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Nov. 23, 2015
Review: Exploring Reading Glasses to Stabilize College Myopia
Peter R. Greene, Ph.D.
B.G.K.T. Consulting Ltd.
Bioengineering
Huntington, New York, 11743
Corresponding author prgreeneBGKT@gmail.com
+1 631 935 56 66
Antonio Medina, O.D., Ph.D.
Research Laboratory of Electronics
Massachusetts Institute of Technology
Cambridge, Mass., 02139
Email
medina_NASA@hotmail.com
+1 714 418 11 83
Word Count = 2,533 not including references, captions
Key Words - emmetropia; progressive myopia; feedback control theory;
time constants; progressive add lenses (PALs); bifocals; reading glasses;
refraction .
Encl. - 17 pages, 5 figures, no tables, 39 references
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ABSTRACT
College students often become -1.0 to -2.0 diopters more myopic, so reading glasses were
explored, using theory and experiment, to partially cancel the effects of the study environment.
Three computer models are developed to predict refraction R(t) versus time.
N = 25
different sets of (+)Add lenses are evaluated, for required adjustment period and reading
comfort, and endurance. Basic control system equations predict exponential myopia shift of
refractive state R(t) with time constant t0 = 100 days, as observed experimentally.
Linear,
exponential and Gompertz computer results are compared calculating refraction R(t) during the
college years, showing correlation coefficients |r| = 0.96 to 0.97, accurate within +/- 0.31 D.
over a 14 year interval.
The experimental design phase of a pilot study at Annapolis is
described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia.
Typical
college myopia rate is - 0.3 to -0.4 D/yr. Reading glasses may be a simple, practical solution to
stabilize college myopia.
Key Words.
time constants;
emmetropia; progressive myopia;
feedback control theory;
progressive add lenses (PALs); bifocals; reading glasses; refraction
Abstract word count = 161
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INTRODUCTION
The literature has many mathematical models of myopia, including computerized control
theory (Hung & Ciuffreda [1] [1a] ),
the double exponential Gompertz function (Thorn,
Gwiazda, Held [2]), feedback theory predicting exponential functions (Medina & Fariza [3];
Greene et al. [4] [5] [5a] ), and linear regression models (Goss & Jackson [6]; Medina et al. [7]
[8] [8a] ) .
In this report, using linear or exponential theory and optical experiments, the
dynamics of progressive myopia during the college years are reported, and the potential for
stabilizing progressive myopia, by using various types of conventional reading glasses.
Cheng et al. [9], Guyton [10] and Goss [11] review an extensive literature on attempting
to stabilize progressive myopia. Typical college myopia rate is <R'> = - 0.3 to -0.4 D/yr.
These progression rates (Lee et al. [12]; Sun et al. [13]; Lin et al. [14]; Yang et al. [15]) also
apply to students at the graduate level, with some medical schools reporting myopia
prevalence rates greater than 70% to 95% (Fledelius [16]; Lin et al. [14]). Recently, several
(+) Add research studies have been published ( Fulk et al. [17]; Gwiazda et al. [18]; Leung &
Brown [19]; Oakley & Young [20]; Yang et al. [15]; the COMET Group [21]; Cheng et al. [9] )
with encouraging results, reporting that the progressive myopia rate can be attenuated by 50% or
more, i.e. partially stabilized (Holden et al. [22]) using various (+) Add technologies, including
bifocals and progressive addition lenses (P.A.L.’s)
Feedback theory predicts that near work causes myopia because it is equivalent to distant
vision with a minus lens, and that plus lenses would therefore cancel the myopization
(myopizing) effect. We helped design an experimental study at Annapolis, using reading glasses,
to reduce college myopia. Our objective was to reduce (stabilize) the myopia rate to 0.0 D/yr
for 4 years.
Navy pilots at Annapolis are required to have 20/20 vision in order to fly [3,19].
However, many become myopic and therefore must quit the program. Gmelin [23] reports that
approximately
50%
of
Cadets start as myopic, but the fraction rises to
two-thirds at
graduation. In addition to the challenge of getting the pilots to graduate while still maintaining
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20/20, there is a similar problem called “cockpit myopia” (Hoogerheide et al. [24]; Provines et
al. [25] ) whereby, after close work at the instrument clusters, maps, instruction manuals, etc.,
military and civilian pilots and co-pilots report finding that distance objects are blurred.
Some of the successful graduating Ensigns from Annapolis may go on to fly various
aircraft-carrier based high-tech planes, including the new F-35 VTOL “Lightning II”, Fig. 1b,
requiring excellent visual acuity both at near and far. A nearwork induced transient myopia
(N.I.T.M.) is also reported by some pilots, more so the navigators, as expected These various
problems, although well defined, currently have no practical solution [24] [25]). Helmet display
and optical design have become an integral part of aircraft design in recent years (Jenkins &
Gallimore [26] ).
