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Journal of Medical and Biological Engineering, 30(1): 1-15 1 Review: Behaviors, Models, and Clinical Applications of Vergence Eye Movements Yung-Fu Chen1 You-Yun Lee2 John L. Semmlow3 Tainsong Chen2 Tara L. Alvarez4,* 1 Department of Health Services Administration, China Medical University, Taichung 404, Taiwan, ROC 2 Institute of Biomedical Engineering, National Cheng Kung University, Tainan 701, Taiwan, ROC 3 Department of Biomedical Engineering, Rutgers University, Piscataway, NJ 08854, USA 4 Department of Biomedical Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA Received 19 Nov 2009; Accepted 1 Feb 2010 Abstract It is known that vergence allows the brain to perceive depth. Although convergence (inward turning of the eyes) and divergence (outward turning of the eyes) movements utilize the same extraocular muscles and visual field, emerging evidence supports that they are different neural control systems. Both adapt (the system’s ability to alter its dynamics) and are correlated to phoria (the resting state of the visual system); however the behavior is different depending upon the system. This review discusses the classical and new tools used to analyze vergence movements, the neural control of each system, and its interaction with version. A review of the current models shows that new models are needed to explain these recent behavior studies which will facilitate the understanding of vergence dysfunctions. Eye movement from far to near (convergent movement) or from near to far (divergent movement) are performed quickly and accurately. The convergence and divergence movements appear to be mediated by different neural control processes. For example, while divergence can be faster at near, convergence can be faster at far. The vergence resting level adapts to sustained stimuli and this adaptation can influence the dynamics of both systems. Movement dynamics can also adapt as repetitive movements and alter the peak velocity of each system. However, typical vergence movements in daily living rarely consist of pure symmetrical vergence movements but exhibit a combination of version and vergence movements. Reviewing recent models shows that none adequately describe the influence of phoria, adaptation, the differences between convergence and divergence control and its interaction with version. The development of a new model is needed to describe the neural control of convergence and divergence taking into account the influence of adaptation, phoria and its interaction with the version system. Once this model is developed, it can yield more insight into abnormalities of the vergence system such as convergence and divergence insufficiencies or excess which can develop from numerous neurological dysfunctions. Keywords: Vergence, Convergence, Divergence, Phoria, Adaptation model, Saccade, Convergence insufficiency 1. Introduction The oculomotor system is the simplest motor unit for humans, yet it can move the eyes to attain visual information with astonishing speed and accuracy. These two properties have been modeled using vastly different control strategies [1]. The human eye has only three pairs of ocular muscles to move the eyeballs to various angular positions and is much less * Corresponding author: Tara L. Alvarez Tel: +1-973-596-5272; Fax: +1-973-596-5222 E-mail: [email protected] complicated than other motor units. There are several significant advantages of studying eye movement control to investigate the neural control of the brain [1]. First of all, it lacks the mechanism of monosynaptic stretch reflexes which are generally found in other motor units. Secondly, different functions and anatomical substrates can be identified for various types of eye movements. Thirdly, the pathology of the affected areas can generally be distinguished and traced for abnormal eye movements. Fourth, eye movements are restricted to rotation in three planes, which enables the possibility of precise recording for quantitative analysis. Finally, eye movements can easily be performed without head 2 J. Med. Biol. Eng., Vol. 30. No. 1 2010 motion lending itself as an ideal motor system to study using functional imaging. Hence, quantitative analysis of eye movements has been extensively applied in probing the function of various brain areas and in diagnosing brain abnormalities caused by injury or degeneration. Throughout the day, saccades and vergence components are generally intermixed in oculomotor movements. Saccades are frequently found in vergence eye movements even under pure symmetrical vergence stimuli. The movements of the eyes are controlled by three pairs of extraocular muscles: the medial and lateral recti, superior and inferior recti, and superior and inferior oblique muscles. The motor neurons that innervate the extraocular muscles are found in the III (oculomotor), IV (trochlear) and VI (abducens) cranial nerve nuclei. In order to acquire, fixate, and track a visual stimulus, eye movements are generated voluntarily or involuntarily to keep the visual stimulus in focus and on the fovea. According to whether two eyes rotate in the same or opposing directions, eye movements can be categorized as versional or vergent. The eyes rotate conjugatively for the former and disconjugatively for the latter. Version can be further divided into gaze-holding and gaze-shifting eye movements [2]. Three types of gaze-holding eye movements are the vestibulo-ocular reflex (VOR), optokinetic nystagmus (OKN), and visual fixation. Gaze-shifting eye movements are classified as saccades and smooth pursuits. Properties and functions of various types of eye movements are briefly reviewed below. For more detailed information, please refer to [1-3]. The VOR can be evoked when the head moves or rotates. It is a reflexive eye movement to keep the image of the target on the fovea by moving the eyes in the opposite direction to head movement [3]. A visual stimulus is not necessary to elicit VOR, hence it functions in total darkness or when the eyes are closed. OKN is a rapid and small movement of the eyes which is activated to stabilize images on the retina when tracking a moving target. The eyes can see moving images clearly until they are out of the visual field by generating OKN [3]. Fixation occurs when the eyes look at a stationary target, which facilitates maintaining the object of interest with zero velocity on the fovea. Hence, a clear image of the target is perceived. Fixation was believed to be a pursuit eye movement for a stationary target. However, recent research indicates that the neural control mechanism is different between fixation and smooth pursuit. Three other small eye movements occur during fixation: drift, tremor and microsaccades [2,3]. Saccadic movements are conjugate (version) where the eyes move in tandem. These movements are commonly done when reading a book. It is the fastest type of eye movements with velocities reaching up to 700 deg/sec [1,3]. When tracking a continuous moving target, the eyes perform smooth pursuit eye movements to keep the image of the target located on the fovea [1]. Vergence, in contrast, is a disconjugative eye movement which enables depth perception by using the medial and lateral recti muscles to rotate the eyes inward (convergence) or outward (divergence). For example, it is the eye movement tracking system that a baseball batter uses when tracking a