Topology of the near response triad Glenn A. Myers* and Lawrence Stark
Department of Electrical Engineering and Computer Science, University of California at Berkeley, CA 94720, USA (Received 7 September 1989, in revised form 12 January 1990) The near response complex comprises three elements: accommodation, convergence, and pupillary constriction. The synkinesis between vergence and accommodation is well understood functionally, if not neuroanatomically. The latencies of near response components were measured in four healthy, experienced subjects to determine how the pupillary component is mediated. Addition of disparity stimulus to blur, yielding a near stimulus, reduces the latency of vergence eye movements and of accommodation by an amount that is significantly greater than the corresponding reduction in pupil latency. None of the existing hypotheses: vergence-pupil, accommodation-pupil or symmetric dual interaction, can account for this difference. Therefore, we present a new hypothesis: asymmetric dual interaction between accommodation and vergence.
The near response comprises three elements (the near response triad): as a sighted object approaches a viewer, the lenticular system (comprising the crystalline lens and the capsule) becomes more spherical (accommodates) to keep the object in focus. The eyes turn in (converge) to keep the image of the object on the fovea, and the pupil constricts. Following Krishnan et al.’, Figure I (upper panel) shows these three systems, and their synkinetic interactions. The accommodation-vergence and vergence-accommodation synkinetic pathways are drawn in continuous solid lines. The dashed lines correspond to four hypothetical forms of accommodation-vergence-pupil synkinesis. The neurological pathways to accomplish this synkinesis are not well understood. This paradigm is not intended to be interpreted in a detailed anatomical fashion. Rather, it should be regarded as a tool to aid in expressing and testing our hypotheses. How is the pupillary near response mediated? There are three hypotheses in the literature.
1. Vergence-pupil synkinesis - Path VP in Figure 1 (upper panel) illustrates a hypothetical link between the vergence motor controller and the pupillary motor controller. 2. Accommodation-pupil synkinesis - Path AP in Figure I (upper pa el) illustrates a hypothetical link between the accomm dation motor controller and the pupillary system motor controller.
9b
* Present address: Department of Biomedical Engineering, University of Iowa, Iowa City, I A 52242, USA. Q 1990 Butterworths for British College of Optometrists 0275-5408/90/020175-07
3. Symmetric dual interaction mode - The paths labelled SDIA and SDI, in Figure I (upper panel) (i.e. paths AP and VP respectively)together comprise a symmetric dual interaction mechanism with parallel paths from accommodation (SDI,) and vergence motor controllers (SDI,) to the pupillary motor controller. We present a fourth hypothesis:
4. Asymmetric dual interaction mode
- Comprising the paths labelled AD1 in Figure I (upper panel), one from the vergence motor controller to the pupillary motor controller (ADI,), and one from the accommodation sensor to the pupillary motor controller (ADIA). Our task is to determine the topology of the near response complex, and especially to determine how the pupillary near response is mediated. In engineering terms, this is a problem in structural identification, a most difficult task’. Most prior investigators studied the magnitudes of the input-output relationships. This method is inappropriate to the task since accommodation and vergence are strongly and symmetrically linked and thus move together in a ‘synkinesis.’ Therefore it is not always possible to distinguish between cause and effect in this complex system. For this and other reasons (see Discussion) we elected to study latencies of accommodative, vergence, and pupillary responses to blur, disparity, near (blur plus retinal disparity) and light stimuli. In two of our subjects, our results support the dual interaction theory3, with asymmetric synkinesis among the near response systems. In the other two subjects, our results support symmetric dual interaction4.
