||通过正电子发射断层扫描（PET）的成像已被用于大约四十年作为癌症成像中的有效工具。这种强大的成像模型现在在其他医疗区域中有许多拟议和实践中的用途。其中之一是相对较新的再生医学领域，因糖尿病或肝病等慢性病症受损的器官或组织的再生。通常，再生医学取决于细胞疗法，实现其目标和分子成像是量化所得数据的唯一有效方法。分子成像包括宠物，但使用PET的传统方法主要集中在癌症的成像上。细胞疗法通常依赖于不同类型的分子成像 - 光学。光学成像涉及将基因（报告基因）放置在某些生物中的生物发光或荧光的基因（报告基因）纳入不含它们的细胞中。结合细胞疗法，通过测量通过生物发光或荧光产生的光来进行细胞的表达的测量。光学成像的缺点是它在深组织中不起作用，因此在患者中不起作用。宠物，因为名称断层扫描建议，没有这个问题，并将在任何深度工作。 PET also utilizes reporter genes, but also requires the use of molecular probe molecules – positron emitting radionuclides that are analogues of naturally occurring molecules acted on by the proteins produced by the reporter genes. In the traditional use in cancer imaging, the probe molecule is 18F-Fluorodeoxyglucose, an analogue of glucose, with the reporter gene being the naturally occurring hexokinase used in glycolysis. A probe proposed for imaging of cell therapy, the probe being studied in this research, is 18F-Fluorohydroxymethylbutylguanine (FHBG), an analogue of Penciclovir, itself an analogue of guanosine and thymidine, with the reporter gene being the gene for thymidine kinase from the herpes simplex virus (HSV1-tk). The issue with PET imaging is in its sensitivity, five orders of magnitude less than the sensitivity of optical imaging. Previous studies place the number of cells that can be imaged in PET at around 200 million, with any attempts to image fewer cells prevented by an inability to separate signal from background. Therefore, the overall goal of this project is to figure out a way to improve PET sensitivity to optical imaging levels or determine any possible limiting factors that might prevent imaging at that level of sensitivity through the use of mathematical kinetic modeling. The models created for this Master’s dissertation were three compartment models - a recreation of a model described in previous work, a model describing the system as a semibatch bioreactor, an unsteady diffusion-reaction model in rectangular coordinates, a model based on the pre-existing Krogh Cylinder model, and a diffusion-reaction model in cylindrical coordinates not based on any specific model. This final kinetic model was broken into steady state models with a single cell layer in the third compartment, a 100 cell layer in the third compartment, and unsteady models of the first two compartments.