The techniques of surface deformation and mapping are useful tools for the visualization of medical surfaces, especially for highly undulated or branched surfaces. In this thesis, two algorithms are presented for flattened visualizations of multi-branched medical surfaces, such as vessels. The first algorithm is an angle preserving approach, which is based on conformal analysis. The mapping function is obtained by minimizing two Dirichlet functionals. On a triangulated representation of vessel surfaces, this algorithm can be implemented efficiently using a finite element method. The second algorithm adjusts the result from conformal mapping to produce a flattened representation of the original surface while preserving areas. It employs the theory of optimal mass transport via a gradient descent approach. A new class of image morphing algorithms is also considered based on the theory of optimal mass transport. The mass moving energy functional is revised by adding an intensity penalizing term, in order to reduce the undesired "fading" effects. It is a parameter free approach. This technique has been applied on several natural and medical images to generate in-between image sequences.

Indiana University-Purdue University Indianapolis (IUPUI) / The endothelium is a single layer of cells lining the arteries and is involved in many physiological reactions which are responsible for vascular tone. Free radicals are important participants in these chemical reactions in the endothelium. Here we quantify free radicals, ex vivo, in biological tissue with continuous wave electron paramagnetic resonance (EPR). In all of the experiments in this thesis, we use a novel EPR spin trapping technique that has been developed for tissue segments. EPR spin trapping is often considered the ‘gold standard’ in reactive oxygen species (ROS) detection because of its sensitivity and non-invasive nature. In all experiments, tissue was placed in physiological saline solution with 190-mM PBN (N-tert-butyl-α-phenylnitrone), 10% by volume dimethyl-sulphoxide (DMSO) for cryopreservation, and incubated in the dark for between 30 minutes up to 2 hours at 37°C while gently being stirred. Tissue and supernatant were then loaded into a syringe and frozen at -80°C until EPR analysis. In our experiments, the EPR spectra were normalized with respect to tissue volume. Conducting experiments at liquid nitrogen temperature leads to some experimental advantages. The freezing of the spin adducts renders them stable over a longer period, which allows ample time to analyze tissue samples for ROS. The dielectric constant of ice is greatly reduced over its liquid counterpart; this property of water enables larger sample volumes to be inserted into the EPR cavity without overloading it and leads to enhanced signal detection. Due to Maxwell-Boltzmann statistics, the population difference goes up as the temperature goes down, so this phenomenon enhances the signal intensity as well. With the ‘gold standard’ assertion in mind, we investigated whether slicing tissue to assay ROS that is commonly used in fluorescence experiments will show more free radical generation than tissue of a similar volume that remains unsliced. Sliced tissue exhibited a 76% increase in ROS generation; this implies that higher ROS concentrations in sliced tissue indicate extraneous ROS generation not associated with the ROS stimulus of interest. We also investigated the role of ROS in chronic flow overload (CFO). Elevation of shear stress that increases production of vascular ROS has not been well investigated. We hypothesize that CFO increases ROS production mediated in part by NADPH oxidase, which leads to endothelial dysfunction. ROS production increased threefold in response to CFO. The endothelium dependent vasorelaxation was compromised in the CFO group. Treatment with apocynin significantly reduced ROS production in the vessel wall, preserved endothelial function, and inhibited expressions of p22/p47phox and NOX2/NOX4. The present data implicate NADPH oxidase produced ROS and eNOS uncoupling in endothelial dysfunction at 1 wk of CFO. In further work, a swine right ventricular hypertrophy (RVH) model induced by pulmonary artery (PA) banding was used to study right coronary artery (RCA) endothelial function and ROS level. Endothelial function was compromised in RCA of RVH as attributed to insufficient endothelial nitric oxide synthase cofactor tetrahydrobiopterin. In conclusion, stretch due to outward remodeling of RCA during RVH (at constant wall shear stress), similar to vessel stretch in hypertension, appears to induce ROS elevation, endothelial dysfunction, and an increase in basal tone. Finally, although hypertension-induced vascular stiffness and dysfunction are well established in patients and animal models, we hypothesize that stretch or distension due to hypertension and outward expansion is the cause of endothelial dysfunction mediated by angiotensin II type 1 (AT1) receptor in coronary arteries. The expression and activation of AT1 receptor and the production of ROS were up regulated and endothelial function deteriorated in the RCA. The acute inhibition of AT1 receptor and NADPH oxidase partially restored the endothelial function. Stretch or distension activates the AT1 receptor which mediates ROS production; this collectively leads to endothelial dysfunction in coronary arteries.