Ophthal. Physiol. Opt., 1990, VoI. 10, April
175
Topology of the near response triad: G. A . Myers and L. Stark
Cispority
Sensory Processor
Disparily-Verg
i Mo'or
i
163
Plonl
Conlroller
Dispority
Disparity-Verq
1%
Dispority Accorn 306 Blur-Accorn. Sensory Processor
IMotor
4%
I Plonl
Controller
Figure 1 Upper: block diagram of the near response triad. Four hypothetical forms of pupil synkinesis are shown by dotted lines (see text). This block diagram is not intended to be interpreted in a detailed anatomical fashion. Vertical solid lines with arrows indicate accommodative-vergence and vergence-accommodation synkinetic pathways. Middle: detailed latency distribution for one subject (NE) supporting asymmetric dual interaction hypothesis. Lower: detailed latency distribution for one subject (GM) supporting symmetric dual interaction hypothesis. For middle and lower panels: average response latencies in milliseconds given at the right. Numbers in the blocks represent the 'component' latencies in milliseconds. Component latency assignments are based on topological and physiological considerations (see text)
Methods Four healthy experienced subjects were studied to determine their responses to four kinds of stimuli: light, blur, retinal disparity, and near stimuli (blur plus retinal disparity). Three kinds of responses were recorded: pupillary responses (constriction), accommodation, and vergence eye movements. The experimental set-ups are shown schematically in Figure 2. To investigate the
176 Ophthal. Physiol. Opt., 1990, Vol. 10, April
topology of the systems of interest, stimulus configurations were chosen to minimize all the latencies measured, within the constraint that prediction not be present. Our experimental paradigms take advantage of the consensual nature of pupillary responses to near and light stimuli4. Light-pupil responses - A Maxwellian view stimulus subtending a square solid visual angle of 20 degrees by 20 degrees was presented centrally and the consensual pupillary response measured with an infrared video eye monitor system5. A fixation point served to control accommodation and to minimize eye movements. Light intensity was 4 log foot Lamberts (fL)against a dark background. In this and in all other stimulus paradigms, the subject was seated comfortably with his or her head in an ophthalmic head-rest with chin-rest. Light stimulus was delivered through a modified ophthalmoscope slitlamp apparatus by a gas discharge tube (Sylvania R1131C) with a rise time of less than 1 ms. In this and all other paradigms, pupillary responses were recorded from the right eye. Blur-accommodation responses - A dynamic optometer6 was used to measure accommodation in response to blur stimuli. Two targets of equal size and subjectively equal brightness were presented alternately along the visual axis of the right eye. The left eye was occluded to eliminate disparity stimuli. The times between changes in stimulus were varied randomly to eliminate prediction. Artifacts due to small movements of the right eye were noted in the record, but were easily distinguished from accommodative responses. Targets were positioned at the maximum comfortable limits of accommodative range (typically from 0 to 5-10 D). Blur-oergence responses - Using the same stimulus apparatus as above, and infrared limbus eye monitors7, vergence eye movements in response to blur stimuli were monitored. These responses were confirmed with the video eye monitor system. Blur-pupil responses - Using the same stimulus apparatus as above, and the video eye monitor, changes in pupil size in response to blur stimuli were monitored. Near stimulus-pupil - The subject viewed binocularly a pair of targets which were presented alternately along the visual axis of the right eye. Pupil size was monitored and target ranges were set at the maximum comfortable range for each subject as above. The far point was constrained by the apparatus to be 1 m. The near point was typically 10-20 cm. Near stimulus-accommodation - In response to near stimuli, both vergence and (unless the target moves in the medial plane) versional eye movements are observed. These movements make accurate measurement of accommodative responses very difficult. Thus accommodative responses to near stimuli are much more difficult to measure than blur accommodation responses, since the eye movements are greater. The values used for disparity accommodation are computed by subtracting 100 ms from the blur-accommodation latency for our subjects. This corresponds to the difference in latencies observed by Krishnan et al.' Near stimulus-oergence - Using the stimulus apparatus described above, and the limbus eye trackers, vergence eye movements in response to near stimuli were monitored. Disparity vergence latency is much less than accommodative vergence latency'. Thus near response-vergence latency is essentially equivalent to disparity-vergence latency.
Topology of the near response triad: G. A . Myers and L . Stark
9
0 Fixation point 1 m distant low light
\
I
I \
I I
I
I
Light stimulus 4.0 log f
Y !
