Gait & Posture xxx (2006) xxx–xxx www.elsevier.com/locate/gaitpost
Linking clinical measurements and kinematic gait patterns of toe-walking using fuzzy decision trees Ste´phane Armand a,b,c,*, Eric Watelain a,d, Emmanuel Roux e, Moı¨se Mercier b,f, Franc¸ois-Xavier Lepoutre a a
Laboratoire d’Automatique, de Me´canique et d’Informatique industrielles et Humaines, Universite´ de Valenciennes et du Hainaut-Cambre´sis, Le Mont Houy, 59313 Valenciennes Cedex 9, France b Unite´ Clinique d’Analyse de la Marche du Mouvement, Institut Saint-Pierre, 34250 Palavas-Les-Flots, France c Laboratoire de Cine´siologie, Hoˆpital cantonal Universitaire de Gene`ve, 24 Rue Micheli du Crest, 1211 Geneva 14, Switzerland d De´partement de Me´decine Physique et de Re´adaptation, Centre Hospitalier Re´gional Universitaire de Lille, Hoˆpital Swynghedauw, 59037 Lille Cedex, France e LTSI-INSERM U642, Universite´ de Rennes 1, Campus de Beaulieu-Baˆt. 22, 35042 Rennes Cedex, France f Service de Neurope´diatrie, Centre Hospitalier Saint-Eloi, 2, Avenue Bertin-Sans, 34295 Montpellier Cedex, France Received 21 February 2005; received in revised form 18 May 2006; accepted 20 May 2006
Abstract Toe-walking is one of the most prevalent gait deviations and has been linked to many diseases. Three major ankle kinematic patterns have been identified in toe-walkers, but the relationships between the causes of toe-walking and these patterns remain unknown. This study aims to identify these relationships. Clearly, such knowledge would increase our understanding of this gait deviation, and could help clinicians plan treatment. The large quantity of data provided by gait analysis often makes interpretation a difficult task. Artificial intelligence techniques were used in this study to facilitate interpretation as well as to decrease subjective interpretation. Of the 716 limbs evaluated, 240 showed signs of toe-walking and met inclusion criteria. The ankle kinematic pattern of the evaluated limbs during gait was assigned to one of three toewalking pattern groups to build the training data set. Toe-walker clinical measurements (range of movement, muscle spasticity and muscle strength) were coded in fuzzy modalities, and fuzzy decision trees were induced to create intelligible rules allowing toe-walkers to be assigned to one of the three groups. A stratified 10-fold cross validation situated the classification accuracy at 81%. Twelve rules depicting the causes of toe-walking were selected, discussed and characterized using kinematic, kinetic and EMG charts. This study proposes an original approach to linking the possible causes of toe-walking with gait patterns. # 2006 Published by Elsevier B.V. Keywords: Gait analysis; Clinical interpretation; Biomechanics; Fuzzy decision tree; Toe-walking
1. Introduction Associated with many diseases, such as cerebral palsy, myopathy and neuropathy [1], toe-walking is a very common gait deviation that is defined as an absence of the first rocker. Three distinct kinematic ankle patterns (Fig. 1) have been identified in the toe-walker gait for a large variety of diseases [1]. The first pattern shows progressive dorsiflexion during the stance phase, while the second * Corresponding author. Tel.: +41 22 37 27 827; fax: +41 22 37 27 799. E-mail address:
[email protected] (S. Armand).
presents a short dorsiflexion, followed by a progressive plantarflexion. The third group exhibits a double bump aspect, moving successively from a short dorsiflexion, to a short plantarflexion, returning to a short dorsiflexion and ending with a plantarflexion until toe-off [1]. These three gait patterns conformed to those identified in the literature [1]. Perry [2] offers several possible causes of the lack of heel rocker: (a) pretibial muscle weakness, (b) inadequate tibialis anterior activity, (c) plantar flexion contracture, (d) soleus and gastrocnemius spasticity, (e) excessive voluntary ankle plantarflexion in compensation for quadriceps weakness, (f)
0966-6362/$ – see front matter # 2006 Published by Elsevier B.V. doi:10.1016/j.gaitpost.2006.05.014 GAIPOS-2263; No of Pages 10
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consideration to be expressed using natural language. FDT permit knowledge to be derived from data by providing an intelligible and interpretable input–output mapping. Since the ‘‘if-then’’ rules derived from FDT are easily intelligible, using FDT is a good way to deduce which clinical measurements can be associated with the three ankle gait patterns in toe-walking. This article highlights the links between the possible causes of toe-walking and the three toe-walking ankle gait patterns to create knowledge repository of this gait deviation. This knowledge could be used to support gait analysis interpretation.
