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. 2021 Jul 14;239(6):1400–1408. doi: 10.1111/joa.13509

How can directional and fluctuating asymmetry help in the prognosis of scoliosis along the course of the condition?

José María González‐Ruiz 1,✉, María Isabel Pérez‐Núñez 2, Mª Dolores García‐Alfaro 2, Markus Bastir 1
PMCID: PMC8602023  PMID: 34263453

Abstract

Fluctuating asymmetry (FA) is an indicator of developmental instability referred to random deviations from mean asymmetry. That average asymmetry is the directional asymmetry (DA), which, in the particular case of adolescent idiopathic scoliosis (AIS), corresponds to a right thoracic and left lumbar curves. Investigating the presence of FA and DA in AIS has never been done, and it is a key element of the pathophysiology of the scoliotic condition. Thirty‐six X‐rays of patients with AIS were digitized and analysed using Geometric Morphometric analyses to test for both statistical effects. The individual FA score for each patient was calculated using Procrustes ANOVA and a methodology based on the components of shape was used to estimate the individual DA score. DA is a stronger effect than FA (2.12 to 1), as it has been found in other clinical conditions. The individual DA score, with an effect size of 0.58, is a better predictor of the Cobb angle than FA score. The methodology presented in this paper to estimate DA score is a valid approach in the study of asymmetries in AIS. FA should be correlated in future studies with environmental covariates to serve as a variable in the medical prognosis, while DA will serve as a good predictor of the Cobb angle during the course of the condition, avoiding the abuse of X‐rays. This potential use of DA should be tested on 3D shape due to the three‐dimensional clinical presentation of AIS.

Keywords: adolescent idiopathic scoliosis, directional asymmetry, fluctuating asymmetry

A new methodology has been developed that measures directional and fluctuating asymmetry, and these individual scores make it possible to predict the Cobb angle (from the DA score) and measure developmental instability (from the FA score) in patients with adolescent idiopathic scoliosis.

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1. INTRODUCTION

Fluctuating asymmetry (FA) is a phenomenon present in adolescent idiopathic scoliosis (AIS; Dangerfield et al., 1997; Goldberg et al., 1995, 1997b), which includes all random deviations between the left and the right sides of the human torso. It has been described in the literature as an expression of developmental instability and a consequence of environmental and/or genetic factors (Klingenberg, 2003a, 2003b; Valen, 1962). Hypothetically, the left and the right sides of the torso share the same genome, and as far as development is considered to be regulated by genetics, a perfectly symmetrical phenotype should be expected in the frontal plane. In the practice, the FA comprises the random deviations from the mean asymmetry of the shape in the sample subjected to study, a type of asymmetry that has been termed ‘directional asymmetry (DA)’ (Klingenberg, 2003a, 2003b). Nevertheless, the exposition to non‐genetic factors like nutrition, gravity or lifestyle could modify the way an organism grows by perturbating its developmental system (Klingenberg, 2003a, 2003b). These environmental factors may cause the asymmetries in the human torso (Burwell et al., 2011), and these asymmetries, in the particular case of scoliosis, are tridimensional and potentially could affect the spine, the thorax and the trunk (Janicki & Alman, 2007; Negrini et al., 2018).

To the extent to which FA is a product of developmental instability (Klingenberg & Polak, 2003; Palmer, 1996), its link with environmental factors offers the opportunity to determine how much of a scoliosis patient's asymmetry could be due to environmental factors. A recent study, based on a multivariate approach asymmetry, has shown the possibility to disentangle the different dimensions of asymmetry (Ekrami et al., 2020). Furthermore, the authors highlighted improved understanding of the biological processes related to these different dimensions (Ekrami et al., 2020). Thus, estimating the proportion of DA and FA in a patient with AIS could drive us into a deeper level of understanding of the condition. Although DA and FA are both related to developmental instability (Graham et al., 1998), the latter is the gold standard in studies of interaction between environmental factors and asymmetry (Benítez et al., 2020). Besides, the factors that cause the random phenomenon of FA could be identified as previously published (Burwell et al., 2011). Indeed, FA has been used in other fields of study to measure the impact of the environment on the shape of other biological organisms (Benítez et al., 2020; Parsons, 1990). Therefore, we can take advantage of this evolutionary biological background in the study of human scoliosis.

