Introduction

Vertebral Body Tethering (VBT) is an alternative treatment for selected patients with adolescent idiopathic scoliosis (AIS), a 3-dimensional deviation of the spinal axis. VBT is a non-fusion technique in skeletally immature patients, that preserves spinal flexibility while reducing the curve magnitude. The working mechanism of VBT is based on Hueter-Volkman’s and Wolff’s principles that are based on growth modulation and tissue remodeling. For both principles to work, it is believed, that the timing of the surgery and the durability of the implant are crucial [1, 2].

Clinical studies have proven that VBT offers adequately curve correction, but also that tether breakage is a common problem [2, 3].Tether breakages can have a major impact on the clinical outcome, specifically when they occur within the first 12 months post-surgery [4]. The incidence of tether breakage after thoracic VBT has been reported up to 48% at two years post-surgery [5]. Thoracolumbar VBT, however, have been observed with an up to 90% tether breakage incidence at two years [6]. However, little is known about the risk factors for tether breakages. Published studies mainly focused on clinical risk factors. Thoracolumbar VBT and large, rigid curves have been identified as main risk factors for tether breakage whereas age and skeletal maturity has not [7].

Only one study has tried to identify biomechanical explanations for breakage, which found the screw-tether interface as main risk factor [8]. Overall, there is a paucity of biomechanical studies. The intervertebral compression or tether forces after VBT surgery aren’t well understood [9]. Today, the tether´s pre-tension is based on the surgeon's feeling and experience.

There is still a lack of evidence regarding dynamic and biomechanical outcome data. However, this data is essential to evaluate the risks and the working and failure mechanism. Published studies have serval limitations, including tests on non-scoliotic, cadaveric spines, or finite element (FE) modelling for static cases [10, 11]. Thus, the aim of this study is to investigate the influence and effects of different tether pre-tensions and screw positions on the resulting tether and intervertebral compression forces by using multibody simulation.

Methods

Multibody simulation (MBS) is a numerical approach to simulate spinal biomechanics during various movements and allows therefore to objectify the biomechanical consequences of a VBT surgery. With the inverse-dynamic method, MBS is the only simulation method, which allows to calculate the joint reaction forces in the human body based on realistic movements and physiological muscle and ligament properties. MBS considers the physiological behavior of the spine and the dependence of the ROM between vertebrae, which is a major advantage over finite element simulation (FE). Furthermore, the computational effort for MBS is much lower than for FE. Different motion tasks as well as the physiological interaction between the required muscle forces and the introduced tether can be simulated in a short amount of time.

Musculoskeletal model of the spine

For this proof-of-concept study, AnyBody Modelling System was used as multi-body simulation software. Since there are no biomechanical cadaver experiments on scoliotic spines, it's difficult to validate a scoliotic spine model. Current static scoliotic MBS spine models [12,13,14] use EMG-measurement as validation tool. In order to simulate physiological movements, a health-shaped, validated spine model with integrated tether was used in this proof-of-concept study to objectify the raw data as a first step (Fig. 1). This approach also allows to compare the calculated values with experimental results. Furthermore, a straight spine most closely approximates the desired postoperative outcome.

Fig. 1
figure 1

Lateral view of the VBT spine model with integrated tether device (blue) between T7-L3

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The model is based on an existing, experimentally validated thoracolumbar spine model with articulated ribcage developed by Ignasiak et al. [15, 16]. Briefly, this model represents pelvis with sacrum, lumbar and thoracic vertebrae, ribs and sternum as rigid bodies. Spherical joints are defined between the individual vertebrae, revolute joints between the vertebrae and the ribs, and 6 DOF joints between the ribs and the sternum. Several hundreds of muscle fascicles represent the musculature of the main muscle groups of the thoracolumbar spine and ribcage. The elastic effects of intervertebral discs, paraspinal ligaments, and ribcage elastic properties are defined in the rotational stiffness in the spherical joints. This model allows to analyze static and dynamic spinal loads for various postures, tasks, and modeled spinal conditions.

The validated spine model has been extended in three ways. First, additional representative movement tasks are implemented in the existing model allowing to simulate not only flexion–extension (70°– 0° –20°), but also lateral bending (50°–0°–50°), and axial rotation (50°–0°–50°). Second, the relative contribution of the thoracic and lumbar spine to the total spinal ROM has been redefined based on [17,18,19]. Third, an individually adjustable tether system with realistic material properties has been implemented.

Material model for the tethering system

The modelled VBT device consists of several individually adjustable and modifiable components, linking consecutive vertebral bodies (Fig. 1). The tether cord is represented in the spine model as linear elastic element. Monoaxial screws are fixed laterally in the desired vertebral bodies and are defined as attachment points of the tether cord. Then, the screws are tethered in the virtual model with a flexible 4 mm diameter tether cord.

To compare the effects of more ventral and dorsal screw positions, the screw position can be varied in the antero-posterior direction. The tether stiffness and pre-tension can be defined individually for each spinal segment. In the performed simulations, the tether stiffness and pre-tension has been assumed the same along the tethered spinal region. A global, realistic tether stiffness of 9000 N/m has been used for all the simulations [8].

