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Description  |
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BACKGROUND OF THE INVENTION
Many diseases of the eye result in localized retinal disfunction. An
example of this is glaucoma in which high intraocular pressure causes
damage to the nerve fiber layer of the retaina. The areas of retinal
disfunction are perceived subjectively by the patient as areas of
decreased reaction to light or stimulation by light as is said in the art.
If the damage is such that no light, however intense, will stimulate a
particular area of the retina, i.e., generate electrical activity, then
that area is said to be an absolute scotoma in the patient's visual field.
If the retina can be stimulated, but only by light of an intensity higher
than some average predetermined baseline, then the scotoma is said to be
relative.
Present methods of measuring one's visual field are purely subjective. The
dimensions of one's visual field are measured in terms of visual angle,
and typically measure 90.degree. temporally and 60.degree. nasally and
vertically from a point of fixation. The standard method of measuring a
patient's visual field is called Goldman perimetry. In this method one eye
of the patient is patched. The eye to be tested fixates on a target spot
in the middle of a hemispherical globe which has a certain constant
background illumination. Visual stimuli (i.e., light) of various
intensities and areas are presented in standard ways at different
locations on the surface of the hemispherical globe. With the presentation
of each stimulus, the patient is asked to respond by a hand signal or
other means as to whether he saw the stimulus while focusing on the fixed
target spot. The responses of the patient are used as measurements to
determine the visual threshold at various points in the patient's visual
field, thereby delineating the presence of scotomas.
An example of the utility of the Goldman perimetry technique is in the
diagnosis and monitoring of glaucoma. The diagnosis of glaucoma is based
on the presence of scotomas which are characteristic of the disease as
well as the appearance of the optic nerve and the intraocular pressure.
The visual fields of glaucoma patients are monitored closely first as an
aid to making the diagnosis, and secondly to detect any progression of
these visual field defects or scotomas. Any progression of the scotomas
implies inadequate control of the intraocular pressure and indicates the
need for additional therapy.
A problem with this technique is that it is subjective and hence subject to
the judgement of the patient. Thus any inattention due, for example, to
fatigue, inability to understand the test, and age degrade the quality and
reliability of the test. This technique can be automated, but is still
subjective and hence subject to the same vagaries.
Other techniques for testing a person's visual field have included
electroretinograms (ERG's) which measure the electrical response of the
entire retina to light incident upon any part of one's visual field. In
order to determine the health of particular segments of the retina from
the ERG responses, each spot of one's visual field must be illuminated
with a focused spot of light that is flashed many times over a period of
about twenty seconds. To complete such a test takes a substantial amount
of time. Consequently such techniques have not shown any advantage over
the subjective or other methods of testing one's visual field.
SUMMARY OF THE INVENTION
The invention described herein addresses these foregoing problems by
substituting an objective measure of point-by-point retinal response for
the above described subjective measure. Specifically, the present
invention provides an objective method and device for examining local
responses of the retina to light. A series of spatially and possibly
temporally varying patterns of light intensity is presented to the eye.
For each pattern, the response of the eye is measured. The patterns are
chosen from a family of orthogonal functions such that each measured
response corresponds to a coefficient of the transform associated with the
family of orthogonal functions. The inverse transform of the transform is
calculated to provide the point to point response of the retina to light
stimuli.
In a preferred embodiment, a computer generates a series of patterns
spatially varying in light intensities and displays the patterns before
the patient on a screen. The pattern intensities spatially vary according
to a function chosen from a family of orthogonal functions. The change in
voltage potential across the eye, known as the electroretinogram (ERG)
response of the patient's eye, to each pattern is measured by an electrode
which is placed upon the patient's eye. A magnetoretinogram (MRG) or other
response may also be used for this measurement. The measurements are
transferred in the form of voltage signals from the electrode to a signal
averager which produces an average of the responses of the eye to a
particular pattern averaged over many presentations of the pattern. The
signal averager improves the signal to noise ratio of the measurement
signals. The averaged signal is received by the computer which relates the
responses to the corresponding generated patterns and produces a set of
coefficients of the transform associates with the chosen orthogonal
function of the pattern. The computer then calculates the inverse
transform of the transform associated with the chosen orthogonal functions
and produces a map of the retinal response as a function of position over
the retina.
