Anterior pelvic plane estimation for total hip arthroplasty using a joint ultrasound and statistical shape model based approach

Orienting properly the prosthetic cup in total hip arthroplasty is key to ensure the postoperative stability. Several navigation solutions have been developed to assist surgeons in orienting the cup regarding the anterior pelvic plane (APP), defined by both anterior superior iliac spines (ASIS) and the pubic symphysis. However acquiring the APP when the patient is ready for surgery, i.e., mainly in lateral decubitus, is difficult due to the contralateral ASIS being against the operating table. We propose a method to determine the APP from both (1) alternative anatomical landmarks which are easy to acquire with a navigated ultrasound probe and (2) a Statistical Shape Model (SSM) of the pelvis. After creating a pelvic SSM from 40 data, a SSM-based morphometric analysis has been carried out to identify the best anatomical landmarks allowing the easy determination of the APP. The proposed method has then been assessed with both in silico and in vivo experiments on respectively forty synthetic data, and five healthy volunteers. The in silico experiment shows the feasibility to determine the APP with an average error of 4.7^∘ by only acquiring the iliac crest, the anterior superior iliac spine, the anterior inferior iliac spine, and the pubic symphysis. The average in vivo error using the ultrasound modality was 7.3^∘ with an estimated impact on both the cup anteversion and inclination of 4.0^∘ and 1.7^∘ respectively. The proposed method shows promising results that could allow the determination of the APP in lateral decubitus with a clinically acceptable impact on the computation of the cup orientation.

Three-dimensional muscle loss assessment: a novel computed tomography-based quantitative method to evaluate rotator cuff muscle fatty infiltration

BACKGROUND

Rotator cuff fatty infiltration (FI) is one of the most important parameters to predict the outcome of certain shoulder conditions. The primary objective of this study was to define a new computed tomography (CT)-based quantitative 3-dimensional (3D) measure of muscle loss (3DML) based on the rationale of the 2-dimensional (2D) qualitative Goutallier score. The secondary objective of this study was to compare this new measurement method to traditional 2D qualitative assessment of FI according to Goutallier et al and to a 3D quantitative measurement of fatty infiltration (3DFI).

MATERIALS AND METHODS

102 CT scans from healthy shoulders (46) and shoulders with cuff tear arthropathy (21), irreparable rotator cuff tears (18), and primary osteoarthritis (17) were analyzed by 3 experienced shoulder surgeons for subjective grading of fatty infiltration according to Goutallier, and their rotator cuff muscles were manually segmented. Quantitative 3D measurements of fatty infiltration (3DFI) were completed. The volume of muscle fibers without intramuscular fat was then calculated for each rotator cuff muscle and normalized to the patient's scapular volume to account for the effect of body size (NV_fibers). 3D muscle mass (3DMM) was calculated by dividing the NV_fibers value of a given muscle by the mean expected volume in healthy shoulders. 3D muscle loss (3DML) was defined as 1 - (3DMM). The correlation between Goutallier grading, 3DFI, and 3DML was compared using a Spearman rank correlation.

RESULTS

Interobserver reliability for the traditional 2D Goutallier grading was moderate for the infraspinatus (ISP, 0.42) and fair for the supraspinatus (SSP, 0.38), subscapularis (SSC, 0.27) and teres minor (TM, 0.27). 2D Goutallier grading was found to be significantly and highly correlated with 3DFI (SSP, 0.79; ISP, 0.83; SSC, 0.69; TM, 0.45) and 3DML (SSP, 0.87; ISP, 0.85; SSC, 0.69; TM, 0.46) for all 4 rotator cuff muscles (P < .0001). This correlation was significantly higher for 3DML than for the 3DFI for SSP only (P = .01). The mean values of 3DFI and 3DML were 0.9% and 5.3% for Goutallier 0, 2.9% and 25.6% for Goutallier 1, 11.4% and 49.5% for Goutallier 2, 20.7% and 59.7% for Goutallier 3, and 29.3% and 70.2% for Goutallier 4, respectively.

CONCLUSION

The Goutallier score has been helping surgeons by using 2D CT scan slices. However, this grading is associated with suboptimal interobserver agreement. The new measures we propose provide a more consistent assessment that correlates well with Goutallier's principles. As 3DML measurements incorporate atrophy and fatty infiltration, they could become a very reliable index for assessing shoulder muscle function. Future algorithms capable of automatically calculating the 3DML of the cuff could help in the decision process for cuff repair and the choice of anatomic or reverse shoulder arthroplasty.