Our approach involved conventional (+) Add reading glasses, +1.5 to +3.0
diopters, to be used during long hours of college study to lessen focusing effort (Cheng et al.
[9]). In theoretical terms, (+) Add reading glasses, Fig. 1, are considered "optical-offset distance
compensators", designed to optically shift a book or computer at a typical reading distance of
1/3-meter to 1/2-meter (13-inches to 20-inches) to infinity, thereby easing the focusing workload on the eye. Conventional reading glasses may be a simple, practical, solution to stabilize
college myopia and pilot myopia.
(+) Add studies require large numbers of students to improve the significance level, (e.g.
p < 0.05) required to discriminate the average diopter difference dR between experimental and
control groups, Fig. 2b, [8,16]. This difference is not always as pronounced as we might hope
(Cheng et al. [27]). Fulk et al. [17] report N = 42, dR = 0.25 D., p = 0.046, using a +1.50 D. add.
Gwiazda et al. [18] report N > 450 , dR = 0.20 D, p < 0.004, using a +2.00 D. add. Yang et
al. [15], using a +1.50 D. add, report N = 149 subjects, dR= 0.25 D , p=0.01 . Leung &
Brown, [19] report dR = 0.7 D., p < 0.0001, using = +1.50 D and +2.00 D , N = 36 . Cheng et
al. [27] report
dR = 1.05 D., N = 135,
using +1.5 D Add and +1.5D with prism,
p<
0.001 . Oakley & Young [20] report dR = 1.0 D, N = 216, Fig. 2a, using +1.5 D and +2.0 D
Add , significant at the p < 0.001 level for each of 10 different EL-HI age brackets. Fig. 2b
shows the basic statistical techniques used to discriminate the experimental and control groups.
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MATERIALS & METHODS
Three computer models of refractive state shift over an 11 to 14 year interval are
developed, including the linear regression model (Goss & Jackson [6]; Medina et al. [7][8][8a]),
the exponential model (Medina & Fariza [3]; Greene et al. [4] [5] [28] ), and the Gompertz
double exponent model (Thorn, Gwiazda & Held [2] ). Age matched data sets, Fig. 2 and Fig. 5,
are used to optimize model parameters. Results are calculated using MicroSoft and Office Excel
programs.
In terms of the optical experiments involving various types of reading glasses, the
comfort level, feasibility, and endurance factors were evaluated for 25 different (+) Add lens
combinations Greene & Grill [5a]. Cheng et al. [9], Guyton [10], Hung & Cuiffreda [1a] and
Goss [11] review plus lenses, bifocal, and PAL studies. Typical college myopia rate is R' = - 0.3
to -0.4 diopters per year. Our objective was to reduce the rate to 0.0 D / yr. for 4 years.
Under
proper supervision, we evaluated 11 different types of (+) Add lenses, with powers ranging from
+0.5 D. to +4.0 D., Greene & Grill [5a]. Tenets of the Helsinki declaration and the internal
review boards were adhered to.
RESULTS
Mathematical models of progressive myopia from the literature involve exponential or
linear functions.
The refractive state is altered with a myopic shift equal to the near-point
optical demands of a new environment <E>, where typically <E> = -1 D. to -2 D., Fig. 4a.
During one semester, refractive state can become more negative, about -0.3 diopters, with a time
constant t0 = 100 days , Fig. 4b :
R(t) = -1.1 D + 0.8 D exp [ -t / t0 ]
Eq. (1)
Exponential functions are used by Medina & Fariza [3], and Greene et al. [4] [5].
In terms of theory, we have explored 3 possibilities in detail: 1. Linear regression (Goss
& Jackson [6]; Medina et al. [7] [8]) 2. Exponential progression (N=367) (Oakley & Young [20];
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Medina & Fariza, 1993) and 3. The Gompertz function (Thorn et al. [2]), N = 32 iterations. The
Gompertz 4-parameter double-exponent is given by :
R(t) = Re + Rc * (0.07295) ^ ( a ^ ( t – to) )
Eq. (2)
where R(t) = refraction at time t . For one subject, we use parameters Re = - 0.75 D initial
refraction, Rc = - 5.25 D amplitude , onset age t0 = 12 yrs., and a = 0.70 optimal shape
factor , accurate within +/- 0.31 diopters. The results for linear regression show average diopter
rate <R’> = -0.47 D/yr., age at stabilization 22 years, correlation coefficient r = -0.96 .
For the exponential model time constant is t* = 3.2 to 4.4 yrs., correlation coefficient r
= 0.97 accurate over an 11 to 14 year interval, Figs. 2, 4 and 5 . Fig. 5 shows that the initial
refraction rate is dR/dt = -1.3 D/yr, slowing to dR/dt = -0.14 D/yr after college.
