CADCS simulation of the closed-loop cardiovascular system

Acausal Modelling of Advanced-Stage Heart Failure and the Istanbul Heart Ventricular Assist Device Support with Patient Data

BACKGROUND

In object-oriented or acausal modelling, components of the model can be connected topologically, following the inherent structure of the physical system, and system equations can be formulated automatically. This technique allows individuals without a mathematics background to develop knowledge-based models and facilitates collaboration in multidisciplinary fields like biomedical engineering. This study conducts a preclinical evaluation of a ventricular assist device (VAD) in assisting advanced-stage heart failure patients in an acausal modelling environment.

METHODS

A comprehensive object-oriented model of the cardiovascular system with a VAD is developed in MATLAB/SIMSCAPE, and its hemodynamic behaviour is studied. An analytically derived pump model is calibrated for the experimental prototype of the Istanbul Heart VAD. Hemodynamics are produced under healthy, diseased, and assisted conditions. The study features a comprehensive collection of advanced-stage heart failure patients' data from the literature to identify parameters for disease modelling and to validate the resulting hemodynamics.

RESULTS

Regurgitation, suction, and optimal speeds are identified, and trends in different hemodynamic parameters are observed for the simulated pathophysiological conditions. Using pertinent parameters in disease modelling allows for more accurate results compared to the traditional approach of arbitrary reduction in left ventricular contractility to model dilated cardiomyopathy.

CONCLUSION

The current research provides a comprehensive and validated framework for the preclinical evaluation of cardiac assist devices. Due to its object-oriented nature, the featured model is readily modifiable for other cardiovascular diseases for studying the effect of pump operating conditions on hemodynamics and vice versa in silico and hybrid mock circulatory loops. The work also provides a potential teaching tool for understanding the pathophysiology of heart failure, diagnosis rationale, and degree of assist requirements.

Remodeling of the cardiovascular hemodynamic environment by lower limb heat exposure: A computational fluid dynamic study

BACKGROUND

Lower limb heat exposure (LLHE) is a promising strategy for the daily management of cardiovascular health because of its non-pharmaceutical advantages. To support the application of this strategy in cardiovascular protection, we examined its impact on the global hemodynamic environment.

METHODS

Skin blood flow (SBF) of eight locations on the lower limbs was measured before and after LLHE (40 °C and 44 °C) in ten healthy subjects by using a laser Doppler flowmeter. A closed-loop model of circulation uses changes in SBF to quantify the influence of LLHE on the blood flow of the arterial trunk (from ascending aorta to the femoral artery) and visceral branches (coronary, celiac, renal, and mesenteric arteries).

RESULTS

The SBF in all locations tested on the lower limbs increased significantly (p<0.001) with LLHE and a 3.39-fold and 7.40-fold increase in mean SBF were observed under 40 °C and 44 °C conditions, respectively. In the model, the peak (3.9-25.1%), end-diastolic (13.7-107.3%), and mean blood flow (8.5-86.5%) in the arterial trunk increased with the increase in temperature, but the retrograde flow in the thoracic aorta and abdominal aorta Ⅰ increased at least twice in the diastolic period. Furthermore, LLHE also increased the blood flow of the visceral branches (2.5-20.7%).

CONCLUSION

These findings suggest that LLHE is expected to be a daily strategy for enhancing the functions of both the arterial trunk and visceral arteries, but the increased blood flow reversal in the thoracic and abdominal aortas warrants further investigation.

Reallocation of cutaneous and global blood circulation during sauna bathing through a closed-loop model

OBJECTIVE

Sauna bathing (SB) is an important strategy in cardiovascular protection, but there is no mathematical explanation for the reallocation of blood circulation during heat-induced superficial vasodilation. We sought to reveal such reallocation via a simulated hemodynamic model.

