Lumped Parameter Model of Cardiovascular-Respiratory Interaction

Journal of Engineering Mathematics, 2000

Arterial pressure and flow result from the interaction between the (actively) ejecting ventricle and the (passive) arterial circulation. The main objective was to construct a model, accounting for this interaction, that is simple enough so that (i) model parameters can be derived from data measured in experimental and/or clinical conditions, and (ii) the model can be applied to support the analysis and interpretation of these data. It is demonstrated how an established conceptual model of ventricular function (the time-varying elastance) can be coupled to a four-element windkessel model of the arterial system to yield an elegant model of heart-arterial interaction. The coupling leads to a set of three ordinary differential equations. The model allows the study of the effect of changes in cardiac and/or arterial properties on arterial pressure and flow. As an illustration, cardiac and arterial model parameters are derived from measured experimental data in the systemic circulation of a pig and in the pulmonary circulation of a dog. It is evaluated how well measured cardiac and arterial function actually adhere to their assumed theoretical models (time-varying elastance and four-element windkessel model). It is further assessed how well the simple model of heart-arterial interaction describes systemic and pulmonary hemodynamics by comparing simulated and measured experimental data. The limitations and pitfalls of the model, as well as possible applications in the clinical field, are discussed.

Applied Mathematics and Computation, 2007

This paper aims to design a mathematical model for determining blood pressures response to cardiac and respiratory parameters. For this purpose a three-compartmental model is investigated to provide a two-nonlinear coupled ordinary differential equations. Stability conditions are established and inverse technics are proposed for identifying model parameters. The validation of the model is achieved throughout a comparative study with an existing model.

This study develops a coupled cardiovascular-respiratory model that predicts cerebral blood flow velocity (CBFV), arterial blood pressure, end-tidal CO 2 , and ejection fraction for a patient with congestive heart failure. The model is a lumped parameter model giving rise to a system of ordinary differential equations. We use sensitivity analysis and subset selection to identify a set of model parameters that can be estimated given the patient data. Gradient based nonlinear optimization is used to estimate the subset of parameters. Optimization was caried out first for the cardiovascular submodel and subsequently for the respiratory model. Once a set of optimal parameters were found, the coupled model was computed to confirm that the model is still able to predict the observed data. Results showed that with the approach and methods presented in this paper it is possible to examine and quantify identifiability of model parameters. Using this approach we identified 5 key cardiovascular parameters and 4 key respiratory parameters. Nonlinear optimization techniques was used to estimate these parameters and we tested that values for all parameters were physiologically reasonable for a patient with congestive heart failure.

We have developed a mathematical model of the human cardiopulmonary system that is able to simulate the normal functions of the cardiovascular and pulmonary systems, as well as their coupled interactions. Included in the model are descriptions of atrial and ventricular mechanics, the hemodynamics of the systemic and pulmonic circulations, baroreflex control of arterial pressure, airway and lung mechanics, as well as, gas transport at alveolar-capillary membrane. With the suitable parameter set, the integrated cardiopulmonary model yielded pressure, volume and flow waveforms that agree well with published data. In addition, The model demonstrated stability under large amplitude perturbations of the physiological variables, such as Valsalva Maneuver.

Acta Biotheoretica, 2010

Several key areas in modeling the cardiovascular and respiratory control systems are reviewed and examples are given which reflect the research state of the art in these areas. Attention is given to the interrelated issues of data collection, experimental design, and model application including model development and analysis. Examples are given of current clinical problems which can be examined via modeling, and important issues related to model adaptation to the clinical setting.

The International journal of artificial organs, 2016

The analysis of the efficiency and optimum use of cardiovascular and respiratory support systems is of great importance in research and development as well as in clinical practice. To understand the complex interaction between human cardiovascular or respiratory systems and the mechanical assist devices, a number of physical, computational or hybrid (physical-electrical or physical-computational) models/simulators have been developed and used in recent years. The hybrid models combine the advantages of both the physical models (interaction with assist devices) and of the computational/electrical models (accuracy, flexibility). This paper reviews the existing solutions and briefly describes their characteristics, advantages and disadvantages, chiefly emphasizing the features of the hybrid models that are most promising for future development.

