Volume Constraints Research Articles

Yttrium-90 Hepatic Therapy and the Importance of Volumetric Voxel-Based Post Therapy Dosimetry: A Case Report on Renal Radiation Dose Volume Analysis with Follow Up

This paper is a follow-up report concerning a patient treated with Yttrium-90 to a hepatocellular carcinoma. The radiation therapy dose distribution was published as a case report in 2022, https://doi.org/10.18103/mra.v10i11.3379. The hepatic target volume for directed therapy abutted the right kidney and this report provides clinical follow up information on the patient relative to renal function on unintentional radiation renal dose. Yttrium-90 therapy has become an important therapy component for patient care directed to multiple malignancies with emphasis on treating lesions in close proximity to the hepatic parenchyma. The targets are treated with an intra-arterial approach with a goal of applying target directed radiation therapy. Historically, prior to the development of voxel-based dose volume computation software, dose to target was prescribed as activity of isotope delivered with a qualitative assessment of isotope delivery based on images obtained from single positron emission computer tomography. As a qualitative image, single positron emission computer tomography served as an image reference and qualitative surrogate for representing radiation dose. Today, commercial software is available to fuse single positron emission computer tomography images into radiation oncology planning images and calculate dose to volume in a manner similar to how radiation oncology physics dosimetry teams calculate radiation dose to target volume for external therapy and brachytherapy with image guidance. In this particular case, we demonstrated that the proximity of the right kidney to the target resulted in unintentional radiation dose to renal parenchyma evaluated using voxel-based dosimetry. In this report, we review progressive decrease in renal function with blood urea nitrogen/creatinine of 45 and 2.75 respectively with continued normal liver function. Although potentially multi-factorial in origin, the decrease in renal function is at a time point consistent with radiation injury. In this paper we review radiation oncology dose volume constraints for renal tolerance and strategies for patient care moving forward. The goal is to provide additional knowledge of this issue and provide an additional knowledge layer for patient safety with emphasis on improving patient outcomes.

Optically Transparent Antenna for Smart Glasses

The optically transparent antenna technology has been gaining attention in consumer electronic industry owing to its potential to release the antenna volume constraints in compact mobile devices. Earlier studies have been heavily focused on the transparent antenna integration to the display for smartphone applications, for example, to improve its spatial coverage of 5G mm-wave at the forehead side. To our knowledge, the application of the transparent antenna technology to smart glasses and augmented reality glasses, especially considering the constraints from the coexistence with optical features in the lens stack-up, has remained unexplored. Thus, for the first time, we suggest a feasible existence solution between antennas and the RF lossy layers in the lens stack-up, to reduce the negative impacts on antenna performances. A slot loop antenna formed by metal-mesh based transparent antenna film and metallic glass frame has been investigated. Experimental results of such an antenna on human head phantom shows a total efficiency better than −4.5 dB in 2.4 GHz band. Even though it is demonstrated through a 2.4 GHz antenna example, the same principle can be applied to any other sub-6 GHz antenna applications, i.e., LTE, WiFi, GNSS, etc.

Topology optimization for elasto-plastic problems based on exact volume constraint method

Topology optimization for elasto-plastic problems based on exact volume constraint method

An isoperimetric inequality for the first Steklov–Dirichlet Laplacian eigenvalue of convex sets with a spherical hole

In this paper we prove the existence of a maximum for the first Steklov-Dirichlet eigenvalue in the class of convex sets with a fixed spherical hole under volume constraint. More precisely, if $\Omega=\Omega_0 \setminus \bar{B}_{R_1}$, where $B_{R_1}$ is the ball centered at the origin with radius $R_1>0$ and $\Omega_0\subset\mathbb{R}^n$, $n\geq 2$, is an open bounded and convex set such that $B_{R_1}\Subset \Omega_0$, then the first Steklov-Dirichlet eigenvalue $\sigma_1(\Omega)$ has a maximum when $R_1$ and the measure of $\Omega$ are fixed. Moreover, if $\Omega_0$ is contained in a suitable ball, we prove that the spherical shell is the maximum.

