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Functional Data Analysis of Running Kinematics in Chronic Achilles Tendon Injury


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Medicine & Science in Sports & Exercise: July 2008 - Volume 40 - Issue 7 - p 1323-1335
doi: 10.1249/MSS.0b013e31816c4807
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Chronic Achilles tendon (AT) injury affects many of those involved in running- and jumping-based activities and, in extreme cases, can prevent participation in sport. Extensive reviews covering the incidence of this injury, symptoms, contributing factors, and treatment options are available in the literature (4,17,32,34). Like most musculoskeletal conditions, chronic AT injury is multifactorial, and the kinematics represent but one aspect of this. It is generally accepted that there are two specific mechanisms of AT injury: (i) excessive or prolonged pronation causing rotational stresses to the tibia and the tendon (4) or (ii) the rapid transitions between eccentric actions of the triceps surae during the support phase (22). The authors are aware of only one study that has carried out a kinematic gait comparison of this specific injury group with controls (22). In their two-dimensional study, McCrory et al. (22) found a large calcaneal inversion angle at touchdown and shorter time to maximum pronation in the injured group, although plantarflexion peak torque and years running were also good discriminators of AT injury. This supports the "excessive pronation" hypothesis of Clement et al. (4). Subjects presenting with this mechanism of injury would be expected to present with similar movement patterns to those recruited for studies comparing "excessive" pronators to controls, i.e., greater eversion (EV) during stance (21). However, many individuals presenting with high levels of pronation show no sign of injury (26). The specific mechanisms that determine whether the AT is the affected structure have not been determined from current research, suggesting that the exact mechanisms of this injury require further study. Orthoses are commonly used in the treatment of AT injury and many other lower limb pathologies. Although literature reviews conclude that these devices often provide symptom relief for these injuries, they do so by mechanisms that are not yet well understood (1,14,18,19). Research examining how inserts and orthoses are effective in this specific subject group is sparse (11,20,22), with most studies focusing on a general movement pattern or foot structure (16,23,25).

Traditionally, gait analysis has examined discrete measures such as angles at heel strike (HS), peak angles and range of motion (ROM) obtained during stance, or the timing of specific events. Research commonly uses these parameters as descriptors of gait (7) to compare and examine, for example, injured and uninjured groups, and the effects of orthoses, footwear, and surface types. Given the huge amount of information that a fully comprehensive gait analysis can provide, studies reduce data to these descriptors to allow a more convenient and efficient analysis. However, these discrete values do not fully describe the relative movements of the limbs in attaining these positions (9) and often mask deviations from the typical angle-time curves that are seen in most individuals. Also, if individuals display different levels of movement, the values of these discrete angles may show high between-subject variation, yet the underlying pattern of the curves may be very consistent. Curve analysis uses information from the entire time series, thus revealing the nature of the movement and the smoothness of the transitions between movements. Deviations from so-called "normal" curves may provide important information about the mechanisms of injury and may distinguish between the groups being examined. It is suggested that examining the patterns of movement is a more appropriate approach in analyzing biomechanics of many tasks (9).

Advanced methods of detecting patterns in multidimensional signals are established in the sciences but are not yet commonly used in biomechanics research. Functional data analysis (FDA) is one such approach that has been dealt with extensively in two textbooks by Ramsay and Silverman (27,28). The basic paradigm underpinning FDA is that an entire sequence of measurements for a movement or condition is viewed as a function or a single entity rather than a series of individual numbers (29). Principal component analysis (PCA) is a multivariate statistical technique, which is used to reduce the dimensionality of a problem by extracting relevant information from high-dimensional data sets. An essential part of FDA is the application of PCA to functional data (i.e., functional principal component analysis, FPCA) as outlined in Ryan et al. (29). These authors recognized the potential of this approach in analyzing knee joint kinematics during vertical jump and used it to distinguish between the stages of motor development. Although various PCA approaches have been used to examine lower limb symmetry in several studies involving healthy subjects (30,31) and subjects with osteoarthritis (7), there is little, if any, literature detailing the use of FPCA in groups with lower extremity injuries.

Daffertshofer (6) recognized the potential solution that a PCA approach could provide in analyzing coordination and human movement. In gait analysis, FDA has the capacity to detect factors that discriminate between subjects with chronic AT injury and uninjured controls. Current methods have so far been unable to provide an in depth insight into the factors which most influence movement and the mechanisms involved in this injury. It is likely that kinetic analysis and possibly musculoskeletal modeling would also be required; however, using FPCA to extract the relevant information from these kinematic data may provide useful, preliminary information to address this challenge. The aims of this study were, firstly, to use FDA to identify patterns of variation (with respect to time) that are associated with or distinguish the mechanism(s) of AT injury. This was achieved by comparing the rearfoot and lower limb kinematics of subjects with a history of AT injury and matched controls. The second aim was to compare modes of variation identified by FPCA scores across groups and conditions. It was hoped that these comparisons would provide some insight into the functional effects of orthoses when treating AT patients.


