Gait phenotypes in paediatric hereditary spastic paraplegia revealed by dynamic time warping analysis and random forests

Abstract

The Hereditary Spastic Paraplegias (HSP) are a group of heterogeneous disorders with a wide spectrum of underlying neural pathology, and hence HSP patients express a variety of gait abnormalities. Classification of these phenotypes may help in monitoring disease progression and personalizing therapies. This is currently managed by measuring values of some kinematic and spatio-temporal parameters at certain moments during the gait cycle, either in the doctor´s surgery room or after very precise measurements produced by instrumental gait analysis (IGA). These methods, however, do not provide information about the whole structure of the gait cycle. Classification of the similarities among time series of IGA measured values of sagittal joint positions throughout the whole gait cycle can be achieved by hierarchical clustering analysis based on multivariate dynamic time warping (DTW). Random forests can estimate which are the most important isolated parameters to predict the classification revealed by DTW, since clinicians need to refer to them in their daily practice. We acquired time series of pelvic, hip, knee, ankle and forefoot sagittal angular positions from 26 HSP and 33 healthy children with an optokinetic IGA system. DTW revealed six gait patterns with different degrees of impairment of walking speed, cadence and gait cycle distribution and related with patient's age, sex, GMFCS stage, concurrence of polyneuropathy and abnormal visual evoked potentials or corpus callosum. The most important parameters to differentiate patterns were mean pelvic tilt and hip flexion at initial contact. Longer time of support, decreased values of hip extension and increased knee flexion at initial contact can differentiate the mildest, near to normal HSP gait phenotype and the normal healthy one. Increased values of knee flexion at initial contact and delayed peak of knee flexion are important factors to distinguish GMFCS stages I from II-III and concurrence of polyneuropathy.

Fig 1

A) Dendrogram obtained from hierarchical clustering analysis of gait cycles of HSP patients. The vertical axis represents the distance DTW. A vertical line that reaches the base indicates each cycle. Horizontal lines that interconnect the vertical ones indicate DTW distances between the cycles. The higher the horizontal lines joining two cycles, the less similar they are. The lower bar indicates whether the classified cycle is from the right limb (red) or the left (green). Six clusters and an “outlier” (pink cycle) are detected. The majority of cycles are grouped within the red and the blue cluster. B) The heatmap presents Z-scores (standardized comparison to healthy average value) of the spatio-temporal parameters (rows) of each HSP cycle (columns). Green colour indicates a higher spatio-temporal value in the cycle than in healthy children and red, a lower value. The more intense the colour of the square, the further the value of the cycle is from healthy controls. In comparison to healthy controls, red, blue and brown patterns represent less impaired spatio-temporal performance; while orange, green and part of the cycles from the purple pattern show more altered values.

Fig 2. Cumulated kinematic plots of five joints grouped according to seven sagittal patterns yielded by dendrogram in Fig 1.

Each column represents a pattern and each row, a joint. The x-axis of each graph corresponds to the percentage of gait cycle. The y-axis represents the joint range in degrees (zero is the neutral position, positive values indicate flexion and negative values, extension). The healthy children’s cycles are depicted in grey lines, their average healthy patterns in black, and the overall healthy average is shown with a thick black line. Patterns I and II (red and blue, respectively) are the most similar to normal. The outlier (pink) corresponds to an “outlier” cycle.

Fig 3. Distribution of sagittal patterns in left and right cycles and clinical features of each patient.

Patients were ordered according to the type of gait patterns they use (left) and clinical features were represented with colour scales (right). Notice that clinical features are partially related to the gait phenotype.

Fig 4. Importance of gait parameters in the classification of gait cycles in sagittal patterns generated by the random forest.

It is measured by the mean decrease in accuracy when the variable is out of the bag. The most important are mean pelvic tilt and hip flexion at initial contact.

Fig 5. Heatmap showing the Z-scores (standardized measure of the distance to healthy average value) of the 12 most important gait parameters to classify cycles into gait patterns according to random forest models.