Variable-density topology optimization and bending test of quasi-honeycomb sandwich structures

The topology optimization is considered to enhance the strength, stiffness, and specific energy absorption of a quasi-honeycomb sandwich structure since it can achieve the optimal distribution of materials. However, the existing material interpolation models do not make the topology structure have good clarity and stability. In the present study, a novel variable-density topology optimization based on an improved interpolation model is developed for the design of a quasi-honeycomb core. The combined cells are circularly spreading outward from the geometric center of the design domain, and the wall thickness function of the equivalent cell (i.e. a simplified model of the combined cell) is established on the basis of relative density. The SR material interpolation model is modified by adding the minimum elastic modulus term, fitting the weighting and penalty factors, and adopting the volume constraint of Bi-directional Evolutionary Structural Optimization (BESO). The optimization is conducted to minimize the compliance of the quasi-honeycomb core, in which the relative densities of equivalent cells are chosen as the design variables due to the mapping between topology elements and equivalent cells. The three-dimensional (3D) geometric models of original and optimized quasi-honeycomb cores, upper face sheets, and lower face sheets are built using SolidWorks and printed on a 3D printer. The deflection, strain, bending stiffness, and energy absorption under different material retention rates, restraint positions, and face sheet thicknesses are investigated by three-point bending tests. It is found that the improved SR material interpolation model is efficient for suppressing the grid dependence and checkerboard, and the mechanical properties of optimized quasi-honeycomb sandwich structures are significantly enhanced in comparison with original structures, confirming that the developed method provides important guidance for designing and optimizing the quasi-honeycomb sandwich structure.

Topology optimization for structures with bi-modulus material properties considering displacement constraints

In this paper, an efficient topology optimization method is developed for bi-modulus structures considering displacement constraints. In order to overcome the numerical difficulty caused by the non-smoothness bi-modulus material properties, a new smooth elastic modulus matrix concerned with the principal strain states is firstly constructed to approximate the discontinuous modulus matrix for bi-modulus materials. Based on the smooth approximation, topology optimization model for structures under both single and multiple load cases is built to minimize structural compliance with volume and displacement constraints. Considering the nonlinear equilibrium equations, the sensitivities of the objective function and constraints are explicitly achieved based on the adjoint method, and then the gradient-based method of moving asymptotes algorithm is employed to update the topological design variables. A cooperation platform is constructed for the proposed bi-modulus topology optimization, which provides an effective tool for the design optimizations. The proposed method is proved to have good efficiency and applicability to deal with problems with multiple load cases and multiple constraints by several typical numerical examples.

Two-scale concurrent optimization of composites with elliptical inclusions under microstress constraints within the FE2 framework

In order to avoid the adverse effects of structural damage caused by stress concentration, the optimization problem considering stress constraints is very important in structural design. This paper aims at introducing microstress constraints within a multilevel finite element (FE2) analysis framework to perform the two-scale concurrent optimization and reduce the stress concentration while exhibiting better overall stiffness properties for composites with elliptical inclusions. In order to do that, at the macroscale, relying on the solid isotropic material with penalization (SIMP), a density-based optimization algorithm is raised for a maximum stiffness design and free material distribution optimization under a volume constraint, these displacement solutions and material distributions at the macroscopic structural scale provide kinematic constraints for microscale optimization. At the microscale, the parameterized composite microstructure (inclusion orientation and aspect ratio) is optimized under the principal strain direction constraints of the macroscale element’s Gauss integration point. The optimized microstructure in turn updates the macroscopic effective stress directly from the volume average of the microscopic stress field. The clustering strategy is used in order to improve the computation efficiency of the optimization. The novelty of the work lies in the use of microstress constraints to solve the concurrent optimization problems of two-phase composites within the FE2 framework. The effectiveness of the proposed concurrent optimization approach is validated through three numerical examples.

Level set-based topological design of multiphase micro-architectured materials using alternating active-phase method

Micro-architectured materials with periodically configured microstructures are widely used in various engineering fields due to their superior mechanical properties. Compared with conventional topology design with one single material, topological design with multiple materials can provide a better solution as the expanded design freedom. This paper presents a level set-based multi-material topological design method for micro-architectured materials involving three phases or more. In this method, a difference-set-based multi-material level set model is employed to represent the topology of each phase, in which N + 1 phases can be precisely represented by the sequential difference-set of N level set functions without any overlaps and redundant regions. By using an alternating active-phase algorithm, the multi-material topology design problem with N + 1 phases is splitted into N(N + 1)/2 binary-phase topological design sub-problems, where each sub-problem involves fewer design variables and volume constraints. The effective properties of multiphase micro-architectured materials are evaluated by a numerical homogenization approach, and their topological evolutions of two active phases in each sub-problem can be readily achieved by updating a single level set function, which greatly facilitate the extension to topological design problems with more phases. Both numerical examples and additive-manufactured specimens demonstrate the effectiveness of the proposed method for designing multiphase micro-architectured materials.

