Modeling ventricular contraction with heart rate changes

Hemodynamic effects of pulsatile frequency of right ventricular assist device (RVAD) on pulmonary perfusion: a simulation study

Right ventricular assist devices (RVADs) have been extensively used to provide hemodynamic support for patients with end-stage right heart (RV) failure. However, conventional in-parallel RVADs can lead to an elevation of pulmonary artery (PA) pressure, consequently increasing the right ventricular (RV) afterload, which is unfavorable for the relaxation of cardiac muscles and reduction of valve complications. The aim of this study is to investigate the hemodynamic effects of the pulsatile frequency of the RVAD on pulmonary artery. Firstly, a mathematical model incorporating heart, systemic circulation, pulmonary circulation, and RVAD is developed to simulate the cardiovascular system. Subsequently, the frequency characteristics of the pulmonary circulation system are analyzed, and the calculated results demonstrate that the pulsatile frequency of the RVAD has a substantive impact on the pulmonary artery pressure. Finally, to verify the analysis results, the hemodynamic effects of the pulsatile frequency of the RVAD on pulmonary artery are compared under diffident support modes. It is found that the pulmonary artery pressure decreases by approximately 6% when the pulsatile frequency changes from 1 to 3 Hz. The increased pulsatile frequency of RA-PA support mode may facilitate the opening of the pulmonary valve, while the RV-PA support mode can more effectively reduce the load of RV. This work provides a useful method to decrease the pulmonary artery pressure during the RVAD supports and may be beneficial for improving myocardial function in patients with end-stage right heart failure, especially those with pulmonary hypertension.

Investigation into the two-way interaction of coronary flow and heart function in coronary artery disease predicted by a computational model of autoregulation of coronary flow

This study presents a closed-loop computational model to investigate the interplay between heart function, coronary flow, and systemic circulation during exercise, with a specific focus on the impact of coronary artery stenosis. The model incorporates a lumped representation of the heart, main arteries, and coronary arteries, establishing a closed circulatory system. The simulation investigates the autoregulation of coronary flow in response to myocardial oxygen demands during physical exercise by incorporating sympathetic and parasympathetic functions. This study establishes a closed supply-demand loop and investigates the effect of coronary flow deficiency on heart function and systemic circulation in coronary artery diseases during exercise. In coronary artery diseases with low stenosis, heart function and systemic flow resemble those of a healthy person. However, as stenosis intensifies with physical exercise, an additional regulatory mechanism (reg2) is activated. This mechanism adjusts coronary flow by reducing myocardial contractility (E) and increasing heart rate (HR) while maintaining cardiac output (CO). The study results indicate that, at the highest exercise intensity for a healthy individual (HR = 150), the value of E increases from 6 to 8.65mmHg/ml. Meanwhile, for a patient with 85 % coronary artery stenosis in the same exercise intensity, the HR increases to 200, and the value of E decreases to 3.45mmHg/ml. The results also demonstrate that the initiation of the (reg2) mechanism at rest occurs at 83 % stenosis, while at the highest exercise intensity, this mechanism commences at 67 % stenosis.

Baroreflex control model for cardiovascular system subjected to postural changes under normal and orthostatic conditions

Baroreflex dysfunction is one of the common causes associated with the cardiovascular system. The buffering capability and baroreflex gain influences large variation in blood pressure for short term control. For regulating the blood pressure, an integrated analytical model for baroreflex control along with the cardiovascular system is presented to study the complex interactions between autonomic nervous system and cardiovascular system. In the proposed model, the autonomic nervous system utilizes sympathetic and parasympathetic nerve activities. This comprises a heart modeled by Mulier's approach, systemic vasculature, baroreceptor sensor using stress-strain based Voigt model and Hodgkin-Huxley based autonomic nervous control. This model can handle the distribution of total blood volume changes under the influence of gravity upon postural changes by means of short term baroreflex control. The simulation is carried out for the integrated model along with (i) non pulsatile and (ii) pulsatile model of heart. The proposed model is validated for supine to standing position under influence of gravity. To show the efficiency of the proposed model, the simulation is carried out further for (i) postural changes like supine to standing and standing to supine under normal condition and (ii) Orthostatic hypotension and hypertension conditions. Also the robustness of the proposed pulsatile model is tested by introducing disturbance signal in mean arterial pressure under various postural changes.