fastball. Vergence has four major inputs which include disparity, accommodative, proximal, and tonic vergence [3]. Disparity is the retinal difference between where a target is projected onto the retinal and the fovea. Accommodative vergence is driven by a blur response of the image because of the change in focal length when looking at a visual target located at difference distances of depth from the person. This phenomenon is manifested by observing the nasalward movement of a covered eye with the other eye looking at an object moving from far to near. Proximal vergence is elicited by the change in vergence angle caused by the perceived nearness of an object. In the absence of the above three inputs to the vergence system, tonic vergence is the resting level of the vergence system in the absence of all visual stimulation. Tonic vergence will be a convergent position based upon midbrain stimulation to the vergence system. Phoria is similar to tonic vergence but with phoria one eye has a visual stimulus. Dissociated heterophoria or simply ‘phoria’ is the steady state position of one eye that has no visual stimulus such as when it is occluded while the other eye is fixated on a target located along midline. The viewing eye can be fixated on a target typically located at near (40 cm) or at far (6 m). The occluded eye may maintain its position, rotate nasally, or rotate temporally; these three possible positions are termed orthophoria, esophoria and exophoria, respectively. This paper discusses the state of the art in behavior research, current models and the clinical application of vergence eye movements. Within the behavioral research section, current methodologies to quantify parameters of vergence to attain a better understanding of neural control will be reviewed. Recent behavioral findings include an understanding of how convergence and divergence subsystems differ in characteristics, how adaptation influences the neural control of vergence adaptation, and how version interacts with symmetrical vergence responses. The modeling section reviews the current models, limitations and proposed future direction of modeling. There are numerous clinical applications that can benefit from a deeper understanding of vergence eye movements. This paper will conclude by suggesting future directions to advance the science of oculomotor research. 2. Behaviors of vergence eye movements 2.1 Parameters for quantitative analysis to understand neural control Several parameters, including latency, peak velocity, and duration, are used to analyze the dynamics of a vergence eye movement. These parameters yield insight into the neural control of how the brain visually acquires a new target located at different depths. The latency of a vergence eye movement is defined as the time interval between target appearance and when the eye starts moving towards the target of interest, Figure 1(a). As shown in Figure 1(b), vergence duration and peak velocity are generally assessed from the velocity profile. Models and Clinical Applications in Vergence 4.5 30 (b) 4 Velocity (deg/sec) 25 3.5 Amplitude (deg) 3 2.5 2 25 20 15 10 1.5 1 30 (c) Peak velocity Velocity (deg/sec) (a) 3 5 20 15 10 5 0.5 0 0 -0.5 0 Duration Latency 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -5 0 0.2 0.4 0.6 Time (sec) 0.8 1 1.2 Time (sec) 1.4 1.6 1.8 2 -5 -0.5 0 0.5 1 1.5 2 2.5 Amplitude (deg) 3 3.5 4 4.5 Figure 1. Typical (a) position and (b) velocity profiles of a vergence response and its (c) phase plot. Vergence velocity is calculated by differentiating the position profile. The vergence position and velocity responses are typically analyzed using either the transient or steady state portion of the response. During the transient portion, the maximum velocity occurs. Peak velocity can be manipulated through many different experimental conditions and is a primary parameter routinely quantified in eye movement research. The duration of a vergence is defined as the entire time of the movement between when vergence is initiated to when the eyes reach steady state. Latency, peak velocity and duration yield important insights into the vergence system. For example, the mean latency of disparity vergence is shorter than accommodative vergence [3,4] showing these vergence inputs are delayed compared to each other and hence should be modeled using different pathways. The main sequence is an established analysis which measures the system’s first order dynamics. It quantifies the relationship between duration and amplitude or between peak velocity and amplitude using the phase plane plot shown in Figure 1(c) [5]. For normal subjects, the duration is approximately proportional to amplitude, whereas an exponential curve can be fitted to describe the relationship between peak velocity and amplitude [5]. The main sequence is also used for the quantitative analysis of vergence eye movements [5-9]. It is a plot of the magnitude of peak velocity versus the response amplitude [5,6], and is particularly useful for comparing the dynamics of a large number of eye movements over a range of response amplitudes. It provides a measurement of the equivalent first-order dynamics of the response. The peak velocity increases as the vergence amplitude increases. Additionally, it was reported that the slope of main sequence is greater for convergence than divergence [9]. Figure 2 demonstrates the main sequence of divergence responses for 4 subjects stimulated by different high-velocity ramps and 4° steps with various initial positions [10]. The time constant of an exponential function fitted to a position profile has also been commonly used for analyzing vergence dynamics [9-12]. A fast vergence eye movement tends to have a shorter time constant. Hence, convergence which can be a faster system generally has a smaller time constant than divergence. The main sequence and time constant represent only the first-order behavior of a response which does not describe its dynamics in detail, as shown in Figure 1(c). An alternative second-order parameter can be used by measuring the slope of the rising and falling portions of the phase plot which correspond to the major and minor time constants [13]. 2.2 Differences between convergence and divergence Many studies have compared convergence and divergence behaviors reporting differences between the systems. Divergence is a movement in the opposite direction of convergence; yet, it is not merely negative convergence. Several studies suggested that the dynamics of convergence are faster than divergence [7,9,14,15] while other studies reported that pure divergence and convergence have similar velocity characteristics [8] or even that divergence is faster than convergence [16]. For example, the peak velocity of convergence was demonstrated to be twice as fast as divergence [7]. However, other findings reported by Patel et al. [16], believed that divergence was faster than convergence because of the accommodation demand (held in 0 diopter) and the vergence posture of their experimental paradigms. Alvarez and colleagues [17] showed that divergence dynamics were dependent on the stimulus initial position. Hence depending on where the visual stimuli were located, divergence could be faster, slower or approximately equal to convergence speed. The systems also differ in their temporal properties. Rashbass and Westheimer [18] reported that divergence and convergence have similar