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Change in Intralenticular Pressure during Accommodation
Author Response: Change in Intralenticular Pressure during Accommodation
Change in Intralenticular Pressure during Accommodation
Author Response: Change in Intralenticular Pressure during Accommodation
The Change in Intralenticular Pressure during Human Accommodation
The MRI Data of Strenk et al. Do Not Suggest Lens Compression in the Unaccommodated State
Our Findings Suggest a Compressible Lens Material and Support the Helmholtz Theory of Presbyopia
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Ronald A. Schachar
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ron{at}2ras.com Ronald A. Schachar
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The magnitude of the volume change associated with any increased intralenticular pressure is determined by the bulk modulus of the crystalline lens. Strenk et al.1 try to justify their calculated 6.8 % volume reduction in crystalline lens volume during resting accommodation by implying that that bulk modulus obtained by Brillouin scattering is significantly different from the bulk modulus of the whole crystalline lens. As I have previously stated,2 the bulk modulus of the cortex and nucleus of 19 intact human lenses measured by Brillouin scattering was 2.8 GPa and 3.7 GPa for the cortex and nucleus, respectively. The bulk modulus of the whole crystalline lens is 2.8 GPa, obtained by using the following formula: K = rc2 where r = 1032 kg/m3 for the average density of the whole lens, and c = 1647 m/sec for the average velocity of ultrasound in the whole lens.3 Contrary to the statements by Strenk et al., I find that the bulk modulus determined by Brillouin scattering and the bulk modulus of the whole crystalline lens are essentially the same. Since the bulk modulus of the crystalline lens is comparable to or greater than other soft tissues,3 hydrated proteins,4,5 and water,6 only application of high non-physiological pressure can change crystalline lens volume. The intralenticular pressure change that I have calculated for a syneretic response is based on the fact that the compressibility of water is negligible.6 Therefore, to compress 6.8% of the lens protein syneretically, as postulated by Strenk et al., would require at least 760 mm Hg to move 6.8% of the lenticular water from the free to the bound state (see Table 1 of Bettelheim and Zigler's paper7). The unphysiologic results of the experiments by Strenk et al. are exemplified by examination of Fig. 1 of their 2004 IOVS paper.8 Comparison of the unaccommodated and accommodated eye reveals that the anterior peripheral lens surface appears to become steeper with accommodation (Fig. 1). Flattening, not steepening, of the anterior peripheral surface of the crystalline lens has been well documented by the change in size of reflections obtained during accommodation.9
Strenk et al.1 state that their "data have been cross-validated with Dr. Koretz's Scheimpflug data set." Only baseline measurements of unaccommodated eyes were compared in that study.10 A comparison of the accuracy, precision, and reproducibility of the MRI and Scheimpflug techniques to measure lenticular accommodative changes was not performed. I again emphasize that, in my opinion, Strenk et al.8 have not provided adequate controls in their studies. I believe that this has led to erroneous results and unsupported conclusions. Ronald A. Schachar References 1. Strenk S, Strenk LM, Semmlow JL. Author response: change in intralenticular pressure during accommodation (letter). Invest Ophthalmol Vis Sci [serial online]. Available at http://www.iovs.org/cgi/eletters/45/2/539#171. Accessed on August 17, 2004. |
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Susan A. Strenk
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sstrenk{at}wowway.com Susan A. Strenk
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Fincham’s Work Supports the Helmholtz Theory of Accommodation Dr. Schachar's reference to Fincham's 1937 monograph1 is significant: Fincham provided the first direct in vivo demonstration of Helmholtz's mechanism of accommodation, observing an accommodative decrease in the diameter of both the ciliary processes and lens equator and an increase in lens thickness in an aniridic subject. Similar direct support for the Helmholtz theory of accommodation has been more recently reported in an albino subject studied with retroillumination video photography2 and another albino subject studied with optical coherence tomography.3 The MRI technique developed by Strenk and colleagues is unique in permitting in vivo visualization of the ciliary muscle and lens equator in subjects with normally pigmented and intact irises and has provided direct and statistically significant verification of the Helmholtz mechanism of accommodation.4,5 Dr. Schachar specifically cites Fincham's findings on lens shape in an isolated case of drug-induced accommodation. It must be noted that the significant optical distortions inherent in Fincham's slit lamp study were uncorrected and, further, that these distortions increase with distance perpendicular to the lens pole as well as along it anterior to