Inhomogeneity Correction Factors Research Articles

Uniting Nonempirical and Empirical Density Functional Approximation Strategies Using Constraint-Based Regularization.

In this work, we present a general framework that unites the two primary strategies for constructing density functional approximations (DFAs): nonempirical (NE) constraint satisfaction and empirical (E) data-driven optimization. The proposed method employs B-splines, bell-shaped spline functions with compact support, to construct each inhomogeneity correction factor (ICF). This choice offers several distinct advantages over traditional polynomial expansions by enabling explicit enforcement of linear and nonlinear constraints as well as ICF smoothness using Tikhonov and penalized B-splines (P-splines) regularization. As proof-of-concept, we use the so-called CASE (constrained and smoothed empirical) framework to construct a constraint-satisfying and data-driven global hybrid that exhibits enhanced performance across a diverse set of chemical properties. We argue that the CASE approach can be used to generate DFAs that maintain the physical rigor and transferability of NE-DFAs while leveraging high-quality quantum-mechanical data to remove the arbitrariness of ansatz selection and improve performance.

Technical note: A fast and accurate analytical dose calculation algorithm for 125 I seed-loaded stent applications.

The safety and clinical efficacy of 125 I seed-loaded stent for the treatment of portal vein tumor thrombosis (PVTT) have been shown. Accurate and fast dose calculation of the 125 I seeds with the presence of the stent is necessary for the plan optimization and evaluation. However, the dosimetric characteristics of the seed-loaded stents remain unclear and there is no fast dose calculation technique available. This paper aims to explore a fast and accurate analytical dose calculation method based on Monte Carlo (MC) dose calculation, which takes into account the effect of stent and tissue inhomogeneity. A detailed model of the seed-loaded stent was developed using 3D modeling software and subsequently used in MC simulations to calculate the dose distribution around the stent. The dose perturbation caused by the presence of the stent was analyzed, and dose perturbation kernels (DPKs) were derived and stored for future use. Then, the dose calculation method from AAPM TG-43 was adapted by integrating the DPK and appropriate inhomogeneity correction factors (ICF) to calculate dose distributions analytically. To validate the proposed method, several comparisons were performed with other methods in water phantom and voxelized CT phantoms for three patients. The stent has a considerable dosimetric effect reducing the dose up to 47.2% for single-seed stent and 11.9%-16.1% for 16-seed stent. In a water phantom, dose distributions from MC simulations and TG-43-DP-ICF showed a good agreement with the relative error less than 3.3%. In voxelized CT phantoms, taking MC results as the reference, the relative errors of TG-43 method can be up to 33%, while those of TG-43-DP-ICF method were less than 5%. For a dose matrix with 256 × 256 × 46 grid (corresponding to a phantom of 17.2 × 17.2 × 11.5cm3 ) for 16-seed-loaded stent, it only takes 17s for TG-43-DP-ICF to compute, compared to 25h for the full MC calculation. The combination of DPK and inhomogeneity corrections is an effective approach to handle both the presence of stent and tissue heterogeneity. Exhibiting good agreement with MC calculation and computational efficiency, the proposed TG-43-DP-ICF method is adequate for dose evaluation and optimization in seed-loaded stent implantation treatment planning.

Theoretical "t-z" Curves for Piles in Radially Inhomogeneous Soil

Accurate estimates of pile settlement are key for efficient design of axially loaded piles. Calculations of pile settlement can be simplified using one-dimensional “t-z” curves describing pile settlement at a certain depth as a function of side friction. In the realm of this simplified framework, theoretical “t-z” curves can be derived by substituting an attenuation function describing the variation of shear stress with distance from the pile, into a soil constitutive model relating shear strain to shear stress, then integrating with respect to distance to get the settlement at the pile circumference due to an applied shear stress. A handful of analytical “t-z” curves are available in the literature using the concentric cylinder model to define an attenuation function; these include solutions for linear-elastic, power-law and hyperbolic constitutive models. However, radially homogeneous soil has often been assumed, ignoring the effect of the pile installation resulting in unconservative calculations of pile settlement. This paper considers the installation of the pile, resulting in a radially variable shear modulus distribution in the surrounding soil. A radial inhomogeneity correction factor has been developed for selected constitutive models based on two simplified functions for the soil inhomogeneity, which can be applied to the previously derived “t-z” curves produced assuming radially homogeneous soil. The performance of this simplified method is investigated.

