## Introduction

Treadmills are valuable tools for research on both human and animal locomotion as well as applied sport and medical diagnostics. They enable the study of human and animal motion under controlled conditions while requiring little laboratory space. Treadmills differ greatly in size, geometry, materials and actuation/control systems.

When locomoting on treadmills, the total body center of mass of humans and animals remains almost stationary in the horizontal direction relative to a global reference. However, horizontal velocity fluctuates relative to the moving reference frame of the treadmill belt. Treadmill belt velocity (TBV) fluctuation involves a complex interplay of friction forces between the belt and supporting surface, the actuation of the belt, and the control algorithms in powered treadmills1. Some more traditional powered treadmills rely on the inertia of the drive train (flywheel, heavy rollers etc.) to minimize TBV fluctuations. While there is evidence suggesting TBV fluctuation differs between different types of treadmills1, there has not been a systematic quantification of TBV fluctuation across different treadmills.

In dry conditions, the force of friction (Ffr) is less than or equal to the product of the normal force (Fn) and the coefficient of friction (µ)

$${\text{F}}_{{{\text{fr}}}} \le \, \upmu \, \cdot {\text{ F}}_{{\text{n}}}$$
(1)

While µ depends upon the properties of the interacting materials, Fn in human and animal locomotion is proportional to body mass and locomotion speed2,3,4. Therefore, TBV regulation likely differs between people of different body mass or when moving at different locomotion speeds. However, a systematic analysis of the effects of body mass and locomotion speed on TBV regulation in different treadmill types has not been published.

Quantifying TBV fluctuations is important because accurate values of average and instantaneous TBV are essential in the calculation of several fundamental physiological variables. For example, the calculation of the cost of transport (i.e., metabolic cost per distance5) or locomotion economy (i.e. metabolic energy consumption rate at a given locomotion speed6) for moving on a treadmill requires precise knowledge of the average belt velocity. Further, the quantification of external center of mass (CoM) power (i.e. cross product of ground reaction force and CoM velocity vectors) during locomotion necessitates precise tracking of instantaneous TBV7,8. In addition, while different approaches for the quantification of mechanical work during locomotion exist, most of them assume a constant TBV9. While there are precise measures to calculate average TBV (using, e.g., stopwatches or tachometers), the quantification of TBV fluctuations during the gait cycle is not commonly performed.

Further, when generalizing results from treadmill studies to field conditions, it should be considered whether the instantaneous CoM velocity pattern observed on a treadmill matches typical patterns for overground conditions. Nonetheless, TBV is not a standard variable reported in studies assessing locomotion related problems. Potentially, the lack of a time-efficient and feasible method to measure TBV fluctuation has contributed to the omission of this variable in the past.

Therefore, the goals of the present study were: (1) To develop a method for easily determining instantaneous TBV and TBV fluctuation using standard 3D motion capture system technology and (2) To analyze the effects of treadmill type, locomotion speed, and body mass on TBV regulation. We hypothesized that treadmill type, speed, and body mass would significantly alter TBV fluctuation.

## Materials and methods

### Participants

We recruited seven healthy, active, young participants (6 male; 1 female; body mass: 60.7–108.2 kg; body height: 1.63–1.98 m; age: 18–35) for this study. The participants gave written informed consent before data collections. The Ethical Commission of the German Sport University Cologne approved all methods employed in this study, which were in accordance with the Declaration of Helsinki.

### Experimental procedure

The operator attached circular cut-outs of retro-reflective adhesive foil (radius = 8 mm; 3 M, St. Paul, MN, USA) at regular intervals to the lateral aspects of the treadmill belts (Fig. 1). We chose the distance between cut-out markers such that ten of them (five per lateral side) were visible on the top side of the belt at each time. We used the tracked 3D coordinates of these markers to calculate TBV. For the application of the new method it is of critical importance that the treadmill is perfectly aligned with the antero-posterior axis of the laboratory coordinate system. We checked this assumption by checking the coordinates of two markers positioned in the front and back of the treadmill at the same medio-lateral position. This way, we could also verify that the treadmill inclination was zero during data collection.

Additionally, the operator attached seven markers to anatomical landmarks on the subjects’ pelvis and right leg: Right and left posterior superior iliac spine, right greater trochanter, right lateral femoral condyle, right lateral malleolus, right posterior heel, right tip of the great toe. Those markers were used for stance-phase detection.

### Data analysis

#### Gait event detection

We filtered the 3D coordinates of markers attached to the participants' pelvis and right leg using a 4th order, recursive, digital Butterworth low-pass filter (cut-off frequency: 6 Hz), implemented in Matlab (R2018b, The Mathworks, Natick, MA, USA).

For the walking trials, we extracted touchdown and toe-off events using a previously published method10 using the peak horizontal distances between markers placed on the pelvis and on the heel or toe to determine initial and final contact during the stance phase, respectively. For running trials, we applied a previously evaluated method which uses peak knee extension angles to determine initial and final ground contact11.

