2006JRSEctasiaModelPartII

Probability Model of the Inaccuracy of
Residual Stromal Thickness Prediction to
Reduce the Risk of Ectasia After LASIK
Part II: Quantifying Population Risk
Dan Z. Reinstein, MD, MA(Cantab), FRCSC; Sabong Srivannaboon, MD;
Timothy J. Archer, BA(Oxon), DipCompSci(Cantab); Ronald H. Silverman, PhD;
Hugo Sutton, MD; D. Jackson Coleman, MD
ABSTRACT
PURPOSE: To derive a statistical model to estimate the
rate of excessive keratectomy depth below a selected
cut-off residual stromal thickness (RST) given a minimum
target RST and specific Clinical Protocol; apply the model
to estimate the RST below which ectasia appears likely to
occur and back-calculate the safe minimum target RST
that should be used given a specific Clinical Protocol.
METHODS: Myopia and corneal thickness distribution
were modeled for a population of 5212 eyes that underwent LASIK. The probability distribution of predicted
target RST error (Part I) was used to calculate the rate
of excessive keratectomy depth for this series. All treatments were performed using the same Clinical Protocol;
one surgeon, Moria LSK-One microkeratome, NIDEK
EC-5000 excimer laser, Orbscan pachymetry, and a
minimum target RST of 250 µm—the Vancouver Clinical
Protocol. The model estimated the RST below which ectasia appears likely to occur and back-calculated the safe
minimum target RST. These values were recalculated for
a series of microkeratomes using published flap thickness statistics as well as for the Clinical Protocol of one
of the authors—the London Clinical Protocol.
RESULTS: In the series of 5212 eyes, 6 (0.12%) cases of ectasia occurred. The model predicted an RST of
191 µm for ectasia to occur and that a minimum target
RST of 329 µm would have reduced the rate of ectasia
to 1:1,000,000 for the Vancouver Clinical Protocol. The
model predicted that the choice of microkeratome varied the rate of ectasia between 0.01 and 11,623 eyes
per million and the safe minimum target RST between
220 and 361 µm. The model predicted the rate of ectasia would have been 0.000003:1,000,000 had the
London Clinical Protocol been used for the Vancouver
case series.
CONCLUSIONS: There appears to be no universally
safe minimum target RST to assess suitability for LASIK
largely due to the disparity in accuracy and reproducibility of microkeratome flap thickness. This model may
be used as a tool to evaluate the risk of ectasia due
to excessive keratectomy depth and help determine the
minimum target RST given a particular Clinical Protocol.
[J Refract Surg. 2006;22:861-870.]
C
orneal ectasia following keratomileusis was defined
by Jose I. Barraquer as “progressive myopisation
due to reduction of the corneal radius.”1 The precise
causes for ectasia after laser refractive surgery have not been
fully defined; however, high myopia, reduced preoperative
corneal thickness, percentage of cornea removed, low residual
stromal thickness (RST), keratoconus, and multiple retreatments have all been cited as risk factors.2-7 Many of the published cases of ectasia indicate that preoperative keratoconus
was the probable cause for ectasia.2,4-6,8-11 This has hastened
the requirement for improved methods of screening for keratoconus, including anterior and posterior surface topography.
Leaving a thin RST is accepted as a known risk factor for
ectasia and all surgeons use a minimum target RST to assess
suitability for LASIK. Barraquer described cases of ectasia after keratomileusis in his 1980 textbook on keratomileusis.1 He
found that steep corneas (ie, possibly keratoconus) and deep
resections were risk factors for the development of ectasia after keratomileusis. He suggested that the corneal cap should
From London Vision Clinic, London, United Kingdom (Reinstein, Archer); the
Department of Ophthalmology, University of British Columbia, Vancouver,
Canada (Reinstein, Srivannaboon, Sutton); the Department of Ophthalmology,
Weill Medical College of Cornell University, NY (Reinstein, Silverman,
Coleman); the Department of Ophthalmology, St. Thomas’ Hospital - Kings
College, London, United Kingdom (Reinstein); Centre Hospitalier National
d’Ophtalmologie, Paris, France (Reinstein); and Siriraj Hospital, Mahidol
University, Bangkok, Thailand (Srivannaboon).
Drs Reinstein, Silverman, and Coleman have a proprietary interest in the
Artemis technology (Ultralink LLC, St Petersburg, Fla) through patents
administered by the Cornell Research Foundation, Ithaca, NY. The remaining
authors have no proprietary or financial interest in the materials presented
herein.