I
1 , I
II
0 Monocular left e y e occluded
7
0 T a r g e t s aligned along
4
r i g h t visual axis
0 Binocular stimulus
otherwise identical w i t h blur stimulus
0 Stimulus r a n g e maximum comfortable f o r each subject 0 T a r g e t lighted alternately in quasi-random fashion
0
0 Brightness o f t a r g e t s
a
subjectively equalized
b
C
Figure 2 Experimental arrangements
Disparity-vergence - The subject viewed binocularly a pair of vertical lines presented on a CRT screen at 20 cm distance. A partition ensured that one line was seen by each eye. The lines were deliberately blurred electronically to reduce accommodative gain. Employing limbus eye trackers and the video eye monitor, vergence eye movements in response to retinal disparity stimuli were recorded. Disparity stimuli typically ranged from 1 to about 5 prism D. Disparity-pupil - Employing the binocular disparity stimulus configuration described above, and the video eye monitor, pupillary responses to retinal disparity stimuli were recorded. Previous investigators have employed a variety of methods to detect the onset of response. The three methods used most often are:
The investigator manually measures the latency to the onset of each response, then the average latency is computed. Latency is computed on an averaged response, e.g. by matching a prototype response to an averaged actual response'. A threshold is set (e.g. 10% of the maximum magnitude of response), beyond which the response is considered to have begung. The second method is unsatisfactory for this application because it depends upon a fit to averaged data, taking response latencies to be constant for any given stimulus magnitude. Although Lee et al.' found relatively fixed latencies in the light-pupil reflex, the pupillary near response latency varies widely from response to response for the same stimulus magnitude. The third method incorporates some delay due to the response dynamics of the system being measured. Thus it is unsuitable when comparing the responses of different systems with different dynamics from different types of stimuli. Thus the method of choice was the first, i.e. the experimenter measured each response individually based upon visual inspection of a computer display of the stimulus and response. Latencies were measured on a computer video display with the aid of a cursor whose position was calibrated in increments of 1/60th of a second (the video rate of the pupilometer). The pupillary data were smoothed with a non-real-time zero phase lag filter comprising convolution with the sequence ( 1/4,1/2,1/4) centred about time zero. This filter removes the apparent jitter in the pupil data due to video interlacing, but does not alter the latency
measurements. Both pupil area and its derivative were recorded. The delay and variance due to the video pupilometer were corrected*. Outlier points ( > 3 standard deviations from the mean) were discarded, as were points with excessive noise. In no case were more than 10% of responses or more than six responses in total discarded. It was particularly important to eliminate points which were suspected of representing anticipation or prediction on the part of the subject". Each datum represents 20-25 responses. Standard deviations (after outliers were removed, and after correcting for the variance in the pupilometer) were approximately 10 ms for the light reflex, 15 ms for the responses to disparity or near stimuli, and 20-25 ms for the responses to blur stimuli.
Experimental results Latency of pupil response to disparity plus blur, i.e. a near stimulus, is approximately equal7 to that of the pupillary response to blur (Table I; Figure 3 ) . The latencies of pupillary responses to disparity stimuli are longer than those to near in two of the three subjects for which disparity data are available. In the third subject (GM) the latencies are essentially equal. Latency of vergence eye movements in response to near stimuli (disparity plus blur), is less than that to blur alone by an average of 50 ms for the four subjects. The individual differences are statistically significant ( P < 0.01; a one-tailed student t-test was used throughout) in each of the four subjects. In all three subjects for whom disparity-vergence data are available, the disparityvergence latency is longer than near-vergence latency. Symmetric dual interaction In two of the subjects (JCA and GM) the reduction in vergence latency when ~
*Standard deviations were corrected for the variable latency of the pupilometer, due to the random time of occurrence of pupil response within the 16 ms interval between half frames: Sigma,,,,,,tcd
= SQRT
(sigma3?,,,,
- sigma&)
where: sigma,, = SD of latency of TV pupilometer. ?The small difference (less by an average of 15 ms for the four subjects) is statistically significant (P
Department of Electrical Engineering and Computer Science, University of California at Berkeley, CA 94720, USA (Received 7 September 1989, in revised form 12 January 1990) The near response complex comprises three elements: accommodation, convergence, and pupillary constriction. The synkinesis between vergence and accommodation is well understood functionally, if not neuroanatomically. The latencies of near response components were measured in four healthy, experienced subjects to determine how the pupillary component is mediated. Addition of disparity stimulus to blur, yielding a near stimulus, reduces the latency of vergence eye movements and of accommodation by an amount that is significantly greater than the corresponding reduction in pupil latency. None of the existing hypotheses: vergence-pupil, accommodation-pupil or symmetric dual interaction, can account for this difference. Therefore, we present a new hypothesis: asymmetric dual interaction between accommodation and vergence.