2019

Cardiovascular diseases cause the majority of deaths in the developed countries. They are strongly interlinked with hemodynamics of the cardiovascular system (CS); thus it is important to study blood flow under normal and pathological conditions. Hemodynamic models of CS can be classified as lumped parameter, one-dimensional, two-dimensional and three-dimensional models. The simplest lumped parameter models are attractive for teaching purposes as well as for clinicians, since they describe the whole CS with a small number of parameters (in terms of compliance, resistance and inertance) having a clear physiological meaning. The results of such a model include pressure and volume time variations of observed compartments and also flow rates between compartments (arterial and vein trees are considered as compartments, too). Upgraded with a short-term regulatory system model (arterial baroreflex system, cardiopulmonary baroreflex system and neural control of the heart rate) and resting p...

Lumped parameter model is a very useful type of mathematical modelling where the physical system is made analogous to an electrical network. Lumped parameter model is represented graphically by a circuit diagram in which vertices represent the voltages and the edges the current in the circuit. The mathematical analysis of such a circuit model is very convenient and eases the analysis of the actual physical system. These models are constructed by building the analogy between cardiovascular system and electrical circuit.This analogy makes use of simple ordinary differential equations in time which can be solved either numerically or analytically. A mathematical model to model the blood pressure variation in the four chambers of heart at representative altitudes of h= 2 km, h = 4 km and h = 5 kmusing lumped compartments of blood circulation is presented in this paper. This lumped parameter model consists of eight compartments that include the pumping heart, the systemic circulation and the pulmonary circulation. The governing equations for pressure and flow in each compartment are derived from the following three equations: Ohm's law, conservation of volume and the definition of compliances. The g-factor is added to the model in order to accommodate for the effects due to gravitation.

We aimed to validate the mathematical validity and accuracy of the respiratory components of the Nottingham Physiology Simulator (NPS), a computer simulation of physiological models. Subsequently, we aimed to assess the accuracy of the NPS in predicting the effects of a change in mechanical ventilation on patient arterial blood-gas tensions. The NPS was supplied with the following measured or calculated values from patients receiving intensive therapy: pulmonary shunt and physiological deadspace fractions, oxygen consumption, respiratory quotient, cardiac output, inspired oxygen fraction, expired minute volume, haemoglobin concentration, temperature and arterial base excess. Values calculated by the NPS for arterial oxygen tension and saturation ( 2 O a P and 2 O a ), S mixed venous oxygen tension and saturation 2 O V (P and 2 O V ), S arterial and mixed venous carbon dioxide tension 2 CO ( a P and 2 CO V )

Computer Methods and Programs in Biomedicine, 2018

Background and Objective This work introduces an object-oriented computational model to study cardiopulmonary interactions in humans. Methods Modeling was performed in object-oriented programing language Matlab Simscape, where model components are connected with each other through physical connections. Constitutive and phenomenological equations of model elements are implemented based on their non-linear pressure-volume or pressure-flow relationship. The model includes more than 30 physiological compartments, which belong either to the cardiovascular or respiratory system. The model considers non-linear behaviors of veins, pulmonary capillaries, collapsible airways, alveoli, and the chest wall. Model parameters were derived based on literature values. Model validation was performed by comparing simulation results with clinical and animal data reported in literature. Results The model is able to provide quantitative values of alveolar, pleural, interstitial, aortic and ventricular pressures, as well as heart and lung volumes during spontaneous breathing and mechanical ventilation. Results of baseline simulation demonstrate the consistency of the assigned parameters. Simulation results during mechanical ventilation with PEEP trials can be directly compared with animal and clinical data given in literature. Conclusions Object-oriented programming languages can be used to model interconnected systems including model non-linearities. The model provides a useful tool to investigate cardiopulmonary activity during spontaneous breathing and mechanical ventilation.