Data collection.

Ethical approval for this study was obtained from the university's ethics committee. Twenty-four subjects provided written informed consent to participate in the study. Twelve subjects (1 woman, 11 men) with a history of chronic, low-grade AT injury were recruited from the Podiatry Department private patient files at the university (age = 38.7 ± 8.1 yr, height = 1.75 ± 0.05 m, weight = 73.3 ± 8.5 kg). Eight subjects had unilateral symptoms, whereas four had bilateral symptoms resulting in 16 injured legs. In the year before testing, all AT subjects visited the collaborating podiatrist for a consultation. The podiatrist carried out a series of clinical observations including qualitative analysis of barefoot running, calcaneal alignment in relaxed standing position, and supine neutral subtalar position. All subjects displaying levels of pronation during running, which, based on the podiatrist's judgment, were likely to be related to the clinical presentation of AT injury, were invited to participate in the study. Subjects with AT injury but who displayed a rigid foot type with little visible pronation during dynamic stance were excluded. After the initial consultation, all subjects were provided with custom-made ethylene vinyl acetate orthoses, all of which consisted of an arch support and an appropriate medial wedge (ranging up to 10°). These devices relieved the symptoms of injury; hence, subjects were asymptomatic at the time of testing. Twelve control subjects (1 woman, 11 men) with no history of AT injury were recruited from local running clubs (age = 44.3 ± 8.4 yr, height = 1.78 ± 0.05 m, weight = 79.3 ± 12.2 kg). The control subjects were matched as closely as possible to the AT subjects for age, sex, height, and weight; however, they were not matched for foot type or levels of pronation. All subjects were involved in running-based sports, had good fitness levels, no injuries at the time of testing, and had no unusual running patterns.

Subjects wore dark, tight-fitting clothing and their own running shoes for testing. A marker setup similar to that of Clarke et al. (3) was used with reflective markers placed on the posterior and lateral aspects of both lower extremities as follows: two on the posterior aspect of the shoes bisecting the heel, two bisecting the posterior shanks (one on the AT, one below the belly of the gastrocnemius), one on each of the fifth metatarsals, lateral malleoli, fibular heads, and greater trochanters. All subjects completed a familiarization session and stretching before data capture, in which they selected their own comfortable running speeds. Three-dimensional kinematic data were captured using a Qualysis motion capture system (Gothenburg, Sweden) with eight, synchronous ProReflex MCU240 cameras operating at a sampling frequency of 200 Hz. Cameras were in an arc around the posterior and lateral aspects of the treadmill. A marker was placed on the rigid frame at the front of the treadmill to indicate the position of the treadmill surface on the motion capture screen. The podiatrist placed all subjects in subtalar neutral stance position before each running condition and the marker coordinates were obtained. AT subjects ran in orthoses (O) and no-orthoses (NO) conditions, whereas controls ran in the NO condition only (average speed = 2.8 ± 0.3 m·s−1). Data capture took place during the third minute of continuous running and subjects took full recovery (minimum 3 min) between conditions.

Data analysis.

Raw marker coordinate data were exported from Qualysis and imported as scaled coordinates into the Peak Motus™ analysis system (Peak Performance Technologies, Englewood, CO). The frontal and sagittal plane angles described in Table 1 were calculated from the three-dimensional coordinate data. These data were exported to Microsoft Excel where all angles were calculated relative to the subtalar joint neutral position taken before the running trials. HS and toe-off events for individual footfalls were determined when the displacement of the treadmill marker between adjacent time points was larger than a threshold value equivalent to the static noise in the motion analysis system. A Bland and Altman method comparison analysis (2) found high agreement between this approach and visual inspection of the Qualysis motion capture data in detecting contact events, with HS reliably detected within ±0.01 s. Previous research has reported that visual inspection detects HS accurately within ±0.02 to ±0.03 s, whereas footswitches detect the event up to 0.06 s too late compared with force plate data (24,36). This highlights the relatively good accuracy of this approach. A consistent adjustment was made to toe-off event time to account for the longer period of unloading that characterizes the end of stance (13) and the decreasing influence of the foot on the motion of the treadmill marker. As orthoses are usually designed to influence the foot during early stance (25), the limited accuracy of toe-off event detection was not considered as a serious limitation. Raw data from the stance phases of five footfalls for each subject and each condition were obtained for each of the five angles. This resulted in three "groups" of data: AT(O), AT(NO), and controls. Data were padded with 10 additional frames at the start and end of each kinematic series to prevent end point distortion.

