Simulating transient ventricular interaction using a minimal cardiovascular system model

Isolated cardiac muscle contracting against a real-time model of systemic and pulmonary cardiovascular loads

Isolated cardiac tissues allow a direct assessment of cardiac muscle function and enable precise control of experimental loading conditions. However, current experimental methods do not expose isolated tissues to the same contraction pattern and cardiovascular loads naturally experienced by the heart. In this study, we implement a computational model of systemic-pulmonary impedance that is solved in real time and imposed on contracting isolated rat muscle tissues. This systemic-pulmonary model represents the cardiovascular system as a lumped-parameter, closed-loop circuit. The tissues performed force-length work-loop contractions where the model output informed both the shortening and restretch phases of each work-loop. We compared the muscle mechanics and energetics associated with work-loops driven by the systemic-pulmonary model with that of a model-based loading method that only accounts for shortening. We obtained results that show simultaneous changes of afterload and preload or end-diastolic length of the muscle, as compared with the static, user-defined preload as in the conventional loading method. This feature allows assessment of muscle work output, heat output, and efficiency of contraction as functions of end-diastolic length. The results reveal the behavior of cardiac muscle as a pump source to achieve load-dependent work and efficiency outputs over a wider range of loads. This study offers potential applications of the model to investigate cardiac muscle response to hemodynamic coupling between systemic and pulmonary circulations in an in vitro setting.NEW & NOTEWORTHY We present the use of a "closed-loop" model of systemic and pulmonary circulations to apply, for the first time, real-time model-calculated preload and afterload to isolated cardiac muscle preparations. This method extends current experimental protocols where only afterload has been considered. The extension to include preload provides the opportunity to investigate ventricular muscle response to hemodynamic coupling and as a pump source across a wider range of cardiovascular loads.

A hybrid mock circulation loop for a total artificial heart

Rotary blood pumps are emerging as a viable technology for total artificial hearts, and the development of physiological control algorithms is accelerated with new evaluation environments. In this article, we present a novel hybrid mock circulation loop (HMCL) designed specifically for evaluation of rotary total artificial hearts (rTAH). The rTAH is operated in the physical domain while all vasculature elements are embedded in the numerical domain, thus combining the strengths of both approaches: fast and easy exchange of the vasculature model together with improved controllability of the pump. Parameters, such as vascular resistance, compliance, and blood volume, can be varied dynamically in silico during operation. A hydraulic-numeric interface creates a real-time feedback loop between the physical and numerical domains. The HMCL uses computer-controlled resistance valves as actuators, thereby reducing the size and number of hydraulic elements. Experimental results demonstrate a stable interaction over a wide operational range and a high degree of flexibility. Therefore, we demonstrate that the newly created design environment can play an integral part in the hydraulic design, control development, and durability testing of rTAHs.

A cardiovascular mathematical model of graded head-up tilt

A lumped parameter model of the cardiovascular system has been developed and optimized using experimental data obtained from 13 healthy subjects during graded head-up tilt (HUT) from the supine position to . The model includes descriptions of the left and right heart, direct ventricular interaction through the septum and pericardium, the systemic and pulmonary circulations, nonlinear pressure volume relationship of the lower body compartment, arterial and cardiopulmonary baroreceptors, as well as autoregulatory mechanisms. A number of important features, including the separate effects of arterial and cardiopulmonary baroreflexes, and autoregulation in the lower body, as well as diastolic ventricular interaction through the pericardium have been included and tested for their significance. Furthermore, the individual effect of parameter associated with heart failure, including LV and RV contractility, baseline systemic vascular resistance, pulmonary vascular resistance, total blood volume, LV diastolic stiffness and reflex gain on HUT response have also been investigated. Our fitted model compares favorably with our experimental measurements and published literature at a range of tilt angles, in terms of both global and regional hemodynamic variables. Compared to the normal condition, a simulated congestive heart failure condition produced a blunted response to HUT with regards to the percentage changes in cardiac output, stroke volume, end diastolic volume and effector response (i.e., heart contractility, venous unstressed volume, systemic vascular resistance and heart rate) with progressive tilting.

