The validity of the Jessen formula in overnightorthokeratology: a retrospective study

Ben Chan, Pauline Cho and John Mountford

School of Optometry, The Hong Kong Polytechnic University, Hong Kong SAR, China

Abstract

Purpose: To investigate the validity of the Jessen formula, with a compression factor of 0.75, in

determining the back optic zone radius (BOZR) of an orthokeratology (ortho-k) lens for myopic

reduction [i.e. BOZR = flattest K ) (target reduction + 0.75)].

Methods: One hundred and twenty-three consecutive ortho-k patient files from the Optometry Clinic

of The Hong Kong Polytechnic University were reviewed. Pertinent data at the preliminary visit and at

the morning visit after 2 weeks of lens wear for 63 patients who fulfilled the inclusion criteria were

retrieved for analysis. All patients were either fitted with DreimLens (DreimLens Taiwan, Taiwan

Macro Vision Group, Taiwan, China) or eLens (E&E Optics Ltd., Hong Kong SAR, China) designs.

Only data from the right eye were analysed. The validity of the Jessen formula was evaluated by

comparing the equation of the plot of myopic reduction attempted (based on the Jessen formula) and

myopic reduction achieved (based on subjective refraction).

Results: The Jessen formula was found to underestimate the intended target of myopic reduction

following ortho-k. The results suggested that the formula should be revised to BOZR = flattest K )(1.23 target reduction + 1.27).

Conclusion: If the intention is to overcorrect the ortho-k patient by 0.75 D to allow for regression

during the daytime, the Jessen formula with a compression factor of 0.75 is not valid to determine the

BOZR of the ortho-k lens designs.

Keywords: compression factor, Jessen formula, myopic reduction, orthokeratology

Introduction

Overnight orthokeratology (ortho-k) is becoming morepopular for patients with low to moderate myopia andthose who are unwilling to have laser refractive surgery,as well as for parents seeking options for myopic controlfor their children (Cho et al., 2002). Many ortho-k lensdesigns in the market calculate the desired back opticzone radius (BOZR) based on the Jessen formula, forexample DreimLens (DreimLens Taiwan, TaiwanMacro Vision Group, Taiwan, China); Paragon CRT(Paragon Vision Sciences, Mesa, AZ, USA); Fargo(C&E G.P Specialists Ltd., San Clemente, CA, USA);

Emerald (Euclid Systems Co, Herndon, VA, USA);eLens (E&E Optics Ltd., Hong Kong SAR, China), etc.The formula assumes that the amount of myopicreduction can be achieved by fitting the BOZR of thelens flatter than the flattest curvature of the cornea by thesame amount. For example, a 2.00 D refractive correc-tion would require the BOZR of the lens to be fitted2.00 D flatter than the flattest curvature of the cornea.This was the original �orthofocus� technique as describedby Jessen (1962), wherein the tear lens becomes thecorrecting factor. However, since the formula wasincorporated into reverse geometry lens designs, anadditional factor, called the compression factor, hasbeen added. The idea was to compensate for regressionof the ortho-k effect during the no lens-wear period, sothat the wearer can obtain clear distance vision through-out the day (Mountford, 1998). The ortho-k effect istemporary and the reduced myopia will gradually returnto the pre-treatment level after cessation of lens wearduring the day. Therefore, lenses must be worn on aregular basis during sleep so as to retain the corrected

Received: 17 September 2007

Revised form: 25 December 2007, 8 January 2008

Accepted: 10 January 2008

Correspondence and reprint requests to: Mr Ben Chan.

Tel.: +852 2766 4461; Fax: +852 2367 7152.

