities, availability of phospholipid sites, concentration of calcium, extent of activating stimulus, etc.)…”

A Systems Pharmacology Model for Predicting Effects of Factor Xa Inhibitors in Healthy Subjects: Assessment of Pharmacokinetics and Binding Kinetics

“…Until now, it is still difficult to apply published coagulation models to predict the results of laboratory coagulation tests for PT, aPTT, and anti‐FXa assays simultaneously. One reason is that the involved pathways or numerical estimates of rate constants are uncertain 33. Even when biochemical pathways have been measured, a wide variety of values may exist for a given parameter.…”

“…In this study, the model equations partially overlap with equations used in the reported models 33, 34. We started with a comprehensive coagulation model,34 but performed model reduction and extension.…”

Mathematical Models of Blood Coagulation and Platelet Adhesion: Clinical Applications

“…These models also served as the basis for computer studies of drugs in clotting assays, which is discussed in the section "Drug design and therapeutic strategy planning". One of the promising areas of model applications is determination of individual factor concentrations and reaction rate constants from general assays [16,30] that can be useful for diagnostics of coagulation disorders and drug evaluation. On the other hand, the existing models include a number of critical assumptions and are not always able to give a quantitative description of experimental results, which limits their wide practical use.…”