Mathematical modeling for optimal control of BK virus infection in kidney transplant recipients

BK病毒（BKV）感染和肾病是肾移植后器官丧失的主要原因。那里 没有有效的BKV抗病毒药物，标准的临床实践是减少免疫抑制， 同种异体移植排斥反应的风险。对于如何安全地减少免疫抑制和治疗， BKV病毒血症的发生率因主治医生和移植中心而异。为了填补我们知识上的空白 对于如何最佳地管理BKV病毒血症的肾移植受者，我们建议使用数学 建模和最优控制理论，以开发软件指导的免疫抑制管理 为个别患者量身定制。为了将这些模型和算法转化为临床反应，我们需要 校准和验证他们的纵向数据的肾移植受者与BKV病毒血症。我们建议 利用NIAID资助的器官移植临床试验（CTOT）数据集， 与儿童和成人CTOT肾移植数据目前没有在ImmPort，建立最大的纵向 BKV监测数据集，并使用它来校准我们的模型。我们建立这个拟议的工作对我们公布的 BKV病毒血症的数学模型，它准确地模拟了BKV增殖和肾细胞感染， 诱导抗病毒和同种异体特异性细胞毒性T细胞，其损伤肾细胞并降低移植物功能，和 受损的肾细胞得不到补充，导致肌酸酐水平升高。我们建议延长和 改进模型，以更好地拟合BKV病毒血症CTOT肾移植受者的纵向临床数据 准确地为了更好地利用CTOT研究中的大量患者数据，我们还提出了一种创新的 一种通过直接学习描述免疫调节的方程来建立更精确的BKV模型的方法 from data数据.学习将使用神经网络仿真器进行，该仿真器可以任意近似 复杂的数学函数这种机器学习方法的优点是更灵活， 使用允许更大程度的个性化模型表征的辅助数据源。CTOT数据 将被用于通知免疫反应建模，并验证初始模型的改进，以及协助 我们在进一步的模型开发。然后，我们分层滚动时域控制（RHC）算法，也称为模型 预测控制，在数学模型之上，提供最佳的自适应指导 针对患者个体定制的免疫抑制剂量。这些模型的校准至关重要， 我们的建议的关键组成部分是使用先进的统计方法来估计模型参数， 稀疏纵向数据并执行敏感性分析。最后，该提案极大地受益于 三位经验丰富的临床医生谁管理肾移植受者的合作，谁将提供域 专业知识，帮助解释数据，并指导模型和软件开发，以确保临床 效用预期的结果是一个有用的工具，以指导免疫抑制管理，可以测试 其在改善患者预后和降低免疫抑制治疗发病率方面的有效性。

BK virus (BKV) infection and nephropathy is a major cause of organ loss following kidney transplantation. There are no effective antivirals for BKV, and standard clinical practice is to reduce immunosuppression, which raises the risk of allograft rejection. There is no consensus on how to safely reduce immunosuppression, and treatment of BKV viremia varies by the attending physician and transplant center. To address this gap in our knowledge for how to optimally manage kidney transplant recipients with BKV viremia, we propose to use mathematical modeling and optimal control theory to develop software-guided management of immunosuppression personalize for individual patients. To translate these models and algorithms to clinical reactive, we need to calibrate and validate them on longitudinal data of kidney transplant recipients with BKV viremia. We propose to utilize NIAID-funded Clinical Trials in Organ Transplantation (CTOT) data sets available in ImmPort, together with pediatric and adult CTOT kidney transplant data not currently in ImmPort, to build the largest longitudinal BKV monitoring data set and use it to calibrate our models. We build this proposed work on our published mathematical model of BKV viremia, which accurately models BKV proliferation and infection of kidney cells, the elicitation of anti-viral and allo-specific cytotoxic T cells that damage kidney cells and reduce graft function, and the non-replenishment of damaged kidney cells resulting in rising creatinine levels. We propose to extend and refine the model to fit the longitudinal clinical data from CTOT kidney transplant recipients with BKV viremia more accurately. To better utilize the extensive patient data from the CTOT studies, we also propose an innovative approach to build a more accurate BKV model by learning the equations describing immune regulation directly from data. Learning will be performed using a neural network emulator, which can approximate arbitrarily complex mathematical functions. This machine learning approach has the advantage of being more flexible and using ancillary data sources that allow a greater degree of personalized model characterization. The CTOT data will be used to inform immune response modeling and to validate the initial model refinements as well as assist us in further model development. We then layer receding horizon control (RHC) algorithms, also known as model predictive control, on top of the mathematical models, to provide adaptive guidance on optimal immunosuppression doses customized to individual patients. The calibration of these models is critical, and a critical component of our proposal is the use advanced statistical methods to estimate model parameters from sparse longitudinal data and to perform sensitivity analysis. Finally, the proposal benefits immensely from the collaboration of three experienced clinicians who manage kidney transplant recipients, who will provide domain expertise, help with the interpretation of data, and guide model and software development to ensure clinical utility. The expected outcome is a useful tool to guide immunosuppressive management that could be tested for its effectiveness in improving patient outcomes and reducing the morbidity of immunosuppressive therapy.