# Evaluation of Different Pressure-Based Foot Contact Event Detection Algorithms across Different Slopes and Speeds

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participants and Protocol

#### 2.2. Post-Hoc Data Processing

_{sum}) was selected for application on the FCE algorithms, as it constituted a simplified signal that could be easily generated from any PPMS regardless of its configuration (array or discrete) or pressure sensor count [6,7,11]. Additionally, P

_{sum}was selected as a signal which is potentially less susceptible to differences in foot strike patterns, and one that closely approximated vGRF signals in profile [6,24]. Thus, for this investigation, the FCEs, as measured from the plantar pressure data, were derived from the P

_{sum}signal. Next, the vGRF and the P

_{sum}data were temporally aligned based on the synchronizing jumps using cross-correlation [20]. P

_{sum}was then normalized [0–100] based on the maximal value within each trial [6]. Finally, the data were cropped to the 50 s period for each trial.

#### 2.2.1. Reference FCE Detection

#### 2.2.2. Pressure Based FCE Detection

_{sum}signal (see Appendix A for the link to a repository containing a custom Python (version 3.6) implementation of each FCE algorithm). Wherever appropriate, the specific parameters used in each of the following algorithms were taken directly from the literature. Otherwise, parameters were iteratively modified and tested until the greatest number of FCEs were successfully detected. Additionally, for each algorithm, a ‘wait’ period was used, such that any FCE detected in the following 20 samples after the first detected IC or TO were removed to eliminate false positives (see Appendix A for addition details on the wait function).

#### FCE Algorithm 1 (FCE1) 2 Threshold Crossing

#### Algorithm 2 (FCE2) 2 Different Thresholds

#### Algorithm 3 (FCE3) 2 Peak Derivative

_{sum}signal [13]. The signal derivative is then filtered at 12 Hz using a zero-lag low-pass Butterworth filter. A peak detect function is applied on the signal derivative to find the locations of the signal peaks which are then assigned to the locations of IC. The peak detect function is then applied to the inverse of the signal derivative to determine the locations of the negative peaks as the locations of TO.

#### Algorithm 4 (FCE4) 2 Slope Extension Method

#### Algorithm 5 (FCE5) 2 Low-Frequency Unity

_{sum}signal. A peak detect is then used to find the locations of the peaks and valleys of the smoothed signal. The original P

_{sum}signal is then broken into segments of ascending (from valley to peak) and descending (from peak to valley) based on the locations of the peaks and valleys of the 2 Hz filtered signal. A unity line (which is a linear ramp of values going from the start of each segment to the end) is generated. Then the absolute difference between the original signal and its unity line is calculated and the location of the maximal difference is determined to be the location of IC from the ascending segments and TO for the descending segments [19]. Similar to FCE4, this algorithm also does not rely on static values, potentially increasing its reliability regardless of running technique, surface, or grade.

#### Algorithm 6 (FCE6) 2 Harle et al.

_{sum}maximum signal. This provides a late estimate of IC and an early estimate of TO locations. Following this, the first derivative of the input signal is generated. Next, a fine estimate of IC is found using a search window from the derivative signal that is 10 samples backwards from the rough IC location. The algorithm then searches within that window for the last index with a value less than 0.3, as the fine estimate of IC. A fine estimate of TO, is similarly created using a refined search window from the inverse of the derivative signal which has 10 samples going forward from the coarse estimate TO event. The algorithm then searches this window for the first value that goes below 0.3 of the derivative signal as the fine estimate of TO.

#### Algorithm 7 (FCE7) 2 Mann et al. & Hausdorff et al.

_{sum}signal. The first derivative of the P

_{sum}signal is then filtered using a fourth order, 12 Hz, zero lag, low-pass Butterworth filter. Similar to the method presented in FCE6, a search window from the derivative signal that is 30 samples backwards from the rough IC location is generated. IC is defined as the time point within the search window when the first-grade derivative diverged from the zero line but remained below 1. Similar to IC, TO was determined using a search window from the derivative signal that is 30 samples forwards from the rough TO location. Within this search window, TO was defined as the time point when the first-grade derivative converged from a negative value of 1 towards the zero line.