The dependence of inhomogeneity correction factors on photon beam quality index performed with the Anisotropic Analytical Algorithm

Abstract Purpose: The purpose of the study was to investigate the dependence of tissue inhomogeneity correction factors (ICFs) on the photon beam quality index (QI). Materials and Methods: Heterogeneous phantoms, comprising semi-infinite slabs of the lung (0.10, 0.20, 0.26 and 0.30 g/cm3), adipose tissue (0.92 g/cm3) and bone (1.85 g/cm3) in water, were constructed in the Eclipse treatment planning system. Several calculation models of 6 MV and 15 MV photon beams for quality index (TPR20,10) = 0.670±k*0.01 and TPR20,10 = 0.760±k*0.01, k = -3, -2, -1, 0, 1, 2, 3 respectively were built in the Eclipse. The ICFs were calculated with the anisotropic analytical algorithm (AAA) for several beam sizes and points lying at several depths inside of and below inhomogeneities of different thicknesses. Results: The ICFs increased for lung and adipose tissues with increasing beam quality (TPR20,10), while decreased for bone. Calculations with AAA predict that the maximum difference in ICFs of 1.0% and 2.5% for adipose and bone tissues, respectively. For lung tissue, changes of ICFs of a maximum of 9.2% (6 MV) and 13.8% (15 MV). For points where charged particle equilibrium exists, a linear dependence of ICFs on TPR20,10 was observed. If CPE doesn’t exist, the dependence became more complex. For points inside of the low-density inhomogeneity, the dependence of the ICFs on energy was not linear but the changes of ICFs were smaller than 3.0%. Measurements results carried out with the CIRS phantom were consistent with the calculation results. Conclusions: A negligible dependence of the ICFs on energy was found for adipose and bone tissue. For lung tissue, in the CPE region, the dependence of ICFs on different beam quality indexes with the same nominal energy may not be neglected, however, this dependence was linear. Where there is no CPE, the dependence of the ICFs on energy was more complicated.

Target biological tissue and energy influence on dose enhancement factor produced by gold nanoparticles and its relevant radiological properties

Understanding the radiation dose enhancement factor (DEF) influencing parameter and relevant radiological properties is important for the accurate estimation of absorbed dose in nanoparticle enhanced X-ray therapy (NEXT). In this present study, target tumor tissue influence on DEF produced by 18 mg/g gold nanoparticle (GNP) in ten various biological samples and relevant radiological properties were studied over 15KeV-15MeV energies. The DEF was calculated with the help of mass energy-absorption coefficients (μen/ρ) values. Mass attenuation coefficient (μ/ρ), (μen/ρ), photoelectric absorption coefficients were computed with the help of the XCOM program. Energy absorption buildup factor (EABF), exposure buildup factor (EBF) and effective atomic number (Zeff) were calculated by EXABCAL and auto Zeff computer program respectively. DEF were significantly varied according to target biological tissue elemental composition and incident photon energies. Among the ten various biological samples, adipose tissue target produces higher DEF which have the lower Zeff and bone produce lower DEF which possess higher Zeff. Optimal energy for the maximum DEF is 40 KeV and 100 KeV for soft tissues and bone respectively. EABF and EBF of GNP doped tissues were discussed as the function of energy and elemental composition and mean free path up 40 mfp. Energy and inhomogeneity correction factors are necessary for the accurate estimation of DEF. These results are helpful for developing the treatment planning algorithms and dosimetry for NEXT. Age and calcification dependent variation of the elemental composition of the target tissue and its effect on DEF need to account for the future work.

