Cluster analysis for the extraction of sagittal gait patterns in children with cerebral palsy
Introduction
There have been several attempts to categorise gait patterns by researchers in the physical therapy and surgical communities [1], [2], [3], [4], [5], [6], [7], [8], [9], particularly in gait pathology related to cerebral palsy (CP) [1], [2], [3], [4], [6], [7], [9].
One of the reasons to categorise gait patterns is that clinicians would no longer need to produce a detailed explanation of the gait problem, but would rather classify gait more broadly as being one of a few types [4]. This would be particularly useful since many clinicians do not have access to analysis equipment [8], [9] and rely on visual or simple video gait assessment instead. A second reason is that it would enable care pathways to be standardised for each gait category, with subsequent service delivery and efficiency benefits. A further reason is that classification of gait problems would make communication between clinicians easier [4].
A critical issue is the lack of a standardised method of gait classification. Deciding how many different categories of gait types exist can be subjective, prone to variability or lack validity. Should gait types be decided by expert consensus or systematic statistical interrogation of gait data? What is the optimum number of gait categories? How do we decide when to stop breaking down gait disorders into different types? A fundamental question here is the definition of a gait type or category. Our assumption is that patients can be classified under the same gait type when they display gait characteristics that are sufficiently similar to clinically consider them identical in terms of aetiology of the disorder, its effect on gait and its management. Furthermore, the gait characteristics displayed by a patient group must be sufficiently different from characteristics displayed by all other groups. However, such distinctive margins between groups of patients rarely exist, the reality being a broad continuum of gait patterns. Given the diversity of gait types and complexity of their classification, a systematic and analytical approach to classification would be required.
There is a variety of published gait classifications defining groups of children presenting with apparently different gait patterns based on sagittal plane gait kinematics [1], [2], [3], [4], [7], [9] (Table 1). Winters et al. [1] used visual inspection and expert opinion to separate sagittal plane kinematic and electromyographic gait data into four distinct groups with homogenous gait patterns of 46 children and adults with hemiplegic cerebral palsy. Whilst this gait classification has been cited on many occasions and appears to be clinically useful, the rationale for the number of types of gait pattern was based on the researcher's perception as to which similarities and differences between patients were important. Hullin et al. [3] redefined Winters et al.'s grouping scheme by collecting kinematic and kinetic data from 26 children with hemiplegic cerebral palsy. Five groups were identified by visual examination of the data and only one corresponded to Winters et al.'s groups (Group I of Winters et al.).
Rodda et al. [9] devised a classification system including five gait types from 174 children with diplegic cerebral palsy. The gait types were based on the classifications by Winters et al. [1] and Sutherland and Davids [10]: they were selected by visually assessing sagittal plane kinematic gait data and using clinical reasoning.
Other authors have applied a more systematic approach involving a variety of statistical clustering techniques to classify gait types [2], [4], [7]. Using an unspecified clustering technique on kinematic, kinetic and metabolic gait data from 83 children with hemiplegic cerebral palsy, Stout et al. [2] broadly confirmed the four gait groups identified by Winters et al. [1].
O’Byrne et al. [4] used K-means cluster analysis on sagittal plane kinematics from 237 hemiplegic and diplegic cerebral palsy limbs to identify eight homogenous groups. The rationale for the number of groups was not clear. Clinical reasoning dictated that if there were ‘too few’ groups, gait patterns, which were clinically distinct, would be merged together. However, if there were ‘too many’ groups the classification system would be ‘too cumbersome’.
Kienast et al. [7] defined three gait types – normal walking, crouch gait and dynamic hypertonic gait – using K-means cluster analysis on sagittal kinematic data for the pelvis, hip, knee and ankle from 15 neurologically intact children and 24 children with spastic diplegia.
The published literature, therefore, suggests that distinct gait patterns exist within CP gait. These patterns, when recognised, could be helpful in leading clinical management. However, the previous literature is unclear on how the optimum number of gait types was decided and validated.
Cluster analysis is a multivariate statistical method to classify an entire data set into homogeneous groups or “clusters” [11], [12]. There are hierarchical and non-hierarchical clustering methods. Non-hierarchical methods, e.g. K-means cluster analysis, are faster to use than hierarchical ones, but do not allow step-by-step inspection of the clustering process. Fuzzy clustering is a computational approach to categorise data where there is no sharp boundary between clusters. Hierarchical and non-hierarchical clustering methods have been the preferred methods for categorising kinematic gait data, although fuzzy clustering has recently been applied on temporal-distance parameters derived from CP gait [6], [13].
Each group identified by the analysis contains data cases (gait patterns) that are similar in the way several of the variables are related to each other. A different group (different gait pattern) will have a different relationship between these variables and possibly a unique relationship between other variables. The technique searches for relationships in the data that may confirm visually detected patterns or that cannot be identified easily by visual inspection or simple comparison. It requires the setting of rules for the clustering process. These rules as well as the chosen variables are subjective and can affect the search. If different rules are set then a different number and type of groupings of gait patterns will emerge [14]. If too few clusters are requested from the cluster analysis, then clinically different gait patterns will be incorrectly merged into one cluster. If too many clusters are requested, clinically similar gait patterns will be incorrectly separated.
Validation of the resulting gait clusters is an important step in the clustering process. This can be performed by computational methods using cluster validity indexes [15], [16], although these differ in reliability and validity [15]. Visual validation of clusters is felt to be a crucial step in cluster verification, particularly when dealing with two-dimensional data [14]. Halkidi et al. described three criteria to examine cluster validity: ‘external criteria’ were based on the comparison of the resulting clusters to a pre-specified structure (i.e. normal gait data or gait clusters identified by other research). ‘Internal criteria’ were based on examination of the data and relationship within and between the gait clusters themselves. Lastly, ‘relative criteria’ were concerned with the comparison of various clustering schemes on the same data.
In the present work, the purpose of using cluster analysis and the resulting gait clusters differ from previous literature. Whereas previous research aimed at using the clusters in clinical practice, we avoided any external bias on the process of defining the optimum number of clusters. Instead, we took a more objective, systematic approach, implementing hierarchical cluster analysis to identify the optimal number of gait clusters for children with cerebral palsy.
Section snippets
Patients
Sixty-seven subjects participated in the study, from which 132 limbs were suitable for analysis. Fifty-six children (112 limbs) with cerebral palsy (20 girls, 36 boys, mean age 9 years, range 5–16 years) were recruited from the Greater Manchester area and ethical approval was obtained from the local ethics committee. Informed consent was obtained from parents and children.
The diagnoses consisted of hemiplegia (n = 25), diplegia (n = 24), quadriplegia (n = 4), monoplegia (n = 1), mild dystonia (n = 1) and
Cluster analysis
Based on the first criterion, a single cluster was identified in a 14-cluster solution that contained the limbs from 19 neurologically healthy children and the limb from the unaffected side of one child with hemiplegia. In less than 14 cluster solutions, the cluster that contained the limbs of the neurologically intact children also contained 11 limbs from children with cerebral palsy. The standard deviations in this ‘normal gait’ cluster was reduced from the 14th cluster solution upwards and
Discussion
Using Hierarchical cluster analysis, 13 gait clusters were identified that differed from each other in the relationships between sagittal plane hip, knee and ankle kinematics. We took an analytical approach to cluster definition and gait type recognition, combining cluster analysis with visualisation of the gait data to guide the final outcome. Clinical judgement was necessary to guide this exploratory method that requires the search for the optimal number of groupings using objective
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