Outflow boundary conditions for 3D simulations of non-periodic blood flow and pressure fields in deformable arteries

The simulation of blood flow and pressure in arteries requires outflow boundary conditions that incorporate models of downstream domains. We previously described a coupled multidomain method to couple analytical models of the downstream domains with 3D numerical models of the upstream vasculature. This prior work either included pure resistance boundary conditions or impedance boundary conditions based on assumed periodicity of the solution. However, flow and pressure in arteries are not necessarily periodic in time due to heart rate variability, respiration, complex transitional flow or acute physiological changes. We present herein an approach for prescribing lumped parameter outflow boundary conditions that accommodate transient phenomena. We have applied this method to compute haemodynamic quantities in different physiologically relevant cardiovascular models, including patient-specific examples, to study non-periodic flow phenomena often observed in normal subjects and in patients with acquired or congenital cardiovascular disease. The relevance of using boundary conditions that accommodate transient phenomena compared with boundary conditions that assume periodicity of the solution is discussed

A Hybrid Experimental‐Computational Modeling Framework For Cardiovascular Device Testing

Significant advances in biomedical science often leverage powerful computational and experimental modeling platforms. We present a framework named physiology simulation coupled experiment (“PSCOPE”) that can capitalize on the strengths of both types of platforms in a single hybrid model. PSCOPE uses an iterative method to couple an in vitro mock circuit to a lumped-parameter numerical simulation of physiology, obtaining closed-loop feedback between the two. We first compared the results of Fontan graft obstruction scenarios modeled using both PSCOPE and an established multiscale computational fluid dynamics method; the normalized root-mean-square error values of important physiologic parameters were between 0.1% and 2.1%, confirming the fidelity of the PSCOPE framework. Next, we demonstrate an example application of PSCOPE to model a scenario beyond the current capabilities of multiscale computational methods—the implantation of a Jarvik 2000 blood pump for cavopulmonary support in the single-ventricle circulation; we found that the commercial Jarvik 2000 controller can be modified to produce a suitable rotor speed for augmenting cardiac output by approximately 20% while maintaining blood pressures within safe ranges. The unified modeling framework enables a testing environment which simultaneously operates a medical device and performs computational simulations of the resulting physiology, providing a tool for physically testing medical devices with simulated physiologic feedback

Modeling and Estimation of Cardiorespiratory Function, with Application to Mechanical Ventilation

Evidence-based medicine is at the heart of current medical practice where clinical decisions are driven by research data. However, most current therapy recommendations follow generalized protocols and guidelines that are based on epidemiological (population) studies and thus not suited for the individual patient's demands. Patient-tailored therapies are considered, hence, an unmet clinical need. We believe that mathematical models of the physiology can attend to such a clinical need, because they can be tuned to the individual patient. Such models provide a sound mathematical framework for personalized clinical decisions. In particular, physiological models in medicine can serve the following two purposes: 1) They can be an efficient tool to quantify cardiopulmonary dynamics, conduct virtual clinical/physiological experiments, and investigate the effects of specific treatments. 2) Model-based estimation techniques can assess physiological parameters or variables, which are otherwise impractical or dangerous to measure; they can effectively tune a generic model to become patient-specific, able to mimic the behavior of a particular patient. In this thesis, we propose a series of modifications to a previously developed cardiopulmonary model (CP Model) in order to better replicate heart-lung interaction phenomena that are typically observed under mechanical ventilation, hence allowing for a more accurate analysis of ventilation-induced changes in cardiac function. The response of this modified model is validated with experimental data collected during mechanical ventilation conditions. Further, as an industrial application of mathematical models, we present a patient emulator system that comprises the modified CP Model, a physical ventilator, and a piston-cylinder arrangement that serves as an electrical-to-hydraulic transducer. The modified CP Model then serves as the virtual patient that is being ventilated, where disease conditions can be instilled. Such a system is designed to offer a well-controlled experimental environment for ventilator manufacturers to efficaciously test and compare ventilation modalities and therapies, thereby enhancing their verification and validation manufacturing processes. Finally, we develop a model-based approach to estimate (noninvasively) the function of the cardiovascular system, in terms of cardiac performance (i.e., cardiac output) and the dynamics of the systemic arterial tree (i.e., time constant). With this technique, we envision to provide continuous and real-time bedside monitoring of changes in cardiovascular function, such as those induced by changes in ventilator settings

A quantitative estimation of regulation and transport limitations in the human cardiopulmonary system

