Computation of transport function using multiple regression analysis

Abstract

A multiple regression analysis, which allows a simultaneous introduction of smoothing, was adopted for a numerical deconvolution process to obtain the transport function from a pair of indicator dilution curves. This process solves concurrently restricting linear quadratic or cubic equations that are fitted to small sections of the transport function curve, an equation that forces the tail part to zero, and uses conditions that restrict the area under the transport function to unity. Each restricting linear equation can be manually stressed by adjusting its corresponding weight iteratively so that unreasonable oscillations emerging on any particular portion of the transport function curve can be suppressed. Stability of the method was tested with various pairs of dilution curves in terms of mathematical models and with those experimentally obtained from the dog portal circulation. The deconvolution by means of the regression analysis with simultaneous smoothing was shown to be far less sensitive to observational errors in the dilution curves or sampling rates than that by means of the direct method without the regression analysis. Multiple regression analysis with simultaneous smoothing was also applied to the deconvolution process using the multiple fitting functions developed by Knopp et al. (Ann. Biomed. Eng. 4: 44-59, 1976). This process was shown to perform a stable deconvolution as well.