Technical Note: Rapid multi-exponential curve fitting algorithm for voxel-based targeted radionuclide dosimetry.

BACKGROUND: Dosimetry in nuclear medicine often relies on estimating pharmacokinetics based on sparse temporal data. As analysis methods move toward image-based 3-dimensional computation, it becomes important to interpolate and extrapolate these data without requiring manual intervention; that is, in a manner that is highly efficient and reproducible. Iterative least-squares solvers are poorly suited to this task because of the computational overhead and potential to optimise to local minima without applying tight constraints at the outset. METHODOLOGY: This work describes a fully-analytical method for solving three-phase exponential time-activity curves based on three measured time points in a manner that may be readily employed by image-based dosimetry tools. The methodology uses a series of conditional statements and a piecewise approach for solving exponential slope directly through measured values in most instances. The proposed algorithm is tested against a purpose-designed iterative fitting technique and linear piecewise method followed by single exponential in a cohort of 10 patients receiving 177 Lu-DOTA-Octreotate therapy. RESULTS: Tri-exponential time-integrated values are shown to be comparable to previously-published methods with an average difference between organs when computed at the voxel level of 9.8±14.2% and -3.6±10.4% compared to iterative and interpolated methods, respectively. Of the three methods, the proposed tri-exponential algorithm was most consistent when regional time-integrated activity was evaluated at both voxel- and whole-organ levels. For whole-body SPECT imaging, it is possible to compute 3D time-integrated activity maps in less than 5 minutes processing time. Further, the technique is able to predictably and reproducibly handle artefactual measurements due to noise or spatial misalignment over multiple image times. CONCLUSIONS: An efficient, analytical algorithm for solving multi-phase exponential pharmacokinetics is reported. The method may be readily incorporated into voxel-dose routines by combining with widely available image registration and radiation transport tools.