Mathematical Formulation of DMH-Based Inverse Optimization

Purpose: To introduce the concept of dose-mass based inverse optimization for radiotherapy applications.Materials and Methods: Mathematical derivation of the dose-mass based formalism is presented. This mathematical representation is compared to the most commonly used dose-volume based formulation used in inverse optimization. A simple example on digitally created phantom is presented. The phantom consists of three regions: a target surrounded by high and low density regions. The target is irradiated with two beams through those regions and inverse optimization with dose-volume and dose-mass based objective functions is performed. The basic properties of the two optimization types are demonstrated on the phantom.Results: It is demonstrated that dose-volume optimization is a special case of dose-mass optimization. In a homogenous media dose-mass optimization turns into dose-volume optimization. The dose calculations performed on the digital phantom show that in this very simple case dose-mass optimization tends to penalize more the dose delivery through the high density region and therefore it results in delivering more dose through the low density region.Conclusions: It was demonstrated that dose-mass based optimization is mathematically more general than dose-volume based optimization. In the case of constant density media dose-mass optimization transforms into dose-volume optimization

Abscopal effect observed in visceral and osseous metastases after liver SBRT in combination with nivolumab and relatlimab for sinonasal mucosal melanoma—a case report

BackgroundPrimary sinonasal mucosal melanoma (SNMM) is a rare, aggressive histology usually diagnosed at advanced stages and associated with poor prognosis. Evidence regarding etiology, diagnosis, and treatment mainly derives from case reports, retrospective series, and national databases. In the treatment of metastatic melanoma, anti-CTLA-4 and anti-PD-1 checkpoint blockade increased 5-year overall survival from ~10% (prior to 2011) to ~50% (between 2011 and 2016). In March of 2022, the FDA approved the use of relatlimab, a novel anti-LAG3 immune checkpoint inhibitor, for the treatment of melanoma.Case presentationA 67-year-old woman with locally advanced SNMM underwent debulking surgery, adjuvant RT, and first-line immunotherapy (ImT) with nivolumab but developed local progression. The patient started a second course of ImT with nivolumab and ipilimumab, but this was discontinued after two cycles due to an immune-related adverse event (irAE, hepatitis with elevated liver enzymes). Interval imaging identified visceral and osseous metastases including multiple lesions in the liver and in the lumbar spine. She went on to receive a third course of ImT with nivolumab and the novel agent relatlimab with concurrent stereotactic body radiation therapy (SBRT) to the largest liver tumor only, delivered in five 10-Gy fractions using MRI guidance. A PET/CT performed 3 months after SBRT demonstrated complete metabolic response (CMR) of all disease sites including non-irradiated liver lesions and spinal metastatic sites. After two cycles of the third course of ImT, the patient developed severe immune-related keratoconjunctivitis and ImT was discontinued.ConclusionThis case report describes the first complete abscopal response (AR) in an SNMM histology and the first report of AR following liver SBRT with the use of relatlimab/nivolumab combination ImT for metastatic melanoma in the setting of both visceral and osseous lesions. This report suggests that the combination of SBRT with ImT potentiates the adaptive immune response and is a viable path for immune-mediated tumor rejection. The mechanisms behind this response are hypothesis-generating and remain an area of active research with exceedingly promising potential

Mathematical Formulation of Energy Minimization – Based Inverse Optimization

Purpose: To introduce the concept of energy minimization-based inverse optimization for external beam radiotherapy. Materials and Methods: Mathematical formulation of energy minimization-based inverse optimization is presented. This mathematical representation is compared to the most commonly used dose–volume based formulation used in inverse optimization. A simple example on digitally created phantom is demonstrated. The phantom consists of three sections: a target surrounded by high and low density regions. The target is irradiated with two beams passing through those regions. Inverse optimization with dose–volume and energy minimization-based objective functions is performed. The dosimetric properties of the two optimization results are evaluated. Results: Dose–volume histograms for all the volumes of interest used for dose optimization are compared. Energy-based optimization results in higher maximum dose to the volumes that are used as dose-limiting structures. However, the average and the integral doses delivered for the volumes outside of the target are larger with dose–volume optimization. Conclusion: Mathematical formulation of energy minimization-based inverse optimization is derived. The optimization applied on the digital phantom shows that energy minimization-based approach tends to deliver somewhat higher maximum doses compared to standard of care, realized with dose–volume based optimization. At the same time, however, the energy minimization-based optimization reduces much more significantly the average and the integral doses