METHODS

A closed-loop cardiovascular model with a series of electrical parameters was constructed. The body surface was divided into seven blocks and each block was modeled by a lumped resistance. These resistances were adjusted to increase skin blood flow (SBF), with the aim of reflecting heat-induced vasodilation during SB. Finally, the blood pressure was compared before and after SB, and the blood flow inside the aorta and visceral arteries were also analyzed.

RESULTS

With increasing SBF in this model, the systolic, diastolic, and mean blood pressure in the arterial trunk decreased by 13-29, 18-36, and 19-37 mmHg, respectively. Despite the increase in the peak and mean blood flow in the arterial trunk, the diastolic blood flow reversal in the thoracic and abdominal aortas increased significantly. Nevertheless, the blood supply to the heart, liver, stomach, spleen, kidney, and intestine decreased by at least 25%. Moreover, the pulmonary blood flow increased significantly.

CONCLUSION

Simulated heat-induced cutaneous vasodilation in this model lowers blood pressure, induces visceral ischemia, and promotes pulmonary circulation, suggesting that the present closed-loop model may be able to describe the effect of sauna bathing on blood circulation. However, the increase of retrograde flow in the aortas found in this model deserves further examination.

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.

A validated reduced-order dynamic model of nitric oxide regulation in coronary arteries

Nitric Oxide (NO) provides myocardial oxygen demands of the heart during exercise and cardiac pacing and also prevents cardiovascular diseases such as atherosclerosis and platelet adhesion and aggregation. However, the direct in vivo measurement of NO in coronary arteries is still challenging. To address this matter, a mathematical model of dynamic changes of calcium and NO concentration in the coronary artery was developed for the first time. The model is able to simulate the effect of NO release in coronary arteries and its impact on the hemodynamics of the coronary arterial tree and also to investigate the vasodilation effects of arteries during cardiac pacing. For these purposes, flow rate, time-averaged wall shear stress, dilation percent, NO concentration, and Calcium (Ca2+) concentration within coronary arteries were obtained. In addition, the impact of hematocrit on the flow rate of the coronary artery was studied. It was seen that the behavior of flow rate, wall shear stress, and Ca2+ is biphasic, but the behavior of NO concentration and the dilation percent is triphasic. Also, by increasing the Hematocrit, the blood flow reduces slightly. The results were compared with several experimental measurements to validate the model qualitatively and quantitatively. It was observed that the presented model is well capable of predicting the behavior of arteries after releasing NO during cardiac pacing. Such a study would be a valuable tool to understand the mechanisms underlying vessel damage, and thereby to offer insights for the prevention or treatment of cardiovascular diseases.

The evolution of long-term pediatric ventricular assistance devices: a critical review

Introduction: The gap between the number of heart failure patients and the number of potential heart donors has never been larger than today, especially among the pediatric population. The use of mechanical circulatory support is seen as a potential alternative for clinicians to treat more patients. This treatment has proven its efficiency on short-term use. However, in order to replace heart transplant, the techniques should be used over longer periods of time.Areas covered: This review aims at furnishing an engineering vision of the evolution of ventricular assistance devices used in pediatrics. A critical analysis of the clinical complications related to devices generation is made to give an overview of the design improvements made since their inception.Expert opinion: The long-term use of a foreign device in the body is not without consequences, especially among fragile pediatric patients. Moreover, the size of their body parts increases the technical difficulties of such procedure. The balance between the living cells of the body is disturbed by the devices, mostly by the shear stress generated. To provide a safe mechanical circulatory support for long-term use, the devices should be more hemocompatible, preserving blood cells, adapted to the patient's systemic grid and miniaturized for pediatric use.

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.

