flexure of thin rigid contact lenses

Contact Lens and Anterior Eye (2001) 24, 59-64 © 2001 British Contact Lens Association L ~ J

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Original Article

FLEXURE OF THIN RIGID CONTACT LENSES

Michael J. Collins*, Ross Franklint, Leo G. Carney$, Craig Bergielt, Paul Lagost and Daniel Chebib~

(Received 19th September 2000; in revised form 8th November 2000)

Abstract -- The flexure of spherical rigid contact lenses was measured on the eyes of lO young subjects using a videokeratoscope. Five subjects had little or no with-the-rule astigmatism (< O. 75 D) and five had moderate levels of with-the-rule astigmatism (1.00-2.00 D). Two lens materials (polymethylmethacrylate [PMMA] and Boston XO) in three centre thicknesses (0.05, O. 10 and O. 15 mm) were used in the study. No significant difference in the amount of flexure was found between the two materials tested. The degree of regular astigmatism on the lens front surface was found to increase as the centre thickness of the contact lens decreased. For the astigmatic group, the lenses with centre thicknesses of O.05 mm had levels of front surface astigmatism similar to those of the underlying cornea. On spherical corneas the level of regular astigmatism can exceed that of the cornea for thinner lenses. When sphero-cylinder variations are accounted for, residual higher-order aberration (root mean square) levels were found to approach those of the cornea when the lens thickness was reduced to 0.05 mm. Contact Lens and Anterior Eye (2001) 24, 59-64.

KEY WORDS: flexure, astigmatism, contact lens, videokeratoscope, rigid gas permeable

Introduction

R igid contact lenses are known to slightly bend or flex when placed in the eye, and this may lead to

permanent lens warpage. Flexure results f~om factors such as eye lid forces, contact lens fit, thickness, material and the shape of the cornea. 1

The result of flexure may be that the lens induces unwanted astigmatism or aberrations, leading to less than optimum visual acuity. The fit of the lens may also be altered sufficiently to adversely affect patient comfort and corneal integrity.

An early study by Harris and Chu found that thick polymethylmethacrylate (PMMA) lenses did not flex significantly on astigmatic corneas while thin lenses did# Their results showed that a cornea with 4 D of with-the-rule astigmatism fitted with a lens of centre thickness 0.08 mm produced 1.50 D more lens surface astigmatism that if fitted with a centre thickness of 0.16 mm. They also reported that insignificant amounts of flexure occurred in spherical or near spherical corneas.

Herman found that flexure was dependent on the relationship between the back optic zone radius (BOZR) of the lens and corneal curvature? In a study of seven different back optic zone radii on with-the-rule astigmatic corneas, he found that if the BOZR were steeper

*PhD ~BAppSc (Optom) SBAppSc, MSc (Optom), PhD, FAAO

than the flattest corneal meridian, with-the-rule astigmatism resulted. This has also been reported in a study by Pole. 4 When the BOZR was flatter than the flattest corneal meridian, against-the-rule astigmatism was the surprising result. Both Herman and Pole recommended that for minimal flexure, lenses should be fitted on, or slightly flatter than, the flattest corneal meridian.

The 'reverse' flexure (against-the-rule lens surface astigmatism on with-the-rule corneas) found in very flat fits was confirmed by Stone and Collins. ~ They tested flexure of different materials and noted that the rigid gas permeable (RGP) materials flexed in a similar but more pronounced way than PMMA. They also found that thin lenses flexed more than thick lenses. Their study concluded that minus lenses, being thin in the centre, are more prone to flexure than plus lenses. Harris and Appelquist found that flexure decreased as minus power of the lenses increased#

A study by Brown, Baldwin, and Pole found that back optic zone diameter (BOZD) affected flexure, such that smaller diameters produced less flexure. 7 They found that a BOZD of 7.20 mm flexed to 32% of the total corneal toricity, whereas one of 7.80 mm flexed to 56% and one of 8.40 mm flexed to 59%. The differences in flexure were related to the different sagittal depths of the lenses, the larger BOZDs having larger sagittal depths and thus more central corneal clearance than lenses with smaller BOZDs.