latencies of 160–170 msec. However, some studies reported that the latency of convergence is less than divergence [9,12], while other reports stated that the opposite is true [19-21]. Alvarez and colleagues [17] found that the latency of divergence becomes shorter as the target moves closer to the subject while this behavior was not observed for convergence. Other experimental paradigms also show differences between convergence and divergence. During a gap paradigm, a visual target is illuminated and then extinguished before the new visual target is shown. These movements are postulated to be faster than responses without a gap because the brain does not need to disengage or release fixation of the initial stimulus. Using a gap paradigm, researchers report that divergence can demonstrate shorter latencies than non-gap responses; however, convergence did not show temporal differences [22]. When investigating the adaptive effects of sustained near convergence, nonlinear differences in an adaptive mechanism is reported between convergence and divergence [16]. Patel and colleagues [16] studied step changes in disparity after a 4 J. Med. Biol. Eng., Vol. 30. No. 1 2010 (a) 2°/s ramp stimuli 4°/s ramp stimuli 6°/s ramp stimuli 10°/s ramp stimuli 4° step initial position=8° 4° step initial position=12° 4° step initial position=16° 4° step initial position=20° (b) (c) (d) Figure 2. Main sequence analysis of divergence responses for 4 subjects (a-d) stimulated by high-velocity ramps (2°/s, 4°/s, 6°/s, 8°/s, and 10°/s) and 4° steps with various initial positions (8°, 12°, 16°, and 20°/s) [10]. sustained 6° convergence task of 5, 30, 60, and 90 seconds. Their results showed that the peak velocity of divergence responses decreased significantly after 30 seconds or longer of sustained convergence compared to only 5 seconds, while the convergence dynamics were unchanged for all the exposure durations. They conclude that the transient component of the horizontal disparity system adapts nonlinearly and independently for convergence and divergence [16]. Ying and Zee [23] did not study disparity vergence dynamics but systematically studied the passive decay of divergence from a convergence stimulus of 30° after 4 seconds of fixation and again after 36 seconds of fixation. The dynamics of the divergence decay were faster after 4 seconds of fixation compared to 36 seconds of fixation suggesting that sustained convergence influences divergence decay dynamics [23]. Recently, Lee and colleagues [24] showed that divergence dynamics were dependent on the adapted phoria position. As a result of sustained convergence, they showed that divergence peak velocity significantly changed. When the phoria became more esophoric (near adapted), the peak velocity for the divergence steps with an initial position of 16° decreased and vice versa when the phoria was far adapted. Convergence and divergence have been reported to have different influences on saccadic movements during saccade-vergence interaction studies [25]. Vertical saccade-vergence interaction show that convergence velocities do not typically vary but divergence is dependent on the upward or downward vertical saccadic movement [26]. Convergence and divergence also exhibit distinct dysfunctions which are discussed in more detailed in the section 4. Clinical Applications of vergence eye movements [27]. Neurophysiologists have shown different cells encode convergence and divergence [28-33]. Hence, differences between the behaviors of the two systems should be anticipated. Despite these behavioral findings current vergence models do not account for the differences between the convergence and divergence systems. 2.3 Adaptation The adaptation process, a type of motor learning, plays an important role for the survival of different species. It can be found in almost every major physiological system, including the oculomotor system. From an engineering viewpoint, adaptive control is simply a modification of a system parameter irrespective of the time course of that change or its aftereffect. Behaviors of long-term adaptation had been well studied in several oculomotor systems, such as VOR [34-37], saccade [38-40], and smooth pursuit [41-45]. The disparity vergence system also shows clear adaptive behavior. For example, changes in tonic vergence or phoria occur in response to sustained demand [46,47]. Because this sustained demand is usually produced by prisms, this adaptive modification is termed prism adaptation. Behavioral studies have demonstrated that the different oculomotor systems learn adaptation adjustments separately. Schor et al. [48] found that the pursuit paradigm for pursuit adaptation had negligible effect on the saccade system. Additionally, saccadic adaptation did not affect vergence eye movements. Furthermore, it was found that the vergence adaptation mechanism had negligible effects in either saccades or smooth pursuit [48]. Models and Clinical Applications in Vergence 2.3.1 Adaptation in disparity vergence Several studies have demonstrated short-term modification in disparity vergence eye movement. The first short-term modification experiment compared 4 deg steps observed alone and those observed with a step-ramp response in a 1:5 ratio [49]. The results showed that vergence dynamic can be increased depending upon the conditioning stimulation used. Takagi et al. [50] used a double disparity step to induce vergence adaptation, and found that the dynamic change of vergence after adaptation is similar to that of saccadic and pursuit system. Furthermore, Alvarez and colleagues [17] showed that convergence and divergence dynamics could be increased or decreased depending upon the experimental paradigm. Semmlow and Yuan [51] analyzed the change of the fast and slow components of disparity vergence after adaptation by using independent component analysis (ICA). ICA is a blind source separation analysis which can untangle the underlying transient (fast) and sustained (slow) components within a vergence response. They reported that instead of generating additional components, the adaptive process modifies these two components (initial or transient and sustained). The adapted responses showed larger initial transient components and double-step behavior was found in the sustained component [51]. 2.3.2 Effect of phoria adaptation in vergence eye movement In the absence of a binocular stimulus, the occluded eye will decay toward its initial, resting position, namely the hetereophoria or dissociated phoria level. Phoria adaptation, also called prism adaptation, occurs in our daily lives while we look at visual stimuli located at different depths [52]. It has important clinical implications for maintaining binocular vision [53], especially when performing near work [54]. The existence of prism adaptation has been well documented [52,55-59]. Phoria adaptation occurs when sustained convergence is driven either with physical targets [23], a stereoscope [60,61] or positive/negative lenses [62,63]. Phoria also changes with orthoptics or vision rehabilitation that is routinely used to reduce symptoms related to the visual stress of near work which is common for those with convergence insufficiency [53]. A near sustained convergence fixation will cause the phoria to become more esophoric (convergent) compared to the baseline measurement [54,64-66]. Previous studies have shown that after five minutes of adaptation