Publication: Ultrasound detection of externally induced microthrombi cloud formation: a theoretical study
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2010
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Springer
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A mathematical model for the formation of microaggregates (microthrombi) of fibrin polymers in blood flow is considered. It is assumed that the former are induced by an external source (which may be of inflammatory or tumor nature) located in a tissue near the vessel. In either case, specific agents (e.g. cytokines) are emitted from that pathological site. Such substances permeate through the vessel wall to act as primary activators of blood coagulation. A mathematical criterion to describe the formation of an intravascular microthrombi cloud, which is interpreted as an early indicator of subsequent macroscopic thrombi formation is discussed. Such criteria are compared with available experimental detection tests for microthrombi cloud formation by means of ultrasound techniques. Moreover, a similarity-type relation is proposed that links the location of the unfolding microthrombi cloud and the place at which such primary activator reaches the vessel wall.
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Goethe JW (1906) Faust, Part 1 (trans: Swanwick A). George Routledge & Sons, London
McFarlane RG (1966) The basis of the cascade hypothesis of blood clotting. Thromb Diath Haemorrh 15:591–602
Davie EW (1995) Biochemical and molecular aspects of the coagulation cascade. Thromb Haemost 74(1):135–153
Hockin MF, Jones KC, Everse SJ et al (2002) A model for the stoichiometric regulation of blood coagulation. J Biol Chem 277:18322–18333
Beltrami E, Jesty J (1995) Mathematical analysis of activation thresholds in enzyme-catalyzed positive feedbacks: application to the feedbacks of blood coagulation. PNAS 92(19):8744–8748
Ataullakhanov FI, Guria GT (1994) Spatial aspects of human blood clotting dynamics I. Hypothesis. Biophysics 39:89–96
Ataullakhanov FI, Guria GT, Safroshkina AYu (1994) Spatial aspects human blood clotting dynamics II. Phenomenological model. Biophysics 39:979–1068
Ataullakhanov FI, Guria GT, Sarbash VI et al (1998) Spatiotemporal dynamics of clotting and pattern formation in human blood. Biochim Biophys Acta 1425:453–468
Tyurin KV, Khanin MA (2006) Hemostasis as an optimal system. Math Biosci 204:167–184
Wagenvoord R, Hemker PW, Hemker HC (2006) The limits of simulation of the clotting system. J Thromb Haemost 4:1331–1338
Guy RD, Fogelson AL, Keener JP (2007) Fibrin gel formation in a shear flow. Math Med Biol 24:111–130
Guria GTh, Herrero MA, Zlobina KE (2009) A mathematical model of blood coagulation induced by activation sources. Discr Cont Dyn Syst A 25(1):175–194
Mikell FL, Asinger RW, Elsperger KJ et al (1982) Regional stasis of blood in the dysfunctional left ventricle: echocardiographic detection and differentiation from early thrombosis. Circulation 66(4):755–763
Uzlova SG, Guria KG, Shevelev AA et al (2008) Acustically detected intravascular micro-clots as predictors of thrombotic postoperative complications (Russian). In: Bulletin of A.N. Bakilev’s National Centre for Cardiovascular Surgery NCSSH, Cardiovascular diseases, vol 5, pp 55–64
Huang CC,Wang SH, Tsui PH (2005) Detection of blood coagulation and clot formation using quantitative ultrasonic parameters. Ultrasound Med Biol 31(11):1567–1573
Uzlova S, Guria K, Guria GTh (2008) Acoustic determination of early stages of intravascular blood coagulation. Philos Trans R Soc A 366:3649–3661
Daniel WG, Nellessen U, Schroder E, Nonnast-Daniel B, Bednarski P, Nikutta P, Lichtlen PR (1988) Left atrial spontaneous echo contrast in mitral valve disease: an indicator for an increased thromboembolic risk. J Am Coll Cardiol 11(6):1204–1211
