Technical Note: Rapid multiexponential curve fitting algorithm for voxel-based targeted radionuclide dosimetry

Dosimetry in nuclear medicine often relies on estimating pharmacokinetics based on sparse temporal data. As analysis methods move toward image-based three-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 optimize to local minima without applying tight constraints at the outset.

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 ten patients receiving ¹⁷⁷ Lu-DOTA-Octreotate therapy.

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 <5 min processing time. Furthermore, the technique is able to predictably and reproducibly handle artefactual measurements due to noise or spatial misalignment over multiple image times.

An efficient, analytical algorithm for solving multiphase 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.