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Purpose Intensity-modulated radiation therapy (IMRT) utilizes many small fields for producing a uniform dose distribution. Therefore, there are many field junctions in the target region, and resulting dose uncertainties are accumulated. However, such accumulation of the dose uncertainty has not been implemented in the current practice of IMRT dose verification. The purpose of this study is to develop a method to predict the gamma passing rate (GPR) using a dose uncertainty accumulation model. Methods Thirty-three intensity-modulated (IM) beams for head-and-neck cases with step-and-shoot techniques were used in this study. The treatment plan was created using the XiO treatment planning system (TPS). The IM beam was produced by the ONCOR Impression Plus linear accelerator. MapCHECK was used to measure the dose distribution. The distribution of a dose uncertainty potential (DUP) was generated by in-house software that accumulated field shapes weighted by a segmental monitor unit, followed by Gaussian folding. The width of the Gaussian was determined from the width of the lateral penumbra. The dose difference between the calculated and measured doses was compared with the estimated DUP at each point. The GPR of each beam was predicted for 2%/2-mm, 3%/2-mm, and 3%/3-mm tolerances by its own DUP histogram and a GPR-vs-DUP correlation of other beams using the leave-one-out cross-validation method. The predicted GPR was compared with the measured GPR to evaluate the performance of this prediction method. The criteria for the predicted GPR corresponding to a measured GPR ≥ 90% were estimated to examine the feasibility of estimating the measured GPR by this GPR prediction method. Results The DUP was confirmed to have proportionality to the standard deviation (SD) of the dose difference. The SDs of the difference between the measured and predicted GPRs were 3.1, 1.7, and 1.4% for 2%/2-mm, 3%/2-mm, and 3%/3-mm tolerances, respectively. The criteria of the predicted GPR corresponding to the measured GPR ≥ 90% were 94.1 and 95.0% with confidence levels of 99 and 99.9%, respectively. Conclusion In this study, we confirmed the good proportionality between the dose difference and the estimated DUP. The results showed a feasibility to predict the dose difference from DUP as estimated by a DUP accumulation model. The predicted GPR developed in this study showed good accuracy for planar dose distributions of head and neck IMRT. The prediction method developed in this study is considered to be feasible as a substitute for the current practice of measurement-based verification of the dose distribution with gamma analysis.

Aims This review paper intends to summarize the application of machine learning to radiotherapy outcome modeling based on structured and un-structured radiation oncology datasets. Materials and methods The most appropriate machine learning approaches for structured datasets in terms of accuracy and interpretability are identified. For un-structured datasets, deep learning algorithms are explored and a critical view of the use of these approaches in radiation oncology is also provided. Conclusions We discuss the challenges in radiotherapy outcome prediction, and suggest to improve radiation outcome modeling by developing appropriate machine learning approaches where both accuracy and interpretability are taken into account.

Purpose The objective was to design and implement a bivariate extension to the contaminated binormal model (CBM) to fit paired receiver operating characteristic (ROC) datasets -NDASH- possibly degenerate - with proper ROC curves. Paired datasets yield two correlated ratings per case. Degenerate datasets have no interior operating points and proper ROC curves do not inappropriately cross the chance diagonal. The existing method, developed more than 3 decades ago utilizes a bivariate extension to the binormal model, implemented in CORROC2 software, which yields improper ROC curves and cannot fit degenerate datasets. CBM can fit proper ROC curves to unpaired (i.e., yielding one rating per case) and degenerate datasets, and there is a clear scientific need to extend it to handle paired datasets. Methods In CBM non-diseased cases are modeled by a probability density function (pdf) consisting of a unit variance peak centered at zero. Diseased cases are modeled with a mixture distribution whose pdf consists of two unit variance peaks, one centered at positive μ with integrated probability α, the mixing fraction parameter, corresponding to the fraction of diseased cases where the disease was visible to the radiologist, and one centered at zero, with integrated probability (1-α), corresponding to disease that was not visible. It is shown that: (1) for non-diseased cases the bivariate extension is a unit variances bivariate normal distribution centered at (0,0) with a specified correlation ρ1; (2) for diseased cases the bivariate extension is a mixture distribution with four peaks, corresponding to disease not visible in either condition, disease visible in only one condition, contributing 2 peaks, and disease visible in both conditions. An expression for the likelihood function is derived. A maximum likelihood estimation (MLE) algorithm, CORCBM, was implemented in the R programming language that yields parameter estimates and the covariance matrix of the parameters, and other statistics. A limited simulation validation of the method was performed. Results CORCBM and CORROC2 were applied to two datasets containing nine readers each contributing paired interpretations. CORCBM successfully fitted the data for all readers whereas CORROC2 failed to fit a degenerate dataset. All fits were visually reasonable. All CORCBM fits were proper whereas all CORROC2 fits were improper. CORCBM and CORROC2 were in agreement (i) in declaring only one of the nine readers as having significantly different performances in the two modalities; (ii) in estimating higher correlations for diseased cases than for non-diseased ones and (iii) in finding that the inter-modality correlation estimates for non-diseased cases were consistent between the two methods. All CORCBM fits yielded higher area under curve (AUC) than the CORROC2 fits, consistent with the fact that a proper ROC model like CORCBM is based on a likelihood-ratio-equivalent decision variable, and consequently yields higher performance than the binormal model based CORROC2. The method gave satisfactory fits to four simulated datasets. Conclusions CORCBM is a robust method for fitting paired ROC datasets, always yielding proper ROC curves, and able to fit degenerate datasets. This article is protected by copyright. All rights reserved.

Purpose To evaluate and compare the theoretically achievable accuracy of two families of two-parameter photon cross-section models: basis vector model (BVM) and modified parametric fit model (mPFM). Method The modified PFM assumes that photoelectric absorption and scattering cross-sections can be accurately represented by power functions in effective atomic number and/or energy plus the Klein-Nishina cross-section, along with empirical corrections that enforce exact prediction of elemental cross-sections. Two mPFM variants were investigated: the widely used Torikoshi model (tPFM) and a more complex “VCU” variant (vPFM). For 43 standard soft and bony tissues and phantom materials, all consisting of elements with atomic number less than 20 (except iodine), we evaluated the theoretically achievable accuracy of tPFM and vPFM for predicting linear attenuation, photoelectric absorption, and energy-absorption coefficients, and we compared it to a previously investigated separable, linear two-parameter model, BVM. Results For an idealized dual-energy computed tomography (DECT) imaging scenario, the cross-section mapping process demonstrates that BVM more accurately predicts photon cross-sections of biological mixtures than either tPFM or vPFM. Maximum linear attenuation coefficient prediction errors were 15% and 5% for tPFM and BVM, respectively. The root-mean-square (RMS) prediction errors of total linear attenuation over the 20 keV to 1000 keV energy range of tPFM and BVM were 0.93% (tPFM) and 0.1% (BVM) for adipose tissue, 0.8% (tPFM) and 0.2% (BVM) for muscle tissue, and 1.6% (tPFM) and 0.2% (BVM) for cortical bone tissue. With exception of the thyroid and Teflon, the RMS error for photoelectric absorption and scattering coefficient was within 4% for the tPFM and 2% for the BVM. Neither model predicts the photon cross-sections of thyroid tissue accurately, exhibiting relative errors as large as 20%. For the energy-absorption coefficients prediction error, RMS errors for the BVM were less than 1.5%, while for the tPFM, the RMS errors were as large as 16%. Conclusion Compared to modified PFMs, BVM shows superior potential to support dual-energy CT cross-section mapping. In addition, the linear, separable BVM can be more efficiently deployed by iterative model-based DECT image-reconstruction algorithms.

Purpose Dual-energy CT (DECT) enhances tissue characterization because of its basis material decomposition capability. In addition to conventional two-material decomposition from DECT measurements, multimaterial decomposition (MMD) is required in many clinical applications. To solve the ill-posed problem of reconstructing multi-material images from dual-energy measurements, additional constraints are incorporated into the formulation, including volume and mass conservation and the assumptions that there are at most three materials in each pixel and various material types among pixels. The recently proposed flexible image-domain MMD method decomposes pixels sequentially into multiple basis materials using a direct inversion scheme which leads to magnified noise in the material images. In this paper, we propose a statistical image-domain MMD method for DECT to suppress the noise. Methods The proposed method applies penalized weighted least-square (PWLS) reconstruction with a negative log-likelihood term and edge-preserving regularization for each material. The statistical weight is determined by a data-based method accounting for the noise variance of high- and low-energy CT images. We apply the optimization transfer principles to design a serial of pixel-wise separable quadratic surrogates (PWSQS) functions which monotonically decrease the cost function. The separability in each pixel enables the simultaneous update of all pixels. Results The proposed method is evaluated on a digital phantom, Catphan©600 phantom and three patients (pelvis, head, and thigh). We also implement the direct inversion and low-pass filtration methods for a comparison purpose. Compared with the direct inversion method, the proposed method reduces noise standard deviation (STD) in soft tissue by 95.35% in the digital phantom study, by 88.01% in the Catphan©600 phantom study, by 92.45% in the pelvis patient study, by 60.21% in the head patient study, and by 81.22% in the thigh patient study, respectively. The overall volume fraction accuracy is improved by around 6.85%. Compared with the low-pass filtration method, the root-mean-square percentage error (RMSE(%)) of electron densities in the Catphan©600 phantom is decreased by 20.89%. As modulation transfer function (MTF) magnitude decreased to 50%, the proposed method increases the spatial resolution by an overall factor of 1.64 on the digital phantom, and 2.16 on the Catphan©600 phantom. The overall volume fraction accuracy is increased by 6.15%. Conclusions We proposed a statistical image-domain MMD method using DECT measurements. The method successfully suppresses the magnified noise while faithfully retaining the quantification accuracy and anatomical structure in the decomposed material images. The proposed method is practical and promising for advanced clinical applications using DECT imaging.