E-mail address: soben@inet.polyu.edu.hk

Ophthal. Physiol. Opt. 2008 28: 265–268

ª 2008 The Authors. Journal compilation ª 2008 The College of Optometrists doi: 10.1111/j.1475-1313.2008.00545.x

vision during the day. The regression rate has been foundto vary from individual to individual with the meanvalue being approximately 0.34 D per day (Mountford,1998; Nichols et al., 2000). Therefore, a small amount ofovercorrection (0.50–0.75 D) is desired to amelioratedaytime regression. The BOZR is, therefore, calculatedby subtracting the desired myopic reduction (usuallyequal to the initial spherical component of the refractiveerror in the ocular plane) and the corneal compressionfactor from the flattest keratometry reading, as mea-sured using a corneal topographer. Different values ofcompression factor have been used by different manu-facturers, the value ranging between 0.50 and 1.00(Mountford, 2004). The equation for determining theBOZR to use for a particular target is, therefore:

BOZR¼ Flattest k reading� desired myopic reduction

� compression factor

However, clinical experience always gives a lowermanifest refractive change than the attempted changecalculated from the formula (Nichols et al., 2000;Sorbara et al., 2005). A predictable outcome beforeundertaking the course of treatment is essential to ruleout those patients who will not achieve the ideal effecton myopic reduction. Therefore, it is necessary toevaluate the accuracy of the formula in determiningthe BOZR of the ortho-k lens. The present study aims todetermine the validity of the Jessen formula with acompression factor of 0.75 in calculating the BOZR ofortho-k lenses for myopic reduction.

Methods

A total of 123 consecutive ortho-k patient files of theOptometry Clinic of The Hong Kong PolytechnicUniversity were reviewed. Clinical data at the visitbefore commencement of ortho-k treatment (baseline)and at the visit after 2 weeks of lens wear were retrieved.Of the files reviewed, 63 patients fulfilled the followinginclusion criteria – (1) first time ortho-k lens wearerfitted with 4- or 5-zone reverse geometry lenses in botheyes; (2) 2-week morning visit, including non-cycloplegicsubjective refraction and bull�s eye pattern subtractivetopographical result measured by the Medmont E300corneal topographer (version 4.8.0, Medmont Pty. Ltd.,Camberwell, Australia); and (3) the same pair of lenses(at 2-week visit) were used as retainer lenses and wornfor at least 6 months. Only the data of the right eye of 58patients were analysed. The data of five subjects wereexcluded because at the 2-week visit, three of thepatients had less than 5 h of lens wear the night before,and the other two patients had very poor cornealtopographical response. All five subjects had less than50% of the attempted myopic change at this visit.

All patients were either fitted with DreimLens (Dre-imLens Taiwan, Taiwan Macro Vision group, Taiwan,China) (81%), or the eLens (E&E Optics Ltd., HongKong SAR, China) (19%) design. Achieved myopicreduction (DMach) was determined by subtracting thesubjective refractive spheres between the baseline and2-week visits. Visual acuity was assessed using aprojector decimal visual acuity chart which was reflectedfrom a mirror at 3 m. The fitting philosophies of the twolens designs are similar – both designs use the Jessenformula with a compression factor of 0.75 to calculatethe BOZR,

BOZR ¼ K f � T � 0:75 ð1Þ

where Kf is the flattest simulated keratometry readingand T is the target of refractive change. The attemptedrefractive change (DMatt) following ortho-k is therefore,

DMatt ¼ T þ 0:75 ð2Þ

From Equations (1) and (2),

DMatt ¼ K f � BOZR ð3Þ

In this study, the validity of the Jessen formula(Equation 3) was evaluated by comparing the equationobtained from the plot of Kf ) BOZR (i.e. DMatt) andDMach. As there were no statistically significant changesin refractive cylinder during the 2-week lens wear period(results not presented), only refractive sphere was usedfor all analyses.

Results

Kolmogorov–Smirnov D-tests were performed to assessdata normality. A p-value of 0.05 was set to indicatestatistical significance. Only data from the right eye wereconsidered. The distributions of DMatt and DMach werenot significantly deviated from normal (p > 0.05);therefore, Pearson�s correlation coefficient (r) was usedfor analyses.

