Patient-Specific Modeling of Scoliosis

Chapter
Part of the Studies in Mechanobiology, Tissue Engineering and Biomaterials book series (SMTEB, volume 09)

Abstract

Current complication rates for adolescent spinal deformity surgery are unacceptably high and in order to improve patient outcomes, the development of a simulation tool which enables the surgical strategy for an individual patient to be optimized is necessary. In this chapter we will present our work to date in developing and validating patient-specific modeling techniques to simulate and predict patient outcomes for surgery to correct adolescent scoliosis deformity. While these simulation tools are currently being developed to simulate adolescent idiopathic scoliosis patients, they will have broader application in simulating spinal disorders and optimizing surgical planning for other types of spine surgery. Our studies to date have highlighted the need for not only patient-specific anatomical data, but also patient-specific tissue parameters and biomechanical loading data, in order to accurately predict the physiological behaviour of the spine. Even so, patient-specific computational models are the state-of-the-art in computational biomechanics and offer much potential as a pre-operative surgical planning tool.

1 Introduction

Scoliosis is a spinal deformity involving a side-to-side curvature of the vertebrae in the frontal plane (Fig. 1a) and axial rotation of the vertebrae in the transverse plane (Fig. 1e). As such, scoliosis is a three-dimensional deformity with patients often demonstrating an overly prominent ribcage and shoulder blade due to the abnormal axial rotation of the vertebrae as well as hip and shoulder asymmetry (Fig. 1e). Adolescent Idiopathic Scoliosis (AIS) is the most common type of spinal deformity, affecting 2–4% of the population (American National Scoliosis Foundation) and there is neither a known cause nor a known cure for the condition. As such, treatment can only attempt to prevent curve progression and/or reduce the spinal deformity.
Fig. 1

a Scoliosis spinal deformity. b Anterior scoliosis implant. c Implant complication—rod fracture. d Implant complication—top screw pullout (circled). e Transverse slice showing axial rotation of vertebra, posterior rib hump and anterior ribcage prominence

In conservative treatment for AIS, orthotic braces are used in an attempt to prevent curve progression, but in cases where this is not successful in arresting progression, or in patients with a severe deformity, corrective surgery is the only option. This involves attachment of rods to the patient’s spine using screws inserted into the spinal vertebrae (Fig. 1b). The implant construct shown in Fig. 1b is an anterior construct, however posterior constructs (not shown), in which long pairs of rods are attached to the back of the spine using screws, hooks and wires, are also commonly used in scoliosis correction surgery. In either approach, bone graft is applied at the time of surgery to encourage fusion of adjacent vertebrae, so that in a successful procedure the metal implant is required to provide stiffness and stability to the spine for the 3–6 months after surgery so that bony fusion can occur. After this the spinal loading is borne by the fused vertebrae and while the implant often remains in situ, it has no significant load bearing role.

Despite significant stated advantages of the anterior single rod procedure over posterior techniques, including reduced blood loss, reduced muscle dissection and improved cosmesis [22, 29, 41], the anterior fusion procedure still brings with it high (15–20%) implant-related complication rates [4, 31]. Such complications include screw pullout (Fig. 1d) and rod fracture (Fig. 1c). The most significant outcomes for the patient from the surgical screw and rod failures are the potential onset of back pain and loss of deformity correction [4].

Currently, surgical planning decisions are based on factors such as scoliosis curve severity and curve type (assessed using various radiographic classification systems), pre-operative patient assessment (e.g. flexibility tests) and surgeon judgement. These factors introduce a level of subjectivity into the surgical planning and as such, the surgical procedure chosen for a particular patient may differ considerably between surgeons [3]. The ability of the surgeon to correct spinal deformity while avoiding complications requires a balance between the applied corrective forces (excessive forces will cause implant breakage or tissue damage) and the degree of deformity correction attempted (insufficient correction will leave an unbalanced spine after surgery which is prone to further deformity progression even after skeletal maturity). Attaining this balance is a complex biomechanical challenge. To address this challenge our research group has developed spinal simulation techniques, enabling patient-specific finite element (FE) models of individual patient’s spinal anatomy to be created. Using these FE models, the forces and deformations in the implant and spinal tissues are predicted for intra-operative and physiological spinal loads. Spinal deformity correction is essentially a structural problem, so the use of patient-specific finite element models during pre-operative planning of corrective surgery for scoliosis can potentially provide surgeons with a powerful support tool in making more informed decisions regarding the most appropriate procedure for an individual patient. While our research to date has focused on anterior, single rod scoliosis correction constructs, the patient-specific spinal modeling techniques we describe here are broadly applicable for simulating spinal disorders and optimizing surgical planning for other types of spinal surgery.

Other researchers in the field of spine biomechanics and simulation have made substantial contributions to addressing the need for a better understanding of scoliosis biomechanics (for example, [35]) and moreover, the need for patient-specific thoracolumbar spine models to inform surgeons in their clinical decision making (for example, [2, 16, 32]). However, the models developed to date often use highly idealized representations for the spinal anatomy, with either rigid bodies [2] or elastic beam elements [16] representing the spinal vertebrae; and lumped parameter (multi degree-of-freedom spring) representations to simulate the collective behaviour of the spinal ligaments, annulus fibrosus and nucleus pulposus in the intervertebral disc [2, 16]. Physiologically, the spinal vertebrae at each joint are connected by seven separate ligaments, with lines of action between specific bony landmarks on the adjacent vertebral bones. The intervertebral disc alone is a highly complex structure whose mechanics are governed by a complex interplay between collagen fibres embedded within adjacent lamellae of the annulus fibrosus and the fluid-filled, pressurized nucleus pulposus which the annulus surrounds [20]. Furthermore, in previous models the contribution of the ribcage is either not included or represented using an idealized spring stiffness for adjoining spinal segments [32]. However, the ribcage and its articulation with the spinal column (costovertebral joints) have been shown to be of considerable importance in governing the biomechanics of the spine, with as much as 40% decrease in spinal stiffness observed in cadaveric human spines following ribcage removal [27, 40]. All these structures play an important role in the overall biomechanics of both the intact and surgically altered spine.

Modern imaging techniques, visualization algorithms and image post-processing methods permit patient-specific anatomical representations for the osseous structures to be simulated. However, of equal importance in developing patient-specific spine models which are clinically useful, is the ability to derive not only patient specific osseous anatomy but patient specific material properties for the spinal tissues. Of particular importance are the soft tissue structures in the spine (ligaments, muscles and intervertebral discs) as these facilitate the articulation between adjacent vertebrae during physiological motion and primarily govern patient flexibility.

The focus for our spinal modeling has been to develop techniques for generating patient-specific models of scoliosis patients, which are sufficiently detailed (in terms of the spinal anatomy and individual spinal structures represented) to allow accurate simulation of the effects of surgery on the thoracolumbar spine. To this end, our patient-specific spine model includes detailed representations for:
  • the vertebrae (both vertebral body and posterior elements);

  • the intervertebral discs (annulus fibrosus lamellae, collagen fibres and nucleus pulposus);

  • the seven spinal ligaments spanning each joint;

  • the zygapophyseal (facet) joints;

  • the vertebrae-rib articulations (costo-vertebral and costo-transverse joints); and

  • the ribcage (ribs, sternum and costo-sternal joints).

The following sections will detail our methods for simulating both pre-operative flexibility tests and intra-operative deformity corrections; and our investigations to determine patient-specific soft tissue parameters using physiological load cases on the intact and surgically altered scoliotic spine. This chapter concludes with a discussion of current challenges and future work with regard to developing clinically useful and physiologically accurate computer simulations of an individual patient’s spine.