Towards the definition of a patient-specific rehabilitation program for TKA: A new MRI-based approach for the easy volumetric analysis of thigh muscles. Annu Int Conf IEEE Eng Med Biol Soc 2021;2021:3141-3144. [PMID: 34891907 DOI: 10.1109/embc46164.2021.9630726] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

After Total Knee Arthroplasty (TKA), a global post-operative rehabilitation programme is commonly performed. However, this current program is not always adapted to every patient and it could be improved by deeply reinforcing weaker thigh muscles. To do this, a muscle volume estimation coupled with force evaluation is required to therefore adapt the rehabilitation as a specific patient exercise plan. In this paper, we presented an MRI protocol allowing the acquisition of the whole thigh as well as a semi-automated pipeline to segment two main groups of thigh muscles, i.e., the quadriceps femoris and the hamstrings muscles. The pipeline is based on a few cross-sections manually labelled and a 3D-spline interpolation using directed graphs corresponding points. The seven muscles of ten thighs (70 muscles in total) were segmented and reconstructed in 3D. To assess this pipeline, three types of metrics (volumetric similarity, surface distance, and classical measures) were employed. Furthermore, the inter-muscle overlapping was calculated as an additional metric. The results showed mean DICE was 99.6% (±0.1), Hausdorff Distance was 4.9 mm (±1.8) and Absolute Volume Difference was 2.97 cm3 (±1.94) in comparison to the manual ground truth. The average overlap was 2.05% (±0.54).Clinical Relevance- The proposed segmentation method is fast, accurate and possible to integrate in the clinical workflow of TKA.

Bone surface reconstruction and clinical features estimation from sparse landmarks and Statistical Shape Models: a feasibility study on the femur

In this study, we investigated a method allowing the determination of the femur bone surface as well as its mechanical axis from some easy-to-identify bony landmarks. The reconstruction of the whole femur is therefore performed from these landmarks using a Statistical Shape Model (SSM). The aim of this research is therefore to assess the impact of the number, the position, and the accuracy of the landmarks for the reconstruction of the femur and the determination of its related mechanical axis, an important clinical parameter to consider for the lower limb analysis. Two statistical femur models were created from our in-house dataset and a publicly available dataset. Both were evaluated in terms of average point-to-point surface distance error and through the mechanical axis of the femur. Furthermore, the clinical impact of using landmarks on the skin in replacement of bony landmarks is investigated. The predicted proximal femurs from bony landmarks were more accurate compared to on-skin landmarks while both had less than 3.5^∘ degrees mechanical axis angle deviation error. The results regarding the non-invasive determination of the mechanical axis are very encouraging and could open very interesting clinical perspectives for the analysis of the lower limb either for orthopedics or functional rehabilitation.

CT-based volumetric assessment of rotator cuff muscle in shoulder arthroplasty preoperative planning

Aims

The aim of this study was to describe a quantitative 3D CT method to measure rotator cuff muscle volume, atrophy, and balance in healthy controls and in three pathological shoulder cohorts.

Methods

In all, 102 CT scans were included in the analysis: 46 healthy, 21 cuff tear arthropathy (CTA), 18 irreparable rotator cuff tear (IRCT), and 17 primary osteoarthritis (OA). The four rotator cuff muscles were manually segmented and their volume, including intramuscular fat, was calculated. The normalized volume (NV) of each muscle was calculated by dividing muscle volume to the patient’s scapular bone volume. Muscle volume and percentage of muscle atrophy were compared between muscles and between cohorts.

Results

Rotator cuff muscle volume was significantly decreased in patients with OA, CTA, and IRCT compared to healthy patients (p < 0.0001). Atrophy was comparable for all muscles between CTA, IRCT, and OA patients, except for the supraspinatus, which was significantly more atrophied in CTA and IRCT (p = 0.002). In healthy shoulders, the anterior cuff represented 45% of the entire cuff, while the posterior cuff represented 40%. A similar partition between anterior and posterior cuff was also found in both CTA and IRCT patients. However, in OA patients, the relative volume of the anterior (42%) and posterior cuff (45%) were similar.