PURPOSE To develop a new model-based method with spatial and parametric constraints (MB-SPC) aimed at accelerating diffusion tensor imaging (DTI) by directly estimating the diffusion tensor from highly undersampled k-space data. METHODS The MB-SPC method effectively incorporates the prior information on the joint sparsity of different diffusion-weighted images using an L1-L2 norm and the smoothness of the diffusion tensor using a total variation seminorm. The undersampled k-space datasets were obtained from fully sampled DTI datasets of a simulated phantom and an ex-vivo experimental rat heart with acceleration factors ranging from 2 to 4. The diffusion tensor was directly reconstructed by solving a minimization problem with a nonlinear conjugate gradient descent algorithm. The reconstruction performance was quantitatively assessed using the normalized root mean square error (nRMSE) of the DTI indices. RESULTS The MB-SPC method achieves acceptable DTI measures at an acceleration factor up to 4. Experimental results demonstrate that the proposed method can estimate the diffusion tensor more accurately than most existing methods operating at higher net acceleration factors. CONCLUSION The proposed method can significantly reduce artifact, particularly at higher acceleration factors or lower SNRs. This method can easily be adapted to MR relaxometry parameter mapping and is thus useful in the characterization of biological tissue such as nerves, muscle, and heart tissue.

Purpose This work aims to develop a new framework of image quality assessment using deep learning-based model observer (DL-MO) and to validate it in a low-contrast lesion detection task that involves CT images with patient anatomical background. Methods The DL-MO was developed using the transfer learning strategy to incorporate a pretrained deep convolutional neural network (CNN), a partial least square regression discriminant analysis (PLS-DA) model and an internal noise component. The CNN was previously trained to achieve the state-of-the-art classification accuracy over a natural image database. The earlier layers of the CNN were used as a deep feature extractor, with the assumption that similarity exists between the CNN and the human visual system. The PLSR model was used to further engineer the deep feature for the lesion detection task in CT images. The internal noise component was incorporated to model the inefficiency and variability of human observer (HO) performance, and to generate the ultimate DL-MO test statistics. Seven abdominal CT exams were retrospectively collected from the same type of CT scanners. To compare DL-MO with HO, 12 experimental conditions with varying lesion size, lesion contrast, radiation dose, and reconstruction types were generated, each condition with 154 trials. CT images of a real liver metastatic lesion were numerically modified to generate lesion models with four lesion sizes (5, 7, 9, and 11 mm) and three contrast levels (15, 20, and 25 HU). The lesions were inserted into patient liver images using a projection-based method. A validated noise insertion tool was used to synthesize CT exams with 50% and 25% of routine radiation dose level. CT images were reconstructed using the weighted filtered back projection algorithm and an iterative reconstruction algorithm. Four medical physicists performed a two-alternative forced choice (2AFC) detection task (with multislice scrolling viewing mode) on patient images across the 12 experimental conditions. DL-MO was operated on the same datasets. Statistical analyses were performed to evaluate the correlation and agreement between DL-MO and HO. Results A statistically significant positive correlation was observed between DL-MO and HO for the 2AFC low-contrast detection task that involves patient liver background. The corresponding Pearson product moment correlation coefficient was 0.986 [95% confidence interval (0.950, 0.996)]. Bland-Altman agreement analysis did not indicate statistically significant differences. Conclusions The proposed DL-MO is highly correlated with HO in a low-contrast detection task that involves realistic patient liver background. This study demonstrated the potential of the proposed DL-MO to assess image quality directly based on patient images in realistic, clinically relevant CT tasks.

Purpose: Photon fields with energies above ∼7 MeV are contaminated by neutrons due to photonuclear reactions. Their influence on dosimetry—although considered to be very low—is widely unexplored. Methods: In this work, Monte Carlo based investigations into this issue performed with fluka and egsnrc are presented. A typical Linac head in 18 MV-X mode was modeled equivalently within both codes. egsnrc was used for the photon and fluka for the neutron production and transport simulation. Water depth dose profiles and the response of different detectors (Farmer chamber, TLD-100, TLD-600H, and TLD-700H chip) in five representative depths were simulated and the neutrons’ impact (neutron absorbed dose relative to photon absorbed dose) was calculated. To take account of the neutrons’ influence, a theoretically required correction factor was defined and calculated for five representative water depths. Results: The neutrons’ impact on the absorbed dose to water was found to be below 0.1% for all depths and their impact on the response of the Farmer chamber and the TLD-700H chip was found to be even less. For the TLD-100 and the TLD-600H chip it was found to be up to 0.3% and 0.7%, respectively. The theoretical correction factors to be applied to absorbed dose to water values measured with these four detectors in a depth different from the reference/calibration depth were calculated and found to be below 0.05% for the Farmer chamber and the TLD-700H chip, but up to 0.15% and 0.35% for the TLD-100 and TLD-600H chips, respectively. In thermoluminescence dosimetry the neutrons’ influence (and therefore the additional inaccuracy in measurement) was found to be higher for TLD materials whose 6Li fraction is high, such as TLD-100 and TLD-600H, resulting from the thermal neutron capture reaction on 6Li. Conclusions: The impact of photoneutrons on the absorbed dose to water and on the response of a typical ionization chamber as well as three different types of TLD chips was quantified and was as expected found to be very low relative to that of the primary photons. For most practical reasons the neutrons’ influence on dosimetry might be neglected while for absolute precise thermoluminescence dosimetry in high energy photon fields, the use of TLD-700H (

Purpose: Current dosimetry methods in mammography assume that the breast is comprised of a homogeneous mixture of glandular and adipose tissues. Three-dimensional (3D) dedicated breast CT (bCT) data sets were used previously to assess the complex anatomical structure within the breast, characterizing the statistical distribution of glandular tissue in the breast. The purpose of this work was to investigate the effect of bCT-derived heterogeneous glandular distributions on dosimetry in mammography. Methods: bCT-derived breast diameters, volumes, and 3D fibroglandular distributions were used to design realistic compressed breast models comprised of heterogeneous distributions of glandular tissue. The bCT-derived glandular distributions were fit to biGaussian functions and used as probability density maps to assign the density distributions within compressed breast models. The MCNPX 2.6.0 Monte Carlo code was used to estimate monoenergetic normalized mean glandular dose “DgN(E)” values in mammography geometry. The DgN(E) values were then weighted by typical mammography x-ray spectra to determine polyenergetic DgN (pDgN) coefficients for heterogeneous (pDgN{sub hetero}) and homogeneous (pDgN{sub homo}) cases. The dependence of estimated pDgN values on phantom size, volumetric glandular fraction (VGF), x-ray technique factors, and location of the heterogeneous glandular distributions was investigated. Results: The pDgN{sub hetero} coefficients were on average 35.3% (SD, 4.1)more » and 24.2% (SD, 3.0) lower than the pDgN{sub homo} coefficients for the Mo–Mo and W–Rh x-ray spectra, respectively, across all phantom sizes and VGFs when the glandular distributions were centered within the breast phantom in the coronal plane. At constant breast size, increasing VGF from 7.3% to 19.1% lead to a reduction in pDgN{sub hetero} relative to pDgN{sub homo} of 23.6%–27.4% for a W–Rh spectrum. Displacement of the glandular distribution, at a distance equal to 10% of the compressed breast width in the superior and inferior directions, resulted in a 37.3% and a −26.6% change in the pDgN{sub hetero} coefficient, respectively, relative to the centered distribution for the Mo–Mo spectrum. Lateral displacement of the glandular distribution, at a distance equal to 10% of the compressed breast width, resulted in a 1.5% change in the pDgN{sub hetero} coefficient relative to the centered distribution for the W–Rh spectrum. Conclusions: Introducing bCT-derived heterogeneous glandular distributions into mammography phantom design resulted in decreased glandular dose relative to the widely used homogeneous assumption. A homogeneous distribution overestimates the amount of glandular tissue near the entrant surface of the breast, where dose deposition is exponentially higher. While these findings are based on clinically measured distributions of glandular tissue using a large cohort of women, future work is required to improve the classification of glandular distributions based on breast size and overall glandular fraction.« less

Purpose: The aim of the current study was to (a) calculate the organ equivalent dose (OED) and (b) estimate the associated second cancer risk to partially in-field critical structures from adjuvant radiotherapy for stage I seminoma of the testis on the basis of three different nonlinear risk models. Methods: Three-dimensional plans were created for twelve patients who underwent a treatment planning computed tomography of the abdomen. The plans for irradiation of seminoma consisted of para-aortic anteroposterior and posteroanterior fields giving 20 Gy to the target site with 6 MV photons. The OED of stomach, colon, liver, pancreas, and kidneys, that were partially included in the treatment volume, was calculated using differential dose–volume histograms. The mechanistic, bell-shaped, and plateau models were employed for these calculations provided that organ-specific parameters were available for the subsequent assessment of the excess absolute risk (EAR) for second cancer development. The estimated organ-specific lifetime risks were compared with the respective nominal intrinsic probabilities for cancer induction. Results: The mean OED, which was calculated from the patients’ treatment plans, varied from 0.54 to 6.61 Gy by the partially in-field organ of interest and the model used for dosimetric calculations. The difference between the OED of liver derived from the mechanistic model with those from the bell-shaped and plateau models was less than 1.8%. An even smaller deviation of 1.0% was observed for colon. For the rest organs of interest, the differences between the OED values obtained by the examined models varied from 8.6% to 50.0%. The EAR for stomach, colon, liver, pancreas, and kidney cancer induction at an age of 70 yr because of treatment of a typical 39-yr-old individual was up to 4.24, 11.39, 0.91, 3.04, and 0.14 per 10 000 persons-yr, respectively. Patient’s irradiation was found to elevate the lifetime intrinsic risks by 8.3%–63.0% depending upon the organ of interest and the model employed for risk analysis. Conclusions: Radiotherapy for stage I seminoma of the testis may result in an excess risk for the appearance of secondary malignancies in partially in-field organs. The organ- and model-dependent second cancer risk assessments of this study may be of value for patient counseling and follow-up.