#### Belt velocity algorithm

Using the 3D coordinates of the reflective foil cut-outs attached to the treadmill belts, we developed an algorithm to determine the instantaneous TBV. The underlying code is freely available as a Matlab (The Mathworks, Natick, MA, USA) function through Matlab’s file exchange server (“getBeltVelocity.m”). Figure 2 shows a brief description of the individual steps of the algorithm.

The algorithm works with the coordinates of markers attached to the treadmill belt as “unlabeled marker” data to calculate TBV via time differentiation and by averaging over redundant markers. With this approach, there is no need for time-consuming labeling of the belt marker data. The algorithm reads marker data from “.c3d” files by using the Biomechanical Toolkit (BTK), an open-source framework for visualization and processing of biomechanical data12. The code separates the belt markers from other “unlabeled markers” or outliers (markers resulting, e.g., from reflections of apparel materials or short time flickering markers resulting from errors in the reconstruction procedure) by the following method: Initially, the user defines two volumes in the lab coordinate system in which the belt markers on the respective lateral belt sides are moving. The algorithm excludes all markers lying outside of those volumes from further analysis. Also, the algorithm excludes all markers that do not appear for at least 20 consecutive timeframes. Subsequently, the algorithm determines the horizontal belt velocity in the direction of movement for each belt marker, using the average marker distance over three frames and the known measuring frequency. The algorithm excludes outliers by checking if the calculated velocity is exceeding a user defined upper-limit of velocity. In this study, we used an upper limit of + 30% of the target speed as the upper-limit for outlier detection. Finally, the algorithm calculates the average from all markers’ velocities at each time frame and applies a 4th order, recursive Butterworth filter (default setting: 20 Hz cut-off frequency). The default settings were chosen to be similar to cut-off frequencies often used to filter marker data in the analysis of running mechanics13,14,15, but can be adapted for individual purposes.

We calculated the instantaneous TBV fluctuation using the novel method for every trial. Further, we subdivided each trial into individual gait cycles (from the touchdown of the right leg to the next ipsilateral touchdown) . We analyzed all gait cycles occurring in the 17 s data collection time, resulting in at least ten analyzed gait cycles for every trial. Afterwards, we extracted the following discrete parameters for further statistical analysis: Average TBV during stance phase, and during the entire gait cycle as well as the reduction of TBV during the braking phase of stance. These variables were normalized to the respective target speeds in order to exclude any trivial effects of target speed on these parameters during the statistical analysis. Besides TBV amplitude parameters, we also quantified the relative temporal occurrence of the minimum TBV during the stance phase.

### Statistical analysis

We extracted the parameters of interest for each gait cycle. We then averaged these values for each participant in each condition before implementing these averaged values into the statistical analysis. Descriptive statistics present the means ± one standard deviation of the sample data. To analyze the effects of treadmill types, locomotion speed and body mass on TBV regulation, we performed a two factor (treadmill type, locomotion speed) repeated measures analysis of variance (ANOVA) with body mass as a covariate using the ‘ranova’ and ‘fitrm’ functions of Matlab’s Statistics and Machine Learning Toolbox (R2018b, The Mathworks, Natick, MA, USA). All data underlying the statistical analyses are provided in Supplementary Material spreadsheet file.

## Results

Treadmill type, locomotion speed, and body mass each significantly affected TBVs. Figure 3 illustrates the TBV behavior during the entire gait cycle between treadmills at all analyzed locomotion speeds and highlights the differences in amplitude and timing of TBVs.

We observed significant main effects of treadmill type on the average TBV determined during the stance phase (p < 0.001, Fig. 4A) and the entire gait cycle (p < 0.001, Fig. 4B). When averaged over all subjects and locomotion speeds, the most pronounced deviations in average TBV were found for the low-cost, non-instrumented treadmill (during stance: + 1.8 ± 0.7%; during gait cycle: + 1.8 ± 0.9%), followed by the high-cost, non-instrumented treadmill (during stance: + 1.0 ± 0.4%; durig gait cycle: + 1.2 ± 0.1%), the force-instrumented treadmill #1 (during stance: − 0.4 ± 0.4%; during gait cycle: + 0.4 ± 0.5%), and the force-instrumented treadmill #2 (during stance: + 0.3 ± 0.2%; during gait cycle: + 0.4 ± 0.02%). Further, we identified a significant main effect of speed on the average TBV determined during the entire gait cycle (p = 0.013). Averaged over all treadmill types, the relative difference in average TBV determined during the gait cycle compared to the target speed was higher in the running compared to the walking speeds. However, there was a tendency that with faster running speeds these differences became lower, which was mostly affected by the behavior of the low-cost, non-instrumented treadmill (Fig. 4B). Overall, average TBV values ranged between 98 and 103% of the target belt speed. However, differences in average TBV between treadmills were apparent, particularly for the low-cost treadmill during the running trials (Fig. 4).

