Plantar pressure data partially describe the dynamic interaction between the foot and the ground during a variety of activities. They are typically lattice-sampled at temporal and spatial resolutions on the order of 200 Hz and four sensors per squared centimeter, respectively (21), so a typical adult foot, with a surface area of 135 cm2 (13) and an average walking stance phase duration of 800 ms (13,15), produces on the order of 80,000 pressure values per trial.
This considerable volume of data is often handled by reduction through hierarchical subsampling (Fig. 1), first to spatial (x, y) two-dimensional summary images (e.g., maximal spatial pressure) and then to regional metrics (22); we shall refer to two-dimensional image computation and regionalization as "first-level" and "second-level" subsampling, respectively. It has recently been shown that first-level subsampling to spatiotemporal (x, time) pressure patterns can also yield useful diagnostic information (6). Because orthogonal planes (x, y) and (x, time) can separately yield useful information and because the original (x, y, time) data encapsulate all of this information, it follows that it may be biomechanically informative to explore the original three-dimensional volumes before subsampling.
Indeed, by definition, subsampling sacrifices information. Spatial images, for example, cannot contain complete temporal information. Furthermore, information loss related to second-level subsampling can, in certain cases, irreversibly corrupt pressure patterns (19,20) and thereby alter biomechanical interpretations. To our knowledge, information loss due to first-level subsampling has not been explicitly investigated.
The purposes of the current study were (i) to develop an interactive three-dimensional tool for visualizing spatiotemporal plantar pressure data sets; (ii) to use the technique to explore dynamic foot behavior during walking, running, and cutting activities; and (iii) to highlight potential mechanisms of information loss imparted by first-level subsampling.
Three data sets were analyzed. The first consisted of two females (40 yr, 164 cm, 57 kg; and 39 yr, 169 cm, 60 kg) who were manually selected from a running experiment conducted at the University Clinic of Tübingen (11). Five running trials were collected at a specified speed of 3.3 m·s−1 over an Emed-X® pressure plate (100 Hz, spatial resolution = 5 mm; Novel GmbH, Munich, Germany). These two subjects were selected because one had relatively large heel loading and one had relatively high forefoot loading. A secondary reason for their selection was that their contact timings were more similar than would be expected from distinctly midfoot or forefoot strikers (2); that is, both contacted the ground heel-first, and both experienced forefoot contact for a proportionally similar duration (see Results section-Running data set).
The second data set consisted of one male subject (30 yr, 175 cm, 76 kg) who was manually selected from a running-and-cutting experiment conducted at Liverpool John Moore's University (24) (pressure data collected in this study remain unpublished). The subject performed five trials of each of (i) straight running and (ii) straight running with a 30° medial cutting maneuver. Pressure data were collected using a 1.0-m foot scan plate (100 Hz, spatial resolution = 7.62 mm, 5.08 mm in the x and y directions, respectively; RSscan, Olen, Belgium).
The third data set consisted of one male subject (30 yr, 172 cm, 73 kg) who performed 60 walking trials, 20 at each of three speeds: slow, normal, and fast. These published data (18) were collected at the University of Liverpool and are reproduced here to demonstrate that the current technique can also be used to visualize statistical volumes. Pressure data were collected with a 0.5-m Footscan 3D system (500 Hz, spatial resolution as above; RSscan) and were calibrated using a Kistler force plate (model 8281B; Winterthur, Switzerland). Walking speeds were recorded at 100 Hz using a motion tracking system (Qualisys, Gothenburg, Sweden). All experiments were approved by the ethics committees of the respective institutions, and before participation, all subjects above provided written informed consent.
Following previous methods (19), RSscan images were first resampled to a 5 × 5-mm grid using linear interpolation. All images were then registered (i.e., spatially aligned) (9) within-subjects using an optimal three-parameter transformation (dx, dy, rotation) and a frequency-domain alignment technique (4,16). Temporal registration was conducted by interpolating linearly over stance following common ground reaction force preprocessing practice (2).
Spatial (two-dimensional) variables.
Three spatial variables commonly considered in the literature were computed for subsequent qualitative comparison with the volumetric data. The variables included "peak pressure," "pressure impulse," and "contact duration" and were defined as follows:
where i and j index the spatial location in volumetric pressure image I(t),
Peak pressure is the maximum pressure across time, pressure impulse is the pressure-time integral, and contact duration represents the amount of time for which a particular part of the foot is in contact with the ground.