In Vivo Validation of a Cardiovascular Simulation Model in Pigs

Many computer simulation models of the cardiovascular system, of varying complexity and objectives, have been proposed in physiological science. Every model needs to be parameterized and evaluated individually. We conducted a porcine animal model to parameterize and evaluate a computer simulation model, recently proposed by our group. The results of an animal model, on thirteen healthy pigs, were used to generate consistent parameterization data for the full heart computer simulation model. To evaluate the simulation model, differences between the resulting simulation output and original animal data were analysed. The input parameters of the animal model, used to individualize the computer simulation, showed high interindividual variability (range of coefficient of variation: 10.1–84.5%), which was well-reflected by the resulting haemodynamic output parameters of the simulation (range of coefficient of variation: 12.6–45.7%). The overall bias between the animal and simulation model was low (mean: −3.24%, range: from −26.5 to 20.1%). The simulation model used in this study was able to adapt to the high physiological variability in the animal model. Possible reasons for the remaining differences between the animal and simulation model might be a static measurement error, unconsidered inaccuracies within the model, or unconsidered physiological interactions.

Variations of human cerebral and ocular blood flow during exposure to multi-axial accelerations : A mathematical modeling study

Human hemodynamic responses during exposure to multi-axial acceleration was a relatively new topic in the fields of acceleration physiology. This study aimed to focus on these responses, especially variations of blood perfusion to brain and eyes, through mathematical modeling. A mathematical model was established using lumped parameter methods, containing compartments of four heart chambers, systemic arteries and veins, circulation of typical systemic organs, and some compartments for pulmonary circulation, together with autonomic regulation considered. This model was firstly validated by using experimental data from experiment of posture change and centrifuge tests of +Gz accelerations, and then applied to analyze human hemodynamic responses to typical multi-axial accelerations. Validation results demonstrated the mathematical model could generate reasonable responses of human cardiovascular system during posture change and exposure to +Gz accelerations. Simulation results of hemodynamic responses to multi-axial accelerations depicted Gy induced significant differences of blood flow to the left and right eyes. And some contour maps were generated based on these results, which provided a quick way to estimate blood flow variations in brain and eyes during exposure to different accelerations. Graphical Abstract This study aimed to focus on variations of blood perfusion to brain and eyes during exposure to typical multi-axial accelerations through mathematical modeling. This model was firstly validated by using experimental data from experiment of posture change and centrifuge tests of +Gz accelerations, and then applied to analyze human hemodynamic responses to typical multi-axial accelerations. Simulation results of hemodynamic responses to multi-axial accelerations depicted Gy induced significant differences of blood flow to the left and right eyes. And contour maps that generated based on these results provided a quick way to estimate blood flow variations in brain and eyes during exposure to different accelerations.

Patient-specific parameter estimation: Coupling a heart model and experimental data

This study develops a hemodynamic model involving the atrium, ventricle, veins, and arteries that can be calibrated to experimental results. It is a Windkessel model that incorporates an unsteady Bernoulli effect in the blood flow to the atrium. The model is represented by ordinary differential equations in terms of blood volumes in the compartments as state variables and it demonstrates the use of conductance instead of resistance to capture the effect of a non-leaking heart valve. The experimental results are blood volume data from 20 young (half of which are women) and 20 elderly (half of which are women) subjects during rest, inotropic stress (dobutamine), and chronotropic stress (glycopyrrolate). The model is calibrated to conform with data and physiological findings in 4 different levels. First, an optimization routine is devised to find model parameter values that give good fit between the model volume curves and blood volume data in the atrium and ventricle. Patient-specific information are used to get initial parameter values as a starting point of the optimization. Also, model pressure curves must show realistic behavior. Second, parametric bootstrapping is performed to establish the reliability of the optimal parameters. Third, statistical tests comparing mean optimal parameter values from young vs elderly subjects and women vs men are examined to support and present age and sex related differences in heart functions. Lastly, statistical tests comparing mean optimal parameter values from resting condition vs pharmacological stress are studied to verify and quantify the effects of dobutamine and glycopyrrolate to the cardiovascular system.