2 Patient-Specific Modeling and Analysis

2.1 Model Development

The three-dimensional, low dose (2.0–3.7 m Sv radiation dose) computed tomography (CT) dataset (supine positioning, 512 × 512 pixels per slice, 1.25 mm axial slice spacing, 2.5 mm slice thickness) for an individual patient is obtained prior to surgery using a helical CT protocol (GE Lightspeed Plus, General Electric Medical Systems, Milwaukee, WI, USA). CT scans are clinically indicated prior to keyhole anterior scoliosis surgery as CT scanning allows safer screw sizing and positioning [13]. The CT dataset is then imported into custom image processing software (Matlab R2007b, The Mathworks, Natick, MA) where user-selected landmarks on the osseous anatomy (vertebral bodies, superior and inferior endplates, posterior elements, articulating surfaces on the zygapophyseal joints and sternum) are selected and exported as three-dimensional co-ordinate data (Fig. 2). These co-ordinate data define key landmarks at each vertebral level in the thoracolumbar spine.
Fig. 2

Custom developed image processing interface for defining user-selected landmarks on pre-operative CT datasets

These data points are imported into custom preprocessing software (Python 2.5 programming language, Python Software Foundation) where they are used to reconstruct the three-dimensional, patient-specific geometry using parametric descriptions for the bony structures of the spine and ribcage. Using the custom pre-processor, the osseous anatomy is meshed for analysis using Abaqus 6.7 (Simulia, Providence, RI) (Fig. 3) and it is possible to control the mesh density in each of the model components, to optimize the solution time and model accuracy.
Fig. 3

Three-dimensional osseous reconstruction converted to a finite element mesh for analysis using Abaqus 6.7

The parametric description for the outer profile of the vertebral endplates uses a series of elliptical and cubic equations with C1 continuity [21] (Fig. 4d). The axial profile for the vertebral bodies is extrapolated from the endplates, using a second order polynomial derived with user-selected points on the vertebral cortex that describe the concavity in the frontal and sagittal planes. Similarly, the intervertebral discs are interpolated between the transverse profiles of the adjacent vertebral endplates, thus defining the outer profile of the annulus fibrosus. The outer boundary of the nucleus pulposus is defined by scaling the outer anulus profile about its centroid. The curved transverse profile of the zygapophyseal joint articulating surfaces is described using sinusoidal curves derived from user-selected points on the joint surfaces at each vertebral level. The representation of the three-dimensional anatomy for the stiff posterior regions of the vertebrae (spinous processes, transverse processes, pedicles and lamellae) are simplified, using quasi-rigid, linear beams between user-selected points on the posterior elements (Fig. 4d).
Fig. 4

a A posterior view of the meshed thoracolumbar spine and ribcage, showing the intervertebral discs in purple, vertebra in grey and bluebroken lines denoting the inter-costal soft tissue connections (circled in red for spine level T11–T12) between ribs of adjacent thoracic levels. b Posterior view of the upper thoracic spine, bluebroken lines denote the costo-transverse connections (circled in green for spine level T3) between the transverse process and the adjacent rib surface. c Posterior view of T2, showing the costo-vertebral beam connections as clusters of light-blue beams (circledinblue for the T1–T2 and T2–T3 connections). d T12 vertebra, showing the transverse profile of the vertebral endplate highlighted in purple, the posterior bony elements represented as beam elements (shown in green) and the articulating surfaces of the zygapophyseal (facet) joints

The upper and lower edges of the ribs were separately represented using fifth order polynomials to describe the variation of the rib profile with distance along the edge from the costo-vertebral joint. Three separate polynomial equations described the profile of the rib edge in each plane and the polynomial constants were derived from user-selected landmarks along the rib edge. Similarly, user-selected landmarks defined the manubrium and sternum, with these structures represented as planar surfaces. The costal cartilage was modeled using a linear interpolation between the sternum/manubrium and the medial rib ends, while the costo-sternal connections were modeled as beam connectors for thoracic levels T1–T7.

Anatomically, the costo-vertebral joint articulates with both the superior and inferior postero-lateral cortices of the adjacent vertebra as well as the lateral surface of the intermediate intervertebral disc. As mentioned, the costo-vertebral joints have been shown to be of key importance in governing the biomechanics of the spine [27, 40] and in light of this, our thoracolumbar spine model represents these joints in detail [19]. The costo-vertebral joints at each spinal level are represented using ‘clusters’ of beam elements, connecting the medial rib with the adjacent vertebral cortices and intervertebral disc surface (Fig. 4b, c). The beam properties were defined to provide a representative cross-sectional joint area of 46 mm2 which was based on the approximate articulating region between the rib and the postero-lateral vertebrae/disc surfaces. Our computational representation for the costo-vertebral joints is relatively complex in an attempt to capture the biomechanical behaviour of this joint. As such, we have conducted a separate finite element study on a single thoracic motion segment to ensure this representation correctly reproduces the physiological behaviour of a human joint (see below). The left and right costo-transverse joints were represented as rigid, kinematic constraints between the lateral aspect of the transverse processes and the posterior most surface of the adjacent rib (Fig. 4b).

The anterior longitudinal ligament (ALL), posterior longitudinal ligament (PLL), inter/supra-spinous ligament (SL), inter-transverse ligament (ITL), ligamentum flavum (LF) and capsular ligaments (CL) were represented as linear connectors between the bony attachment points for each ligament. No ligament wrapping has been represented. Similarly, the inter-costal soft tissue connections were represented as obliquely oriented linear connectors between the edges of adjacent ribs (Fig. 4a—circled in red for level T11–T12). Anatomically, these soft tissues connect adjacent ribs and vary in orientation along the rib and between ribs, so connector elements were inclined at 50–60° to the edge of the inferior rib.

The element types used to simulate each of the structures represented in the thoracolumbar spine model are detailed in Table 1.
Table 1

Element types, material types and material parameters defined for each structure in the thoracolumbar spine model

Structure

Element type

Material type

Material parameters

Reference

Cortical bone

4-node shell

Linear elastic

E = 11,300 MPa υ = 0.2

[23]

Cancellous bone

First order brick

Linear elastic

E = 140 MPa υ = 0.2

[23]

Posterior elements (pedicles, lamellae, transverse processes, spinous processes)

Linear beam

Linear elastic

Quasi-rigid

 

Zygapophyseal joint bone

4-node shell

Linear elastic

As for cortical

 

Anulus fibrosus—ground substance

First order brick

Hyperelastic, Mooney-Rivlin

C10 = 0.7

C01 = 0.2

[25]

Anulus fibrosus—collagen fibres

Tension-only, embedded rebar

Linear elastic

E = 500 MPa υ = 0.3

[15, 38]

Nucleus pulposus

3D, 4-node fluid

Hydrostatic fluid

Incompressible

[20, 24]

Costal rib bone/Sternum

4-node shell

Linear elastic

E = 9,860 MPa υ = 0.3

[14]

Costal cartilage

4-node shell

Linear elastic

E = 49 MPa

υ = 0.4

[14]

Costo-vertebral joint

Linear beam

Linear elastic

Ecompr = 245 N mm−1

Torsion stiffness, k = 4,167 N mm rad−1

Bending stiffness, k = 6706 N mm rad−1 (average antero-posterior and cranio-caudal flexion stiffness)

[1, 17]

Ligaments—ALL and PLL

Spring

Nonlinear elastic

Piecewise, nonlinear

[26]

Ligaments—SL, ITL, LF,CL

Axial connectors

Nonlinear elastic

Piecewise, nonlinear

CL, SSP–[34];

ITL—[5];

LF—[26]

Inter-costal connections

Axial connectors

Linear elastic

E = 25 MPa

[36]

There is a paucity of experimental data characterising the mechanical behaviour of soft tissues from adolescent, scoliotic spines; with the only methods to derive such parameters being either direct, intra-operative measurement (which is highly challenging due to difficulties in physically accessing and accurately testing tissues) or inverse determination based on biomechanical modeling of pre-operative patient flexibility tests. Few researchers attempt to incorporate patient-specific tissue properties in thoracolumbar spine models for investigating scoliosis biomechanics [16].