All above-mentioned studies of rigid lens flexure have used a keratometer for corneal and lens topo-

Flexure of thin rigid contact lenses MJ Collins et al

60 graphy measurements. As is well known, a keratometer measures along two principal meridians of the central 3 mm and thus does not provide data for the remaining lens surface)

The TMS-1 (Computer Anatomy, software version 1.61) corneal topography system (videokeratoscope) was used in this study. This system measures the central 7 - 8 mm of the surface. When the videokeratoscope axial power data are analysed with appropriate software, the amount of regular astigmatism and higher order abelTations may be determined for the region of choice) The aim of this study was to measure the amount of residual surface astigmatism and higher order aberrations that occur when lens thickness, material and corneal astigmatism are systematically varied.

Methods Six different contact lenses were ordered with three centre thicknesses (0.05, 0.10, 0.15 ram) and two materials: PMMA (oxygen permeability [Dk] of 0), and Boston XO (Dkl00).9 Lenses were ordered as a bi- curve design (i.e. peripheral curve is a single tangential fiat) with back optic zone radius (BOZR) of 7.80 ram, back optic zone diameter of 7.50 mm, total diameter of 9.50 mm, and back vertex power of -3.00 DS. Lens parameters were measured and are shown in Table 1. Lenses were also checked with an optical microsphe- rometer between subject sessions to ensure that permanent warpage had not occurred.

The six contact lenses were fitted to one eye of 10 subjects (four female, six male). Subjects ranged in age from 19-26 years. The mean age of the subjects was 20.3 years. All subjects were flee from ocular disease and suitable for contact lens wear (i.e. subjects with fluorescein tear break-up time greater than 10 s, normal ocular health and no tear film abnormalities).

The subject's flattest meridian, as determined by a keratometer, was required to be in the range from 7.75-7.85 mm, close to the 7.80 mm BOZR of the contact lenses. The experimental contact lenses were fitted to prospective subjects and only those who showed optimum fluorescein patterns and good lens centration were accepted.

Subjects were classified into two groups according to their corneal cylinder in a 3.5 mm zone based on a videokeratoscope map of their cornea:

1. Spherical - corneal astigmatism of 0.00 D to 0.75 D, n=5, mean astigmatism=0.50 D,

2. Astigmatic - corneal astigmatism of 1.00 D to 2.00 D, n=5, mean astigmatism=l.25 D.

The subject selection and subsequent analysis were simplified by only considering with-the-rule astigmatism. For the purposes of this study, with-the-rule astigmatism was defined as flattest corneal meridian at 180 ° _+ 20 °.

The topical anaesthetic benoxinate hydrochloride (0.4%) was used with all subjects to minimise reflex tearing, since not all subjects routinely wore rigid lenses. Subjects were fitted with each of the contact lenses in a random order. Five minutes settling time was allowed after insertion of each contact lens before videokeratoscope images were acquired. To minimise decentration during testing, the subjects were instructed to blink and two seconds were counted prior to each TMS image being taken. Subjects were also instructed to open their eyes as wide as possible to avoid lid interaction with the lens during videokeratoscope image capture. Four videokeratoscope images were captured and processed for each subject while maintaining alignment and focus according to standard manufacturer's recommendations. Maps were chosen so that the lens decentration was minimal in all processed maps.

Topography of the corneal and lens surfaces was compared using TMS axial power maps. These were calculated from the axial radii using a common refractive index of 1.3375. Axial power maps should be thought of as a dioptric representation of curvature rather than as the refractive property of the surface. Using software based on the methods of Maloney et al., axial power maps were analyzed over a 3.5 and 6 mm zone to derive best-fit sphero-cylinder. 1° For the purposes of this study, sphero-cylinder maps with the flattest meridian at 180°+ 20 ° are grouped together as with-the-rule astigmatism, and the cylinder power is averaged without considering the difference in axis. We

Table 1. Parameters of rigid contact lenses used in the study.

