Ebook: Three Dimensional Analysis of Spinal Deformities

Spinal deformities have a long history that scientifically begins in Hippocrates time even though descriptions of people with curved backs can be found in many previous documents: the Old Testament (200-300 years before the Father of Medicine birth), old Chinese, Indian and Egyptians documents (more than 2000 years before the contributions of the Greeks and the Jews), and an image that goes back to the Stone Age (this shows a congenital scoliosis due to a hemivertebrae). Therefore it is evident that the spine deformities have followed mankind since his evolution into an upright being and, furthermore, great importance has always been attributed to all the problems related with this pathology.

Attempts to explain spinal deformity aetiology (in particular scoliosis), to evaluate the possible progression of the disease, to individualise the right therapeutic treatment have been without significant improvement for centuries. Biblical references implicated that for spinal deformities no treatment was possible. Hippocrates, in his famous treaty “ΠEPI’ APΘPΩN”, after a classification of curves and angular deformities, described the first procedure of deformity reduction. One millennium later, Paolo from Egina tried a gradual correction of scoliosis using cast bandages. On the XVI century, Ambroise Paré taught how to fabricate metal cuirass to be applied on the scoliotic trunk.

Since then no more substantial progress has been made, especially as it concerns aetiology, until our century when the three dimensional characteristics of the scoliotic deformities have been pointed out, the first spinal arthrodesis made and the Milwaukee brace used. Constant progress of electronic technology and informatics, together with a good specialisation on surgical techniques and bio-compatible materials, have made possible today the realisation of researches more accurate both on the etiologic side and on prevention and treatment.

Specific three dimensional measurement techniques, based on optical or opto-electronic principles of image capture, can in fact provide a complete set of results to quantify, without any risk for the patient, the morphological/functional state of the spine and the effects induced by various spinal diseases on the whole postural performance.

This volume, including the contributions of the most authoritative researchers in the field, is the end product of the 2nd International Symposium on Three Dimensional Scoliotic Deformities combined with the 8th International Symposium on Surface Topography and Spinal Deformity held on September 1994 in Pescara (Italy). The book covers topics such as 3-D acquisition-reconstruction-modelling techniques, 3-D biomechanical analysis, 3-D etiologic and prognostic aspects, 3-D treatment of scoliosis, surface topography and internal 3-D spinal and/or trunk anatomy.

M. D’Amico, A. Merolli, G.C. Santambrogio (Editors)

December 1994

We have used for several years “RACHIS 91” software, yet presented in Montreal last meeting, in 1993. This program is able to achieve a 3D reconstruction of the scoliotic deformity from lateral and frontal x-rays of the full spine. The sight from above (axial view) is often difficult to understand for the physician. A new program has been performed as a clinical support : each torsional segment of the scoliotic spine can be placed in a part of the surface of a cylinder, built either since the lateral or the frontal plan : in this case, it looks like a shield. The torsional segment walks along the concave side of the shield, the length,the surface,the radius and arch of which materialise the spacial displacement of the scoliotic spine from the initial sagittal and medial plan ; the shield’s shape varies as the scoliosis, and the relation between the frontal and the sagittal size of its different parameters is an approach of a 3d measurement.

This paper describes preliminary work in the application of Fourier Transform Profilometry (FTP) to the measurement of human back shape. Optical fringe patterns are generated on the surface of the back and the FTP method, which is phase sensitive, is used to reconstruct the surface shape of the back. The method is relatively resilient to changes in the reflective properties of the skin and overcomes the problem of low sampling density which is inherent in edge or peak extracting methods.

