# Permutation Entropy for the Characterisation of Brain Activity Recorded with Magnetoencephalograms in Healthy Ageing

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Permutation Entropy

#### 2.2. Modified Permutation Entropy

#### 2.3. MEG Data Reduction and Analysis

#### 2.4. Statistical Analysis

## 3. Results

^{2}and adjusted R

^{2}value as well as having a p < 0.0001.

- The evolution of nmPE values for males and females by highlighting the manner in which permutation entropy changes with age in the brain for both genders.
- Differences in the “rates” of evolution for males and females.
- The estimated age when the highest nmPE values occur in the MEG signals.

## 4. Discussion

#### 4.1. Evaluation of Ideal Input Parameters

#### 4.2. Evaluation of Differences between nPE and nmPE

#### 4.3. Evaluation of Age and Gender Effect

#### 4.3.1. Age Effects

#### 4.3.2. Gender Effects

#### 4.3.3. Age and Gender

#### 4.4. Significance and Clinical Implications of the Results

#### 4.5. Limitations and Future Work

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Sensor-space representation of the layout of the location of the 148 SQUID channels in the neuromag used to record MEG signals. The five highlighted regions represent the sensor groupings used to define the different parts of the brain i.e., anterior (a), central (c), left lateral (ll), right lateral (rl) and posterior (p). These regions were also used for the statistical analyses [4].

**Figure 3.**The means and standard error values of the nPE (

**a**,

**c**) and nmPE (

**b**,

**d**) results in the 5 regions of the brain represented according to age and gender groups. Males are represented by graph the two graphs in (

**a,b**) while females are represented by the graphs in (

**c,d**).

**Figure 4.**The linear increase of the nmPE values, with age as an independent factor, for both genders is shown here, with males shown in blue and females in grey. The slopes for both models indicated a positive tendency of nmPE values in both gender groups. (

**a**) anterior (a); (

**b**) central (c); (

**c**) left lateral (ll); (

**d**) posterior (p); (

**e**) right lateral (rl).

Group | Age | Subjects | Males | Females |
---|---|---|---|---|

1 | <19 | 22 | 11 | 11 |

2 | 19–40 | 84 | 44 | 40 |

3 | 41–60 | 39 | 20 | 19 |

4 | 61–70 | 48 | 11 | 37 |

5 | >70 | 27 | 12 | 15 |

m | 2 | 3 | 4 | 5 | 6 | 7 |

m! | 2 | 6 | 24 | 120 | 720 | 5040 |

B(m) | 3 | 13 | 75 | 541 | 4683 | 47,293 |

B(m)/m! | 1.5 | 2.16 | 3.125 | 4.50 | 6.50 | 9.38 |

**Table 3.**The regional and gender polynomial regression fitting for the nmPE data, including the R

^{2}values, All fitted regressions in each region of the brain (Reg.) with model polynomial degree (Poly Deg.) had significance p < 0.0001 and R

^{2}> 0.85.

Reg. | Gender | Poly Deg. | ${\mathit{b}}_{0}$ | ${\mathit{b}}_{1}$ | ${\mathit{b}}_{2}$ | ${\mathit{b}}_{3}$ | ${\mathit{b}}_{4}$ | ${\mathit{R}}^{2}$ | Peak Age |
---|---|---|---|---|---|---|---|---|---|

a | Male | 4 | 0.6133 | 0.1367 | −0.077 | 0.0186 | −0.0016 | 1 | 63.15 |

Female | 4 | 0.7449 | −0.09028 | 0.05838 | −0.01462 | 0.00127 | 1 | 83.00 | |

c | Male | 2 | 0.6538 | 0.02364 | −0.003164 | 0 | 0 | 0.9873 | 54.98 |

Female | 4 | 0.7027 | −0.04919 | 0.03855 | −0.01015 | 0.00088 | 1 | 83.00 | |

ll | Male | 3 | 0.6607 | 0.0005792 | 0.00468 | −0.0008604 | 0 | 0.9503 | 54.05 |

Female | 3 | 0.6849 | −0.01831 | 0.008348 | −0.0009491 | 0 | 0.9992 | 64.63 | |

p | Male | 2 | 0.6754 | −0.02775 | 0.01707 | −0.0023 | 0 | 0.9982 | 58.53 |

Female | 3 | 0.6841 | −0.02263 | 0.01169 | −0.001394 | 0 | 0.9883 | 64.11 | |

rl | Male | 2 | 0.6493 | 0.0141 | −0.000193 | −0.0003022 | 0 | 0.973 | 55.00 |

Female | 3 | 0.6836 | −0.01962 | 0.008502 | −0.0008528 | 0 | 0.9996 | 87.24 |

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**MDPI and ACS Style**

Shumbayawonda, E.; Fernández, A.; Hughes, M.P.; Abásolo, D. Permutation Entropy for the Characterisation of Brain Activity Recorded with Magnetoencephalograms in Healthy Ageing. *Entropy* **2017**, *19*, 141.
https://doi.org/10.3390/e19040141

**AMA Style**

Shumbayawonda E, Fernández A, Hughes MP, Abásolo D. Permutation Entropy for the Characterisation of Brain Activity Recorded with Magnetoencephalograms in Healthy Ageing. *Entropy*. 2017; 19(4):141.
https://doi.org/10.3390/e19040141

**Chicago/Turabian Style**

Shumbayawonda, Elizabeth, Alberto Fernández, Michael Pycraft Hughes, and Daniel Abásolo. 2017. "Permutation Entropy for the Characterisation of Brain Activity Recorded with Magnetoencephalograms in Healthy Ageing" *Entropy* 19, no. 4: 141.
https://doi.org/10.3390/e19040141