In one embodiment of the present invention, the series of patterns are
chosen to vary according to the family of sine and cosine functions. The
inverse Fourier transform associated with these functions is calculated by
the computer from the measured ERG voltage signal.
In addition, the series of patterns may vary in color, intensity, or
contrast. By adjusting the intensity and/or contrast of the patterns, one
may obtain more linear responses of the eye. The color and/or intensity
can be adjusted so as to test different retinal responses.
The patterns may also vary temporally. In one mode, each pattern is
presented and then reversed in contrast over time. The pattern is
sinusoidally reversed back and forth at a fixed frequency. This is better
known as "counter phase oscillation" at a fixed frequency. In a second
mode, each pattern is presented at high intensity for a brief moment (i.e.
flashed) before the patient. Both temporal modes allow signal averaging of
the response of the eye to improve the signal to noise ratio. The temporal
frequency may also be chosen so as to test different retinal functions or
minimize the nonlinear response of the eye.
In the oscillating mode, a lock-in amplifier can be used in place of the
signal averager to provide signals indicative of the voltage amplitude and
phase lag of the ERG responses of the eye.
BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing and other objects, features and advantages of the invention
will be apparent from the more particular description of preferred
embodiments of the invention, as illustrated in the accompanying drawings
in which like referenced characters refer to the same parts throughout the
different views. The drawings are not necessarily to scale, emphasis
instead being placed upon illustrating the principles of the invention.
FIG. 1 is a schematic of a device embodying the present invention.
FIGS. 2a-2c are illustrations of cosinusoidally varying patterns, along the
x-axis, y-axis and both axes respectively.
FIGS. 3a-3c are illustrations of temporal variance of the patterns of FIGS.
2a-2c respectively.
FIG. 4 is a graph of the change in intensity over time at one point on a
screen displaying patterns which temporally vary sinusoidally.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
The present invention discloses a method and device for obtaining a
point-by-point response of the retina, known as a focal ERG (FERG), from
an ERG response of the retina. A typical ERG response ranges between 0.1
.mu.v to about 100 .mu.v where the signal strength depends upon the
stimulus and state of adaption of the the retina. The ERG response from a
point source stimulus which subtends a small, visual, solid angle in the
subject's visual field would give rise to a small signal and consequent
small signal to noise ratio. Such small signals make any point-by-point
observation of the retina difficult and very time consuming where the ERG
response from a point source stimulus would have to be repeated and
measured to each point throughout the retina in order to map the visual
field. The present invention obtains point by point retinal responses
(FERG's) from ERG's by analyzing a patient's global ERG responses to a
series of patterns of known and controlled construction in such a way that
the FERG can be derived.
In general, a set of patterns spatially varying in intensity is presented
to the eye. For each pattern, the ERG response of the eye is measured. The
patterns are chosen to spatially vary in intensity according to a function
from a family of orthogonal functions such that each measured ERG response
corresponds to a coefficient of the transform associated with the family
of orthogonal functions.
For example, a first pattern spatially varies in intensity according to a
function of the family of sines and cosines at a wave number k.sub.1. The
measured ERG response of the retina to this pattern corresponds to
coefficient c.sub.1 of the transform associated with this family of
orthogonal functions. A second pattern spatially varies in intensity
according to the same function as the first pattern but at wave number
k.sub.2. The measured ERG response of the retina to this pattern
corresponds to coefficient c.sub.2 of the transform associated with the
family of sines and coines. A third and fourth pattern similarly follow
and provide coefficients c.sub.3 and c.sub.4 respectively. This procedure
can be continued with improved spatial resolution resulting from the
measurement of more coefficients.
