Eye movements, particularly vergence movements, are extremely important for the visual exploration of space in depth, both from a kinetic point of view for precision of fixing on the fovea and from a static point of view, for stability of fixation limited to the macular area.
For a long time researchers believed that the vergence dynamic worked using a closed loop system (feedback control). The vergence oculomotor system compared the current position of eye with the desired visual stimulus and would move the eyes until the eyes were adjusted to align on the target. The input signal for this system is vergence disparity required to fix a target that activates the vergence generator, by means of sensorial processing. Effective vergence of the eyes is then subtracted from the required vergence until the difference between the two reaches nil. The vergence model or Dual Mode Theory put forward by John Semmlow in 1984 (Fig.1) now considers there to be double control of the motor command.

Fig. 1: Dual-Mode Theory (Semmlow and Hung - 1986).

This model includes an initial rapid vergence phase or "Transient component" causing the impulse needed to move each eye quickly, despite the viscosity of the eyeball. This initial phase works in an open loop also called preprogrammed control, i.e. it does not depend solely on visual information.
It is then followed by a slower or "Sustained component" phase, which brings the 2 eyes to their final optimal position. This second, visually guided phase, operates in a closed loop.
The combination of speed and precision reflects both the difficulty of the motor task and the complexity of the neuron control systems. This model has also been confirmed by neurophysiological data that shows the existence of phasic cells (Transient Component) and tonic cells (Sustained Component) in the brain areas responsible for vergence movements ^{[3, 4]}. (Fig 1)

This is a very interesting approach since it translates the visual system‘s capacity to partially pre-programmed control in ocular vergence. We believe that this property could play a part in compensation for the optical disparities caused by a new visual environment, notably when adapting to new prescription lenses. Based on this hypothesis, we have been working in collaboration with John Semmlow‘s and Tara Alvarez‘ teams at the New Jersey Institute of Technology (Newark, NJ) since 2003, to study the dynamic characteristics of vergence movements, particularly during modification of the visual task.

ANALYSIS OF THE VERGENCE RESPONSE

Type of movement

In all our experiments, we used stimulation in the mid-sagittal plane only in order to observe pure or symmetric vergence movements compared to asymmetric vergence movements where the eyes move between targets positioned differently, both in terms of direction and distance, with such movements requiring an association of vergence movements and eye saccades.

Experimental conditions

To observe pure vergence movements, stimulations must be used only in the mid-sagittal plane. To do this we used a haploscopic device fitted with two video screens, which project the image for the right eye and the image for the left eye (Fig. 2).

Fig. 2: Device and experimental conditions.

Recording of ocular movements is done using an Skalar (Skalar Iris/model) limbus tracking sensor with 0.1° resolution. Data are acquired at a frequency of 200Hz. This system can record only horizontrol or vertical movements. Last year, the system was improved by integrating a video based system ISCAN which tracks the pupil and corneal reflection at 240Hz and can measure horizontal and vertical movements simultaneously as well as pupil diameter.
Eye movements are recorded and registered separately. The head movement is stabilized using a head and chin rest assembly to reduce any influence from the vestibular system. The target is a green LED to stimulate accommodative vergence and disparity vergence. The target is presented in different positions (8°, 12°, 16° and 20°) based on which vergence movements are recorded in 4° stages. (Fig 2) All measurements were made on a control sample of 8 subjects aged 18 to 35 years.

Identification and quantification of vergence movement components

Independent component analysis (ICA) is a method of data analysis involving statistics, neuron networks and signal processing. Historically it has frequently been used as a method for separating sources which are occurring simultaneously but are independent. The classic illustration is the cocktail party problem. At a cocktail party P microphones are set out in a room where N people are talking in groups. Each microphone records the superposition of the conversations of the people around it, and the problem consists of finding the voice of each individual after "removal" of the other voices, seen as interference. There must be as many microphones are there are independent sources.

ICA is used to solve this problem by considering simply that people talking at a given moment in time have "independent" conversations ^[6]. Within the context of our study, this method was used to isolate and then quantify the motor components of the "Transient" and "Sustained" vergence response (Fig.3) on which the concept of the Dual mode theory vergence model relies ^[2].