The object of this dissertation is to quantitatively describe the regulation of some of the exchange processes within the human body. Conceptually this dissertation is divided into two sections. In the first section a macroscopic view was adopted to describe the overall regulation of the cardiovascular and respiratory systems. These overall system models were used as heuristic tools to gain an understanding of physiological behavior in micro-gravity. In the second section, a microscopic view was used to estimate the role played by the surfactant system of the lung in regulating the transfer of fluid across the pulmonary-capillary wall;The basis of the cardiovascular system model is the maintenance of arterial blood pressure homeostasis. Sub-models constituting the overall model are: the pressure-flow model, the heart action model, the controller model which describes short term-control, and the renal model which describes long term control and the regulation of total body water content. Model predictions show that incorporating the fluid shift from the lower to the upper part of the body in micro-gravity is sufficient to account for the cardiovascular changes occurring in micro-gravity;The respiratory model is concerned with the maintenance of a constant carbon dioxide level in the tissue and body fluids. The sub-models constituting the overall respiratory model are: the gas-exchange model, the mechanics model, and the controller model which determines the ventilation and cardiac output on the basis of arterial blood gas tensions. Simulation results show that pleural pressure homogeneity, increased lung diffusing capacity and decreased lung volume are sufficient to describe respiratory changes in micro-gravity;In the penultimate section the lung mechanics model is coupled with a model of fluid exchange across the pulmonary-capillary wall. The lung mechanics model estimates the influence of the surfactant system of the lung in controlling the interstitial space hydrostatic pressure while the fluid exchange model determines the influence of the interstitial space hydrostatic pressure in regulating fluid movement across the pulmonary-capillary wall. This model quantitatively estimates the influence of the surfactant alone in regulating fluid movement across the pulmonary-capillary wall

TrauMAP - Integrating Anatomical and Physiological Simulation (Dissertation Proposal)

In trauma, many injuries impact anatomical structures, which may in turn affect physiological processes - not only those processes within the structure, but also ones occurring in physical proximity to them. Our goal with this research is to model mechanical interactions of different body systems and their impingement on underlying physiological processes. We are particularly concerned with pathological situations in which body system functions that normally do not interact become dependent as a result of mechanical behavior. Towards that end, the proposed TRAUMAP system (Trauma Modeling of Anatomy and Physiology) consists of three modules: (1) a hypothesis generator for suggesting possible structural changes that result from the direct injuries sustained; (2) an information source for responding to operator querying about anatomical structures, physiological processes, and pathophysiological processes; and (3) a continuous system simulator for simulating and illustrating anatomical and physiological changes in three dimensions. Models that can capture such changes may serve as an infrastructure for more detailed modeling and benefit surgical planning, surgical training, and general medical education, enabling students to visualize better, in an interactive environment, certain basic anatomical and physiological dependencies

Review of Zero-D and 1-D Models of Blood Flow in the Cardiovascular System

<p>Abstract</p> <p>Background</p> <p>Zero-dimensional (lumped parameter) and one dimensional models, based on simplified representations of the components of the cardiovascular system, can contribute strongly to our understanding of circulatory physiology. Zero-D models provide a concise way to evaluate the haemodynamic interactions among the cardiovascular organs, whilst one-D (distributed parameter) models add the facility to represent efficiently the effects of pulse wave transmission in the arterial network at greatly reduced computational expense compared to higher dimensional computational fluid dynamics studies. There is extensive literature on both types of models.</p> <p>Method and Results</p> <p>The purpose of this review article is to summarise published 0D and 1D models of the cardiovascular system, to explore their limitations and range of application, and to provide an indication of the physiological phenomena that can be included in these representations. The review on 0D models collects together in one place a description of the range of models that have been used to describe the various characteristics of cardiovascular response, together with the factors that influence it. Such models generally feature the major components of the system, such as the heart, the heart valves and the vasculature. The models are categorised in terms of the features of the system that they are able to represent, their complexity and range of application: representations of effects including pressure-dependent vessel properties, interaction between the heart chambers, neuro-regulation and auto-regulation are explored. The examination on 1D models covers various methods for the assembly, discretisation and solution of the governing equations, in conjunction with a report of the definition and treatment of boundary conditions. Increasingly, 0D and 1D models are used in multi-scale models, in which their primary role is to provide boundary conditions for sophisticate, and often patient-specific, 2D and 3D models, and this application is also addressed. As an example of 0D cardiovascular modelling, a small selection of simple models have been represented in the CellML mark-up language and uploaded to the CellML model repository <url>http://models.cellml.org/</url>. They are freely available to the research and education communities.</p> <p>Conclusion</p> <p>Each published cardiovascular model has merit for particular applications. This review categorises 0D and 1D models, highlights their advantages and disadvantages, and thus provides guidance on the selection of models to assist various cardiovascular modelling studies. It also identifies directions for further development, as well as current challenges in the wider use of these models including service to represent boundary conditions for local 3D models and translation to clinical application.</p

A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems

Current mathematical models of the cardiovascular system that are based on systems of ordinary differential equations are limited in their ability to mimic important features of measured patient data, such as variable heart rates (HR). Such limitations present a significant obstacle in the use of such models for clinical decision-making, as it is the variations in vital signs such as HR and systolic and diastolic blood pressure that are monitored and recorded in typical critical care bedside monitoring systems. In this paper, novel extensions to well-established multi-compartmental models of the cardiovascular and respiratory systems are proposed that permit the simulation of variable HR. Furthermore, a correction to current models is also proposed to stabilize the respiratory behaviour and enable realistic simulation of vital signs over the longer time scales required for clinical management. The results of the extended model developed here show better agreement with measured bio-signals, and these extensions provide an important first step towards estimating model parameters from patient data, using methods such as neural ordinary differential equations. The approach presented is generalizable to many other similar multi-compartmental models of the cardiovascular and respiratory systems