Kinetic data analysis with a noisy input function.

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 stimulations 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 least 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.