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WE‐C‐BRB‐08: Sensitivity of Dosimetric Margin Distribution and Coverage Estimates to Sampling Parameters

Medical Physics 2009年第6PART24期36卷 2759-2759页

作者： H Xu J Gordon J Siebers Virginia Commonwealth University Richmond VA Virginia Commonwealth University Richmond VA Virginia Commonwealth University Richmond VA

Purpose: The dosimetric margin distribution (DMD) is a planning tool for evaluating target and normal tissue dose coverage probabilities in the presence of geometric uncertainties. This work evaluates sensitivity of coverage estimates derived from the DMD to the angular increment w at which the DMD is sampled, and the distance search increment d. Method and Materials: The study utilized three plans for localized prostate cancer, with prescribed dose of 79.2Gy and 1cm clinical target volume to planning target volume (CTV-to-PTV) margins, planned according to the high dose arm of RTOG0126. Dose was first recalculated with beam fluences convolved with a normal probability density function to simulate the effect of random uncertainties. Dosimetric margins were then calculated between the CTV and the 79.2Gy isodose surface at elevations f from −90° to +90°, and azimuthal angles q from −180° to +180°. In each direction (f,q) the CTV was moved relative to the dose distribution in steps of d until its minimum dose fell below 79.2Gy. Estimated coverage Qest was calculated from the DMD assuming systematic uncertainties (rigid body translations) were normally distributed with standard deviation S along each axis. Minimum and maximum deviations DQest were obtained over a range of S values for w = 5°, 10°, 20° relative to w = 2°, and for d = 0.2, 0.5, 1mm relative to d = 0.1mm. Results: Coverage uncertainty due to finite angular sampling interval w is approximately 0.5% at w = 10° and 1.5% at w = 20°. Uncertainty due to finite step size d is negligible for d £ 0.2 mm, and is approximately 0.6% for d = 1mm. Conclusion: Coverage estimates accurate to ±0.5% will be obtained if the DMD is sampled with w = 10° and d = 0.2 mm. Coverage estimates accurate to this level are desirable for target and normal tissue coverage evaluation in current treatment plans, and to support future treatment planning based on probabilistic coverage criteria.(Supported by NIH P01CA116602).

关键词： Cancer Error analysis Medical treatment planning probability density functions

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SU-FF-T-620: Assessment of Dose Reconstruction Methods for Prostate Image Guided Radiotherapy Protocols

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Medical Physics 2009年第6PART18期36卷 2667-2667页

作者： Q Wu J Adamson William Beaumont Hospital Royal Oak MI Duke University Medical Center Durham NC Wayne State University Detroit MI

Purpose: Many dosimetric evaluations of prostate intrafraction motion disregard effects of treatment duration and translations of the surrounding body per fraction. However the probability of motion has been shown to increase with time and image guidance strategies transfer interfractional uncertainties from the prostate to the surrounding body. We evaluate the dosimetric effect of these two factors for an online image guidance protocol. Method and Materials: Using intrafractional measurements from 22 IGRT patients, we calculated a probability density function (PDF) for each beam and for all beams combined excluding residual setup error. The effect of treatment duration was evaluated by computing cumulative dose using 2 convolution methods: population PDF and beam specific PDF. The calculations were performed on both a 30 cm diameter phantom and a patient. We evaluated the dose discrepancy introduced when PDFs were created using various motion magnitudes. The effect of relative motion from surrounding body was evaluated on the PTV dose discrepancy when the surrounding body was translated anterior and posterior by 0-2cm, and after 20 fractions with the surrounding body displaced randomly about the mean using a multivariate normal distribution with various σ. Results: Differences in D 99 between dose convolved with a beam specific PDF vs. a single PDF were ∼0.3% of mean PTV dose. The discrepancy was ∼5 times smaller than the dose discrepancy between static and convolved dose. Translation of the surrounding body increased dose to target, however the effect was small for clinically relevant translations (∼0.3% change in D 99 for ±5mm AP translation). Random translations of surrounding body over multiple fractions caused differences in D 99 of ∼0.3%, but with no apparent trend. Conclusions: Time dependency and surrounding body motion have modest dosimetric effects (0.3%) to the target, and should be accounted for when high accuracy is desired for dosimetric evaluation of

