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The Effect of Equatorial Stretching of the Human Crystalline Lens on Accommodative Amplitude
Author Response: The Effect of Equatorial Stretching of the Human Crystalline Lens on Accommodative
The Effect of Equatorial Stretching of the Human Crystalline Lens on Accommodative Amplitude
Author Response: The Effect of Equatorial Stretching of the Human Crystalline Lens on Accommodative
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Ronald A. Schachar
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ron{at}2ras.com Ronald A. Schachar
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In their response to my letter,1 Koopmans et al.2 state that: During equatorial stretching, a lens power decrease occurs in the 17-, 32- and 40-year-old lens. Twelve data points were measured in the 0-200 µm range of lens diameter increase in all the lenses and are represented in Figure 6A (several data points are covered due to the size of the symbols). We did not observe an increase of lens power in any of these data points as would be predicted by Schachar’s theory of accommodation. Koopmans et al.2 fail to point out that in their Figure 6A there are at least three data points from the 48- and 49-year-old lenses which demonstrate a small but definite increase in optical power following equatorial stretching of less than 500µm. Unfortunately, the standard deviation associated with all their measurements was 100 µm, making data points imprecise and unlikely to identify any reliable changes in optical power secondary to equatorial lens stretching in the 0 to 200µm range. As Koopmans et al.2 correctly state, we continue to call for studies that are able to measure small lenticular displacements accurately, precisely, and with a resolution better than 10 µm in order to evaluate the predictions from our3 (Chien CM, Huang T, Schachar RA, unpublished data, 2003) and other mathematical models.4 Ronald A. Schachar Dallas, Texas References 1. Schachar RA. The effect of equatorial stretching of the human crystalline lens on accommodative amplitude (letter). Invest Ophthalmol Vis Sci [serial online]. Available at http://www.iovs.org/cgi/eletters?lookup=by_date&days=9999#59. Accessed on May 2, 2003. 2. Koopmans SA, Terwee T, Barkhof J, Haitjema HJ, Kooijman AC. Author response: the effect of equatorial stretching of the human crystalline lens on accommodative amplitude (letter). Invest Ophthalmol Vis Sci [serial online]. Available at http://www.iovs.org/cgi/eletters?lookup=by_date&days=9999#60. Accessed on May 2, 2003. 3. Schachar RA, Bax AJ. Mechanism of human accommodation as analyzed by non-linear finite element analysis. Compr Ther. 2001;33:122-132. 4. Shung VW. An Analysis of a Crystalline Lens Subjected to Equatorial Periodic Pulls. Arlington, TX: University of Texas at Arlington; 2002. Thesis. |
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Steven A. Koopmans University Hospital of Groningen, The Netherlands
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s.a.koopmans{at}ohk.azg.nl Steven A. Koopmans
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In his second letter to the editor, Schachar1 refers to data points in figure 6A from our original article.2 This figure shows the relationship between the lens diameter and the change of lens power when nine lenses between the ages of 17 and 56 years are subjected to equatorial stretching forces. Schachar1 claims that we failed to mention that at least three datapoints of the 48- and 49-year-old lenses demonstrate a small but definite increase in optical power following equatorial stretch.3 Since the standard deviation of the lens power measurements was 0.27 D, only the 0.6 D datapoint is significantly different from zero. In our opinion, we cannot draw any conclusions from one datapoint while the other datapoints are not significantly different from zero or show a decrease of lens power. Schachar1 also maintains a call for studies on accommodation in order to evaluate accommodation as predicted by his and other mathematical models. In our view, the models4,5 mentioned by Schachar1 are not independent models, but models based on one theory of equatorial zonular pull, and therefore they should be regarded as one model. The model by Chien et al. (Chien CM, Huang T, Schachar RA, unpublished data, 2003) is submitted, and therefore we think it should not be mentioned in this discussion since we have no access to it. Steven A. Koopmans Department of Ophthalmology, University Hospital of Groningen, Groningen, The Netherlands References 1. Schachar RA. The effect of equatorial stretching of the human crystalline lens on accommodative amplitude (letter). Invest Ophthalmol Vis Sci [serial online]. Available at http://www.iovs.org/cgi/eletters?lookup=by_date&days=9999#63. Accessed on May 2, 2003. 2. Koopmans SA, Terwee T, Barkhof J, Haitjema HJ, Kooijman AC. Polymer refilling of presbyopic human lenses in vitro restores the ability to undergo accommodative changes. Invest Ophthalmol Vis Sci. 2003;44:250-257. 3. Koopmans SA, Terwee T, Barkhof J, Haitjema HJ, Kooijman AC. Author response: the effect of equatorial stretching of the human crystalline lens on accommodative amplitude (letter). Invest Ophthalmol Vis Sci [serial online]. Available at http://www.iovs.org/cgi/eletters?lookup=by_date&days=9999#60. Accessed on May 2, 2003. 4. Schachar RA, Bax AJ. Mechanism of human accommodation as analyzed by non-linear finite element analysis. Comp Ther. 2001;33:122-132. 5. Shung VW. An Analysis of a Crystalline Lens Subjected to Equatorial Periodic Pulls. Arlington, TX: University of Texas at Arlington; 2002. Thesis. |