posterior. Conversely, the MRI technique of Strenk and colleagues is free of optical distortions and uses physiological (rather than drug-induced) accommodation. Thus it is perplexing that Dr. Schachar would refer to the lens shape observed by Fincham as "physiological" while suggesting that the lens shape observed by MRI is "non-physiological." We believe that the increase in flatness toward the anterior lens periphery observed by Fincham, and earlier by Tscherning, is due to an optical distortion caused by the cornea, as was first suggested by Gullstrand6 in 1924. Consequently, we believe any theory of accommodation that is based on this lens shape is in effect an attempt to model a distortion. We believe Dr. Schachar continues to fail to appreciate the differences between macroscopic and microscopic properties of the lens and we again refer him to our previous letters. Similarly, Dr. Schachar remains unresponsive to our previous comments regarding the external pressure on the lens; once again, we refer him to our previous letter. We agree with Dr. Schachar that the far MRI data of Strenk and colleagues was cross-validated with the far Scheimpflug data of Koretz and colleagues.7 The near data sets from these modalities were each collected at different accommodative states; comparing them is the subject of future work. Susan A. Strenk1 1Department of Surgery, University of Medicine and Dentistry of New
Jersey–Robert Wood Johnson Medical School, Piscataway, New Jersey References 1. Fincham EF. The mechanism of accommodation. British Journal of Ophthalmology, Monograph Supplement VIII. London: George Pulman and Sons, Ltd; 1937. |
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Ronald A. Schachar
Send letter to journal:
ron{at}2ras.com Ronald A. Schachar
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The reply of Strenk et al. 1 does not respond to the issues raised or the inadequacies of their methodology. Their MRI studies2,3 remain flawed because they lack: 1. Proper controls demonstrating their reproducibility Strenk et al.1 state that their data have been cross-validated with pachometry. However, there is no change in corneal thickness associated with accommodation.4 The apparent change in corneal thickness, readily observable in their MRI images2 following accommodation, is an excellent example of the outcome of mal-registration of MRI images in the absence of independent external references. Strenk et al.1 report a 6.8% volume change during human accommodation. They claim that this large volume change is due to a shift from free to bound water (synergetic response) during the change from the accommodated to the unaccommodated state.3 Bettelheim et al.5 demonstrated that for a 6% change in free to bound water in the lens the pressure applied to the crystalline lens would have to change by approximately one atmosphere; i.e., 760 mm Hg. There is no evidence to support intralenticular pressures of this magnitude. Strenk et al.1 incorrectly stated that we used the Young's modulus reported by Vaughan and Randall6,7 and refer to Fisher's measurement of the Young's modulus of the lens capsule,8 rather than his measurement of the lens stroma,9 and confuse Young's modulus and bulk modulus.10 The crystalline lens is totally ectodermal and consists of layered epithelial cells enclosed by the lens capsule, a clear membrane.11 The connections between the individual cortical epithelial cells and their connections between the nucleus and capsule are weak and do not offer any significant mechanical resistance.12 This is readily verified by the ease with which cortical material is removed using irrigation and aspiration (I & A) and separated from the nucleus and lens capsule during clear lensectomy or cataract extraction. Squeezing the lens cortex between one's fingers further demonstrates that it has the consistency of a thick gel. Therefore, it is highly unlikely that the layered epithelial structure of the lens offers any significant mechanical advantage to the conformational lenticular surface changes that occur during accommodation. As noted in our Letter,13 the bulk modulus employed was from Subbaram MV et al. (IOVS 2002;43:ARVO E-Abstract 468), measured mean longitudinal modulus of 2.8 GPa [2.1 x 107 mm Hg] for the cortex and 3.7 GPa [2.8 x 107 mm Hg] for the nucleus based on nineteen intact human lenses. These moduli of the cortex and nucleus mean that the large change in volume of the lens during accommodation reported by Strenk et al. must be due to artifact because such a change in volume would require an extremely high, non-physiological intralenticular pressure as demonstrated by my previous Letter.13 Ronald A. Schachar References 1. Strenk SA, Strenk LM, Semmlow JL. Our findings suggest a compressible lens material and support the Helmholtz theory of presbyopia (letter). Invest Ophthalmol Vis Sci [serial online]. Available at http://www.iovs.org/cgi/eletters/45/2/539#151. Accessed on July 21, 2004. |
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Susan A. Strenk
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sstrenk{at}wowway.com Susan A. Strenk
