Automatic Segmentation of the Eye in 3D Magnetic Resonance Imaging: A novel Statistical Shape Model for treatment planning of Retinoblastoma

Purpose: Proper delineation of ocular anatomy in 3D imaging is a big challenge, particularly when developing treatment plans for ocular diseases. Magnetic Resonance Imaging (MRI) is nowadays utilized in clinical practice for the diagnosis confirmation and treatment planning of retinoblastoma in infants, where it serves as a source of information, complementary to the Fundus or Ultrasound imaging. Here we present a framework to fully automatically segment the eye anatomy in the MRI based on 3D Active Shape Models (ASM), we validate the results and present a proof of concept to automatically segment pathological eyes. Material and Methods: Manual and automatic segmentation were performed on 24 images of healthy children eyes (3.29±2.15 years). Imaging was performed using a 3T MRI scanner. The ASM comprises the lens, the vitreous humor, the sclera and the cornea. The model was fitted by first automatically detecting the position of the eye center, the lens and the optic nerve, then aligning the model and fitting it to the patient. We validated our segmentation method using a leave-one-out cross validation. The segmentation results were evaluated by measuring the overlap using the Dice Similarity Coefficient (DSC) and the mean distance error. Results: We obtained a DSC of 94.90±2.12% for the sclera and the cornea, 94.72±1.89% for the vitreous humor and 85.16±4.91% for the lens. The mean distance error was 0.26±0.09mm. The entire process took 14s on average per eye. Conclusion: We provide a reliable and accurate tool that enables clinicians to automatically segment the sclera, the cornea, the vitreous humor and the lens using MRI. We additionally present a proof of concept for fully automatically segmenting pathological eyes. This tool reduces the time needed for eye shape delineation and thus can help clinicians when planning eye treatment and confirming the extent of the tumor.

Stereological estimation of particle shape and orientation from volume tensors

In the present paper, we describe new robust methods of estimating cell shape and orientation in 3D from sections. The descriptors of 3D cell shape and orientation are based on volume tensors which are used to construct an ellipsoid, the Miles ellipsoid, approximating the average cell shape and orientation in 3D. The estimators of volume tensors are based on observations in several optical planes through sampled cells. This type of geometric sampling design is known as the optical rotator. The statistical behaviour of the estimator of the Miles ellipsoid is studied under a flexible model for 3D cell shape and orientation. In a simulation study, the lengths of the axes of the Miles ellipsoid can be estimated with CVs of about 2% if 100 cells are sampled. Finally, we illustrate the use of the developed methods in an example, involving neurons in the medial prefrontal cortex of rat.

Statistical modeling of the eye for multimodal treatment planning for external beam radiation therapy of intraocular tumors

Ocular anatomy and radiation-associated toxicities provide unique challenges for external beam radiation therapy. For treatment planning, precise modeling of organs at risk and tumor volume are crucial. Development of a precise eye model and automatic adaptation of this model to patients' anatomy remain problematic because of organ shape variability. This work introduces the application of a 3-dimensional (3D) statistical shape model as a novel method for precise eye modeling for external beam radiation therapy of intraocular tumors.

Validation of a statistical shape model-based 2D/3D reconstruction method for determination of cup orientation after THA

The aim of this study was to validate the accuracy and reproducibility of a statistical shape model-based 2D/3D reconstruction method for determining cup orientation after total hip arthroplasty. With a statistical shape model, this method allows reconstructing a patient-specific 3D-model of the pelvis from a standard AP X-ray radiograph. Cup orientation (inclination and anteversion) is then calculated with respect to the anterior pelvic plane that is derived from the reconstructed model.

Articulated Statistical Shape Model-Based 2D-3D Reconstruction of a Hip Joint

In this paper, reconstruction of three-dimensional (3D) patient-specific models of a hip joint from two-dimensional (2D) calibrated X-ray images is addressed. Existing 2D-3D reconstruction techniques usually reconstruct a patient-specific model of a single anatomical structure without considering the relationship to its neighboring structures. Thus, when those techniques would be applied to reconstruction of patient-specific models of a hip joint, the reconstructed models may penetrate each other due to narrowness of the hip joint space and hence do not represent a true hip joint of the patient. To address this problem we propose a novel 2D-3D reconstruction framework using an articulated statistical shape model (aSSM). Different from previous work on constructing an aSSM, where the joint posture is modeled as articulation in a training set via statistical analysis, here it is modeled as a parametrized rotation of the femur around the joint center. The exact rotation of the hip joint as well as the patient-specific models of the joint structures, i.e., the proximal femur and the pelvis, are then estimated by optimally fitting the aSSM to a limited number of calibrated X-ray images. Taking models segmented from CT data as the ground truth, we conducted validation experiments on both plastic and cadaveric bones. Qualitatively, the experimental results demonstrated that the proposed 2D-3D reconstruction framework preserved the hip joint structure and no model penetration was found. Quantitatively, average reconstruction errors of 1.9 mm and 1.1 mm were found for the pelvis and the proximal femur, respectively.