Some of the aspects of this study were presented at the Association for
Research in Vision and Ophthalmology Annual Meeting; May 9-14, 1999; Fort
Lauderdale, Fla.
Preparation in partial fulfillment of the requirements for the doctoral thesis,
University of Cambridge, for Dr Reinstein.
Correspondence: Dan Z. Reinstein, MD, MA(Cantab) FRCSC; London
Vision Clinic, 8 Devonshire Place, London W1G 6HP, United Kingdom.
Tel: 44 207 224 1005; Fax: 44 207 224 1055; E-mail dzr@londonvisionclinic.com
Received: August 14, 2006
Accepted: October 6, 2006
Journal of Refractive Surgery Volume 22 November 2006
861
Safety Model for Preventing Ectasia/Reinstein et al
Figure 1. Artemis VHF digital ultrasound horizontal B-scan of a cornea with a flap created with a Hansatome 160. The B-scan demonstrates interfaces
detected ultrasonically for the epithelial surface (E), surface of Bowman’s interface (B), lamellar flap interface (F), and endothelial/posterior corneal
surface (P). Centrally the flap was measured as 323 µm, which was 163 µm thicker than the predicted flap thickness of 160 µm.
be a maximum of 300-µm thick as a safety criterion
for reducing the risk of ectasia in keratomileusis. This
translates to using a minimum target RST of approximately 250 µm assuming an average corneal thickness
of 550 µm (by slit-lamp optical pachymetry used at that
time12). Although 250 µm remains the widely accepted minimum target RST for suitability for LASIK,13,14
some reports suggest that this should be higher15-17 and
others demonstrate that it could be lower.18
The standard deviation of flap thickness can be
up to (or even above) 30 µm for some commercially
available microkeratomes.19-22 With a flap thickness
standard deviation of 30 µm, an RST error of 90 µm
is likely to occur in 0.5% of eyes (99% of values lie
within 3 standard deviations for a Normal distribution). Spadea et al23 reported a case of ectasia where a
Moria manually guided MDSC microkeratome (Moria,
Antony, France) with a predicted flap thickness of 120
µm was used. The flap was measured histologically as
260 µm; an error of 140 µm. Figure 1 shows an Artemis
VHF digital ultrasound B-scan (Ultralink LLC, St Petersburg, Fla) of a LASIK flap created with a Hansatome
160 microkeratome (Bausch & Lomb, Rochester, NY).
The predicted flap thickness was 160 µm and the flap
was measured to be 323-µm-thick centrally; an error
of 163 µm. Granted that this case may represent user
error such as excess vacuum and/or excess downward
pressure during passage of the microkeratome head.
There are reported cases of ectasia where no evidence
of keratoconus was present and the predicted RST was
250 µm.3,24 However, with the potential for RST errors of 100 µm, it is possible that some of the undetermined cases of ectasia in the literature could be explained by unexpected excessive keratectomy depth.
It seems to be difficult to draw conclusions about the
cause of ectasia from the predicted RST without a direct measurement of the RST. Other etiological factors
862
may contribute to ectasia but for the purposes of this
article, we have assumed that the two principle causes
are: 1) undetected keratoconus and 2) excessive keratectomy depth leaving a low RST.
In Part I of this work, we derived the probability of
obtaining an actual RST below a selected cut-off RST
given the predicted target RST for an individual eye.
In Part II, we set out to apply this probability to statistically model the percentage of eyes that would be
expected to have an actual RST below the selected cutoff RST for a given population of eyes (range of myopia and corneal thickness) and LASIK Clinical Protocol (microkeratome, pachymeter, laser, and surgical
protocols). We describe how the model can be used to
back-calculate the minimum target RST that might be
used to reduce the risk of excessive keratectomy depth
to clinically acceptable levels for a given Clinical Protocol. We also describe a method of obtaining a theoretical estimate of the cut-off RST below which ectasia
appears likely to occur due to excessive keratectomy
depth. The model was applied to a number of example
Clinical Protocols to demonstrate how the methods described can be applied in practice and investigate how
different microkeratomes might affect the potential
rate of ectasia due to excessive keratectomy depth.
