Computational models to delineate 3D gaze-shift strategies in Parkinson's disease

Abstract

Objective:

Parkinson's disease (PD) frequently affects vergence eye movements interfering with the perception of depth and dimensionality critical for mitigating falls. We examined neural strategies that compensate for abnormal vergence and their mechanistic underpinning in PD.

Methods:

The a priori hypothesis was that impaired vergence is compensated by incorporating rapid eye movements (saccades) to accomplish gaze shifts at different depths. Our experiments examined the hypothesis by simulating biologically plausible computational models of saccade-vergence interactions in PD and validating predictions in the actual patient data.

Results:

We found four strategies to accomplish 3D gaze shift; pure vergence eye movements, pure saccadic eye movements, combinations of vergence followed by a saccade, and combination of saccade followed by vergence. The gaze shifting strategy of the two eyes was incongruent in PD. The latency of vergence was prolonged, and it was more so when the saccades preceded the vergence or when the saccades only made 3D gaze shift. Computational models predicted at least two possible mechanisms triggering saccades along with vergence. One is based on the lack of foveal accuracy when the vergence gain is suboptimal. The second mechanism reflects the noise in the gating mechanism, the omnipause neurons, for vergence and saccades. None of the two model predictions alone were completely supported by the patient data. However, a combined model incorporating both abnormal vergence velocity gain and impaired gating accurately simulated the results from PD patients.

Conclusion:

The combined strategy is biologically plausible for two reasons: 1) The basal ganglia that is prominently affected in PD projects to the vergence velocity neurons in the midbrain via the cerebellum. The projection directly affects the vergence velocity gain. 2) The basal ganglia, via superior colliculus, influences the pattern of omnipause neuronal activity. Abnormal basal ganglia activity may introduce noise in the omnipause neurons.

Introduction:

Parkinson's disease (PD) is the 2^nd most common neurodegenerative condition affecting about 10 million individuals worldwide. Visual symptoms in PD are far more common than appreciated and can be due to multiple etiologies (1-3). Impaired gaze shifts (i.e., saccades) cause difficulties in reading or scanning the surrounding environment (4-6). Impaired simultaneous and synchronized movement of both eyes in the opposite direction (i.e., vergence) results in compromised depth perception and spatial navigation in up to 70% of PD patients (4). Misalignment of the two eyes due to abnormal vergence leads to strabismus and impaired visual fusion, causing diplopia (double vision) in about a third of PD patients (7-10). Vergence latency increases, and velocity decreases in PD (7, 10). The Visual Function Questionnaire-25 (VFQ-25) that measures the impact of visual symptoms on quality of life demonstrated significantly poor outcomes in PD patients. The increasing severity of VFQ-25 is correlated with the presence of vergence insufficiency and a decline in acuity (11).

Our overarching goal is to define therapeutic strategies that improve vision-related quality of life in PD. In order to achieve such goals, the current study focused on putative neural mechanisms compensating for inadequate vergence and the physiological underpinnings for such compensatory movements. The a priori hypothesis is that impaired vergence is compensated by incorporating saccadic eye movements to accomplish gaze shifts at different depths. There are at least two possible mechanisms triggering saccades in combination with vergence. One is the lack of foveal accuracy when the vergence is suboptimal. The second mechanism reflects the noise in the gating mechanism that executes vergence and saccades. In order to test these hypotheses, we simulated a computational models and sought for the validation of model predictions in the experimental data collected from PD patients.

Methods

We recruited 14 PD patients (ages: 50-70 yrs.) and six age-matched healthy controls. The diagnosis was based on clinical impression and response to dopaminergic medications. Table 1 depicts the summary of recruited subjects, their demographic information, and details of clinical presentation. All patients gave written, informed consent in accordance with the Institutional Review Board of the Cleveland Clinic and ethical standards consistent with the Declaration of Helsinki. A high-resolution eye-tracker (EyeLink 1000®, SR Research, Ontario, Canada) was used to quantify convergence and divergence abnormalities using LED targets placed at 30, 55, 150, and 240 cm distances along the sagittal plane. As the LED target was turned on, the subject shifted their gaze at the corresponding target location and held there for 5 seconds. Vertical and horizontal positions of both eyes were measured simultaneously at 0.01 degree spatial and 500Hz temporal resolution. The data were further processed and analyzed using MATLAB (Mathworks, Natick, MA). The analysis was based on algorithms developed in our laboratory (12-14).

Table 1:

Demographics and clinical features of neurological and ophthalmological deficits. ID: indentification number, BMI: body mass index, LED: levodopa dose, UPDRSIII: Unified Parkinson’s disease rating scale, RAF: Royal Airforce measurement , PEN: ; DIV EYE, OD: right eye, OS: left eye, STD: standard deviation.