Furthermore, we found differences between treadmills in the TBV reductions and their timing in the early stance phase (Fig. 5A,B). Specificaly, we found a significant interaction effect of body mass, speed, and treadmill type (p < 0.001) on the TBV reduction during the braking phase of stance (Fig. 5A). This interaction effect highlights the different behaviors in response to variations in the participants mass and locomotor speed (Fig. 5A). Velocity reductions ranged between 2 and 10% for all treadmill types except for the instrumented treadmill #1, which showed reductions between 12 and 25% of the target speed (Fig. 5A). While higher body mass generally led to greater TBV reductions during the braking phase of stance, this relationship was specific for different treadmill types and locomotion speeds (Fig. 6). Averaging over all participants and locomotion speeds yielded the largest reductions in TBV during the braking phase for the instrumented treadmill #1 (− 16.6 ± 4.1%), followed by the high-cost, non-instrumented treadmill (− 7.8 ± 1.6%), the low-cost, non-instrumented treadmill (− 7.3 ± 0.9%), and the instrumented treadmill #2 (− 4.2 ± 1.2%).

When taking a closer look at the relative timing of minimal TBV reached during the braking phase of stance, we found significant main effects of speed (p < 0.001, Fig. 5B) and treadmill type (p < 0.001, Fig. 5B). The speed effect likely resulted from the fact that, averaged over all treadmills, at walking speeds the minimum TBV occurred relatively earlier (between 22.4 and 24.8% of stance) compared to running speeds (between 34.7 and 36.4%). Averaged over all speeds, minimum TBV during the braking phase occurred the earliest for the instrumented treadmill #2 (19.8 ± 5.5% of stance), followed by instrumented treadmill #1 (32.0 ± 8.1% of stance), the high-cost, non-instrumented treadmill (32.3 ± 8.6% of stance), and the low-cost, non-instrumented treadmill (40.1 ± 5.1% of stance). For almost all trials (30 of 32), minimum TBV was reached at or before 40% of the stance phase (Fig. 5B).

## Discussion

The first purpose of the present study was to develop an efficient algorithm that allows tracking of the instantaneous velocity of treadmill belts using standard motion capture technology without adding considerable time for post-processing.

Our method represents an extension to previously developed methods that either measured TBV fluctuation from single markers attached to the treadmill belt1 or which determined TBV during the stance phase from markers attached to the feet16. Compared to these previous approaches, our approach has several advantages. Since our method uses a higher number of markers to calculate TBV, it is inherently more robust and reliable. If, for example, a person walking or running on the treadmill is hiding a single marker attached to the treadmill belt, TBV cannot be determined accurately by methods relying on a single marker attached to the belt and must be interpolated during this period. This problem is aggravated when additional devices (e.g. oxygen consumption systems, additional weights, or exoskeletons) are carried by the subject moving on the treadmill. Furthermore, a single marker can track TBV only during the time when it is moving on the top of the treadmill, i.e. during 50% of the time.

When utilizing markers attached to the feet, TBV can only be determined during the stance phase and not during flight phases, which typically occur during running locomotion. Further, foot marker methods assume that during the entire stance phase there is no relative motion between foot and ground. However, this assumption not valid during most intervals of the stance phase, as illustrated by, e.g., the dorsiflexion and plantarflexion motion of the ankle joint to absorb or generate energy at the beginning or end of stance, respectively.

Another advantage of our method is the absence of additional post-processing work (e.g. labeling), making it very time efficient. We achieved this benefit by using “unlabeled markers”, i.e. markers that are not labeled automatically or manually through the motion capture software. “Unlabeled markers” are still given a kind of label (e.g. * plus a number in a Vicon system) by the motion capture system based on the timing of their first appearace in the file. However, further computations are needed to make use of the information stored in these marker coordinates. The results of our systematic analysis of TBVs revealed similar results for TBV fluctuation waveforms compared to previously reported results1, thus providing some evidence to support the validity of our method.

The second purpose of this study was to analyze the effects of treadmill type, locomotion speed, and body mass on TBV regulation. Significant main effects of treadmill type were identified in all parameters analyzed in this study. We further found significant main or interaction effects for locomotion speed and body mass for specific parameters of interest. Therefore, our hypothesis that TBV regulation would be affected by treadmill type, locomotion speed, and body mass was supported.

When looking at the average TBV determined during the stance phase or the entire gait cycle, it becomes apparent that relying on the displayed average speed when performing studies on treadmills is not advisable. We observed average differences of more than three percent between treadmill types for walking at a slow speed (Fig. 4). Therefore, one needs to be careful when comparing results for e.g., metabolic cost or locomotor economy, if they are collected from walking or running using different treadmill types. Essentially, the findings of this study suggest that it would be ideal to track TBV during every experiment or diagnostic analysis in which locomotion speed is used directly or for the calculation of derived variables (for e.g., running economy). If this approach is not feasible, it might be good practice to calibrate average TBV during every data collection and to occasionally verify that TBV fluctuations are small.

This suggestion is further emphasized by the finding of a significant main effect for speed on average TBV determined during the entire gait cycle. We found greater average TBV deviations at running compared to walking speeds. Therefore, even when using the same treadmill type, slightly different precision in the control of average locomotor speed can be expected, in particular when comparing walking with running gaits.