MATERIALS AND METHODS
OVERVIEW
We have described a model, the “RST model,” that
provides a continuous probability function describing the chance of obtaining an actual RST less than
a selected cut-off RST given a predicted target RST.25
This was done by modeling the error of the predicted
target RST as a Normal distribution using the statistically combined bias (accuracy) and uncertainty (standard deviation) of corneal thickness measurement, flap
journalofrefractivesurgery.com
Safety Model for Preventing Ectasia/Reinstein et al
thickness, and ablation depth. The probability of obtaining an actual RST less than a selected cut-off RST
gets smaller as the predicted target RST increases.25 In
practice, the population of eyes presenting for refractive surgery will cover a wide range of predicted target
RSTs depending on the corneal thickness and level of
myopia to be treated. Therefore, if the “RST model” is
individually applied to each eye in the population, the
sum of these probabilities will represent the percentage of eyes that would be expected to have an actual
RST below the selected cut-off RST given the particular Clinical Protocol. The probability output by the
model is subsequently referred to as the predicted rate
of excessive keratectomy depth.
STATISTICAL MODEL FOR THE PERCENTAGE OF EYES WITH
LOW RST FOR A SPECIFIC POPULATION AND EQUIPMENT
Modeling Parameters to Represent a Clinical Protocol. As with the “RST model” from Part I, the model
described below includes a number of parameters so
that it can be customized to represent the instruments
and protocols used in the particular refractive surgery
practice. Throughout the article, the set of parameters
that can be changed (listed below) are defined as the
Clinical Protocol.
●
Minimum target RST used to assess suitability for
LASIK.
●
Selected cut-off RST.
●
Minimum and maximum corneal thickness used to
assess suitability for LASIK.
●
Minimum and maximum level of myopia.
●
Mean, standard deviation, and labeled flap thickness of the microkeratome (assuming that the same
microkeratome is used for all eyes).
●
The bias (accuracy) and standard deviation of the
method of corneal thickness measurement.
●
The standard deviation and the linear regression
equation for the bias (accuracy) of the laser ablation
depth.
Modeling Parameters to Represent the Distribution
of Myopia and Corneal Thickness. To calculate the
percentage of eyes with each predicted target RST,
the distribution of myopia relative to the distribution
of corneal thickness needs to be modeled. Ideally,
the percentage of eyes for each combination of corneal thickness and maximum myopic meridian (corresponding to the ablation depth) would be calculated,
but for simplicity of use, the distributions of corneal
thickness and level of myopia have been separated.
The distribution of myopia was modeled as a histogram using 0.25-diopter (D) groups; the percentage of
eyes for each level of myopia can be manually entered
into the model. This allows flexibility for the distribuJournal of Refractive Surgery Volume 22 November 2006
tion of myopia treated in a refractive surgery practice.
Alternatively, the user can select a default distribution
of myopia for a representative population of eyes presenting for refractive surgery. The mean and standard
deviation of corneal thickness can be adjusted to reflect the population of eyes being treated. The model
assumes that corneal thickness is Normally distributed
and independent of refraction as has been previously
published.26,27 The distributions of corneal thickness
and myopia can then be combined as a table, with the
values in the table representing the percentage of eyes
for each particular combination, calculated by multiplying the percentages for the corresponding corneal
thickness and myopia.
Modeling the Percentage of Patients Deemed Suitable
for Surgery. The percentage of patients who are turned
down for LASIK for reasons relating to corneal thickness is affected by the Clinical Protocol. For example,
using a lower minimum target RST or using a microkeratome with a thinner-labeled flap thickness would
reduce the percentage of eyes turned down for LASIK.
The table of corneal thickness against level of myopia is
filtered to exclude any combinations that do not satisfy
the inclusion criteria according to the Clinical Protocol.
Specifically, the combination of corneal thickness and
level of myopia should satisfy 1) predicted target RST minimum target RST, 2) corneal thickness minimum
corneal thickness, and 3) myopia treated maximum
myopia treated. The percentages for the suitable combinations of corneal thickness and level of myopia in
this table are summed to find the percentage of eyes that
would be suitable for LASIK for the specific Clinical
Protocol. Once the inclusion criteria have been applied,
the filtered distribution of corneal thickness and myopia is scaled up to 100% to represent the distribution of
eyes receiving treatment; a second table multiplies each
value in the filtered table by (100/percentage of suitable
eyes) to obtain the scaled distribution.
Calculating the Predicted Rate of Excessive Keratectomy. A third table contains the result of the “RST
model” applied to each combination of corneal thickness and level of myopia, ie, the probability of obtaining an actual RST below the selected cut-off RST given
the predicted target RST. This table can be used to look
up this probability for an individual case. Finally, a
fourth table multiplies the percentages in the table
representing the scaled distribution of corneal thickness and level of myopia by the probability of obtaining an actual RST below the selected cut-off RST given
the predicted target RST. The values in this table are
summed to obtain the rate of excessive keratectomy
depth to less than the selected cut-off RST for the given
population of eyes and Clinical Protocol.