											Visual Acuity		Objective Convergence			Subjective Convergence
ID	Age	Sex	Ethnicity	BMI	Dominant hand/leg	Disease duration (y)	Affected side	#Falls/6mo	LED	UPDRS- III (off)	OD	OS	RAF (cm)	PEN (cm)	DIV EYE	RAF (cm)	PEN (cm)	DIV EYE
1	76	M	White	24.98	R/R	11	R	7	1040	51	20/25	20/30				31	26	R
2	53	M	White	34.14	R/R	5	R	2	60	12	20/25	20/20	22	33	R	22	33	R
3	52	M	White	34.19	R/R	12	R	0	1505	40.5	20/20	20/20	33.5	27	R	33.5	27	R
4	71	M	White	29.58	R/R	21	R	9	1100	36.5	20/50	20/30	16	29	L	14	30	R
5	69	M	White	29.17	R/R	9	L	4	0	48.5	20/50	20/30	28	19	R	25.5	15	R
6	64	M	White	25.00	R/R	18	L	0	0	56	20/30	20/40	23	28	L	26	28	L
7	71	M	White	27.08	R/R	14	L	60	610	41	20/30	20/25	31	25	L	31	25	16
8	79	M	White	20.42	R/R	17	L&R	2	500	54	20/25	20/25	24	28	R	24	28	R
9	69	M	White	27.27	R/R	8	L	0	500	25.5	20/40	20/40	24	29( w/glasses) 65 woc	L	24	29( w/glasses) 65 woc	R
10	64	M	White	23.01	R/R	10	L	26	348	23.5			19	24	R	20	20	R
11	59	M	White	38.20	R/R	7	R	4	600	30	20/20	20/20	8	15	L		13	L
12	66	M	White	30.70	R/R	2	L	6	1000	23	20/20	20/20	14	13	L	14	13	L
13	65	M	White	25	R/R	6	L&R	2	1200	34	20/20	20/25	9	13 (RE)	L	11	13 (RE)	L
14	68	F	White	26	R/R	8	R	3	1000	30	20/30	20/25	13	16	L	13	16	L
Mean	66.14			28.2		10.57		8.92	675.92	36.11			20.35	23		22.23	22.57
STD	7.66			4.85		5.36		16.12	476.93	13.12			8.05	6.9		7.43	7.25

Data Analysis

The key analyzed parameters were the amplitude, velocity, and onset (latency) of the vergence. The position of each eye was differentiated and smoothed with a Savitzky-Golay filter (polynomial order: 3; frame length: 51) to compute eye velocity. The analysis was performed for both convergence (shifting gaze from farther away to the near target) and divergence (shifting gaze from near to the farther away target) eye movements. In both cases, the vergence onset was determined when the eye position shifted 0.5 degrees away from the steady baseline after the target shift. The onset and offset of vergence were interactively validated and classified into different strategies employed to facilitate gaze shift. MATLAB toolboxes were used for the statistical analyses (ANOVA, Chi-square, and unpaired T-test) and curve fitting (linear interpolation).

Results

We tested the hypothesis that impaired vergence is compensated by incorporating saccadic eye movements to accomplish gaze shifts at different depths. There are at least two possible mechanisms triggering the saccades. One lacks foveal accuracy when the vergence is suboptimal. The second mechanism reflects the noise in the omnipause neurons, the gating mechanism executing vergence and saccades. Here we present three computational models incorporating each of the two mechanisms and their combination. Each model has specific predictions, which are tested in the experimental data from the PD subjects.

Behavioral strategies for vergence eye movements in PD

Fig 1A depicts mean value and standard deviation of the difference in the horizontal angular eye positions of the right and left eye during convergence eye movement, i.e. vergence angle, in PD patients and healthy subjects. Mean vergence angle and standard deviation around the mean are plotted on the y-axis while time is plotted on the x-axis. The mean horizontal vergence angle from healthy subjects is depicted in blue trace (standard deviation, light blue), while PD patient is shown with the black trace (standard deviation, grey). The healthy subjects are age-matched, hence elderly. As a result, even in healthy controls the vergence is not accurate, only some trials reaching desired vergence angle. It is noteworthy that blue solid line does not reach the target (desired vergence angle) but parts of shaded light blue area does (Fig 1A). This deficit is even more remarkable in PD patients, there is a substantial limitation to perform convergence in PD. The eyes do not reach desired target leaving the disparity on the fovea. Latter might reflect in disabling double vision commonly seen in PD patients. Fig 1B depicts the summary of horizontal vergence gain (actual vergence angle/desired vergence angle) in healthy controls (blue box plots) compared to PD (black box plots). The median (interquartile range, IQR) gain in healthy subjects was 1.0(0.14) for convergence and 0.91(0.231) for divergence. The gain was significantly lower in PD patients, 0.65(0.79) for convergence and 0.49(0.75) for divergence. The reduced gain was statistically significant in both convergence and divergence (Unpaired T-test p < 0.01). It is noteworthy that Fig 1 focuses on the horizontal eye movements during convergence and divergence, the vertical eye movements are not shown. As expected, we found that the convergence associated with the downward vertical eye movements and divergence with upward eye movements. The vertical eye movements during convergence and divergence were conjugate. Given the focus of this manuscript examining the strategies to facilitate horizontal convergence and divergence in PD, and examining mechanistic underpinning with computational models, we analyzed pertinent horizontal angular eye position.

