Computational Modeling of Cardiac Biomechanics

The goal of this dissertation was to develop a realistic and patient-specific computational model of the heart that ultimately would help medical scientists to better diagnose and treat heart diseases. In order to achieve this goal, a three dimensional finite element model of the heart was created using magnetic resonance images of the beating pig heart. This model was loaded by the pressure of blood inside the left ventricle which was measured by synchronous catheterization. A recently developed structurally based constitutive model of the myocardium was incorporated in the finite element solver to model passive left ventricular myocardium. Additionally, an unloading algorithm originally designed for arteries was adapted to estimate the stress-free geometry of the heart from its partially-loaded geometry obtained from magnetic resonance imaging. Finally, a regionally varying growth module was added to the computational model to predict eccentric hypertrophy of the heart under various pathological conditions that result in volume overload of the heart. The computational model was validated using experimental data obtained from porcine heart such as in vivo strains measured from magnetic resonance imaging

Removing Sets from Connected Spaces While Preserving Connectedness

As per the title, the nature of sets that can be removed from a product of more than one connected, arcwise connected, or point arcwise connected spaces while preserving the appropriate kind of connectedness is studied. This can depend on the cardinality of the set being removed or sometimes just on the cardinality of what is removed from one or two factor spaces. Sometimes it can depend on topological properties of the set being removed or its trace on various factor spaces. Some of the results are complicated to prove while being easy to state. Sometimes proofs for different kinds of connectedness are similar, but different enough to require separate proofs. Many examples are given to show that part of the hypotheses of theorems cannot be dropped, and some examples describe results about spaces whose connectedness can be established directly but not with the help of our results. A large number of examples are given for such purposes

Removing sets from connected product spaces while preserving connectedness

summary:As per the title, the nature of sets that can be removed from a product of more than one connected, arcwise connected, or point arcwise connected spaces while preserving the appropriate kind of connectedness is studied. This can depend on the cardinality of the set being removed or sometimes just on the cardinality of what is removed from one or two factor spaces. Sometimes it can depend on topological properties of the set being removed or its trace on various factor spaces. Some of the results are complicated to prove while being easy to state. Sometimes proofs for different kinds of connectedness are similar, but different enough to require separate proofs. Many examples are given to show that part of the hypotheses of theorems cannot be dropped, and some examples describe results about spaces whose connectedness can be established directly but not with the help of our results. A large number of examples are given for such purposes

Temporal Changes in Infarct Material Properties: An In Vivo Assessment Using Magnetic Resonance Imaging and Finite Element Simulations.

BACKGROUND: Infarct expansion initiates and sustains adverse left ventricular (LV) remodeling after myocardial infarction (MI) and is influenced by temporal changes in infarct material properties. Data from ex vivo biaxial extension testing support this hypothesis; however, infarct material properties have never been measured in vivo. The goal of the current study was to serially quantify the in vivo material properties and fiber orientation of infarcted myocardium over a 12-week period in a porcine model of MI. METHODS: A combination of magnetic resonance imaging (MRI), catheterization, finite element modeling, and numeric optimization was used to analyze posterolateral MI. Specifically, properties were determined by minimizing the difference between in vivo strains and volume calculated from MRI and strains and volume predicted by finite element modeling. RESULTS: In 1 week after MI, the infarct region was found to be approximately 20 times stiffer than normal diastolic myocardium. Over the course of 12 weeks, the infarct region became progressively less stiff as the LV dilated and ejection fraction decreased. The infarct thinned by nearly half during the remodeling period, and infarct fiber angles became more circumferentially oriented. CONCLUSIONS: The results reported here are consistent with previously described ex vivo biaxial extension studies of infarct material properties and the circumferential change of collagen orientation in posterolateral infarcts. The current study represents a significant advance in that the method used allows for the serial assessment of an individual infarct in vivo over time and avoids the inherent limitations related to the testing of excised tissues

Firefly: The Case for a Holistic Understanding of the Global Structure and Dynamics of the Sun and the Heliosphere

This white paper is on the HMCS Firefly mission concept study. Firefly focuses on the global structure and dynamics of the Sun's interior, the generation of solar magnetic fields, the deciphering of the solar cycle, the conditions leading to the explosive activity, and the structure and dynamics of the corona as it drives the heliosphere