Angle definitions as calculated in this study.

FDA techniques: smoothing.

FDA was carried out using the S-PLUS v7.0 statistical analysis package (Insightful Corporation, Seattle, WA). The basic steps involved in FDA are presented by Ryan et al. (29) in the context of a biomechanics study considering the kinematics of the vertical jump on early child motor development. The basic smoothing step requires representing an unknown function g(t) as a linear combination of K basis functions {ϕ1(t), ϕ2(t), …, ϕK(t)} using associated coefficients {c1, c2, …, cK} as g(t) = σkK=1cikϕk(t), tT. We can think of each basis function ϕk(t) defining a map from the predictor space τ to the real lineSymbol). Suitable choices for {ϕk(t)} include Fourier basis, polynomial basis, B-spline basis, and wavelets basis, etc. There is no universally good basis to be used with all data types. The choice of basis is dependent on the characteristic behavior of the data being analyzed. Ideally, the basis should reflect or have features that match those of the data. For example, Fourier bases are traditionally used when the data are cyclical/periodic, spline bases (usually, B-spline bases due to numerical stability and orthogonality properties) are typically chosen to represent noncyclical/nonperiodic data, and wavelet bases are chosen to represent data displaying discontinuities and/or rapid changes in behavior. The choice of basis can also depend on the quantities of interest in the study, e.g., some bases are not good for derivative estimation. In essence, it is essential to have a good understanding of both the behavior of the data and the quantities of interest in the analysis to ensure the choice of an appropriate basis.


The smooth functions (representing the data for each footfall) were obtained using a least squares (goodness of fit) approach and by adding a roughness penalty to the fitting procedure. Let be smooth estimates of the data curves, obtained via a basis function expansion. The coefficients cik are chosen to minimize the penalized criterion

where PEN2(·) penalizes the curvature of the estimated functions. Here, λ is a user-defined smoothing parameter controlling the tradeoff between affinity to the raw data and variability of the resulting estimates.

The raw data in this study did not need extensive additional smoothing (since K, the number of basis functions, was chosen to be smaller than the number of data points) hence a value of 1 × 10−8 was used to fit the curves for ankle dorsiflexion (ADF), knee flexion (KF), EV, calcaneal, and leg abduction (ABD) angles. The experimental set up had a large number of cameras and a small calibrated volume. This maximizes the accuracy within the motion capture system and minimizes noise within the raw data. Subsequently, the value for λ will also be small. The alternative approach to a subjective choice, is an automatic method that allows the smoothing parameter to be chosen directly from the data. Cross-validation is one of the most widely used automatic methods for determining the smoothing parameter. In general, it is recommended that cross-validation only be used as a guideline or starting point before making a subjective choice of the smoothing parameter (27).

FDA techniques: FPCA.

Mathematically, functional principal components (FPC) are eigenfunctions, extracted (iteratively) from the covariance matrix of the smoothed curves. Anyone familiar with the practice of classic PCA in multivariate data analysis will understand that its major drawback is the difficulty in interpreting the meaning of the extracted PC. The attraction of applying FPCA to biomechanical data is that the extracted components can be easily interpreted because the FPC are defined in the same domain as the original functional observations. In this study, each FPC is a function with a specific shape as shown in Figure 1. FPC were obtained for the combined data of all groups (using an average of five trials for each subject/condition resulting in 48 curves per angle) and for the AT(O), AT(NO), and control groups, separately (16 curves per group per angle). To aid in the explanation and interpretation of the FDA techniques, graphical data for the first component of ADF angle are presented and will be referred to.

The first FPC (FPC1), extracted for ADF angle, accounted for 79.5% of the total variation for all subjects, and it is shown as a function with respect to time-normalized stance period.

A relatively small number of FPC usually describe the essential features of gait (6). Often, the number of FPC accounting for approximately 95% of the variation are analyzed, because FPC beyond this are typically of very small influence. Scree graphs were obtained for the FPC for each angle to determine the number of components to retain for analysis, see Figure 2 for ADF angle scree graph. The eigenvalues were plotted in the order in which they were extracted, i.e., the first eigenvalue representing FPC1, followed by the second eigenvalue representing FPC2, and so on. The eigenvalues decrease in line with the proportion of variation accounted for by each FPC until they form a relatively straight horizontal line. The "elbow" of the scree graph was identified as the point where the eigenvalues curved upward above this straight line. The FPC with eigenvalues above this "elbow" were retained indicating that examination of the first four components for ADF angle was sufficient to describe the movement.