Cage structural topology optimization considering thermo-mechanical coupling

The performance of the cage can directly affect the service life of the bearing. This paper presents a cage topology optimization method for improving the heat dissipation and structural stiffness. Firstly, a multi-objective structural topology optimization model is established based on the SIMP method and MMA algorithm, the effects of force and thermal load are considered comprehensively. Secondly, considering the centrifugal force and frictional heat, under the conditions of a given volume constraint, the bearing cage topology optimization model is carried out with heat dissipation weakness and compliance as the optimization objectives. Using iterative calculations based on the MMA algorithm and boundary smoothing processing, the structure with the optimal material layout is obtained. Finally, compared with the initial structures, the maximum temperature reduces about 27% and the maximum stress reduces about 14.8%. The results show that topology optimization can provide a reference for the design of bearing cages, which can improve the structural performance while reducing weight.

Prostate Cancer Treatment-Related Toxicity: Comparison between 3D-Conformal Radiation Therapy (3D-CRT) and Volumetric Modulated Arc Therapy (VMAT) Techniques.

Objective: This paper illustrates the results of a mono-institutional registry trial, aimed to test whether gastrointestinal (GI) and genitourinary (GU) toxicity rates were lower in localized prostate cancer patients treated with image-guided volumetric modulated arc therapy (IG-VMAT) compared to those treated with IG-3D conformal radiation therapy (IG-3DCRT). Materials and Methods: Histologically proven prostate cancer patients with organ-confined disease, treated between October 2008 and September 2014 with moderately hypofractionated radiotherapy, were reviewed. Fiducial markers were placed in the prostate gland by transrectal ultrasound guide. The prescribed total dose was 70 Gy in 28 fractions. The mean and median dose volume constraints for bladder and rectum as well as total volume of treatment were analyzed as potentially prognostic factors influencing toxicity. The Kaplan−Meier method was applied to calculate survival. Results: Overall, 83 consecutive patients were included. Forty-two (50.6%) patients were treated with 3D-CRT and 41 (49.4%) with the VMAT technique. The median follow-up for toxicity was 77.26 months for the whole cohort. The VMAT allowed for a dose reduction to the rectum and bladder for the large majority of the considered parameters; nonetheless, the only parameter correlated with a clinical outcome was a rectal dose limit V66 > 8.5% for late GI toxicity G ≥ 2 (p = 0.045). Rates of G ≥ 2 toxicities were low among the whole cohort of these patients treated with IGRT. The analysis for rectum dose volume histograms (DVHs) showed that a severe (grade ≥ 2) late GI toxicity was related with the rectal dose limit V66 > 8.5% (p = 0.045). Conclusions: This study shows that moderate hypofractionation is feasible and safe in patients with intermediate and high-risk prostate cancer. Daily IGRT may decrease acute and late toxicity to organs at risk and improve clinical benefit and disease control rate, cutting down the risk of PTV geographical missing. The adoption of VMAT allows for promising results in terms of OAR sparing and a reduction in toxicity that, also given the small sample, did not reach statistical significance.

Topology optimization of compliant mechanisms with distributed compliance (hinge-free compliant mechanisms) by using stiffness and adaptive volume constraints instead of stress constraints

Many approaches have been developed for the synthesis of compliant mechanisms via topology optimization. Most of these approaches produce mechanisms with lumped compliance if not extended appropriately, such as with stress constraints. With mechanisms with lumped compliance, the deformation is concentrated in regions of small dimensions (referred to as “de facto hinges” or “one-node connected hinges”) causing notch overstresses. Some extensions to these approaches overcome this by forcing mechanisms with distributed compliance (also referred to as “hinge-free compliant mechanisms”). However, the currently known extensions have a number of drawbacks. Stress constraints, for example, make the optimization formulation highly nonlinear and non-convex. In this paper, a new extension is presented that permits the synthesis of mechanisms with distributed compliance by combining a constraint for the allowed structural stiffness with an adaptive volume constraint. The presented optimization approach can be easily solved using linear optimization. The basis for the extension presented in this paper is the modal synthesis approach, which permits the synthesis of transverse-load-insensitive compliant mechanisms. The methodology developed is tested on suitable design examples.