Fig 1.

(A) Summary of trajectory of vergence angles in healthy control (blue trace) and PD subject (black trace). The mean vergence angle is plotted on y-axis while corresponding time is plotted on x-axis. Solid line (black in PD and blue in healthy control) depicts mean vergence angle from 13 PD subjects and six healthy controls who were able to make convergence eye movements. The grey shade (PD) and light blue shade (control) depicts standard deviation. (B) Boxplot depicting vergence gain (plotted on y-axis) grouped by convergence and divergence for both PD (black) and control (blue) subjects. Length of box depicts interquartile interval, whiskers depict range, and horizontal line in the box depicts median value.

In order to compensate for impaired vergence, PD subjects incorporated four strategies as depicted in Fig 2. The first strategy was pure vergence eye movement, here called pure slow (Fig 2A). In Fig 2A, horizontal vergence angles plotted on the y-axis while the corresponding time is on the x-axis. The black line depicts the vergence angle, the magenta-colored part of the black line depicts pure slow vergence eye movement. As a second strategy, the subjects made a saccade to compensate for impaired slow vergence, here called pure fast (Fig 2B) eye movement. In Fig 2B the horizontal vergence angle is plotted on the y-axis while the x-axis depicts the corresponding time. The vergence angle, the black line, has a rapid shift (orange-colored epoch) depicting pure saccade. The last two strategies combined slow and fast eye movements. In one instance, slow eye movement preceded fast (slow-fast, Fig 2C), while the other had an opposite sequence of fast and slow movements (fast-slow, Fig 2D). Given the focus of this work on horizontal vergence, the Fig 2 does not show vertical eye movements.

Fig 2.

Examples of 3D horizontal gaze shifting strategies in PD subjects. Each panel depicts one type of strategy. Horizontal vergence angles (difference between right and left angular eye positions) are plotted on y-axis while corresponding time is plotted on x-axis. (A) Pure Slow (PS) strategy is slow continuous disconjugate vergence movement shown in magenta. (B) Pure Fast (PF) strategy is a fast conjugate saccadic movement employed due to impaired vergence. The pure fast movement is shown in orange. (C) Slow Fast (SF) is a combination strategy adapted as a result of inadequate vergence drive leading to an initial unsustainable slow component (magenta) followed by a compensatory fast component (orange). (D) Fast Slow (FS) is a combination strategy executed as a result of a fast component (orange), which then translates into a following slow vergence movement (magenta).

Vergence employing pure fast or fast-slow strategies (i.e., eye movement starting with an initial fast component), had longer latency as compared to the strategies that employ an initial slow component (pure slow or slow-fast, Fig 3). This was seen in both cohorts, healthy controls as well as PD subjects. Median IQR of the latency for convergence strategies was 0.05s (0.004s) for pure slow, 0.06s (0.11s) for slow-fast, 0.29s (0.16s) for pure fast, and 0.34s (0.38s) for fast slow. The median latency for divergence strategies was 0.05s (0.002s) for pure slow, 0.34s (0.1s) for pure fast, 0.02s (0.12s) for slow-fast and 0.36s (0.32s) for fast-slow. Statistical comparison using ANOVA showed that initial slow strategies (pure slow and slow-fast) had significantly shorter latencies as compared to initial fast strategies (pure fast, fast-slow) for both convergences (p < 0.01) and divergence (p < 0.01).

Fig 3.

Comparison of latency in different compensatory strategies. Boxplot depicting vergence latency (plotted on y-axis) are grouped according to movement strategy (pure slow: PS; pure fast: PF; slow fast: SF; and fast slow: FS) in convergence (A) and divergence (B). The box length depicts interquartile interval, whiskers depict range, and horizontal line in the box depicts median value.