Purpose: The motivation of this study was to find and eliminate the cause of errors in dose-averaged linear energy transfer (LET) calculations from therapeutic protons in small targets, such as biological cell layers, calculated using the geant 4 Monte Carlo code. Furthermore, the purpose was also to provide a recommendation to select an appropriate LET quantity from geant 4 simulations to correlate with biological effectiveness of therapeutic protons. Methods: The authors developed a particle tracking step based strategy to calculate the average LET quantities (track-averaged LET, LET t and dose-averaged LET, LET d ) using geant 4 for different tracking step size limits. A step size limit refers to the maximally allowable tracking step length. The authors investigated how the tracking step size limit influenced the calculated LET t and LET d of protons with six different step limits ranging from 1 to 500 μm in a water phantom irradiated by a 79.7-MeV clinical proton beam. In addition, the authors analyzed the detailed stochastic energy deposition information including fluence spectra and dose spectra of the energy-deposition-per-step of protons. As a reference, the authors also calculated the averaged LET and analyzed the LET spectra combining the Monte Carlo method and the deterministic method. Relative biological effectiveness (RBE) calculations were performed to illustrate the impact of different LET calculation methods on the RBE-weighted dose. Results: Simulation results showed that the step limit effect was small for LET t but significant for LET d . This resulted from differences in the energy-deposition-per-step between the fluence spectra and dose spectra at different depths in the phantom. Using the Monte Carlo particle tracking method in geant 4 can result in incorrect LET d calculation results in the dose plateau region for small step limits. The erroneous LET d results can be attributed to the algorithm to determine fluctuations in energy deposition along the tracking step in geant 4. The incorrect LET d values lead to substantial differences in the calculated RBE. Conclusions: When the geant 4 particle tracking method is used to calculate the average LET values within targets with a small step limit, such as smaller than 500 μm, the authors recommend the use of LET t in the dose plateau region and LET d around the Bragg peak. For a large step limit, i.e., 500 μm, LET d is recommended along the whole Bragg curve. The transition point depends on beam parameters and can be found by determining the location where the gradient of the ratio of LET d and LET t becomes positive.

Purpose: Treatment planning for carbon ion therapy requires an accurate modeling of the biological response of each tissue to estimate the clinical outcome of a treatment. The relative biological effectiveness (RBE) accounts for this biological response on a cellular level but does not refer to the actual impact on the organ as a whole. For photon therapy, the concept of equivalent uniform dose (EUD) represents a simple model to take the organ response into account, yet so far no formulation of EUD has been reported that is suitable to carbon ion therapy. The authors introduce the concept of an equivalent uniform effect (EUE) that is directly applicable to both ion and photon therapies and exemplarily implemented it as a basis for biological treatment plan optimization for carbon ion therapy. Methods: In addition to a classical EUD concept, which calculates a generalized mean over the RBE-weighted dose distribution, the authors propose the EUE to simplify the optimization process of carbon ion therapy plans. The EUE is defined as the biologically equivalent uniform effect that yields the same probability of injury as the inhomogeneous effect distribution in an organ. Its mathematical formulation is based on the generalized mean effect using an effect-volume parameter to account for different organ architectures and is thus independent of a reference radiation. For both EUD concepts, quadratic and logistic objective functions are implemented into a research treatment planning system. A flexible implementation allows choosing for each structure between biological effect constraints per voxel and EUD constraints per structure. Exemplary treatment plans are calculated for a head-and-neck patient for multiple combinations of objective functions and optimization parameters. Results: Treatment plans optimized using an EUE-based objective function were comparable to those optimized with an RBE-weighted EUD-based approach. In agreement with previous results from photon therapy, the optimization by biological objective functions resulted in slightly superior treatment plans in terms of final EUD for the organs at risk (OARs) compared to voxel-based optimization approaches. This observation was made independent of the underlying objective function metric. An absolute gain in OAR sparing was observed for quadratic objective functions, whereas intersecting DVHs were found for logistic approaches. Even for considerable under- or overestimations of the used effect- or dose–volume parameters during the optimization, treatment plans were obtained that were of similar quality as the results of a voxel-based optimization. Conclusions: EUD-based optimization with either of the presented concepts can successfully be applied to treatment plan optimization. This makes EUE-based optimization for carbon ion therapy a useful tool to optimize more specifically in the sense of biological outcome while voxel-to-voxel variations of the biological effectiveness are still properly accounted for. This may be advantageous in terms of computational cost during treatment plan optimization but also enables a straight forward comparison of different fractionation schemes or treatment modalities.

The purpose of this work was to generate uncompressed heterogeneous breast phantom models using size-dependent fibroglandular distributions derived from a large cohort of breast CT (bCT) datasets, and to compare differences in normalized glandular dose coefficients for bCT "DgNA cohort of 274 segmented bCT datasets were used to quantify the fibroglandular tissue distribution within the breast parenchyma. Each dataset was interpolated to an isotropic voxel size of 0.25 mm and the breast center-of-mass was aligned for all coronal slices. Each aligned dataset was converted into two binarized volumes representing voxels containing only glandular tissue "G(x,y,z)" and voxels containing glandular or adipose tissue "AG(x,y,z)". The datasets were classified by volume in accordance with previously reported size-dependent, breast-shaped phantoms. Within the five groups - each containing on average 55 datasets, all G(x,y,z) and AG(x,y,z) volumes were summed separately representing the cumulative distribution of glandular tissue or breast parenchyma (glandular + adipose), respectively. G(x,y,z) was divided by AG(x,y,z) on a voxel-by-voxel basis resulting in a glandular fraction "GF(x,y,z)" distribution for each phantom size. The GF(x,y,z) distributions were used to construct heterogeneous mathematical phantoms for the small, median, and large breast sizes with a 1.5 mm skin thickness - based on previously reported measurements from bCT, and a 5 mm skin thickness for comparison with outdated assumptions of skin thickness. A subset of 15 bCT datasets from the cohort (five for each breast size) were used to construct voxelized patient models for validation of the heterogeneous phantom models. Monte Carlo techniques were used to estimate monoenergetic DgN(E)For photon energies ≲45 keV, the homogeneous model overestimates DgN(E) values relative to the realistic heterogeneous model sorted into five volume classes. The 5 mm skin thickness underestimates DgN(E) values relative to the realistic 1.5 mm thickness for lower energies and the differences diminish up to 70 keV. Averaged across all phantom sizes the homogeneous model overestimates pDgNAnatomically accurate heterogeneous phantom models were developed using bCT image-derived fibroglandular tissue distributions. These new models improve the accuracy of bCT dosimetry, and in conjunction with previous models for mammography, may help in providing a more universally accepted breast dosimetry model.

Purpose The purpose of this study was to implement a machine learning model to predict skin dose from targeted intraoperative (TARGIT) treatment resulting in timely adoption of strategies to limit excessive skin dose. Methods A total of 283 patients affected by invasive breast carcinoma underwent TARGIT with a prescribed dose of 6 Gy at 1 cm, after lumpectomy. Radiochromic films were used to measure the dose to the skin for each patient. Univariate statistical analysis was performed to identify correlation of physical and patient variables with measured dose. After feature selection of predictors of in vivo skin dose, machine learning models stepwise linear regression (SLR), support vector regression (SVR), ensemble with bagging or boosting, and feed forward neural networks were trained on results of in vivo dosimetry to derive models to predict skin dose. Models were evaluated by tenfold cross validation and ranked according to root mean square error (RMSE) and adjusted correlation coefficient of true vs predicted values (adj-R2 ). Results The predictors correlated with in vivo dosimetry were the distance of skin from source, depth-dose in water at depth of the applicator in the breast, use of a replacement source, and irradiation time. The best performing model was SVR, which scored RMSE and adj-R2 , equal to 0.746 [95% confidence intervals (CI), 95% CI 0.737,0.756] and 0.481 (95% CI 0.468,0.494), respectively, on the tenfold cross validation. Conclusion The model trained on results of in vivo dosimetry can be used to predict skin dose during setup of patient for TARGIT and this allows for timely adoption of strategies to prevent of excessive skin dose.