The tether force \({f}_{T}\) (N) is calculated by a linear equation of elasticity (Eq. 1). Due to the assumption that the tether can only transfer tension forces, the tether force is zero when the cord is not tensioned (i.e., below or at slack length). For the case that the tether is pretensioned, the tether transfers also normal forces when it is compressed below its slack length. For that, the calculation of the limit length change is introduced (Eq. 2).

$$f_{T} = \Delta L \cdot E_{T} \left\{ {\begin{array}{*{20}c} {\Delta L < \Delta \hat{L}^{l} \to \Delta L = 0} \\ {\Delta L \ge \Delta \hat{L}^{l} \to \Delta L = \left| {\Delta L} \right| } \\ \end{array} } \right.$$
(1)
$$with\; {f}_{T}:\, tether\,force\; [N];\,\,\Delta L:\, length \, change\; [m];\, {E}_{T}: tether \, stiffness\; \left[\frac{N}{m}\right]$$
$$\Delta \hat{L}^{l} = \frac{{f_{p} }}{{E_{T} }}$$
(2)
$$ \begin{aligned}&with\; {\Delta \widehat{L}}^{l}: limit\; length\; change\; [m]; \\&{f}_{p}: pre{\text{-}}tension \;force\; \left[N\right]\end{aligned} $$

Simulations

Several representative motion tasks have been simulated with and without a tether device (Fig. 2). For the simulations, the model spine has been representatively tethered between T7-L3 on the right side of the spine. (Table 1).

Fig. 2
figure 2

Illustration of the VBT spine model during different physiological movements. Lateral bending, flexion–extension and axial rotation were simulated to represent the various possible postoperative movements

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To investigate the effect of pre-tensioning, four tether pre-tension levels have been analyzed [8, 11]. (Table 1) The resulting tether forces and intervertebral compression forces were compared during different motion tasks [20]. In these analyses, the antero-posterior position of the screw has been aligned with the position of the vertebral joint and therefore considered as neutral.

The effect of antero-posterior screw positioning on the tether force has been evaluated for the following simulated positions (Fig. 3): the reference neutral position, 0.5 cm more ventral, and 0.5 cm more dorsal.

Fig. 3
figure 3

Illustration of the different screw positions analyzed at spine level

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Results

The results of the simulations are briefly described in the following section, detailed in Tables 2, 3, and 4, and presented in Figs. 4–7.

Fig. 4
figure 4

Representation of the numerically measured tether forces at the end the simulated movements (lateral bending, flexion–extension, axial rotation) for three different tether pre-tensions scenarios (100 N, 150 N, 200 N)

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Fig. 5
figure 5

Representation of the numerically calculated intervertebral compression forces at the end the simulated movements (lateral bending, flexion–extension, axial rotation) for three different tether pre-tensions scenarios (100 N, 150 N, 200 N)

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Fig. 6
figure 6

The development of the intervertebral compression force between L1-L2 in upright position with respect to higher tether pre-tensions

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Fig. 7
figure 7

Resulting tether force at different screw positions. Maximum segmental tether forces for a specific motion task are presented: L1-L2 for lateral bending and axial rotation tasks, T7-T8 for flexion and T12-L1 for extension

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Effects of different pre-tensions on the tether and intervertebral compression force during different motion tasks (Table 2)

Depending on the motion tasks performed and the spinal segments, the tether and intervertebral compression forces vary greatly. (Figs. 4 and 5).

For some segments and movements (e.g. T8-T9 in right lateral bending), pre-tensioning only results in an exerting tether force at the end of the movement task or at higher pre-tension levels. Overall, tether forces during left axial rotation, flexion, extension, right lateral bending and axial rotation are below 335 N, a level where the tether´s structural integrity isn´t compromised. The highest tether force is 924 N at 50° left lateral bend between L1-L2 at 200 N pre-tension.

Higher tether pre-tension levels increase the resulting intervertebral compression forces with higher forces in the lumbar spine (Fig. 5). The highest compression force (2342 N) is between L1-L2 at 50° right axial rotation at a 200 N pre-tension.

Effects of different pre-tensions on the intervertebral compression force in upright position (Table 3)

The greatest relative increase in compression forces due to tether pre-tensioning has been estimated for the L1-L2 segment in the upright standing position (Fig. 6). A moderate pre-tension of 100 N increases the compression force by 73.76% (780 N) compared to the compression force without tethering (460 N). A pre-tension of 150 N gives an increase of 116.61% (997 N) and a pre-tension of 200 N gives an increase of 156.59% (1181 N) compared to the untethered force.

Effects of different screw positions on the tether force during different motion tasks (Table 4)

As shown in Fig. 7, during right lateral flexion, no effect is observed as the tether is not tensioned. During left lateral bending, flexion, left and right axial rotation, the ventral screw position is the position that produces the lowest tether force. For example, at 50° left lateral bend, the tether forces between L1-L2 are 968 N at the dorsal, 924 N at the neutral and 879 N at the ventral screw position. During extension, the dorsal screw position causes the lowest and the ventral position causes the highest tether force. For instance, at 20° extension, the tether forces between T12-L1 are 280 N at the dorsal, 293 N at the neutral and 306 N at the ventral screw position.