On comparing the performance of PD patients with that of healthy controls, we found a clear difference in the distribution of compensatory strategies in both convergence and divergence, as shown in Fig 4. Healthy subjects were able to perform pure convergence 76.36% and divergence 65.76% of times. The difference was significant when compared with PD subjects who could do pure convergence 15.25% and divergence 7.69% of times. PD subjects utilized saccades followed by slow movements 27.96% of times in convergence 15.38% times in divergence. This strategy was not seen in healthy controls. About a third of the time (29.66% in convergence and 33.3% in divergence), PD subjects had not made any movement in response to the vergence command. Such behavior was not seen in healthy controls. The Chi-square test showed statistical independence in both convergence and divergence eye movements between PD subjects and controls. (Convergence X² = 1.75e⁻²⁰, Divergence X² = 3.1e⁻²⁵).

Fig 4.

Distribution of prevalence of 3D gaze shift strategies in case of PD convergence (A) compared to that in healthy control (B), and PD divergence (C) compared to control divergence (D).

In the subsequent analysis, we examined whether convergence and divergence movements are congruent or incongruent, that is, whether both eyes follow the same strategy while accomplishing the vergence eye movement. Fig 5 depicts the distribution of movement strategies of the right and left eye in the form of a heat map. Fig 5A, B depicts convergence and divergence in healthy controls. As expected, in most instances, healthy subjects make pure slow vergence. Both eyes participate by making binocularly convergent eye movements (i.e., making the same movements in both eyes). When the healthy subject's movement type is not pure slow, it is still congruent between the two eyes. As a result, most data points in healthy subjects fall on the equality line. The results contrast with that of PD subjects, where the eye movements are incongruent, i.e., both eyes follow different strategies (Fig 5C, D).

Fig 5.

Heat maps showing distribution of vergence strategies (PS, PF, SF, FS) in PD and controls in each eye. Categories from the right eye is plotted on x-axis while that from the left eye is on the y-axis. The color of the box depicts the frequency. (A) Distribution of divergence strategies in right vs. left eye in PD subjects; (B) Distribution of divergence strategies in right vs. left eye in healthy controls; (C) Distribution of divergence strategies in right vs. left eye in PD subjects; (D) Distribution of convergence strategies in right versus left eye in healthy controls. In healthy controls there is a high degree of symmetry in movements of right and left eye for both convergence and divergence whereas in PD subjects, the distribution is random and highly asymmetric.

Computational models accounting for the behavioral patterns in 3D gaze shift:

Our results provided the proof of principle that in PD, when vergence eye movements are impaired, saccades become more prominent in facilitating the 3D gaze shift. The fundamental question that remains is how saccades and vergence interact, and how such interaction plays out in PD. In the subsequent section we describe three different models, each with specific predictions. We then seek for the validation of the model predictions in data collected from PD patients. The common feature to all three models is two physiologically plausible networks and their connections via omnipause neurons. One network is comprised of the simulated neural substrate generating saccades, while the other lead to pure vergence. The omnipause neuron gate the activity for the saccade burst neurons as well as saccade related vergence neurons. The differences between the two models are the ways saccade and vergence networks interact. The subsequent section will first describe the saccade generating and vergence generating blocks common to all three models, and then we will discuss three ways PD can affect the communication between the two networks increasing the compensatory saccades as noted in our patients.

The design of the saccade-generator block in our model was templated upon the original saccade model proposed by Robinson and Zee (15, 16). The Robinson’s scheme of the saccade model was based on a motor error signal (desired ΔC, Fig 6A) that drives saccade burst neurons producing the saccade velocity command (VC, Fig 6A). Latter is directly transmitted to the motoneurons forming the pulse of innervation; the signal is also integrated to convert the pulse to step. The pulse-step combination is then filtered to compensate for the dynamic properties of the visco-elastic orbital eye plant (17). The model also features the local feedback loop comprised of the difference in desired change in eye position and serially connected resettable neural integrator (CRI, Fig 6A) (17, 18). The two together comprise of an instantaneous efference copy of the change in the eye position and is projected back and subtracted from the desired change in the eye position signal to create an instantaneous motor error signal (CME, Fig 6A)(17). Top aspect of Fig 6A depicts the organization and corresponding simulation parameters generating pure saccades. The parameter values are outlined in Table 2.

Fig 6.