2. Method 2.1. Subjects Fig. 1. Three kinematic ankle gait patterns, as identified by Armand et al. [1]. The shaded region represents the mean one standard deviation based on 20 able-bodied subjects (age: 11.34 3.2 years; height: 1.45 0.27 m; mass: 40.4 5.3 kg).
knee flexion contracture caused by overactivity of the hamstring and (g) combined spasticity of the hamstring and ankle plantarflexors. Toe-walking can also be caused by a leg length discrepancy [3], a compensation for problems in the contralateral side [4] or a limited dorsiflexion due to calf muscle stiffness [5]. Most of these causes can be assessed by static examination including range of motion, spasticity, strength and anthropometric measurements [6], but the exact details of what combination of clinical measurements can be linked to the three types of toe-walking have not been established. All attempts to provide clinical explanations for toewalking patterns have been empirical and subjective. Linking patterns to causes is complicated by the fact that toe-walking is frequently not the result of a single clinical deviation, but rather a combination of several problems. Skaggs et al. [7] have shown a high degree of variability in gait analysis interpretation, which may stem from this complexity. Given its potential impact on planning treatment, identifying and interpreting the causes of gait deviations, such as toe-walking, remains an important task. Identifying which clinical measurements can be linked to the three kinematic ankle patterns would be a valuable addition to the existing body of knowledge. This knowledge could support gait analysis interpretation, and aid clinical practitioners in choosing the best treatment plan for specific toe-walking patients. Identifying causes of gait deviations is difficult using observation alone. Therefore, artificial intelligence techniques can be a helpful tools. Decision trees are often used in medical fields to classify patients according to clinical characteristics [8]. Fuzzy decision trees (FDT) incorporate a notion of fuzziness that permits inaccuracy and uncertainty to be introduced and allow the phenomena under
A total of 358 case studies of children, who had been evaluated via clinical examination and instrumented gait analysis from 2002 to 2004, were reviewed for this retrospective investigation. Both the examination and the analysis were performed by the same physical therapist and biomedical engineer. To be included in this study, children had to meet the following selection criteria: - absence of heel rocker, as assessed by instrumented gait analysis and video; - completion of a minimum of three gait analysis trials; - no usage of walking aids (cane, walker or orthopaedic device). According to these criteria, 169 children (mean age 9.4 4.2 years), corresponding to 240 lower limbs, were selected to participate in the study. 2.2. Clinical assessment Clinical examination included grading spasticity with the modified Ashworth scale [9]; passive range of motion of the hip, knee and ankle joints; and muscle strength according to a manual five-point scale [10]. Angular measurements were obtained using a handheld goniometer. Range of motion was tested using gentle slow manoeuvres in order to avoid spastic muscle responses. 2.3. Gait analysis Gait analysis was performed using a five-camera motion measurement system (VICON 512; Oxford Metrics1, Oxford, UK), two force plates (AMTI1, Watertown, USA) embedded in the experimental walkway, and a 10channel Electromyography (EMG) system (MA-100, Motion Lab Systems1, Baton Rouge, USA). Reflective markers for video measurement were placed at defined anatomical points on the pelvis and lower limbs according to the Davis protocol [11]. Pre-amplified EMG surface
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electrodes were positioned according to SENIAM’s recommendations [12]. Kinematic and kinetic parameters were calculated using the Vicon Clinical Manager software (Oxford Metrics1, Oxford, UK) and Matlab (The MathWorks1, Natick, USA) was used to process the EMG envelopes. Electromyographic data were full-wave rectified and smoothed using a fourth-order Butterworth low-pass filter with a cut-off frequency of 10 Hz [13], and then normalized for the signal amplitude. All patients were asked to walk at a self-selected speed along a 12 m walkway. Under the direction of a biomechanical engineer, data were collected until five ‘‘clean’’ trials had been recorded for each child. Only trials in which the entire foot made contact with the force-plate without targeting were included in the analysis. 