Zlobina KE, Guria GTh (2006) Acoustically detected intravascular microaggregation phenomenon caused by pathological processes in tissue. Mathematical model. Similarity laws (Russian). Thromb Hemost Rheol 2:3–14
De Cicco M (2004) The prothrombotic state in cancer: pathogenic mechanisms. Crit Rev Oncol Hematol 50:187–196
Levi M, van der Poll T, BüllerHR (2004) Bidirectional relation between inflammation and coagulation. Circulation 109:2698–2704
Esmon CT (2004) Interactions between the innate immune and blood coagulation systems. Trends Immunol 25(10):536–542
Levi M (2009) Disseminated intravascular coagulation in cancer patients. Best Pract Res Clin Haematol 22(1):129–136
Kumar R, Gupta V (2008) Disseminated intravascular coagulation: current concepts. Indian J Pediatr 75(7):733–738
Schmeltzer JWP (2008) Nucleation theory and applications. Dubna, JINR
Jones KC, Mann KG (1994) A model for tissue factor pathway to thrombin. J Biol Chem 269(37):23367–23373
Qiao YH, Liu LJ, Zeng YJ (2005) A kinetic model for simulation of blood coagulation and inhibition in the intrinsic path. J Med Eng Technol 29(2):70–74
Zhu D (2007) Mathematical modeling of blood coagulation cascade: kinetics of intrinsic and extrinsic pathways in normal and deficient conditions. Blood Coagul Fibrinolysis 18(7):637–646
Turing AM (1952) The chemical basis of morphogenesis. Philos Trans R Soc Lond B Biol Sci 237(641):37–72
Gierer A, Meinhardt H (1972) A theory of biological pattern formation. Kybenetik 12:30–39
Meinhardt H (1982) Models of biological pattern formation. Academic Press, London
Murray JD (2003) Mathematical biology II. Springer, New York
Fisher RA (1937) The wave of advance of advantageous genes. Ann Eugen 7:353–369
Kolmogorov AN, Petrovskii IG, Piskunov NS (1937) Study of the diffusion equation with growth of the quantity of matter and its application to a biology problem. In: Bulletin de l’universite d’Etat a Moscou, Serie internationale, SectionA1, pp 1–25 (translation from French to English in: Pelce P (ed) (1988) Dynamics of curved fronts. Academic Press, Boston)
Mikhailov AS (1994) Foundations of synergetics I. Distributed active systems, 2nd edn. Springer, Berlin
Ataullakhanov FI, Zarnitsyna VI, Kondratovich AYu, Sarbash VI (1997) A new class of stopping self-sustained waves: a factor determining the spatial dynamics of blood coagulation. Physics-Uspekhi (Adv Phys Sci) 172(6):671–690
Smoluchowski M (1917) Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen. Z Phys Chem 92:124–168
Chandrasekhar S (1943) Stochastic problems in physics and astronomy. Rev Mod Phys 1:1–91
Friedlander SK (2000) Smoke, dust and haze: fundamentals of aerosol dynamics. Oxford University Press, New York
Stockmayer WH (1943) Theory of molecular size distribution and gel formation in branched-chain polymers. J Chem Phys 11(2):45–55
Leyvraz F, Tschudi HR (1981) Singularities in the kinetics of coagulation processes. J Phys A 14:3389–3405
Herrero MA, Rodrigo MR (2007) Remarks on accessible steady status for some coagulation-fragmentation systems. Discr Cont Dyn Syst A 17:541–552
Wiltzius P, Dietler G, Kanzing W et al (1982) Fibrin aggregation before sol–gel transition. Biophys J 38:123–132
Flory PJ (1941) Molecular size distribution in three dimensional polymers. I. Gelation. J Am Chem Soc 63:3038–3090
Van Dongen P, Ernst MH (1984) Kinetics of reversible polymerization. J Stat Phys 37:301–329
Shaw SM, Kimmey MB (2000) General principles of endoscopic ultrasonographic imaging. Tech Gastrointest Endosc 2(2):50–55
Hill CR, Bamber JC, ter Haar GR (eds) (2004) Physical principles of Medical ultrasonics. Wiley, Chichester
Volkenstein MV (1977) Molecular biophysics. Academic press, New York
Sandkühler P, Sefcik J, Morbidelli M (2004) Kinetics of gel formation in dilute dispersions with strong attarctive particle interactions. Adv Colloid Interface Sci 108(109):133–143