Directional asymmetry, which is the consistent asymmetry in a sample towards one side following a normal distribution with mean different from zero (Graham et al., 1998), is present in scoliosis in the form of right thoracic deviation (Addai et al., 2020; González‐Ruiz et al., 2021) and left lumbar deviation (Goldberg et al., 1994). This pattern of deformity has been observed in many different samples and populations and turns out to be the most common type of scoliosis (Addai et al., 2020; Goldberg et al., 1994). According to Klingenberg (Klingenberg, 2003a, 2003b), DA is a factor common in a given sample (potentially genetic or otherwise ‘non‐random’).

Frequently, studies of asymmetry had been carried out with two methodological limitations. The first one is that FA provides an extremely subtle signal relative to measurement error (Fruciano, 2016), so the statistical estimation of the significance of both factors is needed. Secondly, many studies had failed to exclude DA when reporting the asymmetry of shapes (Simmons, 2007).

With all this background, in the present study, we aimed to develop a systematic method that allows us to measure and estimate, statistically, the effects of DA and the FA separately, in the same subject of a sample, statistically controlling the effect of the measurement error and easy to repeat by future researchers. Then, considering that FA could be linked to environmental factors during AIS development, its individual quantification could be used to explore different etiopathogenic factors, and if treatable, clinical decisions could be improved. Results should be interpreted cautiously because the subtraction of the average asymmetry, which is the DA effect present in the sample, is only a sample‐specific approximation to the FA estimation. Specifically, when DA has a big effect, in that particular case, both body sides will barely serve as controls for comparison, and the results of FA will be weakened (Klingenberg, 2003a, 2003b). Due to DA properties, estimating it directly in patients would improve the prognosis of the severity of AIS because it is known that moderate and severe scoliosis show higher asymmetries, in most cases, with the well‐known directional pattern.

Additionally, we aimed to test the hypothesis of Hallgrímsson, which proposes that FA is a cumulative process during growth and thus tends to increase with age in response to bone remodelling under an accumulation of random deviations (Hallgrímsson, 1988; Hallgrímsson, 1999). This model had never been applied to patients with scoliosis before, and it is the second goal of our research.

2. MATERIALS AND METHODS

2.1. Radiological and 2D shape data acquisition

Antero‐posterior X‐rays of 36 adolescents with AIS were used to study the presence of DA and FA after the approval of the ethics committee of Cantabria (Spain) with internal code 2019.019. Sex, mean age and mean Cobb angle (between the most cranial and caudal vertebrae of the scoliotic curve) of the sample are shown in Table 1. All X‐rays were scaled, and then 68 landmarks were digitized twice in all squares of the vertebral bodies of the thoracic and lumbar vertebrae using tpsDig232 (Rohlf, 2015) as shown in Figure 1. Each landmark was defined by two coordinates (x, y), and the complete datasets with the 2D raw coordinates of each patient (136 coordinates defined each patient) were used for further analyses of geometric morphometrics (GMM).

TABLE 1.

Sex, age and Cobb angle of the primary curve. Mean, standard deviation (SD) and 95% of the confidence interval (C.I.) are shown for age and Cobb angle

Sex distribution Age Cobb angle
Female = 31 (86.11%) Mean (SD) = 12.96 (2.23) Mean (SD) = 21.16 (9.43)
Male = 5 (13.89%) C.I. (95%) = 12.21–13.72 C.I. (95%) = 17.97–24.36
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FIGURE 1.