2.4. Classification method and rules extraction 2.4.1. Discrimination based on the subjective evaluation of gait analysis results and videos Videos of toe-walking patients and the corresponding ankle kinematics were displayed on a screen for evaluation by a person with more than 4 years experience in the interpretation of clinical gait analyses. These videos and ankle kinematics were re-evaluated in random order 1 week later by the same person. Based on these evaluations, toewalking patients were assigned to one of the three toewalking groups, according to the visual information contained in the charts (Fig. 1). The first evaluation permitted the classification of 144 ankle patterns. Of these, 60 belonged to group 1, 35 to group 2 and 49 to group 3; 53 were considered unclassifiable (trials in the same session belonged to at least two different toewalking groups) and 43 presented a different pattern (different from the three patterns being studied). During the second evaluation, 146 ankle patterns were classified: 63 belonged to group 1, 35 to group 2 and 48 to group 3; 52 were considered unclassifiable and 42 presented a different pattern. Ankle patterns that were twice assigned to the same group were subjected to further analysis. Of the 143 ankle patterns, 60 belonged to group 1, 35 to group 2 and 48 to group 3. 2.4.2. Data processing The clinical examination measurements for each limb were coded using three normalized triangular fuzzy membership functions (also called fuzzy windows) related to the following three modalities: Low, Average and High (see Fig. 2). Each fuzzy modality was defined by three parameters—ai, bi and ci (i2{1,2,3})—where a1 and c3 tended to 1 and +1, respectively, and a2 = b1, a3 = b2 = c1 and b3 = c2. Consequently, for this characterization of the variable range, only three parameters had to be defined for each clinical index: Lv , Av , and H v (see Fig. 2). These parameters were determined based on the clinical measurements data distributions (Lv and H v corresponding
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Fig. 2. Principle of fuzzy windowing with triangular membership functions used to characterize clinical measurements as Low, Average and High. The parameters Lv , Av and H v were determined based on the clinical measurements data distributions (Lv and H v corresponding to the 5th and 95th percentiles, respectively, and Lv = median) and expert advice for each clinical measurement. x is a measured value of a given clinical variable V, mAverageV ðxÞ and mLowV ðxÞ are, respectively, the membership values of the modalities Average and Low. In this example, the membership value of the modality High is equal to zero: mHighV ðxÞ ¼ 0.
to the 5th and 95th percentiles, respectively, and Lv = median) and expert advice. Table 1 shows the parameters for each clinical measurement. Let MiV be the fuzzy modality relative to the ith fuzzy window of the variable V and defined by the parameters ai, bi and ci. For an observed value x of a given variable V, the membership value mM V ðxÞ of the modality MiV is: i
x ai ci x ; 1; mMiV ðxÞ ¼ max min ;0 c i bi bi ai for example, for the variable ankle plantarflexion, {Lv , Av , H v } = {0, 30, 60} (see Table 1), and a plantarflexion of 208 yields the following membership values: mLowPlantarflexion ð20Þ ¼ 1=3, mAveragePlantarflexion ð20Þ ¼ 2=3 and mHighPlantarflexion ð20Þ ¼ 0. Table 1 Clinical variables with window limits for fuzzy coding Clinical variables
Low
Average
High
Range of movement (8) Hip flexion Hip extension Knee flexion Knee extension Dorsiflexion Plantarflexion
100 30 110 20 20 0
120 10 130 0 10 30
140 10 150 20 40 60
Spasticity (Ashworth Grade) Quadriceps Hamstring Triceps surae Tibialis anterior
0 0 0 0
2 2 2 2
4 4 4 4
Manual muscular testing (Grade) Quadriceps Hamstring Triceps surae Tibialis anterior
1 1 1 1
3 3 3 3
5 5 5 5
Leg length discrepancy (cm)
0
2
4
4
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2.4.3. Fuzzy decision tree and rules Quinlan’s Interactive Dichotomizer 3 (ID3) algorithm for decision tree induction was first described in 1986 [14,15]. Though several methods for adapting this algorithm to fuzzy data [16–18] have been proposed, all of them are based on the same principles. First, a learning set of observations (also called examples) is built. These set members are characterized both by their fuzzy membership values related to the modalities of a set of categorical variables (in our case, the clinical examination measurements) and by their fuzzy or crisp membership values related to the classes of a known category (in our case, the three toe-walking groups). This learning set is then subjected to a four-step procedure [15]:
