Monte Carlo method

This study presents two significant investigations in the field of proton therapy, leveraging advanced Monte Carlo simulations to improve our understanding and modeling of proton beam characteristics and secondary particle dynamics. The first investigation centers on the development and validation of a Monte Carlo model tailored for the single-room Varian ProBeam pencil beam scanning system. The study begins with an in-depth simulation analysis to justify the selection of the "g4h-phy_QGSP_FTFP_BERT" physics list configuration for our TOPASSFPTI model, developed using the TOPAS 3.9 tool with a Geant4 base, version 10.07.p03. Comprehensive verification against clinical measurements in a water phantom demonstrated the accuracy of the model. A comparative analysis between the TOPASSFPTI model and a previously published TOPAS model for the Varian ProBeam system at Emory Proton Therapy Center (TOPASEmory) revealed distinct differences in the beam characteristics. Notably, the TOPASSFPTI model exhibited a closer alignment with the specific beam characterization at SFPTI, showing a strong consistency in beam energy spread (σE) and integrated depth dose distributions (IDDs), with a 98-100% agreement under 2%/2 mm γ-index criteria. Differences in lateral spot sizes were observed, with the TOPASSFPTI model showing slightly larger spot sizes compared to TOPASEmory, which aligns more closely with SFPTI’s clinical setup. Additionally, the calibration of absolute dose values indicated significant differences in the number of protons per monitor unit (MU) between the TOPASSFPTI and the clinical treatment planning system (TPS) data, with the TOPASSFPTI model consistently showing higher values.

Dosimetric uncertainty in very small (< 2 x 2 cm2) photon fields is notably higher that has created research questions when using small-field virtual cone with variable multileaf collimator (MLC) fields. We evaluate the efficacy of the virtual cone with a fixed MLC field for stereotactic radiosurgery (SRS) of small targets such as trigeminal neuralgia.
We employed a virtual cone technique with a fixed field geometry, called fixed virtual cone (fVC), for small target radiosurgery using the EDGE (Varian Medical Systems, Palo Alto, CA) linac. The fVC is characterized by 0.5 cm x 0.5 cm high-definition MLC field of 10 MV flattening filter-free (FFF) beam defined at 100 cm SAD, while jaws are positioned at 1.5 cm x 1.5 cm. A spherical dose distribution equivalent to 5 mm cone was generated by using 10–14 non-coplanar partial arcs. The dosimetric accuracy of this technique was validated using the SRS MapCHECK (Sun Nuclear Corporation, FL) and the EBT3 (Ashland Inc., NJ) film based on absolute dose measurements. For the quality assurance (QA), 10 treatment plans for trigeminal neuralgia consisting of various arc fields at different collimator angles were analyzed retrospectively using 6 MV and 10 MV FFF beams, including the field-by-field study (n = 130 fields). Dose outputs were compared between the SRS MapCHECK measurements and Eclipse treatment planning system (TPS) with Acuros XB algorithm (version 16.1). In addition, important clinical parameters of 15 cases treated for trigeminal neuralgia were evaluated for the clinical performance. Moreover, dosimetric (field output factors, dose/MU) uncertainties considering a minute (± 0.5–1.0 mm) leaf shift in the field defining fVC, were examined from the TPS, SRS diode (PTW 60018) measurements, and Monte Carlo (MC) simulations.

Since the release of the Cyberknife Multileaf Collimator (CK-MLC), it has been a constant
concern on the realistic dose differences computed with its early-available Finite Size
Pencil Beam algorithm (FSPB) from those computed by using industry well-accepted
algorithms such as the Monte Carlo (MC) dose algorithm. In this study dose disparities
between FSPB and MC dose calculation algorithms for selected CK-MLC treatment plans
were quantified. The dosimetry for planning target volume (PTV) and major organs at risks
(OAR) was compared by calculating normalized percentage deviations (Ndev) between the
two algorithms. It is found that the FSPB algorithm overestimates D95 of PTV when
compared with the MC algorithm by averaging 24.0% in detached lung cases, and 15.0%
in non-detached lung cases which is attributed to the absence of heterogeneity correction
in the FSPB algorithm. Average dose differences are 0.3% in intracranial and 0.9% in
pancreas cases. Ndev for the D95 of PTV range from 8.8% to 14.1% for the CK-MLC lung
treatment plans with small field (SF ≤ 2x2cm2). Ndev is ranged from 0.5-7.0% for OARs.

MapCheck measurements for 50 retrospective patient’s treatment plans suggested that MapCheck could be effectively employed in routine patient specific quality assurance in M6 Cyberknife with beams delivered at different treatment angles. However, these measurements also suggested that for highly intensity modulated MLC plans, field segments of width < 8 mm should further be analyzed with a modified (-4%) correction factor. Results of MC simulations of the M6 Cyberknife using the EGSnrc program for 2-5 millions of incident particles in BEAMnrc and 10-20 millions in DOSXYZnrc have shown dose uncertainties within 2% for open fields from 7.6 x 7.7 mm2 to 100 x 100 mm2. Energy and corresponding FWHM were optimized by comparing with water phantom measurements at 800 mm SAD resulting to E = 7 MeV and FWHM = 2.2 mm. Good agreement of dose profiles (within 2%) and outputs (within 3%) were found between the MC simulations and water phantom measurements for the open fields.

