Photodynamic therapy (PDT) currently utilizes drug and light doses which are primarily based on clinical experience. This can lead to a dose which is not sufficient to destroy the entire tumor, or alternatively, it can lead to the undesirable destruction of healthy tissue around the treatment area. PDT of topically applied photosensitizers is one focus of this research. This concerns the diffusion of an externally applied drug into the tissue, as well as its subsequent destruction during the irradiation procedure. This work involves the non-invasive measurement of the inherent fluorescence of the photosensitizer, allowing the determination of the concentration and distribution of drug within the tissue, and thus optimizing this treatment. To do this, one must be able to describe the propagation of light within the tissue. Consequently, a photon diffusion model has been developed to calculate the steady-state spatially resolved fluorescence from a pencil beam excitation in a depth dependent medium. The validity of this model was then verified by comparison with Monte Carlo simulations and measurements made on phantoms with optical properties similar to those of human tissue. Theoretical conditions were then explored, and potential uses of the model were demonstrated. / Thesis / Master of Science (MS)

As more emphasis is put on biodiversity conservation, how best to select a system of protected areas for wildlife conservation is an issue of great importance. There is a rich economics literature on the reserve site selection problem. However, most economic studies assume the independence of risks that affect wildlife species, leaving the issue of spatially correlated risk largely unexplored. This study contributes to the literature in twoaspects. First, this study incorporates spatially correlated risk, into a reserve site selection model. And second, this study incorporates heterogeneous spatial risk, in the context of land development risk in Virginia, both with and without a budget constraint. To evaluate the significance of spatially correlated risk in conservation design, I apply the reserve site selection model to a Virginia landscape. In a basic setting, a hazard is introduced which is allowed to spread to adjacent land parcels, where I investigate the impact of spatially correlated risk at three spatial scales: one-county, four-county, and state-level. Optimal reserve designs are characterized by similar spatial patterns indicating that spatially correlated risk plays an important role in the selection of parcels for reserve. Specifically, as spatially correlated risk increases, I find that, in general, reserve connectivity decreases. I also examine a setting with heterogeneous risk and observe similar patterns in the optimal reserve design. I find that the reserve becomes more dispersed in higher risk areas primarily. Finally, I explore the tradeoffs between species protection and budget constraints in the presence of heterogeneous spatial risk. All comparative statics indicate that spatial correlated risk plays an important role in conservation reserve design. / Master of Science

Spatially fractionated radiation therapy (or grid) using megavoltage x-rays is a relatively new method of treating bulky (>8 cm) malignant tumors. Unlike the conventional approach in which the entire tumor is targeted with a nearly uniform radiation field, in grid the incident radiation is collimated with a special grid collimator. As such, only the volume under the open areas of the grid receives direct irradiation from the incident beam; the rest only sees scattered radiation and hence receives significantly less dose. Those regions seeing less dose serve as regrowth areas for normal tissues, thus reducing the normal tissue complication probability after the treatment. Although the grid dose distribution in a tumor is non-uniform, the regression of tumor mass has exhibited uniform regression clinically. Protons have two advantages over megavoltage x-rays which are typically used for grid: (1) protons scatter less in tissue, and (2) they have a fixed range in tissue (the Bragg peak) that can be used to target a tumor. The goal of this thesis is to computationally and experimentally assess the feasibility of grid using clinical proton beams. The proton pencil beams at the Provision Cancer Center in Knoxville, Tennessee, are used to create an array of beams mimicking the arrangement of beams in grid therapy. The dose distributions at various depths in a solid-water phantom are obtained computationally by the Monte Carlo code MCNP and validated by RayStation experimental Gafchromic film EBT3. The results are compared with those of the grid using megavoltage x-rays.