Lens material and ordered thickness Back vertex power (D )

Measured parameters Centre thickness Total diameter Back optic zone radius

(mm) (mm) (mm)

PMMA 0.05 mm -2.95 0.06 9.53 7.80 PMMA 0.I0 mm -3.02 0.09 9.39 7.82 PMMA 0.15 mm -3.02 0.17 9.51 7.79

Boston XO 0.05 mm -3.09 0.06 9.54 7.78 Boston XO 0.10 mm -2.96 0.12 9.49 7.81 Boston XO 0.15 mm - 3.08 0.17 9.51 7.82

Contact Lens and Anterior Eye

Flexure of thin rigid contact lenses MJ Collins et a/

call this cylinder power the regular astigmatism. Across the same two regions, we also calculated the root mean square (RMS) error of the difference in surface height from the underlying best-fit sphero-cylinder. We call this RMS difference value the residual aberration. The RMS value represents a numerical index for higher order aberrations such as coma and spherical aberration since the best sphero-cylinder power has been removed. These aberrations are known to be detrimental to vision.

Results The mean regular front surface astigmatism of each lens tested has been compared with corneal astigmatism in Figures 1 and 2 for the spherical and astigmatic cornea groups respectively. For both lens materials there was a decrease in mean regular astigmatism with an increase in thickness of the lens.

With the lenses on astigmatic corneas, the level of regular surface astigmatism approached the level in the underlying cornea as thickness decreases (Figure 2). It can be seen that the standard deviation is higher for the thinner Boston XO lenses, indicating greater variability between subjects in the amount of flexure for thinner lenses. For PMMA lenses, this trend is less obvious.

Interestingly, for corneas with little or no astigmatism, the 0.05 mm thick and 0.10 mm thick lenses show greater with-the-rule astigmatism than the cornea alone (Figure 1). However, this difference was not significant

(t-test) for either the 3.5 or 6 mm central zone of the lens for either material.

For regular astigmatism, the effect of lens thickness on flexure was tested for statistical significance using a paired two-tailed t-test. The results are shown in Table 2 (spherical subjects) and Table 3 (astigmatic subjects). A significant difference in regular astigmatism occurred for the 6 mm zone for the Boston XO material, between the 0.06 and 0.17 mm thicknesses and 0.06 and 0.12 mm thicknesses for both the spherical and astigmatic cornea groups. There was also a significant difference over the 3.5 mm zone for both groups between the 0.06 and 0.17 mm thicknesses and for the astigmatic group between the 0.12 and 0.17 mm thicknesses. A similar trend was apparent for the PMMA lenses.

We also tested the difference between the flexure of PMMA and Boston XO materials of similar thicknesses and found no significant difference for any thickness at either zone size (3.5 and 6 ram). However, it should be noted that the PMMA lens of 0.09 mm centre thickness was compared with the Boston XO lens with a centre thickness of 0.12 ram.

For the residual aberration (RMS), the spherical and astigmatic subjects are grouped together since best sphero-cylinder has effectively been removed from the surface topography (Figure 3). Data for one subject were incomplete and were removed from the analysis. The level of residual aberration increases as the lenses

61

P M M A mater ia l

i06 mm zon e j

P M M A mate r i a l

Cornea 0.06 mm thick 0.09 mm thick 0.t7 mm thick

B o s t o n XO mate r ia l

~, 0.8

a.

0.2

o

Cornea 0.06 mm thick 0.12 mm thick 0.17 mm thick

•6 mm zone mm z o n e ,

Figure 1. Regular astigmatism of the cornea/lens surface for the spherical cornea group. Error bars represent±one standard deviation.

B o s t o n XO mate r ia l

1.8


o m z o o o

Figure 2. Regular astigmatism of the cornea/lens surface for the astigmatic cornea group. Error bars represent+one standard deviation.


