A Computer Simulation of the Dynamic Interaction Between Regional Coronary Flow and LV Mechanics

1. Neural Control Cardiovascular System Contractility HR Functional Diagram Left Ventricle Emax PAO SV P P Afterload Preload Aortic Pressure Emax PVA PAO V EDV EDV V SV Assist Device PVA VO2 / beat Oxygen Supply Coronary Circulation Circulatory System Gas Transport & Metabolism Nitric oxide (NO) plays an important role in regulation of blood flow and metabolism; however, its transport properties and mechanisms of action in the microcirculation are not well understood. Our research aim is to elucidate mechanisms of production and transport of NO in the blood and various factors that may affect these processes. CARDIOVASCULAR ENGINEERING RESEARCH P R O G R A M O V E R V I E W We are studying the time-varying relation between regional LV mechanics, local coronary flow, and the important underlying metabolic factors. Our previous LV model was extended to simulate the changes in regional behavior of the heart imposed by modifications in local coronary flow by quantifying the relation between regional heart metabolism and function. The resulting model is capable of predicting the acute changes in heart function during the development of myocardial ischemia following coronary stenosis. A Computer Simulation of the Dynamic Interaction Between Regional Coronary Flow and LV Mechanics Assist Devices Optimization The fundamental hypothesis of this study is that present clinical use of in-series assist devices such as the intraaortic balloon pump is far from optimal and that correct phasing of the pump within the cardiac cycle will result in significant improvement in myocardial energy supply and significant reduction in myocardial energy consumption. We also hypothesize that the effect of intraaortic balloon pumping on coronary perfusion is considerably greater than its effect on ventricular unloading. A Theoretical Study on Autoregulation in the Stenosed Coronary Circulation Stenosis increases coronary resistance and limits the dynamic range of autoregulation. In this study, the limitation on oxygen delivery to the myocardium imposed by stenosed vessels is investigated using a theoretical model. For different degrees of stenosis and for different levels of arteriovenous oxygen content difference, the model predicts the limits of the contractility range for which ventricular oxygen balance is positive. The model also predicts the existence of an optimal contractility level that minimizes the cost of ventricular pressure generation and generates the largest coronary oxygen reserve. Incorporating O2-Hb Reaction Kinetics & the Fahraeus Effect into a Microcirculatory O2-CO2 Transport Model The influence of O2-Hb reaction kinetics and the Fahraeus effect on steady state O2 and CO2 transport in cat brain microcirculation is investigated using a multi-compartmental model. The model is a steady-state multi-compartmental simulation that includes three arteriolar compartments, three venular compartments, and one capillary compartment. • Faculty/Contact: D. Jaron, Ph.D., Drexel University. • E-mail:dov.jaron@coe.drexel.edu

2. Coronary Occlusion Reduced Coronary Perfusion Assist Device Metabolic Effects Contractile Function Effects on Pumping Function Effects on Oxygen Consumption Effects on Myocardial Energy Balance Effects on Systemic Flow Effects on Coronary Flow Effects on Coronary Flow (Autoregulation) Effects on Oxygen Availability A COMPUTER SIMULATION OF THE DYNAMIC INTERACTION BETWEEN REGIONAL CORONARY FLOW & LV MECHANICS P R O J E C T O N E P A G E R Myocardial ischemia is often caused by a coronary occlusion that results in an imbalance between oxygen supply and demand. With the onset of this imbalance, contractile function in the ischemia area rapidly declines. In less than two minutes, paradoxic systolic segment lengthening (dyskinesis) is observed. Mechanical changes are accompanied by biochemical occurrences at the cellular level. When the amount of oxygen delivered to the myocardium is insufficient to support oxidative metabolism, cells mobilize tissue energy reserves. The most abundant energy store, phosphocreatine, is nearly depleted within the first three minutes of severe ischemia. Using a computer model, our research demonstrates that through a simple representation of the underlying metabolic occurrences in the myocardium, it is possible to relate local perfusion and contractile function. This result enables the development of a dynamic heart model whose hemodynamic and metabolic predictions for complete LAD occlusion are within the range of experimental data. The model may prove to be a valuable tool for studying the general short-term effects of regional myocardial ischemia caused by selective coronary occlusion. Computer Simulation • Faculty/Contact: D. Jaron, Ph.D., Drexel University. • E-mail: dov.jaron@coe.drexel.edu • Laboratories: Cardiovascular Engineering Lab.

