COOP notes #8
Today we'll do Chapters 22 & 5
GRAPHICAL ANALYSIS
Graphical analysis is based on the Maddox components/classifications where
Maddox describes four stimuli to accommodation and convergence (tonic innervation,
proximal cue [spatial cue] and disparity [retinal cue] and cross-links [AC/A
and CA/C]).
Clinical case analysis is based on the assumption that there is a linear
summation of these components: When we converge and accommodate, we're summing
those 4 components of accommodation and convergence linearly. 60 years ago,
Dr. Morgan and his colleagues took the Maddox concept and put it in a graphical
format so clinically you can write your data in a form that would show how
accommodative vergence, fusional vergence, and tonic vergence would add
up together. This graphical analysis technique allows you to predict what
real world stimuli your patient can respond to with comfort and helps you
to prescribe lenses and prisms.
Today we'll show how Maddox components are represented in this graphical
representation.
The horizontal axis is convergence & divergence. The zero is when eyes
are parallel looking at infinity. Convergence responses to BO prism are
to the right of zero and divergence responses to BI prism are to the left
of zero.
Test at 2 distances: At 6 m (or infinity) you have zero stimulus to convergence
& accommodation (appropriate horizontal scale is at bottom of graph).
Then test at 40 cm (appropriate horizontal scale is at top of graph). Therefore,
you'll have 2.5D stimulus to accommodation. Level of convergence at 40 cm
is 2.5 meter angles. Convert that to prism diopters by multiplying it by
PD.
e.g. if PD = 6 cm, then (6cm)(2.5D) = 15 prism diopters.
On the graph, go to 15 prism diopter stimulus of of convergence and 2.5
D stimulus to accommodation at 40 cm . Vertical and horizontal lined drawn
through these two intersect (2.5D of accommodation & 15 prism diopter
of convergence), at a point represents the near stimulus at 40 cm.
You can also plot a point for 20 cm of viewing distance: Therefore it would
be 5D of stimulus to accommodation & (5)(6) = 30 prism diopters of convergence.
If you connect all these real world stimuli points, it forms a line called
the "Demand Line" or "Donder's Line" or the "One
to One Line." Mostly it's called the Demand Line because it represents
the stimulus to accommodation and convergence. That single line represents
all physical stimuli in real space at a viewing distance.
The demand line varies for different PD distances. For a 7cm PD, there are
more prism diopters of convergence for every diopter of accommodation. If
your eyes are really far apart you have to converge a lot more to see the
same point than if your eyes are closer together. Therefore, the demand
line depends on the PD distance.
3 Components of Maddox Classification are represented by the graph.
1. Tonic vergence
2. Fusional vergence
3. Accommodative vergence
How do we represent tonic vergence? Remember tonic vergence brings us from
anatomical position of rest to physiological position of rest. When we measure
our phorias, we're measuring the physiological position of rest which is
basically,
Physiological position of rest = Demand + Phoria (vergence error)
e.g. If you're 3 exo at near & 1 exo at far & the near demand is
15 prism diopters, then you diverge by 3 prism diopters from 15 prism diopters
to plot the position of rest at near (sum of physiological position of rest
and any accommodative vergence). As a result, you are only converging 12
prism diopters when one eye is occluded.
To plot the phoria on the graph, draw an X to the left (if exo) or to the
right (if eso) of the demand line at the corresponding test distance. Phoria
is the distance between the demand line to that data point (3 prism diopters).
The phoria is an error of vergence, so under monocular viewing conditions,
you converged 12 prism diopters when ideally you were supposed to converge
15 prism diopters. Next connect the near and far phorias points with a single
line. That line is called the "Phoria Line."
What is interesting about the phoria line is that you can measure phoria
at 40 cm (near) and at 6 m (far). Now when we connect the 2 points (which
gives us the phoria line) we can predict the phoria at any other viewing
distance. Phoria is the separation between the phoria line and the demand
line at a specific viewing distance. Therefore, according to the graph at
20 cm viewing distance, phoria is ~7 prism diopters. Phoria is the amount
of error by which patients miss the mark.
Phoria at near = Phoria at far + Accommodative vergence.
If accommodative vergence is constant,
then Calculated AC/A ratio = reciprocal of the slope of phoria line
Lower AC/A ratio -- steeper phoria line. So when this line is vertical,
then AC/A = 0. When AC/A = PD(in cm), then slope of phoria line equals slope
of demand line. e.g. If AC/A ratio is 6/1 & PD=6cm, then the phoria
line would be parallel to the demand line. But usually AC/A is less than
the demand line (that is, more vertical).
Next step is to measure the convergence & divergence limits. To do this
you need a Risley prism. The Risley prism is made of 2 large prisms. They
spin so that sometimes their bases are on opposite sides and this gives
zero power. Other times their bases are on the same side and in this case
the total power is the sum of the two.