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We believe Dr. Schachar's concerns regarding the MRI methodology have already been addressed. We refer him to our response to his prior letter,1 as well as to our publications,2,3 and we reiterate that our MRI data have been cross-validated with Dr. Koretz's Scheimpflug data set, which has itself been cross-validated with ultrasound and pachometry measurements.4 Dr. Schachar states that there is a change in corneal thickness in the figures of our 1999 IOVS paper; however, we have viewed them and do not believe any differences in corneal thickness exist. Dr. Schachar assumes that lens compression cannot occur (as a result of syneresis), apparently because he calculates that it would require an increase in intraocular pressure of 760 mm Hg. He justifies this calculation by citing an in vitro study of rhesus monkeys.5 However, the study's authors make no claim about any change in lens volume that occurs upon a change in the amount of free versus bound water, neither in the cited manuscript nor in their 2002 publication on human lenses.6 Thus it is unclear to us how Dr. Schachar calculates this hypothetical intraocular pressure. Finally, we believe Dr. Schachar's comments regarding the longitudinal modulus indicate that he misunderstands the difference between measurements made on a microscopic scale and those on a macroscopic scale, as previously noted by us. We refer him to the analogy of the steel spring provided in our prior letter1 and emphasize that a complete treatment of the lens must take into account its internal structure. Susan A. Strenk1,2 1Surgery/Bioengineering, Robert Wood Johnson Medical School, UMDNJ, Piscataway, New Jersey References 1. Strenk SA, Strenk LM, Semmlow JL. Our findings suggest a compressible lens material and support the Helmholtz theory of presbyopia (letter). Invest Ophthalmol Vis Sci [serial online]. Available at http://www.iovs.org/cgi/eletters/45/2/539#151. Accessed on July 22, 2004. |
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Ronald A. Schachar
Send letter to journal:
ron{at}2ras.com Ronald A. Schachar
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Using magnetic resonance imaging (MRI), Strenk et al.1 reported an increase in cross sectional area (CSA) of the crystalline lens during human accommodation. From this measurement the authors infer that the crystalline lens is compressible and that the volume of the lens is changing during accommodation. They state: ...these accommodative changes in CSA reflect accommodative changes in lens volume and suggest that the lens material is slightly compressed when accommodation is relaxed and the external forces exerted on the lens are greatest. These results challenge a long-held belief that the lens is incompressible, a belief based on the fact that the lens contains a large amount of water, which is incompressible.1 The authors have suggested that there is a volume change associated with their measured change in CSA during accommodation (Strenk SA, et al. IOVS 2001;42:ARVO Abstract 55).1 Since the authors have only documented a change in CSA and never quantified any change in volume, we have no idea how small (or large) the purported change may be. Could a lenticular volume change be sufficient in size to be observed by the authors' MRI technique? Does it even exist? What level of intralenticular pressure would be required to produce such a volume change? Is this pressure physiologically possible? To evaluate the plausibility of a change in lenticular volume, let us assume that they are correct. Even water is compressible under pressure. For over a century mechanical engineers have been able to quantify the compressibility of an object by measuring its bulk modulus. By applying a uniform pressure to the entire surface of an object and then measuring its change in volume the bulk modulus can be determined. Bulk modulus is equal to2:
The compressibility of the crystalline lens has been measured using Brillouin scattering. Brillouin scattering uses the frequency shift of an incident laser beam, induced by the variation in density of the material, to calculate the compressibility of an object. Since the compressibility is being measured in one direction, it is called the longitudinal bulk modulus. The longitudinal bulk modulus depends on the shear and bulk modulus of the object. Since the variation of density within the lens cortex and within its nucleus is fairly uniform, and the shear modulus of the lens is small compared to the bulk modulus, we can assume that the longitudinal modulus of the crystalline lens is approximately equal to its bulk modulus.2 The longitudinal modulus is approximately 2.8 GPa [2.1 x 107 mm Hg] for the cortex and 3.7 GPa [2.8 x 107 mm Hg] for the nucleus (Subbaram MV, et al. IOVS 2002;43:E-Abstract 468).3,4 We can now approximate the magnitude of a change in lens volume due to accommodation. Let us consider the authors' proposed change in lens volume when there is a shift from maximum accommodation to the unaccommodated state. The total change in pressure that is applied to the lens (intralenticular pressure), during a maximum accommodative change, will equal the sum of: 1. The change in intralenticular pressure induced by the change in zonular tension. Therefore, a highly generous estimate for the change in intralenticular pressure during maximum accommodation would be 20 mm Hg. This pressure change will induce a lenticular volume change of approximately 0.0001% [i.e. 1/1,000,000 of the total lens volume]:
