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Analyse de la relation entre les déformations scoliotiques du tronc et celles des structures osseuses sous-jacentes
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Conventional terminology of three·dimensional descrip·
tion of spinal deformity is ambiguous and mostly tied to either a frontal or sagittal plane view of the spine. The article proposes a rationalized system for describ· ing the shape of the spine. The spine is viewed as a line in space ('vertebral body line') with three 'angula· tions' specifying the orientation of each vertebra. Four
axis systems are defined for the whole body, the spine,
curve regions, and individual vertebrae, respectively. These in turn define the principal planes of the body, spine, curve regions, and vertebrae. Curvature can be defined as a local measure at a point on the vertebral body line, or as a regional measure between specified end vertebrae. Torsion is defined both as a local geo· metric property of the vertebral body line, and as mea· sure of the relative axial plane angulations between specified vertebrae. Linear distance measures define
the deviations of specified vertebrae from the local, re· gional, spinal, and global axis systems. Practical recom mendations for positioning patients are made. This
new system of terminology recognizes the 3-dimen· sional nature of scoliosis and other spinal deformities and is intended to rationalize communication in both research and clinical practice. [Key words: spinal defor· mity, terminology, standardization, three·dimensions]
Multivariate data analysis permits the study of observations which are finite sets of numbers, but modern data collection situations can involve data, or the processes giving rise to them, which are functions. Functional data analysis involves infinite dimensional processes and/or data. The paper shows how the theory of L‐splines can support generalizations of linear modelling and principal components analysis to samples drawn from random functions. Spline smoothing rests on a partition of a function space into two orthogonal subspaces, one of which contains the obvious or structural components of variation among a set of observed functions, and the other of which contains residual components. This partitioning is achieved through the use of a linear differential operator, and we show how the theory of polynomial splines can be applied more generally with an arbitrary operator and associated boundary constraints. These data analysis tools are illustrated by a study of variation in temperature–precipitation patterns among some Canadian weather‐stations.
The problem of roentgenographic evaluations of vertebral rotations has been studied using upper thoracic, thoracic, and lumbar segments of a normal spine which were marked with wires and which then had roentgenograms made in known increments of rotation. The results showed a definite difference between a grading system based upon the position of the spinous process and a system based on the position of the pedicle located on the convex side of the curve. The pedicle technique proved to have definite merit in its case of application over a wide range of rotation and its over-all consistecy of values evens when applied to the scoliotic spine.
As an additional part of the study, the approximate range of degrees of rotation represented by each grade of rotation was determined.
Finally, by combining the two parts of this study, we were able to propose a simplified method of describing vertebral rotation, which correlates the amount or percentage of convex pedicle displacement seen on roentgenograms with the approximate degrees of rotation present in that vertebra.
Interobserver variations for measurements of the Cobb angle on radiographs of patients who had kyphosis were comparable with those on the radiographs of patients who had scoliosis. Four staff orthopaedists and one physical therapist measured eight radiographs that showed scoliosis and twenty that showed kyphosis. The measurements were made on two occasions and in random order. For scoliosis, the average difference between readings was 3.8 degrees, and 95 per cent of the differences were 8 degrees or less (range, 0 to 10 degrees). These findings were in keeping with those of other published reports. For kyphosis, the average difference between readings was 3.3 degrees, and 95 per cent of the differences were 7 degrees or less (range, 0 to 30 degrees). One investigator rated the kyphosis radiographs with respect to clarity. There was a trend to less variation with clearer radiographs, but this was not significant. The end-vertebrae were pre-selected for some radiographs and were freely chosen by the interpreter for others. Reliability was not significantly improved when the end-vertebrae of the curve had been pre-selected. Using the statistical method called tolerance limits, we determined that if one were to be 95 per cent confident that a measured difference represented a true change, the difference would have to be 10 degrees for scoliosis radiographs and 11 degrees for kyphosis radiographs. The probability that a measured difference is due to measurement error alone (that is, a false-positive reading) was calculated.
In this paper we propose a new method of classification, which goes beyond the frontal plane projection of the spine, to describe the 3-D shape of a scoliotic spine. A 3D analysis of the spine in terms of geometric torsion has revealed three distinct patterns of torsion in major scoliotic curves. Geometric torsion had extreme values at the levels of upper and lower vertebrae and zero or nearly zero values at the levels of the apices. Torsion phenomenon can be unidirectional or bi-directional in both single and double major curves.
Clustering of gene expression data collected across time is receiving growing attention in the biological literature since time-course experiments allow one to understand dynamic biological processes and identify genes governed by the same processes. It is believed that genes demonstrating similar expression profiles over time might give an informative insight into how underlying biological mechanisms work. In this paper, we propose a method based on functional data analysis (FNDA) to cluster time-dependent gene expression profiles. Consideration of clustering problems using the FNDA setting provides ways to take time dependency into account by using basis function expansion to describe the partially observed curves. We also discuss how to choose the number of bases in the basis function expansion in FNDA. A synthetic cycle data and a real data are used to demonstrate the proposed method and some comparisons between the proposed and existing approaches using the adjusted Rand indices are made.
Scoliosis severity, measured by the Cobb angle, was estimated by artificial neural network from indices of torso surface asymmetry using a genetic algorithm to select the optimal set of input torso indices. Estimates of the Cobb angle were accurate within 5° in two-thirds, and within 10° in six-sevenths, of a test set of 115 scans of 48 scoliosis patients, showing promise for future longitudinal studies to detect scoliosis progression without use of X-rays.