Mathematically, the linear regression model is the easiest to use (Medina et al. [7] [8] ),
the Gompertz model is the most difficult, but potentially the most accurate, and the exponential
model, of intermediate difficulty, Figs. 2, 4 and 5, has the ability to predict the slower myopia
drift after college, (for instance, Fledelius [16] reports that an additional 25% of the students
become myopic during graduate school) . Myopia can continue to progress beyond the college
years to age 40-45, a fact rarely mentioned in reports (Hoogerheide et al. [24]; Bullimore et al
[29]; COMET Group [21] ). Bullimore, et al., 2002 report that 36% of adults continue to
progress at a rate of - 0.75 diopt. per 5-year interval (ages > 28 yrs., N = 197). Note that the
exponential model, Fig. 4, predicts a slow continuing myopia drift after the college years,
approximately
-0.50 D. over a 5 year interval, consistent with the results of Bullimore
et al [29], Fledelius, [16], Greene et al. [28], and Medina et al. [7] [8] .
In terms of experimental results for the (+) Add lenses, 25 sets were tried by the design
team, to determine appropriate power level, +0.50 D to +4.00 D., Greene & Grill [5a]. Clip-on
plus lenses and bifocal sunglasses were also explored [5a]. Cost of the plus lenses can range
from $12 to $250 [5a]. After a variable adjustment period, most find +2.0 D is comfortable and
practical, although the basic equations do suggest stronger values. One of the most cost-effective
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possibilities explored were the Fresnel stick-on adhesive lenses (not reported here), which can
easily convert a pair of conventional single vision glasses to custom bifocals, for just a few
dollars.
DISCUSSION
There is a natural tendency of the eye to become myopic with long hours focusing at a
near-point environment, confirmed by laboratory experiments (dR= -1.7 D, t = 1 yr., N =7,
Young [30]), whereby young primates consistently acquire -1.7 diopters of myopia over a 1-year
interval. Typically, conventional bifocals and PALs in various studies are used with progressing
myopes with refractions from R = -1.0 D to -6.0 D, diopter rates R' = -0.2 to -1.0 D/yr.,
thereby slowing these myopia rates by 50 % or more (Holden et al. [22]). The PAL and similar
studies use multifocal (+) Add lenses, Fig. 1, for progressing myopes, of strength +1.00 D.
to +2.00 D. in the lower portion of the frame.
Amplitude of Accommodation
Amplitude of accommodation is a measurable parameter that varies considerably with
age, and from one individual to another, Fig. 5b. For juveniles ages 5 – 10 years, the amplitude
is 12 to 18 diopters, but for college age students ages 20 – 25, because of stiffening of
various components of the human lens system, the amplitude is reduced in half to 7 to 9
diopters (McBrien & Millodot [31]; Momeni-Moghaddam et al. [32]; Sergienko et al. [33]).
The
amplitude of accommodation is an easily measureable indicator of the flexibility of the
focusing system. This may be correlated with the rate of progressive myopia, and ultimately the
stabilization level. Eventually, in the age range 40 – 45 years, the accommodative amplitude is
reduced to 1 to 2 diopters, hence, reading glasses become necessary (Abraham et al. [34]). As
of this writing, no correlation studies are available relating these various factors, i.e.
accommodative amplitude, progressive myopia rate, and stabilization level, although it is well
known that myopes have greater amplitude of accommodation than emmetropes, Fig. 5b
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(McBrien & Millodot [31];
Abraham et al. [34]). Amplitude of accommodation may be a
reliable predictor of college myopia.
Ultimately, the goal is to develop and provide optical equipment to attenuate the
progressive myopia problem. This R & D effort is quite complicated, far from proven. To date,
the only solution has been to exclude myopes entry into the Academy, beyond a certain level,
hardly a solution to the problem. Herein we report the practical hardware details found by the
design team evaluating N=25 (+) Adds [5a].
From this list of 25 possibilities, the most
promising are (+) Adds in the range +2.0 to +3.0 diopters, including single vision, bifocal, and
progressive addition PALs.
CONCLUSIONS
The purpose of this report is to relate the various parameters and factors for a study of
this type, using (+) Add technology for the control of college myopia. Across the board, our
most difficult problem has been teaching and explaining the rationale of this new optical
technique. Unless you have tried (+) Add reading glasses personally, it remains an abstract
concept. Basically, this is a matter of prescribing reading glasses, normally used by those of age
40+, to students age 20. The eight successful (+) Add studies reported here (Gwiazda et al.
[18]; Leung & Brown [19]; Fulk et al. [17]; Oakley & Young [20]; Yang et al. [15]; COMET
Group [21]; Cheng et al. [9] [27]) provide a considerable data base for ages 6 – 18 .