[Picture]
You can set up this prism to stimulate convergence of the eye until the
patient sees double (cannot fuse) and also stimulate divergence of the eye
until the patient sees double.
We can plot how much we can converge & diverge from that phoria line.
That range ends up being a constant distance from the phoria line. If you
consider the phoria line as the fusion free position of rest which is the
sum of tonic and accommodative vergence, what that means is that you have
a constant amount of fusional convergence or divergence you can add at any
viewing distance.You'll find that convergence range with prism is nearly
constant for all viewing distances for that phoria line (it increases slightly
with proximity due to proximal vergence). This means that we are adding
a constant amount of (+) positive fusional convergence to a constant amount
of accommodative vergence to a constant amount of tonic vergence. The graph
represents this linear summation.
What you end up with is a parallelogram which represents a combination
of all prism and lens stimuli which your binocular system can respond to
with clear, single binocular vision. So you can converge or diverge to see
singly & adjust your focus to see clearly. Therefore you can converge
& accommodate accurately but only to stimuli that lie inside the parallelogram.
This parallelogram is called the "Zone of Clear, Single Binocular Vision".
This parallelogram gives you a lot of predictive power. The top of the zone
is limited by the amplitude of accommodation.
The range of disparity vergence is called fusional (positive and negative
fusional convergence PFC & NFC) when measured with respect to the phoria
line and relative (positive and negative relative convergence PRC &
NRC)when measured with respect to the demand line.
Relative Convergence measurement procedure:
Assume PD = 6 cm. Start with zero prism. Stimulus is simply 40 cm. Therefore
convergence stimulus = 15 prism diopters (= 2.5D x 6 cm) and accommodation
stimulus = 2.5D. Then start adding prism until you see double. We call that
relative convergence because it is relative to the demand line. Sometimes
a patient extends the range of singleness by purposely increasing or decreasing
accommodation to add or subtract a little accommodative vergence. This will
result in a visible blur of the target. When this occurs, the amount of
prism is called the blur point. We plot the blur point on the graph to represent
the limits of fusional vergence that is unaided by accommodative vergence.
The width of the zone from the phoria line is nearly constant and is called
"fusional convergence range". The zone tends to be parallel to
the phoria line. If slope of phoria line is different from the slope of
the demand line then the distance from the fusion limit from demand line
(relative vergence) will change with viewing distance.
Clinically we measure relative fusional convergence but we really want to
know the absolute fusional convergence from the phoria line. To get that,
subtract phoria from (+) relative convergence.
e.g. if you can converge 20 prism diopters from the demand line, and your
phoria is 5 eso, then your actual fusional convergence is 15. Fusional convergence
is relatively constant at all viewing distances. Fusional vergence is the
actual physiological property of the Maddox hierarchy but we measure relative
fusional convergence which is the combination of fusional and phoria.
How do we use all this information?
e.g. person with PD = 6.4 cm
They're exophoric & get more exophoric as they come to nearer viewing
distances. So slope of phoria line is steeper than demand line.
(+) relative convergence is getting smaller with nearer viewing distance.
(+) fusional convergence is staying relatively constant.
(-) relative convergence is getting bigger with nearer viewing distance
(because we're getting more exospheric)
(-) fusional convergence is staying relatively constant (the distance
from phoria line).
2 Criteria to evaluate patient comfort clinically
1. Percival's Criteria: (see figure above)
a) The middle 1/3 of the zone of clear single binocular vision (shaded region)
is the range where we could respond comfortably. Percival said the demand
line should lie within that range. If you're very exo the demand line would
be on the right half of the zone; therefore we would prescribe enough BI
prism or (-) Lens to slide demand line leftward to within the middle third
of the zone.
b) If patient doesn't have symptoms of binocular stress, dont prescribe
anything even if you find an unusual data point. However be sure lack of
symptoms is not caused by avoiding reading.
c) Always correct vertical phoria before horizontal phoria. Vertical phoria
will disrupt binocular vision & decrease range of horizontal convergence.
2. Sheard's criteria:
So how do we correct exophorias? When we converge the eyes to overcome the
exo, we dont want to use more than half of our relative vergence range (the
reserve) or 2/3 of our fusional convergence range. You always want the amount
of convergence beyond the demand point (relative vergence or the reserve)
to be 2 times the amount of phoria (the demand), which means you're only
going to be using 1/3 of the total positive fusional vergence range to overcome
this phoria.
Reserve fusional vergence (which is = positive relative convergence for
exo) or (= excessive fusional vergence) should be at least 2 times the amount
of phoria.
Positive relative convergence should be at least twice as great as the phoria.
This is a more exact criteria than Percival's.
