3D reconstruction process of the spine: (**a**) anatomical landmarks are digitized; (**b**) the initial model is retroprojected on X-rays to allow model adjustments; (**c**) 3D reconstruction in superior view; (**d**) 3D reconstruction in frontal view

This three-dimensional modelling of the vertebral column provides new insight into the quantitative analysis of scoliotic deformities, described qualitatively by the pioneers René Perdriolle [8], Jean Dubousset, Henri Graf and Ginette Duval Beaupère. Thus it is now established that the main scoliosis curvature has at its extremities, called junctional zones , a limit vertebra which is rotated in the horizontal plane with respect to the adjacent vertebrae (intervertebral axial rotation, IAR—in the inferior and superior zones). The apical vertebra, the most laterally deviated, is also usually the most rotated in the horizontal plane (vertebral axial rotation, VAR). Within the main curvature, each vertebra is rotated relative to the other, from the apex to the lower limit and from the apex to the upper limit, thus describing a torsion phenomenon which is clearly visible in Fig. 1 [9]. Finally, this scoliotic curvature is also characterized by hypokyphosis in the apical region, when observed in the plane of curvature.

Coupled with the modelling of the rib cage, this 3D reconstruction makes it possible to objectify the effect of conservative [10, 11] or surgical [12] treatments. In a study carried out in collaboration with the teams of Saint Etienne University Hospital (Dr Ebermeyer and Courtois) and Trousseau Hospital (Pr Vialle), the analysis of 42 scoliosis patients treated before and after bracing shows that if the brace corrects overall, the angle of Cobb, the lordosis is however decreased in 60% of the cases, and the parameters of the horizontal plane (VAR, torsion, gibbosity) are unchanged in more than 60% of the cases. Vertebral axial rotation is even increased in 14% of cases [13]. Larger scale analyses , linked to the clinical outcome of brace treatment, should lead to a better understanding leading to improved practices and equipment.

Indeed, numerical models make it possible to build large databases in multicentric studies, provided that acquisition protocols are harmonized. The use of data analysis techniques and/or artificial intelligence provides powerful means to classify the data, find the most influential parameters, and ultimately identify useful biomechanical markers for diagnosis and/or development of the therapeutic strategy.

An illustration concerns the identification of a severity index allowing early detection of progressive scoliosis . Screening is important because the treatment is all the more effective when undertaken early. Quantitative observations made on many scoliosis curves lead to establish a “scoliotic deformity signature” , that is to say to characterize the pattern of deformity using a few descriptor parameters (Cobb angle, AIR, AVR, hypokyphosis in apical zone, rotation). A normal spine may randomly present one or other of these attributes, but not this structured combination, and its “signature” will be very different. This very specific pattern of deformity may appear in the early phase. Therefore, it is possible, from the first examination, to establish the signature of each spine and, using a mathematical classification method known as factorial discriminant analysis, to compute a severity index that varies from 0 to 1 depending on whether the signature of the studied spine is closer to that of normal spines or that of severe scoliosis. An initial validation was performed on 56 patients, for whom the severity index was established at the first examination and followed until the end of their growth. The results showed that, in more than 80% of cases, scalability or stability can be predicted from this first examination [14]. These promising results have led to the initiation of data collection on a larger scale to consolidate scientific evidence and to reliably use this index in clinical practice. The follow-up time for the validation is long because it is sometimes necessary to wait several years for the future progression of the patient to be proven; we are now at 64 patients with similar conclusive results.

For degenerative scoliosis in adults, such approaches can be considered and have been initiated [15] to look for early warning signals, especially related to intervertebral rotations which could further be translated into true rotational dislocations destabilizing the spine.

These examples illustrate how quantitative three-dimensional analysis is likely to shed new light on spinal pathology. In addition, these geometric models provide a valuable foundation for the biomechanical models that will be presented below.

## Biomechanical Modelling of Spine

^{2}) as a function of the strain (relative variation in length or angulation, in %). The constitutive equations can be very complex and we will provide a simplified vision. By way of example, the stress–strain curve of a sample of cortical bone is shown in Fig. 3a. The equation is linear and the slope of the line corresponds to the modulus of elasticity E (or Young’s modulus), which characterizes the stiffness of the considered tissue. Another essential mechanical characteristic is the mechanical strength of the tissue considered, that is to say the maximum stress that can be supported before damage to this material. Soft tissue behaviour is generally nonlinear (Fig. 3b), with stiffness progressively increasing with increasing deformation.

### Biomechanical Modelling and Conceptual Analysis

Mechanical modelling therefore requires the completion of geometric modelling by describing schematically the mechanical characteristics of each material in each region of the model. Internal kinematic links must also be modelled (for example, inter-facet contact). A particularly powerful modelling technique, finite element modelling (FEM), is widely used in mechanics and other areas of physics and developed for the spine since the 1980s.

### Subject-Specific Modelling and Treatment Planning

Beyond the conceptual models, it is important to use personalized modelling when the question is, for a given patient, to understand the factors explaining a degenerative process or a mechanical complication because each patient is unique and has his own specificities. A subject-specific geometric model can be obtained from biplanar radiography, or sectional imaging (CT, MRI) or even from ultrasound imaging. However, to build a biomechanical model, it is also essential to document the mechanical properties of the components. There are still technical difficulties, even if great progress has been made in recent years, either by inverse methods for surgery simulation [22, 23] or by direct characterization by ultrasonic elastography, in particular for intervertebral discs [24]. It is also necessary to customize the mechanical loads that may vary depending on the normal or altered postural alignment, and the effectiveness of the muscular actuators. These components will be the subject of paragraph 4.

We will illustrate the interest of these subject-specific models by two very different clinical applications, relating on the one hand to osteoporosis fractures and on the other hand to the simulation of the effect of bracing for scoliosis.