Cycles are represented in columns and ordered following the dendrogram shown in Fig 1. Gait parameters are shown in rows and ordered according to the relationships between relationships with each other (dendrogram on the left). The Z-scores are represented following the colour legend in the top left corner.

Fig 6. Importance of gait parameters for the random forest model to distinguish between cycles from HSP sagittal Pattern I and healthy controls.

It is measured by Breiman-Cutler permutation variable importance (VIMP). Stance time and time to peak knee flexion in stance are the most important parameters to distinguish patients with sagittal Pattern I from healthy controls.

Fig 7. Relationships between model estimator ŷ (vertical axis) with values of the stance time (A), time to peak knee flexion (B), maximum hip flexion in swing (C), hip flexion at initial contact (D), knee flexion at initial contact (E) and second double support (E).

Estimator ŷ is represented in the vertical axis, its range is from 0 to 1, with 0 representing minimum chance of being red and 1, maximum. On the horizontal axis, the value for the gait parameters. A) Longer percentage of single support time indicates a higher chance of being classified in the red pattern (values higher than 70% are indicative of disease); B) Percentage values of time to peak knee flexion greater than 75% of the cycle indicates the presence of HSP. C) High values of maximum hip flexion in swing (more than 45 degrees) indicate high possibility of presenting a mild form of HSP. D) The possibility of having HSP increases markedly when the values of hip flexion at initial contact are higher than 40 degrees. E) Values of knee flexion at initial contact higher than 20 degrees indicate high possibility of HSP presence. F) High percentage values in double support and hip flexion at initial contact indicate a greater chance of being affected.

Fig 8. Distribution of clinical features between gait cycles for each gait pattern.

Distribution of age between patterns were shown by means of violin plots. Frequencies of GMFCS, sex, polyneuropathy, abnormal VEP (visual evoked potentials) and corpus callosum thinning were shown by means of bar plots. See text for details.

Fig 9. Relationships of the four most important gait parameters to predict age in HSP according to random forest model.

Age is shown in the x-axis and each gait parameter in the y-axis. We represent healthy and HSP children data (blue and red points) and the adjusted linear mixed model for each group (blue and red lines). In the case of cadence (upper right), age and cadence are similarly related in both groups. In the case of normalized walking speed (upper left), the decrease of normalized walking speed with age tends to be higher in children with HSP, although it is not statistically significant (see text). Range of pelvic rotation in terminal swing (lower left) increases only with age in children with HSP, while it seems to remain stable in healthy subjects along the age spectrum. Maximum knee flexion (lower right) decreases with age both in HSP children and healthy children, but in the case of disabled children, it seems to decrease significantly faster.

Fig 10. Violin plots of the four most important gait parameters to distinguish between patients with GMFCS I and GMFCS II-III according to random forest model.

The vertical axis represents the value of the gait parameters studied. The shape of the violin plot depends on the distribution of the values of the gait parameters in each group. Grey violin plots show data distribution from healthy children, the green ones data distribution from children with HSP and GMFCS I and the red ones distribution from children with HSP and GMFCS II-III. In each violin plot, the white point represents the median value of each group; the vertical black line represents the range.

Fig 11. Violin plots of the six most important gait parameters to distinguish between patients with normal and abnormal EMG.

The vertical axis represents the value of the gait parameters studied. The shape of the violin plot depends on the distribution of the values of the gait parameters in each group. Grey violin plots show data distribution from healthy children, the green ones data distribution from children with HSP and normal EMG and the red ones distribution from children with HSP and abnormal EMG. In each violin plot, the white point represents the median value of each group; the vertical black line represents the range.

Fig 12. Violin plots of the four most important gait parameters to distinguish between patients with apparently normal corpus callosum and patients with thin corpus callosum according to random forest model.

The vertical axis represents the value of the gait parameters studied. The shape of the violin plot depends on the distribution of the values of the gait parameters in each group. Grey violin plots show data distribution from healthy children, the green ones data distribution from children with HSP and apparently normal corpus callosum and the red ones distribution from children with HSP and thin corpus callosum. In each violin plot, the white point represents the median value of each group; the vertical black line represents the range.