Evaluation of a model-based hemodynamic monitoring method in a porcine study of septic shock

INTRODUCTION

The accuracy and clinical applicability of an improved model-based system for tracking hemodynamic changes is assessed in an animal study on septic shock.

METHODS

This study used cardiovascular measurements recorded during a porcine trial studying the efficacy of large-pore hemofiltration for treating septic shock. Four Pietrain pigs were instrumented and induced with septic shock. A subset of the measured data, representing clinically available measurements, was used to identify subject-specific cardiovascular models. These models were then validated against the remaining measurements.

RESULTS

The system accurately matched independent measures of left and right ventricle end diastolic volumes and maximum left and right ventricular pressures to percentage errors less than 20% (except for the 95th percentile error in maximum right ventricular pressure) and all R(2) > 0.76. An average decrease of 42% in systemic resistance, a main cardiovascular consequence of septic shock, was observed 120 minutes after the infusion of the endotoxin, consistent with experimentally measured trends. Moreover, modelled temporal trends in right ventricular end systolic elastance and afterload tracked changes in corresponding experimentally derived metrics.

CONCLUSIONS

These results demonstrate that this model-based method can monitor disease-dependent changes in preload, afterload, and contractility in porcine study of septic shock.

Validation of subject-specific cardiovascular system models from porcine measurements

A previously validated mathematical model of the cardiovascular system (CVS) is made subject-specific using an iterative, proportional gain-based identification method. Prior works utilised a complete set of experimentally measured data that is not clinically typical or applicable. In this paper, parameters are identified using proportional gain-based control and a minimal, clinically available set of measurements. The new method makes use of several intermediary steps through identification of smaller compartmental models of CVS to reduce the number of parameters identified simultaneously and increase the convergence stability of the method. This new, clinically relevant, minimal measurement approach is validated using a porcine model of acute pulmonary embolism (APE). Trials were performed on five pigs, each inserted with three autologous blood clots of decreasing size over a period of four to five hours. All experiments were reviewed and approved by the Ethics Committee of the Medical Faculty at the University of Liege, Belgium. Continuous aortic and pulmonary artery pressures (P(ao), P(pa)) were measured along with left and right ventricle pressure and volume waveforms. Subject-specific CVS models were identified from global end diastolic volume (GEDV), stroke volume (SV), P(ao), and P(pa) measurements, with the mean volumes and maximum pressures of the left and right ventricles used to verify the accuracy of the fitted models. The inputs (GEDV, SV, P(ao), P(pa)) used in the identification process were matched by the CVS model to errors <0.5%. Prediction of the mean ventricular volumes and maximum ventricular pressures not used to fit the model compared experimental measurements to median absolute errors of 4.3% and 4.4%, which are equivalent to the measurement errors of currently used monitoring devices in the ICU (∼5-10%). These results validate the potential for implementing this approach in the intensive care unit.

Assessment of ventricular contractility and ventricular-arterial coupling with a model-based sensor

Estimation of ventricular contractility and ventricular arterial coupling is clinically important in diagnosing and treating cardiac dysfunction in the critically ill. However, experimental assessment of indexes of ventricular contractility, such as the end-systolic pressure-volume relationship, requires a highly invasive maneuver and measurements that are not typical in an intensive care unit (ICU). This research describes the use of a previously validated cardiovascular system model and parameter identification process to evaluate the right ventricular arterial coupling in septic shock. Model-based ventricular arterial coupling is defined by the ratio of the end systolic right ventricular elastance (E(esrvf)) over the pulmonary artery elastance (E(pa)) or the mean pulmonary inflow resistance (R(pulin)). Results are compared to the clinical gold-standard assessment (conductance catheter method). Six anesthetized healthy pigs weighing 20-30kg received a 0.5mg kg(-1) endotoxin infusion over a period of 30min from T0 to T30, to induce septic shock and veno-venous hemofiltration was used from T60 onward. The results show good agreement with the gold-standard experimental assessment. In particular, the model-based right ventricular elastance (E(esrvf)) correlates well with the clinical gold standard (R(2)=0.69) and the model-based non-invasive coupling (E(esrvf)/R(pulin)) follow the same trends and dynamics (R(2)=0.37). The overall results show the potential to develop a model-based sensor to monitor ventricular-arterial coupling in clinical real-time.