Knowing the coefficients (c.sub.1, c.sub.2, c.sub.3, c.sub.4, . . . ), the
transform is determined. The spatial wave numbers k.sub.i are chosen so
that the functions with different wave numbers are orthogonal. By
calculating the inverse transform of the transform, point-by-point
responses along the retina are obtained.
Alternatively, an MRG response may be used in place of the ERG response of
the eye for each pattern. Measurement of other responses of the eye are
also suitable, for example the pupilary response or the visually evoked
potential of the eye. One of these or a combination of the forementioned
types of measurements may be used to determine the coefficients of the
pertinent transforms associated with different visual functions.
The foregoing describes the essence of the present invention and is a
greatly simplified description. In practice, the measured ERG signal is
not pure; that is, it includes noise. Hence other techniques are
incorporated to compensate for the noise. In one technique, several ERG
responses are measured for each pattern and are averaged. These averaged
ERG measurements are used to define determine the coefficients of the
transform.
In another noise compensation technique, each pattern is temporally varied
in its presentation to the eye. The time control of the presentation of
each pattern allows noise to be filtered out of the ERG response. Each
pattern may be temporally varied sinusoidally or according to other
pertinent functions. Alternatively, each pattern may be temporally varied
in a flash mode. In the flash mode, each pattern is presented at high
luminance for a brief moment. This allows repeated presentation of the
same pattern with signal averaging used to improve the signal to noise
ratio.
It is understood that any combination of the above described and other
noise compensation techniques may be used to enhance the accuracy of the
ERG response measurement and thereby the point-to-point response outcome
of the present invention.
Further, different levels of intensity and/or contrast may be used in the
patterns. Retinal response to the patterns may then be controlled to
provide a linear response, even though the retinal response is generally
non-linear. The linear regime of response is necessary in order to
properly calculate the inverse transform from the transform associated
with the patterns' family of orthogonal functions. The temporal frequency
of the patterns may also be chosen so as to minimize the nonlinear
response of the eye.
The temporal frequency, color and/or intensity of the patterns may be
varied so as to measure different functions of the eye. For example, rod
and come functions can be distinguished by varying the color and intensity
of the patterns or temporal frequency and color of the patterns, or the
like.
The following describes details of the present invention incorporating
noise compensation techniques in which the series of patterns is presented
in a counter phase oscillation at a fixed frequency. That is, each pattern
continually reverses its contrasting lines sinusoidally over time, or
oscillates in contrast reversal as is said in the art, at a constant
frequency. Any other modes, such as the flash mode, can be treated
similarly.
A device embodying the present invention is illustrated in FIG. 1. A
computer 7 generates a series of spatially and temporally varying patterns
and displays each pattern on a terminal screen 9. An example of such a
display system is the Venus system from the Neuroscientific Corporation of
N.Y. In particular, each pattern is spatially varying in the x or y
direction or both directions according to a sine or cosine function as
illustrated in FIGS. 2a-2c. FIG. 2a illustrates a pattern cosinusoidally
varying in space along the x-axis at a fixed time t. The pattern
progressively changes from light to dark to light from left to right. FIG.
2b illustrates cosinusoidal spatial variance in the y direction at a fixed
time t. This time the pattern progressively changes from light to dark to
light from bottom to top. FIG. 2c illustrates a pattern cosinusoidally
varying in space along both the x and y axis at a fixed time t. Hence, the
progressive changing from light to dark to light occurs both from left to
right and from top to bottom. The choice of sines and cosines for the
spatial variation of the patterns is one example of many different
choices.