The near response comprises three elements (the near response triad): as a sighted object approaches a viewer, the lenticular system (comprising the crystalline lens and the capsule) becomes more spherical (accommodates) to keep the object in focus. The eyes turn in (converge) to keep the image of the object on the fovea, and the pupil constricts. Following Krishnan et al.’, Figure I (upper panel) shows these three systems, and their synkinetic interactions. The accommodation-vergence and vergence-accommodation synkinetic pathways are drawn in continuous solid lines. The dashed lines correspond to four hypothetical forms of accommodation-vergence-pupil synkinesis. The neurological pathways to accomplish this synkinesis are not well understood. This paradigm is not intended to be interpreted in a detailed anatomical fashion. Rather, it should be regarded as a tool to aid in expressing and testing our hypotheses. How is the pupillary near response mediated? There are three hypotheses in the literature.
1. Vergence-pupil synkinesis - Path VP in Figure 1 (upper panel) illustrates a hypothetical link between the vergence motor controller and the pupillary motor controller. 2. Accommodation-pupil synkinesis - Path AP in Figure I (upper pa el) illustrates a hypothetical link between the accomm dation motor controller and the pupillary system motor controller.
9b
* Present address: Department of Biomedical Engineering, University of Iowa, Iowa City, I A 52242, USA. Q 1990 Butterworths for British College of Optometrists 0275-5408/90/020175-07
3. Symmetric dual interaction mode - The paths labelled SDIA and SDI, in Figure I (upper panel) (i.e. paths AP and VP respectively)together comprise a symmetric dual interaction mechanism with parallel paths from accommodation (SDI,) and vergence motor controllers (SDI,) to the pupillary motor controller. We present a fourth hypothesis:
4. Asymmetric dual interaction mode
- Comprising the paths labelled AD1 in Figure I (upper panel), one from the vergence motor controller to the pupillary motor controller (ADI,), and one from the accommodation sensor to the pupillary motor controller (ADIA). Our task is to determine the topology of the near response complex, and especially to determine how the pupillary near response is mediated. In engineering terms, this is a problem in structural identification, a most difficult task’. Most prior investigators studied the magnitudes of the input-output relationships. This method is inappropriate to the task since accommodation and vergence are strongly and symmetrically linked and thus move together in a ‘synkinesis.’ Therefore it is not always possible to distinguish between cause and effect in this complex system. For this and other reasons (see Discussion) we elected to study latencies of accommodative, vergence, and pupillary responses to blur, disparity, near (blur plus retinal disparity) and light stimuli. In two of our subjects, our results support the dual interaction theory3, with asymmetric synkinesis among the near response systems. In the other two subjects, our results support symmetric dual interaction4.