P298] The influence of variations of the beam quality for high energy photon beams on tissue inhomogeneity correction factors for radiotherapy treatment plans

Purpose The purpose of this study was to assess the effect of variations of the beam quality (TPR20,10) for photon beams on tissue inhomogeneity correction factors (ICFs). Methods A total of 90 three-dimensional conformal radiotherapy (3DCRT) treatment plans for three locations (3DCRT lung, gynaecological, prostate) and 15 SRS lung plans were considered for this study. For 3DCRT plans, the ICFs were calculated for a range of beam qualities. For 6 MV, the range of TPR20,10 was 0.670 ± 3%, and for 15 MV, the range of TPR20,10 was 0.760 ± 3%. The stereotactic plans were prepared with two 6 MV beams from a Varian TrueBeam accelerator - one generated with a flattening filter (X6, TPR20,10 = 0.688) and one flattening filter free (X6FFF, TPR20,10 = 0.632). Calculations were performed using Eclipse treatment planning system (TPS) with the anisotropic analytical algorithm (AAA). ICFs were also measured in a CIRS Tissue Simulation Phantom (thorax with lungs) for two fields 5 × 5 and 10 × 10 for X6 and X6FFF beams. PTW Farmer and semiflex ionization chambers were used for measurements. Results Calculations for 3DCRT plans showed that the 6% variations in energy (TPR20,10) lea to average changes of ICFs of 2.0% (6 MV) and 2.6% (15 MV) for lung cases. For gynaecological and prostate patients, the mean differences of ICFs were less than 1%. The difference of 5.6% of TPR20,10 values between X6 and X6 FFF for lung SRS treatment plans led to a difference of ICFs of less than 2%. Measurements with the CIRS phantom also demonstrated differences of ICFs consistently less than 5% between X6 and X6 FFF beams. Conclusions The influence of energy on inhomogeneity correction factors is rather small. Correction factors measured on one accelerator may be used for another accelerator with similar energy provided quality control tests are performed.

Dependence of tissue inhomogeneity correction factors on photon-beam energy

Abstract Introduction: Commissioning of the treatment-planning system includes the accuracy of dose calculations in the inhomogeneous absorber. Several results of measurements with regard to inhomogeneity correction factors (CFs) have been published. However, the dependence of CFs on photon-beam energy may preclude such results from being applied to the photon beams of general users. Purpose: The aim of this study was to assess the dependence of CFs on the photon-beam energy. Materials and methods: CFs were calculated by the Batho method for several slab geometries comprised of concentrations of lung tissue and water of 0.25 and 1.00 g/cm3, respectively. The CFs were calculated at 6 MV (TPR20 10 = 0.67 ± k * 0.01) and 15 MV (TPR20 10 = 0.76 ± k * 0.01) where k = -3, -2, -1, 0, 1, 2, 3. All calculations were performed in the region where a charged-particle equilibrium exists. Results: Changes in CFs of less than 2% were observed across the considered energy ranges. With a change in TPR20,10 of 0.01, both at 6 and 15 MV at a depth of 5 cm below the lung; and lung thicknesses of 3, 5 and 8 cm over a fi eld surface area of 10 × 10 cm2, the change in CF never exceeded 2.4%. The dependences of changes in CFs in terms of TPR20,10 were 1.74% and 1.20% for field surface areas of 5 × 5 cm2 and 20 × 20 cm2, respectively. A comparison of 42 linear accelerators (LINACs) exhibiting 6 MV and 15 MV of energy installed in Poland showed that the maximum differences in terms of TPR20,10 at 6 MV and 15 MV were 4.2% and 2.2%, respectively. Conclusion: A linear dependence of CFs on energy was observed. According to observations, the smaller the surface area of the field and deeper the point of interest below the lung, the more dependent CFs are on energy.

