Time-varying mechanical properties of the left ventricle--a computer simulation

Simulating impaired left ventricular-arterial coupling in aging and disease: a systematic review

Aortic stenosis, hypertension, and left ventricular hypertrophy often coexist in the elderly, causing a detrimental mismatch in coupling between the heart and vasculature known as ventricular-vascular (VA) coupling. Impaired left VA coupling, a critical aspect of cardiovascular dysfunction in aging and disease, poses significant challenges for optimal cardiovascular performance. This systematic review aims to assess the impact of simulating and studying this coupling through computational models. By conducting a comprehensive analysis of 34 relevant articles obtained from esteemed databases such as Web of Science, Scopus, and PubMed until July 14, 2022, we explore various modeling techniques and simulation approaches employed to unravel the complex mechanisms underlying this impairment. Our review highlights the essential role of computational models in providing detailed insights beyond clinical observations, enabling a deeper understanding of the cardiovascular system. By elucidating the existing models of the heart (3D, 2D, and 0D), cardiac valves, and blood vessels (3D, 1D, and 0D), as well as discussing mechanical boundary conditions, model parameterization and validation, coupling approaches, computer resources and diverse applications, we establish a comprehensive overview of the field. The descriptions as well as the pros and cons on the choices of different dimensionality in heart, valve, and circulation are provided. Crucially, we emphasize the significance of evaluating heart-vessel interaction in pathological conditions and propose future research directions, such as the development of fully coupled personalized multidimensional models, integration of deep learning techniques, and comprehensive assessment of confounding effects on biomarkers.

Co-simulation of hypertensive left ventricle based on computational fluid dynamics and a closed-loop network model

OBJECTIVE

Hypertension is one of the most common chronic and cardiovascular diseases, with the largest number of deaths. According to clinical experience, long-term hypertension will cause cardiac hypertrophy and other complications, and heart structure remodeling will significantly change the energy characteristics of the heart chambers, and impair heart function. Research shows that, early hypertension can be diagnosed by the blood flow and energy loss in the left ventricle. Therefore, it is important to choose an appropriate method to simulate and predict the flow domain of this ventricle.

METHODS

This study took the left ventricular flow field of patients with hypertensive myocardial hypertrophy as the research object, used MATLAB-SIMULINK to establish a closed-loop network cardiovascular model, provided flow boundary conditions for the computational fluid dynamics (CFD) numerical simulation method, and, finally, completed a co-simulation.

RESULTS

This article compared the degree of agreement between the energy loss in different phases of the heart cavity and clinical experimental data and summarized the characteristics of the flow field in patients with hypertensive myocardial hypertrophy. The analysis of three simulation groups (control group, non-left ventricular hypertrophy group, and left ventricular hypertrophy [LVH] group) showed that the vortices in the LVH group were irregular and not fully developed, accompanied by significant energy loss.

CONCLUSION

The simulation method used in this study is basically consistent with the clinical data. Myocardial hypertrophy has a significant influence on the blood flow of the left ventricle. Changes in the blood flow make the left ventricular vortex distribution abnormal during the rapid systole and rapid ejection periods, leading to a series of dangerous factors, including increased energy loss and a low cardiac ejection fraction.

Predictive Modeling of Secondary Pulmonary Hypertension in Left Ventricular Diastolic Dysfunction

Diastolic dysfunction is a common pathology occurring in about one third of patients affected by heart failure. This condition may not be associated with a marked decrease in cardiac output or systemic pressure and therefore is more difficult to diagnose than its systolic counterpart. Compromised relaxation or increased stiffness of the left ventricle induces an increase in the upstream pulmonary pressures, and is classified as secondary or group II pulmonary hypertension (2018 Nice classification). This may result in an increase in the right ventricular afterload leading to right ventricular failure. Elevated pulmonary pressures are therefore an important clinical indicator of diastolic heart failure (sometimes referred to as heart failure with preserved ejection fraction, HFpEF), showing significant correlation with associated mortality. However, accurate measurements of this quantity are typically obtained through invasive catheterization and after the onset of symptoms. In this study, we use the hemodynamic consistency of a differential-algebraic circulation model to predict pulmonary pressures in adult patients from other, possibly non-invasive, clinical data. We investigate several aspects of the problem, including the ability of model outputs to represent a sufficiently wide pathologic spectrum, the identifiability of the model's parameters, and the accuracy of the predicted pulmonary pressures. We also find that a classifier using the assimilated model parameters as features is free from the problem of missing data and is able to detect pulmonary hypertension with sufficiently high accuracy. For a cohort of 82 patients suffering from various degrees of heart failure severity, we show that systolic, diastolic, and wedge pulmonary pressures can be estimated on average within 8, 6, and 6 mmHg, respectively. We also show that, in general, increased data availability leads to improved predictions.