Purpose High dose–rate brachytherapy is a method of radiotherapy for cancer treatment in which the radiation source is placed within the body. In addition to give a high enough dose to a tumor, it is also important to spare nearby healthy organs [organs at risk (OAR)]. Dose plans are commonly evaluated using the so‐called dosimetric indices; for the tumor, the portion of the structure that receives a sufficiently high dose is calculated, while for OAR it is instead the portion of the structure that receives a sufficiently low dose that is of interest. Models that include dosimetric indices are referred to as dose–volume models (DVMs) and have received much interest recently. Such models do not take the dose to the coldest (least irradiated) volume of the tumor into account, which is a distinct weakness since research indicates that the treatment effect can be largely impaired by tumor underdosage even to small volumes. Therefore, our aim is to extend a DVM to also consider the dose to the coldest volume. Methods An improved DVM for dose planning is proposed. In addition to optimizing with respect to dosimetric indices, this model also takes mean dose to the coldest volume of the tumor into account. Results Our extended model has been evaluated against a standard DVM in ten prostate geometries. Our results show that the dose to the coldest volume could be increased, while also computing times for the dose planning were improved. Conclusion While the proposed model yields dose plans similar to other models in most aspects, it fulfils its purpose of increasing the dose to cold tumor volumes. An additional benefit is shorter solution times, and especially for clinically relevant times (of minutes) we show major improvements in tumour dosimetric indices.

PURPOSE This study proposes a proactive maintenance model utilizing historical Multileaf collimator (MLC) performance data to predict potential MLC dysfunctions, promote preemptive maintenance and thereby reduce treatment disruptions. METHODS MLC failures were assumed to correlate with MLC performance quantitation from trajectory logs. A cohort of data from service reports and trajectory logs was used to establish a model for predicting MLC dysfunctions. Specifically, the service reports logged by our in-house engineers recorded failure status, including service date, service reason and actions taken, while trajectory logs recorded the ordered/actual leaf positions in 20-ms intervals. Leaf performance from trajectory logs was quantified, where an event was defined as detecting a leaf's position deviation ≥a mm. Three a values, 0.05, 0.1, and 0.5 mm, were used as candidates to determine the appropriate threshold for deviation event quantitation. Logged MLC failures from service reports were retrieved and classified into two categories based on the patterns of their deviation events calculated from trajectory logs: (a) failures with continuous deviations: deviation events lasted several days before failure, and (b) failures with a burst of deviations: deviation events only lasted 1 or 2 days and then MLC failed suddenly. The proposed proactive model focused on the failures with continuous deviations since abnormal trends in their deviation events lasted couple of days, allowing preventive maintenance. The model was predefined with three parameters (x, y, z): if a leaf scored ≥x deviation events per day in any y days within up to a z-day window, the leaf was marked as a "potential failure." The distributions of the deviation events as functions of time (days or weeks) and leaves using the found a-value were then associated with logged failures to find model parameters. In a retrospective demonstration, a total of 28 logged failures with continuous deviations and 66 397 trajectory logs from two TBs' 3-yr records were used to determine the model parameters (x, y, z). The established model was then applied to a third TB for validation. RESULTS Deviation event threshold, a, was determined to be 0.1 mm, and the resulting model parameters were (x = 20, y = 6, z = 10). When validating the third TB's 3-yr record with 12 logged continuous deviation failures, the model predicted 16 failures: seven were confirmed from the records with a hit rate of 58.3%, while nine were not; further investigation of each unconfirmed failure convinced that some could be actual failures, but somehow not recorded. CONCLUSION The model offers an addition to preemptive maintenance for reducing treatment disruptions.

PURPOSE Multishot interleaved echo-planar imaging (iEPI) can achieve higher image resolution than single-shot EPI for diffusion tensor imaging (DTI), but its application is limited by the prolonged acquisition time. To reduce the acquisition time, a novel model-based reconstruction for simultaneous multislice (SMS) and parallel imaging (PI) accelerated iEPI DTI is proposed. MATERIALS AND METHODS DTI datasets acquired by iEPI with SMS and PI acceleration can be regarded as 3D k-space data, which is undersampled along both the slice and phase encoding directions. Instead of reconstruction of individual diffusion-weighted image, diffusion tensors are directly estimated by the joint reconstruction of undersampled 3D k-space from all diffusion-encoding directions using a model-based formulation to exploit the correlation across different directions. DTI simulation and in vivo acquisition were used to demonstrate the superior performance of the proposed method. RESULTS The proposed method reduced the estimation errors and artifacts than traditional parallel imaging reconstruction in DTI simulation. In the in vivo DTI experiment, the acquisition time of 4-shot iEPI was reduced from 11 min 7 s to 3 min 53 s with an acceleration factor of 4, and the image quality and precision of quantitative parameters were comparable with the fully sampled acquisition. CONCLUSIONS The proposed model-based reconstruction for iEPI DTI with SMS and PI can achieve fourfold acceleration while maintaining high accuracy for tensor measurements.

Purpose Many biological objects, including neuronal dendrites, blood vasculature, airways, phylogenetic trees, produce tree structured data. Current methods of analysis either ignore the complex structure of trees or use distance-based methods which limit the scope of multivariate modeling. Methods We propose a branching process model which enables analysis of both the branching structure and associated properties. Our novel parametrization preserves an important aspect of tree structure, namely its branch order. The model is amenable to standard methods of analysis, like generalized linear/additive models. Results The model fit the distribution of the observed data quite well when applied to a collection of 98 brain artery systems. The estimated probability of branching decreases log linearly with branch order. Likewise, the average diameter of arteries decreases, while average length increases with branch order. Frontal arterial branches are on average longer and thinner than those in the back at equivalent branch orders. A mechanistic arterial branching model based on Poiseuille's blood flow law, which uses vessel length and diameter information, fit the observed branching structure significantly better. This model is further improved by including branch order, suggesting viscoelastic flow impacts branching in narrower vessels. Conclusion After adjustment for branch order, brain arterial branching probabilities decreased significantly with age and length, but increased with diameter. Arteries become thicker and branch less frequently with increasing age, but the age effect decreases with branch order.

Purpose To develop a statistical model that incorporates the treatment uncertainty from the rotational error of the single isocenter for multiple targets technique, and calculates the extra PTV (planning target volume) margin required to compensate for this error. Methods The random vector for modeling the setup (S) error in the three-dimensional (3D) patient coordinate system was assumed to follow a 3D normal distribution with a zero mean, and standard deviations of σx , σy , σz . It was further assumed that the rotation of clinical target volume (CTV) about the isocenter happens randomly and follows a three-dimensional (3D) independent normal distribution with a zero mean and a uniform standard deviation of σδ . This rotation leads to a rotational random error (R), which also has a 3D independent normal distribution with a zero mean and a uniform standard deviation of σR equal to the product of σδπ180 and dI⇔T, the distance between the isocenter and CTV. Both (S and R) random vectors were summed, normalized, and transformed to the spherical coordinates to derive the Chi distribution with three degrees of freedom for the radial coordinate of S+R. PTV margin was determined using the critical value of this distribution for a 0.05 significance level so that 95% of the time the treatment target would be covered by the prescription dose. The additional PTV margin required to compensate for the rotational error was calculated as a function of σR and dI⇔T. Results The effect of the rotational error is more pronounced for treatments that require high accuracy/precision like stereotactic radiosurgery (SRS) or stereotactic body radiotherapy (SBRT). With a uniform 2-mm PTV margin (or σx = σy = σz = 0.715 mm), a σR = 0.328 mm will decrease the CTV coverage probability from 95.0% to 90.9%, or an additional 0.2-mm PTV margin is needed to prevent this loss of coverage. If we choose 0.2 mm as the threshold, any σR > 0.328 mm will lead to an extra PTV margin that cannot be ignored, and the maximal σδ that can be ignored is 0.45° (or 0.0079rad ) for dI⇔T = 50 mm or 0.23° (or 0.004rad ) for dI⇔T = 100 mm. Conclusions The rotational error cannot be ignored for high-accuracy/-precision treatments like SRS/SBRT, particularly when the distance between the isocenter and target is large.

Purpose The setup errors and organ motion errors pertaining to clinical target volume (CTV) have been considered as two major causes of uncertainties in the determination of the CTV-to-planning target volume (PTV) margins for prostate cancer radiation treatment planning. We based our study on the assumption that interfractional target shape variations are not negligible as another source of uncertainty for the determination of precise CTV-to-PTV margins. Thus, we investigated the interfractional shape variations of CTVs based on a point distribution model (PDM) for prostate cancer radiation therapy. Materials and Methods To quantify the shape variations of CTVs, the PDM was applied for the contours of 4 types of CTV regions (low-risk, intermediate- risk, high-risk CTVs, and prostate plus entire seminal vesicles), which were delineated by considering prostate cancer risk groups on planning computed tomography (CT) and cone beam CT (CBCT) images of 73 fractions of 10 patients. The standard deviations (SDs) of the interfractional random errors for shape variations were obtained from covariance matrices based on the PDMs, which were generated from vertices of triangulated CTV surfaces. The correspondences between CTV surface vertices were determined based on a thin plate spline robust point matching algorithm. The systematic error for shape variations was defined as the average deviation between surfaces of an average CTV and planning CTVs, and the random error as the average deviation of CTV surface vertices for fractions from an average CTV surface. Results The means of the SDs of the systematic errors for the 4 types of CTVs ranged from 1.0 to 2.0 mm along the anterior direction, 1.2 to 2.6 mm along the posterior direction, 1.0 to 2.5 mm along the superior direction, 0.9 to 1.9 mm along the inferior direction, 0.9 to 2.6 mm along the right direction, and 1.0 to 3.0 mm along the left direction. Concerning the random errors, the means of the SDs ranged from 0.9 to 1.2 mm along the anterior direction, 1.0 to 1.4 mm along the posterior direction, 0.9 to 1.3 mm along the superior direction, 0.8 to 1.0 mm along the inferior direction, 0.8 to 0.9 mm along the right direction, and 0.8 to 1.0 mm along the left direction. Conclusions Since the shape variations were not negligible for intermediate and high risk CTVs, they should be taken into account for the determination of the CTV-to-PTV margins in radiation treatment planning of prostate cancer. This article is protected by copyright. All rights reserved.