关键词： Dosimetry Medical imaging probability density functions Radiation therapy Medical image reconstruction Image reconstruction Image guided radiation therapy

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Approximation by finite mixtures of continuous density functions that vanish at infinity

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COGENT MATHEMATICS & STATISTICS 2020年 7卷

作者： T Tin Nguyen Nguyen, Hien D. Chamroukhi, Faicel McLachlan, Geoffrey J. Normandie Univ Dept Math & Comp Sci UMR CNRS LMNO UNICAEN Caen France La Trobe Univ Dept Math & Stat Melbourne Vic Australia Univ Queensland Sch Math & Phys Brisbane Qld Australia

Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is often left unclear. We prove that finite mixture models constructed from pdfs in C-0 can be used to conduct approximation of various classes of approximands in a number of different modes. That is, we prove approximands in C-0 can be uniformly approximated, approximands in C-b can be uniformly approximated on compact sets, and approximands in L-p can be approximated with respect to the L-p, for p epsilon [1,infinity). Furthermore, we also prove that measurable functions can be approximated, almost everywhere.

关键词： Approximation theory probability density functions finite mixture models Riemann summation uniform approximation

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MO-D-ValB-07: Comparison of Inline and Orthogonal Imaging and Treatment Beam Geometries for Monitoring the Motion of Implanted Markers

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Medical Physics 2006年第6PART14期33卷 2162-2162页

作者： Y Suh S Dieterich P Keall Virginia Commonwealth University Richmond VA Georgetown University Hospital Washington DC

Purpose: The purpose of this study is to investigate the accuracy of different 2D methods monitoring implanted markers, compared to 3D method for real-time tumor tracking radiotherapy. The different imaging-treatment beam geometries were the imaging beam parallel to treatment beam (inline) and orthogonal to treatment beam. Method and Materials: The 3D motion datasets of ten patients from Cyberknife treatments were used. For given beam angles, the positions of implanted markers were calculated and its geometric uncertainty was quantified for two 2D monitoring methods. Since neither can monitor the motion of markers in the imaging beam axis, the geometric errors were determined in that direction with respect to the treatment beam. Assuming that 3D pre-treatment online positioning was performed and thus errors are predominantly random, treatment margins due to the limitations of 2D methods were quantified. For the orthogonal monitoring, margin, M=1.65σ, was used with the assumption of zero systematic errors; while for the inline, the required margin can be calculated by integrating the probability density function of the geometric uncertainty with the dose falloff along the beam direction. Results: In terms of couch motion, the positioning uncertainty is lowest for coplanar treatments, consistent with predominantly superior-inferior motion. Regarding gantry angles, it is lowest for lateral beams, consistent with the smallest left-right motion. The average positioning uncertainty along the imaging beam axis is 0.05–0.16cm (1 SD) with maximum values for individual patients ranging 0.09–0.33cm, which result in 0.08–0.26cm margins for orthogonal monitoring. Conclusion: The impact of the geometric relationship between the imaging and treatment beam has been studied by quantifying the error from out of plane motion for inline and orthogonal imaging-treatment geometries. The errors for inline geometry result in negligible additional margin required. In the absence of other er

关键词： Medical imaging Cancer Dosimetry Radiation therapy probability density functions Therapeutics

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SU-E-J-158: A Phantom Study Based Simulation to Quantify the Motion and Tumor Volume Affected 18F-FDG PET Uptake Distribution Within the Tumor

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Medical Physics 2013年第6PART9期40卷 187-187页

作者： K Wijesooriya C Griffin T Pan P Read S Benedict J Larner University of Virginia Health Systems Charlottesville VA UT MD Anderson Cancer Center Houston TX

