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Biomedical Applications of Mathematics in Cardiocirculatory Physiology

This course explores the application of mathematical principles in understanding and analyzing various aspects of cardiocirculatory physiology. Topics include cardiac anatomy, physiological functions, clinical applications, and the role of electrical activity in the heart. Suitable for clinicians and cardiologists.

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Biomedical Applications of Mathematics in Cardiocirculatory Physiology

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  1. III CourseBiomedical Applications of MathematicsElements of cardiocirculatoryphysiology Roberto Bonmassari S.C. di Cardiologia APSS-Ospedale Santa Chiara Trento

  2. Preamble A Course of Biomedical Applications of Mathematics ……when the Hospital goes out and meet the University I’m not a physiologyst I am a clinician, a cardiologist

  3. Agenda Three lessons: 7-9-21 october 2015 (five hours) Aspects of cardiac anathomy The cardiac and circolatory function: phisiologic aspects Examples of clinical application of a phisiologic application in a pathologic condition: coronary stenosis and aortic stenosis

  4. The heart is costituted from 4 chambers:2 atria (right and left)2 ventricles (right and left)

  5. Atriarecive blood,Ventricleseject blood

  6. POLMONE CUORE ORGANI Scambio Gassoso Piccolo Circolo Funzione di Pompa Grande Circolo Consumo di Ossigeno

  7. The Heartis a pump The cardiac pump is the ground of the circulation The are two circulation systems that works in series: systemic and pulmonary circulation The cardiac pump has the primary function of insurance an adeguate amount of blood flow through the systemic and the pulmonary vessel bed The cardiac pump works with two mechanisms : blood aspiration and pushing

  8. The Heartis a pump The cardiac pump produce a mechanical result (the circulation of the bood) due to the contraction and relaxation of the muscolar wall of the cardiac chambers (ventriculi and atria) But what is the primum movens of the cardiac function? Upstrem the mechanical function is necessary the electric function: the electric excitation

  9. The conduction system: Physiology and pathology Nodo del seno Nodo atrio-ventricolare Fascio di His Branca sinistra Branca destra Fibre di Purkinje

  10. The Heartis a pump The cardiac electrical activity is an automatic activity Is only marginally influenced by nervous system These are the basis of the electro-mechanical coupling partneship

  11. Arterial Pressure Curve Ventricular Ejection Phase Atrial Systole Ventricular Filling Isovolumetric Contraction Isovolumetric Relaxation 120 Semi-Lunar Valve Closes Semi-Lunar Valve Opens 100 Arterial Pressure 80 60 Pressure (mm Hg) 40 AV Valve Closes AV Valve Opens 10 Ventricular Pressure 0 R Electrocardiogram T P S Q Atrial Systole Ventricular Systole Diastole Approx. Time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 The cardiaccycle Fasi 1 contrazione Vs 2 rilasciamento Vs 3 riempimento Vs Ciclo di Wiggers 1915 1 2 3 3

  12. Ventricular Ejection Phase Atrial Systole Ventricular Filling Isovolumetric Contraction Isovolumetric Relaxation 120 Semi-Lunar Valve Closes Semi-Lunar Valve Opens 100 Arterial Pressure 80 60 Pressure (mm Hg)‏ 40 AV Valve Closes AV Valve Opens 10 Ventricular Pressure 0 R Electrocardiogram T P S Q Atrial Systole Ventricular Systole Diastole Approx. Time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Arterial Pressure Curve

  13. The cardiac cycle pressure/volume V sin ratio

  14. Ventricular Ejection Phase Atrial Systole Ventricular Filling Isovolumetric Contraction Isovolumetric Relaxation 120 Semi-Lunar Valve Closes Semi-Lunar Valve Opens 100 Arterial Pressure 80 60 Pressure (mm Hg)‏ 40 AV Valve Closes AV Valve Opens 10 Ventricular Pressure 0 R Electrocardiogram T P S Q Atrial Systole Ventricular Systole Diastole Approx. Time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Ventricular Filling Arterial Pressure Curve