Development of an adaptive pulmonary simulator for in vitro analysis of patient populations and patient-specific data

BACKGROUND AND OBJECTIVE

Patient-specific modeling (PSM) is gaining more attention from researchers due to its ability to potentially improve diagnostic capabilities, guide the design of intervention procedures, and optimize clinical management by predicting the outcome of a particular treatment and/or surgical intervention. Due to the hemodynamic diversity of specific patients, an adaptive pulmonary simulator (PS) would be essential for analyzing the possible impact of external factors on the safety, performance, and reliability of a cardiac assist device within a mock circulatory system (MCS). In order to accurately and precisely replicate the conditions within the pulmonary system, a PS should not only account for the ability of the pulmonary system to supply blood flow at specific pressures, but similarly consider systemic outflow dynamics. This would provide an accurate pressure and flow rate return supply back into the left ventricular section of the MCS (i.e. the initial conditions of the left heart).

METHODS

Employing an embedded Windkessel model, a control system model was developed utilizing MathWorks' Simulink® Simscape™. Following a verification and validation (V&V) analysis approach, a PI-controlled closed-loop hydraulic system was developed using Simscape™. This physical system modeling tool was used to (1) develop and control the in silico system during verification studies and (2) simulate pulmonary performance for validation of this control architecture.

RESULTS

The pulmonary Windkessel model developed is capable of generating the left atrial pressure (LAP) waveform from given pulmonary factors, aortic conditions, and systemic variables. Verification of the adaptive PS's performance and validation of this control architecture support this modeling methodology as an effective means of reproducing pulmonary pressure waveforms and systemic outflow conditions, unique to a particular patient. Adult and geriatric with and without Heart Failure and a Normal Ejection Fraction (HFNEF) are presented.

CONCLUSIONS

The adaptability of this modelling approach allows for the simulation of pulmonary conditions without the limitations of a dedicated hardware platform for use in in vitro investigations.

A patient-specific lumped-parameter model of coronary circulation

A new lumped-parameter model for coronary hemodynamics is developed. This model is developed for the whole coronary network based on CT scans of a patient-specific geometry including the right coronary tree, which is absent in many previous mathematical models. The model adopts the structured tree model boundary conditions similar to the work of Olufsen et al., thus avoiding the necessity of invasive perfusion measurements. In addition, we also incorporated the effects of the head loss at the two inlets of the large coronary arteries for the first time. The head loss could explain the phenomenon of a sudden increase of the resistance at the inlet of coronary vessel. The estimated blood pressure and flow rate results from the model agree well with the clinical measurements. The computed impedances also match the experimental perfusion measurement. The effects of coronary arterial stenosis are considered and the fractional flow reserve and relative flow in the coronary vessels for a stenotic vessel computed in this model show good agreement with published experimental data. It is believed that the approach could be readily translated to clinical practice to facilitate real time clinical diagnosis.

Bridging the gap between measurements and modelling: a cardiovascular functional avatar

Lumped parameter models of the cardiovascular system have the potential to assist researchers and clinicians to better understand cardiovascular function. The value of such models increases when they are subject specific. However, most approaches to personalize lumped parameter models have thus far required invasive measurements or fall short of being subject specific due to a lack of the necessary clinical data. Here, we propose an approach to personalize parameters in a model of the heart and the systemic circulation using exclusively non-invasive measurements. The personalized model is created using flow data from four-dimensional magnetic resonance imaging and cuff pressure measurements in the brachial artery. We term this personalized model the cardiovascular avatar. In our proof-of-concept study, we evaluated the capability of the avatar to reproduce pressures and flows in a group of eight healthy subjects. Both quantitatively and qualitatively, the model-based results agreed well with the pressure and flow measurements obtained in vivo for each subject. This non-invasive and personalized approach can synthesize medical data into clinically relevant indicators of cardiovascular function, and estimate hemodynamic variables that cannot be assessed directly from clinical measurements.

