Carl-Eric Aubin

Assessment of the 3-D reconstruction and high-resolution geometrical modeling of the human skeletal trunk from 2-D radiographic images

This paper presents an in vivo validation of a method for the three-dimensional (3-D) high-resolution modeling of the human spine, rib cage, and pelvis for the study of spinal deformities. The method uses an adaptation of a standard close-range photogrammetry method called direct linear transformation to reconstruct the 3-D coordinates of anatomical landmarks from three radiographic images of the subjects trunk. It then deforms in 3-D 1-mm-resolution anatomical primitives (reference bones) obtained by serial computed tomography-scan reconstruction of a dry specimen. The free-form deformation is calculated using dual kriging equations. In vivo validation of this method on 40 scoliotic vertebrae gives an overall accuracy of 3.3 /spl plusmn/ 3.8 mm, making it an adequate tool for clinical studies and mechanical analysis purposes.

Finite Element Model of Polar Growth in Pollen Tubes

The generation of different shapes in plant cells depends on the spatial regulation of the cell wall mechanical properties. A finite element modeling approach was used to simulate the unidirectional growth process in pollen tubes. Predictions made by the model suggest a crucial role for the chemical configuration of pectin in determining cell shape. Cellular protuberance formation in walled cells requires the local deformation of the wall and its polar expansion. In many cells, protuberance elongation proceeds by tip growth, a growth mechanism shared by pollen tubes, root hairs, and fungal hyphae. We established a biomechanical model of tip growth in walled cells using the finite element technique. We aimed to identify the requirements for spatial distribution of mechanical properties in the cell wall that would allow the generation of cellular shapes that agree with experimental observations. We based our structural model on the parameterized description of a tip-growing cell that allows the manipulation of cell size, shape, cell wall thickness, and local mechanical properties. The mechanical load was applied in the form of hydrostatic pressure. We used two validation methods to compare different simulations based on cellular shape and the displacement of surface markers. We compared the resulting optimal distribution of cell mechanical properties with the spatial distribution of biochemical cell wall components in pollen tubes and found remarkable agreement between the gradient in mechanical properties and the distribution of deesterified pectin. Use of the finite element method for the modeling of nonuniform growth events in walled cells opens future perspectives for its application to complex cellular morphogenesis in plants.

Morphometric evaluations of personalised 3D reconstructions and geometric models of the human spine

In the past, several techniques have been developed to study and analyse the 3D characteristics of the human spine: multi-view radiographic or biplanar 3D reconstructions, CT-scan 3D reconstructions and geometric models. Extensive evaluations of three of these techniques that are routinely used at Sainte-Justine Hospital (Montréal, Canada) are presented. The accuracy of these methods is assessed by comparing them with precise measurements made with a coordinate measuring machine on 17 thoracic and lumbar vertebrae (T1-L5) extracted from a normal cadaveric spine specimen. Multi-view radiographic 3D reconstructions are evaluated for different combinations of X-ray views: lateral (LAT), postero-anterior with normal incidence (PAOo) and postero-anterior with 20o angled down incidence (PA20o). The following accuracies are found for these reconstructions obtained from different radiographic setups: 2.1±1.5 mm for the combination with PAOo-LAT views, and 5.6±4.5 mm for the PAOo-PA20o stereopair. Higher errors are found in the postero-anterior direction, especially for the PAOo-PA20o view combination. Pedicles are found to be the most precise landmarks. Accuracy for CT-scan 3D reconstructions is about 1.1±0.8 mm. As for a geometric model built using a multiview radiographic reconstruction based on six landmarks per vertebra, accuracies of about 2.6±2.4 mm for landmarks and 2.3±2.0 mm for morphometric parameters are found. The geometric model and 3D reconstruction techniques give accurate information, at low X-ray dose. The accuracy assessment of the techniques used to study the 3D characteristics of the human spine is important, because it allows better and more efficient quantitative evaluations of spinal dysfunctions and their treatments, as well as biomechanical modelling of the spine.

Finite element investigation of the loading rate effect on the spinal load-sharing changes under impact conditions

Sudden deceleration and frontal/rear impact configurations involve rapid movements that can cause spinal injuries. This study aimed to investigate the rotation rate effect on the L2-L3 motion segment load-sharing and to identify which spinal structure is at risk of failure and at what rotation velocity the failure may initiate? Five degrees of sagittal rotations at different rates were applied in a detailed finite-element model to analyze the responses of the soft tissues and the bony structures until possible fractures. The structural response was markedly different under the highest velocity that caused high peaks of stresses in the segment compared to the intermediate and low velocities. Under flexion, the stress was concentrated at the upper pedicle region of L2 and fractures were firstly initiated in this region and then in the lower endplate of L2. Under extension, maximum stress was located in the lower pedicle region of L2 and fractures started in the left facet joint, then they expanded in the lower endplate and in the pedicle region of L2. No rupture has resulted at the lower or intermediate velocities. The intradiscal pressure was higher under flexion and decreased when the endplate was fractured, while the contact forces were greater under extension and decreased when the facet surface was cracked. The highest ligaments stresses were obtained under flexion and did not reach the rupture values. The endplate, pedicle and facet surface represented the potential sites of bone fracture. Results showed that spinal injuries can result at sagittal rotation velocity exceeding 0.5 degrees /ms.

