Fig 1.
Posterior-anterior view of a female adolescent with thoracic right convex scoliosis: a.) body scanner image, with slightly inclined waistline (dashed line) and more pronounced waist on the right side, marked by arrow. b.) X-ray image (left/right flipped) with Cobb angle annotation. The red markers indicate the center positions of the vertebral bodies, using analysis tools described in [29]. The orange dashed line shows the result of a least squares polynomial fit through the marker positions. This fit, hence describes the course of the vertebral column in the coronal plane and is then further used for comparison with the model simulations.
Fig 2.
Principle components used to built the model of the ribcage and vertebral column of a female adult and corresponding anatomical dimension parameters, after [31]. (See this reference also for definition in detail of parameters ①, ②, ④–⑧, ⑩.) a.) and b.): Top and side view of the vertebra T6. c.) and d.): Top and side view of the left and right 6th rib. e.) and f.): Front and side view of the combined manubrium and sternum.
Fig 3.
Model of ribcage and vertebral column (MoRCaVC) of an adult female, based on anatomical geometry and dimension parameters after [31, 32].
Table 1.
Acronyms, names and parameters.
Table 2.
Material properties of the model components.
ND: non deformable object; Px: patient number.
Table 3.
Contacts.
Fig 4.
Distorted model inside patient’s body scan image.
Transparent back face of an adolescent female 3D body scan with the resulting FEM calculated model inserted at its best match in posterior-anterior view. The markers denote the centre positions of the vertebral bodies along the vertebral column from T1 to L5. The dashed line denotes the course of the distorted vertebral column obtained by least square polynomial fit passing through the marker positions.
Fig 5.
Transverse cuts at the vertebral levels T1 to L3 through the body scan image (shown in Fig 4) with the FEM calculated model inserted visualizing the individual lateral translation and axial rotation of the vertebrae and ribcage at its best match.
Fig 6.
Sequential model distortion in relation to the static body scan image upon opposite lateral translations at the vertebrae T8 and L2 (panels a.) to c.) and subsequent active clockwise axial rotation of vertebra T8 (panels d.) and e.)). While the coronal views (left panels) visualize the overall lateral model distortion, the resulting anti-clockwise rotation of vertebral T8 from only lateral translations at the vertebrae T8 and L2 is visible in the transverse views (right panels).
Fig 7.
Overlay of X-ray and simulation result images at best match according to visual inspection, with different transparencies from left to right (for better visualization). The colour code shows the total displacement from the initial state—a straight vertebral column in the coronal view.
Fig 8.
Comparison of the courses of the vertebral column extracted from X-ray (dashed lines) and model calculation (solid lines) for patients P1 and P2 (a.) and c.)), respectively, showing their absolute lateral deviation. The absolute lateral differences between the curves at the vertebral levels for either patient are depicted in b.) and c.). The parameter A quantifies the grey area between the curves and hence represents a measure for the degree the courses derived from X-ray and model calculation matches each other. (Note that the X-axes have been scaled for better visualization).
Fig 9.
Stress on intervertebral discs.
Effective stress integrated per volume of all IVDs (left) and at three principle nodes in the transverse plane between the vertebral level T8 and T9 (right). The states zero to ten correspond to the prescribed lateral displacements at the vertebral levels T8 and L2 and the states eleven to twenty correspond to the subsequent rotation around the z-axis of the vertebra T8, in accordance with the sequential representation in Fig 6.
Fig 10.
Strain on intervertebral discs.
Effective Lagrange strain integrated per volume of all IVDs (left) and at three principle nodes in the transverse plane between the vertebral level T8 and T9 (right). The states zero to ten correspond to the predefined lateral displacements at the vertebral levels T8 and L2 and the states eleven to twenty correspond to the subsequent rotation around the z-axis of the vertebra T8, in accordance with the sequential representation in Fig 6.