Patient-specific parameter estimation in single-ventricle lumped circulation models under uncertainty

Computational models of cardiovascular physiology can inform clinical decision-making, providing a physically consistent framework to assess vascular pressures and flow distributions, and aiding in treatment planning. In particular, lumped parameter network (LPN) models that make an analogy to electrical circuits offer a fast and surprisingly realistic method to reproduce the circulatory physiology. The complexity of LPN models can vary significantly to account, for example, for cardiac and valve function, respiration, autoregulation, and time-dependent hemodynamics. More complex models provide insight into detailed physiological mechanisms, but their utility is maximized if one can quickly identify patient specific parameters. The clinical utility of LPN models with many parameters will be greatly enhanced by automated parameter identification, particularly if parameter tuning can match non-invasively obtained clinical data. We present a framework for automated tuning of 0D lumped model parameters to match clinical data. We demonstrate the utility of this framework through application to single ventricle pediatric patients with Norwood physiology. Through a combination of local identifiability, Bayesian estimation and maximum a posteriori simplex optimization, we show the ability to automatically determine physiologically consistent point estimates of the parameters and to quantify uncertainty induced by errors and assumptions in the collected clinical data. We show that multi-level estimation, that is, updating the parameter prior information through sub-model analysis, can lead to a significant reduction in the parameter marginal posterior variance. We first consider virtual patient conditions, with clinical targets generated through model solutions, and second application to a cohort of four single-ventricle patients with Norwood physiology. Copyright © 2016 John Wiley & Sons, Ltd.

A simulation protocol for exercise physiology in Fontan patients using a closed loop lumped-parameter model

BACKGROUND

Reduced exercise capacity is nearly universal among Fontan patients, though its etiology is not yet fully understood. While previous computational studies have attempted to model Fontan exercise, they did not fully account for global physiologic mechanisms nor directly compare results against clinical and physiologic data.

METHODS

In this study, we developed a protocol to simulate Fontan lower-body exercise using a closed-loop lumped-parameter model describing the entire circulation. We analyzed clinical exercise data from a cohort of Fontan patients, incorporated previous clinical findings from literature, quantified a comprehensive list of physiological changes during exercise, translated them into a computational model of the Fontan circulation, and designed a general protocol to model Fontan exercise behavior. Using inputs of patient weight, height, and if available, patient-specific reference heart rate (HR) and oxygen consumption, this protocol enables the derivation of a full set of parameters necessary to model a typical Fontan patient of a given body-size over a range of physiologic exercise levels.

RESULTS

In light of previous literature data and clinical knowledge, the model successfully produced realistic trends in physiological parameters with exercise level. Applying this method retrospectively to a set of clinical Fontan exercise data, direct comparison between simulation results and clinical data demonstrated that the model successfully reproduced the average exercise response of a cohort of typical Fontan patients.

CONCLUSION

This work is intended to offer a foundation for future advances in modeling Fontan exercise, highlight the needs in clinical data collection, and provide clinicians with quantitative reference exercise physiologies for Fontan patients.

Dynamic left ventricular elastance: a model for integrating cardiac muscle contraction into ventricular pressure-volume relationships