In the absence of material parameters describing the mechanical behaviour of the adolescent osseous and soft tissue structures, materials in our models were initially derived from data for adult spinal tissues (Table 1). Bending and torsional stiffness parameters prescribed for the beams representing the costo-vertebral joints were derived from Lemosse et al. [17], who quantified the mechanical behaviour of human cadaveric costo-vertebral joints in the three axes of motion. The material parameters listed in Table 1 were defined as a benchmark set of material data.

The following sections will detail our methods for defining physiological loading conditions on both the intact and surgically altered spine and our recent findings relating to determination of individualized patient tissue properties.

2.2 Validation of the Single Motion Segment Representation

We have previously conducted FE investigations of a thoracic single motion segment, in order to validate the modeling assumptions employed in our full thoraculumbar spine model [19] (Fig. 5a). This investigation reproduced the loading and boundary conditions employed by Oda et al. [27] and since anatomical data for the motion segments tested in this previous study were not available, anatomical data from the Visible Woman (The Visible Human Project, US National Library of Medicine) was simulated. Oda et al. [27] conducted an experimental study of a thoracic motion segment, to determine the change in segmental stiffness with successive removal of joint structures (intervertebral disc, right cost-vertebral joint, right costo-transverse joint and left costo-vertebral joint). For a 2,000 N mm applied moment, the average error between the simulated rotations about the three axes of motion in the intact joint and the in vitro data of Panjabi et al. [28] was 17% (Fig. 5b). The computational results for the simulated joint with four stages of destabilisation showed similar reductions in segmental stiffness to those observed experimentally by Oda et al. [27] (Fig. 4b). Given the uncertainty in anatomy mentioned above, these results provided significant confidence in our modeling methodology for representing both the spinal motion segments (including rib attachments) and by extension the full thoracolumbar spine, since the full model is a series of inter-connected motion segments.
Fig. 5

a FE model representation of thoracic single motion segment. b Comparison of in vitro and FE predicted joint stiffness for an applied moment of 2,000 N mm, for the intact case [28] and four successive stages of joint destabilization [27] (Discectomy—complete removal of the intervertebral disc, RtCVJt—removal of the right costo-vertebral joint, RtCTJt—removal of the right costo-transverse joint, LftCVJt—removal of the left costo-vertebral joint)

3 Simulating Load Cases in the Intact and Surgically Altered Spine

To date, our patient-specific modeling research has focused on two load cases; (1) a pre-operative clinical assessment known as the fulcrum bending radiograph, and (2) the actual intra-operative deformity correction performed by the surgeon to attach a single rod anterior implant and correct the scoliotic spinal deformity. These load cases are both well suited to initial model development and validation because they are biomechanically well-defined (muscle activation in both cases is minimal), and we have access to detailed clinical and radiographic data for assessment of model predictions. Given the previously mentioned lack of material property data for paediatric spinal tissues, we sought to investigate the importance of patient-specific soft tissue parameters in accurately predicting both pre-operative patient flexibility and intra-operative deformity correction.

In an initial series of patients, we used CT datasets for five AIS patients to generate patient-specific, full thoracolumbar spine models (Table 2). Each of these models was analysed under the two load cases just mentioned and these are described in more detail below. The Cobb angle is the standard measure of scoliosis severity, defined as the maximum angle between the most tilted upper and lower vertebrae in a scoliosis curve, and is shown graphically in Fig. 7 below. Cobb angle is measured clinically using two dimensional plane radiographs, but can also be readily calculated from the deformed configuration of the computer models.
Table 2

Patient details and clinical Cobb angle measurements (degrees)

Patient ID

Age

Gender

Pre-operative Cobb angle

Fulcrum bending Cobb angle

Surgically corrected Cobb angle

1

14

M

53

34

30

2

14

F

44

26

14

3

13

F

40

15

1.6

4

10

F

58

15

5

5

22

F

42

8

7

3.1 Fulcrum Bending Radiograph: Clinical Load Case 1

The first of these load cases, the fulcrum bending radiograph, is taken pre-operatively to clinically assess patient flexibility prior to surgery [6]. The patient lays laterally over a padded cylindrical bolster (Fig. 6a), with the convex side of their curve toward the bolster surface. When in the final position, the patient’s shoulder should be just suspended above the table with their pelvis and lowermost arm being the only point of contact between their upper-body and the table (Fig. 6a). In lying over the bolster, the patient’s lateral deformity will reduce under the action of gravitational forces due to body weight—note that this is a passive deformity correction since there is no voluntary muscle activation during the activity. The magnitude of the deformity reduction over the fulcrum is a clinically useful parameter because it indicates how much deformity correction the surgeon can expect to achieve clinically. Due to its passive nature (minimal muscle activation), this loading case is well suited for analysis with a passive osseo-ligamentous FE model and was simulated in the intact (surgically un-altered) model for each patient.
Fig. 6

a Fulcrum bending—patient positioned over the bolster. b Patient-specific spine model positioned over the bolster, showing segmental torso loads as greenarrows and point load representing the head/neck weight as red arrow (NB. Arrows are not to scale)

Patient-specific, CT-derived segmental torso weights for each vertebral level were determined using custom-developed software (Matlab R2007b). These weights were calculated using an average tissue density of 1.04 × 10−3 g mm−3 [10] and were applied at the CT-derived centroid of each vertebral level in the transverse plane (Fig. 6b). A load vector representing the full weight of the uppermost arm and half the weight of the lowermost arm was applied at the centroid of the T1 vertebrae in each model. The magnitude of this vector equated to 9% body weight [10]. Additionally, a load vector equivalent to the weight of the head and neck (8% body weight) [10] was simulated as a point load, applied superior to the uppermost vertebrae in each model. The bolster was simulated as a rigid body and rigidly constrained. A frictionless, tangential contact relationship was defined between the bolster surface and each rib and an exponential, normal contact relationship was used to represent the foam layer covering the bolster surface. The spine was free to rotate about a point simulating the contact between the pelvis and the table on which the patient rests.

Clinically, the reduction in Cobb angle while the patient lies over the bolster is compared with the Cobb measured from a standing radiograph, in order to provide a clinical measure of patient flexibility. This measure is called the Fulcrum Flexibility [6], FF, and is calculated according to Eq. 1. Lateral deformity is measured using Cobb Angle [7] (Fig. 7a, b).
Fig. 7

Comparison of lateral deformity, measured using Cobb angle, between a the standing radiograph, b the fulcrum bending radiograph and c the deformed patient-specific spine model for the fulcrum bending load case

$$ {\text{Fulcrum Flexibility, FF}} =\frac{{ ( {\text{Standing\, Cobb\, Angle}} - {\text{Fulcrum\, Cobb\, Angle) }}}}{\text{Standing Cobb Angle}} \times 100\% $$
(1)

Following analysis of the model under the fulcrum bending load case, the simulated FF was calculated for each of the five patient spine models and compared with the clinically measured value. The simulated FF was calculated using the predicted Cobb angle measured from the initial, undeformed spine geometry and the Cobb angle once the spine was positioned over the bolster (Fig. 7c). However, since CT scans on which the initial geometry of the FE models are based are performed while the patient is supine, the Cobb angle measured from the initial, unloaded model spine geometry is always less than the same patient’s Cobb angle measured clinically on a standing radiograph. This difference between scoliosis severity in supine and standing positions has been previously measured, and therefore can be corrected for. On average, the difference between the Cobb angle measured from supine CT images and standing radiographs is 9° [37]. So that the predicted Cobb angle for the undeformed spine geometry could be compared to the clinically measured value (measured from standing radiographs), the predicted model value was therefore increased by 9° before the simulated FF was calculated.

