正电子发射断层成像(PET)作为一种有效的癌症成像工具已经使用了大约40年。这种强大的成像方式现在在其他医疗领域有许多用途，无论是提议还是实践。其中之一是相对较新的再生医学领域，即由糖尿病或肝病等慢性疾病损害的器官或组织的再生。通常，再生医学依赖于细胞治疗来实现其目标，而分子成像是量化结果数据的唯一有效方法。分子成像包括PET，但传统的使用PET的方法主要集中在癌症的成像。细胞疗法通常依赖于一种不同类型的分子成像——光学成像。光学成像涉及到将某些生物体中控制生物发光或荧光的基因(报告基因)放入不包含它们的细胞中。结合细胞治疗，可以通过测量生物发光或荧光产生的光来测量添加的治疗基因的细胞表达。光学成像的缺点是它在深层组织中不起作用，因此对病人也不起作用。PET，正如断层扫描的名字所暗示的那样，没有这个问题，并且在任何深度都可以工作。 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.