Remote EPID-based dosimetric auditing using DVH patient dose analysis.

Objective.The aim of this work was to develop and validate a method for remote dosimetric auditing that enables dose-volume histogram parameter comparisons of measured and planned dose in the patient CT volume.Approach. The method is derived by adapting and combining a remote electronic portal imaging (EPID) based auditing method (Virtual Epid based Standard Phantom Audit-VESPA) and a method to estimate 3D in-patient dose distributions from planar dosimetric measurements. The method was tested with a series of error-induced plans including monitor unit and multileaf collimator (MLC) positioning errors. A pilot audit study was conducted with eleven radiotherapy centres. IMRT plans from two clinical trials, a post-prostatectomy (RAVES trial) plan and a head and neck (HPV trial) plan were utilized. Clinically relevant DVH parameters for the planned dose and estimated measured dose were compared.Main results. The method was found to reproduce the induced dose errors within 0.5% and was sensitive to MLC positioning errors as small as 0.5 mm. For the RAVES plan audit all DVH results except one were within 3% and for the HPV plan audit all DVH results were within 3% except three with a maximum difference of 3.2%.Significance. The results from the audit method produce clinically meaningful DVH metrics for the audited plan and could enable an improved understanding of a centre's radiotherapy quality.

A high-performance method of deep learning for prostate MR-only radiotherapy planning using an optimized Pix2Pix architecture.

PURPOSE: The first aim was to generate and compare synthetic-CT (sCT) images using a conditional generative adversarial network (cGAN) method (Pix2Pix) for MRI-only prostate radiotherapy planning by testing several generators, loss functions, and hyper-parameters. The second aim was to compare the optimized Pix2Pix model with five other architectures (bulk-density, atlas-based, patch-based, U-Net, and GAN). METHODS: For 39 patients treated by VMAT for prostate cancer, T2-weighted MRI images were acquired in addition to CT images for treatment planning. sCT images were generated using the Pix2Pix model. The generator, loss function, and hyper-parameters were tuned to improve sCT image generation (in terms of imaging endpoints). The final evaluation was performed by 3-fold cross-validation. This method was compared to five other methods using the following imaging endpoints: the mean absolute error (MAE) and mean error (ME) between sCT and reference CT images (rCT) of the whole pelvis, bones, prostate, bladder, and rectum. For dose planning analysis, the dose-volume histogram metric differences and 3D gamma analysis (local, 1 %/1 mm) were calculated using the sCT and reference CT images. RESULTS: Compared with the other architectures, Pix2Pix with Perceptual loss function and generator ResNet 9 blocks showed the lowest MAE (29.5, 107.7, 16.0, 13.4, and 49.1 HU for the whole pelvis, bones, prostate, bladder, and rectum, respectively) and the highest gamma passing rates (99.4 %, using the 1 %/1mm and 10 % dose threshold criterion). Concerning the DVH points, the mean errors were -0.2% for the planning target volume V95%, 0.1 % for the rectum V70Gy, and -0.1 % for the bladder V50Gy. CONCLUSION: The sCT images generated from MRI data with the Pix2Pix architecture had the lowest image errors and similar dose uncertainties (in term of gamma pass-rate and dose-volume histogram metric differences) than other deep learning methods.

Long-term two-dimensional pixel stability of EPIDs used for regular linear accelerator quality assurance.

The long-term stability of three clinical electronic portal imaging devices (EPIDs) was studied to determine if longer times between calibrations can be justified. This would make alternatives to flood-field calibration of EPIDs clinically feasible, allowing for more effective use of EPIDs for dosimetry. Images were acquired monthly for each EPID as part of regular clinical quality assurance over a time period of approximately 3 years. The images were analysed to determine (1) the long-term stability of the EPID positioning system, (2) the dose response of the central pixels and (3) the long term stability of each pixel in the imager. The position of the EPID was found to be very repeatable with variations less than 0.3 pixels (0.27 mm) for all imagers (1 standard deviation). The central axis dose response was found to reliably track ion chamber measurements to better than 0.5%. The mean variation in pixel response (1 standard deviation), averaged over all pixels in the EPID, was found to be at most 0.6% for the three EPIDs studied over the entire period. More than 99% of pixels in each EPID showed less than 1% variation. Since the EPID response was found to be very stable over long periods of time, an annual calibration should be sufficient in most cases. More complex dosimetric calibrations should be clinically feasible.

