# A Pressure-Pad-Embedded Treadmill Yields Time-Dependent Errors in Estimating Ground Reaction Force during Walking

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Equipment

^{®}, Germany; belt length: 150 cm; belt width: 50 cm; maximum incline: 15%; maximum speed: 24 km/h), which was used to record VGRF at a sampling frequency of 50 Hz. A motion capture system consisting of ten infra-red cameras (Optitrack Prime

^{X}13, Natural Point, Inc., OR, USA) was used to record coordinates of the retro-reflective markers attached to the participant at a sampling frequency of 100 Hz. A sync box was used to synchronize the initiation of data acquisition from the two systems.

#### 2.3. Experimental Procedure

#### 2.4. Data Processing

^{TM}, C-Motion, Inc., Germantown, MD, USA), we built a fifteen-segment model, which included left and right foot, shank, thigh, upper arm, forearm, and hand, trunk, and head segments. We identified the whole-body center of mass (COM) using this model, and calculated the vertical velocity of COM (V

_{COM}).

#### 2.5. Statistical Analysis

## 3. Results

_{COM}(the difference between the V

_{COM}values at the beginning of one stride and the next one). The mean and SE of these four measures of 20 participants are shown in Figure 3, and the results of the statistical analysis are summarized in Table 2. In contrast with the ANOVA results for VGRF and impulse, two-way repeated measures ANOVA concluded no significant main effect except for the effect of time on the stance duration of the left foot. Even for the only observed effect of time on the stance duration of the left foot, the post-hoc pairwise comparisons concluded no significant difference over each one-minute interval. In addition, BW remained exactly the same for all participants across the three BW measurement time points. Therefore, stance duration, stride duration, BW, and ΔV

_{COM}were seldom affected either by walking duration or the trial number.

## 4. A Curve Fitting Model of the Estimation Error

_{total}is the total VGRF on the left and right foot; m is the mass of the participant; and g is the gravitational acceleration. In typical walking, the kinematics is almost periodic, and therefore V

_{COM}after one gait cycle is expected to remain similar to the value at the beginning of the cycle. Experimental data agree with this expectation; V

_{COM}remains almost constant, making ΔV

_{COM}close to zero throughout 10 min of walking (Figure 3C). However, experimental results also showed a time-dependent decline in VGRF, whereas BW remains almost constant. Hence, the left hand side of Equation (1) should decrease, whereas the right hand side remains close to zero. This discrepancy clarifies the time-dependent decline in the estimated impulse. Combined with the time-dependent decline in VGRFs and almost constant stance durations (Figure 3A), the experimental results conclude that the embedded pad underestimates the pressure, and the error grows as the operation time of the treadmill increases, i.e., if we calculate the error in the measured impulse as the difference between the impulse estimated from the Zebris system, which is $\int \left(VGR{F}_{total}-mg\right)dt$, and the actual impulse obtained from kinematics, mΔV

_{COM}, then, the magnitude of the error (ΔI) will grow as time, stride number, or the traveled distance increases.

_{fit}is the fitted value of the error in the impulse measurement; ΔI

_{steady}is the steady-state value which ΔI

_{fit}will approach after sufficiently many strides; k is the exponential decay constant; x is the stride number; and x

_{initial}and ΔI

_{initial}are the initial values of the stride and the error, respectively. We set x

_{initial}as one.

_{initial}, k, and ΔI

_{steady}iteratively, we need to select their proper initial values for the iteration. We chose initial ΔI

_{initial}as the error in the impulse measurement during the first stride. We chose the initial k as the overall slope of the impulse error with respect to stride, calculated between the last and first strides. Finally, we chose the initial ΔI

_{steady}as the value of the error at the final stride. We iterated the values of ΔI

_{initial}, k, and ΔI

_{steady}using unconstrained multivariate optimization to find the values making ΔI

_{fit}closest to the true error, which we calculated as,

_{fit}, and the maximum number of iterations was set as 1000.

## 5. Goodness of Fit of the Model

^{2}) between ΔI and ΔI

_{fit}after the iteration, separately for each participant and trial. The values of R

^{2}indicate the proportion of variance explained by the curve-fitting model used to encapsulate the error between ΔI and ΔI

_{fit}. Considering that the model might be sensitive to a slight fluctuation in ΔI during each single stride, we additionally assessed the model’s goodness of fit after downsampling the data by averaging ΔI over 5, 10, 15, and 20 strides. It is also highly plausible that the error depends more directly on the distance traveled by the treadmill belt or the operation time of the treadmill rather than the stride number. To address this, we calculated the R

^{2}values after fitting ΔI with respect to time and distance. Again, we performed the curve fitting after downsampling the data by averaging the ΔI over 5, 10, 15, and 20 s; and 5, 10, 15, and 20 m.