#### 2.3. Data Analyses and Statistics

#### 2.3.1. Algorithms across Speed (Level Grade)

#### 2.3.2. Algorithms across Speed, across Grades

## 3. Results

#### 3.1. Algorithms across Speeds (Level Grade)

#### 3.2. Algorithm across Speed and across Grades

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

- fc is equivalent to initial contact (IC), as used in the text of this paper
- fo is equivalent to toe off (TO), as used in the text of this paper.

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**Figure 1.**Novel

^{®}Pedar™ pressure insole system. (

**a**) Complete system (

**b**) Pedar insole positioned within an insole (taken from https://www.novel.de/products/pedar/ accessed on 15 January 2023).

**Figure 2.**(

**a**) Data processing (N = 18) flowchart detailing the processing of the reference vGRF data from the force instrumented treadmill (black) and P

_{sum}data from the PPMSs (blue) for each trial and for each stance within a given trial. (

**b**) Single stance with overlayed vGRF signal (black) and P

_{sum}(blue). Overlayed reference of vGRF initial contact events (red dashed) and reference vGRF toe off events (green dashed) FCEs, as determined using the P

_{sum}signal using a given FCE algorithm (solid orange for initial contact and solid green for toe off).

**Figure 3.**Plot (

**left**) displaying a single stride and location of the reference IC and TO events (dashed vertical), as determined by a standard threshold crossing algorithm (

**right**) using a 40 N threshold on the vGRF signal.

**Figure 4.**Plot (

**left**) displaying a single stride and the location of the reference FCEs (dashed vertical lines) and the FCEs (solid vertical) determined by the FCE1 algorithm (

**right**) using a 10% of the maximum signal threshold on the P

_{sum}signal.

**Figure 5.**Plot (

**left**) displaying a single stride and the location of the reference FCEs (dashed vertical) and the FCEs (solid vertical) determined by the FCE2 algorithm (

**right**) using a 5% of the maximum signal threshold for IC and a 10% of the maximum signal threshold for TO.

**Figure 6.**Plot (

**left**) displaying a single stride and the location of the reference FCEs (dashed vertical) and the FCEs (solid vertical), as determined by the FCE3 algorithm (

**right**).

**Figure 7.**Plot (

**left**) displaying a single stride and the location of the reference FCEs (dashed vertical) and the FCEs (solid vertical), as determined by the FCE4 algorithm (

**right**).

**Figure 8.**Plot (

**left**) displaying a single stride and the location of the reference FCEs (dashed vertical) and the FCEs (solid vertical), as determined by the FCE5 algorithm (

**right**).

**Figure 9.**Plot (

**left**) displaying a single stride and the location of the reference FCEs (dashed vertical) and the FCEs (solid vertical), as determined by the FCE6 algorithm (

**right**).

**Figure 10.**Plot (

**left**) displaying a single stride and the location of the reference FCEs (dashed vertical) and the FCEs (solid vertical), as determined by the FCE7 algorithm (

**right**).

**Figure 11.**(

**a**) Mean absolute error (MAE) for the detection of initial contact (IC). * FCE1 was significantly smaller than all other algorithms, † FCE3 was significantly higher than all others except FCE7, and ‡ FCE7 was significantly higher than all other FCE algorithms. (

**b**) MAE for the detection of toe off (TO). * FCE1 had significantly smaller than FCE3 and FCE7, † FCE3 was significantly higher than all other algorithms, and ‡ FCE3 was significantly higher at 2.6 m/s than all other speeds. (

**c**) MAE for stance time (GCT). * FCE3 was significantly higher than all other algorithms by speed, and † FCE7 was significantly higher except for FCE3 than all other algorithms. Error bars represent standard deviations.

**Figure 12.**(

**a**) Mean absolute error (MAE) for the initial contact events (IC) across all grades (* FCE3 was significantly higher on inclines than all other grades, and † indicates that FCE4 showed as significantly higher on inclines than at all other grades. (

**b**) Mean absolute error (MAE) for the toe off events (TO) across all grades (

**c**) Mean absolute error (MAE) for stance time (GCT) across all grades. Error bars represent standard deviations.

**Table 1.**Mean and standard deviations of the MAE (ms) for IC, FO, and GCT determined for each algorithm across all speeds (2.6, 3.0, 3.4, and 3.8 m/s) on a level grade.