Conclusion

This study shows that rotator cuff muscle volume is significantly decreased in patients with OA, CTA, or IRCT compared to healthy patients, but that only minimal differences can be observed between the different pathological groups. This suggests that the influence of rotator cuff muscle volume and atrophy (including intramuscular fat) as an independent factor of outcome may be overestimated.

Cite this article: Bone Jt Open 2021;2(7):552–561.

A Multidisciplinary Approach to Optimizing Long-Term Functional Prognosis of A Girl With Quadriceps Fibrosis

The consequences and optimal treatment of quadriceps fibrosis following intramuscular quinine injection during childhood remain unclear. We report here a case of a 17-year-old girl who experienced unilateral quadriceps fibrosis following intramuscular injection of quinine as a baby. This case report describes the evolution of the condition during the child's growth, the long-term impact of early fibrosis on range of motion, muscle volumes, strength, gait, and activities of daily living. Rehabilitation involved orthoses and physiotherapy from the age of 6 years, when her knee flexion was reduced to 90°. A Judet quadricepsplasty was performed at 12 years because of continued loss of knee range with consequences for gait. At 16 years, knee range was satisfactory and gait variables were normalized. Functional evaluations and quality of life scales showed excellent recovery. Isometric strength of the involved quadriceps remained lower than the expected age-matched strength. Magnetic resonance imaging identified amyotrophy of the quadriceps, specifically the vastus intermedius. Despite being a focal impairment, quadriceps fibrosis had wider consequences within the involved limb, the uninvolved limb and functioning. This case report illustrates how children with quadriceps fibrosis can have a good prognosis, with excellent functional results at the end of the growth period, following early and appropriate management.

Clinical relevance of augmented statistical shape model of the scapula in the glenoid region

OBJECTIVE

To illustrate (a) whether a statistical shape model (SSM) augmented with anatomical landmark set(s) performs better fitting and provides improved clinical relevance over non-augmented SSM and (b) which anatomical landmark set provides the best augmentation strategy for predicting the glenoid region of the scapula.

METHODS

Scapula SSM was built using 27 dry bone CT scans and augmented with three anatomical landmark sets (16 landmarks each) resulting in three augmented SSMs (aSSM_proposed, aSSM_set1, aSSM_set2). The non-augmented and three augmented SSMs were then used in a non-rigid registration (regression) algorithm to fit to six external scapular shapes. The prediction error by each type of SSM was evaluated in the glenoid region for the goodness of fit (mean error, root mean square error, Hausdorff distance and Dice similarity coefficient) and for four anatomical angles (critical shoulder angle, lateral acromion angle, glenoid inclination, glenopoar angle).

RESULTS

Inter- and intra-observer reliability for landmark selection was moderate to excellent (ICC>0.74). Prediction error was significantly lower for SSM_{non-augmented} for mean (0.9 mm) and root mean square (1.15 mm) distances. Dice coefficient was significantly higher (0.78) for aSSM_proposed compared to all other SSM types. Prediction error for anatomical angles was lowest using the aSSM_proposed for critical shoulder angle (3.4°), glenoid inclination (2.6°), and lateral acromion angle (3.2°).

CONCLUSION AND SIGNIFICANCE

The conventional SSM robustness criteria or better goodness of fit do not guarantee improved anatomical angle accuracy which may be crucial for certain clinical applications in pre-surgical planning. This study provides insights into how SSM augmented with region-specific anatomical landmarks can provide improved clinical relevance.

Quantifying skeletal muscle volume and shape in humans using MRI: A systematic review of validity and reliability

AIMS

The aim of this study was to report the metrological qualities of techniques currently used to quantify skeletal muscle volume and 3D shape in healthy and pathological muscles.

METHODS

A systematic review was conducted (Prospero CRD42018082708). PubMed, Web of Science, Cochrane and Scopus databases were searched using relevant keywords and inclusion/exclusion criteria. The quality of the articles was evaluated using a customized scale.