Scree graph for ADF angle. The number of eigenvalues above the elbow is used to indicate how many FPC should be retained for analysis. All eigenvalues below this represent only a small proportion of the variance.

Visualizing the effects of the FPC is quite straightforward. A useful technique is to examine plots of the overall mean angle-time function and the functions obtained by adding and subtracting a suitable multiple of the FPC in question to the mean curve, see Ramsay and Silverman (28) for details. The effect of adding the FPC to the mean function is illustrated by the plus curve in Figure 3(i). An individual presenting a curve shifted in the direction of this plus curve in relation to the mean curve, i.e., less ADF throughout stance, is termed a high scorer on this FPC. The minus signs illustrate the effect of subtracting the FPC from the mean curve and illustrate the type of curve presented by a low scorer on this component, i.e., greater ADF throughout stance. FPCA relies mainly on a graphical approach to illustrate how the kinematics of an individual are affected by scoring high or low on a particular component. Although the plus and minus curves show the directions in which the curves would be shifted during stance, they do not necessarily represent the actual angles that would be attained. The decision on whether it is good or bad to score high or low depends on the functional interpretation of the particular component. The clinician or researcher must interpret this based on knowledge of the risk factors for injury and the movement in question.

Left panels show the mean ADF angle-time series curve for all groups combined, represented by the solid line. The effect of adding and subtracting a multiple of (i) FPC1 and (ii) FPC2 to the mean curve is shown by the plus and minus curves, respectively. Right panels show boxplots of the FPC scores for AT(O), AT(NO), and control groups. All FPC with moderate or large effect sizes for differences between AT and control groups or between orthoses and no-orthoses conditions are included.

FPC scores were then derived for each angle function. These scalar values were determined by multiplying each data function by the relevant FPC and integrating over (0, 1) to obtain the FPC score for that particular FPC. This was repeated for all FPC and provided scores for all linear combinations. These scores were compiled and graphed as boxplots according to AT(O), AT(NO), and control groups, see Figure 3(i). The data collected in this experiment can be considered an "incomplete design" because it is not possible to study all treatment combinations. There were two groups [Control vs Injured] and two treatment conditions [Orthoses vs No Orthoses]. This would normally suggest four treatment combinations, namely, Injured without orthoses, Injured with orthoses, Control without orthoses, and Control with orthoses, but the Control with orthoses condition does not exist because it is not meaningful, practical, or ethical to study uninjured subjects wearing corrective devices. Statistical tests examining differences in FPC scores between groups and conditions were carried out using an ANOVA model that was specified in Data Desk 6.2 (Data Description, Inc, Ithaca, NY). The model allowed analysis of this incomplete design and calculated Tukey's LSD post hoc differences between the cell means for AT(O) − AT(NO), and AT(NO) − Control. The comparisons were based on an estimate of the residual error for the Error Sum of Squares and provided a balanced design with 16 measurements in each cell. In accordance with recommendations by Sterne and Smith (35), specific P values were examined along with Cohen's effect sizes (d) derived using the pooled standard deviation (5). Effect sizes were interpreted using a subjective scale, where: 0 to 0.19 = trivial, 0.2 to 0.59 = small, 0.6 to 1.19 = moderate, 1.2 to 2.0 = large, >2.0 = very large (15). All of the P values are based on the incomplete design ANOVA model. The effect sizes are provided, less for their own importance, but as an alternative approach in small sample experiments.

The influences of the FPC on the mean curves for each individual group were then examined visually to determine whether additional information was available. Because the FPC account for progressively smaller proportions of the variation, there is an increased likelihood that the sequence in which the components are extracted will differ when individual groups are examined. This makes it more difficult to interpret the smaller FPC as they may not describe the same features of stance. As the first few FPC for each angle always accounted for larger proportions of the variation, it was evident that these described the same function in all groups. Hence, only further analysis of FPC1 and FPC2 was carried out for the individual groups. Comparison of FPC of each angle across AT(O), AT(NO), and control groups was possible as each was scaled according to the same multiple.


Scree graphs revealed that four FPC sufficiently described the leg and foot movements for each angle. As it is not feasible to present all FPC for each angle graphically, moderate and large effect sizes were used to determine the FPC that represented clinically significant differences; all components fulfilling this criteria, were then presented graphically with the relevant P values and effect sizes included. Statistical tests revealed that all other FPC had P values >0.1 combined with small or trivial effect sizes.

ADF angle.