Dosimetric properties of an amorphous-silicon EPID used in continuous acquisition mode for application to dynamic and arc IMRT.

Dosimetric properties of an amorphous-silicon electronic portal imaging device (EPID) operated in a real-time acquisition mode were investigated. This mode will be essential for time-resolved dose verification of dynamic (sliding window) intensity modulated radiation therapy (IMRT) and intensity modulated arc radiation therapy (arc-IMRT). The EPID was used in continuous acquisition mode (i.e., "cine" mode) where individual sequential image frames are acquired in real time. The properties studied include dose linearity, reproducibility of response, and image stability. Results of using the continuous acquisition mode with several example treatments including dynamic IMRT, arc treatment, and single-arc-IMRT are compared to results using the well-studied integrated acquisition mode (i.e., "frame averaging" or "IMRT" mode). Real-time EPID response was also compared to real-time ion-chamber data for selected points in the deliveries. The example treatment deliveries in both continuous and integrated acquisition modes were converted to arbitrary EPID dose units via a calibration field. The summation of all acquired continuous mode images was compared using percentage dose difference to the single image acquired in the integrated mode using in-field pixels only (defined as those pixels > 10% of maximum, in-field signal). Using the continuous acquisition mode, the EPID response was not linear with dose. It was found that the continuous mode dose response corresponded approximately to dropping one image per acquisition session. Reproducibility of EPID response to low monitor units (MUs) was found to be poor but greatly improved with increasing MU. Open field profiles were found to be stable in the cross-plane direction but required several frames to become stable in the in-plane direction. However, both of these issues are clinically insignificant due to arc-IMRT deliveries requiring relatively large monitor units (> 100 MU). Analysis of the five IMRT, arc, and arc-IMRT tests revealed that all examples compared to within 2% of maximum dose for more than 95% of in-field pixels. The continuous acquisition mode is suited to time-resolved dosimetry applications including arc-IMRT and dynamic IMRT, giving comparable dose results to the well-studied integrated acquisition mode, although caution should be used in low MU applications. Time-resolved EPID dose information also compared well to time-resolved ion-chamber measurements.

CT-ED conversion on a GE Lightspeed-RT scanner: influence of scanner settings.

The influence of tube voltage (kV) and current (mA) on the resulting relationship of computed tomography number to electron density (CT-ED) was investigated for a wide-bore GE scanner. The influence of kV and mA scan settings were examined in combination with a 16-bit image reconstruction algorithm made available via the scanner software and which allowed resolution of CT numbers for high density materials. By using titanium and stainless steel inserts in an electron density phantom, mA variation was found to have minimal impact on the CT-ED relationship, whereas variation in kV led to significant differences in CT number for the high density materials. The scanner is also equipped with automatic tube-current modulation capabilities. The influence of automatic tube-current modulation on CT number was investigated for a range of materials in a phantom geometry. It was found that tube current modulation has negligible effect on CT number, though the changing dimension of the phantom did influence CT number of an aluminium insert for scans undertaken with both fixed and modulated tube currents. In light of evidence from other studies examining the influence of CT number on dose calculation, it is recommended that scanner settings and specific CT-ED look-up tables be considered when calculations will be required with high-density materials present.

Software tool for portal dosimetry research.

This paper describes a software tool developed for research into the use of an electronic portal imaging device (EPID) to verify dose for intensity modulated radiation therapy (IMRT) beams. A portal dose image prediction (PDIP) model that predicts the EPID response to IMRT beams has been implemented into a commercially available treatment planning system (TPS). The software tool described in this work was developed to modify the TPS PDIP model by incorporating correction factors into the predicted EPID image to account for the difference in EPID response to open beam radiation and multileaf collimator (MLC) transmitted radiation. The processes performed by the software tool include; i) read the MLC file and the PDIP from the TPS, ii) calculate the fraction of beam-on time that each point in the IMRT beam is shielded by MLC leaves, iii) interpolate correction factors from look-up tables, iv) create a corrected PDIP image from the product of the original PDIP and the correction factors and write the corrected image to file, v) display, analyse, and export various image datasets. The software tool was developed using the Microsoft Visual Studio.NET framework with the C# compiler. The operation of the software tool was validated. This software provided useful tools for EPID dosimetry research, and it is being utilised and further developed in ongoing EPID dosimetry and IMRT dosimetry projects.

Correlations between contouring similarity metrics and simulated treatment outcome for prostate radiotherapy.