A photogrammetric measuring device has been under development for automating the detection of variations in back surface shape, in order to discern improvements or deterioration in scoliotic patient conditions, for comparing one patient with another patient, or to collect statistical data on the condition. The system is designed to take into account as carefully as possible the requirements of the medical practitioner as the end-user of the results, especially by providing output that can be exploited. Careful consideration has been paid to clinical requirements, not only in terms of cost and accuracy, but also in terms of convenience to clinical staff and the patient. In this way, the instrumentation is designed to surmount apparent difficulties in having photogrammetric instrumentation accepted into routine clinical use. The surface measurement follows the widely-accepted photogrammetric configuration of a pair of stereoscopic digital cameras, with a projected light pattern to provide texturisation on the human body. It is intended to require no handling by a medical practitioner. The detection of features in the pattern, the determination of stereoscopic correspondence and the formation of the surface model, are carried out in an automated manner. The two images are collected within 0.1 seconds of each other. Although computations are not instantaneous, the current system operates in accordance with requirements, obtaining from 500 to 1000 points to define the back surface to an accuracy of about 1 mm. In addition, the hardware is currently being linked to software which enables one measured back surface to be compared with another by least squares matching methods, to detect differences between the two back shape surfaces. This component is seen as crucial for the acceptance of the instrument by medical specialists.

The trunk deformity associated with scoliosis is considered by many patients and physicians as more important than the spinal deformity itself. For this reason it is important to access the three-dimensional characteristics of the surface deformity. A surface modelling system has been developed to study this surface deformity. This system is comprised of software modules running on an IBM RISC6000 engineering workstation. This system displays a realistic model of the trunk which can be rotated and viewed from any orientation. The surface modeller contains three major components; systems for determining the boundary of the trunk data, for modelling the trunk using triangles and for display and manipulation of trunk images. Triangles were chosen for their computational simplicity which minimizes the time to construct and move the 3-D image of the trunk. Boundary generation from discrete data points is ill-defined and subjective. Any surface model of the trunk requires the boundary to be defined. Otherwise, triangles would be placed in regions which are not part of the trunk surface. A boundary determination routine has been developed which provides a best estimate of the trunk boundary and then permits the user to interactively eliminate unwanted artifacts. The surface modelling routine uses a modified form of McLain’s algorithm to define the triangles which constitute the surface model. This algorithm was modified to greatly increase its speed and a novel method is used to eliminate triangles which fall outside the boundary. The display provides a realistic three dimensional image of the trunk which appears illuminated from ambient light and spot light sources. Multiple views of the trunk or different trunk images can be shown for comparison purposes. This permits the clinician to compare changes which occur over time in trunk deformity. The software system can simultaneously show a model of the spine or photo image in conjunction with the trunk surface model. This helps relate surface deformity to the underlying spinal misalignment.

Three-dimensional stereoradiographic reconstruction of scoliotic spines and rib cages is routinely done at Ste-Justine Hospital. For each patient, two postero-anterior X-ray views (PA-0° and PA-20°) are taken at approximately 25 seconds interval to obtain 3-D reconstruction of rib midlines. One major source of error in this reconstruction technique is related to the possible displacement of the patient between the two X-ray exposures even if positioning devices are used. Results of a new rib cage reconstruction method which evaluates and takes into account the patient displacement are presented. Graphical 3-D representation of the rib cage reconstruction showed an evident improvement compared to the previous reconstruction method. This new reconstruction technique has important clinical significance because it allows to measure patient displacement during stereoradiography and to improve the quality of the 3-D rib cage representation given to the clinician for evaluation of scoliotic deformities.

In order to evaluate spinal deformities in scoliosis, a new non-ionising technique has been adopted. This technique allows to measure the 3D spatial positions of small unobtrusive hemispheric passive markers placed on anatomical repere points. After having acquired the raw data, a very sophisticated signal processing algorithm, that will be described herein after, has been developed in order to obtain from the measurements of the spine landmarks, the extraction of clinical parameters related to those usually calculated on the radiographic image. The implemented procedure is completely automatic, insensible to edge effects, applicable to short data sets, reliable in filtering and derivative assessment and fast. Various examples of the results obtained of various analysed subjects showing the algorithm reliability and clinical efficacy are presented.