Purpose: Molecular imaging studies reveal tumor heterogeneity which may explain therapeutic resistance. Alternatively, variations observed in the SUV uptake may not be due to intrinsic heterogeneity of the tumor, but due to effects of position resolution (volume dependence) or tumor motion . The objective of this study is to evaluate motion artifacts on PET SUV uptake within tumors for different volumes. Methods: We conducted a phantom study: spheres of homogeneous18F-FDG activity of motion amplitudes (0, 5, 10, 15, 20, 25, 30 mm) and volumes (internal diameter 10, 13, 17, 22, 28, 37 mm). Any variation observed in SUV uptake distribution with homogeneous activity spheres must be due to motion and volume effects. Therefore, we used this data to quantify uptake variations as a function of motion and volume. PET SUV uptake values for each tumor were fit with a Woods-Saxon model with 2 parameters: radius and skin depth. When the ratio of radius to skin depth becomes small, this simplifies to a Gaussian. By using this parameterization for stationary phantoms, using the probability density function for motion, and using an image convolution technique we were able to simulate the SUV uptake distribution of moving tumor in the central 2D plane. Taking voxel by voxel SUV uptake distribution in 2D we quantified the accuracy of our simulation for motion affected, tumor volume affected SUV uptake heterogeneity within the phantom. Results: Phantom study for stationary spheres show motion has a high impact on SUV uptake distributions. Maximum percentage uptake variation across the phantoms was 22%. Convolution results confirm that motion is the largest contributor to the SUV heterogeneity of the tumors. Average difference between convolution and measurement is 6.7%. Conclusion: These results will impact the studies that utilize tumor heterogeneity such as tumor detection, planning with dose painting, and treatment response. UVA Radiation Oncology george Amarino Grant - 2012

关键词： Cancer Medical imaging Alternating current power transmission probability density functions Dosimetry Radiation treatment Biomedical modeling Therapeutics

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SU-GG-T-69: A Windowing Technique for Assigning GEUD Optimization Objectives as Target Constraints in IMRT Inverse Treatment Planning

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Medical Physics 2008年第6PART10期35卷 2742-2742页

作者： G Cranmer-Sargison Saskatoon Cancer Centre Saskatoon SK CA

Purpose: The purpose of this work was to: (1) investigate the response of gEUD to varying levels of dose heterogeneity and (2) develop and test a method for assigning gEUD objectives for target ROIs. Method and Materials: A total of six hypothetical target dDVHs were generated by randomly sampling (10 6 times) from Gaussian probability density functions centered at 55, 60 and 65 Gy with standard deviations of 5% and 10%. gEUD was calculated for each simulated dDVH using an a-parameter that increased (decreased) from 1 (−1) to 20 (−20). Based on the results of this exercise we developed a windowing technique for defining gEUD optimization objectives for target ROIs. The technique uses the min and max EUD objectives as defined in the Pinnacle 3 treatment planning system. Two cases were used to test the new technique: (1) a treatment planning phantom that incorporated a PTV 66 within a PTV 54 and (2) a left para-pharyngeal head-and-neck case. Two plans were generated for each case; the first using only dose volume (DV) objectives and the second using the gEUD windowing technique. Results: PTV results are presented as the percent difference in maximum (ΔD max ) and mean (ΔD mean ) dose normalized to the prescription dose. The planning phantom PTV 54 results were as follows: and . The planning phantom PTV 66 results were as follows: and . The results for the left para-pharyngeal PTV 50 were as follows: and . Conclusion: The gEUD windowing technique was shown to produce equivalent target coverage to plans derived using only DV objectives. One benefit to using this technique is the subsequent availability of DV objectives for target ROIs. Including gEUD objectives into routine IMRT planning will provide planners with more options and should facilitate better plans.