negligible changes occur in phoria level [67]. Similar findings have also been demonstrated for the associated phoria [68] which manifests as a small change in vergence error or fixation disparity under binocular viewing conditions [55]. Some studies reported that phoria adaptation influence vergence dynamics. Patel and colleagues [16] studied vergence dynamics after a sustained 6 deg convergence task of 5, 30, 60, and 90 seconds. They found that divergence peak velocity decreased about 25% after 30 seconds sustained convergence compared to 5 seconds, while no significant change was found in convergence for all the exposure durations. Hence, the transient component in vergence control 5 adapts and the adaptation is dependent on the direction of vergence [16]. Ying and Zee [23] reported that the natural divergence decay after sustained symmetrical convergence to a 30 deg stimulus for 4 and 30 seconds. Short-term phoria adaptation was observed for the long period convergence (30 seconds). Furthermore, the dynamics of divergence decay changed and the change depended upon how long the sustained convergence was maintained. Their results suggest that the divergence decay dynamics is influenced by phoria adaptation. To extend the work done by Patel et al. [16], Lee and colleague [24] systematically used slow phoria adaptation to determine if this adaptation influences the dynamics of transient disparity divergence eye movements that start at two different initial positions (a near initial position of 16 degrees and a further initial position of 4.5 degrees). It was found that the divergence dynamics are influenced by phoria adaptation and the change in dynamics was dependent on the sustained convergence task. Furthermore, divergence dynamics were influenced by initial target position and the phoria was adapted using a sustained convergence task [24]. As will be discussed in the following modeling section, vergence models do not adequately incorporate adaptation of the transient component or phoria adaptation in their design. 2.4 Saccade-vergence interaction Most eye movements involve a combination of version (conjugate movements) and vergence (disconjugate movements), hence saccades and vergence components are typically intermixed in oculomotor movements. Interestingly, saccades are frequently found in vergence eye movements even when the stimulus is carefully aligned to be binocularly symmetrical [8,9,15,69]. Semmlow et al. [70] found that most responses to a pure vergence stimulus do contain saccades. For more than half of their subjects, every response contained at least one saccade. A similar finding has been reported by Coubard and Kapoula [71] who found either horizontal or vertical saccades in 84% of all vergence responses. Zee et al. [15] reported that, in pure vergence, saccades occurred more often during divergence and more frequently for large amplitudes. For the vergence stimuli with wider range spanning from 5–25°, Collewijn et al. [8] reported that pure vergence was accompanied by saccades, especially for divergence. A pure saccadic stimulus would elicit an initial divergence followed by convergence response in addition to the saccadic response for nearly all normal subjects. Although pure vergence stimuli are rare in daily life, they are easy to construct in the laboratory and have been used to study the disparity vergence eye movement system. Such stimuli can be presented using a stereo pair of images moving in equal and opposite directions or by two targets placed at different depths along the mid-sagittal (i.e., central or cyclopean) axis. In the latter case, an accommodative (i.e., blur-driven) stimulus may also drive the vergence response. These stimuli are often referred to as pure vergence stimuli and might be expected to produce a pure vergence response: one in which the two eyes rotate an equal amount in opposite or disjunctive directions. Pure vergence J. Med. Biol. Eng., Vol. 30. No. 1 2010 6 responses would follow along the mid-sagittal plane (or cyclopean axis) and there would be no version component to the response. However, careful and systemic behavioral studies show different behaviors. 2.4.1 Version and vergence components In the response to a pure vergence stimulus, the version component should theoretically be equal to zero. In normal subjects with good binocular vision, the net version component must be very small by the end of the movement, since steady fixations errors are close to zero [72]. There are two factors that lead to version movements during a typical symmetrical vergence response. First, vergence responses often contain saccades [8,15,70,73,74] which clearly generate a version movement. Even a small saccade will generate a substantial deviation for the midline. Second, even if no saccades are present, vergence movements in response to a symmetrical vergence stimulus are often asymmetrical because one eye often moves faster than the other in pure vergence responses [69]. For example, Horng et al. [69] showed that during vergence responses to symmetrical stimuli, one eye can respond twice as fast as the other during the transient portion of the response. During the initial response, a large difference in amplitude was always observed between the two eyes and was corrected later by a slow vergence or saccadic movement to bring the eyes to their final symmetric position. Irrespective of how the version component is generated, it must go to zero by the end of the response in order to achieve accurate binocular fixation. When both vergence and version components are found, it is widely held that asymmetries induced in the saccadic response assist in moving the eyes disjunctively; that is, in opposition [15,75-77]. Although the two oculomotor components may act collaboratively, they still appear to be independent [78]. The version and vergence components of an intermixed response can be obtained from the following equations [70]: Avergence = AL − AR (1) Aversion = ( AL + AR ) / 2 (2) where AL and AR indicate the amplitudes of the left and right eyes, respectively. 2.4.2 The roles of saccade in saccade-vergence interaction Responses from a symmetrical vergence stimulus often contained saccades or asymmetries between the left and right eye movements. Saccades occurring during the transient portion of the movement actually generate more error because the saccadic movement takes one away further away from the target while bringing the other eye closer to the target. This error can be corrected by either a corrective saccade or an asymmetric vergence. Horng et al. [69] demonstrated that sometimes saccades were initiated to correct the errors produced by asymmetrical vergence. Semmlow et al. [70] found that the initial saccade in the responses to pure vergence stimuli usually increased the deviation from the midline. Although most initial saccades produced error, all subjects had some responses where the initial saccade reduced the midline deviation by compensating for a vergence-induced midline deviations. It was suggested that most error-inducing initial saccades were the result of a monocular distraction produced by transient diplopia of the vergence stimulus along with ocular preference or dominance [70]. A similar suggestion has been made by van Leeuwen et al. [74] who showed that subjects without a strong monocular preference were much more likely to produce saccade-free vergence responses