Dependence of tissue inhomogeneity correction factors on nominal photon beam energy

Introduction Before the first clinical use of the treatment planning system commissioning of dose calculation algorithms must be performed. One of the most difficult tasks is to check the accuracy of calculations in the inhomogeneous absorber. Several results of so called inhomogeneity correction factors were published but it is not clear, if they might be used for the user beam due to differences in beam energies. Purpose The aim of the study was to check how much the correction factors depend on the energy of the beam. Materials and methods The Batho correction method, which is the ratio of powers of Tissue Air Ratios (TARs), was used for calculation of the set of correction factors for lung. The TAR factors for wide range of energies were calculated using depth doses with the Gerbi’s formula (Gerbi, Med. Phys.18(4), 724, 1991) and peak scatter factors with the Li’s formula (Allen Li, Med. Phys. 26(6), 962, 1999). The correction factors were calculated for lung of 0.25 g/cm 3 density for several beam sizes and points lying at several depths inside of and below lung. Results The linear dependence of the correction factors on the energy were obtained. For nominal energies of 6 MV (TPR20/20 = 0.670) and 15 MV (TPR20/20 = 0.750), the 1% difference in energy lead to changes of CF of 0.7% and 0.8% respectively inside of lung. The maximum differences for points below lung were 1%. Conclusion For two photon beams of energies differed no more than 1%, the correction factors differ of less than 0.8%.

Dose heterogeneity correction for low-energy brachytherapy sources using dual-energy CT images

Permanent seed implant brachytherapy is currently used for adjuvant radiotherapy of early stage prostate and breast cancer patients. The current standard for calculation of dose around brachytherapy sources is based on the AAPM TG-43 formalism, which generates the dose in a homogeneous water medium. Recently, AAPM TG-186 emphasized the importance of accounting for tissue heterogeneities. We have previously reported on a methodology where the absorbed dose in tissue can be obtained by multiplying the dose, calculated by the TG-43 formalism, by an inhomogeneity correction factor (ICF). In this work we make use of dual energy CT (DECT) images to extract ICF parameters. The advantage of DECT over conventional CT is that it eliminates the need for tissue segmentation as well as assignment of population based atomic compositions. DECT images of a heterogeneous phantom were acquired and the dose was calculated using both TG-43 and TG-43 formalisms. The results were compared to experimental measurements using Gafchromic films in the mid-plane of the phantom. For a seed implant configuration of 8 seeds spaced 1.5 cm apart in a cubic structure, the gamma passing score for 2%/2 mm criteria improved from 40.8% to 90.5% when ICF was applied to TG-43 dose distributions.

SU‐E‐T‐477: An Efficient Dose Correction Algorithm Accounting for Tissue Heterogeneities in LDR Brachytherapy

Purpose:Seed brachytherapy is currently used for adjuvant radiotherapy of early stage prostate and breast cancer patients. The current standard for calculation of dose surrounding the brachytherapy seeds is based on American Association of Physicist in Medicine Task Group No. 43 (TG‐43 formalism) which generates the dose in homogeneous water medium. Recently, AAPM Task Group No. 186 emphasized the importance of accounting for tissue heterogeneities. This can be done using Monte Carlo (MC) methods, but it requires knowing the source structure and tissue atomic composition accurately. In this work we describe an efficient analytical dose inhomogeneity correction algorithm implemented using MIM Symphony treatment planning platform to calculate dose distributions in heterogeneous media.Methods:An Inhomogeneity Correction Factor (ICF) is introduced as the ratio of absorbed dose in tissue to that in water medium. ICF is a function of tissue properties and independent of source structure. The ICF is extracted using CT images and the absorbed dose in tissue can then be calculated by multiplying the dose as calculated by the TG‐43 formalism times ICF. To evaluate the methodology, we compared our results with Monte Carlo simulations as well as experiments in phantoms with known density and atomic compositions.Results:The dose distributions obtained through applying ICF to TG‐43 protocol agreed very well with those of Monte Carlo simulations as well as experiments in all phantoms. In all cases, the mean relative error was reduced by at least 50% when ICF correction factor was applied to the TG‐43 protocol.Conclusion:We have developed a new analytical dose calculation method which enables personalized dose calculations in heterogeneous media. The advantages over stochastic methods are computational efficiency and the ease of integration into clinical setting as detailed source structure and tissue segmentation are not needed.University of Toronto, Natural Sciences and Engineering Research Council of Canada

SU‐E‐T‐24: A Simple Correction‐Based Method for Independent Monitor Unit (MU) Verification in Monte Carlo (MC) Lung SBRT Plans

