Mathematical Modeling and Computer Simulation in Blood Coagulation

Over the last two decades, mathematical modeling has become a popular tool in study of blood coagulation. The in silico methods were able to yield interesting and significant results in the understanding of both individual reaction mechanisms and regulation of large sections of the coagulation cascade. The objective of this paper is to review the development of theoretical research in hemostasis and thrombosis, to summarize the main findings, and outline problems and possible prospects in the use of mathematical modeling and computer simulation approaches. This review is primarily focused on the studies dealing with: (1) the membrane-dependent reactions of coagulation; (2) regulation of the coagulation cascade, including effects of positive and negative feedback loops, diffusion of coagulation factors, and blood flow.

[1]  Mark M. Meerschaert,et al.  Mathematical Modeling , 2014, Encyclopedia of Social Network Analysis and Mining.

[2]  J Jesty,et al.  The role of membrane patch size and flow in regulating a proteolytic feedback threshold on a membrane: possible application in blood coagulation. , 2001, Mathematical biosciences.

[3]  M A Khanin,et al.  A mathematical model of the kinetics of blood coagulation. , 1989, Journal of theoretical biology.

[4]  S. Levine,et al.  Enzyme Amplifier Kinetics , 1966, Science.

[5]  J M Nigretto,et al.  In vitro factor XI activation mechanism according to an optimized model of activated partial thromboplastin time test , 2001, Blood coagulation & fibrinolysis : an international journal in haemostasis and thrombosis.

[6]  Diran Basmadjian,et al.  A mathematical model of thrombin production in blood coagulation, Part I: The sparsely covered membrane case , 1994, Annals of Biomedical Engineering.

[7]  Y. Nemerson,et al.  Surface-mediated enzymatic reactions: simulations of tissue factor activation of factor X on a lipid surface. , 1995, Biophysical journal.

[8]  F I Ataullakhanov,et al.  A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. II. Results. , 1996, Thrombosis research.

[9]  F. Ataullakhanov,et al.  Initiation and propagation of coagulation from tissue factor‐bearing cell monolayers to plasma: initiator cells do not regulate spatial growth rate * , 2005, Journal of thrombosis and haemostasis : JTH.

[10]  P. Walsh,et al.  A Subpopulation of Platelets Responds to Thrombin- or SFLLRN-stimulation with Binding Sites for Factor IXa* , 2004, Journal of Biological Chemistry.

[11]  B. Furie,et al.  Real-time in vivo imaging of platelets, tissue factor and fibrin during arterial thrombus formation in the mouse , 2002, Nature Medicine.

[12]  R. Heinrich,et al.  The Regulation of Cellular Systems , 1996, Springer US.

[13]  Mikhail A Panteleev,et al.  Tissue factor pathway inhibitor: a possible mechanism of action. , 2002, European journal of biochemistry.

[14]  J. Spivak,et al.  Commentary on and reprint of Davie EW, Ratnoff OD, Waterfall sequence for intrinsic blood clotting, in Science (1964) 145:1310–1311 , 2000 .

[15]  Flora Peyvandi,et al.  The Thrombogram in Rare Inherited Coagulation Disorders: Its Relation to Clinical Bleeding , 2002, Thrombosis and Haemostasis.

[16]  Sriram Krishnaswamy,et al.  Formation of Factors IXa and Xa by the Extrinsic Pathway , 2004, Journal of Biological Chemistry.

[17]  F I Ataullakhanov,et al.  Contact Activation of Blood Coagulation : Trigger Properties and Hysteresis Kinetic Recognition of Foreign Surfaces upon Contact Activation of Blood Coagulation : A Hypothesis , 1998 .

[18]  Hans Gregersen,et al.  Dynamic model of the role of platelets in the blood coagulation system. , 2002, Medical engineering & physics.

[19]  Kumbakonam R. Rajagopal,et al.  A Model Incorporating Some of the Mechanical and Biochemical Factors Underlying Clot Formation and Dissolution in Flowing Blood , 2003 .

[20]  E. Beltrami,et al.  Mathematical analysis of a proteolytic positive-feedback loop: dependence of lag time and enzyme yields on the initial conditions and kinetic parameters. , 1993, Biochemistry.

[21]  H. Hemker,et al.  Phenotyping the Clotting System , 2002, Thrombosis and Haemostasis.

[22]  M A Khanin,et al.  Analysis of the activated partial thromboplastin time test using mathematical modeling. , 2001, Thrombosis research.

