Ligas J R, Saidel G M, Primiano F P
J Biomech Eng. 1985 Nov;107(4):315-20. doi: 10.1115/1.3138562.
A model for the static pressure-volume behavior of the lung parenchyma based on a pseudo-elastic strain energy function was tested. Values of the model parameters and their variances were estimated by an optimal least-squares fit of the model-predicted pressures to the corresponding data from excised, saline-filled dog lungs. Although the model fit data from twelve lungs very well, the coefficients of variation for parameter values differed greatly. To analyze the sensitivity of the model output to its parameters, we examined an approximate Hessian, H, of the least-squares objective function. Based on the determinant and condition number of H, we were able to set formal criteria for choosing the most reliable estimates of parameter values and their variances. This in turn allowed us to specify a normal range of parameter values for these dog lungs. Thus the model not only describes static pressure-volume data, but also uses the data to estimate parameters from a fundamental constitutive equation. The optimal parameter estimation and sensitivity analysis developed here can be widely applied to other physiologic systems.
测试了基于伪弹性应变能函数的肺实质静态压力-容积行为模型。通过将模型预测压力与来自切除的、充满盐水的狗肺的相应数据进行最优最小二乘拟合，估计了模型参数的值及其方差。尽管该模型对来自12只肺的数据拟合得非常好，但参数值的变异系数差异很大。为了分析模型输出对其参数的敏感性，我们研究了最小二乘目标函数的近似海森矩阵H。基于H的行列式和条件数，我们能够设定正式标准来选择最可靠的参数值及其方差估计。这进而使我们能够为这些狗肺指定参数值的正常范围。因此，该模型不仅描述了静态压力-容积数据，还利用这些数据从基本本构方程估计参数。这里开发的最优参数估计和敏感性分析可广泛应用于其他生理系统。