863
Safety Model for Preventing Ectasia/Reinstein et al
A screen shot of the model is displayed in Figure 2.
The model can be found at http://www.londonvisionclinic.com/ectasiamodel. Microsoft Excel 2003 (Microsoft, Seattle, Wash) was used to develop the statistical
model.
Figure 2. Model Section 1, Accuracy: the user is required to enter parameters including labeled flap thickness, mean flap thickness, corneal thickness bias, and ablation depth bias regression equation. The flap thickness
bias is calculated as the difference between the labeled and mean actual
flap thickness. Model Section 2, Precision: the user is required to enter
standard deviations for flap thickness, corneal thickness, and ablation
depth. The combined standard deviation is calculated. Model Section 3,
Treatment: the user is required to enter parameters including minimum
target RST, treatment zone, and laser. Model Section 4, Population: the
user is required to enter population parameters including corneal thickness
mean and standard deviation, minimum and maximum corneal thickness
treated, and minimum and maximum myopia treated. The percentage of
eyes that would not be suitable for LASIK with the selected Clinical Protocol
is calculated. Model Section 5, Percentage of Eyes Below Cut-off RST: the
user is required to enter the cut-off RST. The model then calculates the
percentage of eyes where the actual RST would be expected to be less
than the selected cut-off RST. This percentage is also displayed in terms
of eyes per hundred thousand and eyes per million. The model displayed
is set up for the Vancouver Clinical Protocol where the RST below which
ectasia appears likely to occur was modeled to be 191 µm.
864
APPLICATIONS FOR THE MODEL TO A REFRACTIVE
SURGERY PRACTICE
The model described above was designed to study
how the minimum target RST used within a refractive
surgery practice affects LASIK candidacy and the risk
of excessive keratectomy depth given the imprecision
of the pachymeter, microkeratome, and laser used. The
“RST model” described in Part I provided a tool for assessing the risk of excessive keratectomy depth for individual eyes. The model described in this article extends
this function to assess the rate of excessive keratectomy
depth for a population of eyes undergoing LASIK. Specifically, the model has the following applications:
1. Estimation of the RST at which ectasia appears likely to occur. The model can be used to back-calculate
a theoretical estimate of the RST at which ectasia
due to excessive keratectomy depth appears likely
to occur. If the model is set up to represent a Clinical Protocol for which the number of occurrences
of ectasia was known, the RST below which ectasia
appears likely to occur can be found by adjusting
the selected cut-off RST until the predicted rate of
excessive keratectomy depth matches the observed
rate of ectasia. For example, if the observed rate of
ectasia in a case series was 1:1000, the RST below
which ectasia appears likely to occur would be
equal to the selected cut-off RST where the model
predicts a rate of excessive keratectomy depth equal
to 1:1000.
2. Calculation of the target RST necessary to reduce
ectasia rate to a specified level. Using a higher value
for the minimum target RST will decrease the risk of
ectasia. For a given Clinical Protocol, the model can
be used to find the minimum target RST that would
reduce the risk of ectasia to a chosen level. This
minimum target RST will subsequently be referred
to as the safe minimum target RST. If the cut-off RST
is set as the RST at which ectasia appears likely to
occur (see 1. above), then the safe minimum target
RST can be found by adjusting the minimum target
RST until the rate of ectasia predicted by the model
is equal to a chosen level. For example, if the chosen
rate of ectasia was 1:1,000,000, the safe minimum
target RST would be equal to the minimum target
RST where the model predicts a rate of ectasia of
1:1,000,000 with the cut-off RST set to the RST at
which ectasia appears likely to occur.
3. Examining the effect of equipment type on the rate
journalofrefractivesurgery.com
Safety Model for Preventing Ectasia/Reinstein et al
of ectasia. Different pachymeters, microkeratomes,
and lasers all have different imprecisions associated with them. By adjusting the model parameters
for corneal thickness, flap thickness, and ablation
depth, the model can be used to demonstrate the
impact that changing any or all of these instruments
might have on the rate of excessive keratectomy
depth and the percentage of eyes that would be suitable for LASIK.
APPLICATION OF THE MODEL TO EXAMPLE CLINICAL
PROTOCOLS
We applied the model to a consecutive case series
of 5212 LASIK procedures preformed between 1996
and 1999 in a high-volume refractive surgical practice (LASIK Vision Canada, Vancouver, Canada) with
mean maximum myopic meridianstandard deviation of 5.062.54 D (range: 0.25 to 16.00 D). The
database was divided into groups by 0.25-D steps of
the maximum myopic meridian and the percentage for
each group was calculated and entered into the model. Corneal thickness statistics were not available for
this consecutive series so a mean of 54134.4 µm was
used, which was found by averaging the results from
13 peer-reviewed studies of population corneal thickness by ultrasound.27-39 Figure 3 shows the distribution
of preoperative corneal thickness and myopic refractive error. The distribution volume is “cut off” where
the combination of corneal thickness and level of myopia do not satisfy the selected safety criteria.
