# Evaluation of Simple Algorithms for Proportional Control of Prosthetic Hands Using Intramuscular Electromyography

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Subjects

#### 2.2. Recorded Signals

- The short residual limb (SRL) protocol targeted the following muscles: flexor carpi radialis (FCR), extensor carpi radialis (ECR), pronator teres (PT), flexor digitorum profundus (FDP), extensor digitorum communis (EDC), and abductor pollicis longus (APL);
- The long residual limb (LRL) targeted the following muscles: flexor digitorum profundus (FDP), extensor digitorum communis (EDC), abductor pollicis longus (APL), flexor pollicis longus (FPL), extensor pollicis longus (EPL) and extensor indicis proprius (EIP).

^{11}Ω on the entire bandwidth, and a noise level lower than 1 µV

_{RMS}. To reduce the interferences induced in the leads between the fine wires and the amplifier, shielded differential preamplifiers were used in close proximity to the fine-wire skin entry points. In parallel with the iEMG recordings, forces resulting from hand muscles contractions were also recorded using the measurement device which kept the hand stationary during the procedure. In total, 9 force gauges picked up the resulting hand forces: one per finger (D2 (index finger)–D5 (little finger)), two for the thumb, and three for the wrist. The recording protocol was guided by an automated graphical user interface which, in a strictly timed manner, displayed commands and cues to the volunteer. It also provided feedback on the exerted force which was crucial for force matching/tracking tasks. An example of this functionality is the sine wave tracking task which started by instructing the volunteer to perform maximal voluntary flexion and the extension of a finger, thumb or the wrist, the adduction–abduction of the thumb, or the pronation–supination of the wrist. Although the inserted electrodes targeted only a subset of the muscles involved in the abovementioned hand movements, the protocol was consistent for all volunteers and all electrode placements. This way, it was possible to compare muscle synergies and crosstalk between iEMG channels, which is not in the focus of this study, but might be of interest for other studies that use the database. Then, the software generated a low-frequency sine wave with an amplitude equal to 20% of the maximal voluntary flexion/extension and a frequency of 0.1 Hz and displayed it in the same graph with the finger or wrist force that the volunteer produced (see Figure 1). The idea here was that the volunteer would match the computer-generated sine wave by continuously eliciting an equivalent force.

#### 2.3. Signal Pre-Processing

_{0}) and its harmonics (f

_{0}× i, i = 2, 3, 4…), which also exceeded iEMG signal amplitude, a band-stop comb filter comprising third-order Butterworth notch filters (f

_{0}= 50 Hz and Δf = ± 2 Hz) was applied to the recorded signals [27]. The next pre-processing step was the segmentation of recorded signals based on the automatic data labeling performed during the recordings. In this stage, force outputs were divided between positive and negative values or phases (flexions–extensions, adductions–abductions, pronations–supinations) so that they could be independently associated with different muscles. Finally, as the last step preceding the algorithm stage, optimal matchings between targeted muscles, elicited movements and the force gauges were established. On top of that, within the selected force channel, a phase (positive or negative) was associated with the actions of specific muscles. In other words, for each iEMG signal (muscle) there was an associated hand movement that specifically activated the muscle where the fine-wire electrode was placed. Furthermore, there was a sensor within the force measurement device that registered the force generated by the muscle contraction of interest. For example, activation in the PT muscle was always associated with the command to pronate the forearm and the elicited force was measured by the sensor designated for the measurement of wrist pronation. Nevertheless, for some muscles, there could be a variety of different matchings for different subjects due to the multi-compartment nature of the muscles in which the fine-wire electrodes were anchored or the individuals’ strategies for producing the commanded contractions. Such examples include the FDP, which could flex any of the D3–D5 fingers depending on the activated compartment, or EDC, which extended the D2–D4 fingers. Furthermore, depending on individuals’ synergies, APL could be more active during the command to push the thumb to the left (right-handed setup) or upwards. An example of the signal pre-processing method is shown in Figure 2.

