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Simulations of Model Pacemaker VI1 and Cardiorythmor


Ceci est la modélisation mathématique et électrique du coeur avec des équations ODE non linéaires de dimension 2 et 3. La simulation avec matlab et runge kutta montre les phénomènes cardiaques, chaos et bifurcation. Cet ouvrage est le premier volume d?une série de trois.

M. NDao vient du 3e cycle électronique, section traitement de l'information et automatique de l?université Orsay Paris en 1978 et INSTN Saclay. Il était allocataire boursier DGRST de 1977 à 1979 au projet d'automatisation de la source d'ion cryebis à l'Institut de physique nucléaire d'Orsay, service des accélérateurs, en collaboration avec le laboratoire Saturne 2 Saclay CEA 1978.

It is a mathematical and electrical modelization of the cardiac cells and the heart parametrized with ODE equations of dimension 2 and 3 of non linear equations. The computation with matlab and runge kutta shows simulations of all the cardiac phenomenon ,chaos and bifurcation, in this volume 1 other 3.

From 3rd cycle electronic section treatment of information and automatic university Orsay Paris 1979,grant student DGRST France from 1977 to 1979 to automatization of ion source cryebis project in Nuclear Institute of Orsay IN2p3 and labo Saturne 2 CEA Saclay.

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 INTRODUCTION In 1992 i was inspirated,reading the text ofBalth Van Der Polabout relaxation oscillation.Balth Van Der Pol is first to propose a cardiac  simulator with electronic tubes at year 1928.The 24 may 1928,Balth  Van Der Pol gives a conference at paris,invited be the biologycal  society and the electrical society of France.The integral text of the con&  ference is published at journal Onde Electrique,and,intituled,the heart  can be considered like a relaxation oscillation and an electrical model  of the heart.At this time of 1992,my min dis kept on by the diable of  heart and relaxation oscillation.So i have on mind to discover acardiac  simulator,like Balth Van Der Pol,and i will call it,cardiorythmor.My  dream is realized in 2005 when i publish in France 2 patents on an elec&  tronic and machanic cardiac simulator.(seewww.inpi.fr,www.espacenet.  com).I begin to study the cardiac cells electrophysiology,so i find for the  first time tje names of,A.L.Hodgkin and A.F.Huxley.Hodgkin and Huxley  was first to propose a mathamatical model ,and an electrical model for the  cardiac cells in 1952.Latter in 1962 they receive the nobel price for his  work.For learning cardiac electrophysiology i request to be integrated in  clinical cardiology of Dantec hospital in dakar senegal. Si i would like to  express my great thanks to DR Semou diouf,Moustapha sarr,Bara Ibrahima  diop,Fallou cisse,Gora seck,and Ba.  A)in the volume 1 i present the theoritical basic foundation of what would  be the cardiac science theory,when we apply the results of dynamic system,  stability,existence of periodic solution,existence of hysterisis cycle,existen&  ce of chaos,and to verify with my models all the properties of the heart,and  to observe in simulations all the knowed phenomenon of the heart and the  unknowed.I propose a parametrized mathematical model and an associated  electrical circuit,called themodel pacemaker VI1,in non linear ODE  equations, dV/dt=P(V,I1,K)  dI1/dt=Q(V,I1,K) Where V is the potential of the membrane cells,I1 is an excitable variable  and K is the set of 8 cardiac parameters.I proove the existence of stable  periodic solution,the existence of chao and bifurcation,and observe in  simulations all the properties of the heart like,electrical stimulation,and  blocks.The model is integrated with runge kutta 4 and matlab software  R2007a.
 To take in consideration the existence of basic ion currents,Na forso+  dium,and ,K for potassium,I propose themodel pacemaker VINAIK. B)in the volume 2 i investigate chao in phase plan ofHenri Poincare,  and propose a parametrized mathematical model and electrical model  of the heart calledheart VI1. C)in the volume 3 i modelize the propagation of cardiac excitation with  PDE,partial differential equations and propose methods to construct  periodical solution and non periodical solutions.  I dedicace my work to my professors at lyon 1 and university paris orsay,  Mr Andre Blanc Lapierre,Mr Bernard Picinbono,Mr Debraine INSTN  Saclay,Mr Gabet and Mr Bonnemay.  ‘’In my life i had to have one question i really love ‘’  Bob Marley  ‘’One day,he sings at london,the next day to paris,the day after at  belgium,and the next day to spanish,working for the next day’’.  D.P.L.NDao