Fully non-linear blob basis based fluorescence photoacoustic pharmaco-kinetic tomography using non-sequential...

Objective.In this work, we solve the fully non-linear dynamic pharmacokinetic fluorescence photoacoustic tomography (PK-FPAT) problem for pointwise reconstructions for the first time in literature.Approach.We use the 2D-blob basis functions to represent the object, which have been known to yield very good localization in reconstructions, while significantly reducing the number of unknowns. The underlying state derivatives are evaluated via an efficient non-sequential sensitivity scheme for obtaining the derivatives of the two-compartment model. The inverse problem is solved in a dual-grid framework, where the forward problem is solved on a standard finite element grid at each iterate, while reconstructing the parameters in blob basis via Gauss-Newton and gradient filtering schemes.Main results.To the best of our knowledge, the current work demonstrates the first pointwise formulation and reconstructions for fully nonlinear PK-FPAT. Non-sequential sensitivity based gradient and Gauss-Newton filters-based reconstruction frameworks in a blob-basis representation have been developed. Numerical studies on cancer-mimicking phantoms validate the proposed scheme, yielding good localization of the reconstructed parameters with satisfactory correspondence to the ground-truth parameter values.Significance.The proposed non-sequential state derivative framework with the blob-basis representations offers significant computational advantages via both efficient evaluation of state derivatives and the sparse representations of the parameters, therein enabling the scalability of PK-FPAT based PK imaging to full 3D point-wise reconstructions for real world imaging.