Mathematical Modeling of Biological and Biomedical Engineering Processes

PI将在她的家乡路易斯安那理工大学（Louisiana Tech University）的生物医学工程项目中学习一年，在那里她将在两个研究领域工作，同时为每个领域的博士生提供建议。第一个项目将整合神经科学，纳米和微型技术工程，数学建模和反馈控制。钙离子动力学的数据集将成为脑细胞网络活动的数学分析和建模的基础，包括开发计算脑细胞控制器。钙离子作为体内最重要的第二信使之一，参与细胞内和细胞间的协调。神经元动力学的数学模型的开发将为设计反馈控制器奠定基础，以估计脑细胞中的钙浓度，这有可能进一步了解人体对大脑疾病的反应和大脑的预测行为。第二个项目将整合纳米技术工程，数学建模和反馈控制设计。所涉及的数学建模将导致基于药物生物利用度的实时估计来准确预测到达肿瘤部位的纳米治疗剂的量。反过来，这将为设计计算反馈控制器奠定基础，该控制器将用于非侵入性测量和调节体内药物浓度。虽然目前对癌症肿瘤的治疗可能非常有效，但没有办法在治疗过程中进行监测。事实上，化疗剂量的唯一方法是由患者的体重决定。通过将数学建模和反馈控制技术结合在一起，该项目旨在提供一种预测纳米颗粒化疗药物在患者体内作用的机制，从而为药物方案和管理提供更好的模型。

The PI will spend a year in the Program of Biomedical Engineering at her home institution, Louisiana Tech University, where she will work in two research areas while advising a PhD student in each area. The first project will integrate neuroscience, nano- and micro-technology engineering, mathematical modeling, and feedback control. Data sets of calcium ion dynamics will be the basis for mathematical analysis and modeling of brain cell network activity, to include development of a computational brain cell controller. As one of the most important secondary messengers in the body, calcium ions are involved in both intracellular and intercellular coordination. Mathematical model development of neuron dynamics will lay the foundation for design of a feedback controller to estimate calcium concentration in brain cells, which has the potential to further understanding of how the human body reacts to disorders of the brain and the predictive behavior of the brain.The second project will integrate nanotechnology engineering, mathematical modeling, and feedback control design. The mathematical modeling involved will result in the development of an accurate prediction of the amount of a nano-therapeutic agent that reaches a tumor site based on real-time estimates of drug bioavailability. This, in turn, will lay the groundwork for the design of a computational feedback controller that would be used to noninvasively measure and regulate drug concentration in the body. Although the current treatment of cancerous tumors can be very effective, there is no way of monitoring the therapy as it is being administered. In fact, the only way the amount of chemotherapy to be administered is determined by the patient's body mass. By joining together mathematical modeling and feedback control techniques, this project seeks to provide a mechanism for prediction of the effects of the nano-particle chemotherapy drugs in a patient's body, thus leading to better models for drug regimen and administration.