254 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 57, NO. 2, FEBRUARY 2010 Parameter-Optimized Model of Cardiovascular– Rotary Blood Pump Interactions Einly Lim, Socrates Dokos, Shaun L. Cloherty, Member, IEEE, Robert F. Salamonsen, David G. Mason, John A. Reizes, and Nigel H. Lovell ∗ , Senior Member, IEEE Abstract—A lumped parameter model of human cardiovascular–implantable rotary blood pump (iRBP) in- teraction has been developed based on experimental data recorded in two healthy pigs with the iRBP in situ. The model includes descriptions of the left and right heart, direct ventricular interaction through the septum and pericardium, the systemic and pulmonary circulations, as well as the iRBP. A subset of parameters was optimized in a least squares sense to faithfully reproduce the experimental measurements (pressures, flows and pump variables). Our fitted model compares favorably with our experimental measurements at a range of pump operating points. Furthermore, we have also suggested the importance of various model features, such as the curvilinearity of the end systolic pressure–volume relationship, the Starling resistance, the suction resistance, the effect of respiration, as well as the influence of the pump inflow and outflow cannulae. Alterations of model parameters were done to investigate the circulatory response to rotary blood pump assistance under heart failure conditions. The present model provides a valuable tool for experiment designs, as well as a platform to aid in the development and evaluation of robust physiological pump control algorithms. Index Terms—Heart failure, heart–pump interaction model, im- plantable rotary blood pump (iRBP), ventricular assist devices. I. INTRODUCTION I MPLANTABLE rotary blood pumps (iRBPs) have potential as bridge-to-transplantation and destination therapy devices for end-stage heart failure patients. However, insensitivity of iRBPs to preload, overpumping, or underpumping may endan- ger implant recipients if pump control is not properly imple- mented. This is further complicated by the remaining intrinsic ventricular function, which is dependent on residual contractil- Manuscript received February 19, 2009; revised May 12, 2009. First published September 18, 2009; current version published January 20, 2010. Asterisk indicates corresponding author. E. Lim and S. Dokos are with the Graduate School of Biomedical Engineer- ing, University of New South Wales, Sydney, N.S.W. 2052, Australia (e-mail: z3179719@student.unsw.edu.au; s.dokos@unsw.edu.au). S. L. Cloherty is with the Research School of Biology, Australian National University, Canberra, A.C.T., Australia (e-mail: shaun.cloherty@anu.edu.au). R. F. Salamonsen is with the Cardiothoracic Intensive Care, Alfred Hospital, Melbourne, Vic., Australia, and also with Monash University, Melbourne, Vic. 3800, Australia (e-mail: r.salamonsen@alfred.org.au). D. G. Mason is with the School of Information Technology and Electri- cal Engineering, University of Queensland, Brisbane, Qld., Australia (e-mail: mason@itee.uq.edu.au). J. A. Reizes is with the School of Mechanical and Manufacturing Engineer- ing, University of New South Wales, Sydney, N.S.W. 2052, Australia, and also with the Faculty of Engineering, University of Technology Sydney, Sydney, N.S.W. 2000, Australia. ∗ N. H. Lovell is with the Graduate School of Biomedical Engineering, University of New South Wales, Sydney, N.S.W. 2052, Australia (e-mail: n.lovell@unsw.edu.au). Digital Object Identifier 10.1109/TBME.2009.2031629 ity and venous return, causing the pump differential pressure (head) to vary with each heart beat. Interaction between iRBPs and the cardiovascular system (CVS) may be partially explored through in vivo animal studies. However, such studies are inconclusive at present due to limi- tations in animal models of heart failure and complexity of the experimental procedures [1]. Numerical models, able to simu- late the response of the human CVS in the presence of an iRBP, can provide additional insights into the dynamics of the assisted circulation. Such models also offer an excellent platform for the development and evaluation of robust physiological pump control algorithms by easily allowing reproducible numerical experiments under identical conditions. Various heart–pump interaction computational models have been described in the literature, with varying degrees of com- plexity depending on their purpose [1]–[3]. However, previous work has not focused on fitting the entire waveforms (the mean and complete dynamics of the waveforms) to actual experimen- tal measurements and examining the dynamics of the responses during various pumping state transitions in a quantitative sense. This is despite the fact that dangerous pump operating con- ditions, including suction/ventricular collapse and back flow are closely related to the transient dynamics rather than mean hemodynamic values [4]. In recent experiments, a number of commonly accepted phenomena have been challenged. These include the insufficiency of the widely used time-varying elas- tance theory [5], the question of the interpretability of the well- established end systolic pressure–volume relationship (ESPVR) under left ventricular (LV) assist device (LVAD) assist [6], and the significant increase of mean aortic pressure with progressive LVAD unloading [7]. The aim of the present study is to develop a heart–pump interaction model, taking into careful consideration various dis- crepancies between experimental findings and model simulation results. A number of important features, including curvilinear- ity of the ESPVR, the Starling resistance, respiration effect, and suction and pump cannulae have been included and tested for their significance. Our model is validated using data collected from in vivo animal experiments, mock-loop experiments as well as other published data. II. METHODS A. Animal Experiments The VentrAssist iRBP (Ventracor Ltd., Sydney, Australia) was acutely implanted in two healthy, anaesthetized, open-chest pigs supported by mechanical ventilation. The inflow cannula 0018-9294/$26.00 © 2009 IEEE