To introduce and evaluate an increment matrix approach (IMA) describing the signal statistics of energy-selective photon counting detectors including spatial-spectral correlations between energy bins of neighboring detector pixels. The importance of the occurring correlations for image-based material decomposition is studied.An IMA describing the counter increase patterns in a photon counting detector is proposed. This IMA has the potential to decrease the number of required random numbers compared to Monte Carlo simulations by pursuing an approach based on convolutions. To validate and demonstrate the IMA, an approximate semirealistic detector model is provided, simulating a photon counting detector in a simplified manner, e.g., by neglecting count rate-dependent effects. In this way, the spatial-spectral correlations on the detector level are obtained and fed into the IMA. The importance of these correlations in reconstructed energy bin images and the corresponding detector performance in image-based material decomposition is evaluated using a statistically optimal decomposition algorithm.The results of IMA together with the semirealistic detector model were compared to other models and measurements using the spectral response and the energy bin sensitivity, finding a good agreement. Correlations between the different reconstructed energy bin images could be observed, and turned out to be of weak nature. These correlations were found to be not relevant in image-based material decomposition. An even simpler simulation procedure based on the energy bin sensitivity was tested instead and yielded similar results for the image-based material decomposition task, as long as the fact that one incident photon can increase multiple counters across neighboring detector pixels is taken into account.The IMA is computationally efficient as it required about 10(2) random numbers per ray incident on a detector pixel instead of an estimated 10(8) random numbers per ray as Monte Carlo approaches would need. The spatial-spectral correlations as described by IMA are not important for the studied image-based material decomposition task. Respecting the absolute photon counts and thus the multiple counter increases by a single x-ray photon, the same material decomposition performance could be obtained with a simpler detector description using the energy bin sensitivity.

The free-response receiver operating characteristic (FROC) method is being increasingly used to evaluate observer performance in search tasks. Data analysis requires definition of a figure of merit (FOM) quantifying performance. While a number of FOMs have been proposed, the recommended one, namely, the weighted alternative FROC (wAFROC) FOM, is not well understood. The aim of this work is to clarify the meaning of this FOM by relating it to the empirical area under a proposed wAFROC curve.The weighted wAFROC FOM is defined in terms of a quasi-Wilcoxon statistic that involves weights, coding the clinical importance, assigned to each lesion. A new wAFROC curve is proposed, the y-axis of which incorporates the weights, giving more credit for marking clinically important lesions, while the x-axis is identical to that of the AFROC curve. An expression is derived relating the area under the empirical wAFROC curve to the wAFROC FOM. Examples are presented with small numbers of cases showing how AFROC and wAFROC curves are affected by correct and incorrect decisions and how the corresponding FOMs credit or penalize these decisions. The wAFROC, AFROC, and inferred ROC FOMs were applied to three clinical data sets involving multiple reader FROC interpretations in different modalities.It is shown analytically that the area under the empirical wAFROC curve equals the wAFROC FOM. This theorem is the FROC analog of a well-known theorem developed in 1975 for ROC analysis, which gave meaning to a Wilcoxon statistic based ROC FOM. A similar equivalence applies between the area under the empirical AFROC curve and the AFROC FOM. The examples show explicitly that the wAFROC FOM gives equal importance to all diseased cases, regardless of the number of lesions, a desirable statistical property not shared by the AFROC FOM. Applications to the clinical data sets show that the wAFROC FOM yields results comparable to that using the AFROC FOM.The equivalence theorem gives meaning to the weighted AFROC FOM, namely, it is identical to the empirical area under weighted AFROC curve.

A fully heterogeneous population averaged mechanistic tumor control probability (TCP) model is appropriate for the analysis of external beam radiotherapy (EBRT). This has been accomplished for EBRT photon treatment of intermediate-risk prostate cancer. Extending the TCP model for low and high-risk patients would be beneficial in terms of overall decision making. Furthermore, different radiation treatment modalities such as protons and carbon-ions are becoming increasingly available. Consequently, there is a need for a complete TCP model.A TCP model was fitted and validated to a primary endpoint of 5-year biological no evidence of disease clinical outcome data obtained from a review of the literature for low, intermediate, and high-risk prostate cancer patients (5218 patients fitted, 1088 patients validated), treated by photons, protons, or carbon-ions. The review followed the preferred reporting item for systematic reviews and meta-analyses statement. Treatment regimens include standard fractionation and hypofractionation treatments. Residual analysis and goodness of fit statistics were applied.The TCP model achieves a good level of fit overall, linear regression results in a p-value of0.000 01 with an adjusted-weighted-R(2) value of 0.77 and a weighted root mean squared error (wRMSE) of 1.2%, to the fitted clinical outcome data. Validation of the model utilizing three independent datasets obtained from the literature resulted in an adjusted-weighted-R(2) value of 0.78 and a wRMSE of less than 1.8%, to the validation clinical outcome data. The weighted mean absolute residual across the entire dataset is found to be 5.4%.This TCP model fitted and validated to clinical outcome data, appears to be an appropriate model for the inclusion of all clinical prostate cancer risk categories, and allows evaluation of current EBRT modalities with regard to tumor control prediction.

Purpose: The purpose of this study was to detect and analyze anomalies between a large number of computed tomography (CT) scanners, tracked over time, utilized to collect human pulmonary CT data for a national multicenter study: chronic obstructive pulmonary disease genetic epidemiology study (COPDGene). Methods: A custom designed CT reference standard “Test Object” has been developed to evaluate the relevant differences in CT attenuation between CT scanners in COPDGene. The materials used in the Test Object to assess CT scanner accuracy and precision included lung equivalent foam (−856 HU), internal air (−1000 HU), water (0 HU), and acrylic (120 HU). Nineteen examples of the Test Object were manufactured. Initially, all Test Objects were scanned on the same CT scanner before the Test Objects were sent to the 20 specific sites and 42 individual CT scanners that were used in the study. The Test Objects were scanned over 17 months while the COPDGene study continued to recruit subjects. A mixed linear effect statistical analysis of the CT scans on the 19 Test Objects was performed. The statistical model reflected influence of reconstruction kernels, tube current, individual Test Objects, CT scanner models, and temporal consistency on CT attenuation. Results: Depending on the Test Object material, there were significant differences between reconstruction kernels, tube current, individual Test Objects, CT scanner models, and temporal consistency. The two Test Object materials of most interest were lung equivalent foam and internal air. With lung equivalent foam, there were significant (p < 0.05) differences between the Siemens B31 (−856.6, ±0.82; mean ± SE) and the GE Standard (−856.6 ± 0.83) reconstruction kernel relative to the Siemens B35 reference standard (−852.5 ± 1.4). Comparing lung equivalent foam attenuation there were also significant differences between CT scanner models (p < 0.01), tube current (p < 0.005), and in temporal consistency (p < 0.005) at individual sites. However, there were no significant effects measurable using different examples of the Test Objects at the various sites compared to the reference scans of the 19 Test Objects. For internal air, significant (p < 0.005) differences were found between all reconstruction kernels (Siemens B31, GE Standard, and Phillips B) compared to the reference standard. There were significant differences between CT models (p < 0.005), and tube current (p < 0.005). There were no significant effects measurable using different examples of the Test Objects at the various sites compared to the reference scans of the 19 Test Objects. Differences, across scanners, between external air and internal air measures in this simple (relative to the in vivo lung) test object varied by as much as 15 HU. Conclusions: The authors conclude that the Test Object designed for this study was able to detect significant effects regarding individual CT scanners that altered the CT attenuation measurements relevant to the study that are used to determine lung density. Through an understanding of individual scanners, the Test Object analysis can be used to detect anomalies in an individual CT scanner and to statistically model out scanner differences and individual scanner changes over time in a large multicenter trial.

