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Application of the Bahill model to the electrooculographic records of patients with Ataxia type 2 M.Sc. Camilo Mora-Batista 1 , Dr.C Rafael Ávila-Ávila 2 , M.Sc. Camilo Velázquez-Rodríguez 3 , Dr.C Rosa Urquiza-Salgado 4 , Dr.C Efrén Vázquez-Silva 5

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Page 1: Application of the Bahill model to the electrooculographic ...tikhonov.fciencias.unam.mx/.../2018-mie-Camilo.pdf · Application of the Bahill model to the electrooculographic records

Application of the Bahill model to the

electrooculographic records of patients with

Ataxia type 2

M.Sc. Camilo Mora-Batista1, Dr.C Rafael Ávila-Ávila2, M.Sc. Camilo Velázquez-Rodríguez3,

Dr.C Rosa Urquiza-Salgado4, Dr.C Efrén Vázquez-Silva5

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Frequency Distributions of the SCAs

CANAD

JAPAN

South-AFRICA

BRAZIL

GERMANY

SPAINFRANCE

ITALY

Epidemiological data on SCAs are limited.Latin America is one of the most affectedregionworldwide.

Prevalencerate:5casesX 100.000inhabitants

A

Durr et al., 2010.

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7,96

34,92

48,30

274

229,7

274

113

72,55 127,80 72,55

283,85

149,61

131,55 1,68

715 273,94

Epidemiology of SCA2 Mutation in Cuba

Number of SCA2

patients and carriers

Prevalence Rate

Holguì

n

Velázquez-Pérez et al, Neurosc Letters 454 (2009) 157–160

2051 SCA2 patients and 163

families

8000 asymptomatic at risk

subjects

45 SCA2 Patients and 30

Preclinical Subjects are

diagnosed / years

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Introduction

Slowing of Horizontal Saccades

Control Subject Preclinical SubjectVelázquez-Pérez L, et al. Clin neurophys, 2009

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Introduction

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Introduction

𝑥1′ = 𝑥4 (1)

𝑥2′ =

𝐾𝑆𝐸2

𝐾𝐿𝑇 +𝐾𝑆𝐸 𝐵𝐴𝐺𝑥1 −

𝐾𝑆𝐸

𝐵𝐴𝐺𝑥2 +

𝐾𝑆𝐸

𝐾𝐿𝑇 +𝐾𝑆𝐸 𝐵𝐴𝐺 𝑥5

(2)

𝑥3′ =

𝐾𝑆𝐸2

𝐾𝐿𝑇 +𝐾𝑆𝐸 𝐵𝐴𝑁𝑇𝑥1 −

𝐾𝑆𝐸

𝐵𝐴𝑁𝑇𝑥3 −

𝐾𝑆𝐸

𝐾𝐿𝑇 + 𝐾𝑆𝐸 𝐵𝐴𝑁𝑇𝑥6

(3)

𝑥4′ =

−2𝐾𝑆𝐸 −𝐾𝑝

𝐽𝑥1 +

𝐾𝑆𝐸

𝐽 𝑥2 +

𝐾𝑆𝐸

𝐽 𝑥3 −

𝐵𝑝

𝐽 𝑥4 (4)

𝑥5′ =

𝑐𝑁𝐴𝐺 − 𝑥5

𝜏𝐴𝐺

(5)

𝑥6′ =

𝑐𝑁𝐴𝑁𝑇 − 𝑥6

𝜏𝐴𝑁𝑇

(6)

Bahill propose a new model in 1980, which involves the following six

differential equations [1]:

Page 7: Application of the Bahill model to the electrooculographic ...tikhonov.fciencias.unam.mx/.../2018-mie-Camilo.pdf · Application of the Bahill model to the electrooculographic records

Application of Independent Component

Analysis (ICA) to saccades

Figure 1. Part of a

electrooculographic

record of a patient with

SCA2.

Figure 2. Part of a

electrooculographic

record of a healthy

subject.

16. F. Rojas, R.

García, O.

Valenzuela, and B.

San Roman,

Classification of

spinocerebellar

ataxia type 2 based

on the pulse-step

saccadic model,"

International Journal

of Psychophysiology,

vol. 85, no. 3, p. 396,

Sep. 2012. [Online].

Available:

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Application of Independent Component

Analysis (ICA) to saccades

The signals of figure 1 and 2

ICA

Inputs signals to Bahill’s Model Pulse and Step = N_an, Nant

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Application of Independent

Component Analysis (ICA) to saccades

Figure 4. Pulse and step components of neural inputs

in the Bahill model.

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Results with Block Diagrams Simulink

Figure 5. Superior diagram of the model of the eye horizontal movement.

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Results with Block Diagrams Simulink

Figure 5. Superior diagram of the model of the eye horizontal movement.

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Results with Block Diagrams Simulink

Figure 8. Model describing the equations (11), (12),

(13) y (14).Figure 7. Filtering of the signal 𝑁_ 𝐴𝑁

described by the equation (16).

Figure 6. Filtering of the signal 𝑁𝐴𝐺

described by the equation (15).

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Results with Block Diagrams Simulink

Figure 9. Dependence of

the position with the time

Figure 11. Dependence of the velocity with the time Figure 12. Dependence of the acceleration with the time

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Comparisons

Figure 13. Comparison of a saccade

movement of a healthy person (blue line)

with the response of the model (red line).

Figure 14. Comparison of the profiles of

corresponding velocities.

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Comparisons

Figure 15. Comparison of a saccade of a sick

person (blue line) with the response of the model

(red line).

Figure 16. The profiles of corresponding

velocities.

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Conclusions

The developed model describes ocular movements but in a

very smooth way. In consequence, the model is in not full

correspondence with the movement observed in the practice

with data of patients of SCA2.

The analysis of the electrooculographic records of the patients

give the idea of the presence of chaotic movement in the data

provided by the measurements.

The carried out study lays the foundations for new alternatives

that include its possible correction or the proposal of other

models that describe these movements in patients of SCA2.

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Page 18: Application of the Bahill model to the electrooculographic ...tikhonov.fciencias.unam.mx/.../2018-mie-Camilo.pdf · Application of the Bahill model to the electrooculographic records

Application of the Bahill model to the

electrooculographic records of patients with

Ataxia type 2

M.Sc. Camilo Mora-Batista1, Dr.C Rafael Ávila-Ávila2, M.Sc. Camilo Velázquez-Rodríguez3,

Dr.C Rosa Urquiza-Salgado4, Dr.C Efrén Vázquez-Silva5