Modeling of cardiovascular circulation for the early detection of coronary arterial blockage

Coronary arteries are responsible for maintaining blood supply to the heart. When these arteries get blocked due to plaque deposition, the corresponding pathological condition is referred to as coronary artery disease. This disease develops gradually over the years and consequently, the function of the heart deteriorates, leading to a heart attack in many cases. As the symptoms manifest themselves only when it has become severe, detection of the disease often gets delayed. In order to detect it early and take preventive action, this work is aimed at detecting the arterial blockage in its early stage via cardiovascular modeling. To achieve this, the cardiovascular circulation has been modeled as a sixth order nonlinear system. Blood circulation in a body is viewed as an electrical system using the pressure-voltage analogy. In this case, the heart is considered as a self-excited generator. The rest of the body tissues form a systemic load. In the models reported in the literature, coronary circulation has been assumed to be a part of the systemic load. However, this circulation path has its own importance as it is responsible for the blood supply to the heart. Therefore, in our work, the coronary path is separated out from the rest of the body tissues. This enables us to explicitly model the coronary arterial resistance and thereby helps us to detect coronary arterial blockage condition by estimating this parameter from blood pressure measurements. Increase in the coronary resistance is found to reduce the left ventricular ejection fraction; this information can therefore be used as an index for coronary arterial blockage. It has been shown that the systolic function of the heart deteriorates when the resistance of the coronary path increases beyond a critical value; the situation can be related to a severe blockage condition. The model has been tested on a chosen sample of 20 subjects suffering from coronary artery disease and the results are found to be quite promising.

A mathematical model of human heart including the effects of heart contractility varying with heart rate changes

Incorporating the intrinsic variability of heart contractility varying with heart rate into the mathematical model of human heart would be useful for addressing the dynamical behaviors of human cardiovascular system, but models with such features were rarely reported. This study focused on the development and evaluation of a mathematical model of the whole heart, including the effects of heart contractility varying with heart rate changes. This model was developed based on a paradigm and model presented by Ottesen and Densielsen, which was used to model ventricular contraction. A piece-wise function together with expressions for time-related parameters were constructed for modeling atrial contraction. Atrial and ventricular parts of the whole heart model were evaluated by comparing with models from literature, and then the whole heart model were assessed through coupling with a simple model of the systemic circulation system and the pulmonary circulation system. The results indicated that both atrial and ventricular parts of the whole heart model could reasonably reflect their contractility varying with heart rate changes, and the whole heart model could exhibit major features of human heart. Results of the parameters variation studies revealed the correlations between the parameters in the whole heart model and performances (including the maximum pressure and the stroke volume) of every chamber. These results would be useful for helping users to adjust parameters in special applications.

A regulated multiscale closed-loop cardiovascular model, with applications to hemorrhage and hypertension

A computational tool is developed for simulating the dynamic response of the human cardiovascular system to various stressors and injuries. The tool couples 0-dimensional models of the heart, pulmonary vasculature, and peripheral vasculature to 1-dimensional models of the major systemic arteries. To simulate autonomic response, this multiscale circulatory model is integrated with a feedback model of the baroreflex, allowing control of heart rate, cardiac contractility, and peripheral impedance. The performance of the tool is demonstrated in 2 scenarios: neurogenic hypertension by sustained stimulation of the sympathetic nervous system and an acute 10% hemorrhage from the left femoral artery.

IN-SILICO MODELING OF LEFT VENTRICLE TO SIMULATE DILATED CARDIOMYOPATHY AND CF-LVAD SUPPORT

Numerical modeling of the left ventricle dynamics plays an important role in testing different physiological scenarios and treatment techniques before the in vitro and in vivo assessments. However, utilized left ventricle model becomes vital in the simulations because validity of the results depends on the response of the numerical model to the parameter changes and additional sub-models for the applied treatment techniques. In this study, it is aimed to evaluate different numerical left ventricle models describing healthy and failing ventricle dynamics as well as the response of these models under continuous flow left ventricular assist device support. Six different numerical left ventricle models which include time varying elastance and single fiber contraction approaches are selected and applied in combination with a closed loop electric analogue of the circulation to achieve this purpose. The time varying elastace models relate ventricular pressure and volume changes in a simplistic way while the single fiber contraction models combine different scales ranging from protein to organ level. Change of the hemodynamic signals at the organ level for healthy, failing and CF-LVAD supported left ventricle models shows functionality of these models and helps to understand usability of them for different purposes.

