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Ph.D. Thesis]: Leiden University University of Calabria Faculty of Engineering Department of Mechanical Engineering INVESTIGATING THE INTERACTION BETWEEN THE CARDIOVASCULAR SYSTEM AND AN AXIAL FLOW VENTRICULAR ASSIST DEVICE: MATHEMATICAL MODEL AND AN ACUTE ANIMAL STUDY Coordinator Prof. Maria Laura Luchi Candidate Supervisors Francesco Moscato Prof. Guido A. Danieli Prof. Heinrich Schima Dissertation submitted to obtain the degree of Doctor in Mechanical Engineering (ING-IND 34) Academic Year 2006/2007 Dissertation submitted to obtain the degree of Doctor in Mechanical Engineering (ING-IND 34, Industrial Bioengineering) – Academic Year 2006/2007 – XX cycle Department of Mechanical Engineering University of Calabria Via Ponte P. Bucci, Cubo 44/C 97036 Arcavacata di Rende (CS) ITALY Correspondence to: [email protected] [email protected] This research work has been conducted in collaboration with the Medical University of Vienna (Austria), Center for Biomedical Engineering and Physics and the Ludwig- Boltzmann-Cluster for Cardiosurgical Research (Prof. Heinrich Schima) © Parts of this book may be reproduced if accompanied by clear reference to the source. Suggested citation: Moscato F. Investigating The Interaction Between The Cardiovascular System And An Axial Flow Ventricular Assist Device: Mathematical Model And An Acute Animal Study. PhD dissertation. University of Calabria; 2007. To my family. To everybody and to every emotion, passion and experience that you can only find and read in the white space between the lines of this manuscript. Table of Contents Symbols used in text I Abbreviations and acronyms III Introduction IV Introduzione (in italiano) VI Chapter 1 1 Introduction to cardiovascular physiology and mechanical circulatory assist devices. Physiology and Pathology of Heart and Circulation 2 Anatomy of heart and circulation 2 Cardiac mechanics 4 Ventricular Preload and Afterload 8 Stroke work, mechanical efficiency, wall stress 10 Vascular system 12 Input vascular impedance 13 Systemic arterial load 14 Pulmonary arterial load 15 Cardiac output regulation 16 Circulatory, systemic and pulmonary mean pressures 17 Patterns of cardiac output curves 18 Patterns of venous return curves 20 Mathematical equations for the venous return curve 22 Mathematical equations for the cardiac output curve 26 Heart failure 26 Postsurgical myocardial dysfunction 27 Cardiogenic shock resulting from acute myocardial infarction 27 Decompensated chronic heart failure 28 Acute myocarditis 28 Mechanical Circulatory Assist Devices 29 Indications for Ventricular Assist Devices support 30 Devices 31 Positive displacement pumps 31 Rotary pumps 33 Chapter 2 35 A numerical model of the cardiovascular system. Introduction 36 Model Implementation 37 Heart 37 Left ventricle 38 Right ventricle 44 Left and right atria 45 Heart valves 46 Arterial load 47 Venous returns 50 Autoregulatory mechanisms 51 Waveforms and average hemodynamic values 53 Model Validation 56 Cardiac functions 56 Pressure Volume loop 57 Chapter 3 59 A hydrodynamic numerical model of the MicroMed-DeBakey VAD® : software and hardware tools used for identification. Introduction 60 Materials and Methods 61 Identification procedure and theoretical background 61 Frequency domain identification algorithms 63 Time domain identification algorithms 64 Axial flow VAD: steady state identification and theory 65 VAD Identification: experimental setup 69 Displacement Pump Identification 71 Displacement-Pump Control 79 VAD Identification: experiments performed 84 Identification experiments 84 Validation experiments 86 VAD Identification Results and Discussion 87 Results 87 Discussion 89 Cannulae Identification 90 Outflow graft identification: materials and methods 90 Outflow graft identification: results and discussion 94 Results 94 Discussion 98 Inflow cannula identification 100 Conclusions 100 Chapter 4 101 In-vivo investigation of VAD-cardiovascular system interaction: left ventricular pressure volume loop analysis during continuous cardiac assist in acute animal trials. Introduction 102 Materials and methods 102 Experimental protocol 102 Graphic User Interface 104 Theoretical considerations on the PVloop analysis 107 Statistical analysis performed 108 Results and Discussion 109 Results 109 Discussion 113 Conclusions 115 Chapter 5 116 Axial flow VAD control strategy to reduce the left ventricle afterload impedance and help perfusion. Introduction 117 Materials and methods 118 Cardiovascular system and VAD models 118 VAD control strategy 119 Estimation algorithm 121 Simulation protocol steps 121 Results 122 Discussion 126 Conclusion 127 Conclusions 129 References 130 Symbols used in text a, b = fluid resitance parameters for the VAD model Cap = arterial pulmonary compliance Cas = arterial