# Comparison of Sneo-Based Neural Spike Detection Algorithms for Implantable Multi-Transistor Array Biosensors

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Figures of Merit

#### 2.2. Extracellular Recordings Datasets

^{3}of virtual brain tissue. The 7-honeycomb pattern is shown in Figure 1a. Thanks to the small size of the pixels and the reduced pixel spacing, the AP produced by a single neuron is captured by more than 1 pixel, albeit with different amplitudes (related to the neuron-pixel distance). This effect can be observed in the simulation of Figure 1b, which shows signals detected by two sensor pixels, for a neuron positioned on the west side of the sensor (in the absence of interference and noise). In practice, the detected APs are submerged in noise, as shown in Figure 1c, where the AP signal detected from pixel #1 is displayed, for SNR = 3 dB. Figure 2a,b shows the effect of different noise levels (SNR) on the same AP detected by pixel #1. At a lower SNR value, the AP shape is corrupted (see Figure 2a), making the detection procedure more difficult.

#### 2.3. SNEO Algorithm

#### 2.4. Thresholding

_{C}is the size of the sliding window used to estimate the mean, and C is the scale factor determined by the experiment with the ROC curves, as suggested in [33]. A schematic of the classical SNEO method is shown in Figure 4. Taking advantage of spatial correlation leads to a higher probability of detecting a true spike and thus improves performance. This is shown by the ROC curves in Figure 5.

#### 2.5. Proposed Approaches

_{i}, is normalized (divided by) the corresponding channel noise standard deviation σ

_{i}. Then, the mean of the normalized channel is calculated:

_{mean}is sent to the SNEO operator, as in the basic algorithm of Section 2.4. The noise variance of x

_{mean}is estimated and a spike is detected when:

#### 2.6. Noise Estimation Techniques

#### 2.6.1. Median

#### 2.6.2. Mean Absolute

_{n}is equal to the standard deviation of x, when x is a zero-mean signal with a Gaussian distribution. Considering the main operations required for this estimate, we name this technique absolute average, or AA.

#### 2.6.3. Winsorization

- An initial noise standard deviation σ′ is required for the clipping (we used AA for this initial estimate).
- σ′ is then used for the clipping of the absolute value of the signal as follows:$$x{}^{\prime}(n)=\{\begin{array}{ll}|x(n)|& if|x(n)|{\sigma}_{n}^{\prime}\\ {\sigma}_{n}^{\prime}& if|x(n)|\ge {\sigma}_{n}^{\prime}\end{array}$$
- from the clipped signal x′(n), the standard deviation is finally estimated as:$${\sigma}_{n}^{\u2033}=1.58\frac{1}{M}{\displaystyle \sum _{n}x{}^{\prime}(n)}$$

## 3. Results

#### 3.1. Performance Results

#### 3.2. Resource Consumption

^{2}, division 13N + 20N

^{2}, comparator 7N, and register 9N, where N is the number of bits.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) The 7-honeycomb sensor pattern (

**b**) signals detected by pixel #1 and pixel #6, for a neuron positioned on the west side of the sensor (in the absence of interference and noise). (

**c**) Synthetic neural recording with SNR = 3 dB, adding white noise on a noiseless synthetic recording.

**Figure 2.**Signal detected by pixel #1 for a neuron positioned on the west side of the sensor at different SNR levels, adding white noise on a noiseless synthetic recording. (

**a**) SNR = 0 dB and (

**b**) SNR = 6 dB.

**Figure 3.**The smoothed non-linear energy operator (SNEO) output at different resolution parameters considering a noiseless spike as input.

**Figure 4.**SNEO block diagram. Signals from the seven channels are filtered and averaged, to exploit the correlation between data captured by adjacent pixels. The memory block (MEM) stores the samples needed to compute the nonlinear energy operator (NEO). Then, threshold T is a scaled version of the mean of the filtered NEO.

**Figure 5.**(

**a**) receiver operating characteristic (ROC) curve using data from a single pixel of the multi transistor arrays (MTA), for SNR = 3 dB. (

**b**) ROC curve exploiting the correlation between signals coming from the 7 honeycomb pixels is exploited, for SNR = 3 dB. In both plots, true-positive and false-alarm rates are averaged on 10 datasets.