SIMULATION OF A CLOSED LOOP MODEL EQUIVALENT ELECTRONIC OF NORMAL CARDIOVASCULAR SYSTEM AND VALVULAR AORTIC STENOSIS

This work presents a developed zero-dimensional cardiovascular (CV) system model, based on an electrical analogy, with a detailed compartmental description of the heart and the main vascular circulation which is able to simulate normal and diseased conditions of CV system, especially the stenosis valvular aortic. To know the effect of each parameter on hemodynamics, the number of parameters is increased by adding more segments. The developed model consists of 14 compartments. The results show that the severity of aortic stenosis (AS) effect varies with the effective orifice area and the mean pressure gradient for the case of no AS; the effective orifice area is 4[Formula: see text]cm2 and the mean pressure gradient is 0[Formula: see text]mmHg, while for the case of mild AS, the effective orifice area is 1.5[Formula: see text]cm2 and the mean pressure gradient is 27.24[Formula: see text]mmHg. For the case of moderate AS, the effective orifice area is 1.0[Formula: see text]cm2 and the mean pressure gradient is 44.68[Formula: see text]mmHg. For the case of the severe AS, the effective orifice area is 0.61[Formula: see text]cm2 and the mean pressure gradient is 77.51[Formula: see text]mmHg. It is found that the developed model can estimate an accurate value of the effective orifice area for any value of mean pressure gradient in AS. The results obtained for the CV system under normal and diseased conditions show a good agreement compared to published results.

Cardiovascular Function and Ballistocardiogram: A Relationship Interpreted via Mathematical Modeling

OBJECTIVE

To develop quantitative methods for the clinical interpretation of the ballistocardiogram (BCG).

METHODS

A closed-loop mathematical model of the cardiovascular system is proposed to theoretically simulate the mechanisms generating the BCG signal, which is then compared with the signal acquired via accelerometry on a suspended bed.

RESULTS

Simulated arterial pressure waveforms and ventricular functions are in good qualitative and quantitative agreement with those reported in the clinical literature. Simulated BCG signals exhibit the typical I, J, K, L, M, and N peaks and show good qualitative and quantitative agreement with experimental measurements. Simulated BCG signals associated with reduced contractility and increased stiffness of the left ventricle exhibit different changes that are characteristic of the specific pathological condition.

CONCLUSION

The proposed closed-loop model captures the predominant features of BCG signals and can predict pathological changes on the basis of fundamental mechanisms in cardiovascular physiology.

SIGNIFICANCE

This paper provides a quantitative framework for the clinical interpretation of BCG signals and the optimization of BCG sensing devices. The present paper considers an average human body and can potentially be extended to include variability among individuals.

A One-Dimensional Hemodynamic Model of the Coronary Arterial Tree

One-dimensional (1D) hemodynamic models of arteries have increasingly been applied to coronary circulation. In this study, we have adopted flow and pressure profiles in Olufsen's 1D structured tree as coronary boundary conditions, with terminals coupled to the dynamic pressure feedback resulting from the intra-myocardial stress because of ventricular contraction. We model a trifurcation structure of the example coronary tree as two adjacent bifurcations. The estimated results of blood pressure and flow rate from our simulation agree well with the clinical measurements and published data. Furthermore, the 1D model enables us to use wave intensity analysis to simulate blood flow in the developed coronary model. Six characteristic waves are observed in both left and right coronary flows, though the waves' magnitudes differ from each other. We study the effects of arterial wall stiffness on coronary blood flow in the left circumflex artery (LCX). Different diseased cases indicate that distinct pathological reactions of the cardiovascular system can be better distinguished through Wave Intensity analysis, which shows agreement with clinical observations. Finally, the feedback pressure in terminal vessels and measurement deviation are also investigated by changing parameters in the LCX. We find that larger feedback pressure increases the backward wave and decreases the forward one. Although simplified, this 1D model provides new insight into coronary hemodynamics in healthy and diseased conditions. We believe that this approach offers reference resources for studies on coronary circulation disease diagnosis, treatment and simulation.

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.

