This project develops mathematical and computational models of the cardiovascular system that couple dynamics of blood flow to vessel wall viscoelasticity at the scale of individual vessel segments and vessel networks. The project design integrates novel mathematical modeling, new numerical techniques for soft tissue viscoelasticity, and extensive data analysis via collaboration with experimentalists at the Republic University, Montevideo, Uruguay. Models of both individual vessel segments and networks of multiple vessels will be developed in coordination with a systematic analysis of experimental data that employs parameter estimation and sensitivity analysis techniques. The highly integrative and interdisciplinary nature of this study will yield outcomes that can lead to new standards for modeling cardiovascular dynamics in vessel networks. In particular, the importance of arterial wall viscoelasticity will be analyzed according to vessel location and type, species (sheep, humans) and experimental conditions (in-vivo, ex-vivo). In addition, effects of disease will be simulated with an emphasis on variables of clinical relevance. The models developed in this project will facilitate accurate prediction of waveforms for blood flow, blood pressure, and vessel cross-sectional area in cardiovascular networks.

This project develops a novel, integrative approach to analyzing cardiovascular dynamics both in single vessels as well as vessel networks by coordinating mathematical and computational modeling with a systematic and comprehensive approach to analysis of experimental data. Present approaches rely on models that neglect energy loss (viscoelasticity) in the deformation of individual vessel walls, or models that do not consider downstream effects on blood pressure, blood flow, and vessel cross-sectional area in cardiovascular networks of blood vessels. The models developed in this project will be assessed, calibrated and refined in coordination with experimental collaborators allowing analysis of data from varying experimental conditions, different species (sheep, human), and in different states of health (healthy vs. hypertensives). The techniques and outcomes of this project have the potential for setting a new standard in modeling cardiovascular blood flow and can also be applied to study effects of other diseases (e.g., diabetes) that significantly affect cardiovascular health. The models of vessel networks developed in this project have the potential to provide clinicians with a reference library of blood pressure waveforms that can be incorporated into medical simulators and databases for diagnostic applications in cardiovascular medicine.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Mary Ann Horn
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North Carolina State University Raleigh
United States
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