[23]  F I Ataullakhanov,et al.  [Spatial aspects of the dynamics of blood coagulation. II. Phenomenological model]. , 1994, Biofizika.

[24]  José A Fernández,et al.  Plasma Lipoproteins, Hemostasis and Thrombosis , 2001, Thrombosis and Haemostasis.

[25]  Piet Hemker,et al.  Mathematical modelling in blood coagulation ; Simulation and parameter estimation , 1997 .

[26]  E. Beltrami,et al.  Demonstration of a Threshold Response in a Proteolytic Feedback System: Control of the Autoactivation of Factor XII , 2006, Pathophysiology of Haemostasis and Thrombosis.

[27]  Y. Nemerson,et al.  An ordered addition, essential activation model of the tissue factor pathway of coagulation: evidence for a conformational cage. , 1986, Biochemistry.

[28]  H. Sauro,et al.  Control analysis of time-dependent metabolic systems. , 1989, Journal of theoretical biology.

[29]  F Keller,et al.  The quick machine--a mathematical model for the extrinsic activation of coagulation. , 1994, Haemostasis.

[30]  F. Martorana,et al.  On the kinetics of enzyme amplifier systems with negative feedback , 1974 .

[31]  P. Walsh,et al.  Factor X bound to the surface of activated human platelets is preferentially activated by platelet-bound factor IXa. , 1996, Biochemistry.

[32]  J. Rosing,et al.  Kinetic studies of prothrombin activation: effect of factor Va and phospholipids on the formation of the enzyme-substrate complex. , 1984, Biochemistry.

[33]  Mikhail A. Panteleev,et al.  Blood Coagulation and Propagation of Autowaves in Flow , 2006, Pathophysiology of Haemostasis and Thrombosis.

[34]  X. H. Xu,et al.  The kinetic model and simulation of blood coagulation--the kinetic influence of activated protein C. , 2004, Medical engineering & physics.

[35]  A. T. Bharucha-Reid,et al.  On the kinetics of enzyme amplifier systems , 1969 .

[36]  A. Lobanov,et al.  The Effect of Convective Flows on Blood Coagulation Processes , 2006, Pathophysiology of Haemostasis and Thrombosis.

[37]  V. I. Zarnitsina,et al.  Dynamics of spatially nonuniform patterning in the model of blood coagulation. , 2001, Chaos.

[38]  Interaction of feedback control and product inhibition in the activation of factor X by factors IXa and VIII. , 1991, Haemostasis.

[39]  K. Mann,et al.  "Clotspeed," a mathematical simulation of the functional properties of prothrombinase. , 1984, The Journal of biological chemistry.

[40]  Hans V Westerhoff,et al.  Control analysis for autonomously oscillating biochemical networks. , 2002, Biophysical journal.

[41]  Mikhail V Ovanesov,et al.  Hemophilia A and B are associated with abnormal spatial dynamics of clot growth. , 2002, Biochimica et biophysica acta.

[42]  W Liniger,et al.  Mathematical model of the activation of prothrombin by factor Xa and factory Vt. , 1980, Bulletin of mathematical biology.

[43]  R. Heinrich,et al.  Metabolic control analysis of relaxation processes , 1991 .

[44]  J Jesty,et al.  Mathematical analysis of activation thresholds in enzyme-catalyzed positive feedbacks: application to the feedbacks of blood coagulation. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[45]  M A Khanin,et al.  Mathematical model for the blood coagulation prothrombin time test. , 1998, Thrombosis research.

[46]  K. Mann,et al.  A model for the tissue factor pathway to thrombin. II. A mathematical simulation. , 1994, The Journal of biological chemistry.

[47]  Running pulses of complex shape in a reaction-diffusion model. , 2004, Physical review letters.

[48]  A model for analyzing the formation of thrombin in vessels. , 1994, Computers in biology and medicine.

[49]  K. C. Jones,et al.  A Model for the Stoichiometric Regulation of Blood Coagulation* , 2002, The Journal of Biological Chemistry.

[50]  Complex dynamics of the formation of spatially localized standing structures in the vicinity of saddle-node bifurcations of waves in the reaction-diffusion model of blood clotting. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  Optimality principle and determination of kinetic constants for biochemical reactions. , 2005, Mathematical medicine and biology : a journal of the IMA.