Mathematical modelling of the maternal cardiovascular system in the three stages of pregnancy

In this study, a mathematical model of the female circulation during pregnancy is presented in order to investigate the hemodynamic response to the cardiovascular changes associated with each trimester of pregnancy. First, a preliminary lumped parameter model of the circulation of a non-pregnant female was developed, including the heart, the systemic circulation with a specific block for the uterine district and the pulmonary circulation. The model was first tested at rest; then heart rate and vascular resistances were individually varied to verify the correct response to parameter alterations characterising pregnancy. In order to simulate hemodynamics during pregnancy at each trimester, the main changes applied to the model consisted in reducing vascular resistances, and simultaneously increasing heart rate and ventricular wall volumes. Overall, reasonable agreement was found between model outputs and in vivo data, with the trends of the cardiac hemodynamic quantities suggesting correct response of the heart model throughout pregnancy. Results were reported for uterine hemodynamics, with flow tracings resembling typical Doppler velocity waveforms at each stage, including pulsatility indexes. Such a model may be used to explore the changes that happen during pregnancy in female with cardiovascular diseases.

Effect of stenosis eccentricity on the functionality of coronary bifurcation lesions-a numerical study

Interventional cardiologists still rely heavily on angiography for the evaluation of coronary lesion severity, despite its poor correlation with the presence of ischemia. In order to improve the accuracy of the current diagnostic procedures, an understanding of the relative influence of geometric characteristics on the induction of ischemia is required. This idea is especially important for coronary bifurcation lesions (CBLs), whose treatment is complex and is associated with high rates of peri- and post-procedural clinical events. Overall, it is unclear which geometric and morphological parameters of CBLs influence the onset of ischemia. More specifically, the effect of stenosis eccentricity is unknown. Computational fluid dynamic simulations, under a geometric multiscale framework, were executed for seven CBL configurations within the left main coronary artery bifurcation. Both concentric and eccentric stenosis profiles of mild to severe constriction were considered. By using a geometric multiscale framework, the fractional flow reserve, which is the gold-standard clinical diagnostic index, could be calculated and was compared between the eccentric and concentric profiles for each case. The results suggested that for configurations where the supplying vessel is stenosed, eccentricity could have a notable effect on and therefore be an important factor that influences configuration functionality.

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.

Adaptive physiological speed/flow control of rotary blood pumps in permanent implantation using intrinsic pump parameters

An adaptive speed/flow controller was developed based on previous work using the intrinsic pump parameters. Those intrinsic parameters were measured by long-term reliable sensors. The adaptive controller was designed to track the varying total peripheral resistance and update the controller parameters correspondingly. The controller was studied in computer simulation on two different types of pumps, whose hydrodynamic characteristics are described by static and dynamic equation, respectively. The pump pressure rise of both pumps is accessible. With the designed adaptive controller, the abnormal hemodynamic values indicating congestive heart failure, including total blood flow, mean aortic pressure, left ventricular end-diastolic pressure, are all successfully restored to normal ranges. This good performance is consistent for both pumps in the variation of activities and left ventricular failure levels. The results show that the designed controller can be applicable for rotary blood pumps whose pump pressure rise can be measured or derived from pump intrinsic parameters.

Hemodynamic Controller for Left Ventricular Assist Device Based on Pulsatility Ratio

Hemodynamic control of left ventricular assist devices (LVADs) is generally a complicated problem due to diverse operating environments and the variability of the patients: both the changes in the circulatory and metabolic parameters as well as disturbances that require adjustment to the operating point. This challenge is especially acute with control of turbodynamic blood pumps. This article presents a pulsatility ratio controller for LVAD that provides a proper perfusion according to the physiological demands of the patient, while avoiding adverse conditions. It utilizes the pulsatility ratio of the flow through the pump and pressure difference across the pump as a control index and adjusts the pump speed according to the reference pulsatility ratio under the different operating conditions. The simulation studies were performed to evaluate the controller in consideration of the sensitivity to afterload and preload, influence of the contractility, and effect of suction sensitivity. The controller successfully adjusts the pump speed according to the reference pulsatility ratio, and supports the natural heart under diverse pump operating conditions. The resulting safe pump operations demonstrate the solid performance of the controller in terms of sensitivity to afterload and preload, influence of the contractility, and effect of suction sensitivity.