Monte Carlo (MC) and Pencil Beam (PB) calculations are compared to their measured planar dose distributions using a 2-D diode array for lung Stereotactic Body Radiation Therapy (SBRT). The planar dose distributions were studied for two different phantom types: an in-house heterogeneous phantom and a homogeneous phantom. The motivation is to mimic the human anatomy during a lung SBRT treatment and incorporate heterogeneities into the pre-treatment Quality Assurance process, where measured and calculated planar dose distributions are compared before the radiation treatment. Individual and combined field dosimetry has been performed for both fixed gantry angle (anterior to posterior) and planned gantry angle delivery. A gamma analysis has been performed for all beam arrangements. The measurements were obtained using the 2-D diode array MapCHECK 2™.

The purpose of this research is to determine the feasibility of introducing the Monte Carlo (MC) dose calculation algorithm into the clinical practice. Unlike the Ray Tracing (RT) algorithm, the MC algorithm is not affected by the tissue inhomogeneities, which are significant inside the chest cavity. A retrospective study was completed for 102 plans calculated using both the RT and MC algorithms. The D95 of the PTV was 26% lower for the MC calculation. The first parameter of conformality, as defined as the ratio of the Prescription Isodose Volume to the PTV Volume was on average 1.27 for RT and 0.67 for MC. The results confirm that the RT algorithm significantly overestimates the dosages delivered confirming previous analyses. Correlations indicate that these overestimates are largest for small PTV and/or when the ratio of the volume of lung tissue to the PTV approaches 1.

The purpose of this thesis is to validate the Monte Carlo algorithm for
electron radiotherapy in the Eclipse™ treatment planning system (TPS), and to
compare the accuracy of the Electron Monte Carlo algorithm (eMC) to the Pencil
Beam algorithm (PB) in Eclipse™. Dose distributions from GafChromic™ EBT3
film measurements were compared to dose distributions from eMC and PB
treatment plans. Measurements were obtained with 6MeV, 9MeV, and 12MeV
electron beams at various depths. A 1 cm thick solid water template with holes
for bone-like and lung-like plugs was used to create assorted configurations and
heterogeneities. Dose distributions from eMC plans agreed better with the film
measurements based on gamma analysis. Gamma values for eMC were
between 83%-99%, whereas gamma values for PB treatment plans were as low
as 38.66%. Our results show that using the eMC algorithm will improve dose
accuracy in regions with heterogeneities and should be considered over PB.

Evaluation of dose optimization using the Pencil Beam (PB) and Monte Carlo (MC) algorithms may allow physicists to apply dosimetric offsets to account for inaccuracies of the PB algorithm for lung cancer treatment with Stereotactic Body Radiotherapy (SBRT). 20 cases of Non-Small Cell Lung Cancer (NSCLC) were selected. Treatment plans were created with Brainlab iPlanDose® 4.1.2. The D97 of the Planning Target Volume (PTV) was normalized to 50 Gy on the Average Intensity Projection (AIP) using the fast PB and compared with MC. This exact plan with the same beam Monitor Units (MUs) was recalculated over each respiratory phase. The results show that the PB algorithm has a 2.3-2.4% less overestimation at the maximum exhalation phase than the maximum inhalation phase when compared to MC. Significantly smaller dose difference between PB and MC is also shown in plans for peripheral lesions (7.7 ± 0.7%) versus central lesions (12.7±0.8%)(p< 0.01).

This thesis describes a numerical technique for modeling the vibrational behavior of a complex structure in the mid-frequency range. The structure is divided into subsystems, and each subsystem is modeled using Finite Elements. The obtained results are then manipulated to model variations in the response due to nominal variations in the structure. Based on a Component Mode Synthesis representation, the calculations lead to a deterministic energy flow model. The model represents the deterministic dynamic behavior of the structure for mid frequencies. However, in mid frequencies, the response is sensitive to perturbations in the properties of the structure. An appropriate way to represent those perturbations is to calculate the response of an ensemble of structures. The ensemble is defined in terms of the statistics of the local natural frequencies. A technique combining a Monte Carlo simulation with the Perturbation approach is used to relate the perturbations in the local natural frequencies to the statistics of the energy flow. This combined method is computationally tractable, being several times faster than a full Monte Carlo simulation of the whole global structure.

The embedded cluster Monte Carlo (ECMC) method which combines the Korringa-Kohn-Rostoker coherent potential approximation embedded cluster method (KKR-CPA-ECM) and the Monte Carlo method has been developed in order to study phase diagrams of binary alloys. The KKR-CPA-ECM provides interchange energies to the Monte Carlo code. In this thesis, a pair-interaction (PI) method is used to provide interchange energies to the Monte Carlo code. The code of the PI method is obtained based on the KKR-CPA-ECM code. The interchange energies of Cu0.5 Zn0.5 alloys are calculated with the PI method. The critical temperature and the phase boundary of Cu-Zn alloys are obtained by carrying out both Monte Carlo calculations with above interchange energies and the ECMC calculations. A comparison between the results of both methods is made.