#### 2.4. Testing of Algorithms

- 1.
- Mean Absolute Value

- 2.
- Variance

- 3.
- Slope Sign Change

- 4.
- Zero Crossing

- 5.
- Willison Amplitude

- 6.
- Waveform Length

- 7.
- Envelope

- 8.
- Total signal energy

- 9.
- Teager energy in time domain

- 10.
- Teager energy in frequency domain

- 11.
- Modified Teager energy

- 12.
- Mean of signal frequencies

- 13.
- Median of signal frequencies

- 14.
- Firing rate

- PC with Intel i7-6700K, 64-bit processor at 4 GHz;
- Teensy 4.0 with Cortex-M7, 32-bit processor at 600 MHz;
- Teensy 3.6 with Cortex-M4, 32-bit processor at 180 MHz;
- BLE-Nano with Cortex-M0 (NRF51822), 32-bit processor at 16 MHz;
- Arduino-Nano with ATmega328, 8-bit processor at 16 MHz.

#### 2.5. Evaluation

## 3. Results

^{−6}) between the mean ranks of MNF, MDF and FR and the rest of the algorithms. In addition, other statistical differences could also be found between some of the other algorithms, as shown in Table 4. This table was derived from the best performances of each algorithm and for each signal, regardless of the algorithm parameters (such as window size).

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Table A1.**Statistical significance between window sizes for var algorithm. Green indicates statistically significant difference (p < 0.05; Bonferroni-corrected) for the RMSE metric, and orange indicates significant difference (p < 0.05; Bonferroni-corrected) for the cross-correlation metric. Grey indicates diagonal fields.

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**Table A2.**Statistical significance between window sizes for WL algorithm. Green indicates statistically significant difference (p < 0.05; Bonferroni-corrected) for the RMSE metric, and orange indicates significant difference (p < 0.05; Bonferroni-corrected) for the cross-correlation metric. Grey indicates diagonal fields.

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**Table A3.**Statistical significance between window sizes for ENV algorithm. Green indicates statistically significant difference (p < 0.05; Bonferroni-corrected) for the RMSE metric, and orange indicates significant difference (p < 0.05; Bonferroni-corrected) for the cross-correlation metric. Grey indicates diagonal fields.

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**Table A4.**Statistical significance between window sizes for Etot algorithm. Green indicates statistically significant difference (p < 0.05; Bonferroni-corrected) for the RMSE metric, and orange indicates significant difference (p < 0.05; Bonferroni-corrected) for the cross-correlation metric. Grey indicates diagonal fields.

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**Table A5.**Statistical significance between window sizes for Ttd algorithm. Green indicates statistically significant difference (p < 0.05; Bonferroni-corrected) for the RMSE metric, and orange indicates significant difference (p < 0.05; Bonferroni-corrected) for the cross-correlation metric. Grey indicates diagonal fields.

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**Table A6.**Statistical significance between window sizes for Tf algorithm. Green indicates statistically significant difference (p < 0.05; Bonferroni-corrected) for the RMSE metric, and orange indicates significant difference (p < 0.05; Bonferroni-corrected) for the cross-correlation metric. Grey indicates diagonal fields.

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**Figure A7.**RMSE (

**left**) and cross-correlation (

**right**) of Tf_mod algorithm for different window sizes.

**Table A7.**Statistical significance between window sizes for Tf_mod algorithm. Green indicates statistically significant difference (p < 0.05; Bonferroni-corrected) for the RMSE metric, and orange indicates significant difference (p < 0.05; Bonferroni-corrected) for the cross-correlation metric. Grey indicates diagonal fields.

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**Table A8.**Statistical significance between window sizes for MNF algorithm. Green indicates statistically significant difference (p < 0.05; Bonferroni-corrected) for the RMSE metric, and orange indicates significant difference (p < 0.05; Bonferroni-corrected) for the cross-correlation metric. Grey indicates diagonal fields.

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**Table A9.**Statistical significance between window sizes for MDF algorithm. Green indicates statistically significant difference (p < 0.05; Bonferroni-corrected) for the RMSE metric, and orange indicates significant difference (p < 0.05; Bonferroni-corrected) for the cross-correlation metric. Grey indicates diagonal fields.

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**Figure A10.**RMSE (

**left**) and cross-correlation (

**right**) for ZC with different thresholds (Q multipliers of MAV at rest) and window widths (actual value of Q is shown/10).