Purpose:Lung‐SBRT uses hypo‐fractionated dose in small non‐IMRT fields with tissue‐heterogeneity corrected plans. An independent MU verification is mandatory for safe and effective delivery of the treatment plan. This report compares planned MU obtained from iPlan‐XVM‐Calgorithm against spreadsheet‐based hand‐calculation using most commonly used simple TMR‐based method.Methods:Treatment plans of 15 patients who underwent for MC‐based lung‐SBRT to 50Gy in 5 fractions for PTV V100%=95% were studied. ITV was delineated on MIP images based on 4D‐CT scans. PTVs(ITV+5mm margins) ranged from 10.1‐ 106.5cc(average=48.6cc). MC‐SBRT plans were generated using a combination of non‐coplanar conformal arcs/beams using iPlan XVM‐Calgorithm (BrainLAB iPlan ver.4.1.2) for Novalis‐TX consisting of micro‐MLCs and 6MV‐SRS (1000MU/min) beam. These plans were re‐computed using heterogeneity‐corrected Pencil‐Beam (PB‐hete) algorithm without changing any beam parameters, such as MLCs/MUs. Dose‐ratio: PB‐hete/MC gave beam‐by‐beam inhomogeneity‐correction‐factors (ICFs):Individual Correction. For independent‐2nd‐check, MC‐MUs were verified using TMR‐based hand‐calculation and obtained an average ICF:Average Correction, whereas TMR‐based hand‐calculation systematically underestimated MC‐MUs by ∼5%. Also, first 10 MC‐plans were verified with an ion‐chamber measurement using homogenous phantom.Results:For both beams/arcs, mean PB‐hete dose was systematically overestimated by 5.5±2.6% and mean hand‐calculated MU systematic underestimated by 5.5±2.5% compared to XVMC. With individual correction, mean hand‐calculated MUs matched with XVMC by – 0.3±1.4%/0.4±1.4 for beams/arcs, respectively. After average 5% correction, hand‐calculated MUs matched with XVMC by 0.5±2.5%/0.6±2.0% for beams/arcs, respectively. Smaller dependence on tumor volume(TV)/field size(FS) was also observed. Ion‐chamber measurement was within ±3.0%.Conclusion:PB‐hete overestimates dose to lung tumor relative to XVMC. XVMC‐algorithm is much more‐complex and accurate with tissues‐heterogeneities. Measurement at machine is time consuming and need extra resources; also direct measurement of dose for heterogeneous treatment plans is not clinically practiced, yet. This simple correction‐based method was very helpful for independent‐2nd‐check of MC‐lung‐SBRT plans and routinely used in our clinic. A look‐up table can be generated to include TV/FS dependence in ICFs.

Exploring the limit of accuracy for density functionals based on the generalized gradient approximation: local, global hybrid, and range-separated hybrid functionals with and without dispersion corrections.

The limit of accuracy for semi-empirical generalized gradient approximation (GGA) density functionals is explored by parameterizing a variety of local, global hybrid, and range-separated hybrid functionals. The training methodology employed differs from conventional approaches in 2 main ways: (1) Instead of uniformly truncating the exchange, same-spin correlation, and opposite-spin correlation functional inhomogeneity correction factors, all possible fits up to fourth order are considered, and (2) Instead of selecting the optimal functionals based solely on their training set performance, the fits are validated on an independent test set and ranked based on their overall performance on the training and test sets. The 3 different methods of accounting for exchange are trained both with and without dispersion corrections (DFT-D2 and VV10), resulting in a total of 491508 candidate functionals. For each of the 9 functional classes considered, the results illustrate the trade-off between improved training set performance and diminished transferability. Since all 491508 functionals are uniformly trained and tested, this methodology allows the relative strengths of each type of functional to be consistently compared and contrasted. The range-separated hybrid GGA functional paired with the VV10 nonlocal correlation functional emerges as the most accurate form for the present training and test sets, which span thermochemical energy differences, reaction barriers, and intermolecular interactions involving lighter main group elements.

ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy

A 10-parameter, range-separated hybrid (RSH), generalized gradient approximation (GGA) density functional with nonlocal correlation (VV10) is presented. Instead of truncating the B97-type power series inhomogeneity correction factors (ICF) for the exchange, same-spin correlation, and opposite-spin correlation functionals uniformly, all 16,383 combinations of the linear parameters up to fourth order (m = 4) are considered. These functionals are individually fit to a training set and the resulting parameters are validated on a primary test set in order to identify the 3 optimal ICF expansions. Through this procedure, it is discovered that the functional that performs best on the training and primary test sets has 7 linear parameters, with 3 additional nonlinear parameters from range-separation and nonlocal correlation. The resulting density functional, ωB97X-V, is further assessed on a secondary test set, the parallel-displaced coronene dimer, as well as several geometry datasets. Furthermore, the basis set dependence and integration grid sensitivity of ωB97X-V are analyzed and documented in order to facilitate the use of the functional.

Characterizing and Understanding the Remarkably Slow Basis Set Convergence of Several Minnesota Density Functionals for Intermolecular Interaction Energies.

For a set of eight equilibrium intermolecular complexes, it is discovered that the basis set limit (BSL) cannot be reached by aug-cc-pV5Z for three of the Minnesota density functionals: M06-L, M06-HF, and M11-L. In addition, the M06 and M11 functionals exhibit substantial, but less severe, difficulties in reaching the BSL. By using successively finer grids, it is demonstrated that this issue is not related to the numerical integration of the exchange-correlation functional. In addition, it is shown that the difficulty in reaching the BSL is not a direct consequence of the structure of the augmented functions in Dunning's basis sets, since modified augmentation yields similar results. By using a very large custom basis set, the BSL appears to be reached for the HF dimer for all of the functionals. As a result, it is concluded that the difficulties faced by several of the Minnesota density functionals are related to an interplay between the form of these functionals and the structure of standard basis sets. It is speculated that the difficulty in reaching the basis set limit is related to the magnitude of the inhomogeneity correction factor (ICF) of the exchange functional. A simple modification of the M06-L exchange functional that systematically reduces the basis set superposition error (BSSE) for the HF dimer in the aug-cc-pVQZ basis set is presented, further supporting the speculation that the difficulty in reaching the BSL is caused by the magnitude of the exchange functional ICF. Finally, the BSSE is plotted with respect to the internuclear distance of the neon dimer for two of the examined functionals.

A simplified analytical dose calculation algorithm accounting for tissue heterogeneity for low-energy brachytherapy sources

The American Association of Physicists in Medicine Task Group No. 43 (AAPM TG-43) formalism is the standard for seeds brachytherapy dose calculation. But for breast seed implants, Monte Carlo simulations reveal large errors due to tissue heterogeneity. Since TG-43 includes several factors to account for source geometry, anisotropy and strength, we propose an additional correction factor, called the inhomogeneity correction factor (ICF), accounting for tissue heterogeneity for Pd-103 brachytherapy. This correction factor is calculated as a function of the media linear attenuation coefficient and mass energy absorption coefficient, and it is independent of the source internal structure. Ultimately the dose in heterogeneous media can be calculated as a product of dose in water as calculated by TG-43 protocol times the ICF. To validate the ICF methodology, dose absorbed in spherical phantoms with large tissue heterogeneities was compared using the TG-43 formalism corrected for heterogeneity versus Monte Carlo simulations. The agreement between Monte Carlo simulations and the ICF method remained within 5% in soft tissues up to several centimeters from a Pd-103 source. Compared to Monte Carlo, the ICF methods can easily be integrated into a clinical treatment planning system and it does not require the detailed internal structure of the source or the photon phase-space.