to pure vergence stimuli. In a few subjects, initial error-inducing saccades brought the preferred eye closer to the target, which could lead to faster recognition at the expense of delayed binocular vision. There are four immediately apparent explanations for the presence of those seemly unnecessary saccades [70]. First, they could be used to bring one eye, likely the preferred or dominant eye, more quickly to the target [74]. Embedded saccades might delay the acquisition of full binocular vision, but having one eye on target, particularly the preferred eye, may be sufficient for visual recognition. Second, the transient diplopia induced by a pure vergence stimulus produces a compelling saccadic stimulus, particularly if there is a strong ocular preference for one eye. Third, there is considerable evidence that saccades can enhance vergence movements [8,76,77] through saccade-like burst cell activity that appears to be integrated into the vergence feedback [79,80]. Such enhancements to vergence may bring both eyes more quickly to the target despite the symmetry error caused by the saccade. Fourth, the saccades could be in response to symmetry errors produced by asymmetrical vergence. It was shown that major differences between the speeds at which the two eyes move in a disparity vergence response even in responses that are free of saccades [69]. Recent evidence presented that all of these mechanisms are active in all subjects, at least in a few responses, but some subjects exhibit a predominance of one or more of these mechanisms [70]. 2.4.3 Dual roles of error generation and correction for both saccade and vergence For symmetrical vergence stimuli, saccades may occur at the beginning [15] or at the latter stage [69] and play dual roles as either the distracters in increasing the errors or the correctors in decreasing the errors. Asymmetric vergence, on the other hand, may also act as dual roles for error generation or error correction [70,81]. Irrespective of the motivation for error-inducing saccades, some compensation must occur by the end of the movement. While larger errors, particularly conjugate errors, may be tolerated under certain conditions, normal subjects can achieve highly accurate binocular fixation with errors of minutes of arcs [72]. If the initial saccade in the vergence response moves the eyes away from the midline, then either a subsequent compensatory saccade, an offsetting vergence asymmetry (or slow version), or both is required to bring the eyes back to the midline [81]. As shown in Table 1, there are four possible scenarios for the development of errors in vergence symmetry and their compensation by combining vergence asymmetries with saccades. Models and Clinical Applications in Vergence 7 a b c d e f Figure 3. Responses from two subjects to a symmetrical convergent 4.0 deg. step stimulus. In both responses, an early saccade creates a symmetry error. (a) and (d) Individual left (red dashed line) and right (blue solid line) eye movements showing the presence of saccades along with the vergence response. Convergence is plotted upward for both eyes. (b) and (e) The version components with the rightward movement is plotted positive and leftward movement is negative with zero at the mid-sagittal plane. (c) and (f) The vergence components with convergence plotted upward [70]. a b d e c f Figure 4. Responses from two subjects to a symmetrical convergent 4.0 deg. step stimulus. In both responses, an early vergence asymmetry creates a symmetry error. (a) and (d) Individual right (red) and left (blue) eye movements. (b) and (e) The version component. (c) and (f) The vergence responses are again smooth due to either saccade cancellation (c) or the absence of saccades (f) [70]. Table 1. Sources of Symmetry Errors and Corrective Mechanisms during Pure Vergence Stimuli. Vergence Saccade Error Generation Error correction Saccade Vergence Saccadic errors, Saccadic corrections Saccadic errors, Vergence correction Vergence asymmetry, Saccadic correction Vergence asymmetry, Vergence correction Figure 3 shows responses from two subjects to a symmetrical convergence 4° step stimulus. In both responses, an early saccade (asymmetry-inducing) creates a symmetry error. Individual left (red dashed line) and right (blue solid line) eye movements showing the presence of saccades along with the vergence response. The vergence components are obtained from Eq. (1), while the version components are calculated according to Eq. (2). As shown in Figures 3(b) and (d), the saccade-induced symmetry errors are corrected by a slow version movement (vergence asymmetry) and a corrective saccade, respectively. Responses with asymmetry vergence which generates symmetry errors are shown in Figure 4. In Figure 4(b), two saccades appear to be correcting the symmetry error produced by an initial fast disparity vergence asymmetry, while in Figure 4(e) the fast disparity vergence asymmetry is corrected by a compensatory vergence asymmetry. 8 J. Med. Biol. Eng., Vol. 30. No. 1 2010 DI VE Target VT + Position VP - Integrator + + Delay Eye Plant Vergence Position Feedback Figure 5. Continuous feedback model, in which VT, Vp, and VE indicate the target angle, desired vergence angle and disparity angle, respectively. DI represents the derivative-integrative component added by Krishnan and Stark [83]. For Rashbass and Westheimer’s model, Integrator: k/s, Delay: e-sτ, and Eye Plant: zero-order; for Krishnan and Stark’s model, Integrator (leaky): 10Ki/(10s+1), DI: sKs/(s+10), Delay: e-0.16τ, and Eye Plant: 3rd order. These recent behavioral findings of saccadic movements within symmetrical vergence responses have yet to be incorporated in vergence models, presumably because it is more difficult to describe this complex behavior. However in order to attain a better understanding of oculomotor control, more sophisticated models that incorporate not only vergence but its interactions with other systems is necessary because in visual search humans do not perform simple vergence movements but a combination of movements. 3. Models for vergence Physiological modeling facilitates the understanding of a system. Vergence eye movements were first modeled using a simple feedback control system by Rashbass and Westheimer [18]. Numerous models have been developed since their first attempt but controversy still exists regarding the basic control structure mediating this motor response. Models of vergence control can generally be classified into three basic configurations: continuous feedback, switched-channel with feedback, and feedback with preprogrammed control [82]. Their limitations of describing new behaviors recently reported in the literature are summarized here. 3.1 Continuous feedback model As shown in Figure 5, the first model proposed by Rashbass and Westheimer [18] used simple linear feedback with a feedforward controller, consisting of an integrator with a delay, and a zero-order eye plant with unity gain. A negative feedback control system was used to continuously reduce the vergence disparity (VE), defined as the difference between target position (VT) and vergence position (VP). During an open loop experiment, the feedback loop of vergence is ‘opened’ by monitoring the current position of the eye to keep the error (difference between the stimulus and the current eye position) constant. Rashbass and Westheimer [18] used an open loop experiment by applying