**Figure A11.**RMSE (

**left**) and cross-correlation (

**right**) for WA with different thresholds (Q multipliers of MAV at rest) and window widths (actual value of Q is shown/10).

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**Figure 1.**Measurement setup. The participants were following the slowly changing sine wave (repetition frequency was 0.1 Hz) with a finger DoF by producing isometric contractions. The forces were acquired by the force measurement device and displayed in real-time on the screen. Fine-wire electrodes were taped at the skin entry point to prevent accidental pulls. To reduce induced noise, the preamplifiers were placed as close as possible to the entry points of the fine wires. In addition, the wires between the entry point and preamplifiers were taped to the skin. The metal frame of the force measurement device was grounded to reduce powerline noise.

**Figure 2.**Schematic representation of the signal pre-processing and testing of algorithms steps. For each iEMG channel (left side, blue signals), the MAV feature was extracted. In the following step, the MAV features were normalized for each movement based on only two first sine tracking periods (out of 10 repetitions). Hand and wrist forces (right side) were divided into positive (teal) and negative phases (red signals), after which individual phases were normalized (0–1) for each movement. To establish a correlation between iEMG channels (differential wires) and the phases of the force channels, a systematic evaluation of RMSE metrics between normalized MAV features and forces was conducted. The result of this process was a lookup table connecting iEMG channel, force channel (gauge), force phase, and movement (see the file “Fine-wire force-emg pairs” provided in the database paper [24]). The example signals are based on subject 4’s FPL muscle and thumb flexion/extension.

**Figure 3.**Measured force (blue—bottom row) and estimated forces using different algorithms. Each algorithm output (and the force signal) was normalized using the maximal amplitude within the first two repetitions as the scaling factor. The example signals are based on subject 15, EDC muscle and ring finger extension.

**Figure 4.**RMSE metric for all methods. These data comprise all subjects and all joint force estimates (except for the channels labeled as “poor”, see [24]).

**Figure 5.**Cross-correlation between the algorithms and joint forces (ground truth). These data comprise all subjects and all joint force estimates (except for the channels labeled as “poor”). * p < 0.05, ** p < 0.01.

**Figure 6.**RMSE (

**left**) and cross-correlation (

**right**) of MAV algorithm for different window sizes. The cases of significant differences (p < 0.05; Bonferroni-corrected) are marked with *.

**Figure 7.**RMSE (

**left**) and cross-correlation (

**right**) for firing rate with different thresholds and window widths.

**Figure 8.**RMSE (

**left**) and cross-correlation (

**right**) for SSC with different thresholds (Q multipliers of MAV at rest) and window widths (actual value of Q is shown/10). Finding: with threshold = 2 × MAV (rest) the window can be short (150–250 ms).

**Table 1.**Formulas used to compute algorithms that were evaluated. $N$ denotes window length, ${x}_{n}$ is the n-th iEMG sample within the current window, M is the number of frequency bands, ${P}_{n}$ is the spectral power of the n-th frequency band, ${f}_{n}$ is the central frequency of the n-th frequency band, and AP the number of detected action potentials over the threshold within the sliding window function.

Algorithm | Acronym | Formula | |
---|---|---|---|

1 | Mean absolute Value | MAV | $\mathrm{MAV}=\frac{1}{N}{\displaystyle {\displaystyle \sum}_{n=1}^{N}}\left|{x}_{n}\right|$ |

2 | Variance | Var | $\mathrm{Var}=\frac{1}{N-1}{\displaystyle {\displaystyle \sum}_{n=1}^{N}}{x}_{n}^{2}$ |

3 | Slope sign change | SSC | $\mathrm{SSC}={\displaystyle {\displaystyle \sum}_{n=2}^{N-1}}f\left[\left({x}_{n}-{x}_{n-1}\right)\times \left({x}_{n}-{x}_{n+1}\right)\right]$ $f\left(x\right)=\{\begin{array}{c}1,ifx\ge threshold\\ 0,otherwise\end{array}$ |