Flexure of thin rigid contact lenses M3 Collins et al

62 Table 2. Difference in regular lens surface astigmatism (spherical subjects) - thickness effects.

3.5 mm zone 6 mm zone Spherical group d.f t-value p-value d.f t-value p-value

PMMA 0.06 vs 0.17 mm 4 4.533 0.011" 4 2.846 0.047* 0.06 vs 0.09 mm 4 1.248 0.280 4 2.54 0.064# 0.09 vs 0.17 mm 4 2.840 0.047* 4 2.404 0.074#

Boston XO 0.06 vs 0.17 mm 4 3.098 0.036* 4 3.305 0.030* 0.06 vs 0.12 mm 4 2.175 0.095 4 2.899 0.044* 0.12 vs 0.17 mm 4 1.704 0.163 4 1.715 0.161

*Indicates significance at the 5% level. tIndicates tests approaching 5% significance.

Table 3. Difference in regular lens surface astigmatism (astigmatic subjects) - thickness effects.

3.5 mm zone 6 mm zone Astigmatic group d.f t-value p-value d.f t-value p-value

PMMA 0.06 vs 0.17 mm 3 5.136 0.014" 4 14.005 <0.001" 0.06 vs 0.09 mm 4 2.209 0.092 4 4.168 0.014" 0.09 vs 0.17 mm 3 2.558 0.083 4 1.963 0.144

Boston XO 0.06 vs 0.17 mm 4 2.932 0.043* 4 3.500 0.025* 0.06 vs 0.12 mm 4 1.984 0.118 4 2.795 0.049* 0.12 vs 0.17 mm 4 3.071 0.037* 4 2.632 0.058t


PMMA m a t e r i a l

cornea 0 00 mm thick 0,09 mm thick 0.17 mm thick

B o s t o n X O mater ia l


Figure 3. Residual aberration for all subjects.

B3.5 rnrn zone Ioo ..... r l

become thinner, approaching the residual aberration level in the cornea.

The difference in residual aberrations over a 6 m m zone was significant for the Boston XO material, between the 0.06 and 0.17 m m thicknesses and 0.12 and 0.17 m m thicknesses (Table 4). T h e difference in residual aberrations approached significance (/'=0.06) between the 0.12 and 0.17 m m thickness lenses for the 3.5 m m zone.

The effect of thickness on contact lens flexure is illustrated in the axial topography maps for one subject in Figure 4. T h e levels of regular ast igmatism and residual aberrations can be seen to increase as lens thickness decreases.

Discussion We have shown in this study that there are similar increases in regular front surface ast igmatism and residual aberrations as the thickness of rigid lenses is reduced. Both regular astigmatism and residual higher order aberrations will reduce the quality of visual performance through the lenses. The ability of the rigid lens material to mask these aberrations is, as expected, dependent on thickness. Soft lenses are generally not able to mask these higher order aberrations at clinically practical thicknesses. 11


Flexure of thin rigid contact lenses ~ - ~ MJ Collins et al

Table 4. Difference in residual aberrations - thickness effects.

3.5 mm zone 6 mm zone All subjects d.f t-value p-value d.f t-value p-value

63

PMMA 0.06 vs 0.17 mm 8 1.681 0.131 8 2.156 0.063t 0.06 vs 0.09 mm 8 0.772 0.462 8 0.602 0.564 0.09 vs 0.17 mm 8 1.086 0.309 8 0.874 0.407

Boston XO 0.06 vs 0.17 mm 8 1.825 0.106 8 2.393 0.044* 0.06 vs 0.12 mm 8 0.894 0.398 8 1.449 0.185 0.12 vs 0.17 ram 8 2.171 0.062t 8 2.368 0.045*


PMMA

0.06 mm 0.09 mm 0.17 mm thick thick thick

BOSTON XO

0.06 mm 0.12 mm thick thick

Figure 4. Videokeratoscope axial radii maps for rigid lenses on the eye of one subject.

0.17 mm thick

One of the significant optical advantages of rigid contact lenses over soft lenses is their ability to allow neutralisation of corneal astigmatism. When corneal astigmatism closely matches ocular astigmatism, the rigid lens-tear fluid lens combination can allow the clinician to use a spherical lens power and avoid the need for a toric lens design.