Furthermore, an acceptable error range of ±5° was defined for comparisons of the predicted and clinically measured Cobb angles, since this is the accepted variability associated with clinical measurements of plane radiographs [39]. The model predicted results for the fulcrum bending Cobb angle agreed with the clinically measured fulcrum flexibility (FF) for only two of the five patients and these two patients were those with a clinical FF of less than 50% (Fig. 8). In the context of the fulcrum bending radiograph, patients with a clinical FF of less than 50% are defined as ‘stiff’ and with a clinical FF greater than 50% are defined as ‘flexible’.
Fig. 8

Comparison of clinical and predicted values for the fulcrum bending Cobb angle (degrees) and FF (%). Tick symbol denotes simulation results within the clinically accepted error in Cobb angle measurement of ±5°, cross denotes simulation results outside the clinically accepted error range

Figure 9 shows a qualitative comparison of the predicted and the clinically observed deformed shapes for the spinal column—to obtain this figure the outline of the model-predicted, deformed spinal column was overlaid on the clinically obtained fulcrum bending radiograph for two patients (patients two and four). (We note that other researchers [11, 33] have conducted a quantitative investigation of spinal curvature measured from radiographs and we intend to adopt similar quantitative techniques in future investigations comparing the clinical and FE-predicted deformity.) Clinically, patient two was classified as a ‘stiff’ curve and the predicted results were within the acceptable error range for the deformed Cobb angle and FF (Fig. 8). Qualitatively, the predicted curvature of this patient’s spinal column once over the bolster was similar to the clinically observed curvature for the vertebral levels T5–T12—which was the deformed region of the thoracic spine over which the Cobb angle was measured (Fig. 9a). Conversely, the predicted results for patient four were outside the acceptable error range for deformed Cobb angle and FF and the qualitative comparison of predicted and clinically observed spinal column curvature showed dissimilarities in deformed spine shape for vertebral levels T1–T8 (Fig. 9b).
Fig. 9

Overlay of the binary outline from the deformed spinal column and the coronal fulcrum bending radiograph. a Patient 2, stiff patient; b Patient 4, flexible patient

The mismatch between simulated and clinical spine curve shapes displayed in Fig. 9b was similar for all three patients with a predicted FF outside the acceptable clinical error range (Fig. 8, patients 3–5). Both the qualitative and quantitative comparison of the model predicted and clinical FF results suggested that the patient-specific spine models for these patients (using adult spine tissue properties from Table 1) were overly stiff, with the predicted segmental rotations in the coronal plane too small for the given segmental torso weights. For these patients, the use of personalized tissue parameters which characterize the patient-specific tissue response would be expected to result in improved predictions of the spine behaviour. However, the predicted results for patients with a clinical FF less than 50% (clinically ‘stiff’), showed good agreement (i.e. less than ±5° error) with the clinical data, suggesting that for a subset of patients the benchmark tissue material properties derived from adult data are an appropriate representation for the adolescent tissues.

3.2 Towards Patient-Specific Soft Tissue Properties: What Have We Learned from the Fulcrum Bending Load Case?

Having compared the clinical and predicted FF for the benchmark set of (adult) tissue parameters with a pilot group of five patients, the next challenge is to determine an appropriate method to adjust these tissue parameters to achieve accurate patient-specific tissue properties for those patients where the benchmark (adult) tissue properties from existing literature do not provide a correct prediction of the physiological spine biomechanics. Spinal flexibility is influenced by several soft tissue structures, including the spinal ligaments, the intervertebral disc (annulus fibrosus and nucleus pulposus), the zygapophyseal joints and the cost-vertebral connections. Moreover, the influence of these structures may vary depending on the particular loading condition experienced by the spinal joints. Since spinal flexibility as measured by the fulcrum bending radiograph is a single numeric parameter (FF), the problem of determining a unique set of patient-specific tissue parameters which characterize this flexibility is difficult. However, our previous studies investigating patient-specific tissue parameters have concluded that only a few of these structures are of key importance in governing spinal flexibility [9, 19] and these structures will now be discussed.

In a previous FE modeling study, we conducted a detailed FE investigation of a single motion segment (SMS) to better understand the influence of the individual spinal ligaments and disc structures on the segmental stiffness (as measured by vertebral rotation) [9]. The SMS model was developed using the same modeling parameters and methods as the full thoracolumbar spine model. The loading condition simulated the physiological limits of rotational displacement in the three planes of motion (flexion, extension, left/right lateral bending, left/right axial rotation) [30], with rotations applied about a centre of rotation which simulated the physiological joint. The results from these analyses showed firstly, that by individually removing the spinal ligaments (setting stiffness parameters equal to zero), the SMS stiffness could be reduced (Fig. 10) and secondly, that only a few soft tissue structures have an appreciable effect on the SMS joint biomechanics. Specifically, this study demonstrated the importance of the intervertebral disc in governing spinal flexibility, showing that removal of the disc annular collagen fibres significantly reduced the SMS stiffness. The study also concluded that correct representation of the capsular ligament mechanical properties was important in simulating the biomechanics of the SMS.
Fig. 10

Predicted changes in single motion segment (SMS) joint stiffness following removal of individual soft tissue structures, expressed as a percentage of the Intact value, following removal of SMS joint structures. AF annulus fibrosus, ITVL inter-transverse ligament, PLL posterior longitudinal ligament, ALL anterior longitudinal ligament, LF ligamentum flavum, CL capsular ligament, SISL inter-/supra-spinous ligament, NP nucleus pulposus

Following this, as a first step toward determining patient-specific soft tissue properties, we used the fulcrum bending load case to determine which soft tissue structures were of most importance in governing spinal flexibility [18]. In this study, the disc collagen fibre elastic modulus and the ligament nonlinear elastic stiffnesses were reduced by up to 40% in separate analyses and the effect on predicted vertebral rotations assessed. Note that in this study, stiffnesses for all ligaments were reduced at the same time. Results showed an average increase in coronal vertebral rotation of 3.1 and 13.4% with a 40% reduction in the ligament and collagen fibre stiffnesses, respectively. In a separate analysis, the change in FF due to complete removal of the intervertebral discs was investigated (this was a limiting case since this represented a 100% reduction in the stiffness of all disc materials). The results of this disc removal simulation demonstrated a three-fold increase in the predicted FF compared to the results for the fulcrum bending simulation using the intact model and benchmark tissue stiffnesses (FF = 39% for intact spine, increasing to FF = 120% after intervertebral disc removal). Note that just reducing the disc collagen fibre stiffness had a minimal effect on FF, only increasing it from FF = 39% (intact spine) to FF = 40% (60% reduction in disc collagen fibre stiffness). This study confirmed the importance of the intervertebral disc in influencing spinal flexibility (as measured by vertebral rotation) and showed that a lumped approach to altering the ligament stiffnesses does not necessarily capture the complex interaction in ligament load sharing which occurs across the spinal joints.