2.4.4. Patient classification In our study, the conditions of the rules are defined by the fuzzy characterization of the clinical measurements, and the conclusions indicate membership or non-membership in a toewalking class. The fuzzy rules are, in fact, a sort of knowledge repository, with each rule containing a probable cause of toewalking. Thus, this rule base can be used to objectively and automatically assign any given patient to the toe-walking class to which she/he probably belongs—which is precisely what we hoped to achieve. To test the accuracy, specificity and sensitivity of this rule-based classification system, a stratified 10-fold cross validation [15,20] was performed. 2.5. Rule illustration
(1) A discriminating measure is used to determine which categorical variable best explains the distribution of the patients among the classes, and a node is created. (In this study, a discrimination measure based on information entropy was used (See Marsala [19] for more information)). (2) The dataset is partitioned to build as many subsets as there are modalities for the variable chosen in step 1. (This study has three modalities per variable of the clinical examination measurements). (3) A termination condition is tested with the help of a termination criterion b. (The termination condition in this study is defined, for a given node level, with the conditional probability p of being in a class, given that the conjunction of fuzzy conditions from the ‘‘root’’ to the node is verified). In the present study, b was initially set at b0 = 0.7, which appeared to be a good compromise allowing the two antagonistic criteria, reliability and generality, to be managed. (4) If the termination condition is verified, then the subset is considered to be a ‘‘leaf’’ of the tree. If the termination condition is not verified, then steps 1 to 3 are repeated. Once the fuzzy decision tree has been created, each branch of the tree (i.e. the path from the root to the leaf of a fuzzy decision tree) can be converted into a rule. The rule ends at the leaf level, indicating the membership or the nonmembership in the class for which the tree was induced. At the leaf level, p corresponds to the rule’s fire strength. Each rule is then optimized according to the Yuan and Shaw method [16], by removing all fuzzy conditions that penalize the rule’s fire strength. Since the discrimination measure is particularly well adapted to two classes, as many trees are induced as there are classes, and each tree concludes with the membership or non-membership in a class. (The complete method was explained in detail by Marsala [19] and applied to biomechanical data by Roux [15].) In our application, three FDT were induced, one for each of the three toe-walking groups. A rule that concludes in membership in a group is called a ‘‘yes’’ rule, and a rule that concludes in nonmembership in a group is called a ‘‘no’’ rule.
A rule’s premise – characterized by a combination of clinical measurements – provides an explanation of the membership of a class and thus constitutes a possible cause of a toe-walking pattern. Since several rules can conclude in the same ankle gait pattern, we felt it was important to illustrate how the different combinations of clinical measurements affected the other gait parameters (e.g. hip and knee kinematics, kinetics, EMG). Thus, patient gait analysis data were averaged according to membership weights (membership of a patient in a given rule), which produced a characteristic gait pattern (kinematics, kinetics for each joint and EMG) for each rule.
3. Results 3.1. Classification accuracy Eighty-three rules (available as Appendix B, Supplementary data on the gait and posture website) were obtained using the method described in the preceding Section 2.4. The number of conditions per rule varied from 1 to 11, with an average of 4.2. The results of the stratified 10-fold cross validation are presented in Table 2 for each of the three patterns. Overall, our method was able to correctly classify toe-walkers most of the time, using the kinematic ankle patterns revealed by clinical examination, for a general accuracy rating of 81%. The general specificity rating was 84% and general sensitivity rating was 65%. The percentages of toe-walkers correctly classified in relation to their disease are reported in Fig. 3. Classification accuracy for idiopathic toe-walkers was less than 50%. The best results were for diseases presenting muscular weakness, Table 2 Results of stratified 10-fold cross validation for each of the Armand et al. [1] toe-walking groups
Accuracy (%) Sensitivity (%) Specificity (%)
General
Group 1
Group 2
Group 3
81 65 84
83 60 95
77 67 73
80 67 78
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Fig. 3. Classification accuracy of the fuzzy decision tree method and patient distribution by disease. ‘‘Various’’ includes all the patients from an identified disease with less than five patients. ‘‘Mean’’ represents the mean for accuracy.
