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Nonlinear Filtering Methodologies for Parameter Estimation and Uncertainty Quantification in Noisy, Complex, Biological Systems.

机译：用于噪声，复杂，生物系统中参数估计和不确定性量化的非线性滤波方法。

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摘要

A model is a set of equations constructed to represent the interactions of various variables within a biological or physical process. These mathematical models are used to obtain a more thorough understanding of a system or to gain information not easily obtained through other means. Measurements of system components are frequently collected and are used to validate the model through the solution of the inverse problem. The inverse problem is defined as calculating the optimal parameter values to obtain the best possible fit of the model the data. However, as the systems of interest become more complex, the solution to the inverse problem becomes increasingly difficult.;A common method to solve the inverse problem is to use a nonlinear least squares (NLS) approach which aims to minimize the residual, the difference between the data and the model. However, this methodology presents a certain set of assumptions which may not hold for complicated biological models. An alternate method addressed in this thesis is the use of Kalman filtering. The Kalman filter is a recursive algorithm that optimally combines the uncertainties in the model and data to yield an improved final estimate. Carrying out the inverse problem utilizing this methodology has a number of advantages and has shown favorable results.;One area where these methodologies have proven fruitful is in cardiovascular modeling. The cardiovascular system is a branching network of vessels which transports blood and nutrients throughout the body while removing wastes. At the center of this process is the heart, which is the mechanism that facilitates transport through pumping. The heart and vasculature are controlled through the autonomic nervous system. As the cardiovascular system is so important to homeostasis, obtaining measurements on immediate variables of interest is difficult. Mathematical modeling is one way to gather more understanding. Using a simplified model of the cardiovascular system and the autonomic nervous system, the Kalman filter is used to illustrate their interplay. The advantages are shown over a NLS approach due to the ability to take into account modeling errors.;For many problems, measurements are collected for a multitude of individuals, representing a population. A standard approach is to fit each individual using NLS and then do statistical analysis on the individual parameters. However, this has been known to introduce bias to the final estimates. An improved method is introduced that accounts for inter- and intra-individual variability called nonlinear mixed effects. Using the Kalman filter within this framework allows the estimation of the population parameters, along with model misspecification, and time varying parameters. Using a population pharmacokinetic study, nonlinear mixed effects was carried out utilizing the Kalman filter referred to as stochastic nonlinear mixed effects. The results of this highlight the utility of the stochastic nonlinear mixed effect method through refinement of noisy model components.
机译：模型是一组方程，构造为代表生物或物理过程中各种变量的相互作用。这些数学模型用于获得对系统的更彻底的了解或获取通过其他方式不容易获得的信息。系统组件的测量值经常被收集，并用于通过反问题的求解来验证模型。反问题定义为计算最佳参数值以获得模型数据的最佳拟合。然而，随着感兴趣的系统变得越来越复杂，反问题的解决变得越来越困难。解决反问题的一种常用方法是使用非线性最小二乘法（NLS），其目的是最小化残差，差异。在数据和模型之间。但是，这种方法提出了某些假设，这些假设可能不适用于复杂的生物学模型。本文提出的另一种方法是使用卡尔曼滤波。卡尔曼滤波器是一种递归算法，可以将模型和数据中的不确定性最佳地组合在一起，以产生改进的最终估计值。利用这种方法进行逆问题具有许多优点，并显示出令人满意的结果。；这些方法被证明卓有成效的领域之一是心血管建模。心血管系统是血管的分支网络，可以在体内输送血液和营养素，同时消除废物。这个过程的中心是心脏，这是通过泵促进运输的机制。心脏和脉管系统通过自主神经系统控制。由于心血管系统对动态平衡非常重要，因此很难获得有关所关注的直接变量的测量值。数学建模是收集更多理解的一种方法。使用心血管系统和自主神经系统的简化模型，卡尔曼滤波器用于说明它们之间的相互作用。由于具有考虑建模误差的能力，因此相对于NLS方法显示出了优势。对于许多问题，收集了代表人口的多个个体的度量。一种标准方法是使用NLS使每个人适应，然后对各个参数进行统计分析。但是，已知这会给最终估计值带来偏差。引入了一种改进的方法，该方法考虑了个体之间和个体内部的变异性，称为非线性混合效应。在此框架内使用卡尔曼滤波器可以估算总体参数，以及模型错误指定和时变参数。利用总体药代动力学研究，利用称为随机非线性混合效应的卡尔曼滤波器进行了非线性混合效应。结果表明，通过对噪声模型成分进行细化，可以采用随机非线性混合效应方法。

著录项

  • 作者

    Matzuka, Brett James.;

  • 作者单位

    North Carolina State University.;

  • 授予单位 North Carolina State University.;
  • 学科 Biology Bioinformatics.;Applied Mathematics.
  • 学位 Ph.D.
  • 年度 2014
  • 页码 139 p.
  • 总页数 139
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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