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Chapter 17
ACCOMMODATION:
MADDOX COMPONENTS AND ACCURACY

Key words: Maddox, tonic, proximal, blur, convergence, focus

Outline
XII. Near Response: Pupil constriction, Accommodation and Vergence. 

Part I: Accommodation (contí): Maddox Components and Accuracy

  • Maddox-Heath Components & stimuli
    Tonic accommodation (resting focus 1.5D myopic) and adaptation - The myopias
    Proximal accommodation-Coarse adjustment, Spatiotopic cues
    Blur driven accommodation - Fine adjustment
    Cross-coupling- Convergence- CA/C (covered in Chapter 21)
     
  • Accuracy (Lazy Lag)- Hysteresis and depth of focus (01. - 0.75D)
    Pupil size (mm)
    Image quality - spherical and chromatic aberrations
    Visual sensitivity- acuity, contrast sensitivity, target size and spatial components
     
  • Static response- Accommodative response function
    Initial plus refraction bias
    Linear response
    Soft and final saturation at amplitude limit
     
  • Dynamic Responses
    Latency, 350-400 msec; 20 msec shorter for far to near
    Response time, 1 second
    Velocity, exponential decay starting 5-10 D/sec/D, faster near to far
    Continuous sampling
    Poor predictor- lags sinusoidal stimuli by 0.4 sec
     
  • Binocular accommodation- enhanced over monocular
    Conjugacy and Differential accommodation


Components of Accommodation
Maddox devised a classification scheme for convergence that applies very well to accommodation. He classified stimuli to accommodation into four categories: tonic or intrinsic; proximal or perceptual-spatiotopic; retinal optical; and cross-coupled or associated with another motor response. These categories were defined by Heath as tonic accommodation, proximal accommodation, blur-driven accommodation, and convergence accommodation. This chapter discusses the first three. The fourth, convergence accommodation, is discussed in Ch. 20.

The proximal or perceived distance cues are used to shift focus from one target of interest to another much like a saccade changes foveal fixation from one target to another. The blur cue is used to maintain clarity of a fixated image as the head and or target move about. The tonic cue is a set point or resting bias that represents the balance of all intrinsic innervations in the absence of an external stimulus. Finally, the cross-coupled stimulus is an associated response between accommodation and convergence that allows a stimulus to either motor system to activate both responses. This coupling helps coordinate actions of motor systems that are responding to a common target.
 
Tonic accommodation
Tonic accommodation is referred to as the resting focus of accommodation and it represents a balance of activity of the two branches of the autonomic nervous system. Normally this resting focus is about 1.5 D myopic compared to the far point of the eye measured in an optometric examination. This is referred to as a pseudo myopia that can be manifest under a variety of conditions. These conditions include 1) darkness which manifests the condition of night myopia, 2) empty fields such as encountered in aviation and is called empty field or space myopia, and 3) while looking through a microscope with a large depth of field, which is called instrument myopia. The most troublesome of these is night myopia which will afflict many of your patients. They will complain that their prescription is not strong enough for night driving and they may require a special night vision prescription.

 

Fig 17.1
Factors contributing to night myopia.

There are optical and sensory components of night myopia Optical components include pupil dilation and spherical aberration. Normally the lens has positive spherical aberration, i.e. it is more powerful in the periphery than along the optical axis. The periphery focuses images in front of the retina and this myopic error is more pronounced as the pupil diameter increases. In addition there is a sensory phenomenon called the Purkinje shift in which the dark adapted eye is more sensitive to short (blue 505) than medium (yellow 555) wavelengths of light. Thus the eye has a shift in luminance sensitivity toward shorter wavelengths in the dark. Because the eye has positive chromatic aberration, the long wavelengths are focused behind the short ones. Accommodation is presumed to focus the most sensitive wavelength components of the image. Accordingly refractions with multiwavelength photopic stimuli result in myopic errors for shorter wavelength stimuli. In darkness, the Purkinje shift combined with chromatic aberration of the eye causes a change in refractive error under scotopic condition. Taken together the sensory and optical factors, this amounts to 0.75 D of myopia. This leaves another 0.75 D of myopia that results from imbalance of the autonomic nervous system caused by innate imbalance, drugs or motor aftereffects of prolonged near work that produces accommodative spasm. The latter condition can affect any of the myopias and is very common. Accommodative spasm aftereffects can be relieved by periods of rest every 20-30 minutes during which patients are encouraged to get up, stretch their legs, and focus on distant targets.