^{2}values for 20 participants when fitting ΔI with respect to strides, time, and distance are shown in Figure 4. The mean R

^{2}of 20 participants was above 0.88 in every case and above 0.95 in most cases. A representative fitting curve that approximates the growing errors in VGRF estimation is shown in Figure 5. The R

^{2}values for the first trials were larger than those for the second trial. Downsampling by averaging increased the R

^{2}values. We performed two-way repeated measures ANOVA to evaluate any statistical differences between the values of R

^{2}for 20 participants depending on the data resolution (stride: 1, 5, 10, 15, and 20 strides; time: 5, 10, 15, and 20 s; distance: 5, 10, 15, and 20 m) and trial (2 levels: trials 1 and 2). The results are summarized in Table 3. For all three variables (strides, time, and distance), there were significant main effects of data resolution and trial on R

^{2}, and there was a significant interaction between data resolution and trial.

## 6. Discussion

_{COM}; the right hand side of Equation (3) should be very close to zero if VGRF, body weight, and ΔV

_{COM}are all measured correctly. However, this expectation directly contradicts the experimental results. To assess body weight and ΔV

_{COM}, we used the gold-standards: a reliable and accurate scale and a motion capture system. Hence, the only possible explanation for the time-dependent errors is erroneous sensing of VGRF; capacitive sensor-embedded treadmills are not reliable in long-term VGRF measurement during walking.

^{2}values above 0.95 in most cases (Figure 4). Note that we developed one curve fitting model per each individual participant; the three parameters of the fitting model are different for each participant, which we summarized in the Supplementary Tables S1–S3. Considering that the experimenter should collect the walking data of each participant, deriving a curve-fitting model customized for each participant’s walking dynamics, rather than a general model with universal parameter values, is more adequate and efficient.