Rickles FR, Falanga A (2001) Molecular basis for the relationship between thrombosis and cancer. Thromb Res 102:V215–V224
Zwaal RFA, Hemker HC (eds) (1986) Blood coagulation. Elsevier, Amsterdam
FitzHugh R (1955) Mathematical models of threshold phenomena in the nerve membrane. Bull Math Biophys 17:257–278
Keener J, Sneyd J (1998) Mathematical physiology. Springer, New York
Kolobov AV, Gubernov VV, Polezhaev AA (2009) Autowaves in a model of growth of an invasive tumor. Biofizika 54(2):334–342
Zel’dovich YaB, Frank-Kamenenetzki DA (1938) A theory of thermal propagation of flame. Acta Physicochim U.S.S.R IX(2):341–350 (in Russian) (English translation in Pelce P (ed) (1988) Dynamics of curved fronts. Academic Press, Boston)
Fife PC, Mc Leod JB (1977) The approach of solutions of nonlinear diffusion equations to travelling front solutions. Arch Ration Mech Anal 65:335–361
Fife PC, Mc Leod JB (1981) A phase plane discussion of convergence to travelling fronts for nonlinear diffusion. Arch Ration Mech Anal 75:281–314
Belintsev BN, Dibrov BF, Livshits MA et al (1978) Nonlinear stability in distributed trigger system. Biological barrier. Biofizika (Russian) 23(5):864–869
Lobanov AI, Starozhilova TK, Guria GT (1997) Numerical investigation of pattern formation in blood coagulation. Matematichaskoe Modelirovanie (Russian) 9(8):83–95
Barenblatt GI (1996) Scaling, self-similarity, and intermediate asymptotics. Cambridge University Press, New York
Liggett JM (1994) Fluid mechanics. McGraw Hill, New York
Anderson JDJr (1995) Computational fluid dynamics: the basics with applications. McGraw-Hill, New York
Hagen CHL (1839) Uber die Bewegung des Wassers in engen cylindrischen Rohren. Ann Phys Chem 42:423–442
Poiseuille J (1840) Recherches experimentelles sur le mouvement des liquids dans les tubes de tres petits diametres. Comptes Rendus 11:961–1041
Schmidt RF, Tews G (eds) (1989) Human physiology, 2nd edn. Springer, Berlin
DeBakey ME (1997) New living heart. Adams, Holbrook
Guyton AC, Hall JE (2000) Textbook of medical physiology. WB Saunders, Philadelphia
Ataullakhanov FI, Volkova RI, Guriya GT, Sarbash VI (1995) Spatial aspects of the dynamics of blood coagulation. III. Thrombus growth in vitro. Biophysics 40:1320–1328
Kastrup CJ, Runyon MK, Shen F, Ismagilov RF (2006) Modular chemical mechanism predicts spatiotemporal dynamics of initiation in the complex network of hemostasis. PNAS 103(43):15747–15752
Brown EB, Boucher Y, Nasser S, Jain RK. (2004) Measurement of macromolecular diffusion coefficients in human tumors. Microvasc Res 68(3):313–314
Ramanujan S, Pluen A, McKee TD, Brown EB, Boucher Y, Jain RK (2002) Diffusion and convection in collagen gels: implications for transport in the tumor interstitium. Biophys J 83(3):1650–1660
Lewis SD, Shields PP, Shafer JA (1985) Characterization of the kinetic pathway for liberation of fibrinopeptides during assembly of fibrin. J Biol Chem 260(18):10192–10199
Weisel JW, Veklich Y, Gorkun O (1993) The sequence of cleavage of fibrinopeptides from fibrinogen is important for protofibril formation and enhancement of lateral aggregation. J Mol Biol 232:285–297
Hantgan RR, Hermans J (1979) Assembly of fibrin. A light scattering study. J Biol Chem 254(22):11272–11281
Bru A, Albertos S, Subiza JL et al (2003) The universal dynamics of tumor growth. Biophys J 85(5):2948–2961
Oran ES, Boris JB (1987) Numerical simulation of reactive flow. Elsevier Science, New York
Sherratt JA, Chaplain MAJ (2001) A new mathematical model for avascular tumour growth. J Math Biol 43:291–312
Reynolds A, Rubin J, Clermont G et al (2006) A reduced mathematical model of the acute inflammatory response: I. Derivation of model and analysis of anti-inflammation. J Theor Biol 242(1):220–236
Astanin S, Tosin A (2007) Mathematical model of tumour cord growth along the source of nutrient. Math Model Nat Phenom 2(3):153–177