Model-free numerical deconvolution of recirculating indicator concentration curves

Abstract

This paper investigates two model-free methods for numerical deconvolution of recirculating indicator concentration curves. The two methods, damped least squares and discrete orthogonal polynomial deconvolution, are applied to simulated data to verify the reliability of the algorithms. Both deconvolution methods provide damping that results in estimated transport functions that are smooth and reasonable estimates of the actual simulated transport function. On convolution with the simulated input curve, the estimated transport functions provide good fits to the simulated output curve. In addition, methods for identifying an optimal solution and for truncating the artifactually long oscillatory tails of the estimated transport functions are proposed, which appear to allow for reasonably accurate estimation of the mean transit times and variances of the transport functions as well. When either method was applied to indicator dilution data obtained from the pulmonary artery and left atrium, it was computationally stable while producing transport functions that when convolved with the input concentration curves provided good fits to the output concentration curves. The combined simulation and experimental results suggest that the proposed methods should be useful for estimating circulation transport functions from indicator dilution data.