(A) Block diagram of the model simulating vergence and saccade interaction with emphasis on foveal demand. The specific values and definitions of the parameters are depicted in Table 2 The time between two iterations was 0.2 ms, the equations depicting depicting the nonlinear relationships between conjugate motor error (CME) and output of the saccade burst neurons (SBN), and between vergence motor error (VME) and the output of vergence velocity neurons (VVN) and of saccade-related vergence burst neurons (SVBN) are depicted in Table 2. The gain (triangle symbols) depicts the neurons on which non0linearties are generated. The specific values of the nonlinearities are depicted in Table 2. CRI: conjugate resettable integrator, VRI, vergence resettable integrator, OPN: omnipause neuron, VPN: vergence pause neurons, s: Laplace transform operators. Table 2 depicts all values of the operators. (B-D) Simulation of the model depicting (B) Surface plot of simulation values for amplitude of gaze shift. The amplitude gain parameters are plotted on x-axis, the y-axis depicts velocity gain parameters; the color gradient depicts the amplitude of the gaze shift. (C): Surface plot of simulation results depicting velocity of gaze shift. The amplitude gain parameters are plotted on x-axis, the y-axis depicts velocity gain parameters, while the color gradient depicts the gaze shift velocity. (D) Simulated vergence eye position signal depicting expected simulation for initial velocity but not the amplitude. Simulated eye position is plotted on y-axis while corresponding time is on the x-axis.

Table 2:

Model simulation parameters.

	Parameters	Value
Saccadic system
Gain of conjugate pulse	Gpc	0.06
Gain of slide	Gsl	0.165
Tc slide	Tsl	0.08s
Tc conjugate neural integrator	Tcn	20s
Tc motor error pole	Tep	0.003s
Tc conjugate resettable integrator	Tcr	20s
Saccade local feedback delay	DelC	0.006s
SBN nonlinearity
yR=AR{1.0-exp[-(e0+x)/λR]}	e0	5
yL=AL{1.0-exp[-(e0+x)/λL]}	AL	440
For -e0<x<e0	AR	400
y-yR-yL	λL	10
	λR	10
Plant
	Tz	0.08s
	T1	0.3s
	T2	0.010 s abd
		0.013 s add
	ω	200 radians/s
	ζ	1.2
Vergence system
Gain of vergence pulse	Gpv (conv)	0.08
	Gpv (div)	0.01
Tc vergence neural integrator	Tvn	10s
Vergence local feedback delay	DelV	0.003s
VVN nonlinearity
Y=kxn/(xn+θn)	nC	1.0
	nD	0.8
	kC	120
	kD	125
	θC	15
	θD	30
Recruitment lag
	Tr1	0.02s
Tzr=(k1)(k2)	Tr2	0.005s
K1=VPAUSE/[(sTr1+1)(sTr2+1)]	K2 (conv)’	1.0
	K2(div)	0.1
VVN filter	Tf(conv)	0.01s
	Tf(div)	0.05s
SVBN nonlinearity
	AC	60
Y=A[1.0-exp(−x/λ)]	AD	80
	λC	6
	λD	4

The vergence model was based on the concept proposed by Zee and Levi (19, 20) that the vergence in response to 3D gaze shift is driven by the premotor commands from the neural network that is fundamentally similar to that of saccades (17, 21). The model features the vergence motor drive from the vergence velocity neurons (VVN, Fig 6A) producing a vergence velocity command (VVC, Fig 6A). Latter is in response to the vergence motor error (VME, Fig 6A) comprised of the difference between the desired change in the vergence angle and an instantaneous efference copy of the change in the vergence angle. After passing through the low-pass filter, the vergence velocity command is transmitted to the motoneurons. In addition, it also passes through the vergence neural integrator resulting in the vergence position command. The vergence velocity command is then transmitted through the filters and transfer function comprising the orbital plant. Blue colored model in Fig 6A depicts the organization and corresponding simulation parameters generating pure vergence. The values of simulated parameters are outlined in Table 2.

The subsequent step in our simulations that differentiates the three models is to determine how the vergence network could be affected in PD, and how PD affects saccade vergence interaction. PD is known to change the output of the subthalamic nucleus, latter is connected with the deep cerebellar nuclei via pontine pre-cerebellar neurons (22, 23). The deep cerebellar neurons directly project to mesencephalic vergence velocity neurons that are responsible for the optimal vergence function (24). Reduced vergence velocity neuron gain, leading to impaired vergence, cause vergence error projecting to the saccade generating network. The saccade, as a compensatory phenomenon, is triggered when the vergence error crosses the threshold (maroon arrow, Fig 6A). The same error also increases the gain of vergence velocity neuron (maroon arrow, Fig 6A) This first model, called “vergence gain model” also emphasizes stable omnipause neuron activity without any noise. The “vergence gain model” simulated different foveal demand paradigms by varying the vergence gain and the gain applied to the vergence velocity neuron (Fig 6A). The simulations are summarized in Fig 6B-D. The simulated gaze shift amplitude's surface plot showed no discernible change in amplitude while changing amplitude gain parameter values (Fig 6B). On the contrary, the surface plot of simulating the gaze velocity had an apparent dependence on the velocity gain parameter value (Fig 6C). The model accurately predicted the initial onset phase, but it failed to simulate eye trajectory after reaching the peak velocity. This phenomenon is depicted in Fig 6D where simulated vergence angle is depicted in dashed line while actual vergence angles recorded from the exemplary patient is depicted in solid line. Each line color depicts three different desired vergence positions. The dashed lines and solid lines overlap during initial phase, but they separate towards the end of the gaze shift. In addition, this model also expects that saccades are only triggered if initial vergence velocity is not sufficient to keep up with the foveal demands. As a result, the model could not explain pure fast movements or fast-slow movements.