关键词： Medical treatment planning Intensity modulated radiation therapy Optimization Signal generators probability density functions

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SU-E-T-427: Cell Surviving Fractions Derived From Tumor-Volume Variation During Radiotherapy for Non-Small Cell Lung Cancer: Comparison with Predictive Assays

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Medical Physics 2014年第6PART18期41卷 324-324页

作者： A Chvetsov S Yartsev J Schwartz N Mayr University of Washington Seattle WA London Health Sciences Centre London Ontario

Purpose: To show that a distribution of cell surviving fractions S 2 in a heterogeneous group of patients can be derived from tumor-volume variation curves during radiotherapy for non-small cell lung cancer. Methods: Our analysis was based on two data sets of tumor-volume variation curves for heterogeneous groups of 17 patients treated for nonsmall cell lung cancer with conventional dose fractionation. The data sets were obtained previously at two independent institutions by using megavoltage (MV) computed tomography (CT). Statistical distributions of cell surviving fractions S 2 and cell clearance half-lives of lethally damaged cells T1/2 have been reconstructed in each patient group by using a version of the two-level cell population tumor response model and a simulated annealing algorithm. The reconstructed statistical distributions of the cell surviving fractions have been compared to the distributions measured using predictive assays in vitro. Results: Non-small cell lung cancer presents certain difficulties for modeling surviving fractions using tumor-volume variation curves because of relatively large fractional hypoxic volume, low gradient of tumor-volume response, and possible uncertainties due to breathing motion. Despite these difficulties, cell surviving fractions S 2 for non-small cell lung cancer derived from tumor-volume variation measured at different institutions have similar probability density functions (PDFs) with mean values of 0.30 and 0.43 and standard deviations of 0.13 and 0.18, respectively. The PDFs for cell surviving fractions S 2 reconstructed from tumor volume variation agree with the PDF measured in vitro. Comparison of the reconstructed cell surviving fractions with patient survival data shows that the patient survival time decreases as the cell surviving fraction increases. Conclusion: The data obtained in this work suggests that the cell surviving fractions S 2 can be reconstructed from the tumor volume variation curves measured dur

关键词： Cancer Lungs probability density functions Radiation therapy Computed tomography Statistical distribution Data sets Biomedical modeling Data analysis

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SU-FF-T-27: A Monte Carlo Based Tumor Model

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Medical Physics 2006年第6PART7期33卷 2056-2056页

作者： B Titz R Jeraj University of Wisconsin Madison WI

Purpose: To develop a stochastic, radiobiological tumor model to conduct in silico simulations of cell proliferation and to quantitatively assess biological effects of delivered dose and different irradiation regimes. Method and Materials: We developed a Monte Carlo model to perform computer simulations on initial tumor growth, progression of predetermined cell distributions and cellular response to irradiation following the linear-quadratic model. The single-cell-based configuration is composed of a volumetric grid lattice, with each grid site representing a capillary, clonogenic or normal tissue cell. Mean values for biological parameters such as cell cycle time and cell cycle phase dependent radiosensitivity were adopted from literature and sampled restrictively from Gaussian distributions for each cell. Additionally, angiogenesis, apoptosis and necrosis were implemented and random processes like cell displacement after proliferation and radiation-induced DNA damages were modeled using probability density functions. Results: Simulations of initial tumor formation and ongoing proliferation illustrate a decelerated growth rate with increasing cell cycle times and hypoxia occurrence, whereas low thresholds for capillary stimulation through tumor angiogenesis factors lead to accelerated proliferation. Analyses of tumor response to different fractionation patterns show faster and stronger expression of necrosis after accelerated time-dose-patterns. A benchmark against published experimental data with human HNSCC-6 tumor cell lines demonstrates good quantitative agreement. Conclusions: Our model is able to qualitatively predict basic radiobiological behavior and implicitly includes the ‘four Rs of radiotherapy’ as a result of the cellular approach. In order to apply the model to a specific tumor, it has to be tuned by including in vivo data and benchmarked against experiments. Given the adequate biological input parameters, good quantitative agreement can be achieved.