The amount of fibroglandular tissue content in the breast as estimated mammographically, commonly referred to as breast percent density (PD%), is one of the most significant risk factors for developing breast cancer. Approaches to quantify breast density commonly focus on either semiautomated methods or visual assessment, both of which are highly subjective. Furthermore, most studies published to date investigating computer-aided assessment of breast PD% have been performed using digitized screen-film mammograms, while digital mammography is increasingly replacing screen-film mammography in breast cancer screening protocols. Digital mammography imaging generates two types of images for analysis, raw (i.e., "FOR PROCESSING") and vendor postprocessed (i.e., "FOR PRESENTATION"), of which postprocessed images are commonly used in clinical practice. Development of an algorithm which effectively estimates breast PD% in both raw and postprocessed digital mammography images would be beneficial in terms of direct clinical application and retrospective analysis.This work proposes a new algorithm for fully automated quantification of breast PD% based on adaptive multiclass fuzzy c-means (FCM) clustering and support vector machine (SVM) classification, optimized for the imaging characteristics of both raw and processed digital mammography images as well as for individual patient and image characteristics. Our algorithm first delineates the breast region within the mammogram via an automated thresholding scheme to identify background air followed by a straight line Hough transform to extract the pectoral muscle region. The algorithm then applies adaptive FCM clustering based on an optimal number of clusters derived from image properties of the specific mammogram to subdivide the breast into regions of similar gray-level intensity. Finally, a SVM classifier is trained to identify which clusters within the breast tissue are likely fibroglandular, which are then aggregated into a final dense tissue segmentation that is used to compute breast PD%. Our method is validated on a group of 81 women for whom bilateral, mediolateral oblique, raw and processed screening digital mammograms were available, and agreement is assessed with both continuous and categorical density estimates made by a trained breast-imaging radiologist.Strong association between algorithm-estimated and radiologist-provided breast PD% was detected for both raw (r = 0.82, p0.001) and processed (r = 0.85, p0.001) digital mammograms on a per-breast basis. Stronger agreement was found when overall breast density was assessed on a per-woman basis for both raw (r = 0.85, p0.001) and processed (0.89, p0.001) mammograms. Strong agreement between categorical density estimates was also seen (weighted Cohen's κ ≥ 0.79). Repeated measures analysis of variance demonstrated no statistically significant differences between the PD% estimates (p0.1) due to either presentation of the image (raw vs processed) or method of PD% assessment (radiologist vs algorithm).The proposed fully automated algorithm was successful in estimating breast percent density from both raw and processed digital mammographic images. Accurate assessment of a woman's breast density is critical in order for the estimate to be incorporated into risk assessment models. These results show promise for the clinical application of the algorithm in quantifying breast density in a repeatable manner, both at time of imaging as well as in retrospective studies.

Purpose: Radiotherapy of solid tumors has been performed with various fractionation regimens such as multi- and hypofractionations. However, the ability to optimize the fractionation regimen considering the physical dose distribution remains insufficient. This study aims to optimize the fractionation regimen, in which the authors propose a graphical method for selecting the optimal number of fractions (n) and dose per fraction (d) based on dose-volume histograms for tumor and normal tissues of organs around the tumor. Methods: Modified linear-quadratic models were employed to estimate the radiation effects on the tumor and an organ at risk (OAR), where the repopulation of the tumor cells and the linearity of the dose-response curve in the high dose range of the surviving fraction were considered. The minimization problem for the damage effect on the OAR was solved under the constraint that the radiation effect on the tumor is fixed by a graphical method. Here, the damage effect on the OAR was estimated based on the dose-volume histogram. Results: It was found that the optimization of fractionation scheme incorporating the dose-volume histogram is possible by employing appropriate cell surviving models. The graphical method considering the repopulation of tumor cells and a rectilinear response in the high dose range enables them to derive the optimal number of fractions and dose per fraction. For example, in the treatment of prostate cancer, the optimal fractionation was suggested to lie in the range of 8-32 fractions with a daily dose of 2.2-6.3 Gy. Conclusions: It is possible to optimize the number of fractions and dose per fraction based on the physical dose distribution (i.e., dose-volume histogram) by the graphical method considering the effects on tumor and OARs around the tumor. This method may stipulate a new guideline to optimize the fractionation regimen for physics-guided fractionation. (C) 2015 American Association of Physicists in Medicine.

Purpose: To develop a binary image reconstruction method for the autolocalization of metallic object(s) in CT with sparse projections. Methods: The authors divide the system into two types of contents: Metal(s) and nonmetal(s). The boundaries of metallic objects are obtained by using a penalized weighted least-squares algorithm with the adequate intensity gradient-controlled. A novel mechanism of “amplifying” the difference between metal(s) and nonmetallic substances is introduced by preprocessing the sinogram data, which is shown to be necessary in dealing with a case with sparse projection data. A series of experimental studies are performed to evaluate the proposed approach. Results: A novel binary CTimage reconstruction formalism is established for the autodetermination of the shape and location of metallic objects in the presence of limited number of projections. Experimental studies reveal that the presented algorithm works well even when the embedded metal object(s) has different shape(s). It is also shown that when the projection data are sparse, a differential manipulation of projection data can greatly facilitate the binary reconstruction process and allow the authors to obtain accurate binary CTimages that would otherwise be unattainable. Conclusions: Binary CTreconstruction provides a viable method for determining the geometric distribution information of the implanted metal objects in CTimaging.

Purpose: In the present work, the authors compare geometrical and Monte Carlo projectors in detail. The geometrical projectors considered were the conventional geometrical Siddon ray-tracer (S-RT) and the orthogonal distance-based ray-tracer (OD-RT), based on computing the orthogonal distance from the center of image voxel to the line-of-response. A comparison of these geometrical projectors was performed using different point spread function (PSF) models. The Monte Carlo-based method under consideration involves an extensive model of the system response matrix based on Monte Carlo simulations and is computed off-line and stored on disk. Methods: Comparisons were performed using simulated and experimental data of the commercial small animal PET scanner rPET. Results: The results demonstrate that the orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions yield better images in terms of contrast and spatial resolution than those obtained after using the conventional method and the multiray-based S-RT. Furthermore, the Monte Carlo-based method yields slight improvements in terms of contrast and spatial resolution with respect to these geometrical projectors. Conclusions: The orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions represent satisfactory alternatives to factorizing the system matrix or to the conventional on-the-fly ray-tracing methods for list-mode reconstruction, where an extensive modeling based on Monte Carlo simulations is unfeasible., This work was supported in part by Fondo de Investigaciones Sanitarias del Instituto de Salud Carlos III (Project Nos. PI041017, PS09/01206, and CB06/01/1039), by the Ministerio de Ciencia e Innovacion (Grant No. TEC2007-61047), by the Generalitat Valenciana (Grant No. GV06/246), by the Generalitat de Catalunya (Grant No. SGR1049), Ministerio de Ciencia e Innovacion (Project No. SAF2009-08076), and by Ministerio de Ciencia e Innovacion (CDTI-CENIT) AMIT project and Comunidad de Madrid (project ARTEMIS P2009/DPI-1802). P. Aguiar was awarded a "Sara Borrell" fellowship by Fondo de Investigaciones Sanitarias del Instituto de Salud Carlos III.

Purpose: X-ray phase-contrast tomography (PCT) is a rapidly emerging imaging modality for reconstructing estimates of an object's three-dimensional x-ray refractive index distribution. Unlike conventional x-ray computed tomography methods, the statistical properties of the reconstructed images in PCT remain unexplored. The purpose of this work is to quantitatively investigate noise propagation in PCT image reconstruction. Methods: The authors derived explicit expressions for the autocovariance of the reconstructed absorption and refractive index images to characterize noise texture and understand how the noise properties are influenced by the imaging geometry. Concepts from statistical detection theory were employed to understand how the imaging geometry-dependent statistical properties affect the signal detection performance in a signal-known-exactly/background-known-exactly task. Results: The analytical formulas for the phase and absorption autocovariance functions were implemented numerically and compared to the corresponding empirical values, and excellent agreement was found. They observed that the reconstructed refractive images are highly spatially correlated, while the absorption images are not. The numerical results confirm that the strength of the covariance is scaled by the detector spacing. Signal detection studies were conducted, employing a numerical observer. The detection performance was found to monotonically increase as the detector-plane spacing was increased. Conclusions: The authors have conducted the firstmore » quantitative investigation of noise propagation in PCT image reconstruction. The reconstructed refractive images were found to be highly spatially correlated, while absorption images were not. This is due to the presence of a Fourier space singularity in the reconstruction formula for the refraction images. The statistical analysis may facilitate the use of task-based image quality measures to further develop and optimize this emerging modality for specific applications.« less

Tracking lung tissues during the respiratory cycle has been a challenging task for diagnostic CT and CT-guided radiotherapy. We propose an intensity- and landmark-based image registration algorithm to perform image registration and warping of 3D pulmonary CT image data sets, based on consistency constraints and matching corresponding airway branchpoints. In this paper, we demonstrate the effectivenss and accuracy of this algorithm in tracking lung tissues by both animal and human data sets. In the animal study, the result showed a tracking accuracy of 1.9 mm between 50% functional residual capacity (FRC) and 85% total lung capacity (TLC) for 12 metal seeds implanted in the lungs of a breathing sheep under precise volume control using a pulmonary ventilator. Visual inspection of the human subject results revealed the algorithm's potential not only in matching the global shapes, but also in registering the internal structures (e.g., oblique lobe fissures, pulmonary artery branches, etc.). These results suggest that our algorithm has significant potential for warping and tracking lung tissue deformation with applications in diagnostic CT, CT-guided radiotherapy treatment planning, and therapeutic effect evaluation.