Robust and self-tuning blood flow control during extracorporeal circulation in the presence of system parameter uncertainties

Three different discrete controllers were designed and tuned to be used in conjunction with a rotary blood pump during cardiopulmonary heart-lung support. The controllers were designed to operate in both steady and pulsatile modes. The system and methods were tested in a circulatory haemodynamic simulator. To guarantee stable control of the non-linear circulatory system in the presence of patient parameter uncertainties, a proportional plus integral (PI) and an H infinity controller were robustly tuned, using a non-linear time-varying model. (H infinity refers to the Hardy space, the set of bounded functions, analytic in the right half plane. The H infinity controller is the solution to the H infinity norm optimisation problem.) A self-tuning general predictive controller (GPC), together with an adaptive Kalman filter (KF) estimator, was compared with the two robustly tuned controllers. The closed-loop blood flow control circuit was set up in simulation routines first. The blood flow controllers were validated in a circulatory hydrodynamic simulator (MOCK) combined with a rotary blood pump. Parameters of the system simulator were changed continuously, and the controllers were tested over a wide range of different operating points. Disturbances in the form of discontinuous additive parameter uncertainties were applied. The closed-loop systems remained robustly stable. The robustly tuned H infinity controller showed the best control performance, in contrast to the GPC controller, which was near instability in regions of strongly varying non-linear system gain. Compared with the H infinity controller, the PI controller showed slightly worse behaviour, but the closed-loop response was acceptable, even in regions of strongly varying non-linear system gain and during pulsatile perfusion. The rotary blood pump could provide stationary and pulsatile perfusion under control conditions. Controlled variables were hereby mean blood flow, pulsatility index and heart rate. All three controllers were developed for an arterial mean flow of 0-6 l min(-1) and a heart rate of up to 70 beats per minute. Pulsatile closed-loop perfusion could provide up to 30 mmHg pressure variation in the simulated ascending aorta at a mean flow of 3 l min(-1).

The role of the arterial prestress in blood flow dynamics

Blood flowing in a vessel is modelled using one-dimensional equations derived from the Navier-Stokes theory on the base of long pressure wavelength. The vessel wall is modelled as an initially highly prestressed elastic membrane, which slightly deforms under the blood pressure pulses. On the stressed configuration, the vessel wall undergoes, even in larger arteries, small deformation and its motion is linearized around such initial prestressed state. The mechanical fluid-wall interaction is expressed by a set of four partial differential equations. To account for a global circulation features, the distributed model is coupled with a six compartments lumped parameter model which provide the proper boundary conditions by reproducing the correct waveforms entering into the vessel and avoid unphysical reflections. The solution has been computed numerically: the space derivatives are discretized by a finite difference method on a staggered grid and a Runge-Kutta scheme is used to advance the solution in time. Numerical experiments show the role of the initial stresses in the flow dynamics and the wall deformation.

A multiscale approach for modelling wave propagation in an arterial segment

A mathematical model of blood flow through an arterial vessel is presented and the wave propagation in it is studied numerically. Based on the assumption of long wavelength and small amplitude of the pressure waves, a quasi-one-dimensional (1D) differential model is adopted. It describes the non-linear fluid-wall interaction and includes wall deformation in both radial and axial directions. The 1D model is coupled with a six compartment lumped parameter model, which accounts for the global circulatory features and provides boundary conditions. The differential equations are first linearized to investigate the nature of the propagation phenomena. The full non-linear equations are then approximated with a numerical finite difference method on a staggered grid. Some numerical simulations show the characteristics of the wave propagation. The dependence of the flow, of the wall deformation and of the wave velocity on the elasticity parameter has been highlighted. The importance of the axial deformation is evidenced by its variation in correspondence of the pressure peaks. The wave disturbances consequent to a local stiffening of the vessel and to a compliance jump due to prosthetic implantations are finally studied.