Space or empty field myopia is attributed to the balance of sympathetic and parasympathetic autonomic components and after-effects of prior accommodative responses when an accommodative stimulus is absent, such as in a uniform field. A related effect to space myopia is called plus lens-fog myopia. During a refraction, many clinicians like to relax accommodation of both eyes by placing plus lenses of 0.5D before the eyes and then measure the balance of the proposed refractive correction. Also when we refract we tend to fog vision, and then reduce the lens value until the patient has peak visual acuity. This technique produces a plus bias to the refractive correction. It prescribes the minimum minus or maximum plus lens to avoid over stimulation of accommodation. One potential problem with this technique is that occasionally plus lenses can trigger a space myopia and cause an increase rather than relaxation of accommodation in as many as 40% of your patients. There is no strong familiar distance cue to indicate the correct distance of the target and the patient can perceive the near point card as closer than it really is. This happens with children. You may find that greater minus lens power is needed for the patient to clearly see their acuity limit than had been needed prior to the plus lens fog. If this happens, take a break and use the chromatic duo chrome test. Occasionally, plus lenses will manifest a latent hyperopia, in which patients continue to relax accommodation in the presence of plus lenses.

Proximal accommodation
Coarse adjustments of accommodation in response to perceived spatiotopic location. Most of the time, when we change our fixation from one target to another we also need to alter our accommodation.  This adjustment of accommodation is made without the benefit of a quantitative assessment of retinal image blur. It is as though our accommodation shifted from one perceived distance to another in response to perceptual cues. After reaching the new target distance, a fine adjustment process refines the response by utilizing retinal cues such as blur. The fine adjustment mechanism maintains accommodation without any conscious effort. While this latter type of accommodation is the most studied and emphasized in optometric practice, the proximal accommodative stimulus is probably just as important. It would be like trying to choose between saccadic and pursuit adjustments of gaze. You need both to survive and both are equally prevalent.

There have been several studies that illustrate the effect of proximal distance cues on accommodation. Ames used relative size and overlap and recently Kruger used loom or changing size while blur was eliminated by pin hole pupils. It is clear from these experiments that accommodation does indeed respond to apparent distance.

Blur accommodation (optical reflex) 
Once the retinal image is foveated and an initial coarse adjustment of accommodation has been made, what stimulus is used to maintain the fine adjustment accommodative response? Most of us would say blur. However, blur by itself might not be enough. Take for example the problem of a sudden head movement that puts the target a half diopter out of focus. Blur of this target is identical for targets that are too close or too far away from the eye. Positive and negative blur of the retinal image are identical. Yet we accommodate to this one half diopter error correctly on the first attempt, without a trial-and-error strategy. However, if the error is greater than 2 D, we do make trial and error attempts to focus the image.

What are the additional stimuli that make the initial correct responses to smaller amounts of blur possible? There are several that are used, including chromatic aberration and astigmatism.

The role of chromatic aberration becomes apparent during difficulty in accommodating correctly with monochromatic light. With chromatic aberration we can sense a myopic-overaccommodated state by the higher contrast of red than blue chromatic fringes and for a hyperopic-underaccommodated state we sense the higher contrast of blue than red chromatic fringes. Chromatic fringes are utilized even though they are not visible on a conscious perceptual level. It is possible to experimentally modulated chromatic fringes independently of true focus errors and bias the accommodative response by the fringes (Mathiews and Kruger).

Astigmatism could also provide error information. The focus of the major and minor astigmatic meridians cause blur distortion of the image which could be used to indicate whether the eye was over or under accommodated. Utilization of this cue would require learning the axis of astigmatism and the distal and proximal limits of the interval of Sturm.

Finally, the eye may actually make continuous trial and error adjustments of accommodation (hunting cycle) by using the unstable fluctuations of accommodation that are analogous to fixation drift of the eyes. During attempted steady fixation the lens has slow and abrupt variations in power. The slow variations are on the order of 0.5 diopters and occur once every 2 seconds (0.5 Hz) whereas the fast variations are small 0.1 D and occur twice a second. 