**Figure 6.**(

**a**) ROC curve at SNR = 0 dB, using the mean of the signals coming from the 7 honeycomb pixels. True-positive and false-alarm rates are averaged on 10 datasets. The scale factor C varies from 1 to 9. (

**b**) Accuracy curves for different values of scale factor C.

**Figure 7.**SNEO accuracy at k = 4 varying the action potentials (APs) firing rate from 10–200 Hz, scale factor C = 5.

**Figure 8.**Block diagram of the pre-norm technique. Each channel is normalized with its noise standard deviation estimate and then averaged and processed by SNEO. The comparison with the threshold C gives the detection result.

**Figure 9.**Performances of pre-norm algorithm varying the neuron firing rate from 10–200 Hz, k = 4 and C = 7.

**Figure 10.**Post-norm block diagram. The variance estimate block takes the averaged signal as input and estimates the noise variance.

**Figure 11.**Performance of post-norm algorithm varying the neurons firing rates from 10–200 Hz, k = 4 and C = 50.

**Figure 12.**Performances of pre-norm algorithm with the investigated noise estimation techniques. The neuron firing rate varies 10–200 Hz (C = 7).

**Figure 13.**Performances of post-norm algorithm with the investigated noise estimation techniques (C = 50).

10 Hz | 50 Hz | 100 Hz | 200 Hz | |
---|---|---|---|---|

TPR (%) | 61.02 | 43.25 | 30.31 | 22.65 |

FAR (%) | 1.14 | 0.00 | 0.00 | 0.00 |

Accuracy (%) | 60.01 | 43.24 | 30.30 | 22.64 |

**Table 2.**Detection performances of pre-norm algorithm at different firing rates at SNR = 0 dB (C = 7).

MAD | ||||

10 Hz | 50 Hz | 100 Hz | 200 Hz | |

TPR (%) | 62.38 | 62.05 | 60.28 | 59.58 |

FAR (%) | 1.33 | 0.24 | 0.1 | 0.08 |

Accuracy (%) | 61.74 | 61.94 | 60.24 | 59.49 |

AA | ||||

10 Hz | 50 Hz | 100 Hz | 200 Hz | |

TPR (%) | 62.63 | 62.09 | 59.81 | 58.98 |

FAR (%) | 1.78 | 0.28 | 0.11 | 0.08 |

Accuracy (%) | 61.91 | 61.85 | 59.77 | 58.95 |

WA | ||||

10 Hz | 50 Hz | 100 Hz | 200 Hz | |

TPR (%) | 63.63 | 63.15 | 62.48 | 60.64 |

FAR (%) | 1.02 | 0.31 | 0.12 | 0.08 |

Accuracy (%) | 62.76 | 62.81 | 62.24 | 60.61 |

**Table 3.**Detection performances of post-norm algorithm at different firing rates at SNR = 0 dB (C = 50).

MAD | ||||

10 Hz | 50 Hz | 100 Hz | 200 Hz | |

TPR (%) | 60.82 | 55.21 | 49.10 | 45.15 |

FAR (%) | 1.5 | 0.12 | 0.01 | 0.00 |

Accuracy (%) | 60.25 | 55.17 | 49.10 | 45.14 |

AA | ||||

10 Hz | 50 Hz | 100 Hz | 200 Hz | |

TPR (%) | 61.38 | 50.86 | 40.72 | 34.74 |

FAR (%) | 1.44 | 0.01 | 0.00 | 0.00 |

Accuracy (%) | 60.04 | 50.86 | 40.71 | 34.74 |

WA | ||||

10 Hz | 50 Hz | 100 Hz | 200 Hz | |

TPR (%) | 61.19 | 55.40 | 48.71 | 45.00 |

FAR (%) | 1.49 | 0.09 | 0.02 | 0.00 |

Accuracy (%) | 60.09 | 55.32 | 48.70 | 45.09 |

**Table 4.**Resources required by the hardware implementation of common blocks. The division by 7 in the mean block is implemented by a multiplication for the inverse of 7.