Proceedings / the ... Annual Symposium on Computer Application [sic] in Medical Care. Symposium on Computer Applications in Medical Care, 1994

VentSim is a quantitative model that predicts the effects of alternative ventilator settings on the cardiopulmonary physiology of critically ill patients. VentSim is an expanded version of the physiologic model in VentPlan, an application that provides ventilator-setting recommendations for patients in the intensive care unit. VentSim includes a ventilator component, an airway component, and a circulation component. The ventilator component predicts the pressures and airflows that are generated by a volume-cycled, constant-flow ventilator. The airway component has anatomic and physiologic deadspace compartments, and two alveolar compartments that participate in gas exchange with two pulmonary blood-flow compartments in the circulatory component. The circulatory component also has a shunt compartment that allows a fraction of blood flow to bypass gas exchange in the lungs, and a tissue compartment that consumes oxygen and generates carbon dioxide. The VentSim model is a set of linked...

Methods of information in medicine, 2000

When a Bi-Ventricular Assist Device (BVAD) is used in conjunction with mechanical ventilation (MV) of the lungs with positive intrathoracic pressure (Pt), the latter influences hemodynamics. The aim of our study was to assess the simultaneous influence of BVAD and MV on hemodynamics. We assumed ventricular pathological conditions as reduced elastances and increased rest volumes. Peripheral systemic arterial resistance was assumed to have different values. Data were obtained by computer simulation. Trends in main hemodynamic variables were compared with clinical data from literature. Simulation showed that systemic venous, pulmonary arterial and left atrial pressures are very sensitive to Pt (-2 to 5 mmHg).

The Japanese Journal of Physiology, 2004

parameter models. We also discuss the nonlinear characteristics of the pressure-volume relationship in veins. Then the control pathways that participate in feedback mechanisms (baroreceptors and cardiopulmonary receptors) are described to explain the interaction between hemodynamics and autonomic nerve control in the circulation. Based on a set-point model, the computational aspects of reflex control are explained.

Journal of Biomechanical Engineering, 2013

Both in academic research and in clinical settings, virtual simulation of the cardiovascular system can be used to rapidly assess complex multivariable interactions between blood vessels, blood flow, and the heart. Moreover, metrics that can only be predicted with computational simulations (e.g., mechanical wall stress, oscillatory shear index, etc.) can be used to assess disease progression, for presurgical planning, and for interventional outcomes. Because the pulmonary vasculature is susceptible to a wide range of pathologies that directly impact and are affected by the hemodynamics (e.g., pulmonary hypertension), the ability to develop numerical models of pulmonary blood flow can be invaluable to the clinical scientist. Pulmonary hypertension is a devastating disease that can directly benefit from computational hemodynamics when used for diagnosis and basic research. In the present work, we provide a clinical overview of pulmonary hypertension with a focus on the hemodynamics, current treatments, and their limitations. Even with a rich history in computational modeling of the human circulation, hemodynamics in the pulmonary vasculature remains largely unexplored. Thus, we review the tasks involved in developing a computational model of pulmonary blood flow, namely vasculature reconstruction, meshing, and boundary conditions. We also address how inconsistencies between models can result in drastically different flow solutions and suggest avenues for future research opportunities. In its current state, the interpretation of this modeling technology can be subjective in a research environment and impractical for clinical practice. Therefore, considerations must be taken into account to make modeling reliable and reproducible in a laboratory setting and amenable to the vascular clinic. Finally, we discuss relevant existing models and how they have been used to gain insight into cardiopulmonary physiology and pathology.

2016

In this paper we propose a model of the cardiovascular system, where stressed blood volume is a model parameter instead of an initial condition. Stressed blood volume (SBV) is an important indicator of fluid responsiveness, i.e., this term can help to classify patients between responders and non-responders to fluid therapy. We study a six compartment model, then using the conservation of total blood volume, one differential equation of the original model is omitted and a new model is obtained. Comparing the haemodynamic signals of the previous model and the new version, we show that the simulations are qualitatively similar. One important difference with the original model is that the initial conditions for solving the proposed model are arbitrary. This allows us to perform a sensitivity analysis using automatic differentiation of the reduced model for all model parameters without excluding any parameter a priori, unlike the authors of the original formulation have done. This analysis showed that two parameters, the heart period and the stressed blood volume, have a major effect on the performance of the model.