## 7. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Paoloni, M.; Mangone, M.; Fratocchi, G.; Murgia, M.; Saraceni, V.M.; Santilli, V. Kinematic and kinetic features of normal level walking in patellofemoral pain syndrome: More than a sagittal plane alteration. J. Biomech.
**2010**, 43, 1794–1798. [Google Scholar] [CrossRef] - Creaby, M.W.; Hunt, M.A.; Hinman, R.S.; Bennell, K.L. Sagittal plane joint loading is related to knee flexion in osteoarthritic gait. Clin. Biomech.
**2013**, 28, 916–920. [Google Scholar] [CrossRef] - De David, A.C.; Carpes, F.P.; Stefanyshyn, D. Effects of changing speed on knee and ankle joint load during walking and running. J. Sports Sci.
**2015**, 33, 391–397. [Google Scholar] [CrossRef] - Sturdy, J.T.; Sessoms, P.H.; Silverman, A.K. A backpack load sharing model to evaluate lumbar and hip joint contact forces during shoulder borne and hip belt assisted load carriage. Appl. Ergon.
**2021**, 90, 103277. [Google Scholar] [CrossRef] - Hamill, J.; McNiven, S.L. Reliability of selected ground reaction force parameters during walking. Hum. Mov. Sci.
**1990**, 9, 117–131. [Google Scholar] [CrossRef] - Belli, A.; Bui, P.; Berger, A.; Geyssant, A.; Lacour, J.-R. A treadmill ergometer for three-dimensional ground reaction forces measurement during walking. J. Biomech.
**2001**, 34, 105–112. [Google Scholar] [CrossRef] - Kesar, T.M.; Binder-Macleod, S.A.; Hicks, G.E.; Reisman, D.S. Minimal detectable change for gait variables collected during treadmill walking in individuals post-stroke. Gait Posture
**2011**, 33, 314–317. [Google Scholar] [CrossRef][Green Version] - Willems, P.A.; Gosseye, T.P. Does an instrumented treadmill correctly measure the ground reaction forces? BiO
**2013**, 2, 1421–1424. [Google Scholar] [CrossRef][Green Version] - Faude, O.; Donath, L.; Roth, R.; Fricker, L.; Zahner, L. Reliability of gait parameters during treadmill walking in community-dwelling healthy seniors. Gait Posture
**2012**, 36, 444–448. [Google Scholar] [CrossRef] - Nüesch, C.; Overberg, J.-A.; Schwameder, H.; Pagenstert, G.; Mündermann, A. Repeatability of spatiotemporal, plantar pressure and force parameters during treadmill walking and running. Gait Posture
**2018**, 62, 117–123. [Google Scholar] [CrossRef] - Lee, M.; Song, C.; Lee, K.; Shin, D.; Shin, S. Agreement between the spatio-temporal gait parameters from treadmill-based photoelectric cell and the instrumented treadmill system in healthy young adults and stroke patients. Med. Sci. Mon.
**2014**, 20, 1210–1219. [Google Scholar] - Donath, L.; Faude, O.; Lichtenstein, E.; Nüesch, C.; Mündermann, A. Validity and reliability of a portable gait analysis system for measuring spatiotemporal gait characteristics: Comparison to an instrumented treadmill. J. Neuroeng. Rehabil.
**2016**, 13, 1–9. [Google Scholar] [CrossRef][Green Version] - Miyazaki, S.; Ishida, A. Capacitive transducer for continuous measurement of vertical foot force. Med. Biol. Eng. Comput.
**1984**, 22, 309–316. [Google Scholar] [CrossRef] - Salpavaara, T.; Verho, J.; Lekkala, J. Capacitive insole sensor for hip surgery rehabilitation. In Proceedings of the 2008 Second International Conference on Pervasive Computing Technologies for Healthcare, Tampere, Finland, 30 January–1 February 2008. [Google Scholar]
- Sorrentino, I.; Andrade Chavez, F.J.; Latella, C.; Fiorio, L.; Traversaro, S.; Rapetti, L.; Tirupachuri, Y.; Guedelha, N.; Maggiali, M.; Dussoni, S. A Novel Sensorised Insole for Sensing Feet Pressure Distributions. Sensors
**2020**, 20, 747. [Google Scholar] [CrossRef][Green Version] - Lee, N.; Goonetilleke, R.S.; Cheung, Y.S.; So, G.M. A flexible encapsulated MEMS pressure sensor system for biomechanical applications. Microsyst Technol.
**2001**, 7, 55–62. [Google Scholar] [CrossRef] - Item-Glatthorn, J.F.; Casartelli, N.C.; Maffiuletti, N.A. Reproducibility of gait parameters at different surface inclinations and speeds using an instrumented treadmill system. Gait Posture.
**2016**, 44, 259–264. [Google Scholar] [CrossRef] - Van Alsenoy, K.; Thomson, A.; Burnett, A. Reliability and validity of the Zebris FDM-THQ instrumented treadmill during running trials. Sports Biomech.
**2018**, 18, 501–514. [Google Scholar] [CrossRef] - Riva, F.; Bisi, M.C.; Stagni, R. Gait variability and stability measures: Minimum number of strides and within-session reliability. Comput. Biol. Med.
**2014**, 50, 9–13. [Google Scholar] [CrossRef] - Bruijn, S.M.; van Dieën, J.H.; Meijer, O.G.; Beek, P.J. Statistical precision and sensitivity of measures of dynamic gait stability. J. Neurosci. Methods.
**2009**, 178, 327–333. [Google Scholar] [CrossRef] - Owings, T.M.; Grabiner, M.D. Measuring step kinematic variability on an instrumented treadmill: How many steps are enough? J. Biomech.
**2003**, 36, 1215–1218. [Google Scholar] - Ahn, J.; Hogan, N. Improved assessment of orbital stability of rhythmic motion with noise. PLoS ONE
**2015**, 10, e0119596. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kalron, A.; Dvir, Z.; Frid, L.; Achiron, A. Quantifying gait impairment using an instrumented treadmill in people with multiple sclerosis. ISRN Neurol.
**2013**, 2013, 867575. [Google Scholar] [CrossRef][Green Version] - Giacomozzi, C.; Keijsers, N.; Pataky, T.; Rosenbaum, D. International scientific consensus on medical plantar pressure measurement devices: Technical requirements and performance. Ann. Ist. Super Sanita
**2012**, 48, 259–271. [Google Scholar] [CrossRef] - Urry, S. Plantar pressure-measurement sensors. Meas. Sci. Technol.
**1999**, 10, R16–R32. [Google Scholar] [CrossRef] - Abdul Razak, A.H.; Zayegh, A.; Begg, R.K.; Wahab, Y. Foot plantar pressure measurement system: A review. Sensors
**2012**, 12, 9884–9912. [Google Scholar] [CrossRef][Green Version] - Lord, M. Spatial resolution in plantar pressure measurement. Med. Eng. Phys.
**1997**, 19, 140–144. [Google Scholar] [CrossRef] - Pataky, T.C. Spatial resolution in plantar pressure measurement revisited. J. Biomech.
**2012**, 45, 2116–2124. [Google Scholar] [CrossRef] - Sawilowsky, S.S. New effect size rules of thumb. J. Mod. Appl. Stat. Methods
**2009**, 8, 597–599. [Google Scholar] [CrossRef] - Faul, F.; Erdfelder, E.; Buchner, A.; Lang, A.-G. Statistical power analyses using G* Power 3.1: Tests for correlation and regression analyses. Behav. Res. Methods
**2009**, 41, 1149–1160. [Google Scholar] [CrossRef][Green Version] - Nilsson, J.; Thorstensson, A. Ground reaction forces at different speeds of human walking and running. Acta Physiol. Scand.
**1989**, 136, 217–227. [Google Scholar] [CrossRef] [PubMed] - Weyand, P.G.; Sternlight, D.B.; Bellizzi, M.J.; Wright, S. Faster top running speeds are achieved with greater ground forces not more rapid leg movements. J. Appl. Physiol.
**2000**, 89, 1991–1999. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hatala, K.G.; Dingwall, H.L.; Wunderlich, R.E.; Richmond, B.G. Variation in foot strike patterns during running among habitually barefoot populations. PLoS ONE
**2013**, 8, e52548. [Google Scholar] [CrossRef][Green Version] - Almeida, M.O.; Davis, I.S.; Lopes, A.D. Biomechanical differences of foot-strike patterns during running: A systematic review with meta-analysis. J. Orthop. Sports Phys. Ther
**2015**, 45, 738–755. [Google Scholar] [CrossRef][Green Version] - Pataky, Z.; Assal, J.P.; Conne, P.; Vuagnat, H.; Golay, A. Plantar pressure distribution in Type 2 diabetic patients without peripheral neuropathy and peripheral vascular disease. Diabet. Med.
**2005**, 22, 762–767. [Google Scholar] [CrossRef] - Chisholm, A.E.; Perry, S.D.; McIlroy, W.E. Inter-limb centre of pressure symmetry during gait among stroke survivors. Gait Posture
**2011**, 33, 238–243. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kalron, A.; Frid, L. The “butterfly diagram”: A gait marker for neurological and cerebellar impairment in people with multiple sclerosis. J. Neurol. Sci.
**2015**, 358, 92–100. [Google Scholar] [CrossRef] [PubMed] - Sutkowska, E.; Sutkowski, K.; Sokołowski, M.; Franek, E.; Dragan, S. Distribution of the highest plantar pressure regions in patients with diabetes and its association with peripheral neuropathy, gender, age, and BMI: One centre study. J. Diabetes Res.
**2019**, 2019, 7395769. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**An illustration of the VGRF curve for a single step. The red circles denote three stereotypical time points for each step; the time point of load response (LR), mid stance (MS), and push off (PO). The LR and PO are the time points of two peaks of the double bump pattern of the VGRF curve, and MS is the time point of the minimal value of VGRF between LR and PO.