FIGURE 1

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Digitization in tpsDig232 of the 68 landmarks located in each corner of intersections of vertebral plates and lateral walls of the vertebral bodies of the thoracic and lumbar vertebrae. Thus, each vertebral body is represented by four landmarks

2.2. Geometric morphometrics and statistical analysis

The pairing of symmetrical landmarks was done in MorphoJ® (see Figure 2) before executing the General Procrustes Analysis (GPA; Klingenberg, 2011). This symmetrization is the first step of the reflected and relabeling process (Mardia et al., 2000), and it provides, after the GPA, the symmetric and asymmetric coordinates in shape space for all individuals of the sample. The difference of shape coordinates between the asymmetric component and the symmetric component is the vector of total asymmetry of shape (TAS) of each patient, which had been defined in a previous study in the form of total asymmetry (TA; Ekrami et al., 2020). These authors defined that the TA of a subject is the result of the left–right shape and size differences, in other words, a concept similar to our TAS before the GPA. The quantitative difference between the symmetric configuration and the original raw coordinates is the Procrustes distance to symmetry (Mardia et al., 2000), and this approach has been previously used in a 3D‐GMM study of the human torso (González‐Ruiz et al., 2021).

FIGURE 2.

FIGURE 2

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Pairing of the symmetrical landmarks extracted from X‐rays before the reflection and relabeling process in MorphoJ®. After the GPA analysis, the mean symmetric (a) and asymmetric (b) shape of the sample were obtained and represented with marine blue dots. Light blue dots in B represent the superposition of mean asymmetric and symmetric shapes

To test the statistical effects of DA and FA on the variation in the sample, we used Procrustes ANOVA in MorphoJ® (Fruciano, 2016; Klingenberg et al., 2002; Klingenberg & McIntyre, 1998). Because the FA effect is quite small in comparison with DA, the error of measurement is likely to mask its effect and needs to be measured, and accounted for, as mentioned in the ‘Introduction’ section. With this purpose, the sample was digitized twice, and the error dataset (second digitization) was introduced along with the raw coordinates of the first digitization in the Procrustes ANOVA. The ‘side’ effect defines the significant presence of DA in the sample subjected to study if p < 0.05, while the interaction between ‘individuals’ and ‘side’ defines the significant presence of FA in the sample if p < 0.05. The DA effect in our sample corresponds to the mean DA of shape (Klingenberg, 2003a, 2003b; Kordsmeyer et al., 2020).

Once the presence of DA and FA has been assessed in the sample, it is necessary to quantify both individually in each patient according to the main objective of this research. Thus, an individual FA score of each patient is obtained as a result of the Procrustes ANOVA analysis done in MorphoJ®, and it is the Procrustes distance between the left and the right sides of the spine after excluding the differences that are caused by the DA effect. This FA score will be regressed on age to test Hallgrímsson's hypothesis, which particularly should apply to the scoliosis condition showing greater FA scores in patients with an advanced state of maturity (the older ones).

To obtain the individual DA scores, we have developed the following steps, graphically represented in Figure 3:

  1. We subtracted the individual symmetric component of shape (the reflected and relabelled coordinates, whose mean shape was represented in Figure 2a) from the individual asymmetric component (whose mean shape was represented in Figure 2b) obtaining an individual vector of coordinates that represents the TAS of each patient. This step had been recently validated by other authors (Kordsmeyer et al., 2020) in a study of FA of the human face. TAS contains both the DA and FA components of asymmetry.

  2. The mean DA vector of shape of the sample is the difference between mean symmetry (Figure 2a) and mean asymmetry (Figure 2b). It was then subtracted from the TAS of each individual patient obtained in the first step. Because TAS contains both the estimates of DA and FA, the shape vector obtained in this step is the estimated FA shape of each patient; or in other words, the asymmetry of the individual shape after subtracting the mean DA of the sample. This subtraction of the mean DA had been introduced by Graham et al. (1998) and recently brought into a multivariate analysis of facial asymmetry by Ekrami et al. (2020).