This thesis focuses on the spread of organisms in both ecological and epidemiological contexts. In most of the studies presented, displacement is modeled with a spatial kernel function, which is characterized by scale and shape. These are measured by the net squared displacement (or kernel variance) and kurtosis, respectively. If organisms disperse by the assumptions of a random walk or correlated random walk, a Gaussian shaped kernel is expected. Empirical studies often report deviations from this, and commonly leptokurtic distributions are found, often as a result of heterogeneity in the dispersal process. In the studies presented in two of the included papers, the importance of the kernel shape is tested, by using a family of kernels where the shape and scale can be separated effectively. Both studies utilize spectral density approaches for modeling the spatial environment. It is concluded that the shape is not important when studying the population distribution in a habitat/matrix context. The shape is however important when looking at the invasion of organisms in a patchy environment, when the arrangement of patches deviates from randomly distributed. The introduced method for generating patch distribution is also compared to empirical distributions of patches (farms and old trees). Here it is concluded that the assumptions used for modeling of the spatial environment are consistent with the observed patterns. These assumptions include fractal properties such that the same aggregational patterns are found at different scales. In a series of papers, movements of animals are considered as vectors for between-herd disease spread. The studies are based on data found in databases held by the Swedish Board of Agricultural (SJV), consisting of reported movements, as well as farm location and characteristics. The first study focuses on the distance related probability of contacts between herds. In the following papers, the analysis is expanded to include production type and herd size. Movement data of pigs (and cattle in Paper I) are analyzed with Bayesian models, implemented with Markov Chain Monte Carlo (MCMC). This is a flexible approach that allows for parameter estimations of complex models, and at the same time includes parameter uncertainty. In Paper IV, the effects of the included factors are investigated. It is shown that all three factors (herd size, production type structure and distance related probability of contacts) are expected to influence disease spread dynamics, however the production type structure is found to be the most important factor. This emphasizes the value of keeping such information in central databases. The models presented can be used as support for risk analysis and disease tracing. However, data reliability is always a problem, and implementation may be improved with better quality data. The thesis also shows that utilizing spatial kernels for description of the spatial spread of organisms is an appropriate approach. However, these kernels must be flexible and flawed assumptions about the shape may lead to erroneous conclusions. Hence, the joint distribution of kernel shape and scale should be estimated. The flexibility of Bayesian analysis, implemented with MCMC techniques, is a good approach for this, and further allows for implementation of more complex models where other factors may be included.

Anticipating how stream water quality will respond to change, such as increased pollution or water diversions, requires knowledge of the main mechanisms controlling water and chemical constituent movement and a reasonable representation of those mechanisms. By deriving mathematical models to represent a stream system and collecting supporting field-based measurements, water quality response can be predicted. However, because each stream is unique and the movement of water and constituents is spatially and temporally complex, assessing whether the stream is appropriately represented and whether predictions are trustworthy is still a challenge within the scientific and management communities. Building on decades of stream research, this dissertation provides a step towards better representing some of the complexities found within streams and rivers to better predict water quality responses over long stream distances. First, a method is presented to assess which mechanisms are considered most important in chemical constituent predictions. Next, the number of measurements necessary to represent the general complexities of water, mass, and heat movement in streams was determined. The advancements developed in this dissertation provide a foundation to more efficiently and accurately inform water resource management.

In the last decade, spatially distributed hydrological models have rapidly advanced with the widespread availability of remotely sensed and geomatics information. Particularly, the areas of calibration and evaluation of spatially distributed hydrological models have been attempted in order to reduce the differences between models and improve realism through various techniques. Despite steady efforts, the study of calibrations and evaluations for spatially distributed hydrological models is still a largely unexplored field, in that there is no research in terms of the interactions of snow and water balance components with the traditional measurement methods as error functions. As one of the factors related to runoff, melting snow is important, especially in mountainous regions with heavy snowfall; however, no study considering both snow and water components simultaneously has investigated the procedures of calibration and evaluation for spatially distributed models. Additionally, novel approaches of error functions would be needed to reflect the characteristics of spatially distributed hydrological models in the comparison between simulated and observed values. Lastly, the shift from lumped model calibration to distributed model calibration has raised the model complexity. The number of unknown parameters can rapidly increase, depending on the degree of distribution. Therefore, a strategy is required to determine the optimal degree of model distributions for a study basin. In this study, we will attempt to address the issues raised above. This study utilizes the Research Distributed Hydrological Model (HL-RDHM) developed by Hydrologic Development Office of the National Weather Service (OHD-NWS). This model simultaneously simulates both snow and water balance components. It consists largely of two different modules, i.e., the Snow 17 as a snow component and the Sacramento Soil Moisture Accounting (SAC-SMA) as a water component, and is applied over the Durango River basin in Colorado, which is an area driven primarily by snow. As its main contribution, this research develops and tests various methods to calibrate and evaluate spatially distributed hydrological models with different, non-commensurate, variables and measurements. Additionally, this research provides guidance on the way to decide an appropriate degree of model distribution (resolution) for a specific water catchment.

