Two-dimensional Signal Analysis Reduced from Three-dimensional - - PDF document

Two-dimensional Signal Analysis Reduced from Three-dimensional Nystagmus Eye Movements

Martti Juhola1, Heikki Aalto2 and Timo Hirvonen2 1Computer Science, School of Information Sciences, University of Tampere, Tampere, Finland 2Department of Otorhinolaryngology, Helsinki University Central Hospital, Helsinki, Finland

Introduction

There are three semicircular canals in the inner ear. They are

located almost perpendicularly to each other. Disorders in their function cause balance problems such as vertigo and dizziness.

Semicircular canals

nystagmus beat amplitude [°] slow phase fast time [s] phase Nystagmus is a repeated, bias, ”saw-tooth” eye movement. It is reflexive, for example stimulated by injecting cool or warm air or water (37±7 °C) to a subject’s ear canal. For otoneurological patients nystagmus may spontaneously be induced by a disorder

• f a semicircular canal located in the inner ear.

Video-oculography (VOG) with small videocameras directed at each eye has become a promising way to measure three-dimensional (3D) eye movements. It includes 1D horizontal, vertical and torsional (rotational) components. Measurements are gaze angles [°] in three separate 1D

• signals. To consider nystagmus, we computed angular

velocity curves (approximated first derivatives) from horizontal, vertical and torsional signals. The average angular velocity (spv) of the slow phase of each nystagmus beat was computed with linear regression. The mean of the spv values of a signal was used.

The computation of slow phase velocities in 3D

right horizontal rotation axis

left torsional axis

clockwise counterclockwise up

vertical axis

down

The computational (VOG) and anatomical coordinate systems were approximately the same, the head similarly positioned for each measurement. (A subject’s head is rotated 18° down round the vertical axis to set the horizontal semicircular canals equal to the gravity coordinate space. Thus the ”anatomic” space is similar to that of video-oculography.)

Motivation: Why to reduce from 3D to 2D?

(0) Earlier eye movement measurement devices only included 2D: horizontal and vertical directions. Nowadays 3D also includes torsional direction.

• However, frequently there are also such
• toneurological patients for whom one of three

directions in nystagmus is virtually absent.

• It is then reasonable to model two directions only, one

from pairs: horizontal-vertical, vertical-torsional, or horizontal-torsional.

• Furthermore, mostly vertical direction is absent, not

torsional given by 3D.

all directions effective:

3D: signal of the left eye used not Including noisy spikes Spontaneous nystagmus of 30 s: The blue curves are the horizontal signals, the green curves are the vertical signals, and the red curves (with noisy spikes for the right eye) are the torsional signals. A nystagmus beat includes a slow phase (down in the figure) followed by the fast phase in the opposite direction.

• nly horizontal and

torsional directions effective:

2D: signal of the right eye used Including slightly greater amplitudes 3D signals represented as three 1D signals for both eyes of a patient having nystagmus. The lowest (blue) curve of each subplot is the horizontal signal, the middle curves (red) are the torsional signals, and the uppermost (green) curves are the vertical signals to be left

• ut. The duration of the signals was 30 s.

random steps or peaks nystagmus of small amplitude

We also studied a hypothesis called J.R. Ewald’s law

• riginally from 1892: the trajectory of nystagmus

induced by a semicircular canal ought to reflect the anatomic orientation of that semicircular canal. This had remained a hypothesis since, e.g., the positions of the semicircular canals of living subjects had not obviously been studied earlier than around 10 years ago. Nystagmus induced by a horizontal semicircular canal is mostly horizontal. Nystagmus from anterior or posterior semicircular canals is assumed to be mixed torsional and vertical, since these canals are oriented diagonally.

Measurement

Recordings were peformed with small videocameras embedded in a mask (3D VOG Video-Oculography, Sensomotoric Instruments, Berlin, Germany). The subject was not allowed to move his head while recording. Sampling frequency was 50 Hz.

Calibration

Before a 30 s recording, the calibration was made by asking a subject to alternately look at nine points located symmetrically on the wall. After the calibration the amplitude resolution is better (<) than 0.5°, in principle <0.05°.

The eyes were covered and a subject was in a dim room, since spontaneous nystagmus (if any) of a patient then appears as its largest. Every measurement included 30 s (1500 samples).

Computation

(1) Using linear regression (its slope) compute angular velocity curves for all three 1D signals of each eye. (2) The better from the three 1D signals of two eyes were taken based on less noise and higher amplitudes estimated from the amplitude distributions of the signal samples. (3) Compute the directions of the slow phases of a nystagmus 1D signal by counting whether the majority of velocity values are either positive or negative. We obtain the directions: horizontal right or left, vertical up or down, and torsional clockwise or counterclockwise.

(4) Nystagmus beats are detected according to velocity. A minimum or maximum is found when absolute velocity values drop below 10º/s. (5) Noise peaks or non-nystagmic phenomena are left out by detecting them on the basis of rules of upper bounds for maximum velocities, amplitudes and durations of slow and fast phases of nystagmus. (6) Average angular velocities of all accepted nystagmus beats are computed as slopes of linear regression. (7) On the basis of the velocities, the direction including the smallest average velocity is removed from the horizontal, vertical and torsional directions. Alternatively, this choice can also be made by the user.

(8) A unit circle is formed so that from the 3D unit sphere of three directions the component of the removed direction is

• deleted. Six normal vectors (from Della Santina et al.)

corresponding to three semicircular canals in each ear are projected from the unit sphere onto the unit circle. The accepted unit velocity vectors are mapped as dots on the circle and their mean vector is mapped as a line from the

• rigin through the circle.

Della Santina C.C., Potyagaylo V., Migliaccio A.A., Minor L.B., Carey J.P., Orientation of human semicircular canals measured by three-dimensional multiplanar CT reconstruction, Journal of the Association for Research in Otolaryngology 6 (2005): 191– 206.

(9) Results: The angles from the normal vectors to the preceding mean vector is computed. The closest normal vector predicts the probable origin* (semicircular canal)

• f dysfunction. Average velocities of the two directions

(vector components) and the number of the accepted nystagmus beats are computed (Table 1).

* Usually, the cause is the opposite canal, e.g., if the closest is RH, the cause is in LH

(see the next figure). Rarely, it is the same canal. The former occurs when the

• pposite canal is dead, the latter if the closest canal is overexcited.

The unit circle model for nystagmus: positive horizontal axis (to the left) corresponds to clockwise torsional eye movements (negative is for counterclockwise) and positive vertical axis corresponds to horizontal eye movements to the right (negative to the left). Values equal slow phase velocity as two-dimensional unit vectors. Semicircular canals are by their normal vectors. The angles were computed from the normals to the mean vector (near normal RH) of the dots of the velocity unit vectors. (L=left and R=right inner ear; A=anterior, P=posterior and H=horizontal semicircular canal).

[°/s] [°/s]

Recording and analysing signals of 30 patients we obtained the following results. Such patients were selected that were known to have vertical nystagmus virtually absent or very slight. Table 1. Means and standard deviations of the slow phases of the accepted nystagmus beats from 30 signals after discarding the vertical direction. Average number of nystagmus beats per signal Angle from mean velocity vector to closest normal [°] Horizontal velocity [°/s] Torsional velocity [°/s] 35.9±15.5 9.5±8.6 6.7±5.4 4.8±5.8

Results

Conclusion

The results support Ewald´s law. The method can be used as a means to reveal unilateral disorders of semicircular canals. In unilateral weakness, the normal side drives the nystagmus, but in unilateral stimulation, the stimulated (overexited) side determines the vector orientation.