Ophthal. Physiol. Opt., 1990, VoI. 10, April
175
Topology of the near response triad: G. A . Myers and L. Stark
Cispority
Sensory Processor
Disparily-Verg
i Mo'or
i
163
Plonl
Conlroller
Dispority
Disparity-Verq
1%
Dispority Accorn 306 Blur-Accorn. Sensory Processor
IMotor
4%
I Plonl
Controller
Figure 1 Upper: block diagram of the near response triad. Four hypothetical forms of pupil synkinesis are shown by dotted lines (see text). This block diagram is not intended to be interpreted in a detailed anatomical fashion. Vertical solid lines with arrows indicate accommodative-vergence and vergence-accommodation synkinetic pathways. Middle: detailed latency distribution for one subject (NE) supporting asymmetric dual interaction hypothesis. Lower: detailed latency distribution for one subject (GM) supporting symmetric dual interaction hypothesis. For middle and lower panels: average response latencies in milliseconds given at the right. Numbers in the blocks represent the 'component' latencies in milliseconds. Component latency assignments are based on topological and physiological considerations (see text)
Methods Four healthy experienced subjects were studied to determine their responses to four kinds of stimuli: light, blur, retinal disparity, and near stimuli (blur plus retinal disparity). Three kinds of responses were recorded: pupillary responses (constriction), accommodation, and vergence eye movements. The experimental set-ups are shown schematically in Figure 2. To investigate the
176 Ophthal. Physiol. Opt., 1990, Vol. 10, April
topology of the systems of interest, stimulus configurations were chosen to minimize all the latencies measured, within the constraint that prediction not be present. Our experimental paradigms take advantage of the consensual nature of pupillary responses to near and light stimuli4. Light-pupil responses - A Maxwellian view stimulus subtending a square solid visual angle of 20 degrees by 20 degrees was presented centrally and the consensual pupillary response measured with an infrared video eye monitor system5. A fixation point served to control accommodation and to minimize eye movements. Light intensity was 4 log foot Lamberts (fL)against a dark background. In this and in all other stimulus paradigms, the subject was seated comfortably with his or her head in an ophthalmic head-rest with chin-rest. Light stimulus was delivered through a modified ophthalmoscope slitlamp apparatus by a gas discharge tube (Sylvania R1131C) with a rise time of less than 1 ms. In this and all other paradigms, pupillary responses were recorded from the right eye. Blur-accommodation responses - A dynamic optometer6 was used to measure accommodation in response to blur stimuli. Two targets of equal size and subjectively equal brightness were presented alternately along the visual axis of the right eye. The left eye was occluded to eliminate disparity stimuli. The times between changes in stimulus were varied randomly to eliminate prediction. Artifacts due to small movements of the right eye were noted in the record, but were easily distinguished from accommodative responses. Targets were positioned at the maximum comfortable limits of accommodative range (typically from 0 to 5-10 D). Blur-oergence responses - Using the same stimulus apparatus as above, and infrared limbus eye monitors7, vergence eye movements in response to blur stimuli were monitored. These responses were confirmed with the video eye monitor system. Blur-pupil responses - Using the same stimulus apparatus as above, and the video eye monitor, changes in pupil size in response to blur stimuli were monitored. Near stimulus-pupil - The subject viewed binocularly a pair of targets which were presented alternately along the visual axis of the right eye. Pupil size was monitored and target ranges were set at the maximum comfortable range for each subject as above. The far point was constrained by the apparatus to be 1 m. The near point was typically 10-20 cm. Near stimulus-accommodation - In response to near stimuli, both vergence and (unless the target moves in the medial plane) versional eye movements are observed. These movements make accurate measurement of accommodative responses very difficult. Thus accommodative responses to near stimuli are much more difficult to measure than blur accommodation responses, since the eye movements are greater. The values used for disparity accommodation are computed by subtracting 100 ms from the blur-accommodation latency for our subjects. This corresponds to the difference in latencies observed by Krishnan et al.' Near stimulus-oergence - Using the stimulus apparatus described above, and the limbus eye trackers, vergence eye movements in response to near stimuli were monitored. Disparity vergence latency is much less than accommodative vergence latency'. Thus near response-vergence latency is essentially equivalent to disparity-vergence latency.
Topology of the near response triad: G. A . Myers and L . Stark
9
0 Fixation point 1 m distant low light
\
I
I \
I I
I
I
Light stimulus 4.0 log f
Y !