The costo-vertebral joint (CVJt) was the only soft tissue structure which was not investigated in this prior study [18] and is the subject of a current material property sensitivity study (Little and Adam, unpublished data), exploring the effect of changes in costo-vertebral joint stiffness on FF for a group of 10 AIS patients. As already mentioned, these rib-vertebra joints are of key structural importance in governing spinal stiffness [27, 40] and are represented in detail in our full thoracolumbar spine model. In this material sensitivity study, for patients where the benchmark (adult) tissue parameters (Table 1) did not provide a predicted FF within the accepted clinical measurement error (predicted Fulcrum Cobb angle within ±5° of the clinically measured Cobb angle) [39], the costo-vertebral joint (CVJt) stiffness parameters were either increased or decreased accordingly. Specifically, if the predicted FF differed from the clinical value by less than -10% (i.e. the simulated spine was too flexible) the CVJt stiffness was increased by 100% (doubled) and if the predicted FF differed by more than 10% (i.e. the simulated spine was too stiff) the CVJt stiffness was decreased by 99%. Reducing the CVJt stiffness by 99% was intended to approximate complete removal of the joint stiffness and to represent the maximum possible effect of reducing the stiffness of these joints. These coarse changes in CVJt stiffness were intended to provide initial sensitivity data which can then inform subsequent, more finely grained analyses. The results of this series of simulations are summarized in Table 3.
Table 3

Clinical and predicted Fulcrum flexibility values (%), showing predicted results for both the benchmark tissue properties (Table 1) and altered CVJt stiffness

Patient §

1

2

3

4

5

6

7

8

9

10

Age

14

14

22

14

14

17

16

27

13

10

Gender

M

F

F

F

F

F

F

F

F

F

Pre-operative clinical Cobb angle

53

44

52

53

60

52

42

45

40

48

Clinical FF

36

41

42

43

50

52

55

58

63

74

Predicted FF using Benchmark Tissue Properties (Table 1)

45*

51

37*

60

25

45*

47*

47

34

32

Changed CVJt Stiffness

No

Yes ↑

No

Yes ↑

Yes ↓

No

No

Yes ↓

Yes ↓

Yes ↓

Predicted FF using altered CVJt Properties

 

23*

 

23

44

  

18*

23

37

(↑ = increase CVJt stiffness by 100%, ↓ = decrease CVJt stiffness by 99%, * = predicted FF results are within the acceptable error range) (§ Note that the patient identifier numbers in Table 3 do not correspond to those stated in Table 2 as this table refers to a separate study)

For the benchmark tissue parameters, the predicted FF was outside the acceptable error range for six of the 10 patients (Table 3). Large alterations in CVJt stiffness improved the FF results for all these six patients, but only brought the predicted FF results for two of them within the acceptable error range (Table 3). For the overall group of 10 patients, the mean error between model predicted and clinically measured fulcrum Cobb angle and FF was reduced when altered CVJt stiffness parameters were used (Fig. 11) and six of the 10 patients demonstrated a predicted FF within the acceptable clinical error after the changes in CVJt stiffness. For the remaining four patients even the large alterations in CVJt stiffness (100% increase or 99% decrease) did not sufficiently alter the flexibility of the simulated spine to provide agreement with the clinical values.
Fig. 11

Average error in FE predicted Fulcrum Cobb angle (degrees) and FF (%) after analyzing the 10 patient-specific spine models under the fulcrum bending load case. Results are presented for both the benchmark tissue parameters and after altering the CVJt stiffness

We conclude that changes to the CVJt stiffness can have an appreciable effect on spinal flexibility and this material sensitivity study went some way towards determining which of the spinal soft tissue structures are of most importance in governing spinal flexibility. Taken together with our previous studies, it is apparent that there is neither an individual soft tissue structure which completely governs spinal flexibility, nor is a lumped approach (varying all tissue properties at the same time) necessarily appropriate for varying soft tissue parameters to achieve patient-specific spine behaviour.

Rather, when patients are observed to be clinically ‘stiff’ (FF < 50%) or ‘flexible’ (FF < 50%) following assessment using the fulcrum bending test, this spinal behaviour is likely governed by a group of soft tissue structures acting in partnership. This suggests that, more detailed pre-operative flexibility assessment data than the currently available single scalar parameter (i.e. FF) is necessary to isolate and characterize patient-specific tissue properties for these structures. Ideally, clinical data characterizing the forces applied to the patient’s spine by the bolster while undergoing the fulcrum bending test would be measured for comparison with FE predicted forces, to assess both force and spinal deformation (and thus, vertebral segmental stiffnesses) in the fulcrum bending radiograph. Possibly, the distribution of segmental torso weights differs between clinically ‘stiff’ and clinically ‘flexible’ patients, resulting in variations in segmental weights which are currently not captured in the patient-specific segmental weights we derive from patient CT datasets. Since the fulcrum bending test has not yet been biomechanically characterized, the forces applied to the patient’s spine in contact with the bolster as well as the forces acting at regions of contact with the X-ray bed are not known. These measurements are a required step toward deriving patient-specific spinal tissue properties.

3.3 Intra-Operative Surgical Corrective Forces: Clinical Load Case II

During anterior scoliosis surgery, the key biomechanical step to reduce the spinal deformity occurs when the surgeon attaches a titanium alloy rod to the patient’s spine using screws which are inserted into the vertebrae within the extents of the structural curve.1 The surgeon applies stepwise compressive forces between pairs of screw heads in adjacent vertebrae (starting with the distal two screws and moving toward the proximal two screws in the construct) and once the desired level-wise correction has been achieved, each screw is locked onto the rod. This successive, level-wise deformity correction results in a reduction in the overall deformity of the structural curve. Prior to compression of the screw heads, the intervertebral discs between these vertebrae are partially removed (approximately the lateral half) and bone graft material is inserted into this disc space to encourage the vertebrae to fuse together in the corrected position.

This surgical process is the focus of our intra-operative surgical modeling, in which we attempt to develop a load case which simulates forces applied by the surgeon to the patient’s spine while undergoing the anterior, single rod, scoliosis correction procedure. As already mentioned, our research to date has focused on the anterior, single rod, scoliosis correction procedure since we have access to a detailed set of clinical data including clinically indicated pre-operative CT scans for AIS patients who undergo this surgery thorascopically (via a minimally invasive or key-hole approach). As such, this patient dataset has provided detailed clinical data for model validation of our patient-specific simulation techniques.

In order to simulate the intra-operative load case, it was necessary to first model the surgically altered spinal anatomy and implant components. All five patients chosen for intra-operative simulation underwent a single rod, anterior corrective procedure (Fig. 1b). Clinical data for the surgical procedure (including which vertebral levels were fused, number of screws implanted, rod diameter and alloy) were used to simulate the individual surgical procedure for each patient-specific model. Using our custom pre-processing software it was possible to re-generate each patient’s spine model (both geometry and FE mesh) with surgically altered spinal geometry (Fig. 12a, b), incorporating details for:
Fig. 12

a Full patient-specific spine model (undeformed mesh) showing the single anterior rod and screws prior to insertion. b Detail of thoracic spinal levels showing partial thoracic discectomies and screws (green) embedded within vertebral bodies. Note that the screw heads have been enlarged for visualization purposes

  • Screw placement/orientation—The vertebral screws were represented as embedded continuum elements in the vertebral bodies, assuming an idealized, perfectly bonded contact relationship between the surface of the screw shaft and underlying cancellous bone elements in the vertebral body (Fig. 12b). Note that this representation does not take into consideration the screw threads in contact with the underlying bone;

  • Discectomy levels—During surgery, the intervertebral discs between the vertebral bodies attached to the rod are partially removed (half the disc) and bone graft material is inserted into the disc space to promote bony fusion in the 3–6 months after surgery. These discectomy levels were simulated in the surgically altered spinal geometry by removing half the continuum elements representing the annulus fibrosus mesh, and by removing the entire fluid filled cavity representing the nucleus pulposus (Fig. 12b). Since this was an intra-operative load case, no fusion material was simulated as the bone graft offers no appreciable stiffness to the spine at the time of surgery. Interfacial contact between the exposed endplate surfaces of the adjacent vertebrae was simulated using an exponential, softened contact algorithm (normal contact) and Coulomb friction, μ = 0.3 (tangential sliding).