RESULTS

Thirty articles were included, 6 of which included pathological muscles. Most evaluated lower limb muscles. Partially or completely automatic and manual techniques were assessed in 10 and 24 articles, respectively. Manual slice-by-slice segmentation reliability was good-to-excellent (n = 8 articles) and validity against dissection was moderate to good(n = 1). Manual slice-by-slice segmentation was used as a gold-standard method in the other articles. Reduction of the number of manually segmented slices (n = 6) provided good to excellent validity if a sufficient number of appropriate slices was chosen. Segmentation on one slice (n = 11) increased volume errors. The Deformation of a Parametric Specific Object (DPSO) method (n = 5) decreased the number of manually-segmented slices required for any chosen level of error. Other automatic techniques combined with different statistical shape or atlas/images-based methods (n = 4) had good validity. Some particularities were highlighted for specific muscles. Except for manual slice by slice segmentation, reliability has rarely been reported.

CONCLUSIONS

The results of this systematic review help the choice of appropriate segmentation techniques, according to the purpose of the measurement. In healthy populations, techniques that greatly simplified the process of manual segmentation yielded greater errors in volume and shape estimations. Reduction of the number of manually segmented slices was possible with appropriately chosen segmented slices or with DPSO. Other automatic techniques showed promise, but data were insufficient for their validation. More data on the metrological quality of techniques used in the cases of muscle pathology are required.

Dynamic MRI to quantify musculoskeletal motion: A systematic review of concurrent validity and reliability, and perspectives for evaluation of musculoskeletal disorders

Purpose

To report evidence for the concurrent validity and reliability of dynamic MRI techniques to evaluate in vivo joint and muscle mechanics, and to propose recommendations for their use in the assessment of normal and impaired musculoskeletal function.

Materials and methods

The search was conducted on articles published in Web of science, PubMed, Scopus, Academic search Premier, and Cochrane Library between 1990 and August 2017. Studies that reported the concurrent validity and/or reliability of dynamic MRI techniques for in vivo evaluation of joint or muscle mechanics were included after assessment by two independent reviewers. Selected articles were assessed using an adapted quality assessment tool and a data extraction process. Results for concurrent validity and reliability were categorized as poor, moderate, or excellent.

Results

Twenty articles fulfilled the inclusion criteria with a mean quality assessment score of 66% (±10.4%). Concurrent validity and/or reliability of eight dynamic MRI techniques were reported, with the knee being the most evaluated joint (seven studies). Moderate to excellent concurrent validity and reliability were reported for seven out of eight dynamic MRI techniques. Cine phase contrast and real-time MRI appeared to be the most valid and reliable techniques to evaluate joint motion, and spin tag for muscle motion.

Conclusion

Dynamic MRI techniques are promising for the in vivo evaluation of musculoskeletal mechanics; however results should be evaluated with caution since validity and reliability have not been determined for all joints and muscles, nor for many pathological conditions.

Interactive patient-specific 3D approximation of scapula bone shape from 2D X-ray images using landmark-constrained statistical shape model fitting

We report on an interactive tool for patientspecific 3D approximation of scapula bone shape from 2D X-ray images using landmark-constrained statistical shape model (SSM) fitting. The 3D localization of points on the 2D X-ray images was done through X-ray stereophotogrammetry. The inferior angle, acromion and the coracoid process were identified as reliable landmarks from the anteroposterior (AP) and oblique lateral views in a landmark selection study. The 3D scapula surface was approximated through fitting the scapula SSM to the 3D reconstructed coordinates of the selected landmarks. 3D point localization yielded average (X, Y, Z) coordinate reconstruction errors of (X=0.14, Y=0.07, Z=0.04) mm. The landmark-constrained fitting algorithm yielded an average error between the mean posterior model landmarks and the corresponding target landmarks of 0.49 mm using the three landmarks, and later 0.19 mm with sixteen landmarks. Average surface to surface error between the CT ground truth model and approximated model from within the dataset improved from 3.20 mm to 2.46 mm using three landmarks and using sixteen landmarks, respectively. Average surface to surface error between the CT ground truth model and the approximated model from outside the dataset improved from 4.28 mm to 3.20 mm using three landmarks and using sixteen landmarks, respectively.

Quantitative study of knee joint surface configurations using a morpho-functional approach

Several models exist in the literature to describe knee kinematics. In this paper we propose a morpho-functional approach based on the determination of a simulated kinematics of flexion/extension from a unique CT scan acquisition. We will compare this kinematics to the real one obtained from experiments on one cadaver. In parallel, we have developed quantitative tools for the assessment of the motion. As the computation of these tools depends on the bone morphology, they can describe the state of the joint, which is not classical in the literature. Both tools follow the evolution of the distances between two bones during motion. They are called the Figure of Articular Coherence and the Index of Articular Coherence. In order to verify the relevance of these tools, we have tested them to compare different surgeries of Anterior Cruciate Ligament (ACL) reconstruction.