The median age and mean ± S.D. spherical refractiveerror of patients whose data were retrieved before thetreatment were 10 years (range 6–37 years) and)3.38 ± 1.38 D (range )1.00 to )7.00 D), respectively.Figure 1 presents the relationship between DMach andDMatt. DMach was significantly correlated to DMatt, i.e.(Kf ) BOZR) (Pearson�s r = 0.84, p < 0.001). Linearregression shows that the relationship between these twovariables can be described by the linear equation of:

DMach ¼ 0:81ðK f � BOZRÞ � 0:28 ð4Þ

But, according to the Jessen formula, DMatt = T +0.75 (Equation 2). So, if the formula is valid, DMach

should be equal to DMatt; therefore, from Equations 2and 4, we have

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0:81ðK f � BOZRÞ � 0:28 ¼ T þ 0:75

BOZR ¼ K f � 1:23T � 1:27

Our results suggest that the BOZR of the lens should beflattened by a factor of 1.23T + 1.27 D instead ofI+0.75 D if the intention is to overcorrect myopia by0.75 D with ortho-k.As there is a lot of scatter for those with higher

attempted myopic reduction, we also re-analysed thedata of patients with an attempted myopic reduction lessthan 4.75 D, and Figure 2 presents the relationshipbetween DMach and DMatt for these patients. DMach wassignificantly correlated to DMatt, i.e. (Kf ) BOZR)

(Pearson�s r = 0.87, p < 0.001). Linear regressionshows that the relationship between these two variablescan be described by the linear equation of:

DMach ¼ 0:92ðK f � BOZRÞ � 0:61 ð5Þ

Therefore, from Equations 2 and 5, we have

0:92ðK f � BOZRÞ � 0:61 ¼ T þ 0:75

BOZR ¼ K f � 1:09T � 1:48 ffi K f � T � 1:48

Our results suggest that the BOZR of the lens should beflattened by a factor I+1.48 D instead of I+0.75 D ifthe intention is to overcorrect myopia by 0.75 D withortho-k for those with attempted myopic reduction lessthan 4.75 D.

Discussion

Modern ortho-k temporarily induces central cornealflattening through the use of reverse geometry lenses(RGL). The pressure and forces developed underneaththe RGL during lens wear lead to myopic reduction.The BOZR of the lens is fitted flatter than the flattestcurvature of the cornea, by an amount depending on thedegree of myopic reduction intended. The force createdby the BOZR and the reverse curve of the lens mouldsand flattens the corneal surface to effect myopicreduction. The mid-peripheral alignment curve(s) is/areresponsible for stabilizing the lens thus allowing goodcentration.

The lens designs examined in the current study use theJessen formula to calculate the BOZR of the lenses toorder. Our results show that the formula underestimatesthe degree of myopic reduction after the procedure.Although the amount of myopic reduction after over-night ortho-k is highly dependent on the flatness of thelens fit, i.e. the flatter the BOZR fitted, the greater theamount of myopic reduction achieved (r = 0.84,p < 0.001), the relationship is not 1:1. This is inagreement with the results reported by Rah et al.(2002) that the amount of myopic reduction after1-month of ortho-k lens wear was significantly corre-lated to the flatness of fit of the lens in both eyes of theirsubjects (right eye, r = 0.70; left eye, r = 0.68).

According to the Jessen formula, taking the compres-sion factor into consideration to correct a patient withmyopia of 1.00 D, the BOZR of the lens should be fittedflatter than the flattest corneal curvature by 1.75 D so asto obtain 1.75 D myopic reduction after the procedure.But from our results, we found that the amount ofachieved myopic reduction after the treatment wassignificantly lower than that of the attempted reductioncalculated from the Jessen formula. If it is desirable toovercorrect a patient by the amount of 0.75 D, ourresults suggest that a flattening factor of 1.23 times the

y = 0.92x - 0.61 r = 0.87

0

1

2

3

4

5

0 1 2 3 4 5 6

Flatness of fit (Kf - BOZR) (D)

Ach

ieve

d m

yop

ic r

edu

ctio

n (

D)