such as myopathy or muscular spinal atrophy, yielding an accuracy rating of 100%. 3.2. Rule characterization Table 3 summarizes the ‘‘yes’’ rules with no more than five conditions that were defined from tree branches whose
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leaves contained at least three examples of a given ankle pattern. The gait patterns associated with these 12 rules are presented in Figs. 4–6. In order to limit the discussion in this paper to the most important rules, the ‘‘yes’’ rules with more than five conditions and those that could classify either one or two ankle patterns were excluded from the discussion, as were any ‘‘no’’ rules. A classification performed on the learning set with only the 12 selected rules yielded 12 patients (10.4%) misclassified and 25 patients (17.2%) unclassified. The general accuracy with this reduced rule base was 72.4%. All rules for group 1 (R1) correspond to low or average muscle spasticity in the triceps surae with some specific muscular weaknesses. The foot/floor angle at initial contact for identified patients (Fig. 4d) was between 108 and 08. The rules R1-1 and R1-4 concern toe-walking caused by muscular weakness: the first refers to quadriceps weakness and the second to tibialis anterior weakness. Patients classed according to these rules displayed no knee flexion in stance (Fig. 4b), had plantarflexion at initial contact (Fig. 4c), a continuous flexor moment at the knee (Fig. 4f), and exhibited average activity in the tibialis anterior at mid-stance (Fig. 4o). In addition, patients with weakness in the quadriceps had no hip extension at the end of stance (Fig. 4a). Patients identified by rules R1-2 and R13 had, respectively, a low and an average range of movement for plantarflexion. They displayed no plantarflexion in the
Table 3 ‘‘Yes’’ rules induced from FDT, where n 3 and the number of conditions 5 Rules
p (rule fire strength)
n
Condition 1
Condition 2
R1-1
1.00
22
Low Triceps SPA
R1-2
1.00
3
Low Triceps SPA
R1-3
0.95
8
Low Triceps SPA
R1-4
0.97
9
Low Triceps SPA
R1-5
0.77
4
Average Triceps SPA
Average Quadriceps STR High Quadriceps STR Average Plantarflexion ROM Average Tibialis Anterior STR High Knee Extension ROM
R2-1
0.77
6
High Triceps SPA
R2-2
1
4
High Triceps SPA
R2-3
0.75
5
High Triceps SPA
R3-1
0.75
4
Average Hamstring Average Hamstring High Hamstring High Hamstring
R3-2
1.00
13
R3-3
0.81
5
R3-4
0.76
15
SPA SPA SPA SPA
Condition 3
Condition 4
Condition 5
Low Plantarflexion ROM
Average Hip Extension ROM
Average Quadriceps SPA
Low Dorsiflexion ROM Low Dorsiflexion ROM Average Dorsiflexion ROM
Average Quadriceps SPA High Quadriceps SPA Low Knee Extension ROM
Average Tibialis Anterior STR
Average Plantarflexion ROM
Average Dorsiflexion ROM Average Dorsiflexion ROM Average Knee Extension ROM Average Hip Extension ROM
Low Quadriceps SPA
High Hip Extension ROM High Hip Extension ROM
High Knee Extension ROM
Average Triceps STR
Average Knee Extension ROM
SPA, Spasticity; ROM, Range of movement; STR, strength. Rule numbers, R group-rule. n, number of patients used to create a given rule.
Average Quadriceps SPA Average Plantarflexion ROM High Dorsiflexion ROM
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Fig. 4. The kinematics (a–d), internal moments (e–g), powers (i–k) and EMG (l–o) of the sagittal plane for the ankle (c, g, k), for the knee (b, f, j) and for the hip (a, e, i) illustrating group 1 rules. For a given rule plotted, the average gait waveform is the weighted average of the patterns of the patients classified with this rule during the learning phase (tree induction). The weights are the memberships of the patients within the tree’s leaf (terminal node of the tree) of the considered rule. All graphs are normalized according to the gait cycle.