Eg. In clinic, if patient is 5 exo & positive relative convergence =
10 BO, the patient just meets Sheard's criteria. But if the patient was
5 exo & positive relative convergence = 5, this would mean they had
to use up 1/2 of the total range of fusional convergence to see singly (demand
equaled the reserve) and they're going to get headaches. So prescribe BI
prism which slides the demand line to the left to decrease the phoria &
increase the range of relative convergence. The minimum correction in this
example would be to reduce the phoria to 3.33 exo or 1/3 the fusional vergence
range (10 BO).
Correction scheme is always the same: Prescribe prism &/or lenses that
move real world (demand line) so it falls somewhere within the center of
zone of clear, single BV and also so that the demands on fusion don't exeed
1/3 of the potential range of fusion.
All this analysis is based on the Maddox concept that you linearly sum fusional
vergence with accommodative vergence with tonic vergence.
Homework assignment
Plot out the person's zone of clear, single BV. On the graph, look at the
slope of the phoria line and how it differs from the demand line. Look at
the slope of BO & BI limits as relative to phoria & demand lines
& how they're parallel to one another. They fan out symmetrically about
one of those 2 lines & that fanning out has to do with proximal convergence.
The range that we converge/diverge our eyes increases a little more with
near viewing distance because of proximity.
Chapter 5
3 sources of oculomotor problems:
1. Congenital
2. Developmental
3. Aquired. (Recent onset & usually more serious problems can be due
to trauma)
3 Kinds of eye movement problems:
1. Strabismus (phoria): deviation of one eye. Eye alignment problem.
2. Nystagmus: unsteadiness of eye. Stabilization & vestibular problem.
3. Saccadic disorder: some quick movements are abnormal
Strabismus
1. Comitant: deviation of eye stays constant at different direction of gaze.
It can change with viewing distance. It can be congenital &/or developmental.
You can use Sheard or Percival criteria to correct if the strabismus is
not too large.
2. Noncomitant: angle between eyes varies with different directions of gaze.
It is usually acquired. Use surgery &/or eye exercises for treatment.
We can use other muscles in the eye to compensate for vertical movements
because have 2 sets of muscles in the vertical direction (recti & obliques)
but horizontal movements cannot be compensated by other muscles.
Causes of noncomitant can be muscle damage like Myasthinia gravis or trauma.
Usually cranial nerves (especially III & VI) are affected because they
are long and more tortuous pathways. Try to localize the site of the problem:
muscle or nerve or somewhere more central.
Orbital mechanics
In order to predict the action of any muscle, we need to know the orientations
of eye muscles inside the orbit & around the globe & also where
the muscles are with respect to the head & visual axis.
There are three sets of canals that code motion of our head in 3D space:
1. Anterior canal
2. Posterior canal
3. Horizontal canal (lies in horizontal plane)
These canals lie in 3 planes. The posterior canal on the right side lies
in a common plane as the anterior canal on the left side. The posterior
canal on the left side lies in a common plane as the anterior canal in the
right side.
There are also planes that the eye muscles lie in.
Vertical recti lie in a common plane. Obliques lie in another plane that
nearly runs perpendicular to the vertical recti plane.
Muscle planes of vertical recti & obliques run aproximately parallel
to the canal planes. That means muscles are there to respond to the canals.
If we rotate our head in a meridian, we stimulate some combination of these
canals & these canals go to the muscles that run parallel to them. Our
muscle would counter-roll & keep our eyes stationary. Our eyes are like
ocular gyroscopes to keep our eyes steady in space while our head rotates.
This is not unique to primates.
Vertical recti forms an angle of 23 degrees with respect to the medial wall.
Obliques form an angle at 51 degrees.
Rabbit eyes point off to the side
Cat eyes point forward.
The muscle planes for recti & obliques are parallel to the canal planes
for both rabbits & cats. The only difference in the 2 animals is that
during evolution, the visual axis is moved forward but the eye muscles didn't
move to allow for stereo vision.
The goal of orientation of eye muscles is to remain parallel to the vestibular
canals.
When obliques contract, it is causing the same motion of the globe in cats&
rabbits but the effect on the motion of the visual axis is different. The
difference is where the visual axis is pointing relative to the muscle plane.
In rabbits, the visual axis is pointing temporal from the muscle plane of
the recti. In cats, it is pointing directly along the axis of the vertical
recti. In humans, the visual axis is nasal ward from the vertical recti.
Therefore in cats, vertical recti acts as pure elevators because the visual
axis is already pointing along the axis of that muscle.
In rabbits, the superior rectus (SR) contracts to elevate the eye. The superior
oblique (SO) contracts to elevate the eye. In cats, Obliques act as pure
torters. In humans, SO depresses the visual axis but in the rabbit, SO elevates
the visual axis. The difference is due to where visual axis is pointing.
But the globe is making identical rotations as in cats, rabbits & humans.
So it is important to know where the muscle planes & visual axes are
and how the visual axis moves as we contract the muscle in a plane.
The actions of the individual extraocular muscles starting with the eye
in primary position of gaze are indicated in the figures below.