Initial Contact (IC) | Toe Off (TO) | Stance Time (GCT) | ||
---|---|---|---|---|

Speeds | Algorithms | Mean MAE ± SD (ms) | Mean MAE ± SD (ms) | Mean MAE ± SD (ms) |

2.6 | FCE1 | 0.7 ± 0.3 * | 1.3 ± 0.9 * | 7 ± 5 |

FCE2 | 1.3 ± 2.0 | 1.3 ± 0.9 | 12 ± 11 | |

FCE3 | 3.7 ± 0.9 † | 15.9 ± 4.5 †‡ | 94 ± 24 * | |

FCE4 | 1.3 ± 0.8 | 2.4 ± 0.9 | 12 ± 8 | |

FCE5 | 1.5 ± 0.5 | 3.7 ± 1.4 | 26 ± 8 | |

FCE6 | 1.4 ± 0.6 | 3.4 ± 1.2 | 24 ± 7 | |

FCE7 | 5.1 ± 0.5 ‡ | 2.9 ± 1.1 | 41 ± 7 † | |

3.0 | FCE1 | 1.0 ± 1.1 * | 1.7 ± 1.4 * | 8 ± 5 |

FCE2 | 1.2 ± 1.2 | 1.7 ± 1.4 | 10 ± 6 | |

FCE3 | 3.7 ± 1.4 † | 12.4 ± 5.5 † | 79 ± 25 * | |

FCE4 | 1.5 ± 0.8 | 2.1 ± 1.6 | 13 ± 6 | |

FCE5 | 1.5 ± 0.8 | 4.1 ± 2 | 26 ± 10 | |

FCE6 | 1.4 ± 0.6 | 3.5 ± 1.4 | 22 ± 6 | |

FCE7 | 5.0 ± 1.2 ‡ | 3.7 ± 1.7 | 43 ± 9† | |

3.4 | FCE1 | 1.0 ± 1.1 * | 1.7 ± 1.4 * | 8 ± 5 |

FCE2 | 1.2 ± 1.2 | 1.7 ± 1.4 | 10 ± 6 | |

FCE3 | 3.7 ± 1.4 † | 12.4 ± 5.5 † | 79 ± 25 * | |

FCE4 | 1.5 ± 0.8 | 2.1 ± 1.6 | 13 ± 6 | |

FCE5 | 1.5 ± 0.8 | 4.1 ± 2 | 26 ± 10 | |

FCE6 | 1.4 ± 0.6 | 3.5 ± 1.4 | 22 ± 6 | |

FCE7 | 5.0 ± 1.2 ‡ | 3.7 ± 1.7 | 43 ± 9 † | |

3.8 | FCE1 | 1.0 ± 0.9 * | 2.5 ± 3.3 * | 10 ± 8 |

FCE2 | 1.3 ± 0.8 | 2.5 ± 3.3 | 12 ± 7 | |

FCE3 | 3.1 ± 1.0 † | 10.7 ± 4.6 † | 66 ± 22 * | |

FCE4 | 1.6 ± 0.8 | 2.3 ± 2.2 | 16 ± 8 | |

FCE5 | 1.6 ± 0.7 | 3.3 ± 2.9 | 23 ± 12 | |

FCE6 | 1.6 ± 1.0 | 3.2 ± 2.7 | 20 ± 11 | |

FCE7 | 5.7 ± 0.8 ‡ | 3.4 ± 2.3 | 45 ± 12 † |

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**MDPI and ACS Style**

Blades, S.; Marriott, H.; Hundza, S.; Honert, E.C.; Stellingwerff, T.; Klimstra, M.
Evaluation of Different Pressure-Based Foot Contact Event Detection Algorithms across Different Slopes and Speeds. *Sensors* **2023**, *23*, 2736.
https://doi.org/10.3390/s23052736

**AMA Style**

Blades S, Marriott H, Hundza S, Honert EC, Stellingwerff T, Klimstra M.
Evaluation of Different Pressure-Based Foot Contact Event Detection Algorithms across Different Slopes and Speeds. *Sensors*. 2023; 23(5):2736.
https://doi.org/10.3390/s23052736

**Chicago/Turabian Style**

Blades, Samuel, Hunter Marriott, Sandra Hundza, Eric C. Honert, Trent Stellingwerff, and Marc Klimstra.
2023. "Evaluation of Different Pressure-Based Foot Contact Event Detection Algorithms across Different Slopes and Speeds" *Sensors* 23, no. 5: 2736.
https://doi.org/10.3390/s23052736