Many similarity metrics exist for inter-observer contouring variation studies, however no correlation between metric choice and prostate cancer radiotherapy dosimetry has been explored. These correlations were investigated in this study. Two separate trials were undertaken, the first a thirty-five patient cohort with three observers, the second a five patient dataset with ten observers. Clinical and planning target volumes (CTV and PTV), rectum, and bladder were independently contoured by all observers in each trial. Structures were contoured on T2-weighted MRI and transferred onto CT following rigid registration for treatment planning in the first trial. Structures were contoured directly on CT in the second trial. STAPLE and majority voting volumes were generated as reference gold standard volumes for each structure for the two trials respectively. VMAT treatment plans (78 Gy to PTV) were simulated for observer and gold standard volumes, and dosimetry assessed using multiple radiobiological metrics. Correlations between contouring similarity metrics and dosimetry were calculated using Spearman's rank correlation coefficient. No correlations were observed between contouring similarity metrics and dosimetry for CTV within either trial. Volume similarity correlated most strongly with radiobiological metrics for PTV in both trials, including TCPPoisson (ρ = 0.57, 0.65), TCPLogit (ρ = 0.39, 0.62), and EUD (ρ = 0.43, 0.61) for each respective trial. Rectum and bladder metric correlations displayed no consistency for the two trials. PTV volume similarity was found to significantly correlate with rectum normal tissue complication probability (ρ = 0.33, 0.48). Minimal to no correlations with dosimetry were observed for overlap or boundary contouring metrics. Future inter-observer contouring variation studies for prostate cancer should incorporate volume similarity to provide additional insights into dosimetry during analysis.

Motion prediction in MRI-guided radiotherapy based on interleaved orthogonal cine-MRI.

In-room cine-MRI guidance can provide non-invasive target localization during radiotherapy treatment. However, in order to cope with finite imaging frequency and system latencies between target localization and dose delivery, tumour motion prediction is required. This work proposes a framework for motion prediction dedicated to cine-MRI guidance, aiming at quantifying the geometric uncertainties introduced by this process for both tumour tracking and beam gating. The tumour position, identified through scale invariant features detected in cine-MRI slices, is estimated at high-frequency (25 Hz) using three independent predictors, one for each anatomical coordinate. Linear extrapolation, auto-regressive and support vector machine algorithms are compared against systems that use no prediction or surrogate-based motion estimation. Geometric uncertainties are reported as a function of image acquisition period and system latency. Average results show that the tracking error RMS can be decreased down to a [0.2; 1.2] mm range, for acquisition periods between 250 and 750 ms and system latencies between 50 and 300 ms. Except for the linear extrapolator, tracking and gating prediction errors were, on average, lower than those measured for surrogate-based motion estimation. This finding suggests that cine-MRI guidance, combined with appropriate prediction algorithms, could relevantly decrease geometric uncertainties in motion compensated treatments.

Calculating radiotherapy margins based on Bayesian modelling of patient specific random errors.

Collected real-life clinical target volume (CTV) displacement data show that some patients undergoing external beam radiotherapy (EBRT) demonstrate significantly more fraction-to-fraction variability in their displacement ('random error') than others. This contrasts with the common assumption made by historical recipes for margin estimation for EBRT, that the random error is constant across patients. In this work we present statistical models of CTV displacements in which random errors are characterised by an inverse gamma (IG) distribution in order to assess the impact of random error variability on CTV-to-PTV margin widths, for eight real world patient cohorts from four institutions, and for different sites of malignancy. We considered a variety of clinical treatment requirements and penumbral widths. The eight cohorts consisted of a total of 874 patients and 27 391 treatment sessions. Compared to a traditional margin recipe that assumes constant random errors across patients, for a typical 4 mm penumbral width, the IG based margin model mandates that in order to satisfy the common clinical requirement that 90% of patients receive at least 95% of prescribed RT dose to the entire CTV, margins be increased by a median of 10% (range over the eight cohorts -19% to +35%). This substantially reduces the proportion of patients for whom margins are too small to satisfy clinical requirements.

Comparison of two methods for anterior-posterior isocenter localization in pelvic radiotherapy using electronic portal imaging.