The first four FPC for ADF angle accounted for almost 99% of the total variation in all groups. The first FPC extracted from the data accounted for the largest amount of variation (79.5%) and as with all other angles, it described an overall upward or downward shift compared with the mean curve. Boxplots did not reveal clear differences between AT and control groups despite a low P value and a moderate effect size (P = 0.033, d = 0.86), see Figure 3(i). Figure 3(ii) shows FPC2, which accounted for 13.1% of the total variation for all groups and described peak ADF and ADF ROM. High scorers on this FPC displayed lower peak ADF angles resulting in reduced ADF ROM compared with the mean curve. Low scorers displayed increased peak ADF during stance and subsequently greater ROM. Boxplots revealed that the previously injured group tended toward greater ADF during stance compared with controls (P = 0.063, d = 0.74). Boxplots also revealed differences in the AT group between orthoses and no-orthoses conditions (P = 0.058, d = 0.73). The negative medians indicated that although most AT subjects displayed greater ADF compared with the mean curve in both conditions, scores were less negative when wearing orthoses. This indicated that orthoses reduced peak ADF in midstance resulting in less ADF ROM, thus restoring motion to resemble more closely that seen in controls. The greater spread of the boxplot in the orthoses condition suggested greater between-subject variation in FPC scores when wearing orthoses.

KF angle.

KF angle FPC1 accounted for 89.3% of the total variation, and although it did not distinguish between groups, there was an observable trend of less KF in the control group. FPC2 accounted for 6.8% of the total variation and described peak KF and the resulting KF ROM during stance, see Figure 4(i). Boxplots distinguished between AT and control groups on this FPC (P = 0.029, d= 0.89). AT subjects were mostly high scorers who presented with greater KF during stance compared with the majority of low-scoring control subjects. Figure 4(ii) shows FPC3, which described the timing of peak KF and again discriminated between AT and control groups (P = 0.015, d = 1.01). AT subjects scored high on this component, indicating later and increased peak KF compared with the control subjects. They also underwent greater ROM because of the more extended knee position at contact. Differences between orthoses and no-orthoses conditions were less obvious from the boxplots but this may be explained by the weak moderate effect size (P = 0.073, d = 0.68). Results for FPC4 described a function where peak KF was greater in the control group because of the spread of the boxplot (P = 0.084, d = 0.68), see Figure 4(iii). However, as FPC4 accounted for less than 1% of the total variation in KF angle, this was of limited clinical relevance.

Left panels show the mean KF angle curve for all groups combined, represented by the solid line. The effect of adding and subtracting a multiple of (i) FPC2, (ii) FPC3, and (iii) FPC4 to the mean curve is shown by the plus and minus curves, respectively. Right panels show boxplots of the FPC scores for AT(O), AT(NO), and control groups. All FPC with moderate or large effect sizes for differences between AT and control groups or between orthoses and no-orthoses conditions are included.

EV angle.

The first three FPC for EV angle accounted for 94% of the total variation for all subjects. FPC1 accounted for 58.6% of the variation and described the overall upward or downward shift from the mean curve, see Figure 5(i). Statistical analysis revealed a tendency toward greater EV during stance in subjects with a history of AT injury (P = 0.01, d = 1.08) with further EV seen when orthoses were worn (P = 0.001, d = 1.39). Despite the large effect sizes, the boxplots overlap and so do not illustrate these expected differences. FPC2 accounted for 31.8% of the variation in EV angle and described peak EV and EV ROM. The AT group were high scorers in FPC2 who reached peak EV earlier in stance and displayed increased ROM compared with the control group (P = 0.026, d = 0.91), see Figure 5(ii). In the orthoses versus no-orthoses comparison, boxplots revealed almost equal medians but slightly higher FPC scores, indicating further increases in peak EV and EV ROM for some subjects when orthoses were worn (P = 0.012, d = 1.01). FPC3 described the rate of eversion and accounted for 3.6% of the total variation. Boxplots revealed a tendency for control subjects to evert at a slower rate during stance compared with the AT group (P = 0.100, d = 0.64), but orthoses did not display clear effects despite the moderate effect size (P = 0.029, d = 0.86).

Left panels show the mean EV angle curve for all groups combined, represented by the solid line. The effect of adding and subtracting a multiple of (i) FPC1, (ii) FPC2, and (iii) FPC3 to the mean curve is shown by the plus and minus curves, respectively. Right panels show boxplots of the FPC scores for AT(O), AT(NO), and control groups. All FPC with moderate or large effect sizes for differences between AT and control groups or between orthoses and no-orthoses conditions are included.

Calcaneal angle.

