In this thesis, a system of ordinary differential equations (ODES) is presented to model the population dynamics between poachers and rhino as a predator-prey system in both South Africa (SA) and the Kruger National Park (KNP). The data used in this thesis consists mainly of government and police reports, as well publications from several NGOs and the limitations caused by this lack of applicable data are explored. The system dynamics are based on Lotka-Volterra differential equations, which are extended to include both a carrying capacity and the Allee effect. This thesis parameterises a model of the dynamics of the interaction between rhino and poachers for some time t and makes predictions based on the interpolation of the available data. The unknown rates and parameters relating to the behaviour of populations R and P are optimised by initially using a combination of educated guesses made from the available data or trial and error until set values are obtained. The remaining unknowns are numerically optimised based on the fixed value parameters. This is considered a constrained system, and the results obtained can only be viewed as constrained predictions based on parameter values obtained by a combination of trial and error and numerical optimisation; namely root mean square (RMS) error considering the available data and model solution at time t. Those parameter values obtained through RMS are regarded as error-minimising parameters within the scope of this research, and make up the final models which are referred to as the models which have been fitted to data. This thesis is an introductory, exploratory work into future attempts at modeling population dynamics with very little or no available data. The models are solved for in a constrained system, limiting the resulting predictions to constrained estimates based on the assigned values to unknown parameters. These solutions predict rhino stabilisation for both models, with active poachers dying out in the KNP but general co-existence observed across SA, within the constrained system.

The microcirculation system is crucial for the function of delivering biological markers such as oxygen and removing carbon dioxide from all the cells forming the complex ma- trix of tissue in the body. To keep up with the demands of each and every cell, there is a response from the microvasculature - resulting from for instance changes in blood flow to the tissue area. Infections cause disturbances in this important system, which increases the risk of development into one of the world’s most common syndrome - sepsis. This con- dition can be explained as a biological response affecting each and every vital organ, and can as a result of the dysfunction be life threatening. Studies have shown when monitoring pulse and respiratory rate the response is not visually quick enough to be able to determine the gravity in the state of the patient. The primarily chosen biological markers were oxy- genated hemoglobin and deoxygenated hemoglobin present in blood, respectively melanin in the skin. This was performed using the optical instrument Spatial Frequency Domain Imaging in combination with a Tissue Viability Imager respectively an Enhanced Perfusion and Oxygen Saturation-equipment. The formulated aim for this thesis was separated into an optical part and a mathematical modeling part. Regarding the optical section the aim was to understand if there were any optical methods more preferable to detect changes in the microcirculation, whilst the modeling section aimed to understand how to construct the best adjusted model for the changes in the biological markers and how these could be related to sepsis. Spatial Frequency Domain Imaging is an optical technique able to generate two- dimensional maps of the absorption coefficient and the reduced scattering coefficient of a biological tissue surface. The skin of healthy subjects were illuminated with RGB-LEDs to detect the chromophores of interest. The data obtained from the experimental sessions was then collected to work as a base for building a mathematical model. The experimental session was performed with a total of six healthy subjects and the data was collected dur- ing a control-measurement and a simulated sepsis-measurement using a pressure chamber and applying negative pressure to the lower part of the body. The mathematical model was based on theory regarding the biological events of sepsis in the microcirculation and was described by ordinary differential equations. The results were presented in graphs and the resulting model likewise, with an addi- tional figure to describe the source of associated equations written to describe the events. An observation of a distinct difference in the deoxygenated, respectively oxygenated hemoglobin could be observed and did show in general more changes during the measure- ments using a lower body negative pressure chamber. The chosen optical approach was the Spatial Frequency Domain Imaging equipment along with the mathematical model named as the Macro-Micro model due to its more realistic design. Future improvements were dis- cussed and summarized as a repetition of the experimental sessions and including more parameters and relationships between the biological markers and the model. This would contribute to more robust results.

The osmotic fragility (OF) test is used to determine the extent of red blood cell hemolysis (RBCH) produced by osmotic stress. RBCH is dependent upon cell volume, surface area, and functional integrity of cell membranes. The variation of cell lysis with stress reflects underlying cell subpopulations and their membranes' cytoskeletal functionality. OF was determined on blood from New Zealand white rabbits. The dependence of RBCH on NaCl concentration ([NaCl]) was determined spectrophotometrically by measuring absorbance (Abs) from hemoglobin release at 545 nm. Abs data were fitted to the equation Abs = p3 erfc( ([NaCl] - p1) p2) where p3 reflects maximum RBCH, p1 measures the [NaCl] at 50% RBCH, and p2 shows the dispersion in [NaCl] producing the RBCH. Parameter values for control blood were p1 = 0.4489 ± 0.0016; p2 = 0.0486 ± 0.0016; and p3 = 0.4366 ± 0.0022. Addition of indomethacin (9.6 μg/mL) produced an increased fragility in the RBC's characterized by increased values of p1 and p2. Normalization of the data to p3 did not change the values of p1 or p2. Our equation satisfactorily describes the variation in RBCH as a function of [NaCl]. The parameters of the equation can be used to quantitatively characterize Abs/[NaCl]. The compare pharmacological, Toxicological, and pathological effects on the OF of RBC's.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第20324号 / 工博第4261号 / 新制||工||1660(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 木村 亮, 教授 三村 衛, 准教授 木元 小百合 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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