To integrate myocardial contractile processes into left ventricular (LV) function, a mathematical model was built. Muscle fiber force was set equal to the product of stiffness and elastic distortion of stiffness elements, i.e., force-bearing cross bridges (XB). Stiffness dynamics arose from recruitment of XB according to the kinetics of myofilament activation and fiber-length changes. Elastic distortion dynamics arose from XB cycling and the rate-of-change of fiber length. Muscle fiber stiffness and distortion dynamics were transformed into LV chamber elastance and volumetric distortion dynamics. LV pressure equaled the product of chamber elastance and volumetric distortion, just as muscle-fiber force equaled the product of muscle-fiber stiffness and lineal elastic distortion. Model validation was in terms of its ability to reproduce cycle-time-dependent LV pressure response, DeltaP(t), to incremental step-like volume changes, DeltaV, in the isolated rat heart. All DeltaP(t), regardless of the time in the cycle at which DeltaP(t) was elicited, consisted of three phases: phase 1, concurrent with the leading edge of DeltaV; phase 2, a brief transient recovery from phase 1; and phase 3, sustained for the duration of systole. Each phase varied with the time in the cycle at which DeltaP(t) was elicited. When the model was fit to the data, cooperative activation was required to sustain systole for longer periods than was possible with Ca(2+) activation alone. The model successfully reproduced all major features of the measured DeltaP(t) responses, and thus serves as a credible indicator of the role of underlying contractile processes in LV function.

Equivalent contractility indexes for the assessment of left ventricular systolic function in post-AMI human hearts

We propose new contractility indexes, in the work, which are equivalent to the conventional contractility (Ees) determined with the slope of left ventricular (LV) end-systolic pressure-volume relation. Nineteen patients with acute myocardial infarction (AMI) were recruited in the study. They received thrombolytic therapy within 24 hours after the AMI event, and their LV pressures and volumes were measured with Millar and multi-electrode volume conductance catheters during catheterization examination at the first week and 3 months, respectively. The first equivalent contractility index (eEsv) submitted was defined as the Ees divided by the end-systolic volume (ESV) and normalized to 100 ml, the second (eEdv) as the Ees divided by the end-diastolic volume (EDV) and normalized to 100 ml, and the third (eEmv) as the Ees divided by the midrange of the LV volume and normalized to 100 m. Using linear regression methods, we found that a high correlation coefficient (r > 0.82) exists between the Ees and one of the three new contractility indexes. Furthermore, the eEsv but not Ees was significantly higher measured at 3 months than at one week after thrombolysis. In conclusion, an increase in the equivalent contractility eEsv implies the improvement of the left ventricular systolic function in the post-AMI human hearts long-term after thrombolytic intervention, as the size-dependence of contractility is taken into account.

Modeling of the Norwood circulation: effects of shunt size, vascular resistances, and heart rate

Hypoplastic left heart syndrome is the most common lethal cardiac malformation of the newborn. Its treatment, apart from heart transplantation, is the Norwood operation. The initial procedure for this staged repair consists of reconstructing a circulation where a single outlet from the heart provides systemic perfusion and an interpositioning shunt contributes blood flow to the lungs. To better understand this unique physiology, a computational model of the Norwood circulation was constructed on the basis of compartmental analysis. Influences of shunt diameter, systemic and pulmonary vascular resistance, and heart rate on the cardiovascular dynamics and oxygenation were studied. Simulations showed that 1) larger shunts diverted an increased proportion of cardiac output to the lungs, away from systemic perfusion, resulting in poorer O2 delivery, 2) systemic vascular resistance exerted more effect on hemodynamics than pulmonary vascular resistance, 3) systemic arterial oxygenation was minimally influenced by heart rate changes, 4) there was a better correlation between venous O2 saturation and O2 delivery than between arterial O2 saturation and O2 delivery, and 5) a pulmonary-to-systemic blood flow ratio of 1 resulted in optimal O2 delivery in all physiological states and shunt sizes.

Use of mathematical model to predict hemodynamics in cavopulmonary anastomosis with persistent forward flow

BACKGROUND

The bidirectional cavopulmonary anastomosis with additional pulmonary blood flow is used as a staged procedure or a definitive palliation of univentricular hearts. In this paper the flow competition occurring between the caval and the pulmonary flows is investigated. The hemodynamics in the superior vena cava and the blood flow distribution into the lungs, as well as the systemic arterial oxygen availability, are correlated with the severity of the right ventricle outflow tract obstruction and the pulmonary arteriolar resistance.

MATERIALS AND METHODS

Computer models of the pre- and postoperative hemodynamics of univentricular hearts were developed. The effects of increasing severity of the right ventricle outflow tract obstruction, with a pulmonary arteriolar resistance ranging from 0.8 to 7.9 nonindexed Woods units, were simulated.