The first FPC accounted for 81.8% of the total variation in calcaneal angle, see Figure 6(i). Differences between FPC scores of the AT group in orthoses and no-orthoses conditions were indicated (P = 0.062, d = 1.03); however, the boxplots and medians were quite similar. Figure 6(ii) shows that FPC3 accounted for 4.9% of the variation and described the calcaneal angle at foot contact. Control subjects were mainly high scorers presenting with an everted contact position that became progressively more inverted throughout stance (P < 0.001, d = 1.83). In contrast, most AT subjects contacted the ground in an inverted position, become less inverted for a short period before returning to INV in preparation for toe-off. The medians for FPC scores were similar in orthoses and no-orthoses conditions but there was a tendency for greater variation in low scores when orthoses were worn (P = 0.054, d = 0.74).

Left panels show the mean calcaneal angle curve for all groups combined, represented by the solid line. The effect of adding and subtracting a multiple of (i) FPC1 and (ii) FPC3 to the mean curve is shown by the plus and minus curves, respectively. Right panels show boxplots of the FPC scores for AT(O), AT(NO), and control groups. All FPC with moderate or large effect sizes for differences between AT and control groups or between orthoses and no-orthoses conditions are included.

Leg ABD angle.

Again, FPC1 described an upward or downward shift from the mean curve with differences found between the FPC scores of AT and control groups (P < 0.001, d = 1.55), see Figure 7(i). Boxplots revealed little difference in the medians but a greater spread of scores in the control group. Figure 7(ii) shows FPC2, which described the leg ABD angle at HS. Large and moderate effect sizes were found between AT and control groups (P = 0.001, d = 1.48) and between orthoses and no-orthoses conditions (P = 0.053, d = 0.74), respectively; however, the boxplots did not reveal clear differences. There was a trend for greater ABD at HS in controls and AT subjects without orthoses and greater variation in the boxplot scores for the control group. Significant differences between AT and control groups were observed in FPC3 (P < 0.001, d = 1.50) and FPC4 (P = 0.004, d = 1.24), see Figures 7(iii), (iv). Both of these factors describe "oscillating patterns" relative to the mean curve. High scorers oscillated with low amplitude in FPC3 but high amplitude in FPC4. The practical significance of this is as yet unclear.

Left panels show the mean leg ABD angle curve for all groups combined, represented by the solid line. The effect of adding and subtracting a multiple of (i) FPC1, (ii) FPC2, (iii) FPC3, and (iv) FPC4 to the mean curve is shown by the plus and minus curves, respectively. Right panels show boxplots of the FPC scores for AT(O), AT(NO), and control groups. All FPC with moderate or large effect sizes for differences between AT and control groups or between orthoses and no-orthoses conditions are included.

FPC for Individual Groups

FPC were also obtained for AT(O), AT(NO), and control groups, separately. This provided some important additional information, which distinguished between the control group and those with a history of AT injury. This related to differences in the modes of variation displayed by each group around the mean curves at particular stages of stance. Plotting ADF FPC2 with the mean curves for each group separately, revealed almost a three times greater variation at HS in the control group compared with the AT group, see Figure 8(i). EV angle FPC1 also clearly distinguished between the AT and control groups, see Figure 8(ii). The control group showed variation around the mean curve throughout stance, although the AT group displayed reduced variation between 10% and 60% of stance. At 40% of stance, controls showed six times greater variation than their uninjured counterparts. Orthoses seemed to promote greater variation at the same stage of stance with almost 2.5 times the variability observed in the no-orthoses condition. The control group also displayed greater variation throughout stance in FPC1 for calcaneal angle, see Figure 8(iii). The AT group displayed consistent movement patterns with reduced variation between 10% and 50% of stance compared with the control group. At 40% of stance, variation observed in the control group was almost 6 times the variation observed in the AT group, but this increased to almost 24 times the variation at HS. This particular value is likely to be an artifact of the low levels of variation typically observed in calcaneal EV angle. In addition, orthoses tended to cause greater calcaneal EV at HS compared to when no orthoses were worn. When each group was examined individually in leg ABD angle, the major difference was the increased variation in contact angle, which was almost 3.5 times higher in the control group, see Figure 8(iv).

The effects of adding and subtracting FPC to the mean angle-time series curves for AT(O), AT(NO), and control groups are individually shown for (i) ADF angle FPC2, (ii) EV angle FPC1, (iii) calcaneal angle FPC1, and (iv) leg ABD angle FPC1. The percentage of total variation accounted for by the FPC in each group is outlined on the graphs.


