Linear Boltzmann equation solver for voxel‐level dosimetry in radiopharmaceutical therapy: Comparison with Monte Carlo and kernel convolution
Authors: Kayal Gunjan , Van Benjamin , Andl George , Tu Cheng , Wareing Todd , Wilderman Scott , Mikell Justin , Dewaraja Yuni K. 
Published: March 2024

Background

With recent interest in patient‐specific dosimetry for radiopharmaceutical therapy (RPT) and selective internal radiation therapy (SIRT), an increasing number of voxel‐based algorithms are being evaluated. Monte Carlo (MC) radiation transport, generally considered to be the most accurate among different methods for voxel‐level absorbed dose estimation, can be computationally inefficient for routine clinical use.

Purpose

This work demonstrates a recently implemented grid‐based linear Boltzmann transport equation (LBTE) solver for fast and accurate voxel‐based dosimetry in RPT and SIRT and benchmarks it against MC.

Methods

A deterministic LBTE solver (Acuros MRT) was implemented within a commercial RPT dosimetry package (Velocity 4.1). The LBTE is directly discretized using an adaptive mesh refined grid and then the coupled photon‐electron radiation transport is iteratively solved inside specified volumes to estimate radiation doses from both photons and charged particles in heterogeneous media. To evaluate the performance of the LBTE solver for RPT and SIRT applications, 177Lu SPECT/CT, 90Y PET/CT, and 131I SPECT/CT images of phantoms and patients were used. Multiple lesions (2–1052 mL) and normal organs were delineated for each study. Voxel dosimetry was performed with the LBTE solver, dose voxel kernel (DVK) convolution with density correction, and a validated in‐house MC code using the same time‐integrated activity and density maps as input to the different dose engines. The resulting dose maps, difference maps, and dose‐volume‐histogram (DVH) metrics were compared, to assess the voxel‐level agreement. Evaluation of mean absorbed dose included comparison with structure‐level estimates from OLINDA.

Results

In the phantom inserts/compartments, the LBTE solver versus MC and DVK convolution demonstrated good agreement with mean absorbed dose and DVH metrics agreeing to within 5% except for the D90 and D70 metrics of a very low activity concentration insert of 90Y where the agreement was within 15%. In the patient studies (five patients imaged after 177Lu DOTATATE RPT, five after 90Y SIRT, and two after 131I radioimmunotherapy), in general, there was better agreement between the LBTE solver and MC than between LBTE solver and DVK convolution for mean absorbed dose and voxel‐level evaluations. Across all patients for all three radionuclides, for soft tissue structures (kidney, liver, lesions), the mean absorbed dose estimates from the LBTE solver were in good agreement with those from MC (median difference < 1%, maximum 9%) and those from DVK (median difference < 5%, maximum 9%). The LBTE and OLINDA estimates for mean absorbed dose in kidneys and liver agreed to within 10%, but differences for lesions were larger with a maximum 14% for 177Lu, 23% for 90Y, and 26% for 131I. For bone regions, the agreement in mean absorbed doses between LBTE and both MC and DVK were similar (median < 11%, max 11%) while for lung the agreement between LBTE and MC (median < 1%, max 8%) was substantially better than between LBTE and DVK (median < 16%, max 33%). Voxel level estimates for soft tissue structures also showed good agreement between the LBTE solver and both MC and DVK with a median difference < 5% (maximum < 13%) for the DVH metrics with all three radionuclides. The largest difference in DVH metrics was for the D90 and D70 metric in lung and bone where the uptake was low. Here, the difference between LBTE and MC had a median value < 14% (maximum 23%) for bone and < 4% (maximum 37%) for lung, while the corresponding differences between LBTE and DVK were < 23% (maximum 31%) and < 67% (maximum 313%), respectively. For a typical patient with a matrix size of 166 × 166 × 129 (voxel size 3 × 3 × 3 mm3), voxel dosimetry using the LBTE solver was as fast as ∼2 min on a desktop computer.

Conclusion

Having established good agreement between the LBTE solver and MC for RPT and SIRT applications, the LBTE solver is a viable option for voxel dosimetry that can be faster than MC. Further analysis is being performed to encompass the broad range of radionuclides and conditions encountered clinically.