Construction of a two-phase flow with singular energy by gradient flow methods

We prove the existence of weak solutions to a system of two diffusion equations that are coupled by a pointwise volume constraint. The time evolution is given by gradient dynamics for a free energy functional. Our primary example is a model for the demixing of polymers, the corresponding energy is the one of Flory, Huggins and de Gennes. Due to the non-locality in the equations, the dynamics considered here is qualitatively different from the one found in the formally related Cahn-Hilliard equations.Our angle of attack is from the theory of optimal mass transport, that is, we consider the evolution equations for the two components as two gradient flows in the Wasserstein distance with one joint energy functional that has the volume constraint built in. The main difference to our previous work [6] is the nonlinearity of the energy density in the gradient part, which becomes singular at the interface between pure and mixed phases, and thus requires a more sophisticated analysis.

An alternating direction method of multipliers for optimizing (s, S) policies in a distribution system with joint replenishment volume constraints

In this paper, we study a two-echelon distribution system in which multiple products are jointly replenished at each stocking location and the inventory of each product at each location is controlled by an (s, S) policy. The transportation capacity in volume of products for each joint replenishment is limited, and linear rationing policies are used for both on-hand inventory and transportation capacity allocation in the system in case of shortage. We propose a novel scenario-based model for the optimization of the (s, S) policies in the system that considers the rationing policies. Because of its high complexity when the number of scenarios is large, an Alternating Direction Method of Multipliers is proposed to solve the model. Based on real data, forty instances were generated and tested to evaluate the model and the solution method. Our numerical experiments show that for these instances this method could find a better solution in a much shorter computation time compared with CPLEX 12.9, whereas the latter often runs out of memory for large-size instances on a personal computer. Moreover, the inventory policies found by this scenario-based optimization approach can reduce costs by 5.1% and improve fill rates by 9.7% on average compared with those currently used in Alibaba.

A Robin‐Neumann scheme with quasi‐Newton acceleration for partitioned fluid‐structure interaction

AbstractThe Dirichlet–Neumann scheme is the most common partitioned algorithm for fluid‐structure interaction (FSI) and offers high flexibility concerning the solvers employed for the two subproblems. Nevertheless, it is not without shortcomings: to begin with, the inherent added‐mass effect often destabilizes the numerical solution severely. Moreover, the Dirichlet–Neumann scheme cannot be applied to FSI problems in which an incompressible fluid is fully enclosed by Dirichlet boundaries, as it is incapable of satisfying the volume constraint. In the last decade, interface quasi‐Newton methods have proven to control the added‐mass effect and substantially speed up convergence by adding a Newton‐like update step to the Dirichlet–Neumann coupling. They are, however, without effect on the incompressibility dilemma. As an alternative, the Robin‐Neumann scheme generalizes the fluid's boundary condition to a Robin condition by including the Cauchy stresses. While this modification in fact successfully tackles both drawbacks of the Dirichlet–Neumann approach, the price to be paid is a strong dependency on the Robin weighting parameter, with very limited a priori knowledge about good choices. This work proposes a strategy to merge these two ideas and benefit from their combined strengths. The resulting quasi‐Newton‐accelerated Robin‐Neumann scheme is compared to both Robin‐ and Dirichlet–Neumann variants. The numerical tests demonstrate that it does not only provide faster convergence, but also massively reduces the influence of the Robin parameter, mitigating the main drawback of the Robin‐Neumann algorithm.

Cloud Detection Autonomous System Based on Machine Learning and COTS Components On-Board Small Satellites

One of the main applications of small satellites is Earth observation. CubeSats and different kinds of nanosatellites usually form constellations that obtain images mainly using an optical payload. There is a massive amount of data generated by these satellites and a limited capacity of download due to volume and mass constraints that make it difficult to use high-speed communication systems and high-power systems. For this reason, it is important to develop satellites with the autonomy to process data on board. In this way, the limited communication channel can be used efficiently to download relevant images containing the required information. In this paper, a system for the satellite on-board processing of RGB images is proposed, which automatically detects the cloud coverage level to prioritize the images and effectively uses the download time and the mission operation center. The system implements a Convolutional Neural Network (CNN) on a Commercial off-the-Shelf (COTS) microcontroller that receives the image and returns the cloud level (priority). After training, the system was tested on a dataset of 100 images with an accuracy of 0.9 and it was also evaluated with CubeSat images to evaluate the performance of a different image sensor. This implementation contributes to the development of autonomous satellites with processing on board.