  3. We estimated the Procrustes distance in each patient after a GPA of its original raw coordinates (first digitization) and the FA shape vector coordinates resulting from Step 2 (individual asymmetry of shape, mostly due to FA, because the mean DA of shape has been subtracted). Thus, the Procrustes distance between the original and the FA shape vector is the individual's asymmetry attributed to DA (by exclusion), or as we suggest, the DA score, which could be considered the quantitative shape difference (measured as Procrustes distance) between the original shape of the thoracic and lumbar spine and the hypothetical shape caused by individual FA effect. This variable, which expresses the individual variation of asymmetry in the dimension of DA, is similar to the one that has been termed Fluctuating DA in a recent study of Ekrami et al. (2020). These authors used angles and correlations between shape vectors represented in an orthogonal space instead of Procrustes distances.

  4. The addition of both Procrustes distances (FA score and DA score) can be considered the TA score of a patient. Furthermore, the proportion of FA and DA with respect to TA can be understood as the proportion of asymmetry explained by individual random‐environmental events (FA) and unknown‐general processes (DA), especially if DA is subtle in the sample studied (mild scoliosis) (Klingenberg, 2003a, 2003b; Negrini et al., 2018).

FIGURE 3.

FIGURE 3

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Description of the methodology for estimating DA score. x, y = cartesian coordinates of n = 68 landmarks. z = 36 patients. RR = reflected and relabeling; GPA = General Procrustes Analysis. Sym = symmetric coordinates; asym = asymmetric coordinates. TAS = total asymmetry of shape. FA shape = shape characterized by fluctuating asymmetry. Procrustes DA score = Procrustes distance between original shape (xn , yn ) z and FA shape

Finally, multivariate regression analyses were carried out to explore the relationship between individual scores of FA and DA with Cobb angle and a regression analysis between FA scores, and age was used to test Hallgrímsson's hypothesis.

Statistical significance for regression analyses was set as p‐value < 0.05, and effect size was considered acceptable with R 2 over 0.25 (Sullivan & Feinn, 2012).

3. RESULTS

The mean FA and DA scores are represented in Table 2, and the individual distribution of both types of asymmetry is shown in Figures 4 and 5. We additionally have represented the patients with the higher individual scores and the patients with the higher and lesser TA of the sample in Figure 6. Correlation between FA and DA is significant (p < 0.001), and the DA mean effect in the sample is more than twice the magnitude of the FA effect.

TABLE 2.

Mean (SD) FA score, mean (SD) DA score and correlation between both variables

FA score DA score
Mean (SD) = 0.0539 (0.03) Mean (SD) = 0.1145 (0.06)

Correlation:

† R = 0.94; ‡ R 2 = 0.87; * p‐value < 0.001
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†

Correlation coefficient.

‡

Determination coefficient or effect size.

*

p‐value < 0.05 is statistically significant.

FIGURE 4.

FIGURE 4

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Absolute values of FA (yellow) and DA (blue) measured as the Procrustes distance (y‐axis) in all patients (x‐axis). The higher the sum of both variables, the higher the patient's asymmetry is. Patient 3 shows the highest total asymmetry scores and patient 36 the least total asymmetry score

FIGURE 5.

FIGURE 5

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Percentage values of FA (yellow) and DA (blue) in y‐axis for all patients represented in the x‐axis. Patients with higher amount of FA relative to DA are more likely to have suffered greater developmental instability. Patient 26 show the highest percentage of FA score over her total asymmetry and patient 30 the highest percentage of DA score over her total asymmetry

FIGURE 6.

FIGURE 6

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X‐rays of patients with the highest (a) and the least (b) total asymmetry Score (sum of DA and FA scores), and patients with the higher FA (c) and DA scores (d) in percentage values of their total asymmetry

The result of the multivariate multiple linear regression analysis is shown in Table 3. Both FA (R 2 = 0.34) and DA (R 2 = 0.58) are significant determinants of Cobb angle (p < 0.001). However, DA is a better predictor of Cobb angle increment than FA as can be seen in Figure 7.

