and Spinal Modelling

Fig. 1

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

The possibility of viewing in 3D and from different angles is rich in lessons, as highlighted in the chapter on EOS. In particular, head-to-toe analysis has shown how the erect posture is characterized by maintaining the head above the pelvis [7] and how the aging subject or postural disturbance implements a compensation strategy, by retroverting the pelvis, or even flexing the knees, to maintain this erect posture (Fig. 2).

../images/451372_1_En_32_Chapter/451372_1_En_32_Fig2_HTML.png — Fig. 2

For this patient, the maximized retroversion of the pelvis is insufficient to avoid tilting forward, bending of the knees is necessary to maintain the erect posture, with the head above the pelvis. The head center of mass is close to the center of acoustic meati (CAMs)

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

Biomechanical modelling aims to analyse the response of a mechanical system to forces to which this system is subject. Such modelling consists in schematizing on the one hand the shape of the structure of interest (that is to say, to build a geometric model), and on the other hand the mechanical behaviour of the different components, by describing their constitutive equations. These equations are established by mechanical tests which quantify the internal mechanical stress (force per unit area, in N/mm²) 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.

../images/451372_1_En_32_Chapter/451372_1_En_32_Fig3_HTML.png — Fig. 3

The stress–strain curves make it possible to characterize the stiffness of the material, expressed by the Young’s modulus, as well as its strength, expressed by the maximum admissible stress: (a) typical curve for bone tissue, the behaviour of which is linear, (b) typical curve for a ligament, the behaviour of which is nonlinear

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.

Figure 4 shows two model examples, for a lumbar segment and for a cervical segment. The models are said in finite elements because the virtual structure is mapped in a finite number of elements, each element having its own characteristics. Such an approach makes it possible to differentiate the mechanical characteristics of the cortical and cancellous bone (and to consider their variability within a given vertebra), to differentiate the annulus of the nucleus, the anterior and posterior fibres of the intervertebral disc, each of the ligaments, etc.

../images/451372_1_En_32_Chapter/451372_1_En_32_Fig4_HTML.png — Fig. 4

(a) Lumbar vertebral segment model ; (b) exploded view of the intervertebral disc, highlighting the differentiated modelling between the matrix of the annulus, the collagen fibres included in this matrix and the nucleus; (c) model of cervical spine

Dedicated software then allows to simulate different types of forces exerted on this structure and to compute the mechanical response, in terms of displacements, local strain and global deformation, and mechanical stresses which, if they are excessive, cause the damage to this system. Of course, because of simplifying assumptions and the resultant schemata, the validation of these models is essential to verify the relevance of the numerical response. Spinal models are generally validated by in vitro mechanical tests, in which vertebral segments are fixed at their base and subjected to controlled mechanical loads (compression, flexion, extension, lateral inflexion, rotation). The movements of one vertebra relative to the other are then measured in the three planes of the space, which makes it possible to obtain the behaviour curves (forces or couples vs. linear or angular displacements). Numerical simulation makes it possible to apply virtually the same forces under the same experimental conditions, and the numerical results are compared with the experimental results (Fig. 5) [16]. This model becomes more refined as knowledge evolves.

../images/451372_1_En_32_Chapter/451372_1_En_32_Fig5_HTML.jpg — Fig. 5

For each vertebral level and each type of load, flexion extension, extension, lateral bending and rotation, the in vitro experiments make it possible to quantify the curves of rotations as a function of the applied moment (a grey line by specimen). The behaviour of each model is compared to the different experimental results, to verify that the curves are similar and that the numerical results are within the experimental corridor

Once validated, these models are valuable tools to help thinking: indeed, we can, all things being equal, remove and modify components and analyse their effect. For example, these models allowed to identify the role of geometric parameters in the biomechanical response of the spine [17, 18]. These models are also a powerful means of computer-assisted design of implants: indeed, the simulation of pathology and surgical instrumentation can be realized, and provided that the modelling of the instrumented segment is validated, numerous options can be simulated by varying the different design parameters [19, 20]. Figure 6 shows different examples of implant modelling , and Fig. 7 shows the impact of two posterior implants on the distribution of stresses in the intervertebral disc at the instrumented level and at the adjacent level. Some companies now use modelling on a regular basis because such an approach can drastically reduce the design time of an implant.

../images/451372_1_En_32_Chapter/451372_1_En_32_Fig6_HTML.png — Fig. 6

Simulation of lesions and virtual insertion of different implants

../images/451372_1_En_32_Chapter/451372_1_En_32_Fig7_HTML.png — Fig. 7

Example of a numerical result, showing the stress distribution in the intervertebral disc, for two variants—(a, b) of the same posterior implant

To illustrate the essential enlightenment that modelling offers, we are interested in dynamic instrumentation using pedicular screws and flexible longitudinal connection elements. “Screw loosening” is a mechanical complication resulting in a deterioration of the bone quality around the screws, impacting the holding of the anchorage. A meta-analysis [21] has shown that the rate of screw loosening varies according to scientific publications of 0–72%. This very large variability can be related to differences in implant concepts. Finite element analysis helps to understand that longitudinal stiffness, along the axis of the connecting elements, is of paramount importance. When bending is performed, the interpedicular distance (at the entry points of the screws) increases in an intact vertebral segment (Fig. 8). If the implant breaks this variation, the movement is altered and local stresses can appear. Modelling allows, all things being equal, variation of the stiffness of the longitudinal element. Results show that when the implant, even if it is flexible, has a high longitudinal stiffness, it yields increased mechanical stresses in the pedicles, which may be responsible for the degradation of the anchorage [16]. Although the clinical outcome of a spinal surgery is really very multifactorial, such a conceptual study allows understanding of a key factor of the variability of results from one type of dynamic implant to another, which is useful to better outline the specifications of such implants.

../images/451372_1_En_32_Chapter/451372_1_En_32_Fig8_HTML.png — Fig. 8

Between full flexion and full extension, the interpedicular distance (IPD) between the entry points of the pedicle screws varies. When the longitudinal element does not allow any elongation, the modelling shows that it results in increased stress in the pedicles, which may explain a deterioration of the anchorage

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.

Personalized Simulation to Estimate the Resistance of an Osteoporotic Vertebra

Osteoporosis is a diffuse disease that causes bone fragility, and its prevention is a major issue in public health. Vertebral fractures cause an alteration of the sagittal balance, resulting in severe pain and an increased risk of secondary fractures, impacting the quality of life and independence of the person. Characterization of bone strength is essential to identify at-risk individuals and target preventative therapies. The routine clinical examination is bone osteodensitometry, or DXA (Dual X-Ray Absorptiometry), to estimate bone mineral density (BMD). However, the intrinsic resistance of the vertebra also depends on its shape. Custom finite element models are constructed from QCT (quantitative CT) scanner images, in which the images are previously calibrated for conversion of Hounsfield units ((HU), associated with the attenuation coefficient of the medium traversed) to BMD. The mechanical properties being correlated with the BMD can be personalized for each “element” which composes the model. The latter is then validated by performing mechanical compression tests in vitro on vertebrae that have been scanned beforehand. Subject-specific models are constructed and test conditions are reproduced to compare the estimated fracture strength by numerical simulation with that measured experimentally. Figure 9 shows the ability of such models to estimate the fracture limit for each of the vertebrae.