PURPOSE: The two setup methods commonly used to determine the anterior-posterior isocenter location in pelvic radiotherapy are to align lateral localization lasers with lateral skin tattoos on the patient, or to set the couch height so that the isocenter is at a fixed height (determined during simulation or treatment planning) above the couch top. This study was implemented to determine which technique gives more accurate patient treatment by comparison of the anterior-posterior setup variation measured with electronic portal imaging. METHODS AND MATERIALS: Eleven supine prostate patients were treated with tattoo localization and 159 left-lateral portal images were taken during the treatments. The field displacements were then determined by template matching. These patients were compared to nine patients (205 images) set up to a fixed isocenter height. Similarly, eight prone rectal patients (136 right-lateral images) set up to tattoos were compared to six patients (108 images) set up to a fixed height. The patients were not immobilized and were all treated with three field techniques on a hard couch top. The overall mean treatment position deviation and the standard deviation of the displacements (total setup variation) were calculated for each patient group along with the systematic (simulator-to-treatment) and the random (treatment-to-treatment) setup variation. RESULTS: The mean treatment position deviations were 3.3 mm anterior and 5.2 mm posterior with the tattoo method for the prostate and rectal patients, respectively. These mean position deviations were 0.4/0.1 mm anterior with the fixed height technique. The total setup variations were 4.6/5.2 mm (1 SD) with tattoo localization and 1.7/1.5 mm (1 SD) with the fixed height method. Similarly, random variation was 2.3/3.3 mm (1 SD) with the tattoo method compared to 1.3/1.2 mm (1 SD) with the fixed height method. Systematic variation was 3.7/4.5 mm (1 SD) compared to 1.2/1.1 mm (1 SD). CONCLUSION: The fixed height technique gives much more accurate localization of the anterior-posterior isocenter in pelvic radiotherapy than lateral skin tattoos.

A design for a dual assembly multileaf collimator.

A multileaf collimator for radiation therapy has been designed that splits each leaf bank into two vertically displaced levels with each level consisting of alternate leaves and leaf spaces. The leaves in the upper level shield the spaces in the lower level. Each level can move laterally, in the direction perpendicular to leaf motion by one leaf width. Following lateral movement of one level, the leaves align with the other level and radiation is transmitted through the collimator as multiple slit fields in a grid pattern. This transmission can be used to form an image of the external anatomy and would enable double-exposure portal images to be acquired much more rapidly than at present. These could potentially be acquired during the treatment delivery. The radiation profiles transmitted for image formation through the collimator design were investigated. Individual and grid pattern slit field profiles formed by tungsten and lead alloy collimators were measured with varying slit width, source-collimator distance, collimator-detector distance, and collimation thickness. The slit width was found to have the major influence on the transmitted profiles. As the slit width decreases the profiles become broader than the geometric slit projection resulting in increasing overlap of adjacent profiles. The overlap results in a modulated image of the external anatomy for small slit widths, rather than a sampled or "grid" image for larger widths. The shielding of this design was found to be adequate provided the leaf faces of the adjacent vertically displaced leaves are at least aligned, therefore an overlap or tongue and groove is not required.

Evaluation of an algorithm for the assessment of the MTF using an edge method.

An algorithm to calculate the presampling modulation transfer function (MTF) of an imaging system from an angled edge image has its own inherent transfer function. Factors such as the angle of the sampling aperture to the edge, registration of edge function profiles using the determined edge angle, differentiation, smoothing, and folding all combine to produce the frequency response of the algorithm. In this work, the profile registration transfer function accounting for an error in the determined edge angle has been derived. This has been incorporated with other, previously reported, algorithm component transfer functions to fully characterize the MTF calculation algorithm. When registering profiles, small errors in the edge angle determination were found to result in large errors in the MTF, as the misalignment errors increase with the number of profiles. For example, registering 50 profiles a 0.07 degree error in a 7 degree edge angle (1% error) produces a 36% error in the MTF at the system cutoff frequency f=f(c) when profiles are oversampled at a frequency f(s)=8f(c)(f(c) is defined as the maximum frequency reproducible without aliasing when sampling at the limiting system Nyquist frequency f(s) = 2f(c)). These results highlight the importance of quantifying the transfer function of the algorithm used to determine an imaging system modulation transfer function. The MTF calculation algorithm and the transfer function analysis have been incorporated into a Windows-based software program to be made available for general use.

Anterior-posterior treatment localization in pelvic radiotherapy: tattoos or fixed couch-to-isocentre distance.