<p>This report adresses the problem of software correction of spatially variant blur in digital images. The problem arises when the camera optics contains flaws, when the scene contains multiple moving objects with different relative motion or the camera itself is i.e. rotated. Compensation through deconvolving is impossible due to the shift-variance in the PSF hence alternative methods are required. There are a number of suggested methods published. This report evaluates two methods</p>

Der Rückgang des Steinkauzes (Athene noctua) hat in Thüringen und Sachsen seit den 60er Jahren dramatische Ausmaße angenommen. In den 50er Jahren noch flächendeckend beobachtet, wurden für das Jahr 2000 nur noch 18 Individuen durch Bestandserfassungen registriert. Die vielfach diskutierten Rückgangsursachen beziehen sich vor Allem auf die großflächige Änderung der Landschaftsstrukturen, die zum Verlust der Lebensgrundlagen des Steinkauzes führten. So haben u.a. der Verlust an Brut- und Vorratshöhlen und an ganzjährig kurzgehaltenen Grünlandflächen, sowie der zunehmende Einfluss von Prädatoren erheblich zum Rückgang beigetragen. Eingeleitete Schutzmaßnahmen, ehrenamtlich oder auf dem allgemeinen Naturschutzprogramm des Freistaates Thüringen beruhend, wie das Anbringen von Nisthilfen mit Marderschutz oder Pflegeverträge für Streuobstwiesen, zeigen bisher keine sichtbare Wirkung. Als weitergehende Maßnahmen stehen die Reduzierung von Füchsen (Vulpes vulpes) und Steinmardern (Martes foina), Ausbreitungskorridore für Steinkäuze und ein Auswilderungsprogramm zur Diskussion. Angesichts des Populationsrückgangs des Steinkauz war es Aufgabe dieser Arbeit durch ein Simulationsmodell Untersuchungen zum Überleben einer Steinkauzpopulation (Athene noctua) in Thüringen durchzuführen. Die zusammengetragenen Bestandszahlen ergaben geringe Individuenzahlen in den thüringischen Landkreisen Altenburger Land, Greiz und der Stadt Gera sowie in den sächsischen Landkreisen Chemnitzer Land und Mittweida. Die Bestandszahlen der Jahre 1989-2001, sowie weitere der Literatur entnommene Daten zum populationsökologischen Hintergrund, wie auch Analysen des Gebietes in Thüringen und Sachsen und dessen besetzter Reviere der Jahre 1989- 2001, wurden in ein stochastisches, räumlich-explizites, auf Individuen basierendes Simulationsmodell eingebracht. Es wurde eine Sensitivitätsanalyse durchgeführt, die beruhend auf den erfassten Populationsentwicklungen in Thüringen und Sachsen und auf Literaturangaben, ausgewählte Parameterkonstellationen für die Untersuchungenergab. Die Untersuchungen zum Überleben vor dem Hintergrund möglicher Gefährdungsfaktoren und zur Ermittelung des Nutzens von Managementoptionen, wurden mit Schwerpunkten auf „Prädation“, „Habitatverbesserung“ und „Auswilderung“ durchgeführt. Als Ergebnis der Simulationen kam heraus, dass die Prädation keinen großen Einfluss auf das Überleben der Population hat, und Schutzmaßnahmen die Chancen für das Überleben der Population nicht erhöhen würden. Habitatverbesserungen, die die Juvenilen animieren sich im Umkreis von bis zu 5 km vom elterlichen Revier anzusiedeln, würden aber deutlich zum Überleben der Population, auch in längerfristiger Perspektive, beitragen. Habitatverbesserungen, die zu weiter entfernteren Ansiedlungen animieren, könnten sich dagegen ungünstig auf das Überleben der Population auswirken. Für eine mögliche Auswilderung als Schutzmaßnahme ergab sich im Modell, dass eine Auswilderung von 5 Individuen pro Jahr über einen Zeitraum von 5 Jahren, die Überlebenswahrscheinlichkeit kurzfristig deutlich verbessern würde. Es ergab sich allerdings kein Unterschied, ob 5, 10 oder 15 Individuen ausgewildert werden. Eine länger durchgeführte Auswilderung würde vermutlich die Überlebenswahrscheinlichkeit entsprechend langfristiger verbessern.