Internal organ motion during the course of radiation therapy of cancer affects the distribution of the delivered dose and, generally, reduces its conformality to the targeted volume. Previously proposed approaches aimed at mitigating the effect of internal motion in intensity-modulated radiation therapy (IMRT) included expansion of the target margins, motion-correlated delivery (e.g., respiratory gating, tumor tracking), and adaptive treatment plan optimization employing a probabilistic description of motion. We describe and test the tumor trailing strategy, which utilizes the synergy of motion-adaptive treatment planning and delivery methods. We regard the (rigid) target motion as a superposition of a relatively fast cyclic component (e.g., respiratory) and slow aperiodic trends (e.g., the drift of exhalation baseline). In the trailing approach, these two components of motion are decoupled and dealt with separately. Real-time motion monitoring is employed to identify the "slow" shifts, which are then corrected by applying setup adjustments. The delivery does not track the target position exactly, but trails the systematic trend due to the delay between the time a shift occurs, is reliably detected, and, subsequently, corrected. The "fast" cyclic motion is accounted for with a robust motion-adaptive treatment planning, which allows for variability in motion parameters (e.g., mean and extrema of the tidal volume, variable period of respiration, and expiratory duration). Motion-surrogate data from gated IMRT treatments were used to provide probability distribution data for motion-adaptive planning and to test algorithms that identified systematic trends in the character of motion. Sample IMRT fields were delivered on a clinical linear accelerator to a programmable moving phantom. Dose measurements were performed with a commercial two-dimensional ion-chamber array. The results indicate that by reducing intrafractional motion variability, the trailing strategy enhances relevance and applicability of motion-adaptive planning methods, and improves conformality of the delivered dose to the target in the presence of irregular motion. Trailing strategy can be applied to respiratory-gated treatments, in which the correction for the slow motion can increase the duty cycle, while robust probabilistic planning can improve management of the residual motion within the gate window. Similarly, trailing may improve the dose conformality in treatment of patients who exhibit detectable target motion of low amplitude, which is considered insufficient to provide a clinical indication for the use of respiratory-gated treatment (e.g., peak-to-peak motion of less than 10 mm). The mechanical limitations of implementing tumor trailing are less rigorous than those of real-time tracking, and the same technology could be used for both.

Three-dimensional (3D) diffuse optical tomography is known to be a nonlinear, ill-posed and sometimes under-determined problem, where regularization is added to the minimization to allow convergence to a unique solution. In this work, a generalized least-squares (GLS) minimization method was implemented, which employs weight matrices for both data-model misfit and optical properties to include their variances and covariances, using a computationally efficient scheme. This allows inversion of a matrix that is of a dimension dictated by the number of measurements, instead of by the number of imaging parameters. This increases the computation speed up to four times per iteration in most of the under-determined 3D imaging problems. An analytic derivation, using the Sherman-Morrison-Woodbury identity, is shown for this efficient alternative form and it is proven to be equivalent, not only analytically, but also numerically. Equivalent alternative forms for other minimization methods, like Levenberg-Marquardt (LM) and Tikhonov, are also derived. Three-dimensional reconstruction results indicate that the poor recovery of quantitatively accurate values in 3D optical images can also be a characteristic of the reconstruction algorithm, along with the target size. Interestingly, usage of GLS reconstruction methods reduces error in the periphery of the image, as expected, and improves by 20% the ability to quantify local interior regions in terms of the recovered optical contrast, as compared to LM methods. Characterization of detector photo-multiplier tubes noise has enabled the use of the GLS method for reconstructing experimental data and showed a promise for better quantification of target in 3D optical imaging. Use of these new alternative forms becomes effective when the ratio of the number of imaging property parameters exceeds the number of measurements by a factor greater than 2.

The purpose of this study was to calculate internal absorbed dose distribution in mice from preclinical small animal PET imaging procedures with fluorine-18 labeled compounds ({sup 18}FDG, {sup 18}FLT, and fluoride ion). The GATE Monte Carlo software and a realistic, voxel-based mouse phantom that included a subcutaneous tumor were used to perform simulations. Discretized time-activity curves obtained from dynamic in vivo studies with each of the compounds were used to set the activity concentration in the simulations. For {sup 18}FDG, a realistic range of uptake ratios was considered for the heart and tumor. For each simulated time frame, the biodistribution of the radionuclide in the phantom was considered constant, and a sufficient number of decays were simulated to achieve low statistical uncertainty. Absorbed dose, which was scaled to take into account radioactive decay, integration with time, and changes in biological distribution was reported in mGy per MBq of administered activity for several organs and uptake scenarios. The mean absorbed dose ranged from a few mGy/MBq to hundreds of mGy/MBq. Major organs receive an absorbed dose in a range for which biological effects have been reported. The effects on a given investigation are hard to predict; however, investigators should be awaremore » of potential perturbations especially when the studied organ receives high absorbed dose and when longitudinal imaging protocols are considered.« less

Purpose: In x-ray computed tomography (CT), a violation of the Tuy data sufficiency condition leads to limited-view artifacts. In some applications, it is desirable to use data corresponding to a narrow temporal window to reconstruct images with reduced temporal-average artifacts. However, the need to reduce temporal-average artifacts in practice may result in a violation of the Tuy condition and thus undesirable limited-view artifacts. In this paper, the authors present a new iterative reconstruction method, synchronized multiartifact reduction with tomographic reconstruction (SMART-RECON), to eliminate limited-view artifacts using data acquired within an ultranarrow temporal window that severely violates the Tuy condition. Methods: In time-resolved contrast enhanced CT acquisitions, image contrast dynamically changes during data acquisition. Each image reconstructed from data acquired in a given temporal window represents one time frame and can be denoted as an image vector. Conventionally, each individual time frame is reconstructed independently. In this paper, all image frames are grouped into a spatial–temporal image matrix and are reconstructed together. Rather than the spatial and/or temporal smoothing regularizers commonly used in iterative image reconstruction, the nuclear norm of the spatial–temporal image matrix is used in SMART-RECON to regularize the reconstruction of all image time frames. This regularizer exploits the low-dimensional structure of the spatial–temporal image matrix to mitigate limited-view artifacts when an ultranarrow temporal window is desired in some applications to reduce temporal-average artifacts. Both numerical simulations in two dimensional image slices with known ground truth and in vivo human subject data acquired in a contrast enhanced cone beam CT exam have been used to validate the proposed SMART-RECON algorithm and to demonstrate the initial performance of the algorithm. Reconstruction errors and temporal fidelity of the reconstructed images were quantified using the relative root mean square error (rRMSE) and the universal quality index (UQI) in numerical simulations. The performance of the SMART-RECON algorithm was compared with that of the prior image constrained compressed sensing (PICCS) reconstruction quantitatively in simulations and qualitatively in human subject exam. Results: In numerical simulations, the 240∘ short scan angular span was divided into four consecutive 60∘ angular subsectors. SMART-RECON enables four high temporal fidelity images without limited-view artifacts. The average rRMSE is 16% and UQIs are 0.96 and 0.95 for the two local regions of interest, respectively. In contrast, the corresponding average rRMSE and UQIs are 25%, 0.78, and 0.81, respectively, for the PICCS reconstruction. Note that only one filtered backprojection image can be reconstructed from the same data set with an average rRMSE and UQIs are 45%, 0.71, and 0.79, respectively, to benchmark reconstruction accuracies. For in vivo contrast enhanced cone beam CT data acquired from a short scan angular span of 200∘, three 66∘ angular subsectors were used in SMART-RECON. The results demonstrated clear contrast difference in three SMART-RECON reconstructed image volumes without limited-view artifacts. In contrast, for the same angular sectors, PICCS cannot reconstruct images without limited-view artifacts and with clear contrast difference in three reconstructed image volumes. Conclusions: In time-resolved CT, the proposed SMART-RECON method provides a new method to eliminate limited-view artifacts using data acquired in an ultranarrow temporal window, which corresponds to approximately 60∘ angular subsectors.

Theoretical dose-response models offer the possibility to assess second cancer induction risks after external beam therapy. The parameters used in these models are determined with limited data from epidemiological studies. Risk estimations are thus associated with considerable uncertainties. This study aims at illustrating uncertainties when predicting the risk for organ-specific second cancers in the primary radiation field illustrated by choosing selected treatment plans for brain cancer patients.A widely used risk model was considered in this study. The uncertainties of the model parameters were estimated with reported data of second cancer incidences for various organs. Standard error propagation was then subsequently applied to assess the uncertainty in the risk model. Next, second cancer risks of five pediatric patients treated for cancer in the head and neck regions were calculated. For each case, treatment plans for proton and photon therapy were designed to estimate the uncertainties (a) in the lifetime attributable risk (LAR) for a given treatment modality and (b) when comparing risks of two different treatment modalities.Uncertainties in excess of 100% of the risk were found for almost all organs considered. When applied to treatment plans, the calculated LAR values have uncertainties of the same magnitude. A comparison between cancer risks of different treatment modalities, however, does allow statistically significant conclusions. In the studied cases, the patient averaged LAR ratio of proton and photon treatments was 0.35, 0.56, and 0.59 for brain carcinoma, brain sarcoma, and bone sarcoma, respectively. Their corresponding uncertainties were estimated to be potentially below 5%, depending on uncertainties in dosimetry.The uncertainty in the dose-response curve in cancer risk models makes it currently impractical to predict the risk for an individual external beam treatment. On the other hand, the ratio of absolute risks between two modalities is less sensitive to the uncertainties in the risk model and can provide statistically significant estimates.

The purpose of this study was to calculate a more accurate dose rate constant for the Cs-131 (model CS-1, IsoRay Medical, Inc., Richland, Washington) interstitial brachytherapy seed. Previous measurements of the dose rate constant for this seed have been reported by others with incongruity. Recent direct measurements by thermoluminescence dosimetry and by gamma-ray spectroscopy were about 15 percent greater than earlier thermoluminescence dosimetry measurements. Therefore, we set about to calculate independent values by a Monte Carlo approach that combined three estimates as a consistency check, and to quantify the computational uncertainty. The calculated dose rate constant for the Cs-131 seed was 1.040 cGy h^{-1} U^{-1} for an ionization chamber model and 1.032 cGy h^{-1} U^{-1} for a circular ring model. A formal value of 2.2% uncertainty was calculated for both values. The range of our multi-estimate values were from 1.032 cGy h^{-1} U^{-1} to 1.061 cGy h^{-1} U^{-1}. We also modeled three I-125 seeds with known dose rate constants to test the accuracy of this study's approach.