a ramp stimulus while keeping the disparity magnitude constant and concluded that the response velocity was proportional to the input disparity magnitude one reaction time (approximately 160 ms) before for small disparities up to 0.2°. However, their model was unable to sufficiently model phase from sinusoidal disparity stimuli because the experimental data had shorter lags compared to those predicted by the model. This model also has difficulties in modeling step data that have faster dynamics because it becomes unstable with faster control signals due to the presence of long processing delays. The next feedback model was developed by Krishnan and Stark [83] in which a derivative-integral (DI) element to better represent the transient response was added to the controller in parallel to the integrator to support the sustained response (Figure 5). In contrast to Rashbass and Westheimer’s model, a leaky integrator and a third-order eye plant were used to simulate vergence responses. Additionally, the integrator sustained the response of disparity magnitude while the derivative-integral portion was triggered based on disparity change rather than disparity magnitude, which significantly improved the phase characteristics of Rashbass and Westheimer’s model. The model was later modified by Schor [84] in which a threshold was added to trigger vergence change where he referred to it as a dead zone and incorporated input from the accommodative vergence system. Additionally, the system consisted of a fast neural integrator and a slow neural integrator to simulate the initial step and the steady state portions of the response, respectively. One problem with these models is that the steady state error or fixation disparity from the model is much greater than those found experimentally [85]. 3.2 Switch-channel model with feedback Pobuda and Erkelens [86] were the first to present a model with parallel channels in the feedforward path. As shown in Figure 6, they proposed the following hypotheses (1) vergence disparity is processed through several channels simulated by low pass filters, (2) the filters are sensitive to ranges of disparity amplitude, (3) vergence loops have delays ranging from 80 to 120 ms rather than the 160 ms as previously reported, and (4) the vergence loop is not sensitive to the disparity change. The criticism to the model is that it shows responses taking significantly longer to process disparities compared to those seen experimentally [87]. Another model has expanded the switched-channel model using neural network architecture [88]. The model consisted of seven functional stages and incorporated a variation of the switched-channel model into one of the neural layers with velocity used to select the input channel rather than disparity. The primary limitation of this model is that it could not model the high-velocity step-like component observed in faster ramps [87,89]. 3.3 Preprogrammed feedback model A different approach to vergence modeling uses a preprogrammed open-loop element in conjunction with feedback control as shown in Figure 7 [14]. This dual-mode Models and Clinical Applications in Vergence VT + VE RD1 LP1 RD2 LP2 SL + Is + + + Delay Eye Plant + ….. VP 9 Vergence Position LP5 RD5 Figure 6. Block diagram of switch-channel model, in which RD, LP, Is, and SL represent range detector, low-pass filter, slow integrator, and saturation limit, respectively. A pure delay with 100 ms and a second-order eye plant with time constants of 8 and 150 ms were used for simulation. Slow Component VT + VE + + P VP Fast Component VR + + Eye Plant Vergence Position Figure 7. Block diagram of dual-mode model which incorporates preprogramming with feedback control. model consists of a rapid, preprogrammed, transient control component followed by a much slower sustained component guided by feedback to represent the speed and accuracy of a vergence movement respectively [87,90,91] There is considerable behavioral support for the dual-mode theory [14,69,87,90-92]. Specific behavioral evidence supporting a preprogrammed element within convergence control began with Jones’ research. Jones [93] showed that by stepping a non-fusible target (a vertical line paired with a horizontal line), a transient vergence response was generated. Under these conditions, the vergence system cannot use an external visual feedback system since an error signal is not generated. He then developed a theory that convergence was composed of a fusion initiating and a fusion sustaining component [93,94]. Similarly, Semmlow et al. [90] reported that by presenting a step stimulus that would disappear in a mere 50 or 100 ms, a transient convergence response was generated. The preprogrammed component is also observed in divergence control. Lee and colleagues [10] found that divergence responses to disappearing step stimuli (i.e. the 4° step visual stimulus were illuminated only for 100 ms) have similar first-order dynamic characteristics to pure step responses. Since the preprogrammed component is mostly elicited if the visual stimulus disappears in 100 ms, their finding suggested the existence of a preprogrammed component in divergence control as well. Furthermore, when using an uncrossed stimulus for 200 msec, divergence was observed for small step changes [95]. These behavioral findings led to a model that could accurately simulate responses to a variety of experimental responses such as a pulse, step-pulse, ramp and sinusoidal stimuli. 3.4 Responses simulated using switched-channel model dual-mode model and Recently research has begun to compare responses from both the dual-mode model and the switched-channel model. Both models were reconstructed with the same eye plant described by Robinson et al. [96] to facilitate comparison between the two model controllers. Figure 8 shows simulated 4° vergence step responses using the dual-mode and switched-channel models. In the dual-mode model response, the dashed line indicates the transient component while the dotted line shows the sustained component. For the switched channel model, the five dashed lines represent the signals generated by each channel. Note that the time scales are different between the models. Both the dual-mode model and switched-channel model are adjusted to give the best fit simulated response to the 4° experimental responses for a slower response and a faster response shown in Figures 9 and 10, respectively. As shown in the figures, the model responses are very similar to experimental responses indicating that the behaviors of slow and fast vergence responses can be described by both dual-mode and switched-channel models. 