The AT subjects in this study were recruited on the basis of high levels of EV during running as documented by the collaborating podiatrist. It was hypothesized that kinematic differences would distinguish between uninjured controls and subjects with a history of AT injury. Previous analyses on discrete measures of these data found that the AT group displayed 2°-5° greater INV at HS, peak leg ABD, EV ROM, and ADF ROM compared with the control group. These differences were evident when 90% confidence intervals were examined, but this was not supported by P values and effect sizes. This may be explained by the high levels of between-subject variation. The limited findings from this discrete analysis do not fully reflect the rapid lower limb movements that clinicians often observe inAT subjects. The FDA results reported in this article support these earlier findings and provide additional information. AT subjects were found to have greater peak and range of ADF, KF, and EV during stance. They also displayed less KF and leg ABD but a more inverted calcaneal angle at contact and reached EV earlier in stance compared with control subjects. This supports the greater calcaneal INV at HS reported by McCrory et al. (22) and the greater levels of EV and KF observed in subjects with "excessive" pronation when compared with controls (21). It is suggested that the contact positions promoted a more rigid leg alignment, which then required greater compensatory movement. This resulted in collapse of the knee and foot into prolonged knee flexed, everted, and dorsiflexed movement patterns. When combined with external factors, this may have increased the stress imposed on the AT, resulting in injury. This supports the excessive pronation mechanism that has been proposed to explain AT injury (22).

Hamill et al. (10) used dynamical systems theory approaches to examine the role of variability in lower limb injuries in an attempt to distinguish between those with and without symptoms. They suggested that uninjured individuals would display greater efficiency and variation in their movement patterns compared to injured individuals, who would present lower levels of within-subject variation. To date, these approaches examining variability in coordination relationships are limited to a small number of movement disorders that do not include AT injury. The current study examined total variability in specific angle-time series data, which has also not been reported in previous research. Our interest from a biomechanical perspective is on the variability around the mean, specifically the principal harmonics of the curves. For this reason, we narrowed our analysis to FPCA, but considered both the cases of FPC calculated around (i) the global mean and (ii) the group means. A statistical analysis on the basis of functional linear models, for example, an FDA application of ANOVA, would also be rewarding. For further information on these approaches, the reader is referred to the seminal papers by Faraway (8) and by Shen and Faraway (33).

Analysis of the FPC for individual groups provided the clearest information about variability and this was especially evident in the first FPC for the three frontal plane angles. The AT group showed a distinctive and consistent movement pattern in the first half of stance, which would suggest a consistent pattern of loading in all subjects. In contrast, the control group displayed a markedly different pattern of variation, with increased levels throughout the stance period. The ability to identify this feature represents one of the main advantages of FDA as this was masked by the between-subjects variation when the traditional angle-time curves were examined. Although this study presents total variation rather than specifically examining within-subject variation, it does support the claim that all AT subjects presented with similar movement patterns during the loading phase. This would suggest that the same mechanism of injury was present in all subjects with a history of AT injury. It also suggests that the actual kinematic values may be of less importance and that this specific pattern in early stance is the critical factor in the occurrence of AT injury.

Podiatrists prescribe orthoses to control excessive movements that they perceive to be related to injury and hence relieve the symptoms. All subjects reported resolution of symptoms, with many obtaining complete relief with orthoses, hence, it was expected that this condition would provide a more optimal pattern of motion. Previous analysis revealed high variation in individual responses to orthoses; this affected the discrete measures and thus did not reflect the different mechanisms by which they were effective. The influence of FPC on the mean curves were often similar for the AT group with and without orthoses indicating very subtle differences between conditions. Functionally, the orthoses reduced peak ADF, ADF ROM, and leg ABD at HS but increased calcaneal angle and EV throughout stance and INV at HS. This supports the findings of Harrison et al. (11) who found that orthoses reduced ADF measures in subjects with Achilles tendonitis. The medially wedged orthoses may have increased INV at contact but the increased EV throughout stance was unusual as the devices were designed to reduce this movement as it has been linked to the occurrence of AT injury (4). The mechanisms involved in this increase are unclear, but it is speculated that the devices may have induced foot abduction, increasing the tendency for the arch to collapse as the weight progressed forward. Measurement of transverse plane motion would be necessary to confirm this hypothesis.

On the basis of the predictions of dynamical systems theory approaches, orthoses would be expected to promote an increase in movement variability. Because of the repeated-measures design of this study, subject-induced variation would be considered a relatively consistent factor, whereas any differences in variation may be attributed to the treatment device. Increased variation of FPC scores was evident from the increased spread of several of the boxplots presented in Figures 3-7. Individual group analysis also revealed increased variation in EV movement patterns in early stance and calcaneal angle at HS with orthoses although the magnitude of EV increased. Possibly, the greater variation in these patterns, combined with the reduced ADF, may have been enough to provide subtle alterations to the kinematics and relieve the symptoms of injury. These may have allowed the subject to adapt to and cope with the movement pattern more effectively. The results indicate that orthoses often altered the movement patterns away from that seen in controls. This suggests that the notion of orthoses restoring an individual's kinematics to the levels seen in controls may not be feasible or necessary. It also supports the view that large degrees of motion especially pronation may be present in individuals with no signs of injury (26).