I
1 , I
II
0 Monocular left e y e occluded
7
0 T a r g e t s aligned along
4
r i g h t visual axis
0 Binocular stimulus
otherwise identical w i t h blur stimulus
0 Stimulus r a n g e maximum comfortable f o r each subject 0 T a r g e t lighted alternately in quasi-random fashion
0
0 Brightness o f t a r g e t s
a
subjectively equalized
b
C
Figure 2 Experimental arrangements
Disparity-vergence - The subject viewed binocularly a pair of vertical lines presented on a CRT screen at 20 cm distance. A partition ensured that one line was seen by each eye. The lines were deliberately blurred electronically to reduce accommodative gain. Employing limbus eye trackers and the video eye monitor, vergence eye movements in response to retinal disparity stimuli were recorded. Disparity stimuli typically ranged from 1 to about 5 prism D. Disparity-pupil - Employing the binocular disparity stimulus configuration described above, and the video eye monitor, pupillary responses to retinal disparity stimuli were recorded. Previous investigators have employed a variety of methods to detect the onset of response. The three methods used most often are:
The investigator manually measures the latency to the onset of each response, then the average latency is computed. Latency is computed on an averaged response, e.g. by matching a prototype response to an averaged actual response'. A threshold is set (e.g. 10% of the maximum magnitude of response), beyond which the response is considered to have begung. The second method is unsatisfactory for this application because it depends upon a fit to averaged data, taking response latencies to be constant for any given stimulus magnitude. Although Lee et al.' found relatively fixed latencies in the light-pupil reflex, the pupillary near response latency varies widely from response to response for the same stimulus magnitude. The third method incorporates some delay due to the response dynamics of the system being measured. Thus it is unsuitable when comparing the responses of different systems with different dynamics from different types of stimuli. Thus the method of choice was the first, i.e. the experimenter measured each response individually based upon visual inspection of a computer display of the stimulus and response. Latencies were measured on a computer video display with the aid of a cursor whose position was calibrated in increments of 1/60th of a second (the video rate of the pupilometer). The pupillary data were smoothed with a non-real-time zero phase lag filter comprising convolution with the sequence ( 1/4,1/2,1/4) centred about time zero. This filter removes the apparent jitter in the pupil data due to video interlacing, but does not alter the latency
measurements. Both pupil area and its derivative were recorded. The delay and variance due to the video pupilometer were corrected*. Outlier points ( > 3 standard deviations from the mean) were discarded, as were points with excessive noise. In no case were more than 10% of responses or more than six responses in total discarded. It was particularly important to eliminate points which were suspected of representing anticipation or prediction on the part of the subject". Each datum represents 20-25 responses. Standard deviations (after outliers were removed, and after correcting for the variance in the pupilometer) were approximately 10 ms for the light reflex, 15 ms for the responses to disparity or near stimuli, and 20-25 ms for the responses to blur stimuli.
Experimental results Latency of pupil response to disparity plus blur, i.e. a near stimulus, is approximately equal7 to that of the pupillary response to blur (Table I; Figure 3 ) . The latencies of pupillary responses to disparity stimuli are longer than those to near in two of the three subjects for which disparity data are available. In the third subject (GM) the latencies are essentially equal. Latency of vergence eye movements in response to near stimuli (disparity plus blur), is less than that to blur alone by an average of 50 ms for the four subjects. The individual differences are statistically significant ( P < 0.01; a one-tailed student t-test was used throughout) in each of the four subjects. In all three subjects for whom disparity-vergence data are available, the disparityvergence latency is longer than near-vergence latency. Symmetric dual interaction In two of the subjects (JCA and GM) the reduction in vergence latency when ~
*Standard deviations were corrected for the variable latency of the pupilometer, due to the random time of occurrence of pupil response within the 16 ms interval between half frames: Sigma,,,,,,tcd
= SQRT
(sigma3?,,,,
- sigma&)
where: sigma,, = SD of latency of TV pupilometer. ?The small difference (less by an average of 15 ms for the four subjects) is statistically significant (P
