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

Abstract

Background: 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. 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 ten 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 AE 14.2% and À3.6 AE 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. Conclusions: 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.

Patient-specific dosimetry adapted to variable number of SPECT/CT time-points per cycle for $$^{177}$$Lu-DOTATATE therapy

“…This step leads to a Time Dose-Rate Curve (TDRC) for all injections, similar to the conventional Time-Activity Curve (TAC) except that it is determined with dose rate and not the activity, thus already integrating the cross-dose. In order to compute the total absorbed dose corresponding to the time integral of those curves, the analytical method proposed by Jackson et al [ 35 , 36 ] based on tri-exponential function was used by replacing activity ( A ) with dose rate ( ), as shown in Eq. ( 1 ).…”

“…1 . Tri-exponential parameters were computed with the same algorithm described in [ 35 ]; therefore, all were decay-corrected before fitting TDRC, and the correction was reversed during integration. ODR was assumed to be equal to zero just before the treatment and 600H after the injection.…”

“…ODR was assumed to be equal to zero just before the treatment and 600H after the injection. The parameter was set to − 1.3 in the article by Jackson et al [ 35 ]. Here, we are dealing with TDRC and not TAC so this value cannot be used.…”

Tumor-Targeted Interleukin 2 Boosts the Anticancer Activity of FAP-Directed Radioligand Therapeutics

“…For SPECT/CT analysis, representative ellipsoid or spheric volumes of interest for organs and voxelwise volumes of interest covering the entire tumors were drawn on the basis of the CT component of the SPECT/CT. For estimation of self-absorbed dose (or specific absorbed dose, expressed in Gy/MBq) in organs and tumors, time-activity curves of single animals were fitted according to the method of Jackson et al using the scripted implementation (42). This involved using a model consisting of a triexponential function fitted to the latest 3 acquisitions.…”

Dosimetric Evaluation of 177Lu Peptide Receptor Radionuclide Therapy Using GATE and Planet Dose

“…Similarly, Huizing et al compared the same software packages using both mono-exponential and bi-exponential fittings [30]. Jackson et al, proposed a tri-exponential algorithm for absorbed dose calculation in patients undergoing PRRT with 177 Lu-DOTATATE [31]. From those studies, it is evident that further research on the fitting methods is deemed necessary.…”