Small livestock is an important resource for rural human populations in dry climates. How strongly will climate change affect the capacity of the rangeland? We used hierarchical modelling to scale quantitatively the growth of shrubs and annual plants, the main food of sheep and goats, to the landscape extent in the eastern Mediterranean region. Without grazing, productivity increased in a sigmoid way with mean annual precipitation. Grazing reduced productivity more strongly the drier the landscape. At a point just under the stocking capacity of the vegetation, productivity declined precipitously with more intense grazing due to a lack of seed production of annuals. We repeated simulations with precipitation patterns projected by two contrasting IPCC scenarios. Compared to results based on historic patterns, productivity and stocking capacity did not differ in most cases. Thus, grazing intensity remains the stronger impact on landscape productivity in this dry region even in the future. / Kleinvieh ist eine wichtige Lebensgrundlage für die Landbevölkerung in trockenen Regionen. Wie stark wird sich der Klimawandel auf die Tragfähigkeit der Weideflächen auswirken? Wir benutzten hierarchische Modellierung, um das Wachstum von Sträuchern und einjährigen Kräutern, das wichtigste Futter für Ziegen und Schafe, quantitativ auf die Fläche von Landschaften in der östlichen Mittelmeerregion zu dimensionieren. Die Produktivität ohne Beweidung stieg sigmoidal mit dem mittleren Jahresniederschlag. Je trockener die Landschaft, desto stärker verminderte Beweidung die Produktion. An einem Punkt knapp unter der Tragfähigkeit der Vegetation, sank die Produktion stark mit zunehmender Beweidung, weil die Samenproduktion der Kräuter zu gering war. Wir wiederholten die Simulationen mit Niederschlagsverteilungsmustern gemäß zweier gegensätzlicher IPCC-Szenarien. Zukünftige Produktivität und Tragfähigkeit unterschieden sich in den meisten Fällen nicht von Ergebnissen auf Grund von historischer Niederschlagsverteilung. Allerdings war die zukünftige Produktivität in trockenen Habitaten der semiariden und trocken-mediterranen Regionen niedriger. Somit hat auch in Zukunft die Besatzdichte die größere Auswirkung auf die Produktivität dieser trockenen Landschaft als das Klima. "This abstract is provided by the authors, and is for convenience of the users only. The author certifies that the translation faithfully represents the official version in the language of the journal, which is the published Abstract of record and is the only Abstract to be used for reference and citation."

The paper presents a simulation and parameter-estimation approach for evaluating stochastic patterns of population growth and spread of an annual forest herb, Melampyrum pratense (Orobanchaceae). The survival of a species during large-scale changes in land use and climate will depend, to a considerable extent, on its dispersal and colonisation abilities. Predictions on species migration need a combination of field studies and modelling efforts. Our study on the ability of M. pratense to disperse into so far unoccupied areas was based on experiments in secondary woodland in NE Germany. Experiments started in 1997 at three sites where the species was not yet present, with 300 seeds sown within one square meter. Population development was then recorded until 2001 by mapping of individuals with a resolution of 5 cm. Additional observations considered density dependence of seed production. We designed a spatially explicit individual-based computer simulation model to explain the spatial patterns of population development and to predict future population spread. Besides primary drop of seeds (barochory) it assumed secondary seed transport by ants (myrmecochory) with an exponentially decreasing dispersal tail. An important feature of populationpattern explanation was the simultaneous estimation of both population-growth and dispersal parameters from consistent spatio-temporal data sets. As the simulation model produced stochastic time series and random spatially discrete distributions of individuals we estimated parameters by minimising the expectation of weighted sums of squares. These sums-ofsquares criteria considered population sizes, radial population distributions around the area of origin and distributions of individuals within squares of 25*25 cm, the range of density action. Optimal parameter values, together with the precision of the estimates, were obtained from calculating sums of squares in regular grids of parameter values. Our modelling results showed that transport of fractions of seeds by ants over distances of 1…2 m was indispensable for explaining the observed population spread that led to distances of at most 8 m from population origin within 3 years. Projections of population development over 4 additional years gave a diffusion-like increase of population area without any “outposts”. This prediction generated by the simulation model gave a hypothesis which should be revised by additional field observations. Some structural deviations between observations and model output already indicated that for full understanding of population spread the set of dispersal mechanisms assumed in the model may have to be extended by additional features of plant-animal mutualism.