swing phase (Fig. 4c), and knee flexion was excessive at initial contact (Fig. 4b). Patients designated by rule R1-2 exhibited an abnormal knee extensor moment in mid-stance (Fig. 4f). Rule R1-5 points to average spasticity in the triceps surae, with no noticeable characteristics showing up on the graphs. Three rules from group 2 (R2) denote high spasticity in the triceps. Rules R2-1 and R2-2 indicate a limitation of dorsiflexion and average or high spasticity in the quadriceps. Patients designated by these rules displayed a high foot/floor angle at initial contact, between 258 and 358 (Fig. 5d); a permanent knee flexion (Fig. 5b) and hip flexion in stance (Fig. 5a). They also exhibited a permanent knee extensor moment throughout the cycle (Fig. 5f), a small ankle extensor moment in the end of the stance phase (Fig. 5g) and a high ankle power absorption at initial contact (Fig. 5k). The EMGs (Fig. 5l–o) for these three rules were high for all the muscles at initial contact, and were relatively low at the
terminal stance phase for the triceps surae, which is normally at its maximum at this point. Rule 2–3 indicates a significant limitation in knee extension. Patients designated by this rule exhibited a foot/floor angle near 108 at initial contact (Fig. 5d), a high knee flexion (Fig. 5b), a permanent knee extensor moment in the stance phase (Fig. 5f) and a double bump pattern for the ankle extensor moment (Fig. 5g), as well as a plantarflexion/dorsiflexion angle that varied around 08 (Fig. 5c). Rules from group 3 (R3) indicate moderate or severe spasticity in the hamstrings and limited extension at either the ankle, knee or hip. All patients classified using these rules exhibited a foot/floor angle between 0 and 108 at initial contact (Fig. 6d), knee flexion at initial contact (Fig. 6b) in conjunction with severe hamstring spasticity and normal knee extension in mid stance (Fig. 6b), with one exception: those classified with rule R3-3 had a moderate limitation of knee extension.
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Fig. 5. The kinematics (a–d), internal moments (e–g), powers (i–k) and EMG (l–o) of the sagittal plane for the ankle (c, g, k), for the knee (b, f, j) and for the hip (a, e, i) illustrating group 2 rules. For a given rule plotted, the average gait waveform is the weighted average of the patterns of the patients classified with this rule during the learning phase (tree induction). The weights are the memberships of the patients within the tree’s leaf (terminal node of the tree) of the considered rule. All graphs are normalized according to the gait cycle.
4. Discussion 4.1. The originality of the method This study focused on using FDT to classify the three toewalking patterns obtained from clinical measurements, with the final goal of associating clinical causes to the three patterns. To our knowledge, we are the first to apply FDT to gait analysis. Chau [21], in a review of analytical techniques for gait data, mentioned that decision trees as a method had not yet been applied to this field. Decision trees can be used to classify pathological conditions, to study the relationship between EMG and kinematics, or to search for patterns/ confirm suspect patterns in the data. In this study, FDT was used to link the ankle patterns of toe-walkers to recorded clinical measurements. The notion of fuzziness introduced by the coding method in this study made it possible to address the problem of inherent variability, inaccuracy and uncertainty in evaluations of muscular strength, muscular spasticity and range of
movement. The linguistic terms obtained by fuzzy coding provided rules with intelligible terms that were closer to those used in human reasoning. Fuzziness, then, would appear to be a good way to deal with clinical measurements. 4.2. The accuracy of the method The classification accuracy (81%) of our method is in the same range as the studies using artificial neural networks in conjunction with clinical biomechanics reported in Scho¨llhorn’s synthesis [22]. In this synthesis, the accuracy of the classifications using gait data with neural networks varied from study to study, but can be estimated at around 80%. In the studies reported by Chau [21], the accuracy of gait parameter prediction using other data types yielded a correlation coefficient that varied between 0.71 and 0.98. The accuracy of our classification with respect to disease indicates that clinical measurements provide a good explanation for toe-walking in most diseases, but a poor explanation for idiopathic toe-walkers (ITW). The small
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Fig. 6. The kinematics (a–d), internal moments (e–g), powers (i–k) and EMG (l–o) of the sagittal plane for the ankle (c, g, k), for the knee (b, f, j) and for the hip (a, e, i) illustrating group 3 rules. For a given rule plotted, the average gait waveform is the weighted average of the patterns of the patients classified with this rule during the learning phase (tree induction). The weights are the memberships of the patients within the tree’s leaf (terminal node of the tree) of the considered rule. All graphs are normalized according to the gait cycle.