Discussion

VBT is increasingly being applied for select patients with AIS despite a paucity of biomechanical investigations. Currently, curvature reduction is achieved during surgery by bending of the table, manual chest wall compression and tether tensioning [21]. However, the exact amount of tension required to reduce spinal curvature has still not been quantified or standardized [9]. This study is the first to objectify the forces acting on the spine and VBT device during various motions for different postoperative ROMs by using multi-body simulation [20]. In a nutshell, the main findings are:

  1. 1.

    Increasing pre-tension leads to higher intervertebral compression and tether forces.

  2. 2.

    In upright position, a 200 N pre-tension leads to a percentual increase of 157% of the compression force between L1-L2 compared to an untethered spine.

  3. 3.

    The screw position can cause differences in the spinal force distribution.

Effects of different pre-tensions on the tether and intervertebral compression force during different motion tasks

As expected, higher pre-tensions lead to higher overall tether forces. The tether forces vary depending on the spinal segment and the movement performed (Fig. 4).

Guldeniz et al. have shown that a tension of 582.2 N or more can possibly destroy the tether´s structural integrity [8]. The highest simulated tether forces are observed at 50° lateral bend to the untethered side, the left one in the simulations. The highest tether force with a value of 924 N is between L1-L2 at a 200 N pre-tension and could therefore explain the most common complication, tether breakage. In fact, 200 N pre-tension is a commonly used pre-tension during surgery and 50° lateral bend is a realistic post-operative outcome [22].

The simulations have shown the importance of biomechanical-based and segment-specific pre-tensioning. A too high pre-tension can potentially lead to complications such as tether breakage, screw breakout or overcorrection and can, in the worst case, lead to a revision surgery [3, 22]. Too little pre-tension can lead to undercorrection, but especially this has to investigate further with respect to the fundamental concept of VBT which is growth modulation.

Effects of different pre-tension on the intervertebral compression force in upright position

Pre-tensioning results in higher IVD pressures. Simulations have shown that in a tethered spine with a pre-tension of 200 N, the intervertebral compression force is 2.5 times higher than in a healthy spine. This can lead to a higher load on the intervertebral discs and thus, in theory, accelerate degenerative changes. 1-year-follow-up clinical studies have shown only mild, non-significant disc degeneration in the tethered spinal segment [23, 24]. To make a clear statement about in-vivo disc degeneration, more and longer follow-up studies need to be done.

Effects of different screw positions on the tether force during different motion tasks

Cobetto et al. have compared the effect of lateral, anterior, and triangular screw positions. They have found that all screw positions have a significant impact on the reduction of the thoracic Cobb angle and influence the stress distribution at the epiphyseal vertebral growth plate [11]. However, there is a lack of information on the effects of different screw positions on the force of the tether during different movements.

The performed simulations have shown that the screw position affects the tether force. (Fig. 7) Overall, the screw position can influence the resulting tether force by up to 95 N. Given that these simulations are performed on a non-scoliotic, non-growing spine, the actual difference may be greater and more clinically relevant.

Limitations

In this paper an idealized, validated, healthy spine model is used, which has the following limitations. The growth evolution of the spine is neglected. The anatomical changes due to the scoliotic pathology such as changes in muscle forces and bone morphology, are also not considered. A multi-body simulation does not provide absolute values, but it does allow a qualitative analysis of changes in spinal biomechanics and gives a first impression of the forces occurring in the spine.

The recorded values were obtained from idealized movements, enabling validation solely for quasi-static simulations. Although we observed a strong correlation between intradiscal pressures calculated from our model's compression force predictions with respect to the applied pre-tension. Further refinement is necessary to ensure the accuracy of absolute model predictions. Caution is therefore required when interpreting the validation results, e.g. qualitative comparisons between the applied pre-tensions should be avoided.

Conclusion and outlook

The biomechanical data presented are consistent with published clinical data and give a first impression of the forces that occur along the spinal column during the movements [25]. Even without this biomechanical information, clinicians have started to adapt their surgical technique, for example with a double tether construct.

The forces are not evenly distributed along the tether and the spine and vary depending on the performed movement and the screw position. In the simulations, the highest tether force (924 N) is between L1-L2 at 50° lateral bend to the untethered side. This force can potentially cause screw breakout or damage the tether´s structural integrity, which could explain the most reported complication, tether breakage.

The developed VBT spine model allows to analyze easily different motions and biomechanical consequences on the spine and the VBT device. Compared to FE, multibody simulation allows the analysis of spinal biomechanics during various motions while respecting anatomical characteristics and using less computing power than FE. Furthermore, double tethers and hybrid fusion/tether constructs which are increasingly used in clinical routine could easily integrate in the existing VBT spine model. The results of the model can therefore have an impact on future directions for improved surgical VBT treatment, especially for TL curves.

Future work should apply the results to a patient-specific scoliotic spine model and calculate biomechanics based on preoperative imaging. EMG measurements could be used to validate the flexible VBT scoliotic spine model.