Although many other spatial (x, y) two-dimensional variables are computable (e.g., time to peak pressure (Fig. 1B), spatial pressure gradient), the three variables above are, to our knowledge, by far the commonest. In addition, we are aware of only one previous publication that analyzes (x, time) subsamples (6), and we are not aware of any that analyzes (y, time) subsamples. For the present purposes, we therefore use only the aforementioned (x, y) variables to emphasize potential information loss associated with common subsampling.
Mean (x, y) images (for each of the aforementioned variables) and mean three-dimensional (x, y, time) volumes were computed as unbiased quantifications of central tendency. Further statistical analysis was conducted only on the walking data set. A general linear regression model was used (18) following standard three-dimensional brain imaging methods (5). Briefly, this resulted in an (x, y, time) volume of t statistic values. Just like the Pearson correlation coefficient (r), the current t statistic describes the strength of correlation between walking speed and pressure; positive t values reflect positive correlation and negative values reflect negative correlation. And, just like the univariate Student's t-test, large t values represent large effects. The key differences between the present t values and typical univariate statistics (r and Student's t) are that the present t values are found at specific locations in space and time and that there are tens of thousands of t values. To deal with this large data set effectively, one must consider the geometric relation among neighboring t values when conducting statistical inference (i.e., when computing P values). Here, topological cluster-level inference was used (5); the statistical volume was first thresholded (here at |t| > 3.0), and then the sizes of the remaining suprathreshold clusters were corroborated against cluster-size expectations that follow from random field theory (1,5).
All image processing and statistical analyses were implemented in Python 2.5 using NumPy 1.3 and SciPy 0.8. All Python packages (NumPy, SciPy, and those described below: Visualization Toolkit (VTK) and wxPython) were used as preconfigured in the Enthought Python Distribution 5.0 (Enthought, Inc., Austin, TX).
The three-dimensional data sets were visualized using volumetric rendering (23) via the Visualization Toolkit (VTK) 5.4 (Kitware, Inc., Clifton Park, NY). "Volumetric rending" refers to a set of techniques for displaying a two-dimensional impression of a three-dimensional scene. It is typically used in biomedical applications (e.g., computed tomography-based thoracic organ visualization) (7) to isolate and highlight structures contained in three-dimensional images. The current approach consisted of four main steps: (i) isosurface computation, (ii) surface material parameter specification, (iii) camera positioning and focus, and (iv) rendering. A graphical user interface (Fig. 2) was constructed using wxPython 2.8 to permit interactive specification of these parameters.
Isosurfaces, the three-dimensional equivalent of two-dimensional isocontours, were computed using the marching cube algorithm (8); in the case of three-dimensional plantar pressure data, an isosurface represents constant pressure. Material parameters included surface color and transparency; default material textures and lighting (23) were used. The camera was initially focused on the volume centroid and was positioned along the time axis to yield a default view of the (x, y) plane. The camera could then be rotated interactively in three-dimensions using the mouse and keyboard.
The three main visualization-relevant computational tasks, namely, data loading, isosurface computation, and rendering, were conducted in 105.4 ± 2.4, 9.7 ± 0.6, and 40.1 ± 19.5 ms. These data were obtained from 100 repetitions of running trial visualizations; computations were performed on a laptop (CPU: dual-core 2.13 GHz, RAM: 2 GB, GPU: 550 MHz/256 MB). Durations of other computational tasks were as reported previously; registration ∼50 ms (16), volumetric statistics ∼14,300 ms (18).
Running data set.
The heel loading (HL) and forefoot loading (FL) subjects exhibited notably different average peak pressure distributions (Fig. 3A), and differences were also notable in other two-dimensional variables including pressure impulse (Fig. 3B) and contact duration (Fig. 3C). In particular, FL exhibited considerably lower heel pressures, impulses, and contact durations than HL but considerably greater forefoot pressures and impulses despite lower forefoot contact durations.