 

Fig 17.2
Frequency spectrum of accommodation. 
(Spectral density is plotted on y-axis. In other words, frequencies at which the eye most often accommodates have a higher spectral density.)

Note the large peak at 2 cycles/sec, which correlates with slow variations of the hunting cycle (trial-and-error adjustments)

During the hunting cycle, if the eye kept track of the variations of retinal image clarity and the direction of accommodative change it could focus in the direction that made the image clearer. All of these stimuli are thought to assist the fine adjustment mechanism of accommodation. These stimuli are called odd-error stimuli because they indicate the correct direction in which to accommodate or unaccommodate.


Accuracy of accommodation
The accuracy of the fine adjustment mechanism for accommodation depends upon the ability of the eye to sense reduced contrast (blur) of the retinal image. There is a threshold or minimal amount of defocus that can be detected. This is called the ocular depth of focus (DOF). Generally, the DOF for most everyday targets such as newspaper print ranges between 0.5 D to 0.75 D, but under controlled laboratory conditions it can be as low as 0.1 D. The DOF depends upon a variety of optical and sensory factors. Optical factors include pupil size, optical aberrations of the eye including spherical and chromatic, errors of refraction including spherical and astigmatic, and the wavelength of light. Sensory factors include visual acuity and contrast sensitivity.

The DOF is inversely related to pupil diameter. When the pupil becomes small enough, only paraxial rays enter the eye and images of objects at all viewing distances appear equally clear. However small pupils under 2 mm reduce acuity because they produce diffraction blur of all images. Larger pupils allow non-paraxial rays to enter the eye, which make blur of nonconjugate images more visible. As a result, the DOF gets smaller. Eventually, at sizes greater than 4 mm, peripheral spherical and chromatic aberrations degrade the retinal image and acuity. Thus there is a balance between best visual acuity and smallest depth of focus. The optimal size is about 2 mm where the DOF is large and visual sensitivity is still minimally affected by either peripheral aberrations or diffraction blur.

Chromatic aberration will also increase the DOF by degrading visual acuity. This is demonstrated with achromatizing lenses or monochromatic light. The DOF is smallest at the wavelength at the peak of the spectral luminosity function or at 555nm. Sensory factors also influence the DOF by their impact on contrast sensitivity. Blur detection is basically a contrast decrement task. Anything that impairs contrast sensitivity such as peripheral viewing, baseline refractive error, and subnormal vision will increase the depth of focus. In addition it is mainly the high spatial frequency detail that is affected by small amounts of blur. Blur is essentially a low-pass filter of the image plane and it will impair detection of small objects or test letters more than large ones. This is why we refine refractive corrections with the small letters near the patientís acuity limit.

 

Fig 17.3
Depth-of-field and Lag/ lead of accommodation.

A) Lead of accomodation. (notice position of best focus relative to the retina.)
B) Lag of accommodation. 
Depth of field causes A and B (and all states in-between) to look the same.

C) Far targets usually focus in front of the retina
D) Near targets usually focus behind the retina


Static Response: Accommodative Response Function
The depth of focus (DOF) influences the accuracy of the accommodative response.  The accommodative response is generally smaller than the accommodative stimulus by an amount equal to the depth of focus. This lag or error is called the lazy lag of accommodation.  This lag is demonstrated with the accommodative stimulus response function (See Fig 17.4). This function has four regions: 

  1. There is the initial non-linear portion over which accommodation changes less than the stimulus if at all. 
  2. There is a linear zone over which a change in accommodative stimulus produces a moderately large and proportional change in accommodation.
  3. There is a non-linear transitional region of soft saturation where slope of the function decreases with larger amplitude stimuli. It is followed by a zone of hard saturation where the response has reached its full amplitude. 
  4. The amplitude limit is followed by a reduction in accommodation when the stimulus far exceeds the amplitude and the response declines below its peak.


 

Fig 17.4
Accommodation stimulus response.