Sophisticated methods for real-time motion compensation include using the linear accelerator, MLC, or treatment couch. To design such a couch, the required couch and control system dynamics need to be investigated. We used an existing treatment couch known as the Hexapod{sup TM} to gain insight into couch dynamics and an internal model controller to simulate feedback control of respiration-induced motion. The couch dynamics, described using time constants and dead times, were investigated using step inputs. The resulting data were modeled as first and second order systems with dead time. The couch was determined to have a linear response for step inputs {

Digital tomosynthesis mammography (DTM) is a promising new modality for breast cancer detection. In DTM, projection-view images are acquired at a limited number of angles over a limited angular range and the imaged volume is reconstructed from the two-dimensional projections, thus providing three-dimensional structural information of the breast tissue. In this work, we investigated three representative reconstruction methods for this limited-angle cone-beam tomographic problem, including the backprojection (BP) method, the simultaneous algebraic reconstruction technique (SART) and the maximum likelihood method with the convex algorithm (ML-convex). The SART and ML-convex methods were both initialized with BP results to achieve efficient reconstruction. A second generation GE prototype tomosynthesis mammography system with a stationary digital detector was used for image acquisition. Projection-view images were acquired from 21 angles in 3 degrees increments over a +/- 30 degrees angular range. We used an American College of Radiology phantom and designed three additional phantoms to evaluate the image quality and reconstruction artifacts. In addition to visual comparison of the reconstructed images of different phantom sets, we employed the contrast-to-noise ratio (CNR), a line profile of features, an artifact spread function (ASF), a relative noise power spectrum (NPS), and a line object spread function (LOSF) to quantitatively evaluate the reconstruction results. It was found that for the phantoms with homogeneous background, the BP method resulted in less noisy tomosynthesized images and higher CNR values for masses than the SART and ML-convex methods. However, the two iterative methods provided greater contrast enhancement for both masses and calcification, sharper LOSF, and reduced interplane blurring and artifacts with better ASF behaviors for masses. For a contrast-detail phantom with heterogeneous tissue-mimicking background, the BP method had strong blurring artifacts along the x-ray source motion direction that obscured the contrast-detail objects, while the other two methods can remove the superimposed breast structures and significantly improve object conspicuity. With a properly selected relaxation parameter, the SART method with one iteration can provide tomosynthesized images comparable to those obtained from the ML-convex method with seven iterations, when BP results were used as initialization for both methods.

The normal tissue complication probability (NTCP) is a predictor of radiobiological effect for organs at risk (OAR). The calculation of the NTCP is based on the dose-volume-histogram (DVH) which is generated by the treatment planning system after calculation of the 3D dose distribution. Including the NTCP in the objective function for intensity modulated radiation therapy (IMRT) plan optimization would make the planning more effective in reducing the postradiation effects. However, doing so would lengthen the total planning time. The purpose of this work is to establish a method for NTCP determination, independent of a DVH calculation, as a quality assurance check and also as a mean of improving the treatment planning efficiency. In the study, the CTs of ten randomly selected prostate patients were used. IMRT optimization was performed with a PINNACLE3 V 6.2b planning system, using planning target volume (PTV) with margins in the range of 2 to 10 mm. The DVH control points of the PTV and OAR were adapted from the prescriptions of Radiation Therapy Oncology Group protocol P-0126 for an escalated prescribed dose of 82 Gy. This paper presents a new model for the determination of the rectal NTCP (R(NTCP)). The method uses a special function, named GVN (from Gy, Volume, NTCP), which describes the R(NTCP) if 1 cm3 of the volume of intersection of the PTV and rectum (R(int)) is irradiated uniformly by a dose of 1 Gy. The function was "geometrically" normalized using a prostate-prostate ratio (PPR) of the patients' prostates. A correction of the R(NTCP) for different prescribed doses, ranging from 70 to 82 Gy, was employed in our model. The argument of the normalized function is the R(int), and parameters are the prescribed dose, prostate volume, PTV margin, and PPR. The R(NTCPs) of another group of patients were calculated by the new method and the resulting difference was < +/- 5% in comparison to the NTCP calculated by the PINNACLE3 software where Kutcher's dose-response model for NTCP calculation is adopted.

The aim of this work is to create a model to predict the noise power spectra (NPS) for a range of mammographic radiographic factors. The noise model was necessary to degrade images acquired on one system to match the image quality of different systems for a range of beam qualities.Five detectors and x-ray systems [Hologic Selenia (ASEh), Carestream computed radiography CR900 (CRc), GE Essential (CSI), Carestream NIP (NIPc), and Siemens Inspiration (ASEs)] were characterized for this study. The signal transfer property was measured as the pixel value against absorbed energy per unit area (E) at a reference beam quality of 28 kV, Mo/Mo or 29 kV, W/Rh with 45 mm polymethyl methacrylate (PMMA) at the tube head. The contributions of the three noise sources (electronic, quantum, and structure) to the NPS were calculated by fitting a quadratic at each spatial frequency of the NPS against E. A quantum noise correction factor which was dependent on beam quality was quantified using a set of images acquired over a range of radiographic factors with different thicknesses of PMMA. The noise model was tested for images acquired at 26 kV, Mo/Mo with 20 mm PMMA and 34 kV, Mo/Rh with 70 mm PMMA for three detectors (ASEh, CRc, and CSI) over a range of exposures. The NPS were modeled with and without the noise correction factor and compared with the measured NPS. A previous method for adapting an image to appear as if acquired on a different system was modified to allow the reference beam quality to be different from the beam quality of the image. The method was validated by adapting the ASEh flat field images with two thicknesses of PMMA (20 and 70 mm) to appear with the imaging characteristics of the CSI and CRc systems.The quantum noise correction factor rises with higher beam qualities, except for CR systems at high spatial frequencies, where a flat response was found against mean photon energy. This is due to the dominance of secondary quantum noise in CR. The use of the quantum noise correction factor reduced the difference from the model to the real NPS to generally within 4%. The use of the quantum noise correction improved the conversion of ASEh image to CRc image but had no difference for the conversion to CSI images.A practical method for estimating the NPS at any dose and over a range of beam qualities for mammography has been demonstrated. The noise model was incorporated into a methodology for converting an image to appear as if acquired on a different detector. The method can now be extended to work for a wide range of beam qualities and can be applied to the conversion of mammograms.

Peripheral dose in radiotherapy treatments represents a potential source of secondary neoplasic processes. As in the last few years, there has been a fast-growing concern on neutron collateral effects, this work focuses on this component. A previous established methodology to estimate peripheral neutron equivalent doses relied on passive (TLD, CR39) neutron detectors exposed in-phantom, in parallel to an active [static random access memory (SRAMnd)] thermal neutron detector exposed ex-phantom. A newly miniaturized, quick, and reliable active thermal neutron detector (TNRD, Thermal Neutron Rate Detector) was validated for both procedures. This first miniaturized active system eliminates the long postprocessing, required for passive detectors, giving thermal neutron fluences in real time.To validate TNRD for the established methodology, intrinsic characteristics, characterization of 4 facilities [to correlate monitor value (MU) with risk], and a cohort of 200 real patients (for second cancer risk estimates) were evaluated and compared with the well-established SRAMnd device. Finally, TNRD was compared to TLD pairs for 3 generic radiotherapy treatments through 16 strategic points inside an anthropomorphic phantom.The performed tests indicate similar linear dependence with dose for both detectors, TNRD and SRAMnd, while a slightly better reproducibility has been obtained for TNRD (1.7% vs 2.2%). Risk estimates when delivering 1000 MU are in good agreement between both detectors (mean deviation of TNRD measurements with respect to the ones of SRAMnd is 0.07 cases per 1000, with differences always smaller than 0.08 cases per 1000). As far as the in-phantom measurements are concerned, a mean deviation smaller than 1.7% was obtained.The results obtained indicate that direct evaluation of equivalent dose estimation in organs, both in phantom and patients, is perfectly feasible with this new detector. This will open the door to an easy implementation of specific peripheral neutron dose models for any type of treatment and facility.

We present EGS4 Monte Carlo calculations of the spatial distribution of the dose deposited by a single x-ray pencil beam, a planar microbeam, and an array of parallel planar microbeams as used in radiation therapy research. The profiles of the absorbed dose distribution in a phantom, including the peak-to-valley ratio of the dose distribution from microbeam arrays, were calculated at micrometer resolution. We determined the dependence of the findings on the main parameters of photon and electron transport. The results illustrate the dependence of the electron range and the deposited in-beam dose on the cut-off energy, of the electron transport, as well as the effects on the dose profiles of the beam energy, the array size, and the beam spacing. The effect of beam polarization also was studied for a single pencil beam and for an array of parallel planar microbeams. The results show that although the polarizationeffect on the dose distribution from a 3 cm × 3 cm microbeam array inside a water phantom is large enough to be measured at the outer side of the array (16% difference of the deposited dose for x-ray beams of 200 keV), it is not detectable at the array’s center, thus being irrelevant for the radiation therapy purposes. Finally we show that to properly compare the dose profiles determined with a metal oxide semiconductor field emission transistordetector with the computational method predictions, it is important to simulate adequately the size and the material of the device’s Si active element.