These trends were also apparent in the three-dimensional renderings (Figs. 3D, E). However, these renderings also revealed details that were not inferable from the spatial images. For example, although the heel pressure and impulses were notably larger in HL (Figs. 3A, B), we were surprised to find that the high heel pressures (>495 kPa) were produced during a very brief period, for approximately only 10% of the heel's contact duration (Fig. 3E, upper panel). Given that 495 kPa is only 52% of the maximum pressure (947 kPa), we expected that the (>495 kPa) cluster would be temporally longer. Moreover, Figure 3B shows larger central forefoot pressure impulses in FL versus HL. However, because the forefoot contact duration was much lower in FL versus HL (Fig. 3C), we expected that the FL impulse would be brief. Interestingly the three-dimensional renderings reveal the exact opposite: the high-pressure (>495 kPa) forefoot impulse in FL (Fig. 3E, lower panel) was temporally much longer than the high-pressure heel impulse in HL (Fig. 3E, upper panel). In other words, the durations of the high-pressure heel impulse (Fig. 3E, upper panel) and the high-pressure forefoot impulse (Fig. 3E, lower panel) could not be inferred from the two-dimensional images. This is explained by the fact that contact duration lumps all nonzero pressures together (equation 3), and thus it cannot reveal durations of high-pressure events.
Cutting data set.
Higher pressures and impulses were exhibited in cutting versus straight running, especially in the medial forefoot (Figs. 4A, B), in agreement with previous reports (3,17,25). Judging from contact duration similarities in the medial forefoot (Fig. 4C), we did not expect the high-pressure (>1000 kPa) impulse duration to be markedly longer in cutting (Fig. 4E). This high-pressure loading duration "illusion" is identical to those observed in Figure 3 but is arguably more interesting because it is much more task-relevant. That is, the impulse differences between HL and FL in Figure 3 are essentially inconsequential to the goal of running: forward motion of the body's center of mass. In Figure 4, however, the medial forefoot impulse differences are directly task-relevant: high medial impulses are necessary for 30° medial cutting. The interesting point is that we can be fooled by the impulse duration illusion even in this case of direct task relevance.
A second interesting impulse illusion was observed at the medial heel. Because of a peculiar landing pattern in straight running, it seems that there is bias toward medial heel loading in straight running versus cutting (Figs. 4A-C). Although this may be true of the very medial heel, it is not true of medial heel in general (Fig. 4E). Indeed, Figure 4E reveals that the opposite is true: the heel is much more biased toward the medial side in cutting, as one would expect based on the task demands. Finally, whereas all aforementioned impulse illusions could be resolved using three-dimensional renderings, we found that it was easiest to resolve the illusions with interactive volumetric exploration (see Video, Supplemental Digital Content 1, http://links.lww.com/MSS/A71, which demonstrates the basics of volumetric rendering and interactive exploration).
Walking data set.
The t statistic volume (Fig. 5), similar to previous observations (18,19,21), indicates that walking speed increases induce increased pressures over the heel and midfoot in early stance (5%-25%), decreased pressures throughout the midfoot in midstance (35%-75%), and increased pressures in late stance (75%-95%) (P < 0.001). Although these trends were apparent in the individual two-dimensional time slices (Fig. 5A), their true spatiotemporal extent was more easily perceived in the volumetric renderings (Figs. 5B-E). The vast interconnectedness of statistically similar voxels pointedly highlights that the original three-dimensional pressure volumes contain high-quality experiment-relevant information.
Subsampling-related information loss.
The running and cutting data sets (Figs. 3 and 4) reveal how first-level subsampling (to two-dimensional spatial images) can distort the loading patterns that are present in the original three-dimensional volume. The basic problem is that the observer, when presented with multiple (x, y) variables, must mentally integrate these variables to understand spatiotemporal behavior. In the current examples (Fig. 3), the observer must simultaneously consider six (x, y) images, multiple anatomical locations within those images, and multiple experimental conditions. The perceptual problem is compounded within second-level subsampling (Fig. 1C) because the observer must additionally construct a mental map between region labels and actual anatomy. Thorough mental association between all subsampled data is clearly a daunting task.