Preservation of native aortic valve flow and full hemodynamic support with the TORVAD using a computational model of the cardiovascular system

This article describes the stroke volume selection and operational design for the toroidal ventricular assist device (TORVAD), a synchronous, positive-displacement ventricular assist device (VAD). A lumped parameter model was used to simulate hemodynamics with the TORVAD compared with those under continuous-flow VAD support. Results from the simulation demonstrated that a TORVAD with a 30 ml stroke volume ejecting with an early diastolic counterpulse provides comparable systemic support to the HeartMate II (HMII) (cardiac output 5.7 L/min up from 3.1 L/min in simulated heart failure). By taking the advantage of synchronous pulsatility, the TORVAD delivers full hemodynamic support with nearly half the VAD flow rate (2.7 L/min compared with 5.3 L/min for the HMII) by allowing the left ventricle to eject during systole and thus preserving native aortic valve flow (3.0 L/min compared with 0.4 L/min for the HMII, down from 3.1 L/min at baseline). The TORVAD also preserves pulse pressure (26.7 mm Hg compared with 12.8 mm Hg for the HMII, down from 29.1 mm Hg at baseline). Preservation of aortic valve flow with synchronous pulsatile support could reduce the high incidence of aortic insufficiency and valve cusp fusion reported in patients supported with continuous-flow VADs.

Partial Left Ventriculectomy: Have Well-Succeeded Cases and Innovations in the Procedure Been Observed in the Last 12 Years?

OBJECTIVE

In 1996, the Brazilian cardiovascular surgeon, Dr. Randas Batista, introduced a surgical technique called partial left ventriculectomy, where he admitted the possibility of reducing the diameter of the left ventricle through the sectioning of one section of its wall. After the publication of this study, thousands of case reports and procedure analysis have been published, and due to several disappointing results, many doctors and institutions failed to execute it. As the main objective of this study, stands out the search for success cases of ventriculectomy in the last 12 years and if during this period it was achieved some significant development in this procedure that allows obtaining lower mortality rate postoperatively.

METHODS

Systematic review of indexed scientific literature over the past 12 years and the term "Partial Left Ventriculectomy".

RESULTS

There has been a considerable number of reported successful cases and highly significant findings in regard to determining the most suitable region for the section, proper selection of the patients indicated to the procedure, including the influence of the coronary artery anatomy in the nomination procedure and the need for preservation of ventricular geometry to ensure better quality of ventricular contractions after the sectioning.

CONCLUSION

This surgical procedure has been successfully performed, mainly in Japan, improvements in its efficiency were found and the need for a mathematical modeling of the slice to be severed is a prominent factor in many studies.

A mathematical model of the carp heart ventricle during the cardiac cycle

The poikilothermic heart has been suggested as a model for studying some of the mechanisms of early postnatal mammalian heart adaptations. We assessed morphological parameters of the carp heart (Cyprinus carpio L.) with diastolic dimensions: heart radius (5.73mm), thickness of the compact (0.50mm) and spongy myocardium (4.34mm), in two conditions (systole, diastole): volume fraction of the compact myocardium (20.7% systole, 19.6% diastole), spongy myocardium (58.9% systole, 62.8% diastole), trabeculae (37.8% systole, 28.6% diastole), and cavities (41.5% systole, 51.9% diastole) within the ventricle; volume fraction of the trabeculae (64.1% systole, 45.5% diastole) and sinuses (35.9% systole, 54.5% diastole) within the spongy myocardium; ratio between the volume of compact and spongy myocardium (0.35 systole, 0.31 diastole); ratio between compact myocardium and trabeculae (0.55 systole, 0.69 diastole); and surface density of the trabeculae (0.095μm(-1) systole, 0.147μm(-1) diastole). We created a mathematical model of the carp heart based on actual morphometric data to simulate how the compact/spongy myocardium ratio, the permeability of the spongy myocardium, and sinus-trabeculae volume fractions within the spongy myocardium influence stroke volume, stroke work, ejection fraction and p-V diagram. Increasing permeability led to increasing and then decreasing stroke volume and work, and increasing ejection fraction. An increased amount of spongy myocardium led to an increased stroke volume, work, and ejection fraction. Varying sinus-trabeculae volume fractions within the spongy myocardium showed that an increased sinus volume fraction led to an increased stroke volume and work, and a decreased ejection fraction.