3. Cardiovascular System Model ASSIST DEVICES OPTIMIZATION P R O J E C T O N E P A G E R The fundamental hypotheses of this study are that present clinical use of in-series assist devices such as the intraaortic balloon pump is far from optimal and that correct phasing of the pump within the cardiac cycle will result in significant improvement in myocardial energy supply and significant reduction in myocardial energy consumption. We also hypothesize that the effect of intraaortic balloon pumping on coronary perfusion is considerably greater than its effect on ventricular unloading. To test these hypotheses, our investigation consists of theoretical and experimental elements. We are enhancing our computer simulation of the cardiovascular system to provide us with a theoretical tool to study the energetics of the system. In addition, we are conducting animal experiments to confirm our theoretical studies and to obtain additional physiological data regarding the interaction of the device with the cardiovascular system. The specific aims of the study are to enhance our present cardiovascular model by: • Updating the model of the left ventricle and incorporating important intrinsic and extrinsic control features, which will enable simulation of both healthy and ischemic states. • Adding a detailed model of the coronary circulation. • Incorporating models of physiological control mechanisms, namely, baroreceptor control and local autoregulation. • Faculty/Contact: D. Jaron, Ph.D., Drexel University. • E-mail: dov.jaron@coe.drexel.edu • Laboratories: Cardiovascular Engineering Lab.

4. Five Compartments Model veins arter capillaries venules ioles arteries superficial vessels BRANCH 1 BRANCH 2 superficial vessels BRANCH 3 BRANCH 4 BRANCH 5 Collateral flow A THEORETICAL STUDY ON AUTOREGULATION IN THE STENOSED CORONARY CIRCULATION P R O J E C T O N E P A G E R Stenosis increases coronary resistance and limits the dynamic range of autoregulation. In this study, the limitation on oxygen delivery to the myocardium imposed by stenosed vessels is investigated using a theoretical model. For different degrees of stenosis and for different levels of arteriovenous oxygen content difference, the model predicts the limits of the contractility range for which ventricular oxygen balance is positive. The model also predicts the existence of an optimal contractility level that minimizes the cost of ventricular pressure generation and generates the largest coronary oxygen reserve. To study the response of coronary autoregulation and its dynamic range during changes in preload and contractility, in the presence of coronary arterial stenosis, we use lumped models of the cardiovascular system. The models are used to predict the amount of coronary resistance and flow required to produce equilibrium between myocardial oxygen consumption and supply, which enables us to explore the properties of autoregulation. Adding stenosis to the model allows us to study the limitations imposed on the dynamic range of autoregulation in pathologic states. • Faculty/Contact: D. Jaron, Ph.D., Drexel University. • E-mail: dov.jaron@coe.drexel.edu • Laboratories: Cardiovascular Engineering Lab.