The methods of determining the anterior-posterior isocentre location in pelvic radiotherapy are either by aligning lateral localization lasers to tattoo marks on skin, or by setting a constant daily couch-to-isocentre distance. While using the former method the day-to-day vertical couch movement was recorded and combined with measurements of day-to-day anterior-posterior patient movement made with an electronic portal imaging device to determine whether couch vertical movement contributes to anterior-posterior setup variation. Seven unimmobilized patients were studied, four supine prostate and three prone rectum patients. The two motions were found to be highly correlated (correlation coefficient = 0.82) which supports the constant couch-to-isocentre distance approach. When the day-to-day couch vertical movement was subtracted from the anterior-posterior movement results the setup variation was reduced in six of the seven patients.

Image timing and detector performance of a matrix ion-chamber electronic portal imaging device.

Image timing and input/output characteristics of a Varian PortalVision matrix liquid ion-chamber electronic portal imaging device (EPID) used with a Varian CL2100C/D linear accelerator were investigated to examine the variation in image timing and detector performance with acquisition mode. Contrast-detail curves showed that the input/output results were indicative of the image quality variation with acquisition mode. Overall for this accelerator/EPID arrangement the 500 MU/min repetition rate gives the best image quality for the 6 MV and 18 MV acquisition modes.

The effect of leaf width and sampling distance on the "stair-stepping" of field borders defined by multileaf collimators.

Standard multileaf collimators (MLCs) are now available with 1.0 and 0.5 cm leaf widths. The aim of this work is to compare the dose-undulation and effective penumbra of field edges formed by these MLC leaf widths and to determine how reducing the sampling distance (centre-to-centre distance between adjacent MLC leaves) for the 1.0 cm leaf width compares to the smaller leaf width. The undulation of the 50% isodose line and the 80-20% and 80-30% effective penumbra were compared for a field edge angled at 45 degrees to the MLC leaf motion direction at 8 cm depth. The larger leaf width field was also segmented to form field edges with 0.5, 0.33 and 0.2 cm sampling distance. Random setup variation of 2 mm standard deviation was also incorporated. Dose undulation was 1.5 mm for the 0.5 cm MLC leaf width compared to 4.5 mm for the 1.0 cm width. The 80-20% effective penumbra was 2 mm less for the 0.5 cm leaf width and the 80-30% effective penumbra was approximately 3 mm less. When random setup variation was incorporated the 0.5 cm leaf width isodoses were straight compared with approximately 3 mm undulation for the larger MLC. Reducing the sampling distance for the 1.0 cm MLC leaf width to 0.33 cm resulted in penumbra only slightly greater than the 0.5 cm leaf width and removed the undulation. Effective penumbra and dose undulation are reduced for the 0.5 cm leaf width compared to a 1.0 cm leaf width. Reducing the sampling distance for the 1.0 cm MLC leaf can approximate the 0.5 cm leaf width, at the expense of longer treatment times, and increased quality assurance investment.

Reflected line spread function of the human ocular fundus.

Characterisation of the reflection from the fundus of the eye is important for the development of an improved theoretical description of photoscreening. Measurement has been made of the reflected line spread function of the human fundus in vivo using a slit-lamp microscope with video camera and frame-grabber. Line spread functions representative of red, green, and blue light were obtained from fundus sites just temporal to the macula, 10 degrees temporal to the macula, away from the macula temporal, and 30 degrees temporal to the macula. The results show that the lateral spreading of light is greatest for red light, and support the view that red light penetrates further into the fundus before being reflected than green or blue.

Simulation of real-time EPID images during IMRT using Monte-Carlo.

This study is part of a project concerned with real-time EPID-based verification of the incremental dose delivered during IMRT radiation treatments. Three automated Monte-Carlo methods are devised to calculate the differential dose delivered to the EPID during treatment. All methods break down the normalized total monitor units into a number of equally spaced segments. A method models the dynamic simulation as a series of static fields, each field corresponding to an IMRT segment or a sub-segment. Another method models each segment as a separate dynamic IMRT file. A third method, which modifies the DYNVMLC module of the BEAMnrc code, uses the full-MLC file. The MLC positions for the simulated photons are sequentially selected within DYNVMLC to correspond to individual segments of the delivery. A bash script calls the BEAM shared-library to calculate and store the EPID dose for each segment. Validation is performed by comparing the average dose contributed by all segments with the dose predicted by a canonical dynamic IMRT simulation that uses the same MLC file. The best results are achieved by the methods based on dynamic simulations (where leaf positions within a segment are interpolated for simulated photons) whose normalized root mean square error is at the most 0.2% over the focal area. EPID images can be predicted for individual segments (or smaller intervals) of an IMRT delivery using Monte-Carlo methods. The MLC file can be externally spliced or a simple modification of the DYNVMLC code can achieve accurate results.