Each pattern temporally varies by sinusoidally reversing its lightly shaded
areas to a dark shade and vice versa (i.e. the counter phase oscillation
or contrast reversal) at some frequency f. FIGS. 3a-3c illustrate temporal
variance respectively of FIGS. 2a-2c. FIG. 3a illustrates the pattern of
FIG. 2a at a time t.sub.1 where t.sub.1 is greater than t by half a
period. Note that pattern is lightest in FIG. 3a where it was darkest in
FIG. 2a along the x-axis. FIG. 3b illustrates the pattern of FIG. 2b as
temporally changed at time t.sub.1 >t. The pattern in FIG. 3b is darkest
where it was lightest in FIG. 2b along the y-axis. Similarly, FIG. 3c
illustrates the pattern of FIG. 2c as temporarlly changed at time t.sub.1
>t.
FIG. 4 provides the graph of the change in intensity I over time t at one
fixed position on screen 9 where the modulation of the intensity is 100%,
with the illumination of the above described patterns. It is seen by the
graph that the change in intensity I experienced at the one fixed position
is sinusoidal. Similar sinusoidal changes in intensity with varying
amounts of modulation are experienced at the other positions on screen 9.
The luminance or light intensity I at a time t for each pattern displayed
on screen 9 has the form
I(x,y,t)=I.sub.o [1+m cos .omega.tF.sub.L (x,y)] (Equation 1)
where
I.sub.o is the average overall intensity;
m is modulation or peak value of the contrast between the lightest and
darkest shades;
.omega.=2.pi.f, where f is the temporal frequency of contrast reversal
chosen in the range from about 1 Hz to about 60 Hz (other ranges however
can be used); and
F.sub.L (x,y) is the particular spatial pattern where L labels the
particular choice of function from the family of orthogonal functions.
In this case, it was chosen that
F.sub.L (x,y)=cos kx cos ly
where x and y are coordinates of position on the screen 9; k and l are
appropriate wave vectors; and L refers to the values of k, l and the fact
that cosines were chosen.
After computer 7 generates a pattern constructed to the above equations, it
displays the pattern on screen 9 before the patient. The retina of the
patient's eye 5 responds to the display pattern (referred to in the art as
a stimulus) with a characteristic length of time of about 0.1 seconds or
greater. That is, the eye does not instantaneously respond. An ERG
electrode 11, of the type common in the art, placed on the eye 5 produces
a voltage signal when the retina responds to the pattern. The voltage
signal is a measurement of the change in voltage potential across the eye
and is indicative of the response of the eye to the pattern that has been
displayed prior to that time.
The voltage signal is transferred through lines 13 to a signal averager 15
which is synchronized to the presentation of the patterns, stores the
response, and adds future responses of the retina to the same pattern. The
sum of responses is divided by the number of responses stored and added to
provide an average voltage signal of the eye 5 to the particular pattern
displayed. The averaging of the voltage signals serves to improve the
signal-to-noise ratio in the ERG detection scheme.
The averaged voltage signal is passed to computer 7 which relates the
response of the eye as indicated by the average voltage signal to the
generated and displayed pattern which caused the response. That pattern,
remeber, was generated and displayed at times into the past .tau. before
the time t at which the voltage signal was received by the computer 7. The
ERG voltage signal, V(t), at a time t, that is generated by the eye to the
particular pattern displayed has the form:
##EQU1##
where .tau. is time into the past from the time t;
X,Y are coordinates location position on the retina from the x,y positions
on the screen 9;
I(X,Y,t-.tau.) is the light intensity of the chosen pattern as previously
discussed at a time .tau. before the present time t; and
h(X,Y,.tau.) is the form of the focal ERG(FERG) of the eye. That is,
h(X,Y,.tau.) dX dY is the voltage generated at time t by a pulse of light
of unit strength at time t-.tau. which is incident upon the small area of
the retina dX dY located at the position X,Y.
Note that h(X,Y,.tau.)=0 for .tau.<0. The function h(X,Y,.tau.) is also
known in the art as the memory function of the retina. It provides the
continuing response of the retina to a stimulus presented in the past. The
retina does not response instantaneously and then responds in a decreasing
manner to stimuli that occurred further into the past. Hence, h(X,Y,.tau.)
is zero at .tau.=0, rises to a peak, falls, and then has a decreasing
value with increasing .tau.(time into the past). More importantly,
h(x,y,.tau.) is the FERG signal of interest that can be used to study
retinal response on a point by point basis over the retina and to diagnose
localized retinal disfunction. Computer 7 determines h(X,Y,.tau.) from the
received voltage signals V(t) in the following manner.
