The use of statistical modelling to identify important parameters for the shape of the torso following surgery for adolescent idiopathic scoliosis

Abstract

The surgical strategy in adolescent idiopathic scoliosis (AIS) aims to recreate the symmetry of the torso. This requires the minimisation of both the size of the scoliosis and the angulation between the sides of the torso, along with the recreation of a normal thoracic kyphosis. This study uses predictive modelling to identify the significance of the value of the pre‐operative parameters, and the change in the magnitude of the parameters as a result of an operation on the shape of the torso using the ‘most prominent points’; two areas of maximum prominence on either side of the spine with x, y and z coordinates. The pre‐operative values, and the change in magnitude between the pre and post‐operative values, for scoliosis, kyphosis and skin angulation from a group of Lenke 1 convex to the right AIS were analysed with measures collected using Integrated Spine Imaging System 2 surface topography and compared with those without visible spinal deformity. The models best explained the z coordinate and least well explained the x coordinate, although there was a contribution to all of the models that remained unexplained. The parameters that affected the position of the coordinates in the model differed between the models. This confirms that surgically altering the shape of the spine and torso whilst correcting an AIS does not lead to a symmetrical torso. There are as yet, undefined factors which contribute to the shape of the torso and which if identified and corrected surgically would lead to greater symmetry post‐operatively.

The use of regression analysis to predict the contributions of spinal parameters altered during surgery on the post‐operative torso shape. The image shows the 3D cartesian coordinates used across the posterior torso for the calculation of the models.

1. INTRODUCTION

Adolescent idiopathic scoliosis (AIS) is a three dimensional (3D) deformation of the spine (Stokes, 1994), associated with asymmetry of the posterior torso (Gardner et al., 2019). One of the goals of the surgical correction of scoliosis is to minimise all aspects of the deformity, recreating the shape of the spine and torso to as close to normal as possible (Choudhry et al., 2016). The most common type of AIS curve is a convex to the right thoracic curve (Lenke et al., 2001). The structural components of the spine in a thoracic AIS curve can be observed and measured as a scoliosis, a loss of thoracic kyphosis and torso angulation (Berryman et al., 2008). Within an operation to correct a thoracic AIS curve, the scoliosis, kyphosis and torso angulation are key features that a surgeon looks to influence as best able. It is recognised that a positive outcome from surgery for AIS is related to the minimisation of torso asymmetry and the recreation of a ‘normal’ torso shape (Bennett et al., 2017; Iwahara et al., 1998; Theologis et al., 1993).

What is unclear is how the external shape of the posterior torso is affected by the alteration of the parameters of scoliosis, kyphosis and angulation of the posterior hemithorax during surgery, and when compared with those without visible spinal deformity (WVSD). This paper analyses the contributions of these parameters, and the change that occurs in the parameters as a consequence of surgical intervention to the overall post‐operative posterior torso shape. The purpose is to help surgeons understand how to maximise the symmetry of the posterior torso through intraoperative corrective manoeuvres to the spine.

2. METHODS

Ethical approval for this work was granted by the NRES Committee East Midlands—Northampton (15/EM/0283) and NRES committee West Midlands—South Birmingham (11/H1207/10). This paper is a review of individuals both WVSD and with convex to the right Lenke 1 thoracic AIS (Lenke et al., 2001). Both groups have been imaged using the Integrated Spine Imaging System 2 (ISIS2) (Berryman et al., 2008). In the AIS group, the ISIS2 images were taken pre and post‐operatively. For all of the individuals with AIS who have enrolled in this study (100%), posterior scoliosis surgery was performed.

The 3D posterior torso shape has been described using ISIS2, as the ‘most prominent points’ (Gardner, Berryman, & Pynsent, 2021; Gardner, Berryman, Sur, et al., 2021). The ‘most prominent points’ represent the two points of maximum distance from the coronal plane defined by the vertebra prominens (VP) and the sacrum, with the x and y planes orthogonal to this plane (Figure 1). As the most prominent points, these areas will ‘catch the eye’ of the observer (Huang & Pashler, 2005) and as such are sources of interest for the assessment of torso asymmetry (Misterska et al., 2011; Theologis et al., 1993). The most prominent points are recorded as an alphabetical code with ‘R’ or ‘L’ (right or left) as the side of the torso and ‘x’, ‘y’ and ‘z’ relating to the position of the measure in 3D cartesian coordinates. As shown in Figure 1, the origin of all measures is at the VP, with x defined as positive to the right and negative to the left with respect to VP. The y parameter is negative in an inferior direction from the VP towards the sacrum. The z parameter is positive from a coronal plane through the VP and sacrum towards the observer who is standing behind the subject. Of note the most prominent points are surface points and are not fixed to underlying bony anatomy. However, these points are seen over the medial border of the scapula unless very kyphotic when they become the posterior elements of the vertebral column (Gardner, Berryman, & Pynsent, 2021; Gardner, Berryman, Sur, et al., 2021).