Comparison of 3D kinetic and hydrodynamic models to ROSINA-COPS measurements of the neutral coma of 67P/Churyumov-Gerasimenko

67P/Churyumov-Gerasimenko (67P) is a Jupiter-family comet and the object of investigation of the European Space Agency mission Rosetta. This report presents the first full 3D simulation results of 67P’s neutral gas coma. In this study we include results from a direct simulation Monte Carlo method, a hydrodynamic code, and a purely geometric calculation which computes the total illuminated surface area on the nucleus. All models include the triangulated 3D shape model of 67P as well as realistic illumination and shadowing conditions. The basic concept is the assumption that these illumination conditions on the nucleus are the main driver for the gas activity of the comet. As a consequence, the total production rate of 67P varies as a function of solar insolation. The best agreement between the model and the data is achieved when gas fluxes on the night side are in the range of 7% to 10% of the maximum flux, accounting for contributions from the most volatile components. To validate the output of our numerical simulations we compare the results of all three models to in situ gas number density measurements from the ROSINA COPS instrument. We are able to reproduce the overall features of these local neutral number density measurements of ROSINA COPS for the time period between early August 2014 and January 1 2015 with all three models. Some details in the measurements are not reproduced and warrant further investigation and refinement of the models. However, the overall assumption that illumination conditions on the nucleus are at least an important driver of the gas activity is validated by the models. According to our simulation results we find the total production rate of 67P to be constant between August and November 2014 with a value of about 1 × 10²⁶ molecules s⁻¹.

Single fluoroscopic image based 2D/3D reconstruction of a scaled, patient-specific vertebral model

Purpose Accurate three-dimensional (3D) models of lumbar vertebrae can enable image-based 3D kinematic analysis. The common approach to derive 3D models is by direct segmentation of CT or MRI datasets. However, these have the disadvantages that they are expensive, timeconsuming and/or induce high-radiation doses to the patient. In this study, we present a technique to automatically reconstruct a scaled 3D lumbar vertebral model from a single two-dimensional (2D) lateral fluoroscopic image. Methods Our technique is based on a hybrid 2D/3D deformable registration strategy combining a landmark-to-ray registration with a statistical shape model-based 2D/3D reconstruction scheme. Fig. 1 shows different stages of the reconstruction process. Four cadaveric lumbar spine segments (total twelve lumbar vertebrae) were used to validate the technique. To evaluate the reconstruction accuracy, the surface models reconstructed from the lateral fluoroscopic images were compared to the associated ground truth data derived from a 3D CT-scan reconstruction technique. For each case, a surface-based matching was first used to recover the scale and the rigid transformation between the reconstructed surface model Results Our technique could successfully reconstruct 3D surface models of all twelve vertebrae. After recovering the scale and the rigid transformation between the reconstructed surface models and the ground truth models, the average error of the 2D/3D surface model reconstruction over the twelve lumbar vertebrae was found to be 1.0 mm. The errors of reconstructing surface models of all twelve vertebrae are shown in Fig. 2. It was found that the mean errors of the reconstructed surface models in comparison to their associated ground truths after iterative scaled rigid registrations ranged from 0.7 mm to 1.3 mm and the rootmean squared (RMS) errors ranged from 1.0 mm to 1.7 mm. The average mean reconstruction error was found to be 1.0 mm. Conclusion An accurate, scaled 3D reconstruction of the lumbar vertebra can be obtained from a single lateral fluoroscopic image using a statistical shape model based 2D/3D reconstruction technique. Future work will focus on applying the reconstructed model for 3D kinematic analysis of lumbar vertebrae, an extension of our previously-reported imagebased kinematic analysis. The developed method also has potential applications in surgical planning and navigation.