  15. Ventricular Ejection Phase Atrial Systole Ventricular Filling Isovolumetric Contraction Isovolumetric Relaxation 120 Semi-Lunar Valve Closes Semi-Lunar Valve Opens 100 Arterial Pressure 80 60 Pressure (mm Hg)‏ 40 AV Valve Closes AV Valve Opens 10 Ventricular Pressure 0 R Electrocardiogram T P S Q Atrial Systole Ventricular Systole Diastole Approx. Time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Arterial Pressure Curve Atrial Systole

  16. Ventricular Ejection Phase Atrial Systole Ventricular Filling Isovolumetric Contraction Isovolumetric Relaxation 120 Semi-Lunar Valve Closes Semi-Lunar Valve Opens 100 Arterial Pressure 80 60 Pressure (mm Hg)‏ 40 AV Valve Closes AV Valve Opens 10 Ventricular Pressure 0 R Electrocardiogram T P S Q Atrial Systole Ventricular Systole Diastole Approx. Time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Arterial Pressure Curve Isovolumetric Contraction

  17. Ventricular Ejection Phase Atrial Systole Ventricular Filling Isovolumetric Contraction Isovolumetric Relaxation 120 Semi-Lunar Valve Closes Semi-Lunar Valve Opens 100 Arterial Pressure 80 60 Pressure (mm Hg)‏ 40 AV Valve Closes AV Valve Opens 10 Ventricular Pressure 0 R Electrocardiogram T P S Q Atrial Systole Ventricular Systole Diastole Approx. Time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Ventricular Ejection Arterial Pressure Curve

  18. Ventricular Ejection Phase Atrial Systole Ventricular Filling Isovolumetric Contraction Isovolumetric Relaxation 120 Semi-Lunar Valve Closes Semi-Lunar Valve Opens 100 Arterial Pressure 80 60 Pressure (mm Hg)‏ 40 AV Valve Closes AV Valve Opens 10 Ventricular Pressure 0 R Electrocardiogram T P S Q Atrial Systole Ventricular Systole Diastole Approx. Time 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Arterial Pressure Curve Isovolumetric Relaxation

  19. Left 300 200 Coronary Blood Flow (ml/min)‏ Right 100 0 Diastole Systole Slide courtesy of A.C. Guyton, MD, Textbook of Medical Physiology, Sixth Edition, 1981 W.B. Saunders Company

  20. Howis the Cardiacfunction?Cardiac output and pressure CO= Pr / R= SV x HR Legenda Pr = systemicpressure R = systemicresistance SV = stroke volume (amountofbloodejectevery beat) HR = numberofbeats per minute

  21. Cardiacfunction = CODeterminants Cardiac rate Inotropic condition = contractility Venus return (RV): influenced from neuroumoral factors (Frank-Starling law) Peripheric resistance = CARDIAC OUTPUT 4-6 l/min CARDIAC INDEX 1.6-2.5 l/min/m²

  22. Cardiac output = CO CO= Pr / R= SV x HR examples : Increase of FC -> does not increase GC, decrease of the VOLUME SYSTOLE-SV (if Rv does not increase) Increase of RV -> increases GC 10-20% (increase of Pa A dx 10 mmHg) Increase of FC + increase of RV -> increases GC with = SV Stirring adrenergethic -> increases RV + increase of the function of the pump (HR, contract?) = INCREASES GC Important reduction of FC or alteration of V dx -> increase of Pa A dx = barrier for the venous comeback Organs are able to change their flow working on the oppositions; they are able to regulate the distribution of the CARDIAC RANGE.

  23. Cardiacfunction:Frank-Starlingmechanism

  24. Cardiacfunction:CO-CI & R ; Conduttance= 1/R

  25. Vascularresistance The vascular regulation is a local methabolic process in all organs, a part in kidney and skin. In fact even if in a denervation condition these organs are able to matain a adequate vascular tone modificated by methabolic influences. Flow depend closely by the radius R = L x h8/ x r4 10% in reduction diameter vessel = 50% in increase resistance

  26. diastolica Difetto di riempimento sistolica sistolica Difetto di espulsione

  27. Cardiacpower outputVentricularfunctionindex Cardiac Power output=MAP x CO= SW X HR

  28. Cardiacpower output

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