TABLE 3.

Overall MANOVA and regression coefficients of Cobb angle on FA and DA

Overall MANOVA: Wilks' lambda = 0.2955; p(regression) < 0.001 * p‐value ‡ R 2
Cobb <0.001
DA <0.001 0.58
FA <0.001 0.34
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‡

Determination coefficient or effect size.

*

p‐value < 0.05 is statistically significant.

FIGURE 7.

FIGURE 7

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Linear fit of Cobb angle on DA (black) and FA (red) measured as Procrustes distance. DA is better predictor of Cobb angle than FA

Finally, the regression of the individual FA scores on age to test the Hallgrímsson's hypothesis is not significant (p‐value = 0.12) with a correlation coefficient (R) of 0.26 and a determination coefficient (R 2) of 0.07.

4. DISCUSSION

4.1. About the method

We have introduced for the very first time a method that estimates both predominant types of asymmetry (DA and FA) in each individual with AIS. The method is based upon the subtraction of the mean shape asymmetry of the sample from the TAS of each patient (Klingenberg & Polak, 2003; Kordsmeyer et al., 2020; Rott et al., 2003). This means that the average asymmetry could, clearly, influence the results (Goldberg et al., 1997a). Thus, in a sample with higher deformities in the coronal plane (2D) expressed as higher Cobb angles, the risk of overestimating DA and underestimating FA could be important. However, in our sample, the mean Cobb angle is 21.16° with a standard deviation of ±9.44° and a 95% confidence interval of 17.97°–24.36°, which corresponds to mild scoliosis, without risk of progression (El‐Hawary & Chukwunyerenwa, 2014). For this particular reason, as it was previously reported in the literature (Klingenberg, 2003a, 2003b; Simmons, 2007), the subtraction of the average asymmetry in studies of FA is a good approximation to its understanding, and the results that will be discussed next in this paper should be taken into account in the future studies of asymmetry in AIS.

Future studies about the application of the methodology described in this research should be applied to the 3D shape of patients with AIS and in moderate–severe scoliosis to test the validity of the method. While 2D analysis gives a good account for the potential of this method and also offers relevant information to understand the relation between Cobb angle and asymmetry components of shape, a 3D analysis, accounting for the three‐dimensional aspect and complexity of AIS, should complement the present approach (González‐Ruiz et al., 2021; Stokes et al., 2009). Further necessary steps are the identification of the environmental factors described by Burwell et al. (Burwell et al., 2011) and their correlation with the FA score in our patients. Once it is accepted that AIS is a multi‐factorial condition (Addai et al., 2020; Latalski et al., 2017; Negrini et al., 2018; Porter, 2001), the identification of the individual factors involved in each particular case, and especially the potential correction of those factors when possible, should covariate with the amount of FA in a patient, and consequently, his/her asymmetry should be reduced.

4.2. About the results

The average presence of the DA effect in the subjects of the sample is slightly more than twice of the FA effect as it can be extracted from Table 2 (mean DA score is 2.12 times greater than mean FA score). This proportion between both types of asymmetry is clearly lower than the one observed in other studies, in which the amount of FA is subtle when compared to the DA effect (Balzeau et al., 2011; Benítez et al., 2020; Valen, 1962). However, in a recent study of FA of the bilateral dentoalveolar asymmetries in patients with AIS, a greater presence of significant FA effect on the bilateral trait has been detected in patients rather than in controls (Lewandowska et al., 2019). This result, which is congruent with other studies based on traditional morphometric approaches (Goldberg et al., 1995, 1997, 1997b), is similar to the findings presented in our research. This means that our finding of higher levels of FA in AIS is not strictly new, but firstly quantified by GMM, which is the better approach for the study of the influence of the environmental changes on our patients (Beasley et al., 2013; Benítez et al., 2020). In other words, in future studies, regarding the internal and external covariates (Burwell et al., 2011) on the FA of our patients, the GMM method will be more sensitive than the traditional morphometric studies of asymmetry of bilateral traits, and in consequence, it might be recommended. Notwithstanding the above, the unavailability of control X‐rays data due to ethical reasons requires us to be cautious with the interpretation of the results of our study.