MR simulation for prostate radiation therapy: effect of coil mounting position on image quality.

OBJECTIVE: To eliminate the effects of body deformation for MR-based prostate treatment planning, coil mounts are essential. In this study, we evaluated the effect of the coil set-up on image quality. METHODS: A custom-designed pelvic-shaped phantom was scanned by systematically increasing the anterior body-to-coil (BTC) distance from 30 to 90 mm. The image quality near the organs of interest was determined in order to characterize the relationship between image quality and BTC distance at the critical organ structures. The half intensity reduction (HIR) was calculated to determine the sensitivity of each organ structure to the BTC distance change. RESULTS: As the BTC distance increased, the uniformity reduced at 3% per millimetre. The HIR value indicated that the bladder signal is most sensitive to the change in BTC distance. By maintaining a constant BTC distance set-up, the intensity uniformity was improved by 28% along the B0 directions. CONCLUSION: Positioning the MRI coil on mounts can reduce body deformation but adversely degrades the image quality. The magnitude of this effect has been quantified for prostate MR simulation scanning. The coil needs to be positioned not only with a minimal but also uniform BTC distance in order to maximize image quality. ADVANCES IN KNOWLEDGE: A method to characterize the effect on image quality due to the use of coil mounts was demonstrated. Coil mounts whose height can be adjusted individually to keep BTC distance constant are necessary to maintain a uniform image across the entire field of view.

Model-based prediction of portal dose images during patient treatment.

PURPOSE: Dosimetric verification of radiation therapy is crucial when delivering complex treatments like intensity modulated radiation therapy (IMRT) or volumetric modulated arc therapy (VMAT. Pretreatment verification, characterized by methods applied without the patient present and before the treatment start date, is typically carried out at most centers. In vivo dosimetric verification, characterized by methods applied with the patient present, is not commonly carried out in the clinic. This work presents a novel, model-based EPID dosimetry method that could be used for routine clinical in vivo patient treatment verification. METHODS: The authors integrated a detailed fluence model with a patient scatter prediction model that uses a superposition of scatter energy fluence kernels, generated via Monte Carlo techniques, to determine patient scatter fluence delivered to the EPID. The total dose to the EPID was calculated using the sum of convolutions of the calculated energy fluence distribution entering the EPID with monoenergetic dose kernels, specific to the a-Si EPID. Measured images with simple, square fields delivered to slab phantoms were validated against predicted images. Measured and predicted images acquired during the delivery of IMRT fields to slabs and an anthropomorphic phantom were compared using the χ-comparison for 3% dose difference and 3 mm distance-to-agreement criteria. RESULTS: Predicted and measured images of the square fields with slabs in the field agreed within 2.5%. Predicted portal dose images of clinical IMRT fields delivered to slabs and an anthropomorphic phantom agreed with measured images within 3% and 3 mm for an average of at least 97% of the infield pixels (defined as >10% maximum field dose) for each case, over all fields. CONCLUSIONS: This work presents the first validation of the integration of a comprehensive fluence model with a patient and EPID radiation transport model that accounts for patient transmission, including complex factors such as patient scatter and the energy response of the a-Si detector. The portal dose image prediction model satisfies the 3% and 3 mm criteria for IMRT fields delivered to slab phantoms and could be used for patient treatment verification.

Finding the optimal statistical model to describe target motion during radiotherapy delivery--a Bayesian approach.

Early approaches to characterizing errors in target displacement during a fractionated course of radiotherapy assumed that the underlying fraction-to-fraction variability in target displacement, known as the 'treatment error' or 'random error', could be regarded as constant across patients. More recent approaches have modelled target displacement allowing for differences in random error between patients. However, until recently it has not been feasible to compare the goodness of fit of alternate models of random error rigorously. This is because the large volumes of real patient data necessary to distinguish between alternative models have only very recently become available. This work uses real-world displacement data collected from 365 patients undergoing radical radiotherapy for prostate cancer to compare five candidate models for target displacement. The simplest model assumes constant random errors across patients, while other models allow for random errors that vary according to one of several candidate distributions. Bayesian statistics and Markov Chain Monte Carlo simulation of the model parameters are used to compare model goodness of fit. We conclude that modelling the random error as inverse gamma distributed provides a clearly superior fit over all alternatives considered. This finding can facilitate more accurate margin recipes and correction strategies.