Although the aforementioned "impulse illusions" may be resolved with cleverer choices of two-dimensional variables (e.g., time to a threshold impulse, duration of a suprathreshold impulse), there are two problems with this approach: (i) the user would have to define these variables in an ad hoc manner to fully resolve contradictions that, importantly, are not directly perceivable in two-dimensional images; and (ii) the user would have to mentally integrate even more variables. In other words, considering only two-dimensional images necessitates a great number of inferential mental tasks; because of high-level visual information grouping in the brain, three-dimensional shape perception is cognitively less demanding than two-dimensional shape perception (12), especially for moving volumes (12). This agrees with the present qualitative observation that interactive volumetric exploration easily resolved impulse illusions. Thus, exploring three-dimensional plantar pressure data is likely more cognitively efficient than exploring subsampled data.
Benefits of subsampling.
Subsampling is more easily implemented than volumetric analyses and it is supported by many commercial software packages. It also makes data management much easier; second-level subsampled (regional) data for an entire experiment can be stored and probed in a single spreadsheet. Such conveniences may have driven subsampling's historical adoption.
Subsampling is also naturally linked to hypotheses regarding particular regions and/or particular variables (e.g., "does hallucal insole padding reduce peak hallux pressures"?). Although volumetric techniques can comprehensively address such hypotheses (5), this may be regarded as computational overkill if subsampling arrives at a similar conclusion. We thus do not suggest that subsampling is not useful in certain situations. We simply conclude that it is not possible to fully appreciate spatiotemporal loading patterns from (limited) subsampled data, so investigators should be cautious when subsampling.
Limitations of volumetric analysis.
First, a major limitation of volumetric analyses is that three-dimensional perspectives are difficult to achieve in single static two-dimensional images, even with datum axes (Figs. 3-5) and/or datum planes, so multiple perspectives are needed to report three-dimensional loading patterns (5). Second, interpretations may depend on visualization parameters; here, different thresholds and transparency parameters could have altered one's qualitative impressions of the final images. Indeed, the current parameter values were selected to highlight particular loading patterns of interest. Complicating matters is that many additional visualization parameters exist including surface textures, lighting, and light diffusion, for example (23), and these may also affect the observer's impressions of the data. Third, the current technique uses (only two or three) isosurfaces, so its pressure gradient information cannot be as rich as in continuous two-dimensional images. An alternative would be to use more sophisticated continuous volumetric techniques (e.g., gradient magnitude opacity) (23), which may improve gradient perception, but this is beyond the scope of the current study. A final limitation is that dynamic plantar pressure data are abstract spatiotemporal objects; there is no real-world object to which the observer can mentally compare the rendered three-dimensional volumes. By contrast cardiac renderings (7), for example, are comparatively easier to digest because observers are generally pre-equipped with expectation of shape. For these reasons, we caution that volumetric visualizations should only be rendered for presentation after thorough interactive exploration to ensure that the ultimately selected visualization parameters do not inappropriately bias the underlying data.
Volumetric analyses also pose several statistical limitations. One is that spatiotemporal registration does not ensure overlap. A comparison of high-arched and low-arched subjects, for example, would involve a large number of null observations in the midfoot region for the high-arched group, making parametric statistics inappropriate. Fortunately, there are a variety of nonparametric approaches that can handle such data sets (14). We hope to explore the appropriateness of parametric versus nonparametric statistics in future studies. A second is computational speed: conducting statistical tests over the entire spatiotemporal volume is computationally intensive. The present statistical computations were slow (∼14 s), arising partially from implementation in an interpreted language (Python). Nevertheless, the statistical volume only needs to be computed once, so this need not be a barrier to practical data exploration.
This study has shown that dynamic plantar pressure data may be both qualitatively and statistically analyzed in their original spatiotemporal volumetric form. This applies to shod and unshod data, to statistical volumes, and to arbitrary experimental design. The current results indicate that (i) three-dimensional pressure volumes embody high quality biomechanical data and (ii) subsampling can compromise dynamic information, occasionally yielding "impulse illusions" that can be resolved most generally only through volumetric analysis. We conclude that volumetric analysis yields unique holistic impressions of plantar pressure data and that this may afford unique perspectives on dynamic foot function.
Software related to parts of the article is associated with UK Patent GB0725094.7 (filed December 21, 2007). The authors confirm the scientific integrity of all data presented in this article and report no other conflict of interest.
Funding for this work was provided by Special Coordination Funds for Promoting Science and Technology from the Japanese Ministry of Education, Culture, Sports, Science and Technology.
The authors thank Jos Vanrenterghem for his contributions to this work.
The results of the present study do not constitute endorsement by the American College of Sports Medicine.
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