Haemodynamics and mechanics following partial left ventriculectomy: a computer modeling analysis

Mechanics following partial left ventriculectomy is still poorly understood. A computational cylindrical model of the left ventricle was developed, based on the myocardial fibre behaviour for the evaluation of the mechanical and haemodynamical effects of the operation. A healthy left ventricle with physiological geometry and function and a dilated hypokinetic heart were investigated. Haemodynamic and mechanical data were obtained at baseline and compared with those obtained at different degrees of volume reduction. Data included: ejection fraction (EF); stroke volume (SV); end-systolic and end-diastolic pressure-volume relationships (ESPVR and EDPVR), and efficiency. EF increases following volume reduction in both simulation but, concurrently, SV shows modest improvement (dilated ventricle) or reduction (healthy ventricle) at progressive degrees of resection. The ESPVR and EDPVR slope increases and shifts leftward with the resection extent, but the increase of the ESPVR slope is more pronounced in dilated ventricle. Efficiency is improved in the dilated heart after resections, while does not improve when the healthy-heart volume is reduced. The simulation of partial left ventriculectomy suggests an improvement of systolic performance, counterbalanced by increased diastolic stiffness following inverse remodelling. Efficiency of simulated dilated ventricles is enhanced by volume reduction, suggesting a favourable effect of reduction of the metabolic demand of the failing heart.

An in vitro methodology for evaluating the mechanical properties of aortic vascular prostheses

The main problem in the replacement of pathological segments of the aorta with vascular prostheses consists of matching the fluid admittance of the host artery and the graft. This mismatch results from the different compliance between natural and prosthetic vessels and from the plastic dilatation of the prosthesis diameter that occurs after implantation. An experimental procedure was set up for evaluating the mechanical properties of aortic vascular prostheses. An MTS 858 MiniBionix testing machine was equipped with a purposely designed testing apparatus, which allows loading a ring-shaped prosthesis specimen with forces that can be related easily to the transmural pressure acting on the prostheses in vivo. The reference pressure waveforms are simulated from a lumped parameter model of the cardiovascular system. Preliminary tests on 3 different (woven, warp knitted, and carbon-coated warp knitted fabric) aortic prostheses point out a good reproducibility of the results. The fabric strongly affects the circumferential elasticity and the dimensional stability of the graft. Simulation of hypertension promotes larger diameter dilatation and reduction in compliance. Agreement between in vitro and clinical diameter measurements has been assessed for 8 prosthesis samples and found to be adequate. This method is thus a potentially useful means for preclinical evaluation of compliance of vascular prostheses for the purpose of matching to native vessels.

Simulation and prediction of cardiotherapeutical phenomena from a pulsatile model coupled to the Guyton circulatory model

In order to use simulation prediction for cardiotherapeutical purposes, the well-documented and physiologically validated circulatory Guyton model was coupled to a cardiac pulsatile model which comprises the hemodynamics of the four chambers including valvular effects, as well as the Hill, Frank-Starling, Laplace, and autonomic nervous system (ANS) effects. The program is written in the "C" language and available for everybody. The program system was submitted to validation and plausibility tests both as to the steady-state and the dynamic properties. Pressures, volumes and flows and other variables turned out to be compatible with published experimental and clinical recordings both under physiological and pathophysiological conditions. The results from the application to cardiac electrotherapy emphasize the importance of atrial contraction to ventricular filling, the adequate atrio-ventricular delay, the effect of impaired ventricular relaxation, and the significance of the choice of the adequate cardiac pacemaker, both with respect to the stimulation site and the adequate sensor controlling pacing rate. The simulation will be further developed, tested and applied for cardiological purposes.

