Analysis and simulation of progressive adolescent scoliosis by biomechanical growth modulation

Abstract

Scoliosis is thought to progress during growth because spinal deformity produces asymmetrical spinal loading, generating asymmetrical growth, etc. in a 'vicious cycle.' The aim of this study was to test quantitatively whether calculated loading asymmetry of a spine with scoliosis, together with measured bone growth sensitivity to altered compression, can explain the observed rate of scoliosis progression in the coronal plane during adolescent growth. The simulated spinal geometry represented a lumbar scoliosis of different initial magnitudes, averaged and scaled from measurements of 15 patients' radiographs. Level-specific stresses acting on the vertebrae were estimated for each of 11 external loading directions ('efforts') from published values of spinal loading asymmetry. These calculations assumed a physiologically plausible muscle activation strategy. The rate of vertebral growth was obtained from published reports of growth of the spine. The distribution of growth across vertebrae was modulated according to published values of growth sensitivity to stress. Mechanically modulated growth of a spine having an initial 13 degrees Cobb scoliosis at age 11 with the spine subjected to an unweighted combination of eleven loading conditions (different effort direction and magnitude) was predicted to progress during growth. The overall shape of the curve was retained. The averaged final lumbar spinal curve magnitude was 32 degrees Cobb at age 16 years for the lower magnitude of effort (that produced compressive stress averaging 0.48 MPa at the curve apex) and it was 38 degrees Cobb when the higher magnitudes of efforts (that produced compressive stress averaging 0.81 MPa at the apex). An initial curve of 26 degrees progressed to 46 degrees and 56 degrees, respectively. The calculated stresses on growth plates were within the range of those measured by intradiscal pressures in typical daily activities. These analyses predicted that a substantial component of scoliosis progression during growth is biomechanically mediated. The rationale for conservative management of scoliosis during skeletal growth assumes a biomechanical mode of deformity progression (Hueter-Volkmann principle). The present study provides a quantitative basis for this previously qualitative hypothesis. The findings suggest that an important difference between progressive and non-progressive scoliosis might lie in the differing muscle activation strategies adopted by individuals, leading to the possibility of improved prognosis and conservative or less invasive interventions.

Fig. 1

The vicious cycle that represents the widely accepted qualitative explanation for the mechanism of scoliosis progression by mechanical modulation of growth (Hueter-Volkmann ‘law’)

Fig. 2

Geometry (vertebrae and lines of action of muscles) for the model [21] used to calculate the forces (and symmetry of loading) at each of the lumbar vertebrae for differing curve magnitudes. The spinal geometry shown here represents the lumbar scoliosis of magnitude 38 degrees Cobb, apex at L1-2, obtained by averaging the 3-D stereo radiographic reconstructions of 15 patients with lumbar scoliosis. The muscles that cross the lumbar spine are shown as cylindrical structures. Each muscle has an attachment to a lumbar vertebra or to the thorax that is omitted for clarity

Fig. 3

Geometry used in the stress analysis of a vertebra assumed to have an elliptical shape and subjected to a stress that varies linearly from one side to the other

Fig. 4

Data on human adolescent growth of stature [4], sitting height [1, 6, 14, 17, 28], and spinal growth [27]

Fig. 5

Simulated progression of lumbar scoliosis (quantified by Cobb angle), plotted against age for a spine loaded by each of 11 different effort types. Upper panels: the effort magnitude at the lower effort magnitudes; lower panels: the higher effort magnitudes. Left panels: for each of five pure moment efforts generated about the thorax; Right panels: for each of six pure force efforts generated at T-12. In each case, the dotted line shows the average of the 11 solid lines

Fig. 6

Simulated evolution of the lumbar scoliosis as a result of mechanically modulated asymmetrical growth. The initial geometry (unfilled shapes) is the starting geometry at age 11 (13° Cobb lumbar scoliosis). The final geometry (filled shapes) is averaged from the predicted final shapes for all 11 analyzed loading directions at age 16, for the higher magnitude of effort loading conditions. Axis units are mm