KINETIC DATA-ANALYSIS WITH A NOISY INPUT FUNCTION
KINETIC DATA-ANALYSIS WITH A NOISY INPUT FUNCTION
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DOI：
10.1088/0031-9155/32/12/004
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发表时间：
1987-12-01
影响因子：
3.5
通讯作者：
MAZOYER, BM
中科院分区：
文献类型：
--
作者：
HUESMAN, RH;MAZOYER, BM
针对输入函数有噪声的动态实验分析，提出了参数估计方法。输入函数中的噪声导致计算模型预测值的不确定性，因此残差的协方差矩阵是模型参数的函数。模型预测值中的这些统计不确定性显著地改变了拟合过程的性质和结果的质量。所提出的优化方法采用加权最小二乘准则，并考虑了加权矩阵的三种选择。所提出的加权矩阵，按复杂度排序为：(1)单位矩阵（不加权），(2)数据的协方差矩阵（忽略输入函数中的噪声），(3)残差的全协方差矩阵（同时考虑数据中的噪声和输入函数中的噪声）。该方法应用于心脏的动态发射断层扫描研究，其中每次的血液（输入）和组织示踪剂浓度来源于同一层析片中的两个感兴趣区域。隔室系统的计算机仿真结果表明，以残差的全协方差矩阵作为加权矩阵，比其他两种方法更能准确地估计参数及其协方差矩阵。对于所考虑的实际示例，当忽略输入函数中的噪声时，参数偏差增加了至少4倍，而当使用未加权最小二乘准则时，一个参数的偏差为24%。
Methods of parameter estimation are proposed for the analysis of dynamic experiments in which the input function is noisy. Noise in the input function leads to uncertainties in the calculated model-predicted values, and therefore the covariance matrix of the residuals is a function of the model parameters. These statistical uncertainties in the model-predicted values significantly change the nature of the fitting process and the quality of the results. The proposed optimisation methods use weighted least-squares criteria, and three choices for the weighting matrix are considered. The proposed weighting matrices, in order of complexity are: (1) the identity matrix (no weighting), (2) the covariance matrix of the data (ignoring the noise in the input function), and (3) the full covariance matrix of the residuals (incorporating both the noise in the data and the noise in the input function). The methodology is applied to dynamic emission tomography studies of the heart, where the blood (input) and tissue tracer concentrations at each time are derived from two regions of interest in the same tomographic slice. Computer simulations of compartmental systems show that parameters and their covariance matrix are more accurately estimated when the full covariance matrix of the residuals is used as a weighting matrix rather than either of the other two methods. For the practical example considered, parameter bias was increased by a factor of at last four when the noise in the input function was ignored, and one parameter had a bias of 24% when the unweighted least-squares criterion was used.