Substituting from Equation 1 the light intensity I(x,y,t) of the chosen
pattern into Equation 2, the computer 7 obtains the signal at frequency f
##EQU2##
That is, v.sub.1 is the in-phase response, and v.sub.2 is the 90.degree.
out-of-phase response. v.sub.1 and v.sub.2 may be written in the form
##EQU3##
At any time t, V(t) has a known value as given to computer 7 from signal
averager 15. This value is then set equal to Equation 3 in which all
factors but v.sub.1 and v.sub.2 are known. A value for v.sub.1 (v.sub.2)
is then obtained by multiplying V(t) by cos .omega.t (sin .omega.t),
integrating the result over one period of the signal, and dividing the
result by I.sub.o m.pi./.omega.. These values or amplitudes v.sub.1 and
v.sub.2 are also proportional to the two outputs of a verctor lock-in
amplifier when lock-in detection of the signal is used.
Knowing values for v.sub.1 and v.sub.2 the computer 7 calculates h.sub.i
(X,Y,.omega.). This output is sufficient for many diagnostic procedures.
More detailed information can be obtained by repeating the measurement at
many different frequencies f and using the Fourier theorem to construct
h(X,Y,.tau.) from the measured dependence of h.sub.i (X,Y,.omega.) upon
.omega.. Alternatively, h(X,Y,.tau.) can be measured directly if the
stimulus is flashed temporally.
According to the generalized Fourier Theorem
##EQU4##
where the orthogonal functions F.sub.L satisfy
.intg.dXdYF.sub.L (X,Y)F.sub.L,(X,Y)=A.sub.L .delta..sub.LL,
where A.sub.L is a normalization factor; .delta. is a Kronecker delta; and
h.sub.i is given by
h.sub.i (L,.omega.)=.intg.dXdYh.sub.i (X,Y.omega.)F.sub.L (X,Y).
Thus, from Equation 4, h.sub.i (L,.omega.)=v.sub.i (L,.omega.) and h.sub.i
(X,Y,.omega.) can be determined from the measured values of v.sub.i
(L,.omega.). That is, the subject's FERG can be constructed from his ERG
responses to many spatial patterns of stimulus.
In the flash mode of temporal presentation of the stimulus, the luminance
pattern, Equation 1, is given by
I(x,y,t)=I.sub.o [1+m.delta.(t-t.sub.o)F.sub.L (x,y)],
where .delta.(t-t.sub.o) is a Dirac delta function representing a brief but
intense flash of the pattern F.sub.L at time t.sub.o which is repeated
many times. The temporally varying ERG voltage in response to this
stimulus is
V(t)=I.sub.o mv(L,t),
where
v(L,t)=.intg.dXdYh(X,Y,t-t.sub.o)F.sub.L (X,Y).
Thus, in this case
##EQU5##
and the full temporal behavior of h is determined.
As an example of this technique, the applicants consider a subject's FERT
at the fixed frequency f with a rectangular spatial pattern and products
of sines and cosines for the functions F.sub.L. Applicants then have
-X.sub.o <X<X.sub.o and -Y.sub.o <Y<Y.sub.o where X (Y) is interpreted as
the subject's visual angle measured horizontally (vertically) from the
point of fixation. X.sub.o and Y.sub.o determine the extent of the spatial
pattern in the subject's visual field. The spatial patterns F.sub.L (x,y)
are now specified in detail and are given by
##EQU6##
Examples of these patterns are given in FIGS. 2 and 3. With this choice of
function A.sub.o,q =A.sub.p,o =2X.sub.o Y.sub.o and A.sub.p,q =X.sub.o
Y.sub.o for p,q=1,2 . . . Applicants exclude the pattern with p=q=o since
that entails a net luminance change and stimulates a process in the retina
that is different from the other patterns whose net luminance is constant
in time. If v.sub.i.sup.(r,s) (p,q, ) is the in-phase, i=1 or cut-of
phase, i=2, ERG voltage in response to this stimulus, then
##EQU7##
This is desired FERG as a function of retinal position X Y. Since in
practice only a finite number of terms are included in the sums over p and
q, this is, in the sense of the Fourier theorem, a least squares fit to
the function h.sub.i.