Robust local estimation in anisotropic diffusion process

In this work we propose to use an anisotropic diffusion process using robust statistics. We show that smoothing, while preserving edges, helps the segmentation of upper limb bones (shoulder) in MRI data bases. The anisotropic diffusion equation is mainly controlled using an automatic edge stopping function based on Tukey's biweight function, which depends on the values of gradients pixels. These values are divided into two classes: high gradients for pixels belonging to edges or noisy pixels, low ones otherwise. This process also depends on a threshold gradient parameter which splits both former classes. So a robust local estimation method is proposed to better eliminate the noise in the image while preserving edges. Firstly, the efficiency of the model in the noise reduction is quantified using an entropy criterion on synthetic data with different noise levels to evaluate the smoothing of the regions. Secondly, we use the Pratt's Figure of Merit (FOM) method to evaluate edges preservation. Eventually, a qualitative edge evaluation is given on a MRI volume of the shoulder joint.

A 2D 3D registration with low dose radiographic system for in vivo kinematic studies

The knowledge of the poses and the positions of the knee bones and prostheses is of a great interest in the orthopedic and biomechanical applications. In this context, we use an ultra low dose bi-planar radiographic system called EOS to acquire two radiographs of the studied bones in each position. In this paper, we develop a new method for 2D 3D registration based on the frequency domain to determine the poses and the positions during quasi static motion analysis for healthy and prosthetic knees. Data of two healthy knees and four knees with unicompartimental prosthesis performing three different poses (full extension, 30° and 60° of flexion) were used in this work. The results we obtained are in concordance with the clinical accuracy and with the accuracy reported in other previous studies.

Detection of incoherent joint state due to inaccurate bone motion estimation

In biomechanical modelling and motion analysis, the use of personalised data such as bone geometry would provide more accurate and reliable results. However, there are still a limited number of tools used to measure the evolution of articular interactions. This paper proposes a coherence index to describe the articular status of contact surfaces during motion. The index relies on a robust estimation of the evolution of surfacic interactions between the joint surfaces. The index is first compared to distance maps on simulated motions. It is then used to compare two motion capture protocols (two different localisations of the markers for scapula tracking). The results show that the index detects progressive modifications in the joint and allows distinguishing the two protocols, in accordance with the literature. In the future, the index could, among other things, be used to compare/improve biomechanical models and motion analysis protocols.

Registration of low dose bi-planar acquisitions for motion analysis

In this paper, we introduce a 2d-3d registration method for searching the motion of knee bones. We use a low dose bi-planar acquisition system that provides us with simultaneous frontal and profile radiographs in different positions, and the 3d volume reconstruction of the standing position. The purpose here is to reduce the user intervention during the motion tracking. The registration method is based on the central slice Fourier Transform theorem. Motion results with rotations and translations using synthetic data are shown.

Performing accurate joint kinematics from 3-D in vivo image sequences through consensus-driven simultaneous registration

This paper addresses the problem of the robust registration of multiple observations of the same object. Such a problem typically arises whenever it becomes necessary to recover the trajectory of an evolving object observed through standard 3-D medical imaging techniques. The instances of the tracked object are assumed to be variously truncated, locally subject to morphological evolutions throughout the sequence, and imprinted with significant segmentation errors as well as significant noise perturbations. The algorithm operates through the robust and simultaneous registration of all surface instances of a given object through median consensus. This operation consists of two interwoven processes set up to work in close collaboration. The first one progressively generates a median and implicit shape computed with respect to current estimations of the registration transformations, while the other refines these transformations with respect to the current estimation of their median shape. When compared with standard robust techniques, tests reveal significant improvements, both in robustness and precision. The algorithm is based on widely-used techniques, and proves highly effective while offering great flexibility of utilization.

Modified data fidelity speed in anisotropic diffusion

In this paper, we use an anisotropic diffusion in a level set framework for low-level segmentation of necrotic femoral heads. Our segmentation is based on three speed terms. The first one includes an adaptive estimation of the contrast level. We use the entropy for evaluating our diffusion on synthetic 3D data. We notice that using the data fidelity term in the last iterations excessively penalizes the diffusion process. To provide better segmentation results, we propose some modifications in the data fidelity speed: we propose to build its reference data term from previous iterations results and hence lessening influence of initial noisy data.