SU-E-T-566: Optimization of Permanent Seed Implant Dosimetry Incorporating Tissue Heterogeneity

Purpose: Seed brachytherapy is currently used for adjuvant radiotherapy of early stage prostate and breast cancer patients. In this technique low dose rate (LDR) radioactive seeds are permanently implanted across the treatment volume to deliver a prescribed amount of dose. The current standard for calculation of dose surrounding the brachytherapy seeds is based on American Association of Physicist in Medicine Task Group No. 43 (TG43 formalism) which generates the dose in homogeneous water medium. For low energy sources and especially in breast, the absorbed dose is highly influenced by heterogeneities. Our work focuses on the development of a dose calculation algorithm similar to TG43 applicable in heterogeneous media. Methods: An Inhomogeneity Correction Factor (ICF) is introduced as the ratio of absorbed dose in tissue to that in water medium. ICF is a function of tissue properties and independent of source structure. The absorbed dose in tissue can then be calculated by multiplying the dose as calculated by the TG43 formalism times ICF. We used Monte Carlo simulations in a heterogeneous model of breast to benchmark the improvements achieved in the calculation of dose using the ICF methodology. Results: The dose distributions obtained through applying ICF to TG43 protocol agreed very well with those of Monte Carlo simulations. Over all and across the whole calculation domain, the mean relative error was reduced from 40.8% to 12.7% when ICF correction factor is applied to the TG43 protocol. Conclusion: We have developed a new analytical dose calculation method which enables personalized dose calculations in heterogeneous media. The methodology offers several advantages including the use of standard TG43 formalism, fast calculation time and extraction of the ICF parameters directly from Hounsfield Units. Funding: NSERC

SU-E-T-525: Developing a GYN Cs-Selectron Brachytherapy Treatment Planning Software Accounting for Inter-Source, Applicator and Heterogeneity Effects

Purpose: In this project new treatment software based on TG‐43U1 and Monte Carlo (MC) simulations for treatment of GYN cancers were developed. This treatment software accounted for inter‐source effect, applicator attenuation, and tissue heterogeneity for Cs‐137 selectron machine. Methods: MC Linear TG‐43U1 functions for combination of 8 active‐inactive pellets with 2 cm physical length for filling tandem and ovoid were obtained. Total length of tandem and ovoid filled with three and one linear sources, respectively. With this approach inter‐source effect and applicator attenuations have been hidden in TG‐43U1 functions. To account heterogeneity effect in software design, the library of dose inhomogeneity correction factor (DICF) for various different thickness and position respect to one active Cs pellet for air and aluminum (as a bone) were simulated. A non‐homogen GYN polyethylene phantom were designed, which contain a cylinder of air as a rectum, and two symmetric aluminum spheres as a femur bone heads. GYN reference dosimetry points for TLD detectors were machined in the phantom according ICRU‐38 report. Finally reference points dose rate were compared using new software, STPS software, TLD measurements and full MC simulations. Results: New software data have good agreement with TLD and MC simulations (up to 5%). However STPS data for more reference points are less than TLD and MC simulation (up to 3%) due to not considered applicators and inter‐source attenuation. For tip of tandem and ovoid STPS data are more than TLD, and MC about 26% and 17%, respectively. More over DICF data can create data with accuracy of 2% in comparison to TLD and MC measurements. Conclusion: In this project for first time developed a 3D GYN‐Cs‐Selectron treatment planning software (TPS) based on Linear TG‐43U1 functions and libraries of MC simulations which modified inter‐source effect, applicator attenuations, and heterogeneity effects.

SU-E-T-551: A Novel Analytical Model to Determine Inhomogeneity Correction Factor in TG-43U1 Low Dose Rate Brachytherapy

Purpose: The American Association of Physicists in Medicine (AAPM) Task Group 43 (TG‐43) recommended dosimetric parameters of sources, in homogenous water phantom. However brachytherapy implant volumes are shown large error due to inhomogeneous mediums respect to homogenous water. The goal of this project is to determine a novel fast analytical method to evaluate the impact of the dose Inhomogeneity Correction Factor (DICF). This new method was validated for low (125I) and high (137Cs) energy brachytherapy sources. Methods: The novel analytical DICF is defined as the ratio of dose delivered into heterogeneous media in water to the dose delivered in homogenous water. The DICF is calculated as a function of the media linear attenuation coefficient, mass energy absorption coefficient, water equivalent path length of heterogenic layer, buildup factor coefficients, and media electron density. The actual dose is equal to multiply the TG‐43U1 dose by the DICF of the heterogenic layer in any phantom voxel. This approach was validated using TLD measurement and full Monte Carlo (FMC) simulation techniques. FMC simulations were used for several different air and aluminum heterogenic thickness. The dose data were compared for TG‐43U1 using DICF model and the values, which are directly, obtained using FMC for same Implants. The advantage of this model to FMCS for daily clinical application is the speed of the calculations and ease of the implementations in treatment planning system. Results: For different configurations, the analytical DICF formalism model agrees with FMC simulations up to 4.4% and 3.5% for 125I and 137Cs sources, respectively. The maximum differences of the DICF model in comparison to TLD measurement were 5% for 137CS. Conclusion: This new model can provide inputs for brachytherapy planning software to consider the ICF effect in dose calculations based on TG‐43U1 algorithm and CT images.