limitation of dorsiflexion in ITW evoked by Taussig and Delouvee [5] does not seem to be an adequate explanation for toe-walking in these patients. Armand et al. [1] previously reported that a high proportion of ITW exhibited patterns similar to group 2 in the present study. However, the cause of toe-walking in ITW remains unclear. 4.3. Rule interpretation Among the rules created by FDT (Table 3), rule R1-1, which indicates quadriceps weakness, confirms the causes of toe-walking described in the literature [1,2,23]. Plantarflexion at the ankle (Fig. 4c) and absence of knee flexion in stance (Fig. 4b) are compensatory mechanisms designed to create a permanent internal flexor moment at the knee (Fig. 4f) and thus compensate for this quadriceps weakness. Weakness in the tibialis anterior (rule R1-4) hinders the correct pre-positioning of the foot in the swing phase, leading either to a flat-footed contact with the floor or to toe
contact alone [2,23]. This is confirmed by excessive plantarflexion during the swing phase (Fig. 4c). The limitation of plantarflexion in the swing phase (Fig. 4c), observed for rules R1-2 and R1-3, was described by Karol et al. [24] in children with clubfoot deformity. They did suggest that the lack of plantarflexion might be related to weak plantarflexors. Rules 1–2 and 1–3 of our study, however, indicate a limitation in the plantarflexion range of motion rather than muscular weakness. Spasticity in the triceps surae (average for rule R1-5) is a common cause of toe-walking in cerebral palsy [25]. It is interesting to notice that moderate spasticity of the triceps surae in conjunction with moderate spasticity of the quadriceps or mild spasticity of the hamstrings lead to an ankle pattern similar to that of our group 1. Conversely, severe spasticity of the triceps surae in conjunction with limited dorsiflexion and quadriceps spasticity (rules R2-1, R2-2) leads to a group 2 ankle pattern. These patterns are similar to Rodda et al.’s jump knee group [26] and to
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O’Byrne et al.’s group 2, which is characterized by a stiff crouch with toe-walking [27], with permanent plantarflexion (Fig. 5c) and excessive hip and knee flexion (Fig. 5a and b). The causes described by Rodda et al. [26] included spasticity of the hamstring and hip flexors, in addition to calf spasticity and co-contraction of the rectus femoris causing a stiff knee. In our study, all patients classified by these rules presented with hamstrings spasticity, which did not appear in the rules because it was not a discriminating variable for the classification of patients in group 2. Theses rules could be linked to a fixed contracture of the calf muscles as described by Steinwender et al. [28]. Severe spasticity in the triceps with reduced knee extension (rule R2-3) produces patterns similar to the apparent equinus highlighted by Rodda et al. [26] with significant knee flexion (Fig. 5b) and an ankle angle around 08 (Fig. 5c). The reduced knee extension measured during clinical examination could be the result of hamstrings contracture. Hamstrings spasticity associated with a limited range of movement is characterized by rules from group 3 (R3). The amount of gastrocnemius activity at 40% of the gait cycle (Figs. 5n and 6n) was significant, compared to group 2. The double bump ankle pattern (Fig. 6c) associated with this gastrocnemius activity confirms the dynamic calf tightness evoked by Tardieu et al. [25]. The knee flexion at initial contact (Fig. 6b) was linked to the severity of hamstring spasticity. Creating rules to explain three ankle gait patterns in toe-walkers also includes a learning approach allowing a combination of clinical measurements to be linked to one gait pattern. In our opinion, using the same approach in reverse, – i.e. hypothesizing causes from the gait deviations on gait data charts – would allow clinicians to perform gait interpretation more quickly and accurately. Since interpreting gait data is one of the most important steps in gait analysis, its reliability should improve, as Skaggs et al. [7] observed and as Simon [29] advised in his article on limitations and benefits of gait analysis.
5. Conclusion This study used FDT to link three major toe-walking patterns to their possible clinical causes, using natural language rules and graphic illustrations. Pattern 1 is essentially characterized by muscular weakness of the tibialis anterior and quadriceps or by a moderate triceps surae spasticity. Pattern 2 includes severe spasticity of the triceps surae associated with highly limited range of motion at the ankle. Pattern 3 is characterized by moderate to severe hamstrings spasticity associated with moderately limited range of motion at the ankle or at the knee. Our set of rules provides a knowledge repository that can be exploited to interpret gait analysis data in toe-walking patients. Improved
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understanding and interpretation of toe-walking could lead to better therapeutic choices.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.gaitpost. 2006.05.014.