3.5 Limitations to current vergence models Although both models can accurately simulate vergence step responses to 4° symmetrical stimuli, both models have significant limitations. These models represent divergence with a negative sign and do not adjust parameters compared to convergence. Only a few models have tried to incorporate other factors that may influence the vergence system such as the tonic and/or phoria level. Schor's model [97] uses a recruitment mechanism that is an order of magnitude slower than the transient component. As sustained fixation duration is increased, the recruitment of neurons is greater, thereby increasing the output of the sustained component and reducing the drive from the transient component. Hung's model [98] suggests a variable time-constant mechanism in which neurons increase their time-constants proportionally to the sustained fixation duration. In both models, the transient component is considered to be non-adaptable. Furthermore, both models 10 J. Med. Biol. Eng., Vol. 30. No. 1 2010 5 5 a total model response transient component sustained component 4.5 b 4 4 CH1 3.5 3.5 3 3 4.5 total model response components form different channels Position (deg) Position (deg) CH2 2.5 2 CH5 2 1.5 1 1 0.5 0.5 0.2 0.4 0.6 0.8 1 1.2 Time (sec) 1.4 1.6 1.8 2 CH4 2.5 1.5 0 0 CH3 0 0 0.5 1 1.5 2 Time (sec) 2.5 3 3.5 4 Figure 8. Model responses obtained from (a) dual-mode model (b) switched-channel model. assume identical dynamic behavior during convergence and divergence movements. The only model that could account for near or far adaptation was proposed by Saladin [99]. This model consists of separate sensorimotor pathways for convergence and divergence where each pathway is similar to Schor’s model. New vergence models need to account for the differences between convergence and divergence and adaptation. To model adaptation both adaptation to the transient component through conditioning stimuli and phoria adaptation should be included in the architecture. As discussed in the behavioral review section, several studies show the occurrence of saccades in symmetrical vergence responses. None of the current models simulate the occurrence of saccades in a vergence response. New models should incorporate these behaviors to create a more realistic model of the vergence oculomotor system. When such a model is created more insights can be gained to understand vergence dysfunctions. For instance, one potential reason to use a saccadic response within a vergence movement is to facilitate visual object recognition even if it is perceived monocularly which may be a primary compensatory mechanism in vergence dysfunctions. 4. Clinical applications of vergence eye movements 4.1 Cortical and subcortical studies of vergence oculomotor movements Numerous studies have established the neural circuit for vergence that can serve as a solid foundation to better understand vergence dysfunctions. One study states “specific abnormalities on the eye movement examination may provide clues to the underlying pathology, and suggest strategies for treatment of a variety of neurological disorders” [100]. There are many single cell or lesion studies on primates, human case reports, and transcranial magnetic stimulation studies which yield insights into the operation of the vergence neural circuit. Regions of vergence neural circuit from the sensory input to the motor output are summarized here. Sensory visual pathway: Disparity tuned cells have been described as being located in the primary visual cortex (V1, V2, V3 and V3a) where cells are excitatory or inhibitory. These cells encode for stimuli located at different depths where investigators hypothesize this is the input signal to the binocular vergence system [101]. Parietal lobe: Studies on primates show that the vergence circuit does involve cortical areas within the posterior parietal lobe (lateral intraparietal (LIP) area) that are broadly tuned to have a preferred direction for targets closer or farther away [102,103]. Using transcranial magnetic stimulation over the posterior parietal cortex (PPC), investigations conclude that the right PPC is involved in fixation disengagement; whereas the left PPC is involved in spatial selective mechanisms that concern targets that are closer or near to the subject [104,105]. Frontal lobe: Single cell recordings from primates reveal a distinct area within the bilateral frontal eye fields (FEF) that is allocated for step vergence responses and is located more anterior compared to the cells responsible for saccadic signaling [106]. Other investigators have shown a separate smoothly tracking area in the FEF for vergence [107]. Cerebellum: The vergence signal is present within the deep cerebellar nuclei [108]. Cells within the fastigial oculomotor region modulate their firing rates with a convergence stimulus alone or with convergence and saccadic stimuli. Inactivation of this region with muscimol produces a decrease in convergence velocity and a “convergence insufficiency” [33,109,110]. Investigators show that cells are involved in vergence only movements and in vergence with smooth pursuit[33,107]. Vergence activity has also been reported in the ventral paraflocculus [111] and in the posterior interposed nucleus [32]. The dorsal vermal outputs are sent to the midbrain via the caudal fastigial nucleus [33]. Lesions to the cerebellar vermis VI/VII in primates show a decrease in prism-induced phoria adaptation [109]. Recent human case studies report vergence dysfunctions in those with cerebellar lesions, particularly those within the vermis [112]. Models and Clinical Applications in Vergence 11 Dual-mode model using Robinson’s plant (a) 4 2 experimental response experimental response model response model response 0 0 0.2 0.4 0.6 0.8 1 1.2 Time (sec) 1.4 1.6 1.8 2 4 (c) 2 0 0 0.2 0.4 0.6 0.8 1 1.2 10 (b) experimental response experimental response model response model response 5 0 -5 0 0.2 0.4 0.6 Switched-channel model using Robinson’s plant 6 Velocity (deg/sec) Velocity (deg/sec) Position(deg) (deg) Position Velocity (deg/sec) (deg/sec) Velocity Position(deg) (deg) Position 6 1.4 1.6 1.8 Time (sec) 2 0.8 1 1.2 Time (sec) 1.4 1.6 1.8 2 10 (d) 5 0 -5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (sec) Figure 9. The position (left) and velocity (right) profiles of model simulations (solid line) and selected slow dynamic experimental vergence responses (dashed line). The dual-mode model simulations using Robinson’s plant with experimental data are shown in (a) and (b). The switch-channel model simulations using Robinson’s plant are shown in (c) and (d). Figure 10. The position (left) and velocity (right) profiles of model simulations (solid line) and selected faster dynamic experimental vergence responses (dashed line). The dual-mode model simulations with experimental data are shown in (a) and (b) and the switch-channel model simulations using Robinson’s plant are shown in (c) and (d). Brainstem and oculomotor neurons: Researchers have recorded action potentials from cells in the midbrain and they report different cells for convergence and divergence. Within this population, some cells exhibit bursting behaviors which they termed “velocity-encoding cells” while others have burst-tonic behaviors termed “position-encoding cells” [28,29,113]. Midbrain neurons discharge before vergence eye movements [33]. The vergence signal is also present within the nucleus reticularis tegmenti pontis [108]. Investigators studying single cell recordings from the abducens and oculomotor neurons show that separate cells are encoded for saccadic versus vergence signals to the lateral and medial recti muscles [28]. 