It is possible for PD to alter omnipause neuron function (25) and consequent "noise" in the omnipause neuron induced inhibition causes asynchronous activation of either saccade or vergence eye movements. This noisy inhibition presents as a faulty switch in the saccade generating network as well as in the slow vergence generating network, i.e., "omnipause switch model." This aspect of the modification is depicted in Fig 7A where noise modulates the omnipause neuron activity. The simulation of this physiologically plausible model is depicted in Fig 7B. According to this prediction, the 3D gaze shift can have either pure slow, pure saccadic, or a combination of both depending on the amount of noise affecting the omnipause neurons. The model also accounts for realistic latencies noted in PD patients. The simulated values of velocity during vergence eye movements in response to change in omnipause neuron gain also provide physiologically plausible values, but the corresponding amplitudes were not realistic (Fig 7B). The example of three simulations of patient data is depicted in Fig 7C where vergence angle is plotted on y-axis while x-axis is corresponding time. The dashed line simulates realistic initial velocity seen actual patient data depicted in solid lines. However, the amplitudes are not realistic.

Fig 7.

(A) Block diagram of the omnipause switch model. The specific values and definitions of the parameters are depicted in Table 2 The time between two iterations was 0.2 ms, the equations depicting depicting the nonlinear relationships between conjugate motor error (CME) and output of the saccade burst neurons (SBN), and between vergence motor error (VME) and the output of vergence velocity neurons (VVN) and of saccade-related vergence burst neurons (SVBN) are depicted in Table 2. The gain (triangle symbols) depicts the neurons on which nonlinearties are generated. The specific values of the nonlinearities are depicted in Table 2. CRI: conjugate resettable integrator, VRI, vergence resettable integrator, OPN: omnipause neuron, VPN: vergence pause neurons, s: Laplace transform operators. Table 2 depicts all values of the operators. (B) Simulated values for the amplitude and velocity of gaze shift as modulated by changing OPN gain. The values for velocity range are unrealistic although amplitude are physiologically plausible. (C) Simulated vergence eye position signal depicting expected simulation for initial velocity but not the amplitude. Simulated eye position is plotted on y-axis while corresponding time is on the x-axis.

The models suggested that noisy omnipause neuron inhibition presents as a faulty switch only in the saccade generating network. On the other hand, the abnormal gain is required in the slow vergence generating network. Therefore, it deemed necessary to have coexisting pathophysiological mechanisms, one affecting the omnipause neuron switch and the other affecting the vergence velocity gain. The deficits seen in PD not only lead to abnormal omnipause neuron function but via different pathways they can also account for the impaired vergence gain at the vergence velocity neurons. To fulfill the computational need to accurately simulate PD data we combined features from both models. The new model (Fig 8A) predicted each strategy employed to execute vergence eye movements. The third model, called the "omnipause switch and vergence gain model," simulated discernible change in amplitude by changing the omnipause neuron gain parameters as well as the velocity gain parameters (Fig 8B). The simulations showed even more robust velocity changes in response to omnipause neuron and velocity gain parameters (Fig 8C). Examples of the simulations from actual patient data is shown in Fig 8D, where vergence angle is plotted on y-axis while x-axis is corresponding time. Dashed line (simulated vergence angle) superimposed upon the solid line (actual patient data) (Fig 8D). The model also accounted for the presence of all four types of strategies in 3D gaze shift (pure slow, pure saccade, saccade followed by slow, and slow followed by saccade movements). Given the third model, it is not necessary to have a prolonged latency for the onset of fast eye movement after the onset of slow eye movement, and right and left eye movements can be incongruent. The third model also predicted that in instances where the 3D gaze shift begins with a slow vergence component, the movement continues as pure slow if the eye velocity remains above a threshold, which we refer to as the saccade activation threshold (found to be about 20 degrees per second for our PD cohort). In contrast, in instances when the eye velocity is below this threshold, rapid eye movement such as saccade is triggered. These predictions were supported by the patient data. Fig 9A, B depicts initial and peak velocity distribution of pure slow and slow-fast movements in convergence and divergence, respectively. The box plot in Fig 9C depicts significantly higher initial velocity in those who have pure slow vergence eye movements. The median value (and range) of the initial velocity of pure slow movements were 38.22deg/sec (27.79-39.95 deg/sec) in convergence, and it was 38.35 deg/sec (30.34-42.39 deg/sec) in divergence movements. The results contrasted with slow-fast type of movement category where the eyes initially moved with much slower velocity, and subsequent foveal generated error triggers rapid gaze shift consistent with a saccade. The initial slow velocity for convergence was 3.47deg/sec (0.55-6.94 deg/sec) and it was 6.9deg/sec (1.73-24.34 deg/sec) in divergence.