Ventricular motion during the ejection phase: a computational analysis

In the present paper, the study of the ventricular motion during systole was addressed by means of a computational model of ventricular ejection. In particular, the implications of ventricular motion on blood acceleration and velocity measurements at the valvular plane (VP) were evaluated. An algorithm was developed to assess the force exchange between the ventricle and the surrounding tissue, i.e., the inflow and outflow vessels of the heart. The algorithm, based on the momentum equation for a transitory flowing system, was used in a fluid-structure model of the ventricle that includes the contractile behavior of the fibers and the viscous and inertial forces of the intraventricular fluid. The model calculates the ventricular center of mass motion, the VP motion, and intraventricular pressure gradients. Results indicate that the motion of the ventricle affects the noninvasive estimation of the transvalvular pressure gradient using Doppler ultrasound. The VP motion can lead to an underestimation equal to 12.4 +/- 6.6%.

Intraventricular pressure drop and aortic blood acceleration as indices of cardiac inotropy: a comparison with the first derivative of aortic pressure based on computer fluid dynamics

This paper presents a computational approach to ventricular fluid mechanics to evaluate three inotropic indices of early ejection: the intraventricular pressure drop (deltap). the first derivative of aortic flow rate (df/dt) and the first derivative of aortic pressure dp/dt. dp/dt is one of the most frequently used indices for assessing myocardial inotropy. Deltap and df/dt are characteristic of inertia driven flows and reflect the impulsive nature of the flow inside the ventricle during the ejection phase. The study is based on an axisymmetric fluid dynamics model of the left ventricle, developed according to the finite element approach. The fluid cavity is bounded by a shell containing two sets of counter-rotating contractile fibres. Two simulation sets were performed: the former to investigate the sensitivity of deltap and df/dt peaks (deltap(max) and df/dt(max)) with respect to changes in the inotropic state of the fibre. The latter allows the evaluation of the dependency of deltap(max) and df/dt(max) on afterload by means of two supravalvular stenoses of 50% and 70%. The model simulates the inertial features of ventricle behaviour. The calculated values of the indices investigated are in close agreement with those reported in the literature. The sensitivities of deltap(max) df/dt(max) and dp/dt(max) are calculated for the two simulation sets. Data are normalised with respect to the maximum values reached in the simulation set. The comparison indicates that deltap(max) has a greater sensitivity (3.4 vs. 3.1 ) and a more linear pattern than dp/dt(max) for changes in the inotropic state of the fibre. df/dt(max), shows a sensitivity close to dp/dt(max). Results confirm that the afterload does not affect dp/dt(max), in accordance with experimental observations, while deltap(max) and, to a major degree, df/dt(max) decrease when the afterload is increased.

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.

Mesh updating in fluid-structure interactions in biomechanics: an iterative method based on an uncoupled approach

In this study, a computational uncoupled approach to fluid-structure interaction problems in biofluid mechanics is presented. It is based on the finite element method and is applied to study the local fluid dynamics in two specific situations: the left ventricular ejection phase and the motion of an isolated red blood cell along a small artery. Particularly, the focus is on the algorithms developed to deal with mesh updating, because both examined districts are characterized by geometrical deformations of the fluid domain edges. This is currently a challenging issue in the application of computational fluid dynamics techniques to living systems, especially to the cardiovascular system. Although the chosen approach uses a commercial computational fluid dynamics package for the solution of the fluid domain, original algorithms have been developed to perform the boundary displacement calculations correctly, as well as the corresponding mesh updating. Results are reported and compared with available data in the literature pertinent to the two studied problems.