Cardiovascular modeling in pulmonary arterial hypertension: focus on mechanisms and treatment of right heart failure using the CircAdapt model

In recent years, increased understanding of cardiovascular system dynamics has led to the development of mathematical models of the heart and circulation. Models that enable realistic simulation of ventricular mechanics and interactions under a range of conditions have the potential to provide an ideal method with which to investigate the effects of pulmonary arterial hypertension and its treatment on cardiac mechanics and hemodynamics. Such mathematical models have the potential to contribute to a personalized, patient-specific treatment approach and allow more objective diagnostic decision-making, patient monitoring, and assessment of treatment outcome. This review discusses the development of mathematical models of the heart and circulation, with particular reference to the closed-loop CircAdapt model, and how the model performs under both normal and pathophysiological (pulmonary hypertensive) conditions.

Mathematical multi-scale model of the cardiovascular system including mitral valve dynamics. Application to ischemic mitral insufficiency

Background

Valve dysfunction is a common cardiovascular pathology. Despite significant clinical research, there is little formal study of how valve dysfunction affects overall circulatory dynamics. Validated models would offer the ability to better understand these dynamics and thus optimize diagnosis, as well as surgical and other interventions.

Methods

A cardiovascular and circulatory system (CVS) model has already been validated in silico, and in several animal model studies. It accounts for valve dynamics using Heaviside functions to simulate a physiologically accurate "open on pressure, close on flow" law. However, it does not consider real-time valve opening dynamics and therefore does not fully capture valve dysfunction, particularly where the dysfunction involves partial closure. This research describes an updated version of this previous closed-loop CVS model that includes the progressive opening of the mitral valve, and is defined over the full cardiac cycle.

Results

Simulations of the cardiovascular system with healthy mitral valve are performed, and, the global hemodynamic behaviour is studied compared with previously validated results. The error between resulting pressure-volume (PV) loops of already validated CVS model and the new CVS model that includes the progressive opening of the mitral valve is assessed and remains within typical measurement error and variability. Simulations of ischemic mitral insufficiency are also performed. Pressure-Volume loops, transmitral flow evolution and mitral valve aperture area evolution follow reported measurements in shape, amplitude and trends.

Conclusions

The resulting cardiovascular system model including mitral valve dynamics provides a foundation for clinical validation and the study of valvular dysfunction in vivo. The overall models and results could readily be generalised to other cardiac valves.

Clinical detection and monitoring of acute pulmonary embolism: proof of concept of a computer-based method

Background

The diagnostic ability of computer-based methods for cardiovascular system (CVS) monitoring offers significant clinical potential. This research tests the clinical applicability of a newly improved computer-based method for the proof of concept case of tracking changes in important hemodynamic indices due to the influence acute pulmonary embolism (APE).

Methods

Hemodynamic measurements from a porcine model of APE were used to validate the method. Of these measurements, only those that are clinically available or inferable were used in to identify pig-specific computer models of the CVS, including the aortic and pulmonary artery pressure, stroke volume, heart rate, global end diastolic volume, and mitral and tricuspid valve closure times. Changes in the computer-derived parameters were analyzed and compared with experimental metrics and clinical indices to assess the clinical applicability of the technique and its ability to track the disease state.

Results

The subject-specific computer models accurately captured the increase in pulmonary resistance (R_pul), the main cardiovascular consequence of APE, in all five pigs trials, which related well (R² = 0.81) with the experimentally derived pulmonary vascular resistance. An increase in right ventricular contractility was identified, as expected, consistent with known reflex responses to APE. Furthermore, the modeled right ventricular expansion index (the ratio of right to left ventricular end diastolic volumes) closely followed the trends seen in the measured data (R² = 0.92) used for validation, with sharp increases seen in the metric for the two pigs in a near-death state. These results show that the pig-specific models are capable of tracking disease-dependent changes in pulmonary resistance (afterload), right ventricular contractility (inotropy), and ventricular loading (preload) during induced APE. Continuous, accurate estimation of these fundamental metrics of cardiovascular status can help to assist clinicians with diagnosis, monitoring, and therapy-based decisions in an intensive care environment. Furthermore, because the method only uses measurements already available in the ICU, it can be implemented with no added risk to the patient and little extra cost.