Integral Dose-Based Inverse Optimization May Reduce Side Effects in Radiotherapy of Prostate Carcinoma

PURPOSE: The purpose of this work is to apply a novel inverse optimization approach, based on utilization of quantitative imaging information in the optimization function, to prostate carcinoma. MATERIALS AND METHODS: This new inverse optimization algorithm relies upon quantitative information derived from computed tomography (CT) imaging studies. The Hounsfield numbers of the CT voxels are converted to physical density, which in turn is used to calculate voxel mass and the corresponding integral dose, by summation over the product of dose and mass in each dose voxel. This integral dose is used for plan optimization through its global minimization. The optimization results are compared to the optimization results derived from most commonly used dose–volume-based inverse optimization, where objective functions are formed as summation over all dose voxels of the squared differences between voxel doses and user specified doses. The data from 25 prostate plans were optimized with dose–volume histogram (DVH) and integral dose (energy) minimization objective functions. The results obtained with the energy- and DVH-based optimization schemes were studied through commonly used dosimetric indices (DIs). Statistical equivalence tests were further performed to establish population-based significance results. RESULTS: Both DVH- and energy-based plans for each case were normalized so that 95% of the planning target volume receives the prescription dose. The average differences for the rectum and bladder DIs ranged from 1.6 to 25%, where the energy-based quantities were lower. For both femoral heads, the energy-based optimization-derived doses were lower on average by 32%. The statistical tests demonstrated that the significant differences in the tallied dose indices range from 2.7% to more than 50% for rectum, bladder, and femoral heads. CONCLUSION: For majority of the clinically relevant dosimetric quantities, energy-based inverse optimization performs better than the standard of care DVH-based optimization in prostate carcinoma. The population averaged statistically significant differences range from ~3 to ~50%. Therefore, this newly proposed optimization approach, incorporating explicitly quantitative imaging information in the inverse optimization function, holds potential for further reduction of complication rates in prostate cancer

Integral dose based inverse optimization objective function promises lower toxicity in head-and-neck

The voxels in a CT data sets contain density information. Besides its use in dose calculation density has no other application in modern radiotherapy treatment planning. This work introduces the use of density information by integral dose minimization in radiotherapy treatment planning for head-and-neck squamous cell carcinoma (HNSCC). Eighteen HNSCC cases were studied. For each case two intensity modulated radiotherapy (IMRT) plans were created: one based on dose-volume (DV) optimization, and one based on integral dose minimization (Energy hereafter) inverse optimization. The target objective functions in both optimization schemes were specified in terms of minimum, maximum, and uniform doses, while the organs at risk (OAR) objectives were specified in terms of DV- and Energy-objectives respectively. Commonly used dosimetric measures were applied to assess the performance of Energy-based optimization. In addition, generalized equivalent uniform doses (gEUDs) were evaluated. Statistical analyses were performed to estimate the performance of this novel inverse optimization paradigm. Energy-based inverse optimization resulted in lower OAR doses for equivalent target doses and isodose coverage. The statistical tests showed dose reduction to the OARs with Energy-based optimization ranging from ∼2% to ∼15%. Integral dose minimization based inverse optimization for HNSCC promises lower doses to nearby OARs. For comparable therapeutic effect the incorporation of density information into the optimization cost function allows reduction in the normal tissue doses and possibly in the risk and the severity of treatment related toxicities

The effect of gantry spacing resolution on plan quality in a single modulated arc optimization