Using Kalman Filtering to Predict Time-Varying Parameters in a Model Predicting Baroreflex Regulation During Head-Up Tilt

The cardiovascular control system is continuously engaged to maintain homeostasis, but it is known to fail in a large cohort of patients suffering from orthostatic intolerance. Numerous clinical studies have been put forward to understand how the system fails, yet noninvasive clinical data are sparse, typical studies only include measurements of heart rate and blood pressure, as a result it is difficult to determine what mechanisms that are impaired. It is known, that blood pressure regulation is mediated by changes in heart rate, vascular resistance, cardiac contractility, and a number of other factors. Given that numerous factors contribute to changing these quantities, it is difficult to devise a physiological model describing how they change in time. One way is to build a model that allows these controlled quantities to change and to compare dynamics between subject groups. To do so, it requires more knowledge of how these quantities change for healthy subjects. This study compares two methods predicting time-varying changes in cardiac contractility and vascular resistance during head-up tilt. Similar to the study by Williams et al. [51], the first method uses piecewise linear splines, while the second uses the ensemble transform Kalman filter (ETKF) [1], [11], [12], [33]. In addition, we show that the delayed rejection adaptive Metropolis (DRAM) algorithm can be used for predicting parameter uncertainties within the spline methodology, which is compared with the variability obtained with the ETKF. While the spline method is easier to set up, this study shows that the ETKF has a significantly shorter computational time. Moreover, while uncertainty of predictions can be augmented to spline predictions using DRAM, these are readily available with the ETKF.

Verification of a computational cardiovascular system model comparing the hemodynamics of a continuous flow to a synchronous valveless pulsatile flow left ventricular assist device

The purpose of this investigation is to use a computational model to compare a synchronized valveless pulsatile left ventricular assist device with continuous flow left ventricular assist devices at the same level of device flow, and to verify the model with in vivo porcine data. A dynamic system model of the human cardiovascular system was developed to simulate the support of a healthy or failing native heart from a continuous flow left ventricular assist device or a synchronous pulsatile valveless dual-piston positive displacement pump. These results were compared with measurements made during in vivo porcine experiments. Results from the simulation model and from the in vivo counterpart show that the pulsatile pump provides higher cardiac output, left ventricular unloading, cardiac pulsatility, and aortic valve flow as compared with the continuous flow model at the same level of support. The dynamic system model developed for this investigation can effectively simulate human cardiovascular support by a synchronous pulsatile or continuous flow ventricular assist device.

Patient-specific modeling of cardiovascular and respiratory dynamics during hypercapnia

This study develops a lumped cardiovascular-respiratory system-level model that incorporates patient-specific data to predict cardiorespiratory response to hypercapnia (increased CO(2) partial pressure) for a patient with congestive heart failure (CHF). In particular, the study focuses on predicting cerebral CO(2) reactivity, which can be defined as the ability of vessels in the cerebral vasculature to expand or contract in response CO(2) induced challenges. It is difficult to characterize cerebral CO(2) reactivity directly from measurements, since no methods exist to dynamically measure vasomotion of vessels in the cerebral vasculature. In this study we show how mathematical modeling can be combined with available data to predict cerebral CO(2) reactivity via dynamic predictions of cerebral vascular resistance, which can be directly related to vasomotion of vessels in the cerebral vasculature. To this end we have developed a coupled cardiovascular and respiratory model that predicts blood pressure, flow, and concentration of gasses (CO(2) and O(2)) in the systemic, cerebral, and pulmonary arteries and veins. Cerebral vascular resistance is incorporated via a model parameter separating cerebral arteries and veins. The model was adapted to a specific patient using parameter estimation combined with sensitivity analysis and subset selection. These techniques allowed estimation of cerebral vascular resistance along with other cardiovascular and respiratory parameters. Parameter estimation was carried out during eucapnia (breathing room air), first for the cardiovascular model and then for the respiratory model. Then, hypercapnia was introduced by increasing inspired CO(2) partial pressure. During eucapnia, seven cardiovascular parameters and four respiratory parameters was be identified and estimated, including cerebral and systemic resistance. During the transition from eucapnia to hypercapnia, the model predicted a drop in cerebral vascular resistance consistent with cerebral vasodilation.