The angular resolution of the FERG on the retina is determined by the
number of different patterns used. The angular resolution of the FERG in
the horizontal (vertical) direction will be equal to the width (height) of
the patterns divided by the number of different values of k.sub.p
(l.sub.q) in F(x,y) in Equation 6. Thus, for a 40.times.40 degree pattern
and a total of twenty different values of k.sub.p and l.sub.q, the FERG
will be measured with a 2.times.2 degree spatial resolution. Spurious
spatial signals can be eliminated by averaging h.sub.i over an appropriate
window. Thus, if W.sub.x (X,X') and W.sub.y (Y,Y') are the chosen X- and
Y- windows then the smoothed output is
h.sub.1 (X,Y, )=.intg.dX'dY'W.sub.x (X,X')W.sub.y (Y,Y')h.sub.i
(X',Y',.omega.).
If we use square windows of widths 2x.sub.o and 2y.sub.o in the x- and y-
directions, then this amounts to multiplying f.sub.p.sup.(r) by sin
(k.sub.p x.sub.o)/(k.sub.p x.sub.o) and g.sub.q.sup.(s) by sin (l.sub.q
y.sub.o)/(l.sub.q y.sub.o). This eliminates noise with a high spatial
frequency and improves the convergence of the Fourier expansion.
Although, the eye naturally responds in a non-linear fashion, the
modulation m and temporal freqency f in Equation 1 can be adjusted such
that the eye responds in a more linear fashion as detected by ERG
electrode 11.
If a lock-in amplifier is used in place of signal averager 15, values for
v.sub.1 and v.sub.2 in Equation 3 may be obtained directly. This is
accomplished by the lock-in amplifier measuring and providing the
amplitude A of the ERG voltage and the phase lag of the eye response where
V(t)=I.sub.o m[v.sub.1 cos .omega.t+v.sub.w sin .omega.t] (Equation 3)
and
V(t)=A cos (.omega.t+.omega.)=A[cos .phi. cos .omega.t-sin .phi. sin
.omega.t]
so
I.sub.o mv.sub.1 =A cos .phi.;
and
I.sub.o mv.sub.2 =-A sin .phi..
It is understood that the spatially varying patterns may be chosen to
follow any orthogonal function of the family of orthogonal functions which
forces a set of eye responses to define a transform of the retinal
responses in the frequency domain and enable calculation of the inverse
transform, of the defined transform associated with that function, to
obtain the spatial domain of the retinal response.
For example, F.sub.L (x,y) in Equation 1 could have been chosen to be
F.sub.L (x,y)=cos m.phi.J.sub.o (.gamma..sub.n r/r.sub.o)=sin m.phi.J.sub.o
(.gamma..sub.n r/r.sub.o),
where J.sub.o is a Bessel function and .delta..sub.n is the n.sup.th root
of J.sub.o (.gamma.)=0. .phi. is the azimuthal angle. The indices range is
m=0,1, . . . and n=1,2, . . . The angular radius of the screen 9 is
r.sub.o. In this case, the spatial Fourier transform and associated
inverse Fourier transforms of the Bessel junction J.sub.o are used to
calculate h(X,Y,.tau.) from the measured voltage signals V(t) of the ERG
electrode 11.
While the invention has been particularly shown and described with
reference to embodiments thereof, it will be understood by those skilled
in the art that various changes in form and detailed may be made therein
without departing from the spirit and scope of the invention as defined by
the appended claims.
* * * * *
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