Using a voxel-based krogh cylinder array to simulate microvascular contrast enhancement

The goal of this study is to better simulate microscopic and voxel-based dynamic contrast enhancement in magnetic resonance imaging. Specifically, errors imposed by the traditional two-compartment model are reduced by introducing a novel Krogh cylinder network. The two-compartment model was developed for macroscopic pharmacokinetic analysis of dynamic contrast enhancement and generalizing it to voxel dimensions, due to the significant decrease in scale, imposes physiologically unrealistic assumptions. In the project, a system of microscopic exchange between plasma and extravascular-extracellular space is built while numerically simulating the local contrast agent flow between and inside image elements. To do this, tissue parameter maps were created, contrast agent was introduced to the tissue via a flow lattice, and various data sets were simulated. The effects of sources, tissue heterogeneity, and the contribution of individual tissue parameters to an image are modeled. Further, the study attempts to demonstrate the effects of a priori flow maps on image contrast, indicating that flow data is as important as permeability data when analyzing tumor contrast enhancement. In addition, the simulations indicate that it may be possible to obtain tumor-type diagnostic information by acquiring both flow and permeability data.

Coordinated pricing and inventory management

This dissertation mainly focuses on coordinated pricing and inventory management problems, where the related background is provided in Chapter 1. Several periodic-review models are then discussed in Chapters 2,3,4 and 5, respectively. Chapter 2 analyzes a deterministic single-product model, where a price adjustment cost incurs if the current selling price is changed from the previous period. We develop exact algorithms for the problem under different conditions and find out that computation complexity varies significantly associated with the cost structure. %Moreover, our numerical study indicates that dynamic pricing strategies may outperform static pricing strategies even when price adjustment cost accounts for a significant portion of the total profit. Chapter 3 develops a single-product model in which demand of a period depends not only on the current selling price but also on past prices through the so-called reference price. Strongly polynomial time algorithms are designed for the case without no fixed ordering cost, and a heuristic is proposed for the general case together with an error bound estimation. Moreover, our illustrates through numerical studies that incorporating reference price effect into coordinated pricing and inventory models can have a significant impact on firms' profits. Chapter 4 discusses the stochastic version of the model in Chapter 3 when customers are loss averse. It extends the associated results developed in literature and proves that the reference price dependent base-stock policy is proved to be optimal under a certain conditions. Instead of dealing with specific problems, Chapter 5 establishes the preservation of supermodularity in a class of optimization problems. This property and its extensions include several existing results in the literature as special cases, and provide powerful tools as we illustrate their applications to several operations problems: the stochastic two-product model with cross-price effects, the two-stage inventory control model, and the self-financing model.

Sampling strategies for characterization of neuropeptides using mass spectrometry and functional implications into cell-cell signaling

In this dissertation, there are developed different analytical strategies to discover and characterize mammalian brain peptides using small amount of tissues. The magnocellular neurons of rat supraoptic nucleus in tissue and cell culture served as the main model to study neuropeptides, in addition to hippocampal neurons and mouse embryonic pituitaries. The neuropeptidomcis studies described here use different extraction methods on tissue or cell culture combined with mass spectrometry (MS) techniques, matrix-assisted laser desorption/ionization (MALDI) and electrospray ionization (ESI). These strategies lead to the identification of multiple peptides from the rat/mouse brain in tissue and cell cultures, including novel compounds One of the goals in this dissertation was to optimize sample preparations on samples isolated from well-defined brain regions for mass spectrometric analysis. Here, the neuropeptidomics study of the SON resulted in the identification of 85 peptides, including 20 unique peptides from known prohormones. This study includes mass spectrometric analysis even from individually isolated magnocellular neuroendocrine cells, where vasopressin and several other peptides are detected. At the same time, it was shown that the same approach could be applied to analyze peptides isolated from a similar hypothalamic region, the suprachiasmatic nucleus (SCN). Although there were some overlaps regarding the detection of the peptides in the two brain nuclei, different peptides were detected specific to each nucleus. Among other peptides, provasopressin fragments were specifically detected in the SON while angiotensin I, somatostatin-14, neurokinin B, galanin, and vasoactive-intestinal peptide (VIP) were detected in the SCN only. Lists of peptides were generated from both brain regions for comparison of the peptidome of SON and SCN nuclei. Moving from analysis of magnocellular neurons in tissue to cell culture, the direct peptidomics of the magnocellular and hippocampal neurons led to the detection of 10 peaks that were assigned to previously characterized peptides and 17 peaks that remain unassigned. Peptides from the vasopressin prohormone and secretogranin-2 are attributed to magnocellular neurons, whereas neurokinin A, peptide J, and neurokinin B are attributed to cultured hippocampal neurons. This approach enabled the elucidation of cell-specific prohormone processing and the discovery of cell-cell signaling peptides. The peptides with roles in the development of the pituitary were analyzed using transgenic mice. Hes1 KO is a genetically modified mouse that lives only e18.5 (embryonic days). Anterior pituitaries of Hes1 null mice exhibit hypoplasia due to increased cell death and reduced proliferation and in the intermediate lobe, the cells differentiate abnormally into somatotropes instead of melanotropes. These previous findings demonstrate that Hes1 has multiple roles in pituitary development, cell differentiation, and cell fate. AVP was detected in all samples. Interestingly, somatostatin [92-100] and provasopressin [151-168] were detected in the mutant but not in the wild type or heterozygous pituitaries while somatostatin-14 was detected only in the heterozygous pituitary. In addition, the putative peptide corresponding to m/z 1330.2 and POMC [205-222] are detected in the mutant and heterozygous pituitaries, but not in the wild type. These results indicate that Hes1 influences the processing of different prohormones having possible roles during development and opens new directions for further developmental studies. This research demonstrates the robust capabilities of MS, which ensures the unbiased direct analysis of peptides extracted from complex biological systems and allows addressing important questions to understand cell-cell signaling in the brain.