Figure 2. Relationship between achieved myopic reduction and

flatness of lens fit (i.e. attempted myopic reduction), excluding

patients with attempted myopia reduction over 4.50 D (n = 34).

y = 0.81x - 0.28 r = 0.84

0

1

2

3

4

5

0 1 2 3 4 5 6

Flatness of fit (Kf - BOZR) (D)

Ach

ieve

d m

yop

ic r

edu

ctio

n (

D)

Figure 1. Relationship between achieved myopic reduction and

flatness of lens fit, all patients (i.e. attempted myopic reduction)

(n = 58).

Jessen formula in overnight orthokeratology: B. Chan et al. 267

ª 2008 The Authors. Journal compilation ª 2008 The College of Optometrists

desired refractive power reduction plus 1.27 D in theJessen formula is required to achieve the desiredrefractive change, i.e. to correct a 1.00 D myope, theBOZR of the lens should be fitted flatter than the flattestcurvature by 2.50 D (i.e. BOZR = Kf ) (1.23T +1.27)) instead of 1.75 D as suggested by the originalJessen formula. If we excluded the data of patients withattempted myopic reduction over 4.50 D (large scatter-ing of data observed for these patients), we obtained aformula of BOZR = Kf ) (T + 1.48). So, to correct a1.00 D myope, the BOZR of the lens should be fittedflatter than the flattest curvature by 2.48 D, which isvery similar to the value obtained above. For attemptedmyopic reduction of less than 4.75 D, we suggest usingthe simpler formula of BOZR = Kf ) (T + 1.48).

However, as this formula is generated from analysingclinical data retrospectively, and has not been triedclinically, it is unclear if the extra flattening of BOZRwould actually lead to overcorrection of myopia by0.75 D in clinical practice. Also, it is not clear if theextra flattening of the BOZR would increase the risk ofcorneal complications, for example, corneal staining.Obviously, careful clinical trial is warranted to test theseformulae. Also, there is a need to further investigate theeffectiveness of ortho-k for the reduction of high myopiabecause our results show large variability in the cornealtopographical response to a higher attempted myopicreduction.

Conclusion

This study shows that the Jessen formula with acompression factor of 0.75 in ortho-k for determiningthe BOZR of some ortho-k lens designs underestimates

the myopic reduction outcome. An extra flatteningpower may be required to achieve the desired refractivechange if the desire is to overcorrect by 0.75 D.

Acknowledgement

This study was supported by a grant from The HongKong Polytechnic University (A356).

References

Cho, P., Cheung, S. W. and Edwards, M. H. (2002) Practice oforthokeratology by a group of contact lens practitioners in

Hong Kong – Part 1. General overview. Clin. Exp. Optom.85, 365–371.

Jessen, G. N. (1962) Orthofocus techniques. Contacto. 6, 200–204.

Mountford, J. (1998) Retention and regression of orthokera-tology with time. Int. Contact Lens Clin. 25, 59–64.

Mountford, J. (2004) Design variables and fitting philosophies

of reverse geometry lenses. In: Orthokeratology: Principlesand Practice (eds J. Mountford, D. Ruston and T. Dave),Butterworth-Heinemann, London. Philadelphia, pp. 69–

107.Nichols, J. J., Marsich, M. M., Nguyen, M., Barr, J. T. and

Bullimore, M. A. (2000) Overnight orthokeratology. Optom.

Vis. Sci. 77, 252–259.Rah, M. J., Jackson, J. M., Jones, L. A., Marsden, H. J.,

Bailey, M. D. and Barr, J. T. (2002) Overnight orthoker-atology: preliminary results of the Lenses and Overnight

Orthokeratology (LOOK) study. Optom. Vis. Sci. 79, 598–605.

Sorbara, L., Fonn, D., Simpson, T., Lu, F. and Kort, R.

(2005) Reduction of myopia from corneal refractive therapy.Optom. Vis. Sci. 82, 512–518.

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