Functionality of the baroreceptor nerves in heart rate regulation

Two models describing the afferent baroreceptor firing are analyzed, a basic model predicting firing using a single nonlinear differential equation, and an extended model, coupling K nonlinear responses. Both models respond to the the rate (derivative) and the rate history of the carotid sinus arterial pressure. As a result both the rate and the relative level of the carotid sinus arterial pressure is sensed. Simulations with these models show that responses to step changes in pressure follow from the rate sensitivity as observed in experimental studies. Adaptation and asymmetric responses are a consequence of the memory encapsulated by the models, and the nonlinearity gives rise to sigmoidal response curves. The nonlinear afferent baroreceptor models are coupled with an effector model, and the coupled model has been used to predict baroreceptor feedback regulation of heart rate during postural change from sitting to standing and during head-up tilt. The efferent model couples the afferent nerve paths to the sympathetic and parasympathetic outflow, and subsequently predicts the build up of an action potential at the sinus knot of the heart. In this paper, we analyze the nonlinear afferent model and show that the coupled model is able to predict heart rate regulation using blood pressure data as an input.

Left ventricular model parameters and cardiac rate variability

A recent functional model of the left ventricle characterizes the ventricle's contractile state with parameters, rather than variables. The ventricle is treated as a pressure generator that is time and volume dependent. The heart's complex dynamics develop from a single equation based on the formation and relaxation of crossbridge bonds within underlying heart muscle. This equation permits the calculation of ventricular elastance via E(v) = ∂p(v)/∂V(v). This heart model is defined independently from load properties, and ventricular elastance is dynamic and reflects changing numbers of crossbridge bonds. The model parameters were extracted from measured pressure and volume data from isolated canine hearts. The purpose of this paper is to present in some detail how to describe a particular canine left ventricle from measured data. The model is also extended to include heart rate variability, which arises naturally from the model structure. Computed results compare favorably with measurements both in this study and from the literature.

Sensitivity analysis and model assessment: mathematical models for arterial blood flow and blood pressure

The complexity of mathematical models describing the cardiovascular system has grown in recent years to more accurately account for physiological dynamics. To aid in model validation and design, classical deterministic sensitivity analysis is performed on the cardiovascular model first presented by Olufsen, Tran, Ottesen, Ellwein, Lipsitz and Novak (J Appl Physiol 99(4):1523-1537, 2005). This model uses 11 differential state equations with 52 parameters to predict arterial blood flow and blood pressure. The relative sensitivity solutions of the model state equations with respect to each of the parameters is calculated and a sensitivity ranking is created for each parameter. Parameters are separated into two groups: sensitive and insensitive parameters. Small changes in sensitive parameters have a large effect on the model solution while changes in insensitive parameters have a negligible effect. This analysis was successfully used to reduce the effective parameter space by more than half and the computation time by two thirds. Additionally, a simpler model was designed that retained the necessary features of the original model but with two-thirds of the state equations and half of the model parameters.

Computational modelling of blood-flow-induced changes in blood electrical conductivity and its contribution to the impedance cardiogram

Studies have shown that blood-flow-induced change in electrical conductivity is of equal importance in assessment of the impedance cardiogram (ICG) as are volumetric changes attributed to the motion of heart, lungs and blood vessels. To better understand the sole effect of time-varying blood conductivity on the spatiotemporal distribution of trans-thoracic electric fields (i.e. ICG), this paper presents a segmented high-resolution (1 mm(3)) thoracic cardiovascular system, in which the time-varying pressures, flows and electrical conductivities of blood in different vessels are evaluated using a set of coupled nonlinear differential equations, red blood cell orientation and cardiac cycle functions. Electric field and voltage simulations are performed using two and four electrode configurations delivering a small alternating electric current to an anatomically realistic and electrically accurate model of modelled human torso. The simulations provide a three-dimensional electric field distribution and show that the time-varying blood conductivity alters the voltage potential difference between the electrodes by a maximum of 0.28% for a cardiac output of about 5 L min(-1). As part of a larger study, it is hoped that this initial model will be useful in providing improved insights into blood-flow-related spatiotemporal electric field variations and assist in the optimal placement of electrodes in impedance cardiography experiments.

