A Balance Point Approach to Modeling Hemodynamics in Chronic Heart Failure

Chronic heart failure is a complex disease state that can yield reduced cardiac output, pulmonary edema, and increased peripheral resistance. Pressures, flows, and volumes in these conditions emerge from the complex interaction of multiple mechanical properties of the cardiovascular system. The shear complexity of emergent behavior poses a challenge to both basic scientists, who use reductionist approaches to study subsystems in isolation, and clinical researchers, who use inductive approaches to infer the causes of observed changes in clinical variables. This dissertation instead takes a deductive approach using mathematical models to relate three critical cardiovascular variables impacted by heart failure (cardiac output, pulmonary interstitial pressure, and microvascular resistance) to mechanical properties of three subsystems of the cardiovascular system. In contrast to common modeling approaches, three strategies are employed to reduce the complexity and generalize results. First, systems are strategically lumped into descriptions that can be characterized empirically. Second, algebraic formulas are derived to generalize results. Third, the critical interaction of physiological subsystems is represented with opposing processes in the form of “balance points.” The use of all three strategies allows us to: 1) quantify Guyton’s classic cardiac output-venous return graph, 2) predict pulmonary interstitial pressure from interaction of the heart, vascular, and lymphatic systems, and 3) characterize adaptation of the microvasculature to changes in pulsatile blood flow. Cardiac output and venous return curves can now be predicted from parameters characterizing the mechanical properties of the closed-loop system with chronic heart failure. The primary determinants of pulmonary interstitial pressure can now be identified for different phenotypes of heart failure. Finally, increased peripheral resistance, capillary rarefaction, and the formation of arteriovenous malformations are predicted with a decrease in the pulsatility of blood flow. Taken together, applying a physiological balance point approach to integrate subsystems clarifies how changes in the mechanical properties of the cardiovascular system impacts blood and interstitial pressures, volumes, and flows

Dynamics of pulsatile flow in fractal models of vascular branching networks

Efficient regulation of blood flow is critically important to the normal function of many organs, especially the brain. To investigate the circulation of blood in complex, multi-branching vascular networks, a computer model consisting of a virtual fractal model of the vasculature and a mathematical model describing the transport of blood has been developed. Although limited by some constraints, in particular, the use of simplistic, uniformly distributed model for cerebral vasculature and the omission of anastomosis, the proposed computer model was found to provide insights into blood circulation in the cerebral vascular branching network plus the physiological and pathological factors which may affect its functionality. The numerical study conducted on a model of the middle cerebral artery region signified the important effects of vessel compliance, blood viscosity variation as a function of the blood hematocrit, and flow velocity profile on the distributions of flow and pressure in the vascular network

Tailoring vessel morphology in vivo

Tissue engineering is a rapidly growing field which seeks to provide alternatives to organ transplantation in order to address the increasing need for transplantable tissues. One huge hurdle in this effort is the provision of thick tissues; this hurdle exists because currently there is no way to provide prevascularized or rapidly vascularizable scaffolds. To design thick, vascularized tissues, scaffolds are needed that can induce vessels which are similar to the microvasculature found in normal tissues. Angiogenic biomaterials are being developed to provide useful scaffolds to address this problem. In this thesis angiogenic and cell signaling and adhesion factors were incorporated into a biomimetic poly(ethylene glycol) (PEG) hydrogel system. The composition of these hydrogels was precisely tuned to induce the formation of differing vessel morphology. To sensitively measure induced microvascular morphology and to compare it to native microvessels in several tissues, this thesis developed an image-based tool for quantification of scale invariant and classical measures of vessel morphology. The tool displayed great utility in the comparison of native vessels and remodeling vessels in normal tissues. To utilize this tool to tune the vessel response in vivo , Flk1::myr-mCherry fluorescently labeled mice were implanted with Platelet Derived Growth Factor-BB (PDGF-BB) and basic Fibroblast Growth Factor (FGF-2) containing PEG-based hydrogels in a modified mouse corneal angiogenesis assay. Resulting vessels were imaged with confocal microscopy, analyzed with the image based tool created in this thesis to compare morphological differences between treatment groups, and used to create a linear relationship between space filling parameters and dose of growth factor release. Morphological parameters of native mouse tissue vessels were then compared to the linear fit to calculate the dose of growth factors needed to induce vessels similar in morphology to native vessels. Resulting induced vessels did match in morphology to the target vessels. Several other covalently bound signals were then analyzed in the assay and resulting morphology of vessels was compared in several studies which further highlighted the utility of the micropocket assay in conjunction with the image based tool for vessel morphological quantification. Finally, an alternative method to provide rapid vasculature to the constructs, which relied on pre-seeded hydrogels encapsulated endothelial cells was also developed and shown to allow anastamosis between induced host vessels and the implanted construct within 48 hours. These results indicate great promise in the rational design of synthetic, bioactive hydrogels, which can be used as a platform to study microvascular induction for regenerative medicine and angiogenesis research. Future applications of this research may help to develop therapeutic strategies to ameliorate human disease by replacing organs or correcting vessel morphology in the case of ischemic diseases and cancer