Stochastic modeling of geometrical uncertainties on complex domains, with application to additive manufacturing and brain interface geometries.

We present a stochastic modeling framework to represent and simulate spatially-dependent geometrical uncertainties on complex geometries. While the consideration of random geometrical perturbations has long been a subject of interest in computational engineering, most studies proposed so far have addressed the case of regular geometries such as cylinders and plates. Here, standard random field representations, such as Kahrunen-Loève expansions, can readily be used owing, in particular, to the relative simplicity to construct covariance operators on regular shapes. On the contrary, applying such techniques on arbitrary, non-convex domains remains difficult in general. In this work, we formulate a new representation for spatially-correlated geometrical uncertainties that allows complex domains to be efficiently handled. Building on previous contributions by the authors, the approach relies on the combination of a stochastic partial differential equation approach, introduced to capture salient features of the underlying geometry such as local curvature and singularities on the fly, and an information-theoretic model, aimed to enforce non-Gaussianity. More specifically, we propose a methodology where the interface of interest is immersed into a fictitious domain, and define algorithmic procedures to directly sample random perturbations on the manifold. A simple strategy based on statistical conditioning is also presented to update realizations and prevent self-intersections in the perturbed finite element mesh. We finally provide challenging examples to demonstrate the robustness of the framework, including the case of a gyroid structure produced by additive manufacturing and brain interfaces in patient-specific geometries. In both applications, we discuss suitable parameterization for the filtering operator and quantify the impact of the uncertainties through forward propagation.

Estimation of delivered dose to lung tumours considering setup uncertainties and breathing motion in a cohort of patients treated with stereotactic body radiation therapy.

INTRODUCTION: Dose-response relationships for local control of lung tumours treated with stereotactic body radiotherapy (SBRT) have proved ambiguous, however, these have been based on the prescribed or planned dose. Delivered dose to the target may be a better predictor for local control. In this study, the probability of the delivered minimum dose to the clinical target volume (CTV) in relation to the prescribed dose was estimated for a cohort of patients, considering geometrical uncertainties. MATERIALS AND METHODS: Delivered doses were retrospectively simulated for 50 patients treated with SBRT for lung tumours, comparing two image-guidance techniques: pre-treatment verification computed tomography (IG1) and online cone-beam computed tomography (IG2). The prescribed dose was typically to the 67% isodose line of the treatment plan. Simulations used in-house software that shifted the static planned dose according to a breathing motion and sampled setup/matching errors. Each treatment was repeatedly simulated, generating a multiplicity of dose-volume histograms (DVH). From these, tumour-specific and population-averaged statistics were derived. RESULTS: For IG1, the probability that the minimum CTV dose (D98%) exceeded 100% of the prescribed dose was 90%. With IG2, this probability increased to 99%. CONCLUSIONS: Doses below the prescribed dose were delivered to a considerably larger part of the population prior to the introduction of online soft-tissue image-guidance. However, there is no clear evidence that this impacts local control, when compared to previous published data.

A pilot study on geometrical uncertainties for intra ocular cancers in radiotherapy.

A system for stabilising and monitoring eye movements for linac-based stereotactic radiotherapy associated with the mobile eye, the Eye Tracker, was developed. Whilst the Eye Tracker design is based on a previously reported system, the purpose of this study was to confirm that the modified version can be used with clinically acceptable treatment margins. We report the estimates of the margin required to account for inter- and intra-fraction eye motion based on data from 12 consecutive patients treated with the Eye Tracker system in place. Patients were immobilised in a head and neck mask and were required to fixate on a light source. A camera system monitored eye movements relative to CT simulation baseline measurements. The Exactrac system (Brainlab, Feldkirchen, Germany) combined with the Varian TrueBeamSTx (Varian Medical Systems, Palo Alto, CA) confirmed pre- and intra-treatment setup of the head position. Displacement/rotation of the image of the pupil/iris was determined in the lateral and superior-inferior directions using a video display. A standard margin equation was applied to estimate the margin required to account for inter- and intra-fraction eye movement. The average displacement in both directions was 0.1-0.2 mm (0.36 mm SD). All patients maintained a position within 1 mm of the intended position during treatment. Based on a Bayesian estimation of the systematic and treatment errors, accounting for displacements in two-planes and a standard deviation of the penumbral width of 1.3 mm, the estimated margins to achieve coverage of the GTV with the 95% isodose in 90% of patients was found to be less than 1 mm. Small random and systematic uncertainties due to inter- and intra-fraction movement of the eye were achieved with the Eye Tracker. Whilst the estimated margins are small (<1 mm) they need to be considered in addition to contouring and treatment delivery uncertainties.

Geometric uncertainties in voluntary deep inspiration breath hold radiotherapy for locally advanced lung cancer.

BACKGROUND AND PURPOSE: Deep inspiration breath hold (DIBH) increases lung volume and can potentially reduce treatment-related toxicity in locally advanced lung cancer. We estimated geometric uncertainties in visually guided voluntary DIBH and derived the appropriate treatment margins for different image-guidance strategies. MATERIAL AND METHODS: Seventeen patients were included prospectively. An optical marker-based respiratory monitoring with visual guidance enabled comfortable DIBHs, adjusted to each patient's performance. All patients had three consecutive DIBH CTs at each of the treatment fractions 2, 16 and 31. DIBH reproducibility was evaluated as inter- and intra-fractional variations in lung volume, tumour position and differential motion between primary tumour and mediastinal lymph nodes. RESULTS: Lung volume increased by median 60% in DIBH. Inter- and intra-fractional lung volume variations were median 2.1% and 1.1%, respectively. Inter- and intra-fractional uncertainties in 3D tumour position were 4.8 ± 2.8 mm and 1.7 ± 1.4 mm (mean ± SD). Inter- and intra-fractional differential motion was 4.8 ± 3.3 mm and 0.0 ± 1.1 mm. CONCLUSIONS: For single targets, visually guided voluntary DIBH radiotherapy is highly reproducible provided an image-guidance strategy with tumour registration is performed. If the primary tumour is separated from the mediastinal lymph nodes, inter-fractional differential motion remains a challenge and margins must be adapted to reflect the image registration strategy.

Analysis geometrical uncertainties of 220 cases in helical tomotherapy (HT) / 中华放射肿瘤学杂志

Objective To analyze geometrical uncertainties of the target and provide the margin enlarging from clinic target volume (CTV) to planning target volume (PTV) with HT.Methods Analysis set-up data of 220 cases include 97 cases of head and neck,45 cases of chest and 78 cases of abdomen and pelvic,calculating the systematic error (Σ) and the random error (σ) in the three-dimension and check whether the set-up data accord with the normal distribution or not,then acquire the values expand in the three directions based on formula 2.0Σ + 0.7σandμ ± 2.58σ.Results The systematic error (Σ) and random error (σ) of head and neck,the chest and abdomen and pelvic were (0.7-1.9 mm,1.1-1.4 mm),(0.8-4.2 mm,1.5-3.2 mm),(1.1-4.1 mm,1.8-4.1 mm),respectively,and the margin that expand in the direction of x,y,z were (5.2,6.5,7.7 mum),(7.5,16.2,10.3 mm),(7.6,17.1,15.7 mm),respectively.Conclusions The curative effect of this task need prove with a large sample during HT,but other should establish data of margin by yourself.