The aim of the paper is to present a new processing procedure based on a computer vision methodology in order to reduce the uncertainty and the variability of the measure of the various angles of interest. In fact, for instance, for Scoliosis and spinal deformities analysis widely used parameters are the Cobb as well as Lordosis and Kyphosis angles. The measure of these parameters is usually manually obtained by the orthopaedic surgeon. This leads to a series of problems and to a great variability of the measurements obtained due to the quality of the x-ray measurements, the experience of the surgeon, the media used for the computation and so on. Gradient polygon method and image processing has been applied for extracting clinical features from x-ray images collected for Scoliosis analysis. To this aim a dedicated software has been developed in order to help clinicians to analyse, to interpret and to quantify spinal deformities in a more objective way, avoiding the manual computation of numerical parameters.

This work presents an approach to mathematical description of back surface kinematics. General purpose measurement techniques, based on the last generation of opto-electronic systems for image capture and motion analysis, have been adopted in order to acquire in real-time the 3-D co-ordinates of a suitable grid of passive markers placed on the back surface. A fast, specially-developed bicubic B-spline interpolation algorithm has been then used to increase the spatial resolution of the acquired digital image. This procedure, applied to each acquired frame, has allowed the tracking of the surface movements and the evaluation of the related changes of shape during the execution of some simple motor tasks. A further data processing has completed the quantitative description of the rendered surface (iso-level curves, asymmetries, etc.) in static and dynamic conditions.

The study of the morphological changes induced by movement can be a useful tool both in clinical applications (such as the evaluation of the gibbosity in scoliotic patients and the related plasticity during suitable motor tasks) and in research programmes (such as the analysis of the effects induced by skin elasticity on kinematic measures performed through skin marker systems).

Quantitative 3-D reconstruction of body surface represents a useful tool in many medical fields, such as prosthetics, plastic surgery, orthopaedics. Particularly in this last area, the analysis of back surface may give an essential improvement to the evaluation of spinal deformities and to the follow up of their progressive features. The aim of this paper is to present a new method that is able to measure with great accuracy the 3-D co-ordinates of a whatever number of sample points on the back surface, to compute and render the reconstructed surface, and to analyse quantitatively its shape. Such a method utilises an automatic image analyser (the ELITE System) joined with a suitable device scanning the surface by means of a laser beam. Starting from at least two different views of the subject, the image analyser computes in real time the 3-D co-ordinates of each sample point on the surface. A dedicated software for data processing and graphic representation completes the reconstruction of the back surface.

An image is a two dimensional signal, from which information about the third dimension, height, must be extracted when measuring surface shape. This paper reviews ways in which this may be done, starting with binocular vision systems and then moving on to ways in which additional information may be added to a single image so that height may be extracted. For each system some brief comments are included regarding problems of application and limitations on accuracy.

A computer segmentation method is developed to detect automatically the contour lines of the vertebral pedicles in digital radiographs of the scoliotic spine. These contour lines are used to identify stereocorrespondent anatomical landmarks for the 3D reconstruction of the scoliotic spine using a stereoradiographic technique. Automation of the digitization of the landmarks should reduce the variability of the actual manual digitization method and improve the 3D reconstruction precision. First, a knowledge based model is used to generate anatomical markers near the pedicle centers. These markers are then used to control a morphological segmentation method allowing the automatic detection of the pedicle contour lines. Next, an ellipsis is fitted to the pedicle contour lines and stereocorrespondent landmarks are estimated in the stereoradiograhs to finally obtain their 3D location. The preliminary results demonstrated a reduction of the 2D standard deviation for the digitization of the pedicles from 2.3±1.6 mm (manual) to 0.39±0.37 mm (automatic) and an improvement in the 3D reconstruction precision by an amelioration of the stereocorrespondence estimation (reduction of the DLT error from 42.3±3.4 mm (manual) to 1.9±2.3 mm (automatic)). The automation of the stereocorrespondent landmarks digitization using computer vision methods seem to effectively reduce the variability of the method and improve the landmark correspondence identification.