[52]  V. I. Sarbash,et al.  A new class of stopping self-sustained waves: a factor determining the spatial dynamics of blood coagulation , 2002 .

[53]  Macfarlane Rg,et al.  AN ENZYME CASCADE IN THE BLOOD CLOTTING MECHANISM, AND ITS FUNCTION AS A BIOCHEMICAL AMPLIFIER , 1964 .

[54]  K. Rajagopal,et al.  A Model for the Formation and Lysis of Blood Clots , 2006, Pathophysiology of Haemostasis and Thrombosis.

[55]  A. V. Pokhilko,et al.  Contact activation of blood coagulation: trigger properties and hysteresis. Kinetic recognition of foreign surfaces upon contact activation of blood coagulation: a hypothesis. , 1998, Journal of theoretical biology.

[56]  F. Ataullakhanov,et al.  Unstable trigger waves induce various intricate dynamic regimes in a reaction-diffusion system of blood clotting. , 2003, Physical review letters.

[57]  M. Schenone,et al.  The blood coagulation cascade , 2004, Current opinion in hematology.

[58]  Ken Lo,et al.  Stochastic Modeling of Blood Coagulation Initiation , 2006, Pathophysiology of Haemostasis and Thrombosis.

[59]  D. A. Molchanova,et al.  [A simulated mathematical model of the blood coagulation system intrinsic pathway]. , 1995, Biofizika.

[60]  R. Colman,et al.  Hemostasis and Thrombosis: Basic Principles and Clinical Practice , 1988 .

[61]  R J Leipold,et al.  Mathematical Model of Serine Protease Inhibition in the Tissue Factor Pathway to Thrombin (*) , 1995, The Journal of Biological Chemistry.

[62]  H. Nagashima.  Studies on the Different Modes of Action of the Anticoagulant Protease Inhibitors DX-9065a and Argatroban , 2002, The Journal of Biological Chemistry.

[63]  Aaron L. Fogelson,et al.  Coagulation under Flow: The Influence of Flow-Mediated Transport on the Initiation and Inhibition of Coagulation , 2006, Pathophysiology of Haemostasis and Thrombosis.

[64]  Semenov Vv,et al.  Nonlinear effects in kinetics of blood coagulation , 1990 .

[65]  R. Macfarlane.  An Enzyme Cascade in the Blood Clotting Mechanism, and its Function as a Biochemical Amplifier , 1964, Nature.

[66]  F. Ataullakhanov,et al.  Kinetics of Factor X activation by the membrane-bound complex of Factor IXa and Factor VIIIa. , 2004, The Biochemical journal.

[67]  Hans V Westerhoff,et al.  Control of spatially heterogeneous and time-varying cellular reaction networks: a new summation law. , 2002, Journal of theoretical biology.

[68]  V T Turitto,et al.  Mechanical factors affecting hemostasis and thrombosis. , 1998, Thrombosis research.

[69]  Sharene D. Bungay,et al.  A mathematical model of lipid-mediated thrombin generation. , 2003, Mathematical medicine and biology : a journal of the IMA.

[70]  A. Fogelson,et al.  Surface-mediated control of blood coagulation: the role of binding site densities and platelet deposition. , 2001, Biophysical journal.

[71]  G. Broze,et al.  Regulation of Extrinsic Pathway Factor Xa Formation by Tissue Factor Pathway Inhibitor* , 1998, The Journal of Biological Chemistry.

[72]  P. Comfurius,et al.  Lipid-protein interactions in blood coagulation. , 1998, Biochimica et biophysica acta.

[73]  J. Herbert,et al.  Contribution of Erythrocytes to Thrombin Generation in Whole Blood , 1999, Thrombosis and Haemostasis.

[74]  H C Hemker,et al.  Simulation model for thrombin generation in plasma. , 1991, Haemostasis.

[75]  S. Baldwin,et al.  Coagulation on biomaterials in flowing blood: some theoretical considerations. , 1997, Biomaterials.

[76]  A. Giles,et al.  Studies of the role of factor Va in the factor Xa-catalyzed activation of prothrombin, fragment 1.2-prethrombin-2, and dansyl-L-glutamyl-glycyl-L-arginine-meizothrombin in the absence of phospholipid. , 1990, The Journal of biological chemistry.

[77]  E. Davie,et al.  Waterfall Sequence for Intrinsic Blood Clotting , 1964, Science.

[78]  F I Ataullakhanov,et al.  A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. I. The model description. , 1996, Thrombosis research.