关键词： Cancer Cell growth Computer modeling Monte Carlo methods Tissues Computer simulation Dosimetry DNA Random processes probability density functions

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SU-FF-T-185: Implementation of a Dose Delivery Model to Handle Respiratory Motion with Variability

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Medical Physics 2009年第6PART11期36卷 2563-2563页

作者： J Kang J Unkelbach A Trofimov T Bortfeld Massachusetts General Hospital Boston MA IDSIA Manno Ticino CH

Purpose: To address the problem of respiratory motion uncertainty in IMRT and IM particle therapy by incorporating it in the optimization of the treatment plan. Method and Materials: We propose a probabilistic dose delivery model that accounts for the uncertainty of respiratory motion. Each breathing phase has associated with it a dose matrix whose deformations are calculated from 4D-CT data. The expected dose is then the sum over all dose contributions weighted by a probability density function (PDF) that represents the relative amount of time spent in each phase. The PDF is calculated from Varian Real-time Position Management (RPM) breathing traces. The uncertainty in the breathing pattern is represented by perturbation modes of the PDF determined by a principal components analysis (PCA) of the RPM data. Treatment plans are generated to compare the standard dose model without motion considerations and the described PDF Variation Model. Results: The concept is demonstrated for a liver patient treated with 5-beam IMRT. Five principal components represent the data set well, and two are sufficient for capturing the main features. Using the PDF Variation Model, the mean dose to the gross tumor volume (GTV) remains the same compared to a standard IMRT plan with 5-mm margins; the minimum dose to the GTV+5 mm volume decreases by 27%, and the maximum dose increases by 5%. The significant decrease in the minimum dose is not critical, as would be in the margin approach. Conclusion: We propose a treatment planning approach that takes into account variability in the respiration PDF of a patient. PCA is used to derive the typical variations of the PDF from measured breathing traces. The resultant dose distribution is expected to reduce dose to the lung or liver compared to a margin approach, while ensuring tumor coverage in the context of variable breathing patterns.

关键词： Intensity modulated radiation therapy Liver Cancer Therapeutics Medical treatment planning probability density functions Drug delivery Pneumodynamics Lungs Data analysis

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TH-A-116-01: A Statistical Approach to Quantification and Visualization of Setup and Range Uncertainties for Proton Plan Verification

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Medical Physics 2013年第6PART32期40卷 528-528页

作者： P Park J Cheung X Zhu W Liu N Sahoo L Court R Mohan H Li L Dong The University of Texas MD Anderson Houston TX Scripps Proton Therapy Center San Diego CA

Purpose: Proton therapy is more sensitive to both setup and beam range uncertainties than the conventional photon therapy due to the finite range of protons. For the purpose of evaluation of plan robustness in the face of such uncertainties, we developed a method to quantify and visualize the uncertainties in proton plans using comprehensive statistical analysis. The application of the proposed method is shown for selected patients in various clinical sites. Methods: Clinically approved 20 lung, 10 prostate, and a brain cases were retrospectively analyzed. For a selected volume of interest, probability density function (PDF) describing variation in point dose value for every tissue element under setup and range uncertainties was computed based on over 600 dose calculations per plan. The expected dose-volume histogram (E-DVH) was calculated by weighting the probability of each tissue element receiving a specified dose level. Similarly, standard deviation of the E-DVH was calculated (SD-DVH). Furthermore for each volume element, their probability of receiving greater dose than the dose constraint was visualized as color-wash, mapped onto the patients CT images for spatial visualization and assessment. Results: The E-DVH value of target coverage under the uncertainties was consistently lower than that of the nominal value, with a mean difference of−1.1% (−0.9% for breath-hold), −0.3%, and −2.2% for lung, prostate, and a brain cases respectively. The organs that were most sensitive to the uncertainties were esophagus and spinal cord for lung, rectum for prostate, and brain stem for brain cancer. Conclusion: A clinically feasibly plan robustness analysis tool based on statistical simulation has been developed for proton therapy plans. The passively scattered beam lung plans and scanning beam prostate plans appears to be robust in terms of target coverage. However, structures that are small in volume or located near the target area showed greater sensitivity to uncertaint

关键词： Lungs Brain Protons Cancer Proton therapy Statistical analysis Tissues Photons probability density functions Computed tomography

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