Entropy-Based Transit Tour Synthesis Using Fuzzy Logic

This paper presents an entropy-based transit tour synthesis (TTS) using fuzzy logic (FL) based on entropy maximization (EM). The objective is to obtain the most probable transit (bus) tour flow distribution in the network based on traffic counts. These models consider fixed parameters and constraints. The costs, traffic counts, and demand for buses vary depending on different aspects (e.g., congestion), which are not captured in detail in the models. Then, as the FL can be included in modeling that variability, it allows obtaining solutions where some or all the constraints do not entirely satisfy their expected value, but are close to it, due to the flexibility this method provides to the model. This optimization problem was transformed into a bi-objective problem when the optimization variables were the membership and entropy. The performance of the proposed formulation was assessed in the Sioux Falls Network. We created an indicator (Δ) that measures the distance between the model’s obtained solution and the requested value or target value. It was calculated for both production and volume constraints. The indicator allowed us to observe that the flexible problem (FL Mode) had smaller Δ values than the ones obtained in the No FL models. These results prove that the inclusion of the FL and EM approaches to estimate bus tour flow, applying the synthesis method (traffic counts), improves the quality of the tour estimation.

Integer programming topology optimization for subsonic compressible flows with geometry trimming

The incompressibility hypothesis is successfully applied in a broad range of engineering problems simulated via computational fluid dynamics (CFD) codes. However, depending on the Mach number, the effects of compressibility are no longer negligible. Recently, the first papers about topology optimization considering compressible flows were published. All of them use the continuous design variables method which has some known drawbacks. The present work proposes topology optimization considering the compressible Navier-Stokes equations and discrete variables with a step of geometry trimming. This approach constrains the design variables to a binary set and solves the problem by using sequential integer linear programming, being a feasible alternative to classic density-based methods. Additionally, the solid regions are trimmed out from the physics analysis. A material model is inserted in the governing equations in such a way that, it is possible to calculate the sensitivity and, at the same time, guarantee the adiabatic condition. In this work, it is observed that the minimization of entropy generation as the objective function tends to converge to an undesired trivial solution. Alternatively, this work proposes the maximization of mass flow rate as the objective function to, indirectly, minimize the entropy. Furthermore, it is proposed the use of a new set of inlet boundary conditions. Three optimization cases are solved: the double-pipe, the pipe-bend, and an entropy maximization problem. The optimized solutions for the pipe-bend and double-pipe problems present geometries where the constraints are satisfied with the minimum entropy generation. Using the double-pipe example, it is conducted a study to understand the impacts of TOBS-GT parameters in the solutions. The results evidenced that, in some conditions, the implementation is prone to fall in a local minimum. In the third example, entropy maximization subjected to volume constraint is successfully solved. Moreover, a minimization case is also solved to aid in the interpretation of the results.

Post-radiation primary hypothyroidism in patients with head and neck cancer: External validation of thyroid gland dose–volume constraints with long-term endocrine outcomes

BackgroundPost-radiation primary hypothyroidism is a common late complication in head and neck cancer (HNC) survivors. No radiation dose-volume constraint of the thyroid gland has been externally validated for predicting long-term thyroid function outcomes. Materials and MethodsThis external validation study evaluated the diagnostic properties of 22 radiation dose–volume constraints of the thyroid gland proposed in the literature. Radiation dosimetric data from 488 HNC patients who underwent neck irradiation from January 2013 to December 2015 at two tertiary oncology centers were reviewed. The diagnostic metrics of candidate constraints were computed by inverse probability of censoring weighting and compared using time-dependent receiver operating characteristic (ROC) curves with death designated as a competing event. Multivariable regression analyses were performed using the Fine–Gray sub-distribution hazard model. ResultsOver a median follow-up period of 6.8 years, 205 (42.0 %) patients developed post-radiation primary hypothyroidism. The thyroid volume spared from 60 Gy (VS60) had the largest area under ROC curve of 0.698 at 5 years after radiotherapy. Of all evaluated constraints, VS60 at a cutoff value of 10 cc had the highest F-score of 0.53. The 5-year hypothyroidism risks of patients with thyroid VS60 ≥ 10 cc and < 10 cc were 14.7 % and 38.2 %, respectively (p < 0.001). The adjusted sub-hazard ratio for post-radiation primary hypothyroidism for VS60 < 10 cc was 1.87 (95 % confidence interval, 1.22–2.87; p < 0.001). ConclusionThyroid VS60 is the best radiation dose–volume parameter to predict the long-term risk of primary hypothyroidism in patients with HNC who underwent neck irradiation. VS60 ≥ 10 cc is a robust constraint that limits the 5-year primary hypothyroidism risk to less than 15 % and should be routinely employed during radiotherapy optimization.