This case series was particularly suited for use in
a statistical model because all eyes underwent LASIK
with one surgeon (H.S.), one laser (NIDEK EC-5000;
NIDEK Co Ltd, Gamagori, Japan), one microkeratome
(Moria LSK-One [Moria, Antony, France], “130” head
and 1 ring), one optical treatment zone (6.5 mm with
transition to 7.5 mm), and minimum corneal thickness
by Orbscan (Bausch & Lomb). All eyes that received
surgery had a predicted target RST of at least 250 µm.
Keratoconus was screened for using Orbscan anterior and posterior surface topography combined with
other clinical indicators including simulated keratometric values 47.00 D, against-the-rule astigmatism,
age, corneal thickness, and reduced best spectaclecorrected visual acuity. It was assumed that none of
the observed cases of ectasia were due to undetected
keratoconus. The Clinical Protocol for this case series
is subsequently referred to as the Vancouver Clinical
Protocol.
Flap thickness using the Moria LSK-One microkeratome has been shown previously for a subset of eyes
in the Vancouver Clinical Protocol to have a mean of
163.630.3 µm.20 The readout ablation depths for the
NIDEK EC-5000 excimer laser have been shown previJournal of Refractive Surgery Volume 22 November 2006
Figure 3. Two-dimensional histogram showing the distribution of myopia
relative to the distribution of corneal thickness for patients presenting for
refractive surgery at the Vancouver Clinic. Eyes where the combination of
corneal thickness and level of myopia did not satisfy the safety criteria for
LASIK are excluded as seen by the sharp cut-off on the right hand side
of the distribution marked in black.
ously by Artemis stromal subtraction pachymetry for
a subset of eyes in the Vancouver Clinical Protocol to
have a standard deviation of 11.2 µm with bias according to the equation; actual ablation depth = 0.93 * laser
readout ablation depth 7.59.25 The repeatability of
Orbscan corneal thickness measurements was taken to
be 8.42 µm as published by Yaylali et al28 for the version of Orbscan that was available in 1997.
Six cases of ectasia had been identified after 2
years. There might have been further occurrences of
ectasia for this case series that were not known due
to loss of follow-up. Alternatively, some cases of ectasia observed might have been caused by something
other than excessive keratectomy depth. To account
for this, we applied the model to estimate the RST below which ectasia appears likely to occur for a range
of possible rates of ectasia likely to encompass the real
value and to determine effectively a “margin of error.”
For each RST, the safe minimum target RST was backcalculated using a clinically acceptable rate of ectasia
of 1:1,000,000.
As shown in Part I, the microkeratome is currently
the major source of RST prediction error. Flap thickness statistics for a series of microkeratomes were
entered into the model, as set up for the Vancouver
Clinical Protocol described above, to investigate how
different microkeratomes might affect the rate of excessive keratectomy depth and hence ectasia. The ablation
depth bias was removed to isolate the effect of chang865
Safety Model for Preventing Ectasia/Reinstein et al
Figure 4. Bar chart showing the RST below
which ectasia appears likely to occur (Cutoff(ectasia) RST) and safe minimum target
RST (Target (1:1,000,000) RST) predicted
by the model for a range of 2 to 12 occurrences of ectasia in the Vancouver Clinical
Protocol. After 2 years, 6 reported cases
of ectasia occurred of 5212 eyes treated,
thought to be caused by excessive keratectomy depth. For this rate of ectasia, the
model predicted that the RST below which
ectasia appears likely to occur was 191 µm
and the safe minimum target RST was 329
µm for the rate of ectasia to have been
1:1,000,000. Had the actual number of
ectasia occurrences been 10, the model
predicted that the RST below which ectasia
appears likely to occur would be 197 µm
and the safe minimum target RST would
be 336 µm to reduce the rate of ectasia to
1:1,000,000.