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Ronald A. Schachar
Send letter to journal:
ron{at}2ras.com Ronald A. Schachar
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Koopmans et al.1 evaluated the optical power changes that occur in nine natural human crystalline lenses following equatorial stretching. They demonstrated a decrease in optical power of the crystalline lens by traction on the equator in all but one of their lenses, a 49-year-old natural crystalline lens, where a small increase in optical power was associated with an increase in equatorial diameter (Figure 6A). Three mathematical models have predicted the conditions required for optical power changes. In that range where Helmholtz’s theory of accommodation might be proposed as an explanation, all indicate the need for large lenticular displacements, > 500 microns, and more force than is physiologically possible for the ciliary muscle to apply.2-4 Koopmans et al. have confirmed the predictions in this restricted range. The standard deviation of Koopman’s measurements for a change in equatorial diameter of the crystalline lens was 100 microns, indicating that they were effecting very large displacements. When sufficient force is applied (more than is physiologically possible for the ciliary muscle), a decrease in optical power does occur, as was predicted by the models. This indicates the validity of these mathematical models. What these mathematical models more importantly predict is that in the range of force which is physiologically possible for the ciliary muscle, only a small increase in lenticular equatorial diameter will occur, < 200 microns, but that this is sufficient to produce maximum accommodative amplitude. In the primate5 and the human6 it has been observed that less than 100 microns of outward equatorial movement of the crystalline lens can induce maximum accommodation. This is consistent with a theory of accommodation that I have proposed.2 The authors rely upon Wilson’s experiment7 to support their conclusions that the optical power changes that occurred in their study following equatorial stretching is physiologically relevant. Wilson suggested that a change in equatorial diameter of the accommodating crystalline lens in a 27-year-old is 7%. Unfortunately, I do not believe that this provides support for their conclusions, since my own work suggests that Wilson’s experiment was severely flawed.2 In summary, three mathematical models have now predicted the conditions required for optical power changes of the crystalline lens. The authors have only explored the non-physiologic portion of the curve, where larger than physiologic forces achieve equatorial stretching and cause large lenticular displacements. Studies are now required with techniques that have the ability to measure small lenticular displacements, < 200 microns, where according to these same models, a large change in accommodation should be found. Ronald A. Schachar Dallas, Texas References 1. Koopmans SA, Terwee T, Barkhof J, Haitjema HJ, Kooijman AC. Polymer refilling of presbyopic human lenses in vitro restores the ability to undergo accommodative changes. Invest Ophthalmol Vis Sci. 2003;44:250- 257. 2. Schachar RA, Bax AJ. Mechanism of human accommodation as analyzed by non-linear finite element analysis. Compr Ther. 2001;33:122-132. 3. Shung VW. An Analysis of a Crystalline Lens Subjected to Equatorial Periodic Pulls. Arlington, TX: University of Texas at Arlington; 2002. Thesis. 4. Burd HJ, Judge SJ, Cross JA. Numerical modeling of the accommodating lens. Vision Res. 2002;42:2235-2251. 5. Schachar RA, Black TD, Kash RL, Cudmore, DP, Schanzlin DJ. The mechanism of accommodation and presbyopia in the primate. Ann Ophthalmol. 1995;27:58-67. 6. Schachar RA, Tello C, Cudmore DP, Liebmann JM, Black TD, Ritch R. In vivo increase of the human lens equatorial diameter during accommodation. Am J Physiol. 1996;271 (Regulatory Integrative Comp Physiol 40): R670-R676. 7. Wilson RS. Does the lens diameter increase or decrease during accommodation? Human accommodation studies: A new technique using infrared retro-illumination video photography and pixel unit measurements. Trans Am Ophthalmol Soc. 1997;95:261-270. |
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Steven A. Koopmans University Hospital of Groningen, The Netherlands, Thom Terwee, Jan Barkhof, Henk J. Haitjema, Aart C. Kooijman
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s.a.koopmans{at}ohk.azg.nl Steven A. Koopmans, et al.