RESULTS

The study indicates that the presence of an additional pulmonary blood flow from the native pulmonary artery may be beneficial. Since an excessive additional blood flow may cause central venous hypertension, its optimal value should be chosen according to the value of pulmonary arteriolar resistance. The model was utilized to simulate four clinical cases.

CONCLUSIONS

The simulations show that the model can predict the postoperative hemodynamics and could therefore be usefully applied to predict quantitatively the effect of the native pulmonary blood flow following bidirectional cavopulmonary anastomosis.

Mathematical modelling of the human foetal cardiovascular system based on Doppler ultrasound data

A lumped parameter model of the human foetal circulation primarily based on blood velocity data derived from the Doppler analysis was developed in this study. It consists of two major parts, the heart and the foetal vascular circulation. The heart model accounts for both ventricular and atrial contractility. The circulation was divided into 19 compliant vascular compartments in order to describe all of the clinically monitored sites. The model parameters refer to the final gestation period and were derived either from literature on foetal sheep circulation or from anatomical dimension monitoring of the human foetus. No control mechanism is incorporated into the model. The model was validated by comparing several index values of simulated velocity curves to those of the experimental Doppler waveforms. The mean and maximum percentual errors in the estimation of the experimental results by the model are 7.7% and 20.1%, respectively. Velocity and pressure tracings of the foetal circulation were investigated, as well as regional blood flow rate distribution.

A mathematical model of circulation in the presence of the bidirectional cavopulmonary anastomosis in children with a univentricular heart

The bidirectional cavopulmonary anastomosis is used as a staged procedure or a definitive palliation of univentricular hearts. It is often performed in the presence of an additional blood flow arising from the native pulmonary outflow tract. In this paper, the effects of the severity of the pulmonary outflow obstruction and the pulmonary arteriolar resistance are analysed with regard to the haemodynamics in the superior vena cava and the blood distribution into the lungs. A computer model has been developed, which can represent both the preoperative and the postoperative (systemic and pulmonary) circulations in a patient with a double-outlet univentricular heart. It is particularly detailed in the region of the large vessels and includes components that account for local three-dimensional effects due to the actual shape of the anastomosis. Results have indicated that the mean pressure in the superior vena cava increases from 8.2 to 19.2 mmHg with pulmonary arteriolar resistance ranging from 0.8 to 7.9 Woods units and pulmonary outflow obstruction ranging from 50 to 100%. The percentage flow distribution to the right lung has turned out to be heavily affected by the flow competition and has ranged from 43 to 50% of the total flow to the lungs in the systolic phase, and from 51 to 62% in the diastolic phase. The model allows routinely used clinical indices to be computed, as well as the evaluation of new indices, which is potentially helpful in the clinical assessment of postoperative haemodynamics (e.g. the right-to-left lung flow ratio and the superior vena cava-to-pulmonary flow ratio).

Modeling of mechanical dysfunction in regional stunned myocardium of the left ventricle

Reversible mechanical dysfunction of the myocardium after a single or multiple episode(s) of coronary artery occlusion has been observed in previous studies and is termed myocardial stunning. The hypothesis that stunning could be represented by a decrease in maximum available muscle force in the stunned region was examined by means of a mathematical model that incorporates series viscoelastic elements. A canine experimental model was also employed to demonstrate depressed contractility and a consistent delay of shortening in the stunned region. The mechanical model of the left ventricle was designed to include a normal and stunned region, for which the stunned region was allowed to have variable size. Each region consisted of a volume and time dependent force generator in parallel with a passive elastic force element. The passive elastic element was placed in series with a constant viscosity component and a series elastic component. The model was solved by means of a computer. Passive and active properties of each region could be altered independently. The typical regional measures of muscle performance such as percent shortening, percent bulge, percent thickening, delay of shortening, percent increase in end-diastolic length and other hemodynamic measures were computed. These results were similar to those observed in animal models of stunning. In addition, a nearly linear relationship with end-diastolic length and delay of shortening was predicted by the model. It was concluded that a decrease in the peak isovolumic elastance and augmentation of viscosity effect of creep during stunning can explain mechanical abnormalities of stunned myocardium.

