Closed-loop Cardiovascular System Research Articles

Nonlinear Closed-Loop Predictive Control of Heart Rate and Blood Pressure Using Vagus Nerve Stimulation: An In Silico Study.

We propose a nonlinear model-based control technique for regulating the heart rate and blood pressure using vagus nerve neuromodulation. The closed-loop framework is based on an in silico model of the rat cardiovascular system for the simulation of the hemodynamic response to multi-location vagal nerve stimulation. The in silico model is derived by compartmentalizing the various physiological components involved in the closed-loop cardiovascular system with intrinsic baroreflex regulation to virtually generate nominal and hypertension-related heart dynamics of rats in rest and exercise states. The controller, using a reduced cycle-averaged model, monitors the outputs from the in silico model, estimates the current state of the reduced model, and computes the optimum stimulation locations and the corresponding parameters using a nonlinear model predictive control algorithm. The results demonstrate that the proposed control strategy is robust with respect to its ability to handle setpoint tracking and disturbance rejection in different simulation scenarios.

A Closed-Loop Modeling Framework for Cardiac-to-Coronary Coupling.

The mechanisms by which cardiac mechanics effect coronary perfusion (cardiac-to-coronary coupling) remain incompletely understood. Several coronary models have been proposed to deepen our understanding of coronary hemodynamics, but possibilities for in-depth studies on cardiac-to-coronary coupling are limited as mechanical properties like myocardial stress and strain are most often neglected. To overcome this limitation, a mathematical model of coronary mechanics and hemodynamics was implemented in the previously published multi-scale CircAdapt model of the closed-loop cardiovascular system. The coronary model consisted of a relatively simple one-dimensional network of the major conduit arteries and veins as well as a lumped parameter model with three transmural layers for the microcirculation. Intramyocardial pressure was assumed to arise from transmission of ventricular cavity pressure into the myocardial wall as well as myocardial stiffness, based on global pump mechanics and local myofiber mechanics. Model-predicted waveforms of global epicardial flow velocity, as well as of intramyocardial flow and diameter were qualitatively and quantitatively compared with reported data. Versatility of the model was demonstrated in a case study of aortic valve stenosis. The reference simulation correctly described the phasic pattern of coronary flow velocity, arterial flow impediment, and intramyocardial differences in coronary flow and diameter. Predicted retrograde flow during early systole in aortic valve stenosis was in agreement with measurements obtained in patients. In conclusion, we presented a powerful multi-scale modeling framework that enables realistic simulation of coronary mechanics and hemodynamics. This modeling framework can be used as a research platform for in-depth studies of cardiac-to-coronary coupling, enabling study of the effect of abnormal myocardial tissue properties on coronary hemodynamics.

Linking cross-bridge cycling kinetics to response to cardiac resynchronization therapy: a multiscale modelling study.

Cardiac resynchronization therapy (CRT) is currently the most widely used treatment for heart failure patients with left bundle branch block (LBBB). In recent years, the presence of septal rebound stretch (SRS) has been found to be a positive indicator for CRT response although the mechanism is unknown. In an attempt to understand the relation between cellular mechanics and global pump function in CRT patients, we utilize the CircAdapt closed-loop cardiovascular system model in combination with the MechChem model of cardiac sarcomere contraction. Left bundle branch block has been simulated with increasing delay in left ventricular free wall and septal wall activation. In addition to the electrical dyssynchrony, myocardial mechanical function was diminished by decreasing the cross-bridge cycling rate. Our results have shown that a decrease in the cross-bridge cycling rate in addition to LBBB resulted in a decrease in SRS with a concomitant decreased response to resynchronization. The results of our multiscale modelling study suggest that, while greater SRS during systole clearly indicates electrical dyssynchrony, it also predicts mechanical viability and healthy cross-bridge cycling rates in the myocardium. Hence, SRS positively indicates response to CRT.

Fast Simulation of Mechanical Heterogeneity in the Electrically Asynchronous Heart Using the MultiPatch Module.