Evaluation of inhomogeneity correction factors for 6 MV flattening filter‐free beams with brass compensators

The 6 MV flattening filter‐free (FFF) beam has been commissioned for use with compensators at our institution. This novel combination promises advantages in mitigating tumor motion due to the reduced treatment time made possible by the greatly increased dose rate of the FFF beam. Given the different energy spectrum of the FFF beam and the beam hardening effect of the compensator, the accuracy of the treatment planning system (TPS) model in the presence of low‐density heterogeneities cannot be assumed. Therefore, inhomogeneity correction factors (ICF) for an FFF beam attenuated by brass slabs were measured and compared to the TPS calculations in this work. The ICF is the ratio of the point dose in the presence of inhomogeneity to the dose in the same point in a homogeneous medium. The ICFs were measured with an ion chamber at a number of points in a flat water‐equivalent slab phantom containing a 7.5 cm deep heterogeneity (air or 0.27 g/cm3 wood). Comparisons for the FFF beam were carried out for the field sizes from 5×5 to 20×20 cm2 with the brass slabs ranging from 0 to 5 cm in thickness. For a low‐density wood heterogeneity in a slab phantom, with the exception of the point 1 cm beyond the proximal buildup interface, the TPS handles the inhomogeneity correction with the brass‐filtered 6 MV FFF beam at the requisite 2% error level. The combinations of field sizes and compensator thicknesses when the error exceeds 2% (2.6% maximum) are not likely to be experienced in clinical practice. In terms of heterogeneity corrections, the beam model is adequate for clinical use.PACS number: 87.56.ng

Monte Carlo-based correction factors for ion chamber dosimetry in heterogeneous phantoms for megavoltage photon beams

The purpose of this study was to investigate the perturbation correction factors and inhomogeneity correction factors (ICFs) for a thin-walled cylindrical ion chamber in a heterogeneous phantom including solid water, lung and bone plastic materials. The perturbation factors due to the replacement of the air cavity, non-water equivalence of the wall and the stem, non-air equivalence of the central electrode and the overall perturbation factor, PQ, for a cylindrical chamber, in the heterogeneous phantom were calculated with the EGSnrc/Cavity Monte Carlo code for 6 and 15 MV photon beams. The PTW31010 (0.125 cm3) chamber was modeled with Monte Carlo simulations, and was used for measurements and calculations of percentage depth ionization (PDI) or percentage depth dose (PDD). ICFs were calculated from the ratio of the product of the stopping power ratios (SPRs) and PQ of lung or bone to solid water. Finally, the measured PDIs were converted to PDDs by using ICFs and were compared with those calculated by the Monte Carlo method. The perturbation effect for the ion chamber in lung material is insignificant at 5 × 5 and 10 × 10 cm2 fields, but the effect needs to be considered under conditions of lateral electron disequilibrium with a 3 × 3 cm2 field. ICFs in lung varied up to 2% and 4% depending on the field size for 6 and 15 MV, respectively. For bone material, the perturbation effects due to the chamber wall and the stem were more significant at up to 3.5% and 1.6% for 6 MV, respectively. ICFs for bone material were approximately 0.945 and 0.940 for 6 and 15 MV, respectively. The converted PDDs by using ICFs were in good agreement with Monte Carlo calculated PDDs. The chamber perturbation correction and SPRs should strictly be considered for ion chamber dosimetry in heterogeneous media. This is more important for small field dosimetry in lung and bone materials.