Three-dimensional Classification of Thoracic Scoliotic Curves

Study Design. Three-dimensional (3D) characterization of the thoracic scoliotic spine (cross-sectional study). Objectives. To investigate the presence of subgroups within Lenke type-1 curves by evaluating the thoracic segment indices extracted from 3D reconstructions of the spine, and to propose a new clinically relevant means (the daVinci representation) to report 3D spinal deformities. Summary of Background Data. Although scoliosis is recognized to be a 3D deformity of the spine its measurement and classification have predominantly been based on radiographs which are 2D projections in the coronal and sagittal planes. Methods. Thoracic segment indices derived from 3D reconstructions of coronal and sagittal standing radiographs of 172 patients with right thoracic adolescent idiopathic scoliosis, reviewed by the 3D Classification Committee of the Scoliosis Research Society, were analyzed using the ISOData unsupervised clustering algorithm. Four curve indices were analyzed: Cobb angle, axial rotation of the apical vertebrae, orientation of the plane of maximum curvature of the main thoracic curve, and kyphosis (T4–T12). No assumptions were made regarding grouping tendencies in the data nor were the number of clusters predefined. Results. Three primary groups were revealed wherein kyphosis and the orientation of the PMC of the main thoracic curve were the major discriminating factors with slight overlap between groups. A small group (G1) of 22 patients having smaller, nonsurgical (minor) curves was identified. Although the remaining patients had similar Cobb angles they were split into 2 groups (G2: 79 patients; G3: 71 patients) with different PMC (G2: 65°–81°; G3: 76°–104°) and kyphotic measures (G2: 23°–43°; G3: 7°–25°). Conclusion. Two distinct subgroups within the surgical cases (major curves) of Lenke type-1 curves were found thus suggesting that thoracic curves are not always hypokyphotic. The ISOData cluster analysis technique helped to capture inherent 3D structural curve complexities that were not evident in a 2D radiographic plane. The daVinci representation is a new clinically relevant means to report 3D spinal deformities.

Optimization method for 3D bracing correction of scoliosis using a finite element model

Abstract Scoliosis is a complex three-dimensional deformity of the spine and rib cage frequently treated by brace. Although bracing produces significant correction in the frontal plane, it generally reduces the normal sagittal plane curvatures and has limited effect in the transverse plane. The goal of this study is to develop a new optimization approach using a finite element model of the spine and rib cage in order to find optimal correction patterns. The objective function to be minimized took account of coronal and sagittal offsets from a normal spine at the thoracic and lumbar apices as well as the rib hump. Two different optimization studies were performed using the finite element model, which was personalized to the geometry of 20 different scoliotic patients. The first study took into account only the thoracic deformity, while the second considered both the thoracic and lumbar deformities. The optimization produced an average of 56% and 51% reduction of the objective function respectively in the two studies. Optimal forces were mostly located on the convex side of the curve. This study demonstrates the feasibility of using an optimization approach with a finite element model of the trunk to analyze the biomechanics of bracing, and may be useful in the design of new and more effective braces.

Preoperative Planning Simulator for Spinal Deformity Surgeries

Study Design. Proof of concept of a spine surgery simulator (S3) for the assessment of scoliosis instrumentation configuration strategies. Objective. To develop and assess a surgeon-friendly spine surgery simulator that predicts the correction of a scoliotic spine as a function of the patient characteristics and instrumentation variables. Summary of Background Data. There is currently no clinical tool sufficiently user-friendly, reliable and refined for the preoperative planning and prediction of correction using different instrumentation configurations. Methods. A kinetic model using flexible mechanisms has been developed to represent patient-specific spine geometry and flexibility, and to simulate individual substeps of correction with an instrumentation system. The surgeon-friendly simulator interface allows interactive specification of the instrumentation components, surgical correction maneuvers and display of simulation results. Results. The simulations of spinal instrumentation procedures of 10 scoliotic cases agreed well with postoperative results and the expected behavior of the instrumented spine (average Cobb angle differences of 3.5° to 4.6° in the frontal plane and of 3.6° to 4.7° in the sagittal plane). Forces generated at the implant-vertebra link were mostly below reported pull-out values, with more important values at the extremities of the instrumentation. Conclusion. The spine surgery simulator S3 has proven its technical feasibility and clinical relevance to assist in the preoperative planning of instrumentation strategies for the correction of scoliotic deformities.