**Figure 2.**Changes in the VGRFs at the three stereotypical time points and the impulse due to VGRF with increase in time. (

**A**–

**C**) show the means and standard error bars of VGRFs for 20 participants at LR, MS, and PO, respectively, averaged over every one-minute time interval for the both feet and two trials. (

**D**) shows the means and standard error bars of impulse for 20 participants averaged over every one-minute time interval for the both feet and two trials.

**Figure 3.**The measures used to assess whether the time-dependent decrease in the VGRF is due to alterations in kinematics or dynamics during walking. (

**A**–

**C**) show the means and standard error bars of the stance durations of the both feet, stride durations, the difference in the values of the vertical center of mass velocity between the beginning of one stride and the next one (ΔV

_{COM}) for 20 participants averaged over every one-minute time interval for the two trials. (

**D**) shows the means and standard error bars of the body weights (BW) for 20 participants for three measurement time points: initial (before the first trial), mid (between the first and second trial), and final (after completion of the second trial). BW remained exactly same for all participants across the three time points.

**Figure 4.**The goodness of fit of the curve fitting model of the VGRF estimation error. The figures from left to right are the means and standard error bars of the coefficient of determination (R

^{2}) for 20 participants when fitting the error (ΔI) with respect to the stride number (strides), the operation time of the treadmill (time), and the distance traveled by the treadmill belt (distance), respectively, for the two trials. We assessed the model’s goodness of fit for the curve fitting with respect to every single stride, every 5, 10, 15, and 20 strides. Similarly, we assessed model’s goodness of fit after downsampling ΔI by averaging it over 5, 10, 15, and 20 s; and 5, 10, 15, and 20 m for time and distance, respectively. Generally, downsampling the data increased the mean R

^{2}of 20 participants. The mean R

^{2}of 20 participants for the first trial was larger than the second trial.