Filter | Mean | SNEO *^{2} | |
---|---|---|---|

Adder | 8 | 6 | 4k + 1 |

Multiplicator | 9 | 1 | 4k + 3 |

Divisor | 0 | 0 *^{1} | 0 |

Register | 19 | 8 | 10k + 3 |

Weighted Total | 211N + 54N^{2} | 102N + 6N^{2} | (186k + 46) N+ (96k + 36) N ^{2} |

^{1}the division of 7 is obtained by a multiplication for the inverse of 7. *

^{2}the SNEO block resources are given as a function of tuning parameter k.

**Table 5.**Resources required by the hardware implementation of noise estimate blocks. The length M of the window is assumed to be a power of 2, to avoid hardware division.

AA | WA | |
---|---|---|

Adder | 2 + 1 *^{1} | 4 + 2 *^{1} |

Multiplicator | 1 | 2 |

Comparator | 0 | 1 |

Divisor | 0 | 0 |

Register | 3 + 1 *^{1} | 6 + 2 *^{1} |

Other operations | (1 + 1) *^{2} | (2 + 3) *^{2} |

Weighted Total | 69N + 6N^{2} | 148N + 12N^{2} |

^{1}the adder is weighted as 2N as so its register. *

^{2}some methods require other additional logic such as the inverter and multiplexer evaluated, respectively, as N and 3N.

Standard SNEO | Pre-Norm | Post-Norm | |
---|---|---|---|

Adder | 1 + 1 *^{1} | 0 | 0 |

Multiplicator | 1 *^{1} | 0 | 2 *^{1} |

Comparator | 1 *^{1} | 1 | 1 *^{1} |

Divisor | 0 | 7 | 0 |

Register | 11 | 8 | 2 |

STD | 0 | AA or WA | AA or WA |

Weighted Total | 151N + 24N^{2} | 140N^{2} + 205N + STD | 32N + 48N^{2} + STD |

^{1}the adder, multiplier, and comparator are weighted as 3N, 4N, 2N considering the square operation for the noise variance.

Standard SNEO | Pre-Norm MAD | Pre-Norm WA | Pre-Norm AA | Post-Norm MAD | Post-Norm WA | Post-Norm AA | |
---|---|---|---|---|---|---|---|

#Logic Gates | 42288 | - | 52096 | 51080 | - | 44824 | 43808 |

TPR | 39.22% | 61.07% | 62.18% | 60.88% | 52.57% | 52.46% | 46.78% |

FAR | 0.27% | 0.51% | 0.57% | 0.56% | 0.42% | 0.40% | 0.36% |

Accuracy | 39.12% | 60.87% | 61.80% | 60.66% | 52.42% | 52.32% | 46.65% |

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**MDPI and ACS Style**

Saggese, G.; Tambaro, M.; Vallicelli, E.A.; Strollo, A.G.M.; Vassanelli, S.; Baschirotto, A.; Matteis, M.D.
Comparison of Sneo-Based Neural Spike Detection Algorithms for Implantable Multi-Transistor Array Biosensors. *Electronics* **2021**, *10*, 410.
https://doi.org/10.3390/electronics10040410

**AMA Style**

Saggese G, Tambaro M, Vallicelli EA, Strollo AGM, Vassanelli S, Baschirotto A, Matteis MD.
Comparison of Sneo-Based Neural Spike Detection Algorithms for Implantable Multi-Transistor Array Biosensors. *Electronics*. 2021; 10(4):410.
https://doi.org/10.3390/electronics10040410

**Chicago/Turabian Style**

Saggese, Gerardo, Mattia Tambaro, Elia A. Vallicelli, Antonio G. M. Strollo, Stefano Vassanelli, Andrea Baschirotto, and Marcello De Matteis.
2021. "Comparison of Sneo-Based Neural Spike Detection Algorithms for Implantable Multi-Transistor Array Biosensors" *Electronics* 10, no. 4: 410.
https://doi.org/10.3390/electronics10040410