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In his letter to the editor, Schachar claims that the optical power changes which occur during accommodation are accompanied by an increase of the lens diameter of less than 200 mm, based on predictions from three mathematical models of accommodation.1-3 He states that we did not perform measurements in this range and that we only explored the non-physiological portion of the curve of equatorial lens stretching. Finally he pleads for studies that are able to measure small lenticular displacements in order to prove the predictions from these mathematical models.1-3 Since the outcomes of mathematical models of accommodation depend heavily on the input, care must be taken when interpreting their results. Other mathematical models than quoted by Schachar describe accommodation while using lens diameter changes of 7%4 (~700mm), which is considerably more than 200 mm. In our view, Schachar incorrectly refers to the model of Burd et al.3 These authors describe a monotonic decrease of lens power when the lens diameter increases from 0 to 200 mm and beyond, in contrast with the other two models which indicate an increase of lens power in the 0-200 mm range. Figure 8 and Figure 9 in the paper by Burd et al. contain many datapoints which describe the relationship between optical power and equator displacement of the lens. In their model in a 29-year-old subject, a lens diameter increase of 200 mm corresponds with a lens optical power decrease of 3 D. This is definitely not positive and not comparable to the maximum accommodative amplitude for a person of this age (9D in the model by Burd et al.). Lens diameter changes of 200 microns and more are necessary to describe physiological accommodation amplitudes according to the model by Burd et al. This contradicts Schachar’s statements that the maximum accommodation amplitude is accompanied by a lens diameter increase of less than 200 microns. In Figure 6A in our study,5 we describe the relationship between lens diameter change and lens power change. During equatorial stretching, a lens power decrease occurs in the 17-, 32- and 40-year-old lens. Twelve data points were measured in the 0-200 mm range of lens diameter increase in all the lenses and are represented in Figure 6A (several data points are covered due to the size of the symbols). We did not observe an increase of lens power in any of these data points as would be predicted by Schachar’s theory of accommodation. In fact, at 200 mm lens diameter increase, the lens power change was only –3D for the 32-year-old lens. This indicates that lens diameter increase above 200mm is necessary to cover the whole physiological range of accommodation. That lens diameter changes above 200 mm are necessary to produce the maximum accommodative amplitude is not only supported by Wilson6, but also by Strenk et al.7 and Story.8 In the non-human primate, Glasser and Kaufman9 have observed lens diameter changes of 11% which is much more than 200mm (given a lens diameter of 9 mm). In summary, available experimental data from several studies show that lens diameter changes of more than 200 mm occur during accommodation in young eyes. Our data and the mathematical model of Burd et al. indicate that the optical power of the lens decreases while the lens diameter increases from 0 to 200 mm. If mathematical models based on Schachar’s theory of accommodation fail to comply with available experimental data, other models or theories should be considered. Steven A. Koopmans1
1Department of Ophthalmology, University Hospital of Groningen, Groningen, The Netherlands
References 1. Schachar RA, Bax AJ. Mechanism of human accommodation as analyzed by non-linear finite element analysis. Comp Ther. 2001;33:122-132. 2. Shung VW. An Analysis of a Crystalline Lens Subjected to Equatorial Periodic Pulls. Arlington, TX: University of Texas at Arlington; 2002. Thesis. 3. Burd HJ, Judge SJ, Cross JA. Numerical modelling of the accommodating lens. Vision Res. 2002;42:2235-2251. 4. Weeber HA, Martin H. Finite elements simulation of accommodation. In: Guthoff R, Ludwig K, eds. Current Aspects of Accommodation. Heidelberg: Kaden Verlag; 2001. 5. Koopmans SA, Terwee T, Barkhof J, et al. Polymer refilling of presbyopic human lenses in vitro restores the ability to undergo accommodative changes. Invest Ophthalmol Vis Sci. 2003;44:250-257. 6. Wilson RS. Does the lens diameter increase or decrease during accommodation? Human accommodation studies: A new technique using infrared retro-illumination video-photography and pixel unit measurements. Trans Am Ophthalmol Soc. 1997;95:261-270. 7. Strenk SA, Semmlow JL, Strenk LM, et al. Age related changes in human ciliary muscle and lens: a magnetic resonance imaging study. Invest Ophthalmol Vis Sci. 1999;40:1162-1169. 8. Story, JB. Aniridia: Notes on accommodation changes under eserine. Trans Ophthalmol Soc UK. 1924;44:413-417. 9. Glasser A, Kaufman PL. The mechanism of accommodation in primates. Ophthalmology. 1999;106:863-872. |
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