systemic compliance Cas* = reduced arterial systemic compliance Ccp = characteristic pulmonary compliance Ccs = characteristic systemic compliance Cvp = venous pulmonary compliance Cvs = venous systemic compliance dP/dtmax = peak of ventricular pressure derivative E(t) = time-varying elastance Ea = arterial elastance Emax = maximum elastance Emin = minimum elastance Fc = Coulomb friction force Fiso(t) = ventricular/atrial elastance normalized with respect to T and Emax. Fs = static friction force Fv = viscous friction force ˆ jω GN ()e = Empirical Transfer Function Estimate H(t) = axial VAD pump head i = coil current k = spring constant Kf = force/speed coefficient kSAT = spring stiffening coefficient L = inertance parameter for the VAD model Lcp = characteristic pulmonary inertance Lcs = characteristic sytemic inertance Le = coil inductance Lv = valve inertance M = piston (and moving element) mass P0 = external ventricular/atrial pressure Pao = aortic pressure Pap = pulmonary arterial pressure Pas = arterial systemic pressure Pd = pressure at minimum ventricular volume Vd Plv = left ventricular pressure Prv = right ventricular pressure Pla = left atrial pressure Pm = ϕp parameter Pra = right atrial pressure Pvp = venous pulmonary pressure Pvs = venous systemic pressure I P* = pressure coordinate of the ϕa vertex Qilv = left ventricular inflow Qirv = right ventricular inflow Qolv = left ventricular outflow Qorv = right ventricular outflow QVAD = axial VAD pump flow Q* = flow through the Ras* (reference flow for the VAD) Rap = arterial pulmonary resistance Ras = arterial systemic resistance Ras* = reduced arterial systemic resistance Rcp = characteristic pulmonary resistance Rcs = characteristic sytemic resistance Rcs* = reduced characteristic sytemic resistance Rvp = venous pulmonary pressure Rvs = venous systemic pressure Rdir = direct valve resistance Rinv = inverse valve resistance Ri = internal ventricular resistance Re = coil resistance S = piston surface Str = piston stroke T = heart period Ui = voltage fed to the amplifier Uamp = voltage fed by the amplifier into the coil V0 = ventricular/atrial volume at zero transmural pressure Vd = minimum ventricular volume (also called dead volume) Vlv = left ventricular volume Vm = ϕp parameter Vrv = right ventricular volume Vvpo = unstretched volume of the Cvp Vvso = unstretched volume of the Cvs V* = volume coordinate of the ϕa vertex x = piston position αω = speed-related parmeter for the VAD model α = ϕp parameter β = ϕp parameter Δv = zero velocity interval ϕ[V(t),t] = non-linear time-varying elastance ϕa = active characteristic of the ventricular/atrial muscle ϕp = passive characteristic of the ventricular/atrial muscle N κˆ yu = coherency spectrum ˆ θ N = parameter vector II Abbreviations and acronyms AoP: Aortic Pressure BSA: Body Surface Area CO: Cardiac Output (CO=HR*SV) COI: Cardiac Output Index CVP: Central Venous Pressure DC: Direct Current EDP: End Diastolic Pressure EDPVR: End Diastolic Pressure Volume Relationship EDV: End Diastolic Volume EDVI: End Diastolic Volume Index EF: Ejection Fraction (EF=SV/EDV) EKF: Extended Kalman Filter ESP: End Systolic Pressure ESPVR: End Systolic Pressure Volume Relationship ESV: End Systolic Volume ESVI: End Systolic Volume Index ETFE: Empirical Transfer Function Estimate EV = Extra Volume EW: External Work GUI: Graphic User Interface HR: Heart Rate LAP: Left Atrial Pressure LVP: Left Ventricular Pressure LV: Left Ventricle LVM: Left Ventricular Mass NYHA: New York Heart Association PE: Potential Energy PV: Pressure-Volume PVA: Pressure Volume Area PAP: Pulmonary Arterial Pressure Pmc: Mean Circulatory Pressure Pmp: Mean Pulmonary Pressure Pms: Mean Systemic Pressure RAP: Right Atrial Pressure RMSE: Root Mean Square Error RVP: Right Ventricular Pressure RV: Right Ventricle SV: Stroke Volume SVI: Stroke Volume Index SVR: Systemic Vascular Resistance VAD: Ventricular Assist Device %VAF: Percent Variance Accounted For III Introduction Mechanical circulatory support is evolved substantially since its inception in the late 1960s and in 2001 it was demonstrated a 48% reduction in the risk of death in patient group treated with ventricular assist devices (VADs) compared with medically treated group. Although the majority of VADs are nowadays used as bridge to heart transplantation, permanent use and bridge to ventricular recovery represent a source of intense research and development. Aim of this work was to investigate the interaction between an axial flow VAD and the assisted cardiovascular system, by means both of mathematical modeling and an acute animal study. This interaction is a crucial aspect in the development of mechanical circulatory support intended for long-term use. A numerical model of the whole cardiovascular system
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