Fowler K R, Gray G A, Olufsen M S
Department of Mathematics, Clarkson University, Potsdam, NY, USA.
Cardiovasc Eng. 2008 Jun;8(2):109-19. doi: 10.1007/s10558-007-9048-2.
In part I of this study we introduced a 17-parameter model that can predict heart rate regulation during postural change from sitting to standing. In this subsequent study, we focus on the 17 model parameters needed to adequately represent the observed heart rate response. In part I and in previous work (Olufsen et al. 2006), we estimated the 17 model parameters by minimizing the least squares error between computed and measured values of the heart rate using the Nelder-Mead method (a simplex algorithm). In this study, we compare the Nelder-Mead optimization method to two sampling methods: the implicit filtering method and a genetic algorithm. We show that these off-the-shelf optimization methods can work in conjunction with the heart rate model and provide reasonable parameter estimates with little algorithm tuning. In addition, we make use of the thousands of points sampled by the optimizers in the course of the minimization to perform an overall analysis of the model itself. Our findings show that the resulting least-squares problem has multiple local minima and that the non-linear-least squares error can vary over two orders of magnitude due to the complex interaction between the model parameters, even when provided with reasonable bound constraints.
在本研究的第一部分，我们介绍了一个17参数模型，该模型可以预测从坐姿到站姿的姿势变化过程中的心率调节。在后续的这项研究中，我们关注充分表征观察到的心率反应所需的17个模型参数。在第一部分以及之前的工作（Olufsen等人，2006年）中，我们使用Nelder-Mead方法（一种单纯形算法）通过最小化心率计算值与测量值之间的最小二乘误差来估计这17个模型参数。在本研究中，我们将Nelder-Mead优化方法与两种采样方法进行比较：隐式滤波方法和遗传算法。我们表明，这些现成的优化方法可以与心率模型结合使用，并且只需很少的算法调整就能提供合理的参数估计。此外，我们利用优化器在最小化过程中采样的数千个点对模型本身进行全面分析。我们的研究结果表明，所得的最小二乘问题有多个局部最小值，并且由于模型参数之间的复杂相互作用，即使提供了合理的边界约束，非线性最小二乘误差也可能在两个数量级范围内变化。
