Modeling Autonomic Regulation of the Cardiovascular System

自主神经系统是复杂的，有许多相互作用的组成部分。这就是为什么对不同成分的分析不能给出一个令人满意的晕厥机制的观点。在这项研究中，目的是通过患者特定的数学建模来更好地了解控制机制及其动力学，其中集成了单个元素及其动力学的知识。为此，开发了一个动态心血管系统模型和一个控制模型，使研究人员能够预测自主神经系统调节心脏和血管特性以将血压和心脏的泵血功能维持在参考水平的能力。考虑了几种控制模型，包括一个详细的细胞模型，允许根据离子电流的分析来预测传入压力感受性反射的放电率，一个作为交感和副交感神经流出的函数来预测传出反应(心脏和血管特性的变化)的集中模型，以及一个直接预测传出反应的粗略模型。对于后一种模型，研究了滚动域控制理论的适用性。这些模型是由非线性动力系统组成的，其求解带来了相当大的计算挑战。由于模型和数据中固有的噪声，它们在临床数据中的应用涉及计算和概念上的复杂性。为了确保我们模型的高保真度，研究人员采用了允许计算参数敏感度、可识别性和估计值的方法。敏感度和可辨识性分析用于制定模型校准的指导方针，包括选择最适合估计的参数。特别是，考虑了基于非线性卡尔曼滤波的参数估计问题。该方法具有如下特点：显式地考虑了模型和数据中的噪声，是一种高效而简单的计算工具，可以考虑先验信息。身体从仰卧到坐姿或站姿的简单变化需要激活一系列控制机制来维持体内平衡。体位改变后，压力感受器记录动脉血压下降，心脏充盈减少。自主神经系统的激活然后调整心脏和血管的属性，以增加心脏的压力和泵功能，使其恢复到参考水平。在患有外周和中枢神经系统疾病的患者中，这种调节可能会被打乱。这类患者通常会因为自主神经系统的功能改变而出现头晕和晕厥。这些缺陷常见于糖尿病、高血压等神经系统疾病患者，其中以帕金森病、S病最为常见。本项目利用数学建模、分析和计算工具对与这一现象有关的问题进行分析，目的是深入了解所涉及的动态，并更好地了解这一监管系统如何运作。此外，该项目涉及与实验者的跨学科合作，并包括学生的参与，为更广泛的影响提供了相当大的机会。

The autonomic nervous system is complex with many interacting components. This is why analysis of separate elements does not give a satisfactory view of the syncope mechanisms. In this study, the aim is to achieve a better understanding of the control mechanisms and their dynamics via patient specific mathematical modeling where knowledge of the individual elements and their dynamics is integrated. To this end, a dynamic cardiovascular system model coupled with a control model is developed that allows the investigators to predict the autonomic nervous system's ability to adjust the heart and vessel properties to maintain blood pressure and pumping function of the heart at reference levels. Several control models are considered including a detailed cellular model allowing prediction of the afferent baroreflex firing-rate based on analysis of ionic currents, a lumped model predicting efferent responses (changes in heart and vascular properties) as a function of sympathetic and parasympathetic outflow, and a coarse model directly predicting efferent responses. For the latter model, the applicability of receding horizon control theory is investigated. These models are composed of nonlinear dynamical systems whose solution poses considerable computational challenges. Their application to clinical data involves computational and conceptual complications due to the inherent noise in the model and data. To ensure high fidelity of our model, the investigators employ methodologies allowing computation of parameter sensitivity, identifiability, and estimation. Sensitivity and identifiability analyses are used to formulate guidelines for model calibration including the selection of parameters best suited for estimation. In particular, the nonlinear Kalman filter based approach is considered for the parameter estimation problem. This method possesses several desirable properties, among them: it takes explicitly into account noise in the model and data, it is an efficient and simple to implement computational tool, and it can take into account a priori information. A simple change of the body from supine to sitting or standing position requires activation of a series of control mechanisms to maintain homeostasis. Upon postural change, the baroreceptors register a fall in arterial blood pressure and reduced filling of the heart. Activation of the autonomic nervous system then adjusts the heart and vessel properties to increase pressure and pump function of the heart back toward their reference level. This regulation can be disrupted in patients with peripheral and central nervous system diseases. Such patients usually experience dizziness and syncope due to altered function of the autonomic nervous system. These defects are often observed in patients with diabetes, hypertension, and other neurological diseases of which Parkinson?s disease is the most dominating. This project brings to bear tools from mathematical modeling, analysis, and computation on questions related to this phenomenon, with the goal of gaining insights into the dynamics involved and a better understanding of how this regulatory system functions. Additionally, the project involves interdisciplinary collaborations with experimentalists and includes the participation of students, providing considerable opportunities for broader impacts.