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Chapter 22
CLINICAL REPRESENTATION OF MADDOX COMPONENTS

Key Words: Graphical analysis, Demand line-1:1, distance phoria, relative and fusional vergence, ZCVSBV, Alpern's spur, Sheard's criterion, Percival's criterion

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

Part V: Clinical Representation of Maddox Components

  • Introduction (Graphical analysis of accommodation and convergence)
    Axes and demand line (X convergence, Y accommodation)
    Five Independent variables:
    1.  Inter Pupillary Distance
    2.  Phoria
    3.  Relative and Fusional Vergence limits (BO and BI ) - Blur criterion (ZCSBV), Break criterion (ZSBV)
    4.  Amplitude of Accommodation
    5.  Calculated AC/A ratio
     
  • Positive and Negative Relative Convergence
    Percival's Zone of Comfort
    Sheard's criterion
     
  • Relative Accommodation

 


Graphical Analysis of Accommodation and Convergence
All clinical test results of binocular eye movements and accommodation can be represented graphically as combined functions of accommodation and convergence stimuli.  The horizontal axis of the graph represents convergence with BO prism plotted to the right of zero and BI prism to the left of zero.  Accommodative stimuli are plotted on the vertical axis.  The diagonal line on the graph represents combinations of accommodative and convergence stimuli presented by targets at various viewing distances.  For example, at the standard near test distance of 40 cm, the stimulus to accommodation is 2.5 D and the convergence angle subtended by the near target at the eyes is 2.5 meter angles.  For a 6 cm P.D., 2.5 meter angles equals 15 prism diopters where
   prism diopters = P.D. (cm) X M.A.

 

Fig 22.1
Graphical representation of accommodation and convergence stimuli.

The diagonal line is referred to by several terms including the demand line, Donder's line, and the 1:1 line.  Optometric data taken with targets at various viewing distances are plotted in reference to the demand lines.  For example, the distance phoria is plotted with the symbol (x) to the left for exo and to the right for eso of the demand line as it crosses the bottom of the graph.  The near phoria is plotted in a similar manner with respect to the demand line where it crosses the 2.5D accommodation stimulus level.  A line connecting the two measures of the phoria is referred to as the phoria line and it predicts the phoria at all viewing distances.  The phoria equals the separation of the phoria and demand lines. 

The reciprocal of the slope of the phoria line is a direct measure of the calculated AC/A ratio.  The blur, break, and recovery findings of positive and negative relative convergence are plotted to the right and left of the demand line respectively at the appropriate accommodation stimulus levels.  The separation between blur points for positive and negative relative convergence is referred to as the width of the zone of clear single binocular vision.  Straight lines are fitted to near and distance measures of blur points to base-in prism and to base-out prism.  The lines are usually nearly parallel to the phoria line and form the lateral boundaries of the zone of clear single binocular vision (ZCSBV).  The zone is limited on top by the monocular amplitude of accommodation.

The area within this parallelogram formed by the base-in and base-out limits specifies all possible combinations of convergence and accommodation stimuli to which the binocular visual system can respond.  The advantages of this method of representing clinical data are:

  1. Clinical data can be predicted at test distances other than those already examined.
  2. The influence of added lenses and prisms upon the clarity and comfort of binocular vision can be predicted in advance.
  3. Lenses and prisms and/or orthoptics can be prescribed as a result of observing the width of the zone, the position of the demand line in the zone, and the amplitude of the phoria and its correcting vergence.

Several graphical analysis forms are shown below.  Such forms can be used to record clinical optometric data.  An example of a completed graph of typical test results is shown in Fig 22.3.

 

Fig 22.2
Accommodation/ Convergence graphical analysis form (blank form)

Note that the slope of the demand line increases with IPD.

Fig 22.3
Typical completed form with clinical data.

(Patient exhibits an exophoria)

Zone of clear single binocular vision (ZCSBV) is the area bound on the left and right by the blur lines and on the top by the monocular amplitude of accommodation (in this case, 6D)


Positive and Negative Relative Convergence
The fourth component of the Maddox classification of convergence (fusional vergence) is quantified by duction tests.  The purpose of these tests is to measure the width of the zone of clear single binocular vision (ZCSBV) which indicates the range of fusional vergence.  This range is nearly the same for far and near viewing distances.  There is a small increase in positive fusional convergence (PFC) at near due to proximal convergence.  Fusional vergence is calculated as the sum of relative convergence and the phoria:

  Positive Fusional Convergence (PFC) = Positive Relative Convergence (PRC) - Phoria   (where eso is +)
  Negative Fusional Convergence (NFC) = Negative Relative Convergence (NRC) + Phoria   (where exo is -)

Relative vergence is the term used to describe the amplitude of vergence measured clinically.  These data are plotted on the graph on either side of the demand line.  The position of the demand line within the range of relative vergence is used as an indicator for prescribing prism.

 

Fig 22.4
Typical Plots of relative and fusional vergence.

Percival's criterion states that the prescription should equal the following:
    Vergence (prism diopters) = (1/3)*G - (2/3)*L
    where G = PRC and L = NRC if /PRC/ > /NRC/    and G = NRC and L = PRC if /NRC/ > /PRC/

 

Fig 22.5
Zone of comfort - Percivalís criterion.

Sheard's criterion states the prescription should equal the following:
     Vergence (prism diopters) = (2/3)*demand - (1/3)*reserve

Abnormally narrow zones of clear single binocular vision are symptomatic of a binocular sensory deficit which often can be corrected with orthoptics.  During the test, the prism amplitudes for the blur, break and recovery are noted and plotted on the graph.  Relative vergence should be measured after the phorias are measured to avoid aftereffects from the ductions upon the phoria.  Vertical phorias must be corrected before measuring the lateral ductions.

Relative Accommodation
Tests of positive (PRA) and negative (NRA) relative accommodation are indirect measures of negative and positive relative convergence.  These indirect measures apply primarily to pre-presbyopes.  These near tests at 40 cm are conducted with a fixed amount of convergence (2.5 MA).  As accommodation is stimulated with minus lenses or relaxed with plus lenses, the phoria is altered in the eso or exo direction respectively due to changes in accommodative convergence.  In order to continue seeing the target clearly and singly, the patient must counterbalance the induced change in phoria with fusional vergence.  In the case of added minus lenses, esophoria is compensated with negative fusional vergence and with plus lenses the resulting exophoria is corrected with positive fusional vergence.  In the event of a high AC/A ratio, or a narrow range of fusional vergence, changes in the phoria may require more fusional vergence than is available and as a consequence the patient may not be able to increase or reduce the accommodative response as much under binocular viewing conditions as under monocular conditions.  As a result, changes in the phoria can go uncorrected by fusional vergence.  These data points can be used to aid in plotting the BI and BO limits or the height of the ZCSBV.
 
Review Questions:
1.  What is the demand line?
2. What is the difference between positive fusional and positive relative convergence?
3.  What are Sheard's and Percival's criteria?
4.  What region of the ZCSBV limits the positive relative accommodation?
5.  What aspects of accommodation and convergence determine the blur, break and recovery measures?

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