application of the bahill model to the electrooculographic...
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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
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.
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
Introduction
Slowing of Horizontal Saccades
Control Subject Preclinical SubjectVelázquez-Pérez L, et al. Clin neurophys, 2009
Introduction
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]:
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:
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
Application of Independent
Component Analysis (ICA) to saccades
Figure 4. Pulse and step components of neural inputs
in the Bahill model.
Results with Block Diagrams Simulink
Figure 5. Superior diagram of the model of the eye horizontal movement.
Results with Block Diagrams Simulink
Figure 5. Superior diagram of the model of the eye horizontal movement.
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).
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
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.
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.
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.
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