FPC scores were calculated from data throughout the entire stance phase. The higher levels of variation in the second half of stance may be due to poor tracking and reduced accuracy in marker positions. This greater variation may have influenced the FPC scores and masked the differences observed earlier in stance. It may be useful to weight the FPC for the first 60% of stance, because this is the most relevant period of stance and also the time when the heel remains on the ground. However, further statistical modeling studies would be required to justify this approach. In many cases, boxplots provided a clear indication of how the majority of subjects scored. Nonoverlap of the median of one group with the boxplot of another group indicated that at least 50% of the subjects in one group scored differently to 75% of the other group on that particular FPC. This approach incorporates data from individual subjects rather than focusing purely on group means. In some cases, moderate and high effect sizes did not correlate with the message conveyed by the boxplots. This is because ANOVA and effect size calculations were based on differences between the means, whereas boxplots were based on medians and quartiles. Mostly, this combination of approaches was in close agreement but where this was not the case, interpretation based on the boxplots as outlined in the study of Ryan et al. (29) was favored because it provides a more practical interpretation to the data.

Previous ANOVA-based analysis had difficulty in finding statistically significant differences between groups and conditions. This was mainly because of the high between-subject variation in the groups and the differences in individual responses to orthoses. Traditional experimental approaches focusing on discrete measures masked these differences and reduced the data to measures that could not adequately describe when and how kinematic changes occurred. These approaches are also limited because the most important features of gait are typically identified before data capture and analysis. This increases the chances of focusing on a feature, which clinicians wrongly perceive to be important, while ignoring more relevant information. FDA has advantages in that it can be applied to multidimensional signals and it removes the need for prior identification of the relevant features of gait (6). It identifies the uncorrelated functions that describe the patterns of movement from the entire dataset; that is, it describes how a particular position is attained, taking into account features such as the speed and smoothness of the movement. Often it is the functions that represent lower levels of variation that describe the essential differences between groups or conditions. The results suggest that the information obtained from this approach may be vital in identifying distinguishing features between groups and providing greater insight into the processes underlying AT injury. It also avoids the limitations of other statistical approaches, because it can be used with unequal subject groups, it is performed on raw data to prevent any distortions due to repeated filtering on the data, and it can extract relevant information that is not always evident from the time series data.

Individual group analysis revealed interesting differences in modes of variation between injured and control groups. Given the importance attributed to variation by researchers examining injury occurrence from dynamical systems theory perspectives, this highlights the relevance of examining these issues further. Future well-designed experimental studies should adopt the current FDA approaches to focus on within-subject variation and to gain more insight into the role of variability in injury. This would also appropriately test the proposed hypotheses on the basis of dynamical systems theory. Coordination relationships of the lower limbs, including phase plane and continuous relative phase plots, should also be examined. Harrison et al. (12) used FDA to examine coordination in angle-angle plots and although FDA could potentially be used in combination with other coordination-based approaches, this does require further verification. Further study is also recommended in AT subjects who have a more rigid foot type and display eccentric lengthening of the gastroc-soleus complex during stance along with other clinical populations. FDA may reveal functional information about the mechanisms of these injuries and if these individuals respond differently to orthoses.


The mechanisms involved in AT injury have been suggested in the literature but few scientific studies examining the kinematics have confirmed this. Previous analysis comparing AT and control groups revealed limited findings beyond what would be expected in a group displaying high levels of pronation. FDA supported these findings but it also provided clinical evidence that these groups can be distinguished on the basis of differences in modes of variation during stance. The control group presented with greater variation throughout stance compared to the group with a history of AT injury. This suggests that there is merit in dynamic systems theory approaches and the hypothesis that variability may have a role in the mechanisms of injury. However, further work is required to examine specific components of variability and to verify the cause and effect relationship between variability and injury. Although FDA is a relatively new technique in biomechanics, it provides a useful tool for gait analysis and further use is recommended for examining lower extremity injuries and curve-based datasets.

The authors thank Richard Jones from the Centre for Human Performance and Rehabilitation, University of Salford and Philip Laxton and Barry Richards from the Directorate of Podiatry, University of Salford who assisted with the podiatric techniques and data capture. Funding for this research was provided by the Irish Research Council for Science, Engineering and Technology: funded by the National Development Plan.


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