Estimation of Organ Transport Function: Model-Free Deconvolution by Recursive Quadratic Programming Optimization

Abstract

A model-free deconvolution method is proposed for evaluating the frequency distribution function of organ transit times. The deconvolution is treated as a nonlinear constrained optimization problem and it is solved by using a modified constrained variable metric approach. The only constraint implemented in the solution is that all the discrete transport function values are not allowed to become negative. The method is tested on model mathematical systems of known analytical transport functions. The tests are performed on systems that included noise in both the input and output functions. The criteria of successful deconvolution are the reconvolution error and, most importantly, the deviation of the computed transport function from the known analytical one. The proposed method is then applied, as a pilot experiment, to biological data obtained from an isolated, perfused rabbit lung preparation contained within a plethysmograph. The results indicate that this type of deconvolution produces stable estimates which faithfully follow the analytical function while negating the need to assume either any functional form for the behavior of the transport function or any educated initial guess of its values.