ing the microkeratome. A Medline search was performed for publications up to December 2005 using the
search string “flap AND thickness AND LASIK.” Flap
thickness statistics were averaged from the individual
published statistics for each microkeratome. The rate
of excessive keratectomy depth, safe minimum target
RST, and percentage of eyes that would be suitable
for LASIK if this safe minimum target RST were used
were calculated for each microkeratome. The selected
cut-off RST was set to the RST below which ectasia
appears likely to occur as previously estimated by the
model using the Vancouver Clinical Protocol. The following microkeratomes were found in the Medline
search: SKBM (Alcon Summit Autonomous; Alcon
Laboratories Inc, Ft Worth, Tex); Amadeus (Allergan
Inc, Irvine, Calif); Automatic Corneal Shaper, Hansatome, Hansatome Zero Compression (Bausch & Lomb,
Salt Lake City, Utah); IntraLase (IntraLase Corp, Irvine,
Calif); M2, M2 Single Use, LSK-One, CB, CB Single
Use (Moria); and the MK-2000 (NIDEK Co Ltd).
Finally, the model parameters were set up to reflect the current Clinical Protocol of one of the authors
(D.Z.R., London Clinical Protocol); the Clinical Protocol
included the zero compression Hansatome microkeratome using the z16 head, the MEL80 excimer laser (Carl
Zeiss Meditec AG, Jena, Germany), pachymetry using
the Corneo-Gage Plus handheld ultrasound pachymeter
(Sonogage, Cleveland, Ohio), and the Artemis VHF digital ultrasound arc-scanner was used to confirm the corneal thickness for eyes with low corneal thickness or
where the predicted target RST by handheld pachymetry was 265 µm. The minimum target RST used was
866
250 µm and LASIK was not performed on eyes where
the corneal thickness was 465 µm by Artemis regardless of achieving a predicted target RST 250 µm. The
London Clinical Protocol was applied to the Vancouver
case series to determine how the rate of ectasia and safe
minimum target RST would have been affected had the
London Clinical Protocol been used. The selected cutoff RST was set to the RST below which ectasia appears
likely to occur as previously estimated by the model using the Vancouver Clinical Protocol.
RESULTS
Of the consecutive series of 5212 eyes, 6 occurrences
of ectasia were detected within 24 months after LASIK
that were not explained by keratoconus; a rate of 0.12%
(1151:1,000,000). For this Clinical Protocol, the model
found the RST below which ectasia appears likely to occur to be 191 µm as shown in Figure 2. The model predicted that the safe minimum target RST was 329 µm for
the rate of ectasia to be reduced to 1:1,000,000. Figure
4 shows the RST below which ectasia appears likely to
occur and safe minimum target RST predicted by the
model for a range of 2 to 12 occurrences of ectasia for
this case series. The RST below which ectasia appears
likely to occur ranged from 178 µm had there been 2 cases
of ectasia to 199 µm had there been 12 cases of ectasia. The
safe minimum target RST ranged from 315 µm had there
been 2 cases of ectasia to 338 µm had there been 12
cases of ectasia.
The results of changing the microkeratome charcteristics19,21,22,40-54 are listed in the Table assuming a
RST below which ectasia appears likely to occur of
journalofrefractivesurgery.com
867
Modeled Results of the Effect of Changing Microkeratome Alone Within a Specific Clinical Protocol
Modeled Safety Parameters
for Rate of Ectasia of
1:1,000,000
Nominal
Head
Intended Flap
Thickness
(µm)
Avg Flap
Thickness
(µm)
Avg Flap
Thickness SD
(µm)
Avg Bias
(µm)
Predicted Rate
of Ectasia
(Eyes/Million)
Safe Minimum
Target RST
(µm)
% Eyes Not
Suitable for
LASIK
Nidek MK-200019
145
145
103.0
15.0
42.0
0.01
220
2.5
B&L Hansatome zero compression52
160
160
124.0
17.0
36.0
0.15
239
7.0
B&L ACS45,50,51
160
160
116.7
20.1
43.3
0.32
243
7.9
IntraLase
130
130
114.0
14.0
16.0
0.46
246
3.3
NIDEK MK-200019,47,51
130
130
118.1
14.1
11.9
1.17
251
3.9
B&L Hansatome zero
compression52
180
180
142.0
20.0
38.0
1.40
252
20.3
B&L Hansatome19,50,51,53,54
160
160
128.2
21.1
31.8
4.37
261
14.3
19,21,40,53,54
B&L Hansatome
180
180
136.7
23.8
43.3
5.16
262
26.7
Moria LSK One46
100
100
107.0
14.0
7.0
9.30
267
2.6
NIDEK MK-2000
160
160
134.4
20.9
25.7
10.58
267
17.5
Allergan Surgical
Amadeus19,41
140
140
143.5
16.5
3.5
76.04
280
14.1
130
160
148.2
23.0
11.8
160.04
292
34.2
Moria M2 Single Use
130
130
145.0
17.5
15.0
328.96
296
16.8
Alcon SKBM19,21,45
160
160
155.3
22.7
4.7
339.60
299
39.4
Moria M2
110
130
140.6
24.2
10.6
843.29
318
31.3
Flapmaker22
160
160
145.0
32.0
15.0
1069.20
329
66.3
Moria LSK One
130
160
161.3
29.0
1.3
2343.95
333
69.8
Moria CB19,21,40,49
130
160
160.3
29.6
0.3
2389.88
335
71.3
Moria CB
110
130
165.0
27.0
35.0
8124.84
358
65.8
Allergan Surgical
Amadeus19,40
160
160
181.0
30.5
21.0
11623.32
361
88.5
Microkeratome
40
19,47
Moria M219,42,48,50
43
21,42
20,44
19
For each microkeratome, published flap thickness statistics were averaged and the average bias was calculated. Using the model described in this study, the predicted rate of ectasia and safe minimum target RST for the Vancouver Clinical Protocol were found had each microkeratome been used. The percentage of eyes that would still be suitable for LASIK had the calculated safe minimum
target RST been used was also found. The microkeratomes are listed in ascending order of the predicted rate of ectasia.