FIGURE 1.

An image of the posterior torso demonstrating the most prominent points along with the definitions of the x, y and z coordinates from the origin at the vertebra prominens (Gardner, Berryman, & Pynsent, 2021; Gardner, Berryman, Sur, et al., 2021)

The ISIS2 system automatically measures and records the amount of scoliosis and kyphosis along with a measure of torso angulation (maximum skin angle) (Berryman et al., 2008). The maximum skin angle measurement is similar in nature to a scoliometer measure of trunk angulation as described by Bunnell (1993).

A multiple linear regression model was constructed for both the WVSD and the AIS groups. For the WVSD group, this was to develop an understanding of normative data. For the AIS group this was to identify the contributions to the post‐operative position of the ‘most prominent points’ as x, y and z coordinates for both the right and left points. The models for the WVSD group were constructed using the position of the most prominent point and the values of scoliosis, kyphosis and maximum skin angle. The models for the AIS groups were constructed using the value of the pre‐operative position of the point along with the pre‐operative size of scoliosis, kyphosis and maximum skin angle combined with the change in scoliosis, kyphosis and maximum skin angle from the pre‐operative to post‐operative 3D positions. In both cases the models were constructed in the form (with the small case letters representing the coefficients and Ε representing the regression error).

Without spinal deformity:

$$\begin{array}{c}\text{coordinate}=\text{constant}+a\left(\text{coordinate}\right)+b\left(\text{scoliosis}\right)\hfill \\ +c\left(\text{kyphosis}\right)+d\left(\text{max}\text{. skin angle}\right)+E,\hfill \end{array}$$

AIS:

$$\begin{array}{c}{\text{coordinate}}_{\text{post}}=\text{constant}+a\left({\text{coordinate}}_{\text{pre}}\right)\hfill \\ +b\left({\text{scoliosis}}_{\text{pre}}\right)+c\left({\text{kyphosis}}_{\text{pre}}\right)+d\left(\text{max}{\text{. skin angle}}_{\text{pre}}\right)\hfill \\ +e\left(\mathrm{\Delta }\text{scoliosis}\right)+f\left(\mathrm{\Delta }\text{kyphosis}\right)+g\left(\mathrm{\Delta }\text{max}\text{. skin angle}\right)+E.\hfill \end{array}$$

The parameters of change (in scoliosis, kyphosis and maximum skin angle) are calculated by subtracting the post‐operative value from the pre‐operative value.

All analysis was performed using the R statistical software programme (R Core Team, 2020). The model was assessed using the adjusted R ² statistic. Model components were also assessed for relevance in the model after reducing the model using the stepAIC function from the R MASS package (Venables & Ripley, 2002) where the best fit of model was judged using the smallest Akaike information criterion (AIC) (Akaike, 1974) as parameters were removed from the model. Collinearity was assessed using the vif function from the R car package (Fox & Weisberg, 2011).

3. RESULTS

In the group without spinal deformity, there were 831 individuals for review comprising 117 males and 79 females, repeatedly measured over several years. In the AIS group there were 231 individuals reviewed for this study comprising 204 females and 27 males. Given the small numbers of males in comparison to females, and following the methodology of previous research (Gardner et al., 2017, 2019), the females and males were analysed as combined groups. Details of the demographics are found in Table 1. All of the data were normally distributed. The x, y, z coordinates of the most prominent points both pre and post‐operatively are described in Table 2.

TABLE 1.

The demographics of the study participants (as mean, standard deviation and range)

	WVSD	AIS
N	831	231
Age at pre‐operative ISIS2 scan (years)	12.9 (1.9, 9.2 to 17.9)	13.8 (1.5, 10.2 to 17.9)
Size of scoliosis pre‐operatively (°)	0 (6, 0 to 15)	39 (11, 11 to 71)
Size of kyphosis pre‐operatively (°)	34 (9, 4 to 61)	30 (11, 3 to 54)
Size of maximum skin angle pre‐operatively (°)	3 (2, 0 to 11)	12 (5, 1 to 34)
Change in scoliosis (°)	NA	32 (18, −12 to 82)
Change in kyphosis (°)	NA	7 (10, −15 to 31)
Change in maximum skin angle (°)	NA	3 (5, −23 to 21)
Size of scoliosis post‐operatively (°)	NA	6 (15, −52 to 47)
Size of kyphosis post‐operatively (°)	NA	23 (10, 0 to 60)
Size of maximum skin angle post‐operatively (°)	NA	9 (5, 0 to 40)

Abbreviations: AIS, adolescent idiopathic scoliosis; ISIS2, Integrated Spine Imaging System 2; NA, not applicable; WVSD, without visible spinal deformity.