References [1] Armand S, Watelain E, Mercier M, Lensel G, Lepoutre FX. Identification and classification of toe-walkers based on ankle kinematics, using a data-mining method. Gait Posture 2006;23:240–8. [2] Perry J. Gait analysis normal and pathological function Thorofare, NJ: Slack; 1992. [3] Gurney B. Leg length discrepancy. Gait Posture 2002;15:195–206. [4] Goodman MJ, Menown JL, West Jr JMW, Barr KM, Vander Linden DW, McMulkin ML. Secondary gait compensations in individuals without neuromuscular involvement following a unilateral imposed equinus constraint. Gait Posture 2004;20:238–44. [5] Taussig G, Delouvee E. Idiopathic toe walker child. Diagnosis and spontaneous evolution. Ann Readapt Med Phys 2001;44:333–9 [in French]. [6] Keenan WN, Rodda J, Wolfe R, Roberts S, Borton DC, Graham HK. The static examination of children and young adults with cerebral palsy in the gait analysis laboratory: technique and observer agreement. J Pediatr Orthop B 2004;13:1–8. [7] Skaggs DL, Rethlefsen SA, Kay RM, Dennis SW, Reynolds RA, Tolo VT. Variability in gait analysis interpretation. J Pediatr Orthop 2000;20:759–64. [8] Podgorelec V, Kokol P, Stiglic B, Rozman I. Decision trees: an overview and their use in medicine. J Med Syst 2002;26:445–63. [9] Bohannon RW, Smith MB. Interrater reliability of a modified Ashworth scale of muscle spasticity. Phys Ther 1987;67:206–7. [10] Mendell JR, Florence J. Manual muscle testing. Muscle Nerve 1990;13(Suppl.):S16–20. [11] Davis RB. Reflections on clinical gait analysis. J Electromyogr Kinesiol 1997;7:251–7. [12] Hermens HJ, Freriks B, Disselhorst-Klug C, Rau G. Development of recommendations for SEMG sensors and sensor placement procedures. J Electromyogr Kinesiol 2000;10:361–74. [13] DeVita P. The selection of a standard convention for analyzing gait data based on the analysis of relevant biomechanical factors. J Biomech 1994;27:501–8. [14] Quinlan JR. Induction of decision trees. Mach Learn 1986;1:81–106. [15] Roux E, Godillon-Maquinghen AP, Caulier P, Bouilland S, Bouttens D. A support method for the contextual interpretation of biomechanical data. IEEE Trans Inf Technol Biomed 2006;10:109–18. [16] Yuan Y, Shaw MJ. Induction of fuzzy decision trees. Fuzzy Sets Syst 1995;69:125–39. [17] Olaru C, Wehenkel L. A complete fuzzy decision tree technique. Fuzzy Sets Syst 2003;138:221–54. [18] Janikow CZ. Fuzzy decision trees: issues and methods. IEEE Trans Syst Man Cybern B 1998;28:1–14. [19] Marsala C. Inductive learning in presence of imprecise data: methods to build and to use fuzzy decision trees. PhD Thesis. Paris: Paris VI, 1998 [in French]. [20] Kohavi R. A study of cross-validation and bootstrap for accuracy estimation and model selection. In: Presented at International Joint Conference on Artificial Intelligence (IJCAI); 1995. [21] Chau T. A review of analytical techniques for gait data. Part 2: neural network and wavelet methods. Gait Posture 2001;13:102–20.
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S. Armand et al. / Gait & Posture xxx (2006) xxx–xxx
[22] Scho¨llhorn WI. Applications of artificial neural nets in clinical biomechanics. Clin Biomech 2004;19:876–98. [23] Armand S, Mercier M, Watelain E, Patte K, Pelissier J, Rivier F. A comparison of gait in spinal muscular atrophy, type II and Duchenne muscular dystrophy. Gait Posture 2005;21:369–78. [24] Karol LA, Concha MC, Johnston 2nd CE. Gait analysis and muscle strength in children with surgically treated clubfeet. J Pediatr Orthop 1997;17:790–5. [25] Tardieu C, Lespargot A, Tabary C, Bret MD. Toe-walking in children with cerebral palsy: contributions of contracture and excessive contraction of triceps surae muscle. Phys Ther 1989;69:656–62.
[26] Rodda JM, Graham HK, Carson L, Galea MP, Wolfe R. Sagittal gait patterns in spastic diplegia. J Bone Joint Surg Br 2004;86:251–8. [27] O’Byrne JM, Jenkinson A, O’Brien TM. Quantitative analysis and classification of gait patterns in cerebral palsy using a three-dimensional motion analyzer. J Child Neurol 1998;13:101–8. [28] Steinwender G, Saraph V, Zwick EB, Uitz C, Linhart W. Fixed and dynamic equinus in cerebral palsy: evaluation of ankle function after multilevel surgery. J Pediatr Orthop 2001;21:102–7. [29] Simon SR. Quantification of human motion: gait analysis—benefits and limitations to its application to clinical problems. J Biomech 2004;37:1869–80.