Personalized X-Ray Reconstruction of the Proximal Femur via Intensity-Based Non-rigid 2D-3D Registration

This paper presents a new approach for reconstructing a patient-specific shape model and internal relative intensity distribution of the proximal femur from a limited number (e.g., 2) of calibrated C-arm images or X-ray radiographs. Our approach uses independent shape and appearance models that are learned from a set of training data to encode the a priori information about the proximal femur. An intensity-based non-rigid 2D-3D registration algorithm is then proposed to deformably fit the learned models to the input images. The fitting is conducted iteratively by minimizing the dissimilarity between the input images and the associated digitally reconstructed radiographs of the learned models together with regularization terms encoding the strain energy of the forward deformation and the smoothness of the inverse deformation. Comprehensive experiments conducted on images of cadaveric femurs and on clinical datasets demonstrate the efficacy of the present approach.

Reconstruction of patient-specific 3D bone surface from 2D calibrated fluoroscopic images and point distribution model

Reconstruction of patient-specific 3D bone surface from 2D calibrated fluoroscopic images and a point distribution model is discussed. We present a 2D/3D reconstruction scheme combining statistical extrapolation and regularized shape deformation with an iterative image-to-model correspondence establishing algorithm, and show its application to reconstruct the surface of proximal femur. The image-to-model correspondence is established using a non-rigid 2D point matching process, which iteratively uses a symmetric injective nearest-neighbor mapping operator and 2D thin-plate splines based deformation to find a fraction of best matched 2D point pairs between features detected from the fluoroscopic images and those extracted from the 3D model. The obtained 2D point pairs are then used to set up a set of 3D point pairs such that we turn a 2D/3D reconstruction problem to a 3D/3D one. We designed and conducted experiments on 11 cadaveric femurs to validate the present reconstruction scheme. An average mean reconstruction error of 1.2 mm was found when two fluoroscopic images were used for each bone. It decreased to 1.0 mm when three fluoroscopic images were used.

3D C-arm as an alternative modality to CT in postmortem imaging: technical feasibility

OBJECT: The aim of our study was to demonstrate the image quality of the new device using human cadavers, extending the horizon of available imaging modalities in forensic medicine. MATERIALS AND METHODS: Six human cadavers were examined, revealing C-arm data sets of the head, neck thorax, abdomen and pelvis. High-resolution mode was performed with 500 fluoroscopy shots during a 190 degrees orbital movement with a constant tube voltage of 100 kV and a current of 4.6 mA. Based on these data sets subsequent three-dimensional reconstructions were generated. RESULTS: Reconstructed data sets revealed high-resolution images of all skeletal structures in a near-CT quality. The same image quality was available in all reconstruction planes. Artefacts caused by restorative dental materials are less accentuated in CBCT data sets. The system configuration was not powerful enough to generate sufficient images of intracranial structures. CONCLUSION: After the here-demonstrated encouraging preliminary results, the forensic indications that would be suitable for imaging with a 3D C-arm have to be defined. Promising seems the visualization local limited region of interest as the cervical spine or the facial skeleton.

Statistical shape analysis via principal factor analysis

Statistical shape analysis techniques commonly employed in the medical imaging community, such as active shape models or active appearance models, rely on principal component analysis (PCA) to decompose shape variability into a reduced set of interpretable components. In this paper we propose principal factor analysis (PFA) as an alternative and complementary tool to PCA providing a decomposition into modes of variation that can be more easily interpretable, while still being a linear efficient technique that performs dimensionality reduction (as opposed to independent component analysis, ICA). The key difference between PFA and PCA is that PFA models covariance between variables, rather than the total variance in the data. The added value of PFA is illustrated on 2D landmark data of corpora callosa outlines. Then, a study of the 3D shape variability of the human left femur is performed. Finally, we report results on vector-valued 3D deformation fields resulting from non-rigid registration of ventricles in MRI of the brain.

Multiscale methods for shape constraints in deconvolution: Confidence statements for qualitative features

We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We investigate the moderately ill-posed setting, where the Fourier transform of the error density in the deconvolution model is of polynomial decay. For multiscale testing, we consider a calibration, motivated by the modulus of continuity of Brownian motion. We investigate the performance of our results from both the theoretical and simulation based point of view. A major consequence of our work is that the detection of qualitative features of a density in a deconvolution problem is a doable task, although the minimax rates for pointwise estimation are very slow.