TABLE 2.

The coordinates of the most prominent points for the WVSD group and the AIS group, pre and post‐operatively (as mean, standard deviation and range)

Parameter	WVSD coordinate position (mm)	AIS pre‐operative co‐ordinate position (mm)	AIS post‐operative coordinate position (mm)
Right most prominent point x	80 (15, 15 to 127)	104 (17, 6 to 147)	84 (15, 44 to 124)
Right most prominent point y	−154 (20, −80 to −282)	−145 (17, −203 to −57)	−158 (18, −214 to −88)
Right most prominent point z	45 (13, 10 to 92)	45 (13, 0 to 83)	41 (12, 16 to 91)
Left most prominent point x	−74 (16, 9 to −115)	−52 (31, −103 to 46)	−72 (22, −129 to 26)
Left most prominent point y	−151 (21, −55 to −281)	−108 (31, −201 to −52)	−108 (30, −202 to −48)
Left most prominent point z	42 (12, 15 to 82)	32 (10, 10 to 72)	31 (11, 4 to 72)

Abbreviations: AIS, adolescent idiopathic scoliosis; WVSD, without visible spinal deformity.

The equations for the group without spinal deformity are as follows:

$$\mathrm{R}x=‐197.79+0.39\left(\text{scoliosis}\right)+0.27\left(\text{kyphosis}\right)+E,$$

$$\mathrm{R}y=‐121.85‐0.92\left(\text{kyphosis}\right)+E,$$

$$\mathrm{R}z=2.98+1.13\left(\text{kyphosis}\right)+1.34\left(\text{max}\text{. skin angle}\right)+E,$$

$$\mathrm{L}x=‐73.30+0.37\left(\text{scoliosis}\right)+E,$$

$$\mathrm{L}y=‐116.53‐0.99\left(\text{kyphosis}\right)+E,$$

$$\mathrm{L}z=6.96+1.10\left(\text{kyphosis}\right)‐0.85\left(\text{max}\text{. skin angle}\right)+E.$$

Scatter plots of the measured versus predicted values for each of the constructed models for the AIS group are demonstrated graphically in Figures 2, 3, 4, 5, 6, 7 along with the equations of the model in each case. Table 3 contains the value and statistical significance of each of the coefficients in the final models. For each of the x, y and z coordinates for the most prominent points, it was found that the components of the model differed and this is reflected in the equations of the models. There was no evidence of collinearity within any of the models.

FIGURE 2.

The plot of the model of the x coordinate on the right hand side of the torso comparing the measured value with the predicted value from the model. For reference, the diagonal blue line across the plot represents the line of best fit if the model was 100% accurate. Each point is an individual patient. The line of best fit for the model is the solid black line, surrounded by the limits of prediction (green lines) and the 95% confidence limits of the line of best fit (red lines). The equation of the model is shown. AIC, Akaike information criterion

FIGURE 3.

The plot of the model of the y coordinate on the right hand side of the torso comparing the measured value with the predicted value from the model. The details of the plot are as seen in Figure 2. AIC, Akaike information criterion

FIGURE 4.

The plot of the model of the z coordinate on the right hand side of the torso comparing the measured value to the predicted value from the model. The details of the plot are as seen in Figure 2. AIC, Akaike information criterion

FIGURE 5.

The plot of the model of the x coordinate on the left hand side of the torso comparing the measured value with the predicted value from the model. The details of the plot are as seen in Figure 2. AIC, Akaike information criterion

FIGURE 6.

The plot of the model of the y coordinate on the left hand side of the torso comparing the measured value with the predicted value from the model. The details of the plot are as seen in Figure 2. AIC, Akaike information criterion

FIGURE 7.

The plot of the model of the z coordinate on the left hand side of the torso comparing the measured value to the predicted value from the model. The details of the plot are as seen in Figure 2. AIC, Akaike information criterion

TABLE 3.