**Figure 5.**A representative figure illustrating the curve-fitting model that encapsulates the VGRF estimation error over strides. The blue circles are the individual impulse estimation error values for each stride, and the red line is the curve used to encapsulate the temporal changes in the impulse estimation errors.

Measure | Within-Subjects Effects | ||||
---|---|---|---|---|---|

Time | Trial | Interaction | |||

VGRF | LR | Left | F_{[1.675,31.821]} = 182.775,p < 0.001 | F_{[1,19]} = 62.029, p < 0.001 | F_{[2.365,44.938]} = 14.034,p < 0.001 |

Right | F_{[1.722,32.721]} = 168.093,p < 0.001 | F_{[1,19]} = 75.538,p < 0.001 | F_{[3.015,57.291]} = 14.977,p < 0.001 | ||

MS | Left | F_{[1.512,28.730]} = 139.023,p < 0.001 | F_{[1,19] }= 75.538,p < 0.001 | F_{[3.032,57.600]} = 17.979,p < 0.001 | |

Right | F_{[2.045,38.862]} = 135.190,p < 0.001 | F_{[1,19]} = 77.021,p < 0.001 | F_{[2.577,48.955]} = 16.322,p < 0.001 | ||

PO | Left | F_{[1.516,28.807]} = 93.345,p < 0.001 | F_{[1,19]} = 51.350,p < 0.001 | F_{[2.472,46.962]} = 3.510,p = 0.029 | |

Right | F_{[1.624,30.856]} = 98.168,p < 0.001 | F_{[1,19]} = 32.807,p < 0.001 | F_{[2.623,49.841]} = 5.051,p = 0.006 | ||

Impulse | Left | F_{[1.260,23.934]} = 120.867,p < 0.001 | F_{[1,19]} = 52.881,p < 0.001 | F_{[1.841,34.970]} = 18.048,p < 0.001 | |

Right | F_{[1.391,26.423]} = 134.003,p < 0.001 | F_{[1,19]} = 56.153,p < 0.001 | F_{[2.060,39.143]} = 21.252,p < 0.001 |

Measure | Within-Subjects Effects | |||
---|---|---|---|---|

Time | Trial | Interaction | ||

Stance duration | Left | F_{[2.124,40.360]} = 3.954,p = 0.025 | F_{[1,19]} = 0.229,p = 0.638 | F_{[3.295,62.614]} = 1.137,p = 0.343 |

Right | F_{[2.121,40.299]} = 2.273,p = 0.113 | F_{[1,19]} = 0.228,p = 0.639 | F_{[3.623,68.835]} = 1.178,p = 0.327 | |

Stride duration | F_{[1.991,37.835]} = 1.623,p = 0.211 | F_{[1,19]} = 0.462,p = 0.505 | F_{[3.072,58.369]} = 1.662,p = 0.184 | |

ΔV_{COM} | F_{[5.029,95.557]} = 0.990,p = 0.450 | F_{[1,19]} = 1.718,p = 0.206 | F_{[4.626,87.902]} = 0.491,p = 0.879 |

Measure | Within-Subjects Effects | ||
---|---|---|---|

Resolution | Trial | Interaction | |

Stride | F_{[1.017,19.317]} = 21.053,p < 0.001 | F_{[1,19]} = 17.089,p = 0.001 | F_{[1.225,23.269]} = 12.716, p = 0.001 |

Time | F_{[1.100,20.906]} = 9.526,p = 0.005 | F_{[1,19]} = 18.839,p < 0.001 | F_{[1.476,28.038]} = 9.769,p = 0.002 |

Distance | F_{[1.035,19.661]} = 14.530,p = 0.001 | F_{[1,19]} = 15.773,p = 0.001 | F_{[1.238,23.526]} =4.702,p = 0.033 |

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**MDPI and ACS Style**

Pathak, P.; Ahn, J. A Pressure-Pad-Embedded Treadmill Yields Time-Dependent Errors in Estimating Ground Reaction Force during Walking. *Sensors* **2021**, *21*, 5511.
https://doi.org/10.3390/s21165511

**AMA Style**

Pathak P, Ahn J. A Pressure-Pad-Embedded Treadmill Yields Time-Dependent Errors in Estimating Ground Reaction Force during Walking. *Sensors*. 2021; 21(16):5511.
https://doi.org/10.3390/s21165511

**Chicago/Turabian Style**

Pathak, Prabhat, and Jooeun Ahn. 2021. "A Pressure-Pad-Embedded Treadmill Yields Time-Dependent Errors in Estimating Ground Reaction Force during Walking" *Sensors* 21, no. 16: 5511.
https://doi.org/10.3390/s21165511