  • Rod geometry—The rod was represented with a user-defined length and diameter to match clinical data for each patient. The rod and screws are manufactured from Titanium alloy, which was represented as a linear elastic material (E = 108,000 MPa, υ = 0.3).

This surgical load case simulated the intra-operative compressive forces applied by the surgeon in order to correct the spinal deformity. Following removal of the intervertebral discs and insertion of the screws, the screw-to-screw compressive forces used to reduce the scoliosis deformity are simulated between successive vertebral levels within the structural curve. A compressive force is applied between the screw heads at adjacent vertebrae using connector elements, and once the required segmental correction has been simulated, locking of the screw onto the rod is simulated using bonded contact between the two FE meshes, thus simulating the cumulative, level-wise intra-operative correction of the spinal deformity.

Using a novel clinical measurement technique, our group (Cunningham et al. [8]) have determined the in vivo compressive forces applied intra-operatively for a series of patients undergoing the single rod, anterior corrective procedure. Using a strain-gauged surgical compression tool and data logging system, the study recorded a continual force tracing during the correction of each spinal joint, up until the point at which the screw was locked onto the rod. Using this dataset, Cunningham et al. [8] defined the average level-wise compressive force applied by the surgeons intra-operatively at each spinal level, relative to the apex of the scoliotic curve.2

The compressive force data from this experimental study were utilized to simulate the intra-operative load case for each of the five patient-specific spine models (Fig. 13). The incremental compression steps carried out surgically were simulated with the spine model and the L5 vertebra was constrained from motion during all load steps. To assess the validity of the patient-specific spine models in predicting surgical deformity correction, the corrected Cobb angle (at the end of the surgical deformity correction) predicted by each patient’s FE model was compared with the clinically measured (standing) Cobb angle obtained one week post-operatively. In addition to this, for patient three a supine, coronal radiograph taken immediately post-operatively (while the patient was still in Intensive Care, ICU) was also available. As with the FF load case, an acceptable tolerance in Cobb angle of ±5° was used [39].
Fig. 13

Intra-operative compressive forces applied to the model at vertebral level, based on the mean forces measured by Cunningham et al. [8]. Vertebral level is normalized relative to the apex of the structural curve, with positive levels indicating vertebrae cephalic to the apex and negative indicating vertebrae inferior to the caudal to the apex

Predicted results for the surgically corrected Cobb angle were within the acceptable error range for two of the five patient-specific models when comparing the predicted results to the clinical measurements obtained from radiographs taken one-week post-operatively (Fig. 14). However, for patient three, when comparing the predicted Cobb angle with the clinical value measured immediately post-operatively (ICU radiograph), the predicted result was within the acceptable error range. The ICU radiograph is obtained while the patient is supine, while the one-week post-operative radiographs are obtained while the patient is standing. While previous studies have shown that on average, Cobb angle increases by 9° when comparing supine to standing [37], little is known about the comparative change in Cobb angle for an instrumented spine. These data suggest there may be an increase in Cobb angle of a similar magnitude for the instrumented spine, however, supine radiographs are not routinely obtained immediately post-operatively, so this data was available for only one of the patients in this series.
Fig. 14

Comparison of the clinical and model-predicted Cobb angle after surgery. The clinical Cobb angle was measured from radiographs taken one week post-operatively. *For patient three, the clinical Cobb angle was also measured from a radiograph taken immediately post-operatively (patient supine and in ICU). For patient 3, the negative Cobb angle indicates the simulated surgical procedure ‘over-corrected’ the spinal deformity, creating a 2.3° lateral deformity on the contra-lateral side of the spine to the initial deformity

Patients four and five demonstrated a predicted Cobb angle after surgery of 30 and 15.5°, respectively, which were substantially larger than the actual clinical values of 5 and 7°, respectively. These two patients also demonstrated a predicted FF outside the acceptable error range (Fig. 8). Figure 15 shows the predicted shape of the surgically altered spine for patient two. By comparing the undeformed shape of the spinal column shown in Fig. 12b with the deformed shape shown in Fig. 15b, the reduction in the intervertebral disc space resulting from compressive forces applied between the screw heads can be seen. In some instances this compressive force was sufficient to result in contact between adjacent vertebral endplates.
Fig. 15

a Full thoracic spine after intra-operative compressive forces have been applied (deformed mesh, Patient 2). b Detail showing deformed rod and decreased height of disc space following successive compression of vertebral levels

Qualitative comparison of the predicted and clinically observed surgical deformity correction showed that for patients with a predicted corrected Cobb within the acceptable error range, both the shape of the instrumented curve and the shape of the spinal levels above and below the instrumented curve were similar to the coronal radiograph. Conversely, for the three patients whose simulated surgical correction was outside the acceptable error range compared to the clinical result, the predicted shape of both the instrumented region as well as the spinal curves above and/or below this region tended to deviate from the post-operative radiograph (Fig. 16).
Fig. 16

Overlay of the binary outline from the deformed spinal column and the 1 week post-operative coronal radiograph. This overlay shows the orientation of vertebra both within (a Patient 3) or above (b Patient 4) the instrumented curve deviated from the orientation on the radiographic image

3.4 Towards Patient-Specific Soft Tissue Properties: Insights from the Surgical Load Case

Scoliosis is a complex 3D deformity which results in abnormal curvature of the spine in all three anatomical planes. Generally, the spinal deformity will be observed as both a primary structural curve—which is the region where the lateral, side-to-side curvature is a manifestation of abnormal growth—and compensatory curves—which develop above and/or below the primary curve and are non-structural, occurring in order for the spine to maintain balance (a compensatory lumbar curve is visible below vertebral level T12 in Fig. 9a). In addition to the correction of the primary thoracic deformity adjacent to the implant, previous clinical studies of single rod anterior scoliosis surgery have shown that surgical correction of the primary structural deformity also results in a reduction in the compensatory deformity observed distal to the primary thoracic curve [12]. Qualitative comparisons between the model and clinical results in the patient group just described, showed that the FE simulations predicted changes in both the primary (thoracic) and compensatory (lumbar) spinal curves following analysis of the intra-operative load case simulation. This suggests that the current passive osseo-ligamentous spine models are capable of reproducing at least the passive osseo-ligamentous aspect of this compensatory curve behaviour in the adolescent scoliotic spine.

The results of the intra-operative load case suggest that for a subset of patients, the use of a set of benchmark (adult) tissue properties based on existing literature provides a reasonable approximation to adolescent spinal tissue properties. This is in keeping with the conclusions drawn from the results of the Fulcrum Bending load case. However, for the remaining patients, the simulated deformity correction was considerably low in comparison to the clinical value, implying that the simulated spine was overly stiff in comparison to the actual tissues. In order to improve the agreement between the clinical and predicted results, the use of patient-specific paediatric soft tissue properties is essential.

The intra-operative deformity correction load case was applied using data for compressive forces measured in vivo [8] and such data is novel in the field of scoliosis biomechanics, with few previous studies having included measured force data in computational simulations of scoliosis surgery. However, the loading profile (Fig. 13) applied to each of the models in our pilot analyses to date, is averaged data from force measurements carried out on six patients. Preliminary FE investigations currently underway in our group suggest that the use of individual, patient-specific loading profiles (based on the in vivo data from Cunningham et al. [8]) will yield different predicted deformity corrections than the use of an ‘average’ loading profile for a particular type of surgical procedure. Thus as well as the need for patient-specific anatomy and patient specific tissue mechanical properties, patient-specific intra-operative surgical forces may also be required for realistic simulation of scoliosis surgery.