A new method which allows the 3-D reconstruction of vertebral body endplates from biplanar radiographs was developed in order to evaluate the maximum wedge angulations of scoliotic vertebrae and their corresponding 3-D orientations. This new reconstruction technique, based on an iterative projectionretroprojection procedure which fits an ellipse on the real endplate contours, was applied on 10 adolescent idiopathic scoliotic patients. Results at thoracic apex show mean wedge angles of 9.1±4.5°. Wedging orientation values confirmed that scoliotic wedging is not a 2-D deformation but a 3-D phenomenon because it did not occurred in a plane parallel to the frontal X-ray plane. Preliminary validation showed maximum wedge angle errors less than 2.5°.

In order to illustrate orthotic and surgical scoliosis correction mechanisms, an interpolation method has been developed using a spherical joint to represent the vertebral articulation. The interpolation, computed from two 3D reconstructions of the scoliotic spine (before and after correction) obtained from a stereoradiographic technique, is based on the hypothesis that there are no intervertebral translations. A model of the spine is constructed based on a series of spherical joints with rigid interconnections and L5 anchored at the reference base. Intermediate geometries are then generated by interpolating the orientation in a quaternion space in which the vertebrae are placed in the global 3D space using their relative positions. Visualization is done via a computer graphic software providing an animation of the correction process.

A 3-D acquisition device, dedicated to external measurement of a whole human trunk for an application of modelisation before its use in a CAD process, has been specifically developed. This device offers a non-contact, fast and accurate method to give the user reliable data for modelling and reconstruction of anatomical surfaces ; it would represent at the end, after several clinical tests, a fundamental step for the following processings, allowing analysis and evaluation of the scoliotic treatment taking into consideration morphological and clinical internal and external parameters. Several ways of digitisation of human bodies are offered today ; a few of them are accurate enough in one angle of view (for example on the back) but most of these are affected by the difficulty to deal with the time of acquisition for a 360 degrees digitisation. In this last case the relative movement of the patient during the measurement (that could last several seconds) causes errors which spoil the quality and the reliability of further modelling. The paper describes a device able to take the whole trunk of a patient in less than 2 seconds with a standard deviation of 1 mm in safe and comfortable conditions for the patient. Detailed results are displayed.

Correction of scoliosis imposes a displacement of the vertebrae in 3D. Until now, the movement of the vertebrae is not known. This paper proposes a protocol to measure the displacement of the vertebrae during a surgical correction procedure. The protocol permits the determination of the movement of several vertebrae in 3D using three diodes. The displacements are recorded by a videosystem and they are included by fixing a hook attached to a screw to the vertebra.

A method for scoliosis analysis using stereophotogrammetry has been developed. The technique involves intra-operative stereophotography using an overhead stereo camera system. Stereophoto pairs are taken at specific stages of spinal instrumentation procedures. In this way the effects of specific instrumentation maneuvers can be studied. Photo pairs are put onto Kodak PhotoCD’s and digitized to provide three-dimensional coordinate position for posterior element bony landmarks. Three-dimensional changes in position occurring after specific stages of surgical instrumentation are compared using a computer program developed for this project. Rotational and translational information is calculated for the entire visualized segment of the spine. Accurate results have been achieved with this technique and verified using appropriate statistical methods.

This paper tackles the problem of analysing the variability of the experimental data provided by the AUSCAN System, an opto-electronic measurement device for the detection of the 3-D spinal geometry during static and dynamic posture. Various sources of data variability, ranging from pure errors of detection up to physiological variations of the spinal morphology due the control mechanism of posture, have been considered. The final results of this study show that the dynamic component of posture, associating with the motor-posture control system, causes the largest variability in the measure of the spinal morphology.