Performing Accurate Rigid Kinematics Measurements from 3D in vivo Image Sequences through Median Consensus Simultaneous Registration

While focusing at accurate 3D joint kinematics, this paper explores the problem of how to perform a robust rigid registration for a sequence of object surfaces observed using standard 3D medical imaging techniques. Each object instance is assumed to give access to a polyhedral encoding of its boundary. We consider the case where object instances are noised with significant truncations and segmentation errors. The proposed method aims to tackle this problem in a global way, fully exploiting the duality between redundancy and complementarity of the available instances set. The algorithm operates through robust and simultaneous registration of all geometrical instances on a virtual instance accounting for their median consensus. When compared with standard robust techniques, trials reveal significant gains, as much in robustness as in accuracy. The considered applications are mainly focused on generating highly accurate kinematics in relation to the bone structures of the most complex joints - the tarsus and the carpus - for which no alternative examination techniques exist, enabling fine morphological analysis as well as access to internal joint motions.

Shoulder motion analysis using simultaneous skin shape registration

A new non-invasive approach is proposed to study joint motions. It is based on dynamic tracking of the skin shape. A robust simultaneous registration algorithm (Iterative Median Closest Point) is used to follow the evolving shape and compute the rigid motion of the underlying bone structures. This new method relies on the differentiation of the rigid and elastic parts of the shape motion. A skin marker network is tracked by a set of infrared cameras. Unlike usual techniques, the algorithm tracks the instantaneous polyhedral shape embedding this network. This innovating approach is expected to minimize bias effect of skin sweeps and give some new information about the underlying soft tissue activities. Current application addresses the motion of the shoulder complex (humerus, clavicle and scapula). It is compared with two marker-based methods published in the literature. Preliminary results show significant differences between these three approaches. The new approach measurements give rise to greater rotations.

Determination of age at death: assessment of an algorithm of age prediction using numerical three-dimensional CT data from pubic bones

The determination of age at death is an important part of physical and forensic anthropology. Because of resistance to decomposition and the simplicity/accuracy ratio, the direct observation of the os pubis by Suchey-Brooks phase analysis is the preferred reference system for determination of age at death. We propose an age-prediction system using a pubic symphysis numerical database obtained from CT x-ray through quantification of age-linked parameters. Our system increases the accuracy of age estimation and at the same time preserves the integrity of the archeological material.

Modeling and analysis of 3-D elongated shapes with applications to long bone morphometry

Presents a geometric model to be used as a framework for the description and analysis of three-dimensional (3-D) elongated shapes. Elongated shapes can be decomposed into two different parts: a 3-D curve (the central axis) and a 3-D surface (the straight surface). The central axis is described in terms of curvature and torsion. A novel concept of torsion image is introduced which allows the user to study the torsion of some relevant 3-D structures such as the medulla of long bones, without computing the third derivative. The description of the straight surface is based on an ordered set of Fourier Descriptors (FDs), each set representing a 2-D slice of the structure. These descriptors possess completeness, continuity, and stability properties, and some geometrical invariancies. A polar diagram is built which contains the anatomical information of the straight surface and can be used as a tool for the analysis and discrimination of 3-D structures. A technique for the reconstruction of the 3-D surface from the model's two components is presented. Various applications to the analysis of long bone structures, such as the ulna and radius, are derived from the model, namely, data compression, comparison of 3-D shapes, segmentation into 3-D primitives, and torsion and curvature analysis. The relevance of the method to morphometry and to clinical applications is discussed.

3D geometrical features of anatomic structures: the example of the ulna and radius bones

This paper addresses two important issues of three-dimensional (3D) natural shape analysis. The first concerns the segmentation of these shapes into 3D primitives and the second deals with their geometric characterisation by means of intrinsic features. Restricting ourselves to 3D objects formed from two-dimensional (2D) cross-sectional adjacent slices (i.e., long bones), we present a method of contextual classification and results concerning the ulnar bone. With respect to the second issue, a curvature-torsion analysis of the medullar axis is introduced and the results are represented by means of torsion images. A first application to ulnar structures is given. It is shown that radius bones have zero torsion and that their curvatures can be studied in 2D. A preliminary statistical study of the 2D curvature of the radius is also presented.