A Monte Carlo Investigation of Dose Point Kernel Scaling for α-Emitting Radionuclides

A diffusion-leakage model coupled with dose point kernels (DPK) for dosimetry of diffusing alpha-emitters radiation therapy (DaRT)

BACKGROUND

Diffusing alpha-emitters radiation therapy (DaRT) is a novel brachytherapy technique that leverages the diffusive flow of 224Ra progeny within the tumor volume over the course of the treatment. Cell killing is achieved by the emitted alpha particles that have a short range in tissue and high linear energy transfer. The current proposed absorbed dose calculation method for DaRT is based on a diffusion-leakage (DL) model that neglects absorbed dose from beta particles.

PURPOSE

This work aimed to couple the DL model with dose point kernels (DPKs) to account for dose from beta particles as well as to consider the non-local deposition of energy.

METHODS

The DaRT seed was modeled using COMSOL multiphysics and the DL model was implemented to extract the spatial information of the diffusing daughters. Using Monte-Carlo (MC) methods, DPKs were generated for 212Pb, 212Bi, and their progenies since they were considered to be the dominant beta emitters in the 224Ra radioactive decay chain. A convolution operation was performed between the integrated number densities of the diffusing daughters and DPKs to calculate the total absorbed dose over a 30-day treatment period. Both high-diffusion and low-diffusion cases were considered.

RESULTS

The calculated DPKs showed non-negligible energy deposition over several millimeters from the source location. An absorbed dose >10 Gy was deposited within a 1.8 mm radial distance for the low diffusion case and a 2.2 mm radial distance for the high diffusion case. When the DPK method was compared with the local energy deposition method that solely considered dose from alpha particles, differences above 1 Gy were found within 1.3 and 1.8 mm radial distances from the surface of the source for the low diffusion and high diffusion cases, respectively.

CONCLUSIONS

The proposed method enhances the accuracy of the dose calculation method used for the DaRT technique.

Characterization of a segmented printed circuit board (PCB) as a standard for absorbed dose to water from alpha-emitting radionuclides

BACKGROUND

Our previous work introduced and evaluated a standard for surface absorbed dose rate per unit radioactivity to water from unsealed alpha-emitting radionuclides used in targeted radionuclide therapy (TRT). An overall uncertainty over 4.0% at k = 1 was reported for the absorbed dose to air measurements, which was partially attributed to the rotational alignment uncertainty in the geometrical setup.

PURPOSE

A printed circuit board (PCB) with a segmented guard was constructed to align the extrapolation chamber (EC) and the source plates using a differential capacitance technique. The PCB EC aimed to enhance the repeatability of the ionization current measurements. The PCB EC was evaluated using a thin film 210Po source. The measured absorbed dose to air cavity was compared with the Monte Carlo (MC) calculations. Using the extrapolation method, the surface absorbed dose rate to water was calculated.

METHODS

The PCB EC was constructed with a 4.50 mm diameter collector surrounded by four sectors and a guard electrode. The sectors were isolated for rotational alignment and later connected to the guard for ionization current measurements. A bridge circuit measured differential capacitance between opposing sectors, and a hexapod motion stage rotated the source substrate to minimize the differential capacitance. The EC was evaluated using a 210Po source with a 3.20 mm diameter and 1.253 μ $\mu $ Ci radioactivity. MC simulations were performed to calculate thek p o i n t ${k}_{point}$ ,k b a c k s c a t t e r ${k}_{backscatter}$ , andk d i v ${k}_{div}$ correction factors. Ionization current measurements were performed for air gaps in the 0.3-0.525 mm range and surface absorbed dose rate to water was calculated.

RESULTS

Rotational offsets of up to 3.0° were found and the current repeatability was found to increase with the absorbed dose to air uncertainty calculated to be ∼2.0%. Using the capacitance method, the effective EC diameter was measured to be 4.53 mm. The recombination, polarity, and electrometer corrections were reported to be within 1.00% across all measurement trials. The MC-calculated correction factors were calculated to be much larger than the recombination and polarity correction factors. The averagek p o i n t ${k}_{point}$ ,k b a c k s c a t t e r ${k}_{backscatter}$ , andk d i v ${k}_{div}$ corrections were calculated to be 1.063, 0.9402, and 2.136, respectively. The MC-calculated absorbed dose to air was found to overestimate the absorbed dose by over 4.00% when compared with the measured absorbed dose to air. The surface absorbed dose rate to water was calculated to be2.304 × 10 - 6 $2.304 \times {10}^{ - 6}$ Gy/s/Bq with an overall uncertainty of 4.07%.

CONCLUSIONS

The constructed PCB EC was deemed suitable as an absorbed dose standard. A repeatable rotational alignment was achieved using the differential capacitance technique. The metal electrodes on the PCB made a difference of < 1.00% on the backscatter correction when compared to the EC comprised of polystyrene-equivalent collector. A 20% difference in the surface absorbed dose rate to water was found between the two ECs, which is attributed to the cavity diameter differences leading to different magnitudes of dose fall-off along the lateral direction.