The step response of left ventricular pressure to ejection flow: a system oriented approach

Left ventricular pressure is dependent on both ventricular volume and ventricular ejection flow. These dependencies are usually expressed by ventricular elastance, and resistance, respectively. Resistance is a one-valued effect only, when ejection flow either is constant or increases. Decreasing ejection flow elicits a third effect: a decrease of elastance. The effects of elastance, resistance and elastance depression were modeled in a three-compartment model consisting of a dead-volume compartment, an elastance compartment, and a second series-elastance compartment connected to the elastance compartment by a resistance. This model was identified with the pressure response determined experimentally by imposing pumped constant-flow ejection epochs on isolated rabbit hearts. The experimental flow epochs consisted of two phases of constant flow separated by an increasing or decreasing flow step. It was found that elastance is not changed after the flow step if this is positive or zero. Negative flow steps induced a deactivation of elastance that is linearly dependent on the difference between isovolumic pressure that would be developed at the volume existing at the time of measurement and actual pressure. The parameters found from the identification procedure are ventricular active volume, nondepressed elastance, series-elastance, resistance, and the elastance deactivation factor. The first four parameter values were found in agreement with other results reported in literature. The elastance depression factor is a new parameter that could be of physiological or clinical significance since it may be related to the inability of the force generators in the heart muscle to be restored to their full number, after being inactivated or decoupled by filament sliding associated with ejection. On the basis of the results, an alinear state-model of the ventricle, for arbitrary, including physiological flow patterns is proposed.

Left-ventricular dynamic model based on constant ejection flow periods

Experiments with constant ejection flow periods on the rabbit left ventricle suggest that left ventricular pressure can be described by a time varying three-element model consisting of elastance Ee(t), resistance R(t), and series-elastance Es(t). Previous experiments demonstrated the existence of a "deactivation effect" after the cessation of a constant ejection flow period, which could be described by a decrease of elastance Ee(t). This paper presents a simulation model based on findings of constant ejection flow experiments, and tested on measured pressure and volume data. The results show that when the model is fitted on one single beat, left ventricular pressure can satisfactorily be described by a three-element model without deactivation. However, the model does not predict isovolumic pressure at end-ejection volume. When isovolumic pressure has to be described by the model as well, introduction of deactivation is necessary. The quality of the model was further tested by fitting it to two beats with different ejection parameters. Deactivation again was necessary for a good fit. Only with a deactivation effect in the model, the component values found are close to the normal range found with CFP experiments in the rabbit left ventricles. From the simulation results it can be concluded that (at least for constant ejection flow periods) elastance, resistance, series-elastance, and deactivation effects all are necessary in describing (and predicting) left ventricular pressure.

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 implementation 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.

Model selection for ventricular mechanics: a sensitivity analysis approach

Quantitative characterization of left ventricle pump properties has been recognized as being of great significance for both physiological and clinical purposes. Several descriptions have been proposed in the past to this end, where the ventricle is viewed as an isovolumic pressure generator coupled to an internal impedance, considered as either only viscous, only elastic or viscoelastic. Though these models have been used widely, the respective advantages and limits have not been fully elucidated. In this paper, six models for the left ventricular pumping function, of the viscoelastic type, are compared using both simulated and experimental data in a typical parameter estimation approach. Elastic and viscous parameters are estimated starting from ventricular pressure and aortic flow, together with the isovolumic pressure at the same preload. The basis for the comparison is the well-established criterion relating the fit obtained from collected data and the covariance matrix of the parameter estimates. The latter allows evaluation of the so-called indifference region in the parameter space, which is represented by an ellipse if both elastic and viscous elements are present. The properties of the indifference region are synthetically represented by two indices linked to the area and the eccentricity of the ellipse: the first represents the mean accuracy of the parameter estimate, the second gives information about the different sensitivities to variation of single parameters. This comparison, in both simulated and experimental cases, generally leads to preference for a model where elastance and viscosity vary with time in linear proportion to the isovolumically developed ventricular pressure. Appropriate description of the elastic effect reveals it to be very crucial while the viscous effect, though improving the fitting of data, is less critical.