Fig 8.

(A) Computational model utilizing a combination of the omnipause switch model and vergence gain models. (B) Surface plot of simulation values for amplitude of gaze shift where OPN gain parameters (y-axis) are compared with velocity gain parameter values (x-axis) showing clearly discernible change in amplitude for changing amplitude gain parameter values proving efficient modulation of amplitude (color gradient). (C) Surface plot of simulation values for velocity of gaze shift, where velocity gain parameter values are plotted on x-axis while corresponding OPN gain parameters are plotted on y-axis. The surface diagram clearly depicts that change in velocity for changing velocity gain parameter values suggesting efficient modulation of velocity (color gradient). (D) Simulated vergence eye position signal depicting expected simulation of both initial velocities as well as final amplitude of gaze shift. Simulated eye position is plotted on y-axis while corresponding time is on the x-axis.

Fig 9.

Velocity comparison of strategies involving an initial slow component in Pure Slow (PS) and Slow Fast (SF) in convergence and divergence. (A, B) Velocity values shown depicted as stars (PS) show high initial velocities. Peak velocities remain in the same range for both convergence and divergence. Velocity values shown depicted as triangles (SF) show very low initial velocities. Peak velocities are high due to the following fast saccadic component for both convergence and divergence. (C) Boxplot showing comparison of initial velocity values in PS and SF for convergence. The velocity is plotted on y-axis, x-axis is category. The length of box depicts interquartile interval, while horizontal line in the center of the box is median value. The whisker depicts range.

Discussion:

Both eyes receive slightly different images of the visual scene. Therefore, the fine adjustment aligning the two eyes is necessary to reconcile this disparity and achieve a cohesive 3D vision. Vergence eye movement, an essential component for achieving a coherent visual image, is divided into fusional and accommodative. Fusional eye movement is stimulated by a disparity between the retinal images while accommodative works alongside the lens’ and pupil's accommodation to correct the visual blur. This study is focused on disparity-driven or fusion vergence eye movements that are compromised in PD. We examined the physiological underpinning of four neuronal strategies implemented to compensate for impairment. We simulated anatomically and physiologically plausible vergence and saccade models, making two distinct yet physiologically plausible changes to the model simulating impaired vergence compensation strategies in PD. One mechanism underscored the visually driven trigger of saccade in response to impaired vergence eye movement, i.e., the vergence gain model. In contrast, the other change in the model depicted spontaneous noise generation asynchronously gating saccade versus vergence generating components of the neural circuit, i.e., the omnipause switch model. We found that the isolated models alone could not simulate the eye position signals during vergence eye movements. However, their combination, i.e., the omnipause switch and vergence gain model, accurately simulated vergence abnormalities seen in PD.

Under natural circumstances, the abrupt changes in the 3D gaze shift frequently occur with vergence and saccade (26-28). The saccades during vergence are interpreted as a part of a strategy to promptly take one eye to the target, but at the expense of the other eye being taken away from the target and followed by the slow return to the target. Such behavior, idiosyncratic amongst different subjects, facilitates rapid 3D gaze shift. We find that saccadic interruptions of pure vergence, although present in healthy subjects, is prevalent in PD; the presence of such deficits is enhanced by reduced vergence gain in PD.

The generation of pure saccade depends on the local feedback model (15, 16). In this concept, the motor error signal drives the brainstem burst neuron to generate a saccade velocity command that then causes the rapid gaze shift (29-32). The command then passes to the motor neurons where, along with the integrated and filtered version, compensates for the dynamic orbital elastic properties. In this concept, the omnipause neurons have a fundamental role in saccade generation. The omnipause neurons are tonically active during fixation, but they pause when the saccade is to be made in any direction. The same conceptual network is utilized in the generation of the vergence (19, 20). The omnipause neurons also have a fundamental role in gating the activity of vergence neurons in the horizontal plane. Therefore, we predicted that omnipause neurons might simultaneously trigger saccade or vergence. However, isolated omnipause dysfunction in the computational model did not explain all forms of vergence deficits seen in PD patients.