4 | Zero crossing | ZC | $\mathrm{ZC}={\displaystyle {\displaystyle \sum}_{n=2}^{N-1}}[sgn\left({x}_{n}\times {x}_{n+1}\right)\times f\left[{x}_{n}-{x}_{n+1}\right]]$ $f\left(x\right)=\{\begin{array}{l}1,ifx\ge threshold\\ 0,otherwise\end{array}$ |

5 | Willison amplitude | WA | $\mathrm{WA}={\displaystyle {\displaystyle \sum}_{n=1}^{N-1}}f\left[\left|{x}_{n}-{x}_{n+1}\right|\right]$ $f\left(x\right)=\{\begin{array}{l}1,ifx\ge threshold\\ 0,otherwise\end{array}$ |

6 | Waveform length | WL | $\mathrm{WL}={\displaystyle {\displaystyle \sum}_{n=1}^{N-1}}\left|{x}_{n}-{x}_{n+1}\right|$ |

7 | Envelope | ENV | $\mathrm{ENV}=\sqrt{\frac{1}{N}{\displaystyle {\displaystyle \sum}_{n=1}^{N}}{x}_{n}^{2}}$ |

8 | Total signal energy | Etot | $\mathrm{Etot}=\frac{1}{M-1}{\displaystyle {\displaystyle \sum}_{n=1}^{M-1}}{P}_{n}$ |

9 | Teager energy in time domain | Ttd | ${\mathrm{Ttd}}_{n}={x}_{n}^{2}-({x}_{n-1}*{x}_{n+1})$ + window-based moving average |

10 | Teager energy in frequency domain | Tf | $\mathrm{Tf}={\displaystyle {\displaystyle \sum}_{n=1}^{M-1}}{P}_{n}*{f}_{n}^{2}$ |

11 | Modified Teager energy | Tf_mod | $\mathrm{Tf}\_\mathrm{mod}={\displaystyle {\displaystyle \sum}_{n=1}^{M-1}}{P}_{n}*{f}_{n}$ |

12 | Mean of signal frequencies | MNF | $\mathrm{MNF}=\frac{{{\displaystyle \sum}}_{n=1}^{M}{P}_{n}*{f}_{n}}{{{\displaystyle \sum}}_{n=1}^{M}{P}_{n}}$ |

13 | Median of signal frequencies | MDF | ${\displaystyle \sum}_{n=1}^{\mathrm{MDF}}}{P}_{n}={\displaystyle {\displaystyle \sum}_{n=\mathrm{MDF}}^{M}}{P}_{n$ |

14 | Firing rate | FR | $\mathrm{FR}={\displaystyle {\displaystyle \sum}_{n=1}^{M}}AP$ |

Algorithm | Computational Complexity (O) | Window Size Range | Threshold Range | |
---|---|---|---|---|

1. | MAV | O(n) | (50–1050) ms | NA |

2. | Var | O(n) | (50–1050) ms | NA |

3. | SSC | O(n) | (50–550) ms | 0–4 × MAV (rest) |

4. | ZC | O(n) | (50–550) ms | 0–4 × MAV (rest) |

5. | WA | O(n) | (50–550) ms | 0–4 × MAV (rest) |

6. | WL | O(n) | (50–1050) ms | NA |

7. | Env | O(n) | (50–1050) ms | NA |

8. | Etot | O(n × log(n)) | (50–1050) ms | NA |

9. | Ttd | O(n) | (50–1050) ms | NA |

10. | Tf | O(n × log(n)) | (50–1050) ms | NA |

11. | Tf_mod | O(n × log(n)) | (50–1050) ms | NA |

12. | MNF | O(n × log(n)) | (50–1050) ms | NA |

13. | MDF | O(n × log(n)) | (50–1050) ms | NA |

14. | FR | O(n) | (50–1050) ms | 85th–99th quantile |

**Table 3.**Computational times for different algorithms across different platforms. Each column except for the last is normalized with respect to the quickest algorithm. The values presented in parenthesis are the result of using CMSIS-DSP functions which were possible only for some platforms. In the case of similar or longer processing times of the CMSIS-DSP compared with native functions, the parenthesized values are omitted. The bottom row contains information about the absolute processing time in the case of a 128-sample-wide window. The last column presents the mean of the individually normalized processing times of each algorithm. Values indicated by bold text are the ones with the best performance.