Relations between the timing of the second heart sound and aortic blood pressure

The second heart sound (S2) is triggered by an aortic valve closure as a result of the ventricular-arterial interaction of the cardiovascular system. The objective of this paper is to investigate the timing of S2 in response to the changes in hemodynamic parameters and its relation to aortic blood pressure (BP). An improved model of the left ventricular-arterial interaction was proposed based on the combination of the newly established pressure source model of the ventricle and the nonlinear pressure-dependent compliance model of the arterial system. The time delay from the onset of left ventricular pressure rise to the onset of S2 (RS2) was used to measure the timing of S2. The results revealed that RS2 bears a strong negative correlation with both systolic blood pressure and diastolic blood pressure under the effect of changing peripheral resistance, heart rate, and contractility. The results were further validated by a series of measurements of 16 normal subjects submitted to dynamic exercise. This study helps understand the relationship between the timing of S2 and aortic BP under various physiological and pathological conditions.

Relationships between blood pressure and systolic time-intervals: a lumped-model simulation study

A lumped model of the arterial circulation is applied to the study of the dependencies between blood pressure and systolic time-intervals (PEP, LVET). The left ventricle is handled as a pressure source directly coupled with the varying vascular conditions. Four factors are individually considered: peripheral resistance, LV contractility, end diastolic volume and heart rate. The computed dependence curves of PEP and LVET on systolic and diastolic pressures are in accordance with physiological knowledge. The relations of PEP and LVET with other hemodynamic variables are being enlightened and insight is gained into the use of pulse delays measured from the ECG for predicting non-invasively the arterial blood pressure.

A model-based study of relationship between timing of second heart sound and systolic blood pressure

The onset of second heart sound is triggered by the closure of aortic valve due to the interaction of left ventricle and arterial system. Noninvasive experiments found that RS(2) defined by the time delay from the peak of ECG R wave to the onset of the second heart sound had a close inverse correlation with arterial systolic blood pressure. However, no theoretical study has been carried out to investigate the underline connections between them. A modified model of heart-arterial system is proposed in the present study. In this model the heart is described as a pressure source depending on time, ventricular volume, outflow, and heart rate, and the arterial system as a nonlinear system incorporating a pressure-dependent compliance. Simulation results show that the modified model is able to reflect the cardiovascular function qualitatively. The results also demonstrate that RS(2) is inversely correlated with aortic blood pressure under the effect of changing peripheral resistance, heart rate and contractility. The present study gives insight into the significant functional relations between the parameters characterizing the cardiovascular system and hemodynamics characteristics and provides an interpretation of the experimental observation on the relationship between RS(2) and aortic blood pressure.

A multi-scale computational method applied to the quantitative evaluation of the left ventricular function

A multi-scale computational method, which combines a lumped parameter model of the cardiovascular system (CVS) with a three-dimensional (3D) left ventricle (LV) hemodynamic solver, is developed for quantitatively evaluating the LV function. The parameter model allows reasonable predictions of the cardiac variables in a closed-loop manner under both normal and various pathological conditions. On the basis of the parameter-model-predicted results, 3D hemodynamic computations further provide quantitative insights into the detailed intraventricular flow patterns. Based on a series of computations, it is demonstrated that the pathological change in the shape and size of the LV has a significant effect on the LV pumping performance.

Simulation of hemodynamic responses to the valsalva maneuver: an integrative computational model of the cardiovascular system and the autonomic nervous system