The isolated activation of the vergence requires the efficient generation of the velocity command produced by the vergence premotor neurons in response to a change in the gaze's desired depth. The vergence velocity neurons are regulated by the vergence-related pause neurons that use the trigger to initiate vergence at desired velocity (i.e., vergence velocity gain). The pause neurons are also influenced by the basal ganglia via precerebellar and deep cerebellar nuclei. We hypothesize that in disorders where the vergence velocity is extremely low, the system is likely to trigger saccade command. In contrast, when the vergence velocity gain is higher, the system is expected to activate the isolated vergence command. In a healthy subject, despite some oddities, the prevalence of pure vergence is much higher than PD, where vergence gain is low. PD patients are more likely to depend on saccades to perform 3D gaze shifts. The same concept also relies on the local feedback model; if there is a longer delay or reduced vergence velocity, the system is more likely to trigger saccades. Hence our findings are consistent with the previous explanation of interconnected saccade and vergence systems. It is also possible that the saccade vergence system, regulated by omnipause mediated gating mechanism, is asynchronously activated due to the abnormal noise in the gating mechanism. Indeed, the noise in an omnipause neuron or the burst generators is plausible in PD(25). Abnormal velocity gain could be due to impaired activity of mesencephalic vergence velocity neurons that are under the influence of the pause neurons and the deep cerebellar nuclei. The latter is modulated by the output of basal ganglia via precerebellar nuclei.

The conceptual models of saccade vergence interaction and their abnormal states in PD also follow physiological and pathophysiological realism. The neurodegenerative process in PD is known to affect the neural substrate for saccade and vergence. The midbrain houses the neurons involved in the control of pure vergence and those projecting to the ocular motor neurons innervating slow extraocular muscle fibers(33-35). These cells, located in the mesencephalic reticular formation in a region called supraoculomotor area, are critical to controlling vergence angle(33, 36, 37) and vergence velocity(24). The supraoculomotor area receives inputs from the fastigial nucleus and the interpositus nucleus. The supraoculomotor area sends monosynaptic excitatory projections to medial rectus motor neurons in the oculomotor nucleus. In addition, it projects bilaterally to the abducens nucleus to contact lateral rectus motor neurons.

There is increasing evidence that the subthalamic nucleus, one of the critical regions demonstrating abnormal neural discharge in PD, is connected with the areas that can modulate vergence. These connections can play an essential role in the pathophysiology of abnormal vergence in PD. The subthalamic nucleus modulates vergence via at least two possible pathways. One pathway involves the substantia nigra pars reticulata (SNr). The SNr receives inputs from the subthalamic nucleus and projects to the supraoculomotor area via the superior colliculus(38). Impairment in substantia nigra pars reticulata output as seen in PD affects vergence. The second pathway directly involves the cerebellum(39). This pathway involves subthalamo-ponto-cerebellar projections to the deep cerebellar nuclei via precerebellar pontine nuclei(40). There is obvious evidence of the involvement of the cerebellar pathways: 1) The cerebellar outflow is affected by the abnormal bursting and oscillatory subthalamic nucleus activity(38, 41). 2) Further downstream from the subthalamo-ponto-cerebellar projections, the cerebello-pontine fibers connect the deep cerebellar nuclei to the binocular angle-sensitive neurons and vergence velocity neurons in supraoculomotor area(39, 40, 42).

The saccade system is also affected in those with PD. The saccades are initiated within the frontal and parietal eye fields of the cerebral cortex. The cortical saccade signals follow two main pathways, one via the nucleus reticularis tegmenti pontis of the pontine reticular formation while the other via the superior colliculus. The nucleus reticularis tegmenti pontis neurons project to the oculomotor vermis (lobules 5-7) of the cerebellar cortex that sends GABAergic inhibitory signals to the underlying caudal fastigial nucleus (fastigial ocular motor region). The fastigial ocular motor region then projects to the omnipause neurons. The subthalamic nucleus is also likely to influence fastigial activity, and latter, then affects the omnipause inhibition to the saccade. Altogether the proposed conceptual scheme in the model, where the saccade vergence combination is at the epicenter of the 3D gaze shifting strategy, follows physiological realism. The known connections of the subthalamic nucleus with saccade vergence combination circuits and their implementation in the model successfully simulates the vergence in PD. The model provides an important insight into pathophysiological mechanisms underlying parkinsonian gaze shifting strategy in three dimensions.

In summary, we found that PD patients have significant impairment of both convergence and divergence compared to controls. We found reduced vergence gain and peak velocities, prolonged latencies, and more pronounced binocular asynchrony in PD. Such insufficiency leads to the recruitment of alternate strategies in performing 3D gaze shifts. Our models predict that the cause of insufficiency manifests as an inherent feedback mechanism that triggers a saccade in cases of initial vergence velocity being below the saccade activation threshold as well as a noisy omnipause neuron modulation of both the conjugate and disconjugate circuits. Future therapies to modulate this circuit, electrically or pharmacologically, would effectively treat visual deficits in PD.