Volumetric‐modulated arc technique (VMAT) is an efficient form of IMRT delivery. It is advantageous over conventional IMRT in terms of treatment delivery time. This study investigates the relation between the number of segments and plan quality in VMAT optimization for a single modulated arc. Five prostate, five lung, and five head‐and‐neck (HN) patient plans were studied retrospectively. For each case, four VMAT plans were generated. The plans differed only in the number of control points used in the optimization process. The control points were spaced 2°, 3°, 4°, and 6° apart, respectively. All of the optimization parameters were the same among the four schemes. The 2° spacing plan was used as a reference to which the other three plans were compared. The plan quality was assessed by comparison of dose indices (DIs) and generalized equivalent uniform doses (gEUDs) for targets and critical structures. All optimization schemes generated clinically acceptable plans. The differences between the majority of reference and compared DIs and gEUDs were within 3%. DIs and gEUDs which differed in excess of 3% corresponded to dose levels well below the organ tolerances. The DI and the gEUD differences increased with an increase in plan complexity from prostates to HNs. Optimization with gantry spacing resolution of 4° seems to be a very balanced alternative between plan quality and plan complexity. PACS number: 87.55.d

Carbon fiber couch effects on skin dose for volumetric modulated arcs

The purpose of this study is to evaluate the dosimetric effect of carbon fiber couches (CFCs) on delivered skin dose as well as to explore potential venues for its minimization for volumetric modulated arc (VMAT) treatments. A carbon fiber couch (BrainLab) was incorporated in Pinnacle treatment planning system (TPS) by autocontouring. A retrospective investigation on five lung and five prostate patient plans was performed. Targets and organs at risk (OARs), together with a 0.3 cm thick skin contour interfacing the CFC, were outlined in each plan. For each patient, two VMAT plans were generated: a single arc with 6 MV photon energy and two or three arcs with 18 MV photon energy for the posterior arc(s) and 6 MV energy for the anterior arc (mixed energy plans). Both plans for each patient case were normalized such that 95% of the PTV was covered by the same prescription dose, ranging from 7600 to 7800 cGy. For each patient, the prescription doses were escalated to the maximum allowed by the OAR constraints. CFC bolus effects on skin doses were tallied by the highest dose to 1% of skin volume. With the utilization of higher energy photons for the posterior arcs, the statistically significant differences in skin dose between the two plans were as high as 34% of the prescribed dose, where surface doses changed on average from 3800 to 2940 cGy for 6 MV and mixed energy plans, respectively. In addition, skin doses in excess of 68% and 80% of the prescription doses for mixed and 6 MV energy plans, respectively, were observed in individual cases. The presented findings indicate that mixed energy VMAT plans would result in a substantial skin sparing of more than approximately 34% compared to VMAT plans with only 6 MV arc(s). Additionally, the high skin doses in some cases (81% of the prescription dose) suggest that in hypofractionated SRS/SRT treatments, the carbon fiber couch effects on skin doses need to be evaluated when arc delivery is considered as a treatment option

Quantification of the skin sparing effect achievable with high-energy photon beams when carbon fiber tables are used

To quantify the skin doses resulting from the use of carbon fiber couches (CFCs) for patient support. BrainLab’s CFC was evaluated for five prostate patients and five lung patients. For each patient PTV, organs at risk (OARs), and a 0.3 cm thick skin contour on the patient’s posterior surface were outlined. Two sets of IMRT plans, each consisting of 4, 5, 7, and 9 beams, were generated per patient. The sets were identical with the exception that in the first set only 6 MV energy was used, while in the second set (mixed energy) the photon energy of the beams traversing the CFC was 18 MV. The plans for each patient were normalized to deliver the same dose to 95% of the PTV. The CFC skin dose was evaluated by the maximum dose received by 1% ( D 1%) of the skin volume. Paired one-tailed t-tests were used to establish the statistical significance. The mixed energy plans resulted in D 1% increase from 18% to more than 23% as the number of beams in the plan was decreased from 9 to 4. Skin doses as high as ∼70% of the prescription dose were found even in 9-beam mixed energy plans. Therefore mixed energy plans may be more beneficial for patients treated with higher fractional doses