The Valsalva maneuver is a frequently used physiological test in evaluating the cardiovascular autonomic functions in human. Although a large pool of experimental data has provided substantial insights into different aspects of the mechanisms underlying the cardiovascular regulations during the Valsalva maneuver, so far a complete comprehension of these mechanisms and the interactions among them is unavailable. In the present study, a computational model of the cardiovascular system (CVS) and its interaction with the autonomic nervous system (ANS) was developed for the purpose of quantifying the individual roles of the CVS and the ANS in the hemodynamic regulations during the Valsalva maneuver. A detailed computational compartmental parameter model of the global CVS, a system of mathematical equations representing the autonomic nervous reflex regulatory functions, and an empirical cerebral autoregulation (CA) model formed the main body of the present model. Based on simulations of the Valsalva maneuvers at several typical postures, it was demonstrated that hemodynamic responses to the maneuver were not only determined by the ANS-mediated cardiovascular regulations, but also significantly affected by the postural-change-induced hemodynamic alterations preceding the maneuver. Moreover, the large-magnitude overshoot in cerebral perfusion immediately after the Valsalva maneuver was found to result from a combined effect of the circulatory autonomic functions, the CA, and the cerebral venous blood pressure.

A LabVIEW model incorporating an open-loop arterial impedance and a closed-loop circulatory system

While numerous computer models exist for the circulatory system, many are limited in scope, contain unwanted features or incorporate complex components specific to unique experimental situations. Our purpose was to develop a basic, yet multifaceted, computer model of the left heart and systemic circulation in LabVIEW having universal appeal without sacrificing crucial physiologic features. The program we developed employs Windkessel-type impedance models in several open-loop configurations and a closed-loop model coupling a lumped impedance and ventricular pressure source. The open-loop impedance models demonstrate afterload effects on arbitrary aortic pressure/flow inputs. The closed-loop model catalogs the major circulatory waveforms with changes in afterload, preload, and left heart properties. Our model provides an avenue for expanding the use of the ventricular equations through closed-loop coupling that includes a basic coronary circuit. Tested values used for the afterload components and the effects of afterload parameter changes on various waveforms are consistent with published data. We conclude that this model offers the ability to alter several circulatory factors and digitally catalog the most salient features of the pressure/flow waveforms employing a user-friendly platform. These features make the model a useful instructional tool for students as well as a simple experimental tool for cardiovascular research.

A concentrated parameter model for the human cardiovascular system including heart valve dynamics and atrioventricular interaction

Numerical modeling of the human cardiovascular system has always been an active research direction since the 19th century. In the past, various simulation models of different complexities were proposed for different research purposes. In this paper, an improved numerical model to study the dynamic function of the human circulation system is proposed. In the development of the mathematical model, the heart chambers are described with a variable elastance model. The systemic and pulmonary loops are described based on the resistance-compliance-inertia concept by considering local effects of flow friction, elasticity of blood vessels and inertia of blood in different segments of the blood vessels. As an advancement from previous models, heart valve dynamics and atrioventricular interaction, including atrial contraction and motion of the annulus fibrosus, are specifically modeled. With these improvements the developed model can predict several important features that were missing in previous numerical models, including regurgitant flow on heart valve closure, the value of E/A velocity ratio in mitral flow, the motion of the annulus fibrosus (called the KG diaphragm pumping action), etc. These features have important clinical meaning and their changes are often related to cardiovascular diseases. Successful simulation of these features enhances the accuracy of simulations of cardiovascular dynamics, and helps in clinical studies of cardiac function.

Blood pressure and blood flow variation during postural change from sitting to standing: model development and validation

Short-term cardiovascular responses to postural change from sitting to standing involve complex interactions between the autonomic nervous system, which regulates blood pressure, and cerebral autoregulation, which maintains cerebral perfusion. We present a mathematical model that can predict dynamic changes in beat-to-beat arterial blood pressure and middle cerebral artery blood flow velocity during postural change from sitting to standing. Our cardiovascular model utilizes 11 compartments to describe blood pressure, blood flow, compliance, and resistance in the heart and systemic circulation. To include dynamics due to the pulsatile nature of blood pressure and blood flow, resistances in the large systemic arteries are modeled using nonlinear functions of pressure. A physiologically based submodel is used to describe effects of gravity on venous blood pooling during postural change. Two types of control mechanisms are included: 1) autonomic regulation mediated by sympathetic and parasympathetic responses, which affect heart rate, cardiac contractility, resistance, and compliance, and 2) autoregulation mediated by responses to local changes in myogenic tone, metabolic demand, and CO(2) concentration, which affect cerebrovascular resistance. Finally, we formulate an inverse least-squares problem to estimate parameters and demonstrate that our mathematical model is in agreement with physiological data from a young subject during postural change from sitting to standing.