Fig. 3: Illustration of the Validation of Independent Component Analysis (ICA) in Vergence Responses.

The vergence response shown, in Figure 3 (left side), is broken down into principle components (right side). The known model sources are shown in blue while the sources from ICA are shown in red. The model simulations and known inputs are very similar validating that ICA is appropriate to dissect vergence to study transient component (TC) and sustained component (SC).
To quantify the dynamic performance of vergence, we relied on a quantitative parameter calculated based on the recording of eye movements. This performance criterion or "Peak Velocity" is calculated
based on maximum speed, according to the amplitude of the movement, for each of the components.

CHARACTERISTICS OBSERVED

Differences linked to type of movement

An observation of pure vergence movements shows differences depending on the type of movement. Indeed, vergence dynamics are different for convergence and divergence (Fig.4).

Fig. 4: Example of a recording of dynamic responses for convergence and divergence (4°).

Also, the convergence dynamic would appear to be independent of the initial position of the stimulus[5] whereas divergence movements depend on this position, that is to say, the closer the target the quicker the response. These results are important since they infer divergence is not merely relaxation of convergence. Results of neurological studies have shown, moreover, that the control system is different, due to the identification of distinct nerve cells ^[1].

Differences between individuals

An analysis of the dynamic characteristics of vergence movements also shows differences between individuals. The speed and intensity of the movement vary from one person to another for a given disparity, as shown in Figure 5. The peak of the transient component (blue responses in Figure 5) can vary substantially between individuals. 

Fig. 5: Illustration of differences between four individuals in terms of dynamic performance.

A study of the dynamic components in vergence response shows us that there are different dynamic profiles for a given task. What happens when the visual task is changed or repeated? What is the capacity of the oculomotor system to adapt to a new visual environment?

ADAPTATIVE MODIFICATIONS

Introduction of a new phase to the initial experimental protocol

With the aim of defining the impact of an adaptive modification to the dynamic characteristics of vergence, we introduced a new phase to the initial experimental protocol to study how much a person could change his or her vergence Peak Velocity during an oculomotor learning experiment.
After the control stage, the baseline phase in which we recorded a only 4° steps, the individual began the modification phase. During the modification phase, the individual start saw 4 deg steps randomly intermixed with double steps (2 steps of 4° each with a 200 msec delay between for a total disparity stimulus of 8°). There were five times as many double steps to single step. The experiment sought to determine how the double steps influenced the Peak Velocity of the single steps.

RESULTS

Results show that the dynamic changes during the new phase, particularly for the Transient component. This modification would appear to be specific to each individual, as shown from the examples in Figure 6.

 
Fig. 6: Illustration of adaptation of the Transient component (red) in 3 individuals.

Also, modification of the Transient component would appear to be linked to its initial baseline intensity (peak of the transient component).
In fact the correlation analysis demonstrates the relation between the initial or "baseline" performance of this component and the modifications observed (Fig.7). Graph of the Transient component modification depending on its baseline.

Fig. 7: Graph of the Transient component modification depending on its baseline.

It is observed that, the higher the reference value or "baseline", the more efficient the adaptation. On the other hand, when this component is very weak, or even nil at the outset, adaptation is almost non-existent.

CONCLUSION - PROSPECTS

The study of vergence dynamics enabled the team to characterise the Dual model put forward by John Semmlow and to demonstrate the dynamic properties specific to the type of movement (convergence/divergence). We also observed that these properties can vary depending on nearness.
Differences appeared between individuals, particularly in terms of the Transient component, whose performance index (Peak Velocity) would appear to be linked to the system‘s ability to adapt to the modifications included in the task proposed. This ability to adapt would apparently enable individuals to pre-programme the Transient component.
We believe that this component could predict an individual‘s ability to adapt to a new visual environment, such as that generated by wearing new prescription lenses. Our work continues, studying the link between the dynamic performance measured in presbyopics and adaptation to progressive lenses.