Conclusions

This computer-based monitoring method shows potential for real-time, continuous diagnosis and monitoring of acute CVS dysfunction in critically ill patients.

Three-wall segment (TriSeg) model describing mechanics and hemodynamics of ventricular interaction

A mathematical model (TriSeg model) of ventricular mechanics incorporating mechanical interaction of the left and right ventricular free walls and the interventricular septum is presented. Global left and right ventricular pump mechanics were related to representative myofiber mechanics in the three ventricular walls, satisfying the principle of conservation of energy. The walls were mechanically coupled satisfying tensile force equilibrium in the junction. Wall sizes and masses were rendered by adaptation to normalize mechanical myofiber load to physiological standard levels. The TriSeg model was implemented in the previously published lumped closed-loop CircAdapt model of heart and circulation. Simulation results of cardiac mechanics and hemodynamics during normal ventricular loading, acute pulmonary hypertension, and chronic pulmonary hypertension (including load adaptation) agreed with clinical data as obtained in healthy volunteers and pulmonary hypertension patients. In chronic pulmonary hypertension, the model predicted right ventricular free wall hypertrophy, increased systolic pulmonary flow acceleration, and increased right ventricular isovolumic contraction and relaxation times. Furthermore, septal curvature decreased linearly with its transmural pressure difference. In conclusion, the TriSeg model enables realistic simulation of ventricular mechanics including interaction between left and right ventricular pump mechanics, dynamics of septal geometry, and myofiber mechanics in the three ventricular walls.

Prediction of hemodynamic changes towards PEEP titrations at different volemic levels using a minimal cardiovascular model

A cardiovascular system model and parameter identification method have previously been validated for porcine experiments of induced pulmonary embolism and positive end-expiratory pressure (PEEP) titrations, accurately tracking all the main hemodynamic trends. In this research, the model and parameter identification process are further validated by predicting the effect of intervention. An overall population-specific rule linking specific model parameters to increases in PEEP is formulated to predict the hemodynamic effects on arterial pressure, pulmonary artery pressure and stroke volume. Hemodynamic changes are predicted for an increase from 0 to 10 cm H(2)O with median absolute percentage errors less than 7% (systolic pressures) and 13% (stroke volume). For an increase from 10 to 20 cm H(2)O median absolute percentage errors are less than 11% (systolic pressures) and 17% (stroke volume). These results validate the general applicability of such a rule, which is not pig-specific, but holds over for all analyzed pigs. This rule enables physiological simulation and prediction of patient response. Overall, the prediction accuracy achieved represents a further clinical validation of these models, methods and overall approach to cardiovascular diagnosis and therapy guidance.

Model-based cardiac diagnosis of pulmonary embolism

A minimal cardiac model has been shown to accurately capture a wide range of cardiovascular system dynamics commonly seen in the intensive care unit (ICU). However, standard parameter identification methods for this model are highly non-linear and non-convex, hindering real-time clinical application. An integral-based identification method that transforms the problem into a linear, convex problem, has been previously developed, but was only applied on continuous simulated data with random noise. This paper extends the method to handle discrete sets of clinical data, unmodelled dynamics, a significantly reduced data set theta requires only the minimum and maximum values of the pressure in the aorta, pulmonary artery and the volumes in the ventricles. The importance of integrals in the formulation for noise reduction is illustrated by demonstrating instability in the identification using simple derivative-based approaches. The cardiovascular system (CVS) model and parameter identification method are then clinically validated on porcine data for pulmonary embolism. Errors for the identified model are within 10% when re-simulated and compared to clinical data. All identified parameter trends match clinically expected changes. This work represents the first clinical validation of these models, methods and approach to cardiovascular diagnosis in critical care.