Reconstructing the one-compartment tracer-kinetic field with diffusion and convection

A tracer-kinetic field theory has been proposed for DCE- and DSC-MRI that may reduce error and provide new information by spatial modelling of indicator transport. In this study a 2D simulation of the simplest one-compartment field model is used to investigate whether all model parameters are uniquely identifiable. The discrete system is written as a large sparse linear inverse problem and solved iteratively using constrained gradient descent. A well-defined optimum is found but the reconstructed fields are not sufficiently accurate for a simulation of ideal conditions. It is concluded that a better reconstruction algorithm is required, or additional constraints must be imposed.

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