Mathematical feedback theory helps predict what we may expect to happen, and when, during
the college years, Figs. 2, 5. Often overlooked, as an important design parameter, is the level of
the transition line between the distance and near correction in bifocals and PALs, usually set at
50% of frame height, but to guarantee using the (+) Add segment at near, it is suggested at the
60% to 70% level, (Prof. Young, personal communication).
Lastly, there is the adjustment period, rarely mentioned in reports, approximately 1 – 2
hours for a +1.0 D Add, 1 – 2 days for a +2.0 D Add (20-inches), 1 – 2 weeks for a
+3.0 D Add, and 1 – 2 months for a +4.0 D Add (10-inches reading distance), Table 1 .
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As anyone who has tried contact lenses can tell you, a remarkable degree of bravery, skill, coordination, and persistence are required to learn this task, similar to learning to ice skate, or to
ride a bicycle. (+) Add reading glasses have a similar learning-curve, in terms of the required
adjustment time, although considerably easier to use. This adjustment period factor suggests
that students practice using new reading glasses during August, before the fall semester.
The basic strategy of the (+) Add technique is to reduce the focusing demand on the
visual system during prolonged study, (n.b. - 13" reading distance = -3.0 diopt. accommodative
demand). As an indication of the military importance of this problem, several articles report
myopia developing with Navy submariners, and extensive LASIK use in the Army (Hammond et
al.[35]) to cure the myopia problem, more than 16,000 recruits as of 2003, a total of 26,000
recruits as of 2005, a remarkably large study. Perhaps most notable from an international point
of view, our Russian and Japanese counterparts are also very interested in exactly this myopia
problem for the last 20 to 30 years, inventing an assortment of creative new technologies [36]
[37]. The Annapolis military pilots [38, 23], and pilots in general [24] [25] are required to be in
excellent physical condition - it is a demanding job flying a Mach 2 fighter/bomber. The
different types of (+) Add lenses described here, effectively shift a book or computer
from a typical reading distance of 1/3 meter to 1/2 meter (13 inches to 20 inches) to infinity.
Various types of reading glasses, single vision, bifocals, and the new multi-focal progressive
lenses (PALs), may be a practical way to stabilize college myopia and pilot myopia.
ACKNOWLEDGEMENTS. Assistance was provided by discretionary research funds at the U.S. Naval Academy,
Annapolis MD, and The Johns Hopkins Univ., Baltimore MD, C & O Publishing, Personal Optics Co., Towson
Rotunda Optics, and NIH-NEI Grant R03-EY05013.
n.b.- Reference List is in Pub Med format. Click on Title to view Abstract (and Article).
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Figures
Figure 1 a - Reading glasses for a -5.00 D. college myope. (+) Add technology is used by both bifocals and
progressive addition lenses, “PAL’s”. PAL’s are “no-line” bifocals. Inset shows standard executive style bifocal,
with a +3.00 D. add for reading. ( Photo courtesy of Dr. K. Viikari. )
( Picture of Navy VTOL )
Figure 1 b - Navy F-35 VTOL landing in hover mode . Due to enter carrier service 2016.
( Photo courtesy of Lockheed Martin Aerospace. )
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Figure 2 - +2.0 D bifocals (N=216) can stabilize progressing myopes (N=367) [30] , as indicated by the
horizontal lines. dR = 1.0 D. , p < 0.001 for each of 10 age brackets. Otherwise, normal myopia refraction rates
are R’(t=8 yrs) = - 0.7 D/yr, R’(t=16 yrs) = - 0.4 D/yr . Exponential myopia time constant is t* = 3.2 years.
( from Greene et al. [5a]. )
Figure 3 - (+) Add [ A ] , controls [B], m1 – m2 = dR [D.] , s1 = s2 = +/-0.4 to +/-1.0 D .
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Figure 4 a - Exponential visual system response to a -2.0 D negative step showing delayed myopia onset .
Time constant t0 = 60 –100 days. (Figure courtesy of O.S. Brown, www.myopiafree.i-see.org )
Figure 4 b - Visual system response to a near environment 1,3 , N = 12 eyes, time constant t0 = 100 days,
initial diopter rate = -3.2 D/yr .
( from Greene et al. [5]. )
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Figure 5 a - Typical college student with progressive myopia, exponential time constant t0 = 4.4 yrs.,
correlation coefficient r = 0.97. Initial refraction rate is dR/dt = -1.3 D/yr, slowing to dR/dt = -0.14 D/yr after
college. ( from Greene et al. [5a]. )
Figure 5 b - Accommodative amplitude decreases with age from 15-20 diopters at birth to 1 to 2 diopters at age
40. Myopies typically are slower to respond. ( Figure courtesy of K. Schmid, www.myopia-manual.de 2015. )
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