4 Conclusions and Future Directions

Patient-specific spine modeling presents a complex and multi-factorial challenge to not only accurately simulate the anatomy of the spine but also to appropriately replicate the physiological behaviour of the spinal soft tissues and to individualize the loading conditions applied to the spinal structures during surgical procedures. Our computational studies to date have demonstrated there is no one single soft tissue structure which governs the flexibility of the spine, but rather that there is a complex interaction between the spinal soft tissues which regulates the overall biomechanics of the spine.

In an attempt to better understand and ultimately derive patient-specific soft tissue properties it is appealing to take advantage of existing clinically performed patient flexibility assessments. Patient flexibility as assessed using the Fulcrum bending radiograph is strongly dependent on the relative stiffness of the various spinal soft tissues and derivation of tissue stiffnesses using these assessments provides in vivo data without the necessity for highly invasive testing of patient tissues. However, in order for such patient assessments to be useful in deriving patient-specific tissue properties, it is necessary for biomechanical characterization of these assessments to be carried out, through measurements of the forces applied to the patient’s spine.

Our studies to date demonstrate that the use of patient-specific anatomy alone is not sufficient to accurately simulate the biomechanical behaviour of the adolescent spine. The use of a set of benchmark material properties based on adult data can adequately reproduce the clinically observed behaviour of AIS patients for only a subset of patients. Patient-specific tissue properties are of key importance in creating accurate simulations of the spine and ribcage and in reproducing the clinically observed flexibility and motion of the spine.

In our work to date the focus has been on model development and validation by comparison with readily available clinical data such as FF and post-operative Cobb angle. However, once appropriately validated, the patient-specific models potentially provide a wealth of biomechanical information which can be used to assess the likely success of a proposed deformity correction procedure. For example, predicted rod strain is related to the likelihood of rod fracture under cyclic loads, predicted relative motion between adjacent vertebrae is related to the likelihood of successful bony fusion (as opposed to pseudarthrosis) following surgery, and predicted changes in tissue strain after a surgical intervention are valuable indicators of the degree of tissue remodeling which would be expected to occur in response to the altered spinal loading conditions.

The integration of patient-specific finite element simulations in a pre-operative surgical planning tool shows much potential. By utilizing a spine model which is truly personalized to the patient; in terms of anatomy, tissue properties and intra-operative corrective forces; accurate predictions for the outcomes of a particular surgical procedure should be possible prior to surgery. The overall aim of this approach to surgery simulations is to assist surgeons to plan the optimal biomechanical correction for a particular patient, while avoiding the risk of implant or tissue damage. This concept represents a paradigm shift in scoliosis surgery planning—by complementing a surgeon’s expertise with biomechanical simulation tools, it will be possible to accurately predict treatment outcomes for individual patients and ultimately, improve overall patient health post-operatively. There are significant challenges in realizing the clinical potential of patient specific biomechanical simulations such as these. Imaging modalities must allow pre-operative 3D imaging with sufficient resolution to accurately define patient-specific spinal anatomy, but without excessive radiation dose. Secondly, reliable biomechanical characterization techniques (based on clinical assessments such as the fulcrum bending radiograph for example) must be developed to ensure that patient-specific tissue mechanical properties can be prescribed which will correctly simulate spinal stiffness. Thirdly, prediction of the biomechanics of the surgically altered spine must be extended beyond the operating theatre to simulate physiologically relevant load cases after surgery (i.e. during gait and other post-operative activities involving muscle activation). Finally, issues of model convergence and solution time must be addressed to ensure that results can be obtained in a clinically relevant timeframe. These challenges can only be overcome through sustained effort by the biomechanical modeling community, but the goal of improved outcomes for complex spinal surgery patients make this research effort highly worthwhile.

Footnotes

  1. 1.

    The region of the spine with an intrinsic lateral curvature rather than a deformity related to a functional imbalance of the spinal soft tissues. The structural curve includes vertebrae which are within the extents of the spinal deformity measured by the Cobb angle.

  2. 2.

    The apex of the scoliotic curve is the most laterally deviated vertebra on a frontal radiograph.