4.2 Clinical Disorders of Vergence Eye Movements Vergence dynamics have been reported to decrease with age [114]. This study reported that age-related effects in transient (fast) vergence were observed via an increased latency and decreased peak velocity and acceleration. Sustained (slow) vergence also showed age-related effects with a decrease in accommodative vergence velocity and an increase in latency. In addition to aging, numerous clinical case studies have been reported describing dysfunctions to the vergence system. Case studies show that a symmetric paramedian thalamic infarction disrupts vergence eye movements due to an interruption of the supranuclear fibers to midbrain vergence neurons [115]. Furthermore, unilateral mediolateral pontine infarctions impair ramp vergence tracking movements but not step vergence movements, suggesting that vergence signals are distributed in the pontine nuclei [116,117]. Small midbrain infarctions [118,119], pontine lesions [116,117], cerebellar lesions [113], Parkinson’s disease [120,121], progressive supranuclear palsy [122] and midbrain hemorrhage [123] have all been reported as causing a convergence dysfunction. 12 J. Med. Biol. Eng., Vol. 30. No. 1 2010 Patients with progressive supranuclear palsy made smaller vergence under both asymmetric and symmetric stimuli. The regression slopes of the main sequence were also lower than control for both stimuli [122]. Lesions in both the nucleus reticularis tegment pontis (NRTP) [116] and the mediolateral pontis [117] showed deficits of slow convergence and divergence, but not faster vergence stimuli such as step stimulation. Similar to pontine lesions, fast vergence was also affected for patients with acute cerebellar lesions [112]. It was found that slow vergence gain to sinusoidal stimuli, both in convergence and divergence, was reduced significantly, while only the velocity of divergence (but not convergence) to ramp stimuli was reduced [112]. Impairments to the dorsal vermis within the cerebellum of primates resulted in a decrease in peak velocity and initial acceleration of convergence but not divergence [33]. Kapoula and colleagues [124] reported that the latency of saccadic and vergence movement was extended for a young subject with manifest latent nystagmus (MLN) when viewing binocularly (but not monocularly). Furthermore, it was found that the latency of vergence is longer in children with divergent strabismus [125] and with vertigo in the absence of vestibular dysfunction [126]. Children with vertigo in the absence of vestibular dysfunction also showed poor accuracy, longer duration, and reduced speed in vergence eye movement compared to normal controls [127]. Bucci et al. [128] found that the occurrence of express latencies for divergence is significantly greater for children with dyslexia. In addition to abnormalities in dynamic disparity vergence movements, (quantified via latency, peak velocity, duration, and main sequence analyses) many reports document abnormalities in the phoria adaptation of the vergence system. Several previous researches reported that aging [129] and dysfunction of the cerebellum [130,131] result in the reduced ability to adapt vergence phoria. Although Hain and Luebke [58] reported that horizontal phoria adaptation is not affected due to cerebellar dysfunction, several studies discovered that lesions in the cerebellum result in a decrease or loss of phoria adaptation in humans, both horizontally [130] and vertically [131]. Similar reports have been documented in primates [109]. 4.3 Vision rehabilitation The brain receives most of its afferent information through the visual system. Hence, vision dysfunction can have devastating consequences on a person’s daily living activities. Some visual dysfunctions can be treated with glasses or contact lenses, while others can be remediated via vision rehabilitation. Vision rehabilitation or vision training utilizes repetition of eye movements over many sessions to facilitate oculomotor movements through motor learning speculated to evoke neural plasticity. It has been used to treat many visual disorders such as amblyopia, double vision, convergence insufficiency (CI), and reading disabilities. Several visual stimuli (step or ramp) have been adopted to treat patients with different kinds of vision disorders. For example, vision rehabilitation using step or ramp stimuli was reported to be able to enhance vision in CI patients. Kapoor and Ciuffreda [132] reported that after a period of ramp training, a target moving smoothly and gradually toward or away from the subject, the patient’s ability to fuse a target as well as to maintain that level of vergence had been improved. Convergence insufficiency, a common disorder in the visual system [132-136], has been diagnosed in 42% (68 out of 160) of patients with traumatic brain injury (TBI) [137]. Patients are generally observed with receded near point of convergence, large exophoria, and reduced vergence ranges [132]. The near point of convergence (NPC) break is quantified as the distance along a subject’s midline when the subject begins to see the visual target double or the eye breaks fusion. Recovery is the distance that is required before the doubled object returns to a single image [138,139]. Scheiman and Gallaway reported in 2005 [138], a typical NPC of 20 cm for TBI patients which can be reduced to normal ranges of less than 5 cm after vision rehabilitation. These patient’s symptoms include double vision, fatigue, and blurred vision within a few minutes of near work such as reading a book. Vision rehabilitation increases functionality which is quantified by a closer near point of convergence, larger vergence ranges and reduction in symptoms [139,140]. Yet none of these studies measured eye movements. To date, no modeling study has been performed to suggest how changing a parameter in a vergence model can create a vergence oculomotor dysfunction or how vision rehabilitation facilitates changing oculomotor control. 5. Conclusion and future direction for vergence oculomotor research Many new behaviors have recently been reported in vergence including: (1) divergence and convergence having different dynamic and temporal properties, (2) adaptation of the transient dynamics, (3) phoria and its adaptation influencing the neural control of convergence and divergence which is different for each system, and (4) the occurrence of saccades in symmetrical vergence responses where saccadic responses should not be present because visual stimulation is symmetrical and hence does not contain version stimulation. The current models reviewed here (feedback with preprogrammed control and switched channel feedback) do not incorporate any of these recent behavioral findings. Furthermore, numerous case reports and studies document vergence dysfunctions such as a decrease in vergence velocity and acceleration as well as increased latencies or durations to acquire a new visual target. Dysfunctions can selectively disrupt convergence or divergence and can also selectively affect either the fast or slow portions of the vergence system identified through responses to step or ramp stimuli. Yet despite the prevalence of vergence dysfunction, no modeling studies have been conducted to understand how each dysfunction can be simulated to understand the change that dysfunction is causing in the oculomotor control. Furthermore, several studies suggest that vision rehabilitation can improve patient’s symptoms, yet no modeling work has been conducted Models and Clinical Applications in Vergence to explain what changes in the oculomotor control to account for the patient’s improvement resulting in a reduction of symptoms. Future work should include improved models of vergence oculomotor control to improve our understanding of the basic science and clinical applications of vergence dysfunctions. Acknowledgments Dr. Y. F. 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