On moderately astigmatic eyes (1 to 2 D with-the- rule), we found that the level of lens astigmatism on-eye approaches that of the underlying cornea as the lens thickness reaches 0.06 mm. Even at the 0.17 mm centre thickness we found that the lenses had a small amount (<0.50 D) of astigmatism.

We were surprised by the level of induced regular with-the-rule astigmatism for thin lenses on spherical corneas (<0.75 D with-the-rule). Once the lens thickness dropped below about 0.12 mm we found more front surface astigmatism on the lens than for the underlying cornea, although the difference was not statistically significant. Harris and Chu also measured

mild with-the-rule flexure on a subject with a spherical cornea# When rigid lens flexure is modelled using fu id forces alone, they are not expected to flex more than the corneal toricity. 12 Therefore, the apparent over-flexure on spherical corneas is probably a temporary effect due to the force of the upper lid during blinking.

We did not find any difference between the flexure of PMMA and Boston XO materials. The Young's modulus for PMMA is 2432 MPa, while for Boston XO it is 1350 MPa, indicating that the latter is more flexible# However, this difference in material rigidity did not translate into a significant difference in flexure for lenses manufactured from the two materials in the conditions of this study. Possibly differences would be apparent for subjects with higher corneal toricity.

We have illustrated by means of videokeratoscopy that the flexure of thin rigid lenses on-eye includes both regular astigmatism and higher order residual aberrations. As the thickness of the lenses decreases there is an increase in both regular astigmatism and residual


Flexure of thin rigid contact lenses MJ Collins et al

64 abe r r a t i ons . Bo th of t h e r ig id ma t e r i a l s we t e s t e d s h o w e d s imi la r l eve ls of f lexure .

Address for Correspondence D r M i c h a e l Coll ins , School of Op tome t ry , Q u e e n s l a n d Un ive r s i t y of T e c h n o l o g y , Vic tor ia P a r k Road, Ke lv in Grove, Q u e e n s l a n d , 4059, Aust ra l ia . E-mail: re .col l ins@ q u t . e d u . a u

REFERENCES

1 Herman, J. Flexure, in Bennett E, Grohe R. (Eds). Rigid Gas Permeable Contact Lenses. Fairchild Publications, New York, (1986). Harris, M. and Chu, C. The effect of contact lens thickness and corneal toricity on flexure and residual astigmatism. Am. J. Optom. Physiol. Opt., 49, 304-307 (1972).

3 Herman, J. Flexure of rigid contact lenses on toric corneas as a function of base curve fitting relationship. J. Am. Optorn. Assoc., 54, 209-213 (1983).

4 Pole, J. The effect of the base curve on the flexure of polycon lenses. Int. Contact Lens Clin., 10, 49-52 (1983).

5 Stone, J. and Collins, C. Flexure of gas permeable lenses on toroidal corneas. Optician, 188 (4951), 8-10 (1984).

6 Harris, M. and Appelquist, D. The effect of contact lens diameter and power on flexure and residual astigmatism. Am. J. Optom. Physiol. Opt., 51, 266-270 (1974).

7 Brown, S, Baldwin, M. and Pole, J. Effect of the optic zone diameter on lens flexure and residual astigmatism. Int. Contact Lens Clin., 11,759 - 763 (1984).

8 Binder, P. Videokeratography. CLAOJ., 21, 133-144 (1995). 9 Boston Product Guide, Polymer Technology Corporation, p 10 - 15

(1999). m Maloney, R.K., Bogan, S.J. and Waring, G.O. Determination of

corneal image-forming properties from corneal topography. Am. ]. Ophthalmol., 115, 31-41 (1993).

12 Griffiths, M., Zahner, K., Collins, M. and Carney, L. Masking of irregular corneal topography with contact lenses. CLAOJ., 24, 76- 81 (1998).

1~ Corzine, J.C. and Klein, S.A. Factors determining rigid lens flexure. Optom. Vis. Sei., 74, 639-645 (1997).


flexure of thin rigid contact lenses

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