Journal of Refractive Surgery Volume 22 November 2006
Safety Model for Preventing Ectasia/Reinstein et al
TABLE
Safety Model for Preventing Ectasia/Reinstein et al
191 µm. The predicted rate of ectasia ranged from
0.01:1,000,000 for the NIDEK MK-2000 with the 145µm nominal head to 11,623:1,000,000 for the Allergan
Surgical Amadeus with the 160-µm nominal head. The
safe minimum target RST that predicted a rate of ectasia of 1:1,000,000 ranged from 220 µm for the NIDEK
MK-2000 with the 145-µm nominal head to 361 µm
for the Allergan Surgical Amadeus with the 160-µm
nominal head.
The mean flap thickness of the Hansatome z16 for
flaps created within the London Clinical Protocol have
been measured to be 125.012.4 µm (D.Z. Reinstein,
unpublished data, 2006) using Artemis measured
Reinstein Flap Thickness as described previously.20
The ablation depth bias for the MEL80 studied by Artemis stromal subtraction pachymetry as described in
Part I was found to follow the equation—actual ablation depth = 0.82 * laser readout ablation depth (data
on file, Carl Zeiss Meditec AG, Jena, Germany). The
repeatability of handheld ultrasound pachymetry was
taken to be 5.84 µm.28 The model predicted the rate
of ectasia, given a RST below which ectasia appears
likely to occur of 191 µm, would have been reduced
from 1151 to 0.000003 eyes per million had the London Clinical Protocol been used for the Vancouver
case series.
DISCUSSION
A statistical model was derived to estimate the rate
of excessive keratectomy depth below a selected cut-off
RST given a minimum target RST and specific Clinical
Protocol. The model can be used to 1) assess the risk of
ectasia due to excessive keratectomy depth for a specific
Clinical Protocol, 2) estimate the RST below which ectasia appears likely to occur, 3) calculate the minimum
target RST required to safely assess suitability for LASIK
for a given Clinical Protocol, and 4) assess the impact of
different equipment on the safety of LASIK. Applying
the model to an example Clinical Protocol, the model
predicted that ectasia might be likely to occur in eyes
where the actual RST is 191 µm.
The model was designed to be accessible to surgeons
to provide a theoretical estimate of the minimum target
RST that might be used in their refractive surgery practice. In an attempt to make the model an accurate reflection of a particular refractive surgery practice, changeable user variables have been included where possible.
For ease of use, a range of default values are included
with values taken from the published literature for parameters including an example refractive surgery population, flap thickness statistics for the microkeratomes
listed in the Table, methods of pachymetry, and ablation depths for a number of excimer lasers.
868
The model described in this article assumes that any
cases of ectasia caused by undetected keratoconus are
excluded. Specifically, for the Vancouver Clinical Protocol, it is assumed that keratoconus was effectively
screened for and that all cases of ectasia observed were
due to excessive keratectomy depth. There may be
other, as yet unidentified, risk factors for ectasia. However, this should not affect the validity of the model
as long as such cases are excluded from the analysis
along with any keratoconus cases. A minority of ectasia cases incorrectly diagnosed as excessive keratectomy depth or the possibility of further cases of ectasia
lost to follow-up would have only introduced a small
amount of error; the model predicted the RST below
which ectasia is likely to occur to be between 178 µm
and 199 µm for a range of 2 to 12 occurrences of ectasia
in the Vancouver Clinical Protocol.