Technical note: Errors introduced when using Dose Voxel Kernels for estimating absorbed dose from radiopharmaceutical therapies involving alpha emitters

BACKGROUND

In radiopharmaceutical therapies (RPT) involving beta emitters, absorbed dose (Dabs ) calculations often employ the use of dose voxel kernels (DVK). Such methods are faster and easier to implement than Monte Carlo (MC) simulations. Using DVK methods implies a non-stochastic distribution of particles. This is a valid assumption for betas where thousands to tens of thousands of particles traversing the cell nucleus are required to achieve cell kill. However, alpha particles have linear energy transfers (LET) that are ∼500 times higher than LETs of betas. This results in a significant probability of killing a cell from even a single traversal through its nucleus. Consequently, the activity used for therapy involving alphas is very low, and the use of DVKs for estimating Dabs will generate results that may be erroneous.

PURPOSE

This work aims at illustrating how use of DVKs affect the resulting Dabs in small tumors when irradiated with clinically relevant amounts of beta- and alpha-emitters. The results are compared with those from using a Monte Carlo method where the energy deposition from individual tracks is simulated.

METHODS

To illustrate the issues associated with DVK for alpha radiopharmaceutical therapies at the microscale, a tumor cluster model was used to compare beta (177 Lu) and alphas (211 At, 225 Ac, and 227 Th) irradiations. We used 103 beta particles and 20 alpha particles per cell, which is within the range of the required number of particle traversals through its nucleus to sterilize a cell. Results from using both methods were presented with Dabs histograms, dose volume histograms, and Dabs error maps.

RESULTS

For beta-emitter (177 Lu) irradiating the modeled tumor cluster, resulting Dabs was similar for both DVK and MC methods. For all alpha emitters, the use of DVK led to an overestimation of Dabs when compared to results generated using a MC approach.

CONCLUSIONS

Our results demonstrate that the use of DVK methods for alpha emitters can lead to an overestimation in the calculated Dabs . The use of DVKs for therapies involving alpha emitters may therefore not be appropriate when only referring to the mean Dabs metric.

Development of a stand-alone precalculated Monte Carlo code to calculate the dose by alpha and beta emitters from the Ra-224 decay chain

BACKGROUND

Recent developments in alpha and beta emitting radionuclide therapy highlight the importance of developing efficient methods for patient-specific dosimetry. Traditional tabulated methods such as Medical Internal Radiation Dose (MIRD) estimate the dose at the organ level while more recent numerical methods based on Monte Carlo (MC) simulations are able to calculate dose at the voxel level. A precalculated MC (PMC) approach was developed in this work as an alternative to time-consuming fully simulated MC. Once the spatial distribution of alpha and beta emitters is determined using imaging and/or numerical methods, the PMC code can be used to achieve an accurate voxelized 3D distribution of the deposited energy without relying on full MC calculations.

PURPOSE

To implement the PMC method to calculate energy deposited by alpha and beta particles emitted from the Ra-224 decay chain.

METHODS

The GEANT4 (version 10.7) MC toolkit was used to generate databases of precalculated tracks to be integrated in the PMC code as well as to benchmark its output. In this regard, energy spectra of alpha and beta particles emitted by the Ra-224 decay chain were generated using GAMOS (version 6.2.0) and imported into GEANT4 macro files. Either alpha or beta emitting sources were defined at the center of a homogeneous phantom filled with various materials such as soft tissue, bone, and lung where particles were emitted either mono-directionally (for database generation) or isotropically (for benchmarking). Two heterogeneous phantoms were used to demonstrate PMC code compatibility with boundary crossing events. Each precalculated database was generated step-by-step by storing particle track information from GEANT4 simulations followed by its integration in a PMC code developed in MATLAB. For a user-defined number of histories, one of the tracks in a given database was selected randomly and rotated randomly to reflect an isotropic emission. Afterward, deposited energy was divided between voxels based on step length in each voxel using a ray-tracing approach. The radial distribution of deposited energy was benchmarked against fully simulated MC calculations using GEANT4. The effect of the GEANT4 parameter StepMax on the accuracy and speed of the code was also investigated.

RESULTS

In the case of alpha decay, primary alpha particles show the highest contribution (>99%) in deposited energy compared to their secondary particles. In most cases, protons act as the main secondary particles in the deposition of energy. However, for a lung phantom, using a range cutoff parameter of 10 µm on primary alpha particles yields a higher contribution of secondary electrons than protons. Differences between deposited energy calculated by PMC and fully simulated MC are within 2% for all alpha and beta emitters in homogeneous and heterogeneous phantoms. Additionally, statistical uncertainties are less than 1% for voxels with doses higher than 5% of the maximum dose. Moreover, optimization of the parameter StepMax is necessary to achieve the best tradeoff between code accuracy and speed.

CONCLUSIONS

The PMC code shows good performance for dose calculations deposited by alpha and beta emitters. As a stand-alone algorithm, it is suitable to be integrated into clinical treatment planning systems.