Algorithm | PC | Cortex-M7 | Cortex-M4 | Cortex-M0 | ATmega328 | Mean | |
---|---|---|---|---|---|---|---|

1. | MAV | 1.4 | 1 | 1 | 7.8 | 1.4 | 2.5 |

2. | Var | 1.5 | 1.5 (1) | 1.5 (1) | 1 | 1 | 1.2 |

3. | SSC | 3.3 | 1 | 1.3 | 11.3 | 3.2 | 4.0 |

4. | ZC | 2.9 | 1.5 | 1.7 | 7.9 | 2 | 3.2 |

5. | WA | 4.7 | 4 (1.5) | 3.3 (1.5) | 6.4 | 1.6 | 4.2 |

6. | WL | 1 | 3 (1.5) | 2.7 (1.5) | 10.8 | 2.7 | 4.8 |

7. | Env | 1.1 | 1.5 (0.5) | 1 (0.8) | 1.2 | 1 | 1.1 |

8. | Etot | 5.3 | 20 (7.5) | 170.5 (15.3) | 160.5 | 31 | 65.6 |

9. | Ttd | 1.1 | 1 | 1.5 | 23.4 | 4.3 | 6.3 |

10. | Tf | 5.4 | 20.5 (9.5) | 170.0 (18.2) | 162 | 31.5 | 66.3 |

11. | Tf_mod | 5.4 | 20 (9.5) | 170.0 (18) | 161.2 | 31.6 | 66.1 |

12. | MNF | 5.6 | 20.5 (9.5) | 170.0 (17.7) | 167.1 | 32.1 | 68.3 |

13. | MDF | 16.4 | 20.5 (9.5) | 170.2 (17.2) | 182.7 | 35.1 | 78.1 |

14. | FR | 41.2 | 3.5 | 3.0 | 6.2 | 1.4 | 11.1 |

1 = 6.9 µs | 1 = 2 µs | 1 = 6 µs | 1 = 0.56 ms | 1 = 1.52 ms |

**Table 4.**Statistical significance between algorithms for both RMSE and cross-correlation. Green indicates statistically significant difference (p < 0.05; Bonferroni-corrected) for the RMSE metric and orange indicates significant difference (p < 0.05; Bonferroni-corrected) for the cross-correlation metric. The cases of significant differences for both metrics are marked with * on the cross-correlation part of the table. Grey indicates diagonal fields.

MAV | Var | SSC | ZC | WA | WL | Env | Etot | Ttd | Tf | Tf_ mod | MNF | MDF | FR | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

MAV | * | * | * | * | ||||||||||

Var | * | * | * | |||||||||||

SSC | * | * | * | |||||||||||

ZC | * | * | * | |||||||||||

WA | * | * | * | |||||||||||

WL | * | * | * | * | ||||||||||

Env | * | * | * | |||||||||||

Etot | * | * | * | |||||||||||

Ttd | * | * | * | |||||||||||

Tf | * | * | * | |||||||||||

Tf_mod | * | * | * | |||||||||||

MNF | * | |||||||||||||

MDF | * | |||||||||||||

FR |

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**MDPI and ACS Style**

Malesevic, N.; Björkman, A.; Andersson, G.S.; Cipriani, C.; Antfolk, C.
Evaluation of Simple Algorithms for Proportional Control of Prosthetic Hands Using Intramuscular Electromyography. *Sensors* **2022**, *22*, 5054.
https://doi.org/10.3390/s22135054

**AMA Style**

Malesevic N, Björkman A, Andersson GS, Cipriani C, Antfolk C.
Evaluation of Simple Algorithms for Proportional Control of Prosthetic Hands Using Intramuscular Electromyography. *Sensors*. 2022; 22(13):5054.
https://doi.org/10.3390/s22135054

**Chicago/Turabian Style**

Malesevic, Nebojsa, Anders Björkman, Gert S. Andersson, Christian Cipriani, and Christian Antfolk.
2022. "Evaluation of Simple Algorithms for Proportional Control of Prosthetic Hands Using Intramuscular Electromyography" *Sensors* 22, no. 13: 5054.
https://doi.org/10.3390/s22135054