It is possible that different eyes have different limits for ectasia depending on etiological factors such as
corneal thickness, corneal stiffness, and intraocular
pressure. With the introduction of instruments such as
the Ocular Response Analyzer (Reichert, Buffalo, NY),
biomechanical variables, including corneal stiffness,
could potentially be incorporated into the model described here. It has been suggested that the percentage
of corneal thickness could be used as a safety criterion
for LASIK rather than a minimum target RST.5,55 If this
were confirmed to be the case, the probability model
could be refined to take the percentage of cornea removed into account.
A potential weakness of this study is that the distribution of corneal thickness for the Vancouver series was
unavailable, and so a value averaged from 13 published
population studies was used. This assumption appears
to be reasonable; for example, if an average corneal thickness of 525 µm was used (instead of 541 µm), the model
would predict that the RST below which ectasia appears
likely to occur would be 186 µm (instead of 191 µm). Although lowering the average corneal thickness produces a higher percentage of eyes with a predicted target
RST close to the minimum target RST, lowering the
average corneal thickness also increases the number of
eyes that would be excluded from having LASIK. In
the above example, the model predicted that 10.1% of
eyes would be turned down for LASIK given an average corneal thickness of 541 µm whereas 17.3% of eyes
would be excluded given an average corneal thickness
of 525 µm.
The choice of microkeratome has a major impact
on the risk of excessive keratectomy depth; the Table
showed that the predicted rate of ectasia for different microkeratomes can differ by up to five orders of
magnitude (range: 1 to 10,000 eyes per million).
journalofrefractivesurgery.com
Safety Model for Preventing Ectasia/Reinstein et al
This difference comes primarily from the range of
flap thickness bias (mean versus labeled flap thickness) and flap thickness standard deviation between
microkeratomes. For arguments sake, the model appears to predict that ectasia is occurring for an RST
200 µm. Considering the current generally accepted
minimum target RST of 250 µm, an RST error of 50 µm
needs to be avoided in cases where the predicted target RST is 250 µm. Published flap thickness standard
deviation ranges from 14 to 35 µm. In the case of the
current lowest flap thickness standard deviation of 14
µm, the combined standard deviation of corneal thickness measurement, flap thickness, and ablation depth
would be approximately 18 µm.25 This would translate
to 0.27% of cases with a predicted target RST of 250
µm obtaining an actual RST 200 µm. Labeling the microkeratome with a value 1 standard deviation higher
than the actual mean flap thickness would reduce this
percentage to 0.01%.
It has been suggested that using a thinner flap thickness will reduce the rate of ectasia. For an individual
eye, using a thinner flap compared with using a thick
flap would reduce the risk of ectasia because the predicted target RST will be greater. In general, it is likely
that the population rate of ectasia would be reduced
when using a thin flap compared with using a thick
flap as the majority of eyes (mild and moderate myopia,
not thin corneal thickness) would benefit. This trend is
seen in the Table as the microkeratomes with the lowest predicted rate of ectasia also have lower actual flap
thicknesses. However, the potential benefit is dependent on labeling bias as demonstrated by the rank position within the Table of the Moria LSK-One using the
100-µm head, where the predicted rate of ectasia was
9.3:1,000,000. In this instance, the model found that
98% of eyes would be suitable for LASIK. The model
predicted that the rate of ectasia would be reduced to
1:1,000,000 by using a minimum target RST of 267 µm,
while 97.4% of eyes would still be suitable for LASIK.
This means that the extra 0.6% of eyes that qualify for
LASIK due to the Moria LSK-One 100-µm nominal head
being labeled with a value lower than the actual mean
flap thickness contribute 8.3 eyes per million of the expected ectasia cases. The Table demonstrates that the
safest microkeratomes are all labeled with a value thicker than the actual mean flap thickness. As long as microkeratome flap thickness standard deviation remains
between 14 and 35 µm, a negative bias appears to be
one of the most important elements for diminishing the
risk of ectasia due to excessive keratectomy depth for all
eyes, particularly for the most borderline cases.
The 250-µm limit indirectly proposed by Barraquer
was derived for his specific instruments so it is not
Journal of Refractive Surgery Volume 22 November 2006
necessarily applicable for other Clinical Protocols. The
probability model described demonstrated that there
is no universally safe minimum target RST limit for
LASIK. This model may be used as a tool for surgeons
to evaluate the risk of ectasia due to excessive keratectomy depth and help determine the minimum target
RST to use given a particular Clinical Protocol.
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