Cardiac electrical asynchrony occurs as a result of cardiac pacing or conduction disorders such as left bundle-branch block (LBBB). Electrically asynchronous activation causes myocardial contraction heterogeneity that can be detrimental for cardiac function. Computational models provide a tool for understanding pathological consequences of dyssynchronous contraction. Simulations of mechanical dyssynchrony within the heart are typically performed using the finite element method, whose computational intensity may present an obstacle to clinical deployment of patient-specific models. We present an alternative based on the CircAdapt lumped-parameter model of the heart and circulatory system, called the MultiPatch module. Cardiac walls are subdivided into an arbitrary number of patches of homogeneous tissue. Tissue properties and activation time can differ between patches. All patches within a wall share a common wall tension and curvature. Consequently, spatial location within the wall is not required to calculate deformation in a patch. We test the hypothesis that activation time is more important than tissue location for determining mechanical deformation in asynchronous hearts. We perform simulations representing an experimental study of myocardial deformation induced by ventricular pacing, and a patient with LBBB and heart failure using endocardial recordings of electrical activation, wall volumes, and end-diastolic volumes. Direct comparison between simulated and experimental strain patterns shows both qualitative and quantitative agreement between model fibre strain and experimental circumferential strain in terms of shortening and rebound stretch during ejection. Local myofibre strain in the patient simulation shows qualitative agreement with circumferential strain patterns observed in the patient using tagged MRI. We conclude that the MultiPatch module produces realistic regional deformation patterns in the asynchronous heart and that activation time is more important than tissue location within a wall for determining myocardial deformation. The CircAdapt model is therefore capable of fast and realistic simulations of dyssynchronous myocardial deformation embedded within the closed-loop cardiovascular system.

Simulating transient ventricular interaction using a minimal cardiovascular system model

A minimal closed-loop cardiovascular system (CVS) model has been developed that can simulate ventricular interaction due to both direct interaction through the septum and series interaction through the circulation system. The model is used to simulate canine experiments carried out to study the transient response of the left ventricle due to changes in right ventricle pressures and volumes. The model-simulated trends in left and right ventricle pressures and volumes, septum deflection and arterial flow rates are compared with the experimental results. In spite of the limited physiological data available describing the animals, the model is shown to capture all the transient trends in the experimental data. This is the first known example of a physiological model that can capture all these trends. The model is then used to illustrate the separate effects of direct and series interactions independently. This study proves the value of this modelling method to be used in conjunction with experimental data for delineating and understanding the factors that contribute to ventricular dynamics.

Dynamic properties of cardiovascular systems

A recently derived mathematical model of an isolated heart is extended here to a closed-loop cardiovascular system. Taking the end-diastolic volume as state variable, the authors show that the closed-loop cardiovascular system can be described by a one-dimensional nonlinear discrete dynamical system that depends on parameters describing the systolic and diastolic properties of the heart, heart rate, total peripheral resistance, and arterial capacitance. Studies of this model show that the system possesses a rich spectrum of dynamical behavior, from stable points through stable cycles to a “chaotic” behavior. It is shown that such an analysis of dynamic behavior yields those domains in the parameter space that correspond to a normal and abnormal beating heart, when the heart ejects time-invariant and time-invariant (periodic or aperiodic) stable stroke volumes, respectively. Determination of such domains may lead to better understanding of the specific pathologic mechanism involved in the evolution of an abnormal beating heart.

CADCS simulation of the closed-loop cardiovascular system

A pulsatile simulator of the closed-loop cardiovascular system, designed to solve simulation, identification and control problems in a research and education context, is presented. Its implimentation makes use of a command-driven interactive program for simulation of non-linear ordinary differential equations. The flexibility of the simulator is demonstrated by the results presented which refer to a basal steady-state circulatory condition as well as a transient induced by an abrupt change in peripheral resistance.

Simulation and Parameter-Identification of the Closed-Loop Cardiovascular System by the Use of a Nonlinear Mathematical Model

A non-linear model of human cardio-vascular system, which includes the short-term pressure regulation mechanism was mathematically derived and implemented on a PDP-11/45 in a block-oriented, interactive programming language. In this way the behaviour of the arterial and venous pressures, cardiac output, stroke volume, total peripheral resistance and heart-rate under ergometric workload was studied by simulation, and experimentally proved, that the model matches the system with good accuracy. In a second phase the parameters of the model were identified by the use of the output-error method. For this purpose a non-linear system identification programming package was applied. The parameter values, identified in this way are in good agreement with the relevant physiological data.

Energetics Of The Heart Model With The Ventricular Assist Device

We investigated the energistics of the physiological heart model by comparing predictive indexes of the myocardial oxygen consumption (MOO), such as tension-time index (TTI), tension-time or force-time integral (FTI), rate-pressure product (RPP), pressure-work index, and systolic pressure-volume area (PVA) when using electrohydraulic left ventricular device (LVAD) or not. We developed the model of this VAD incorporated the closed-loop cardiovascular system with a baroreceptor which can control heart rate and time-varying elastance of left and right ventricles On considering the benefit of the LVAD, the effects of various operation modes, especially timing of assistance, were evaluated using this coupled computer model. Overall results of the computer simulation shows that our LVAD can unload the ischemic (less contractile) heart by decreasing the MOC and increasing coronary flow. Because the pump ejection at the end diastolic phase of the natural heart may increase the after load of the left ventricle, the control scheme of our LVAD must prohibit ejecting at this time. Since the increment of coronary flow is proportional to the peak aortic pressure after the ventricle contration, the LVAD must eject immediately following the closure of the aortic valve to increase oxygen availability.