The value and the significance of the coefficients for the parameters in the final models for the adolescent idiopathic scoliosis group

Parameter	Coefficient	Significance
scapRx
Intercept	51.40	<0.0001
scapRx pre	0.52	<0.0001
scoliosispre	−0.32	0.0002
Δ scoliosis	−0.25	<0.0001
Δ kyphosis	−0.31	0.0001
Δ max. skin angle	0.53	0.0019
scapLx
Intercept	−65.63	<0.0001
scapLx pre	0.22	<0.0001
max. skin anglepre	0.98	0.0018
Δ kyphosis	−0.46	0.0012
Δ max. skin angle	−1.19	<0.0001
scapRy
Intercept	−70.58	<0.0001
scapRy pre	0.58	<0.0001
kyphosispre	−0.25	0.0156
Δ kyphosis	0.54	<0.0001
scapLy
Intercept	−65.15	<0.0001
scapLy pre	0.51	<0.0001
scoliosispre	0.55	<0.0001
kyphosispre	−0.54	0.0013
Δ kyphosis	0.97	<0.0001
scapRz
Intercept	10.94	<0.0001
scapRz pre	0.63	<0.0001
kyphosispre	0.20	0.0007
max. skin anglepre	0.24	0.0295
Δ kyphosis	−0.73	<0.0001
Δ max. skin angle	−0.62	<0.0001
scapLz
Intercept	5.40	0.0005
scapLz pre	0.76	<0.0001
kyphosispre	0.18	0.0004
Δ scoliosis	−0.05	0.0459
Δ kyphosis	−0.70	<0.0001
Δ max. skin angle	0.44	<0.0001

4. DISCUSSION

When operating to effect a correction of a thoracic scoliosis, the main parameters that can be altered by the surgeon are a reduction in the amount of scoliosis along with a change in the amount of kyphosis and a reduction in the angulation between the sides of the torso (Choudhry et al., 2016). It is well documented that a positive outcome from scoliosis surgery is contributed to by a reduction in the asymmetry of the posterior torso when judged by those having had the surgery (Bennett et al., 2017; Iwahara et al., 1998; Theologis et al., 1993). Therefore, part of the surgery requires an attempt to create the best possible external appearance through surgical manoeuvres using the spinal instrumentation. It is recognised that an improved self‐image is essential for satisfaction following scoliosis surgery (Hayashi et al., 2020).

The positions of the most prominent points have been shown to alter with increasing asymmetry secondary to scoliosis (Gardner, Berryman, & Pynsent, 2021; Gardner, Berryman, Sur, et al., 2021). Through comparison of the 3D position of these points on the left and right sides of the posterior torso, an appreciation of the amount of bilateral asymmetry can be gained.

In this paper, multiple linear regression models have been used to identify the contributions to the 3D positions of the most prominent points in a group of Lenke 1 right thoracic scoliosis patients from both the pre‐operative values of the scoliosis, kyphosis and skin angulation, and the changes in these values from pre‐ to post‐operative. The coefficients describe the relative contributions of individual components of the model to the 3D position post‐operatively. In this fashion, these coefficients act as a predictor of how altering that parameter, namely scoliosis, kyphosis or skin angulation, is likely to affect the position of the most prominent point. The goodness of fit of the model can be assessed through a number of features, with one of the most useful being the R ² parameter, also known as the coefficient of determination. In this case, the R ² parameter documents how much of the post‐operative position is described by the model, with 100% being a full explanation and 0% being no explanation at all. Normative data along with multiple linear regression equations for the most prominent points in those WVSD are also described to give context to the information from the AIS group. It is of note that even in the WVSD group, there is an amount of asymmetry between the left and right sides of the posterior torso and the spinal parameters do contribute differing amounts to the final position, and this is in agreement with previous work (Gardner, Berryman, & Pynsent, 2021; Gardner, Berryman, Sur, et al., 2021).

The predicted z coordinate is best explained by the models with R ² values of 66% and 69%. On the right side (Figure 4) the significant parameters are the pre‐operative position, pre‐operative kyphosis and pre‐operative skin angulation along with the change in kyphosis and skin angulation. For the left side (Figure 7), the significant parameters are the pre‐operative position and pre‐operative kyphosis along with the change from pre‐operative to post‐operative values in scoliosis, kyphosis and skin angulation.

The y coordinate has R ² values of 35% and 41% (Figures 3 and 6). It is worth reinforcing that by definition, all values inferior to the anatomical location of the VP are negative. Again, there are differences between the left and right sides, with only kyphosis and change in kyphosis, along with pre‐operative position, being significant on the right. On the left the significant parameters are pre‐operative scoliosis and kyphosis and change in kyphosis.

