Statistical shape modelling of hip and lumbar spine morphology and their relationship in the MRC National Survey of Health and Development

Abstract The anatomical shape of bones and joints is important for their proper function but quantifying this, and detecting pathological variations, is difficult to do. Numerical descriptions would also enable correlations between joint shapes to be explored. Statistical shape modelling (SSM) is a method of image analysis employing pattern recognition statistics to describe and quantify such shapes from images; it uses principal components analysis to generate modes of variation describing each image in terms of a set of numerical scores after removing global size variation. We used SSM to quantify the shapes of the hip and the lumbar spine in dual‐energy x‐ray absorptiometry (DXA) images from 1511 individuals in the MRC National Survey of Health and Development at ages 60–64 years. We compared shapes of both joints in men and women and hypothesised that hip and spine shape would be strongly correlated. We also investigated associations with height, weight, body mass index (BMI) and local (hip or lumber spine) bone mineral density. In the hip, all except one of the first 10 modes differed between men and women. Men had a wider femoral neck, smaller neck‐shaft angle, increased presence of osteophytes and a loss of the femoral head/neck curvature compared with women. Women presented with a flattening of the femoral head and greater acetabular coverage of the femoral head. Greater weight was associated with a shorter, wider femoral neck and larger greater and lesser trochanters. Taller height was accompanied by a flattening of the curve between superior head and neck and a larger lesser trochanter. Four of the first eight modes describing lumbar spine shape differed between men and women. Women tended to have a more lordotic spine than men with relatively smaller but caudally increasing anterior‐posterior (a‐p) vertebral diameters. Men were more likely to have a straighter spine with larger vertebral a‐p diameters relative to vertebral height than women, increasing cranially. A weak correlation was found between body weight and a‐p vertebral diameter. No correlations were found between shape modes and height in men, whereas in women there was a weak positive correlation between height and evenness of spinal curvature. Linear relationships between hip and spine shapes were weak and inconsistent in both sexes, thereby offering little support for our hypothesis. In conclusion, men and women entering their seventh decade have small but statistically significant differences in the shapes of their hips and their spines. Associations with height, weight, BMI and BMD are small and correspond to subtle variations whose anatomical significance is not yet clear. Correlations between hip and spine shapes are small.

. Unadjusted correlations between hip modes 1-10 and height, weight, BMI and total hip BMD, by sex Table S2. Unadjusted correlations between spine modes 1-8 and height, weight, BMI and lumbar spine BMD, by sex. Table S3. Unadjusted correlations between hip modes (HM1-10) and spine modes (SM1-8) in (a) men and (b) women. Figure S1. Effects of adjustment for height, weight and BMI on associations between hip mode scores and sex Figure S2. Effects of adjustment for height, weight and BMI on associations between spine mode scores and sex Figure S3. A description of the features varying in a coordinated fashion as identified by the hip mode scores HM1-HM10. The average score for each mode of the whole cohort is zero and positive and negative scores are described relative to the average. Figure S4. A description of the features varying in a coordinated fashion as identified by the spine mode scores SM1-SM8. The average score for each mode of the whole cohort is zero and positive and negative scores are described relative to the average.  Figure S1. Effects of adjustment for height, weight and BMI on associations between hip mode scores and sex. Findings from unadjusted models (Model 1) show associations between sex and hip modes. Except for modes 5 and 7, women had positive scores for modes 3, 9, and 10 but negative scores for modes 1, 2, 4, 6 and 8, as compared with men (Table 2). Adjustment for height (model 2) had the greatest effect on the findings and the association between sex and mode 5 become stronger whereas no associations were then observed between sex and modes 6, 8 and 9. There was little effect of adjusting for BMI (Model 4) whereby similar size estimates to those for model 1 were observed; suggesting that sex-differences found for modes 5, 6, 8 and 9 may be explained by height. Models: 1, unadjusted; 2, adjusted for height; 3, adjusted for height and weight; 4, adjusted for BMI a) Spine modes 1 -4 b) Spine modes 5 -8 Figure S2. Effects of adjustment for height, weight and BMI on associations between spine mode scores and sex. Findings from unadjusted analyses show associations between sex and spine modes 1, 3, 6 and 8. Compared with men, women were more likely to have positive scores for spine modes 1, 3 and 8 but negative scores for mode 6 (Model 1). Adjustment for height slightly attenuated size estimates for mode 1 and the association become null. Conversely, associations between sex and mode 4 become stronger after adjustment for height.   Figure S3. A description of features of the hip joint that vary in a coordinated fashion as identified by the hip mode scores HM1-HM10. The average score for each mode of the whole cohort is zero and positive and negative scores are described relative to the average. The percentage variation is the variance described by each principal component.

Curviness
Total amount and direction of curvature within the spine from L5 to T10.
Positive scores: • Overall greater curvature throughout, increasing lordosis in both lumbar and thoracic sections.

Evenness
Differences in the distribution of curvature along the length of the spine, with consequent small variations in disc space.
Positive scores: • Increasingly evenly distributed curvature throughout all sections from L5-T10 (superimposed on lordotic, straight or kyphotic overall shape described by SM1).

(8.6%)
Relative anterior-posterior diameter Negative scores: • Greater relative vertebral body a-p diameter Positive scores: • Smaller relative vertebral body a-p diameter.

(7.1%)
A combination of vertebral rotation at L5-L4 and T10 together with changes in disc space Negative scores: • Minor snaking of the curvature with greater anti-clockwise rotation at L5, L4, and T10 with smaller caudal disc spaces.
Positive scores: • More uniform shape with smaller cranial disc spaces. Figure S4. A description of the features varying in a coordinated fashion as identified by the spine mode scores SM1-SM8. The average score for each mode of the whole cohort is zero and positive and negative scores are described relative to the average. The percentage variation is the variance described by each principal component.
Negative scores: -Smaller vertebral body heights, relatively larger disc spaces.
Positive scores: -Taller vertebral body heights, relatively smaller disc spaces.