Two-scale topology optimization with heterogeneous mesostructures based on a local volume constraint

A new approach to produce optimal porous mesostructures and at the same time optimizing the macro structure subject to a compliance cost functional is presented. It is based on a phase-field formulation of topology optimization and uses a local volume constraint (LVC). The main novelty is that the radius of the LVC may depend both on space and a local stress measure. This allows for creating optimal topologies with heterogeneous mesostructures enforcing any desired spatial grading and accommodating stress concentrations by stress dependent pore size. The resulting optimal control problem is analysed mathematically, numerical results show its versatility in creating optimal macroscopic designs with tailored mesostructures.

Empirical Relative Biological Effectiveness (RBE) for Mandible Osteoradionecrosis (ORN) in Head and Neck Cancer Patients Treated with Pencil-Beam-Scanning Proton Therapy (PBSPT): A Retrospective, Case-Matched Cohort Study

<h3>Purpose/Objective(s)</h3> To retrospectively investigate empirical relative biological effectiveness (RBE) for mandible osteoradionecrosis (ORN) in head and neck (H&N) cancer patients treated with pencil-beam-scanning proton therapy (PBSPT). <h3>Materials/Methods</h3> We included 1,266 H&N cancer patients, of which, 931 patients were treated with volumetric-modulated arc therapy (VMAT) and 335 were treated with PBSPT. Among them, 26 VMAT and 9 PBSPT patients experienced mandible ORN (ORN group), while all others were included in the control group. To minimize the impact of the possible imbalance in clinical factors between VMAT and PBSPT patients in the dosimetric comparison between these two modalities and the resulting RBE quantification, we formed a 1:1 case-matched patient cohort (335 VMAT patients and 335 PBSPT patients including both the ORN and control groups) using the greedy nearest neighbor matching of propensity scores. Mandible dosimetric metrics were extracted from the case-matched patient cohort and statistically tested to evaluate the association with mandibular ORN to derive dose volume constraints (DVCs) for VMAT and PBSPT, respectively. We sought the equivalent constraint doses for VMAT so that the critical volumes of VMAT were equal to those of PBSPT at different physical doses. Empirical RBEs of PBSPT for ORN were obtained by calculating the ratio between the derived equivalent constraint doses and physical doses of PBSPT. Bootstrapping was further used to get the confidence intervals. <h3>Results</h3> Clinical variables of age, gender, tumor stage, prescription dose, chemotherapy, hypertension or diabetes, dental extraction, smoking history, or current smoker were not statistically related to the incidence of ORN in the overall patient cohort. Smoking history was found to be significantly associated with the ORN incidence in PBSPT patients only. V40 Gy[RBE], V50 Gy[RBE], and V60 Gy[RBE] were statistically different (<i>p</i> < 0.05) between the ORN and control group for VMAT and PBSPT. Empirical RBEs of 1.58 (95% CI: 1.34-1.64), 1.34 (95% CI: 1.23-1.40), and 1.24 (95% CI: 1.15-1.26) were obtained for proton dose at 40 Gy[RBE=1.1], 50 Gy[RBE = 1.1] and 60 Gy[RBE = 1.1], respectively (Table). <h3>Conclusion</h3> Our study suggested that RBEs were larger than 1.1 at moderate doses (between 40 and 60 Gy[RBE=1.1]) with high LET for mandible ORN. RBEs are underestimated in current clinical practice in PBSPT. The derived DVCs can be used for PBSPT plan evaluation and optimization to minimize the incidence rate of mandible ORN.