The x coordinate is least well represented by the model with an R ² of 37% on the right and 21% on the left (Figures 2 and 5). On the right, pre‐operative kyphosis and skin angulation are not significant whereas all other parameters are. On the left, the significant parameters are pre‐operative skin angulation and change in kyphosis and skin angulation.

Consequently, it is noted that through the parameters that a surgeon alters in the three planes during scoliosis surgery, those parameters have the greatest effect on the z coordinate and the least on the x coordinate. This has been demonstrated graphically in previous work (Gardner et al., 2019) where surgery resulted in a greater chance in position of the most prominent point on the concavity, than on the convexity of the curve which remains in a similar position to pre‐operatively. The difference between the models predicted position and the actual post‐operative position cannot be explained through these parameters. It may well be that part could be explained through interactions in the terms of the model. This has not been explored in this paper for two reasons. First is the number of terms that an interaction model would produce is large, making interpretation very difficult. Second is that the interaction terms are composed of the six parameters listed in this additive model as the features that the surgeon can alter. An interaction model would not assist the surgeon to minimise the asymmetry of the torso.

It is not surprising that there is a difference in the left and right sides given the effects on the 3D shape of the torso seen in AIS (Gardner et al., 2017, 2019) where increasing curve size leads to increasing asymmetry. The group analysed here consists only of convex to the right thoracic curves, as this is the most common curve type described in the literature (Lenke et al., 2001), and is anatomically the curve type closest to the location of the most prominent points. This also prevents potential errors within the model from mixing the results of curves that are convex to the left and right sides together. Thus, the results presented here cannot be assumed to be the same for different curve patterns. However, different curve patterns, particularly those with a more significant thoracolumbar and lumbar spine component, present with other features including an excessive coronal offset of the head over the pelvis; a different model would be indicated in these circumstances.

Work to predict the outcome of surgery in AIS, and in other surgical scenarios, has been reported in the past. Pasha and Flynn (Pasha & Flynn, 2018) have reported the use of a 3D classification of shape using biplanar spinal stereoradiography as a method to identify the key parameters of 3D shape in AIS. Through the identification of clusters of patients, they propose a framework for directing treatment in the future. Nault et al., (2020) have recently published a model that predicts progression of adolescent scoliosis based on parameters at a patient's first visit. Wang et al., (2020) have published a nomogram that predicts the occurrence and development of post‐operative neck tilt following AIS surgery. In other surgical fields, prediction of outcome through machine learning has been shown to be accurate in 94.5% of neurosurgical cases (Senders et al., 2018). Another paper demonstrates risk prediction models to predict mortality in cardiac surgery (Sullivan et al., 2016). Predictive analytics is a source of interest in the literature with a Pubmed search returning 33491 hits, 1199 since January 2021.

The ability to discuss the post‐operative torso shape following scoliosis surgery allows a more personalised expression of the end result. This is likely to be of more relevance than the current reported amount of ‘approximately 65% correction’ (Winter et al., 2007), particularly given the understanding that a greater correction in one plane leads to an under correction in another (Schlösser et al., 2021). This is especially true with the recent identification of different subtypes of the Lenke 1 curve when assessed using the parameters of scoliosis, kyphosis and skin angulation (Gardner, Berryman, & Pynsent, 2021; Gardner, Berryman, Sur, et al., 2021) where the clusters comprise varying amounts of the three parameters. An understanding of what features to concentrate the surgical correction of deformity on to get the most symmetrical torso post‐operatively may allow the tailoring of a more personalised correction.

5. CONCLUSION

This paper identifies that the amount of change in the 3D location of the most prominent points on the posterior torso is affected by the parameters of scoliosis, kyphosis and maximum skin angle, both as absolute parameters and by the change that occurs in those parameters during surgery. As these parameters are the major components of AIS that a surgeon can alter during surgery, knowing which parameter has the greatest effect on the shape of the posterior torso will aid in creating a more specific operative plan for each individual dependent on their pre‐operative shape.

CONFLICT OF INTEREST

None of the authors have any conflicts of interest to declare.

AUTHOR CONTRIBUTION

AG Designed study, analysed data, wrote manuscript, did critical revision of manuscript and approval of article. FB collected data, did critical revision of manuscript and approval of article. PB performed concept of study, critical revision of manuscript, statistical oversight and approval of article.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.