Facet joints appear to have a major role in the mechanical behaviour of the spine and the thorax. In order to quantify their role and to represent with precision their behaviour, a previously existing finite element model of the global spine and thorax was improved. The input geometry to the model was obtained using a method which includes stereoradiographic 3-D reconstructions of a given patient as described in the joined paper of Aubin et al.. Zygapophyseal facets were parametrized using simple surface shapes (plane or cylinder) and were modelled by shell, point-to-surface contact and cable elements. Posterior arch and ligaments were also represented. Mechanical and geometrical properties necessary to complete the model were taken from. Geometric and material non-linearities were taken into account. Simulations were done on functional units as well as lumbar segments extracted from the model and results were compared to experimental data. Adequation of results was found, which supports the modelling method. However, further simulations are still in progress on global segments to complete the validation.

Sinusoidal functions provide a suitable mathematical representation of the frontal projection of the scoliotic spine. This is due to their obvious similarity with the spinal curve. Three parameters (amplitude, wavelength and phase) are sufficient for a complete description of the curve. Unfortunately the sinusoidal approach fails in asymmetric curves, e.g. double curves with distinctly different curvatures. In this paper a new approach is presented, which is based on modulated sine curves, leaving 4 parameters to be adjusted. The fit of these functions to radiographic curves (478 cases) is described. The relevance of this approach in reconstructing the spine from back surface measurements is pointed out.

This paper documents a novel technique to estimate the inter-vertebral motion and related coupling in five patients with idiopathic scoliosis and five control subjects. Triads were put over the spinous processes of the subjects. An eight 60-200Hz video camera Motion Analysis Expert Vision System was used to track these markers for right lateral bend trials. The markers’ 3-D coordinates were reconstructed by means of the Direct Linear Transformation technique after camera calibration. Rotations between any two triads were estimated by the Euler angles in the following sequence: bending, rotation and flexion. For a right bend, there is a left rotation of the thoracic spine and a compensatory right rotation of the lumbar spine in both the scoliotic spine and control subjects. Though, peak values were smaller for the scoliotic group but not significantly different, individual ratios involving the thoracic spine were significantly smaller for the scoliotic group denoting spinal rigidity.

The consequences of lateral curvature for the laterally curved lumbar spine were analyzed in a static 3-D biomechanical model. The model used published anatomical data for the positions of the vertebrae and for the muscle insertions and muscle maximum contractile force. It was initially symmetric about the sagittal plane. Subsequently, three dimensional measurements of the spines of patients with lumbar scoliosis (mean Cobb angle 38° ) were used to create a new geometry representing the asymmetry of lumbar scoliosis. The model was used to calculate the maximum values of efforts in the three principal directions applied to the T12 vertebra, and subject to the following constraints: equilibrium of forces and moments acting on all vertebrae, muscle forces > 0, and less than a physiological maximum proportional to their cross-sectional area, and motion segment displacements due to elastic deformations. The maximum efforts were a linear function of the variables (muscle forces and joint forces) so linear programming was used to solve this indeterminate problem. The findings indicated that the overall magnitudes of effort for the three principal directions of effort would not change much in the presence of the spinal curvature. Asymmetric muscle activity would be necessary to perform these efforts, but the total activity (force) of all muscles would not differ much. However, the motion segments of the spine would be more symmetrically loaded in the scoliosis spine than that symmetric in the sagittal plane. This asymmetric loading may contribute to the progression of scoliosis by producing asymmetric growth in young patients, and asymmetric remodelling in skeletally mature patients.

The three-dimensional (3-D) modelling of the spinal shape by least square Fourier series to evaluate local measurement of geometric torsion for scoliotic spine shows limitations. In fact, this method does not allow the definition of a “true” 3-D inflexion point in double major scoliotic curves. Torsion values computed in 3-D inflexion regions are consequently non-representative since they result in numerically instable “large torsion spike”. Simulation were performed to analyzed the torsion “spike” problem and revealed that numerical instabilities occur because the second derivative of parametric functions x(t), y(t) and z(t) does not equal zero for the same t value. The development of a “torsion spike” elimination technique, by the imposition of a “true” 3-D inflexion point, results in numerical stability, without significantly modifying the general shape of the scoliotic curve. Applying Frenet’s formulas to this resulting corrected curve allow the analysis of the geometric torsion phenomenon associated with many types of scoliotic shapes.