Our results have revealed that the DA score is a better predictor of the Cobb angle than the FA score. A substantial 58% of the variance of the Cobb angle is explained by DA, which is sample‐dependent and a well‐reported traditional trait of AIS (Goldberg et al., 1994, 1997). Specifically, previous studies using 3D GMM had shown lower levels of Cobb angle prediction using the Procrustes distance to symmetry (R 2 = 0.14) and the 3D shape (R 2 = 0.01; González‐Ruiz et al., 2021). Other studies based on traditional morphometrics had investigated the strength of vertebral rotation (R 2 = 0.46; Aaro & Dahlborn, 1981), rib hump (R 2 = 0.42; Kuklo et al., 2005) and vertebral translation (R 2 = 0.09; Easwar et al., 2011) as predictors of the Cobb angle, all with lower effect sizes than the one evidenced in our study. We think that measuring the DA score in our patients could be a highly valuable tool in predicting the effect size of the deformity during the course of the AIS condition with respect to its reference sample. This is important because effect size might be proportional to treatment success.

Thus, the use of FA in studies of patients with AIS should be restricted to prove the presence of random deviations from target phenotype and their relation with potentially harmful environmental factors during growth, as it was previously done in other fields (Beasley et al., 2013; Benítez et al., 2020; Graham & Özener, 2016). In this sense, DA could be used as a good estimator in future models of prediction of the Cobb angle, while FA would help to open new research lines that should be developed in the study of the covariance of the environmental factors with the amount of FA present in each subject (Parsons, 1990), as we have suggested in the ‘Discussion’ section dedicated to the method.

This is of vital importance, as Burwell (Burwell et al., 2011) pointed out that ‘research on the role of environmental factors and epigenetic has not been explored in AIS’. The method we introduced in this paper highlights the presence of FA as a stochastic event in each particular patient with AIS, and it modifies in a significant manner their target phenotype and needs to be deeply studied during the clinical assessment to help in the prognosis of the condition. From this conclusion, a future hypothesis to be tested is that the higher the covariance is between the FA score and the different environmental factors, the higher the responsibility of that particular factor(s) for the acquisition of the observed phenotype.

Finally, our results do not support the Hallgrímsson's hypothesis (Hallgrímsson, 1999) of the cumulative presence of FA during growth. Once the connection of the FA phenomenon and environmental factors has been suggested, the failure of the epigenetic mechanisms is critical in AIS in ages before 10 (Burwell et al., 2011). Considering the mean age of the subjects studied in this research (12.96 ± 2.23, C.I. = 12.21–13.72), which exceed 10 years of age, the increment of FA does not necessarily have to be cumulative in response to age. Therefore, other factors such as the mechanical and/or the asymmetrical traits of the patients could probably affect the FA score in a higher degree than their age. Thus, the presence of cumulative FA during growth should be tested in the 3D phenotype of AIS and in control subjects to investigate whether the absence of this fact is exclusive for patients with AIS or for 2D phenotypes (X‐rays).

ACKNOWLEDGEMENTS

We would like to thank the Department of Orthopedic Surgery and Traumatology, University Hospital of Valdecilla, University of Cantabria, Santander for their contribution in the composition of the scoliosis group. We would also like to thank all the patients and their parents and tutors, who voluntarily agreed to participate in this study with their amounts of patience and altruism. Additionally, Markus Bastir was funded by CGL2015‐63648‐P; MINECO (Spain).

González‐Ruiz, J.M. , Pérez‐Núñez, M.I. , García‐Alfaro, M.D. & Bastir, M. (2021) How can directional and fluctuating asymmetry help in the prognosis of scoliosis along the course of the condition? Journal of Anatomy, 239, 1400–1408. 10.1111/joa.13509

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