# Non-Linear Dynamical Analysis of Resting Tremor for Demand-Driven Deep Brain Stimulation

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## Abstract

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## 1. Introduction

## 2. Data Preparation

#### 2.1. Dataset

#### 2.2. Signal Preprocessing

#### 2.3. Data Labelling

## 3. Recurrence Networks

#### 3.1. Embedding Delay: $\tau $

#### 3.2. Embedding Dimension: m

#### 3.3. $\epsilon $-Recurrence Network

## 4. Network Measures

#### 4.1. Global Clustering Coefficient

#### 4.2. Transitivity Dimension

#### 4.3. Assortativity

## 5. Moving Window $\epsilon $-Recurrence Network Analysis

- The trends of the different measures were quite similar since all of them exhibited a shift in their dynamics near the beginning of the TO episode and before the T episode. All measures detected the tremor efficiently before its appearance and therefore before the patient showed any physical symptoms. This fact made these measures good candidates for their application in a demand-driven DBS system.
- During tremor episodes, T and A displayed a growing trend, while C exhibited the behaviour of shifting its dynamics more abruptly. The behaviour during NT and TO was similar across all the measures.

## 6. System

#### 6.1. Start and Stop Stimulation Decision

#### 6.2. System Model

#### 6.3. System Performance

**Shut down the stimulation:**

**Start up the stimulation:**

- A peak above 3$\sigma $ was detected within the TO section of all subjects (specificity = 100%), indicating a clear pattern of sudden non-linearity increase in the neuronal signal of the subthalamic nucleus, just before the patient experienced physical tremor. This peak can be used as a trigger for the decision to begin stimulation by the system. It is a simple and effective system.Notice that despite detecting a peak above 3$\sigma $ in all recordings, a conservative threshold was set at 2$\sigma $ (statistical significance of the peak p< 0.05) in order to ensure that the peak triggered the start of stimulation in unseen futures cases, which might perhaps present a less significant peak.
- An SVM system was trained to distinguish NT samples from TO, obtaining worse results than in the previous usage scenario. This was the expected outcome since the classes to be classified were more similar between them. Remember in this regard that TO is a transition state between NT and TO. Results are presented in Table 2. As can be seen, the specificity did not reach 100% in any of the patients, obtaining higher values of FPR the previous use case. With the addition that in this case, the importance of correctly classifying a sample was more critical than in the previous usage case. If the window being evaluated was incorrectly classified as NT, being a TO sample, the system would continue in standby, not starting the stimulation. As soon as the patient left the TO state and entered the T state, he or she would begin to tremble (as represented in Figure 3a1). It is crucial that the system does not leave the patient needing it without stimulation. This is a red line for the system.

## 7. Related Work

- Adaptive DBS: These methods propose a real-time adaptation of HFS parameters (the frequency, duration and amplitude of a square-wave pulse train), which are currently determined by a clinician during the visit of the patient to the hospital every 3–12 months.
- Demand-driven DBS: These strategies are based on detecting the fingerprints of pathological states and triggering the HFS as a result.In our opinion, the combination of adaptive and demand-driven DBS approximations would provide a complete solution for an autonomous and intelligent DBS system, able to adapt the stimulation parameters by itself and also capable of start-up and shut-down by itself as required by the changing dynamics of the STN in real time.
- Delayed DBS: These strategies consist of providing stimulation in a time-delayed manner, with the added possibility of doing it in different areas using several electrodes. The objective is to concentrate a beam of out-of-phase sinusoidal signals in the target area.
- DBS based on proportional, derivative and integral feedback: These methods propose to design a stimulation signal following the LFP signal sensed in real time. This signal can be designed proportionally to the LFP activity or regarding integral or derivative LFP.
- Optimal control strategies: These techniques base the control of the stimulation policy on finding the minimum of a defined cost function. This cost function would be adjusted to the DBS objectives, such as beta-band oscillation reduction or neuronal desynchronization.

## 8. Discussion

#### 8.1. Preferred Network Measures

#### 8.2. Setting of the System Parameters

#### 8.3. Towards Future DBS Systems

^{®}PC+S neurostimulator, which is only available for research so far, but that points the way to future neurostimulation systems [40].