References

  1. 1.
    Andriacchi, T., Schultz, A., Belytschko, T., Galante, J.: A model for studies of mechanical interactions between the human spine and rib cage. J. Biomech. 7(6), 497–507 (1974)CrossRefGoogle Scholar
  2. 2.
    Aubin, C.E., Labelle, H., Chevrefils, C., Desroches, G., Clin, J., Eng, A.B.: Preoperative planning simulator for spinal deformity surgeries. Spine 33(20), 2143–2152 (2008)CrossRefGoogle Scholar
  3. 3.
    Aubin, C.E., Labelle, H., Ciolofan, O.C.: Variability of spinal instrumentation configurations in adolescent idiopathic scoliosis. Eur. Spine J. 16(1), 57–64 (2007)CrossRefGoogle Scholar
  4. 4.
    Betz, R.R., Harms, J., Clements, D.H., 3rd, Lenke, L.G., Lowe, T.G., Shufflebarger, H.L., Jeszenszky, D., Beele, B.: Comparison of anterior and posterior instrumentation for correction of adolescent thoracic idiopathic scoliosis. Spine 24(3), 225-239 (1999)CrossRefGoogle Scholar
  5. 5.
    Chazal, J., Tanguy, A., Bourges, M., Gaurel, G., Escande, G., Guillot, M., Vanneuville, G.: Biomechanical properties of spinal ligaments and a histological study of the supraspinal ligament in traction. J. Biomech. 18(3), 167–176 (1985)CrossRefGoogle Scholar
  6. 6.
    Cheung, K.M., Luk, K.D.: Prediction of correction of scoliosis with use of the fulcrum bending radiograph. J. Bone Joint Surg. 79(8), 1144–1150 (1997)Google Scholar
  7. 7.
    Cobb, R.J.: Outline for study of scoliosis. In: American Academy of Orthopaedic Surgeons, Instructional Course Lectures. CV Mosby, St Louis, pp. 261–275 (1948)Google Scholar
  8. 8.
    Cunningham, H., Little, J.P., Adam, C.J.: The measurement of applied forces during anterior single rod correction of adolescent idiopathic scoliosis. Paper presented at the ACSR annual meeting, Adelaide, August 2009Google Scholar
  9. 9.
    Cunningham, H., Little, J.P., Pearcy, M.J., Adam, C.J.: The effect of soft tissue properties on overall biomechanical response of a human lumbar motion segment: A preliminary finite element study. In: Brebbia, C.A. (ed.) Modelling in Medicine and Biology VII, WIT Transactions on Biomedicine and Health. WIT Press, Southampton, pp. 93–102 (2007)CrossRefGoogle Scholar
  10. 10.
    Erdmann, W.S.: Geometric and inertial data of the trunk in adult males. J. Biomech. 30(7), 679–688 (1997)CrossRefGoogle Scholar
  11. 11.
    Hasler, C.C., Hefti, F., Buchler, P.: Coronal plane segmental flexibility in thoracic adolescent idiopathic scoliosis assessed by fulcrum-bending radiographs. Eur. Spine J. 19(5), 732–738 (2010)CrossRefGoogle Scholar
  12. 12.
    Hay, D., Izatt, M.T., Adam, C.J., Labrom, R.D., Askin, G.N.: Radiographic outcomes over time after endoscopic anterior scoliosis correction: a prospective series of 106 patients. Spine 34(11), 1176–1184 (2009)CrossRefGoogle Scholar
  13. 13.
    Kamimura, M., Kinoshita, T., Itoh, H., Yuzawa, Y., Takahashi, J., Hirabayashi, H., Nakamura, I.: Preoperative CT examination for accurate and safe anterior spinal instrumentation surgery with endoscopic approach. J. Spinal Disord. Tech. 15(1), 47–51; discussion 51–42 (2002)CrossRefGoogle Scholar
  14. 14.
    Kimpara, H., Lee, J.B., Yang, K.H., King, A.I., Iwamoto, M., Watanabe, I., Miki, K.: development of a three-dimensional finite element chest model for the 5(th) percentile female. Stapp Car Crash J. 49, 251–269 (2005)Google Scholar
  15. 15.
    Kumaresan, S., Yoganandan, N., Pintar, F.A.: Finite element analysis of the cervical spine: a material property sensitivity study. Clin. Biomech. (Bristol, Avon) 14(1), 41–53 (1999)CrossRefGoogle Scholar
  16. 16.
    Lafage, V., Dubousset, J., Lavaste, F., Skalli, W.: 3D finite element simulation of cotrel-dubousset correction. Comput. Aided Surg. 9 (1–2), 17–25 (2004)CrossRefGoogle Scholar
  17. 17.
    Lemosse, D., Le Rue, O., Diop, A., Skalli, W., Marec, P., Lavaste, F.: Characterization of the mechanical behaviour parameters of the costo-vertebral joint. Eur. Spine J. 7(1), 16–23 (1998)CrossRefGoogle Scholar
  18. 18.
    Little, J.P., Adam, C.J.: The effect of soft tissue properties on spinal flexibility in scoliosis: biomechanical simulation of fulcrum bending. Spine 34(2), E76–E82 (2009)CrossRefGoogle Scholar
  19. 19.
    Little, J.P., Adam, C.J.: Effects of surgical joint destabilization on load sharing between ligamentous structures in the thoracic spine: a finite element investigation. Clin. Biomech. (Bristol, Avon) (in press)Google Scholar
  20. 20.
    Little, J.P., Adam, C.J., Evans, J.H., Pettet, G.J., Pearcy, M.J.: Nonlinear finite element analysis of anular lesions in the L4/5 intervertebral disc. J. Biomech. 40(12), 2744–2751 (2007a)CrossRefGoogle Scholar
  21. 21.
    Little, J.P., Pearcy, M.J., Pettet, G.J.: Parametric equations to represent the profile of the human intervertebral disc in the transverse plane. Med. Biol. Eng. Comput. 45(10), 939–945 (2007b)CrossRefGoogle Scholar
  22. 22.
    Lonner, B.S., Kondrachov, D., Siddiqi, F., Hayes, V., Scharf, C.: Thoracoscopic spinal fusion compared with posterior spinal fusion for the treatment of thoracic adolescent idiopathic scoliosis. J Bone Joint Surg. 88(5), 1022–1034CrossRefGoogle Scholar
  23. 23.
    Lu, Y.M., Hutton, W.C., Gharpuray, V.M.: Do bending, twisting, and diurnal fluid changes in the disc affect the propensity to prolapse? A viscoelastic finite element model. Spine 21(22), 2570–2579 (1996)CrossRefGoogle Scholar
  24. 24.
    Nachemson, A.: Lumbar Intradiscal Pressure: experimental studies on post-mortem material. Acta Orthopaedica Scandinavica 43, (1960)Google Scholar
  25. 25.
    Natali, A., Meroi, E. Nonlinear analysis of intervertebral disc under dynamic load. Trans. ASME J. 112, 358–362 (1990)Google Scholar
  26. 26.
    Nolte, L.P., Panjabi, M., Oxland, T.: Biomechanical properties of lumbar spinal ligaments. In: Heimke, G., Soltesz, U., Lee, A.J.C. (eds.) Clinical Implant Materials. Elsevier, Amsterdam, pp. 663–668 (1990)Google Scholar
  27. 27.
    Oda, I., Abumi, K., Cunningham, B.W., Kaneda, K., McAfee, P.C.: An in vitro human cadaveric study investigating the biomechanical properties of the thoracic spine. Spine 27(3), E64–E70 (2002)CrossRefGoogle Scholar
  28. 28.
    Panjabi, M.M., Brand, R.A., Jr., White, A.A., 3rd., Mechanical properties of the human thoracic spine as shown by three-dimensional load-displacement curves. J. Bone Joint Surg. 58(5), 642–652Google Scholar
  29. 29.
    Papin, P., Arlet, V., Marchesi, D., Laberge, J.M., Aebi, M.: Treatment of scoliosis in the adolescent by anterior release and vertebral arthrodesis under thoracoscopy. Rev. Chir. Orthop. Reparatrice Appar. Mot. 84(3), 231–238 (1998)Google Scholar
  30. 30.
    Pearcy, M.J.: Stereo radiography of lumbar spine motion. Acta Orthopaedica Scandinavica Supplementum 56(212), 1–45 (1985)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Reddi, V., Clarke, D.V., Jr., Arlet, V.: Anterior thoracoscopic instrumentation in adolescent idiopathic scoliosis: a systematic review. Spine 33(18), 1986–1994 (2008)CrossRefGoogle Scholar
  32. 32.
    Rohlmann, A., Richter, M., Zander, T., Klockner, C., Bergmann, G.: Effect of different surgical strategies on screw forces after correction of scoliosis with a VDS implant. Eur. Spine J. 15(4), 457–464 (2006)CrossRefGoogle Scholar
  33. 33.
    Sangole, A.P., Aubin, C.E., Labelle, H., Stokes, I.A., Lenke, L.G., Jackson, R., Newton, P.: Three-dimensional classification of thoracic scoliotic curves. Spine 34(1), 91–99 (2008)CrossRefGoogle Scholar
  34. 34.
    Shirazi-Adl, A., Ahmed, A.M., Shrivastava, S.C.: Mechanical response of a lumbar motion segment in axial torque alone and combined with compression. Spine 11(9), 914–927 (1986)CrossRefGoogle Scholar
  35. 35.
    Stokes, I.A., Gardner-Morse, M.: Muscle activation strategies and symmetry of spinal loading in the lumbar spine with scoliosis. Spine 29(19), 2103–2107 (2004)CrossRefGoogle Scholar
  36. 36.
    Stokes, I.A., Laible, J.P.: Three-dimensional osseo-ligamentous model of the thorax representing initiation of scoliosis by asymmetric growth. J. Biomech. 23(6), 589–595 (1990)CrossRefGoogle Scholar
  37. 37.
    Torell, G., Nachemson, A., Haderspeck-Grib, K., Schultz, A.: Standing and supine Cobb measures in girls with idiopathic scoliosis. Spine 10(5), 425–427 (1985)CrossRefGoogle Scholar
  38. 38.
    Ueno, K., Liu, Y.K.: A three-dimensional nonlinear finite element model of lumbar intervertebral joint in torsion. J. Biomech. Eng. 109(3), 200–209 (1987)CrossRefGoogle Scholar
  39. 39.
    Vrtovec, T., Pernus, F., Likar, B.: A review of methods for quantitative evaluation of spinal curvature. Eur. Spine J. 18(5), 593–607 (2009)CrossRefGoogle Scholar
  40. 40.
    Watkins, R., 4th., Watkins, R., 3rd., Williams, L., Ahlbrand, S., Garcia, R., Karamanian, A., Sharp, L., Vo, C., Hedman, T.: Stability provided by the sternum and rib cage in the thoracic spine. Spine 30(11), 1283–1286 (2005)CrossRefGoogle Scholar
  41. 41.
    Wong, H.K., Hee, H.T., Yu, Z., Wong, D.: Results of thoracoscopic instrumented fusion versus conventional posterior instrumented fusion in adolescent idiopathic scoliosis undergoing selective thoracic fusion. Spine 29(18), 2031–2038 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Paediatric Spine Research GroupQueensland University of TechnologyBrisbaneAustralia

Personalised recommendations