Numerical simulation of the blood flow in the human cardiovascular system

This paper describes a numerical model of the human cardiovascular system. The model is composed of 15 elements connected in series representing the main parts of the system. Each element is composed of a rigid connecting tube and an elastic reservoir. The blood flow is described by a one-dimensional time-dependent Bernoulli equation. The action of the ventricles is simulated with a Hill's three-element model, adapted for the left and right heart. The closing of the four heart valves is simulated with the aid of time-dependent drag coefficients. Closing is achieved by letting the drag coefficient approach infinity. The resulting system of 32 non-linear ordinary differential equations is solved numerically with the Runge-Kutta method. The results of the simulation (pressure-time and volume-time dependence for the atria and ventricles and pressure forms in the aorta at a heart rate of 70 beats per minute) agree with the physiological data given in the literature. The model's input aortic impedance is 31.5 dyn s cm-5 which agrees with literature data given for aortic input impedance in man 26-80 dyn s cm-5). Long-term stability of the system was achieved. The cardiovascular system presented here can also be simulated at higher and varying heart rates--up to 200 beats per minute. The results of calculations for some pathological changes (e.g. valvular abnormalities) are discussed.

An improved SPICE heart model that obeys Starling's law

This paper details a versatile and easy to use electrical network model of the heart in which the user can control the heart rate, blood pressure, end-diastolic left ventricular pressure, and proportion of time spent in systole. Several dysrhythmias and cardiac diseases can be simulated, including asystole, second and third degree heart blocks, brady- and tachycardias, premature ventricular contractions, premature atrial contractions, sinus dysrhythmias, hypo- and hypertension, pericardial tamponade and combinations of these. The model's output simulates empiric data with a 99% correlation, and the heart obeys Starling's law and can simulate congestive heart failure. This model is substantially more flexible than our previous version (Goldstein, et al., Comput. Methods Progr. Biomed. 33 (1990) 27-34) making it a more powerful adjunct for studying cardiac neurohormonal feedback theories and for exploring general systemic cardiovascular hemodynamics.

The coronary bed and its role in the cardiovascular system: a review and an introductory single-branch model

To investigate cardiovascular haemodynamics under normal and pathological conditions, a closed-loop model of the cardiovascular system already presented in the literature, has been complemented by a model of the coronary bed. Oxygen available to the myocardium is strictly related to the coronary blood flow; we have developed threshold criteria which correlate cardiac output with the coronary flow. The system utilizes control systems related to the cardiac contractility and frequency, and imitates feedback mechanisms peculiar to the heart. The work exemplifies the autoregulation of events that occur when the equilibrium of the system is disturbed. It is suggested that the heart plays an active role in trying to restore the haemodynamic parameters to their physiological values.

[A stress-dependent pulsatile cardiovascular model as the basis for regulating artificial hearts]

The development and simulation of closed-loop control of blood pumps requires a pulsatile model of the cardiovascular system that takes into account the natural mechanisms of adaptation during exercise. In this article, a model is described which takes account of the baroreceptor reflex, the change in heart rate, contractility of the heart, and the peripheral resistance during exercise, as well as venous tone, and the nonlinearity of vessel compliance. In addition, a model of the artificial heart is presented, in which the nonlinear limitation of the stroke volume is taken into account, and the concept of a pulse frequency modulated (PFM) control system for the circulation with an artificial heart is described.

Sensitivity analysis of the systemic circulation with a view to computer simulation and parameter estimation

A sensitivity analysis study has been performed on a seven-parameter model of the systemic vascular bed in order to obtain structure reductions appropriate for simulation and estimation. This analysis considers separately the systolic and diastolic transfer functions between arterial and venous pressures in order to divide a non-linear problem in two distinct linear problems. The results obtained refer to nominal parameter values corresponding to normal circulatory conditions in man and supply guide-lines for an application-oriented selection of reduced models. Simple resistance-compliance models are preferred because the inertial effects appear to have only slight influence. In particular, the choice of a five-parameter model seems to be convenient for simulation purposes. An additional structure reduction is suggested to reach reliable results in parameter estimation problems. The resulting model is characterized by three elements: peripheral resistance, arterial compliance and venous compliance.