5. a – independent of NO ; b-g – based on different literature data GAS TRANSPORT & METABOLISM P R O J E C T O N E P A G E R Nitric oxide (NO) plays an important role in regulation of blood flow and metabolism; however, its transport properties and mechanisms of action in the microcirculation are not well understood. Our research aim is to elucidate mechanisms of production and transport of NO in the blood and various factors that may affect these processes. The long-term goal of this research is to develop a comprehensive mathematical model to evaluate and quantify hypothesized mechanisms of NO transport, evaluate interactions between mechanisms, and assess the relative contributions of each. This model will simulate the interactions between production, mass transport, feedback regulation, and mechanisms of action of NO in the microcirculation and tissue. Quantitative data obtained from the validated model is used to predict parameters that cannot be measured in vivo, analyze hypotheses, and further the understanding of NO production and transport mechanisms. We use an integrated approach in which the model is developed in conjunction with in vitro and in vivo experiments designed to provide key parameters for the mathematical modeling and to test model validity. Specific interactions among NO, oxygen, carbon dioxide, hemoglobin, calcium, and thiols in blood and tissue are simulated by the model and determined experimentally under controlled conditions. Effects of Nitric Oxide on Oxygen Metabolism The equation for oxygen transport in tissue: In cylindrical coordinates for steady state: Qt = metabolic rate of the tissue t = solubility, Dt = diffusion coefficient for oxygen in tissue • Faculty/Contact: D. Jaron, Ph.D., Drexel University. • E-mail: dov.jaron@coe.drexel.edu • Collaborators: K. Barbee, Ph.D., K. Lamkin-Kennard, Ph.D., and P. Kurnik, M.D. (all from Drexel); D. Buerk, Ph.D. (U. of Penn). • Laboratories: Cardiovascular Engineering Lab.

6. Arteriole Groups (a1) (a2) (a3) Q C8 C1 C1 C2 CV C2 C3 C3 C7 CV CA C4 C5 C8 C5 C7 CA C6 C4 C6 ,CO2 ,O2 ,O2 ,CO2 ,O2 ,CO2 ,O2 ,CO2 ,O2 ,CO2 ,O2 ,O2 ,O2 ,CO2 ,CO2 ,CO2 ,CO2 ,CO2 ,O2 ,O2 Tissue Capillary Group (cap) Q (v2) (v3) (v1) Venule Groups Block diagram of the multicompartmental model for O2 – CO2 coupled transport in the microcirculation. (C: concentration, Q: blood flow rate, A: artery, a: arteriole, cap: capillary, v: venule, V: vein.) INCORPORATING O2-HB REACTION KINETICS & THE FAHRAEUS EFFECT INTO A MICROCIRCULATORY O2-CO2 TRANSPORT MODEL P R O J E C T O N E P A G E R The influence of O2-Hb reaction kinetics and the Fahraeus effect (reduced tube hematocrit in small micro-vessels) on steady state O2 and CO2 transport in cat brain microcirculation is investigated using a multi-compartmental model. The model is a steady-state multi-compartmental simulation that includes three arteriolar compartments, three venular compartments, and one capillary compartment. Three different types of oxygen deficits (stagnant, hypoxic, and anemic conditions) were simulated by respectively reducing blood flow, arterial O2 saturation, and systemic hematocrit to one half of normal. Microcirculatory distributions for PO2, PCO2, and O2 saturation and deviations from equilibrium, as well as the O2 and CO2 fluxes for each compartment, were predicted for the three O2 supply deficits. Differences were found for O2 extraction ratios and relative contributions of arteriolar, venular, and capillary gas fluxes for each type of deficit. The Fahraeus effect and O2-Hb kinetics reduced O2 extraction in all cases and altered microcirculatory gas distributions depending on the specific type of O2 supply deficits. The model continues to predict that capillaries are the major site where gas exchange takes place and demonstrates that the Fahraeus effect and non-equilibrium O2-Hb kinetics are important mechanisms that should not be neglected in O2 and CO2 transport modeling. While this model provides useful insight regarding the influence of the Fahraeus effect and O2-Hb kinetics under steady state, the addition of a distributed and dynamic simulation should further elucidate the effects of the brain's heterogeneous properties and transient behavior. • Faculty/Contact: D. Jaron, Ph.D., Drexel University. • E-mail: dov.jaron@coe.drexel.edu • Collaborators:D. Buerk, Ph.D. (U. of Penn). • Laboratories: Cardiovascular Engineering Lab.