## 9. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Optimal value of the parameters for an exemplary window. Left: optimal delay $\tau $ calculated with auto-mutual information. The dashed line determines the first local minimum $(\tau =6)$. Right: the minimum embedding m employing the False Nearest Neighbourhood (FNN) method. At $m=4$, the FNN statistic is zero.

**Figure 2.**Moving window $\epsilon $-recurrence network analysis showing the median moving average of clustering, transitivity and assortativity, before, during and after the start of the tremor, in that order. The left and right black vertical lines represent the transition from Non-Tremorous resting state (NT) to Tremor Onset (TO) and from TO to Tremor state (T), respectively. The horizontal lines represent the $\pm 2$ and $\pm 3$ standard deviation thresholds for statistical significance.

**Figure 3.**This figure represents the four cases that can take place in our system when turning on/off the stimulation. (

**a**) The Implantable Medical Device (IMD) is not stimulating, and a TO sample arrives (the ground-truth of the sample is therefore TO). If the system fails to classify that sample, the stimulation will remain OFF, and the patient will begin to tremble after a few seconds (Scenario a1 in the figure). If on the contrary, the system correctly identifies the sample as TO, it will order to start the stimulation (Scenario a2 in the figure). (

**b**) If while the system is stimulating, an NT sample arrives: (the ground-truth of the sample is therefore NT): If the system correctly detects this new clinical state, it will turn OFF the stimulation, as it is no longer necessary (Scenario b1 in the figure), while if the detection fails, the system will continue to stimulate (Scenario b1 in the figure). However, in this case, contrary to what happens in Scenario a1, this will have no physical effects on the patient.

**Figure 5.**Moving window $\epsilon $-recurrence network analysis showing the median moving average of transitivity, before, during and after the start of the tremor. The temporal profile of the measure is shown for different values of $m=4,6,8$ and 10. The vertical line represent the time at which the patients transited from NT to TO (left) and from TO to T (right). The horizontal lines represent the $\pm 2$ and $\pm 3$ standard deviations, the thresholds for statistical significance.

File | ACC | Sensitivity | Specificity | FPR | FNR |
---|---|---|---|---|---|

1 | 84.8 | 89.83 | 79.24 | 20.75 | 10.17 |

2 | 98.4 | 97.44 | 100 | 0 | 2.56 |

3 | 94.3 | 95.20 | 90.8 | 9.2 | 4.79 |

4 | 90.3 | 87.13 | 92.05 | 7.94 | 12.86 |

File | ACC | Sensitivity | Specificity | FPR | FNR |
---|---|---|---|---|---|

1 | 69.6 | 74.54 | 50 | 50 | 25.45 |

2 | 77.1 | 60 | 81.57 | 18.42 | 40 |

3 | 86.7 | 80 | 92.06 | 7.93 | 20 |

4 | 82.1 | 81.39 | 84 | 16 | 18.6 |

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**MDPI and ACS Style**

Camara, C.; Subramaniyam, N.P.; Warwick, K.; Parkkonen, L.; Aziz, T.; Pereda, E.
Non-Linear Dynamical Analysis of Resting Tremor for Demand-Driven Deep Brain Stimulation. *Sensors* **2019**, *19*, 2507.
https://doi.org/10.3390/s19112507

**AMA Style**

Camara C, Subramaniyam NP, Warwick K, Parkkonen L, Aziz T, Pereda E.
Non-Linear Dynamical Analysis of Resting Tremor for Demand-Driven Deep Brain Stimulation. *Sensors*. 2019; 19(11):2507.
https://doi.org/10.3390/s19112507

**Chicago/Turabian Style**

Camara, Carmen, Narayan P. Subramaniyam, Kevin Warwick, Lauri Parkkonen, Tipu Aziz, and Ernesto Pereda.
2019. "Non-Linear Dynamical Analysis of Resting Tremor for Demand-Driven Deep Brain Stimulation" *Sensors* 19, no. 11: 2507.
https://doi.org/10.3390/s19112507