It is possible to make the accommodative response lead the stimulus by the DOF by starting with a large accommodative response and reducing the stimulus. The lead represents a hysteresis or spasm aftereffect from the prior accommodative response and shows that accommodation lags the change in stimulus value rather than always being smaller than the current stimulus.

Dynamics of Accommodation
Accommodation is a relatively sluggish system compared to most other eye movements except the pupil. There are several measures of accommodation dynamics including latency or refractive period, response time, prediction ability, and gain or amplitude. Accommodation has a latency of about 350 - 400 msec (.35 to .4 sec). The latency describes the time for the response to begin after the stimulus onset. The response latency from far to near stimuli is about 20 msec shorter than the latency from near to far stimuli. The response duration is nearly 1 second from the time it begins but it may be shorter with some effort. The dynamic time course of the response changes gradually over the one-second period, and follows the form of a decaying exponential. The initial velocity of the accommodative response depends upon the amplitude of the stimulus. It is approximately 5-10 D/sec per diopter of stimulus. The velocity is slightly faster for near to far stimuli than for far to near, simply because there is an active traction force on the lens when it is reduced in power compared to the passive mechanical changes that occur during increase of power.

 

Fig 17.5 Step response of accommodation. Stepped stimuli (bottom) illustrates latency,velocity,andexponential nature of accommodative response (top).

 

 

 

 

Accommodation has difficulty following periodic variations of blur, such as pendular or sinusoidal changes, and requires the .4 second latency. Therefore the response lags behind the periodic stimulus by .4 sec. Accommodation is not a good predictor to slow variations in blur. For this reason it has a limited ability in keeping up with abrupt high frequency changes grater than 0.5 Hz.

 Fig 17.6
Sinusoidal response of accommodation.

Stimulus shown on top and accommodative response shown on bottom for each frequency.

Notice that accommodation has trouble keeping up with stimulus frequencies much greater than 0.5 Hz.

 

Dynamic accommodation is assessed clinically using a lens-flipper apparatus with which the patient views printed material through alternate views of plus 2D and minus 2D lenses. The objective is to clear the near target as quickly as possible following each lens flip. The number of complete plus-minus cycles/minute is the measure of accommodative facility. A normal value is 20 cycles/minute which corresponds to an accommodative response time of 1.5 seconds. Slower rates are easily increased with practice.

Binocular Accommodation:
Conjugacy and differential accommodation

Accommodation appears to follow Hering's law in that it is roughly conjugate in the two eyes as is pupillary constriction. However under certain circumstances the eyes are able to clear the two retinal images with unequal blur. One way this is done is by suppression of the blurred image. The other is to accommodate unequally in the two eyes. This can occur with training up to .5D and occasionally up to 1-2 D. It is seen in anisometropes who manifest less anisometropia at near distances than at far viewing distances, presumably due to aniso accommodation.

 
 Fig 17.7
Effect of cycloplegia on yoked accommodation.

Figure 17.7 above illustrates an experiment which demonstrates the conjugacy of accommodation. Yoking is indicated by comparing the accommodative response of the covered eye when accommodation is stimulated in the open eye that is normal or cyclopelged.

Unequal stimuli for accommodation also occur in asymmetric convergence. Approximately 1D aniso accommodation is stimulated at near distance of 15 cm in 45 degrees eccentric gaze because the target is closer to one eye than the other. The aniso accommodation response produces unequal resting foci aftereffects which suggests that tonic accommodation can adapt unequally in the two eyes.

 

 Fig 17.8
Differential accommodation in asymmetric viewing.

Near objects off to the side are closer to one eye than the other, requiring different amounts of accommodation in each eye to be simultaneously clear.

Review Questions:

1.List the 3 categories of accommodative myopia.
2.What are the coarse and fine adjustment components of accommodation?
3.How does pupil size influence the depth of focus?
4.What is the influence of plus refraction bias on the accommodative response function?
5.What are the limits of differential or aniso accommodation
6.Describe the dynamic characteristics of accommodation.
7.What are examples of odd-error signals or stimuli for accommodation?
8.List four changes in the lens during accommodation
9.What is the function that describes the amplitude of accommodation as a function of age?
10.What is the relaxation theory of accommodation?
11.What physiological factors contribute to the loss of accommodation with age?

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