Progression of vertebral and spinal three-dimensional deformities in adolescent idiopathic scoliosis : A longitudinal study

Study Design. The evolution of scoliotic descriptors was analyzed from three-dimensionally reconstructed spines and assessed statistically in a group of adolescents with progressive idiopathic scoliosis. Objectives. To conduct an intrasubject longitudinal study quantifying evolution of two- and three-dimensional geometrical descriptors characterizing the scoliotic spine and vertebral deformities. Summary of Background Data. The data available on geometric descriptors usually are based on cross-sectional studies comparing scoliotic configurations of different individuals. The literature reports very few longitudinal studies that evaluated different phases of scoliotic progression in the same patients. Methods. The evolution of regional and local descriptors between two scoliotic visits was analyzed in 28 adolescents with scoliosis. Several statistical analyses were performed to determine how spinal curvatures and vertebral deformities change during scoliosis progression. Results. At the thoracic level, vertebral wedging increases with curve severity in a relatively consistent pattern for most patients with scoliosis. Axial rotation mainly increases toward curve convexity with scoliosis severity, worsening the progression of vertebral body deformities. No consistent evolution is associated with the angular orientation of the maximum wedging. Thoracic kyphosis varies considerably among subjects. Both increasing and decreasing kyphosis are observed in nonnegligible proportions. A decrease in kyphosis is associated with a shift in the plane of maximum deformity toward the frontal plane, which worsens the three-dimensional shape of the spine. Conclusions. The results of this study challenge the existence of a typical scoliotic evolution pattern and suggest that scoliotic evolution is quite variable and patient specific.

Patient-specific mechanical properties of a flexible multi-body model of the scoliotic spine

The flexibility of the scoliotic spine is an important biomechanical parameter to take into account in the planning of surgical instrumentation. The objective of the paper was to develop a method to characterisein vivo the mechanical properties of the scoliotic spine using a flexible multi-body model. Vertebrae were represented as rigid bodies, and intervertebral elements were defined at every level using a spherical joint and three torsion springs. The initial mechanical properties of motion segments were defined fromin vitro experimental data reported in the literature. They were adjusted using an optimisation algorithm to reduce the discrepancy between the simulated and the measured Ferguson angles in lateral bending of three spine segments (major or compensatory left thoracic, right thoracic and left lumbar scoliosis curves). The flexural rigidity of the spine segments was defined in three categories (flexible, nominal, rigid) according to the estimated mechanical factors (α). This approach was applied with ten scoliotic patients under-going spinal correction. Personalisation of the model resulted in an increase of the initial flexural rigidity for seven of the ten lumbar segments (1.38≤α≤10.0) and four of the ten right thoracic segments (1.74≤α≤5.18). The adjustment of the mechanical parameters based on the lateral bending tests improved the models ability to predict the spine shape change described by the Ferguson angles by up to 50%. The largest differences after personalisation were for the left lumbar segments in left bending (40±30). Thein vivo identification of the mechanical properties of the scoliotic spine will improve the ability of biomechanical models adequately to predict the surgical correction, which should help clinicians in the planning of surgical instrumentation manoeuvres.

Biomechanical modeling of posterior instrumentation of the scoliotic spine

Scoliosis is a three-dimensional deformation of the spine that can be treated by vertebral fusion using surgical instrumentation. However, the optimal configuration of instrumentation remains controversial. Simulating the surgical maneuvers with personalized biomechanical models may provide an analytical tool to determine instrumentation configuration during the pre-operative planning. Finite element models used in surgical simulations display convergence difficulties as a result of discontinuities and stiffness differences between elements. A kinetic model using flexible mechanisms has been developed to address this problem, and this study presents its use in the simulation of Cotrel-Dubousset Horizon surgical maneuvers. The model of the spine is composed of rigid bodies corresponding to the thoracic and lumbar vertebrae, and flexible elements representing the intervertebral structures. The model was personalized to the geometry of three scoliotic patients (with a thoracic Cobb angle of 45°, 49° and 39°). Binary joints and kinematic constraints were used to represent the rod-implant-vertebra joints. The correction procedure was simulated using three steps: (1) Translation of hooks and screws on the first rod; (2) 90° rod rotation; (3) Hooks and screws look-up on the rod. After the simulation, slight differences of 0-6° were found for the thoracic spine scoliosis and the kyphosis, and of 1-8° for the axial rotation of the apical vertebra and for the orientation of the plane of maximum deformity, compared to the real post-operative shape of the patient. Reaction loads at the vertebra-implant link were mostly below 1000 N, while reaction loads at the boundary conditions (representing the overall action of the surgeon) were in the range 7-470 N and maximum torque applied to the rod was 1.8 Nm. This kinetic modeling approach using flexible mechanisms provided a realistic representation of the surgical maneuvers. It may offer a tool to predict spinal geometry correction and assist in the pre-operative planning of surgical instrumentation of the scoliotic spine.