This is the maximum change in volume that would be associated with the change in intralenticular pressure during maximum accommodation. This change in lens volume is too small to be measured with the authors' MRI technique which has a resolution of 0.156 mm.1 Since their resolution is inadequate to measure a volume change that is this small, we must conclude there is an error in their methodology. The error may be attributable to the authors' method for image selection. The authors used no references external to the lens itself. The authors employed the following technique: For the analysis of lens data it is only necessary that some portion of the 3 mm thick center slice pass through the lens center....The flanking images are observed during the data collection process; if the lens appears qualitatively dissimilar, these images are discarded prior to quantitative analysis and the data retaken. If the lens appears approximately similar, the images are saved and quantitatively analysed. (underlines added)10 The subjective selection of acquisition planes for the MRI lens images, used in their comparisons, makes the authors' interpretation of the accommodative lenticular changes subjective. The lack of incorporation of either external or internal lenticular loci by which to reference any dimensional lens changes associated with accommodation makes any conclusions drawn at best subjective and not verifiable. The authors need to undertake and publish a series of statistically analyzed control measurements of their methodology in a large sample of eyes. Each of the same eyes must be repeatedly imaged in the baseline accommodative state, after repositioning of the head of the subject and changing the position of gaze. This measure of the reproducibility of their method is essential for evaluation. Until then, it is impossible for the discerning reader to accept the accommodative lens contour changes reported by the authors. Ronald A. Schachar Department of Physics, University of Texas at Arlington, Dallas, Texas References 1. Strenk SA, Strenk L, Semmlow JL, DeMarco JK. Magnetic resonance imaging study of the effects of age and accommodation on the human lens cross-sectional area. Invest Ophthalmol Vis Sci. 2004;45:539-545. |
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Stuart J. Judge , Harvey J. Burd
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sjj{at}physiol.ox.ac.uk Stuart J. Judge, et al.
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A recent article in this journal1 reported an in vivo study, using MRI, of the cross-sectional area (CSA) of unaccommodated and accommodated human ocular lenses. Amongst other things, they found that the total* lens CSA and the CSA of the anterior portion increased with accommodation. They suggested from this finding that there may be compression of the lens material during relaxed accommodation. This deduction rests on the assumption that a decrease in cross-sectional area implies a decrease in volume, but this is mistaken. The volume of an object that is formed by rotating a plane region about an axis in the plane of the region is not proportional to the cross-sectional area. Rather, the volume, V, is given by:
where We took Figure 1 of Strenk et al., converted it from GIF to TIF format, and analyzed its geometry using Scion Image – essentially the same software used by Strenk et al. We used the polygon tracing tool to overlay the centre of the bright lines in the image demarcating the anterior and posterior surfaces of the accommodated and unaccommodated lenses, and then used the 'measure' tool that computes centroid and cross-sectional area. (Note that after the tracing is done, the LUT of the image needs to be made uniform for the area to be correctly calculated; if this is not done Scion Image computes not the geometrical centroid but the centre of gravity of the image considered as a solid with weight distributed according to pixel brightness.) To check that the area and centroid calculations were correctly realised we also exported the XY coordinates of the traced sections and directly computed the areas using a spreadsheet. We attempted to consider separately the changes in the anterior and posterior lens, but in our hands this was not a well-defined procedure because very small changes in the position of the boundary between the anterior and posterior lens (within the tolerance associated with the blur in the figure) substantially affected the distribution of the volume between the anterior and posterior lens segments. The total cross-sectional area of the accommodated lens shown in Figure 1 is about 7% greater than that of the unaccommodated lens, but the volume of the accommodated lens is considerably less than 1% greater than the volume of the unaccommodated lens, which is probably within the errors of the measurements. This is not a paradox: it simply reflects the fact that the centroid of the hemisection of the accommodated lens is about 6% closer to the axis than in the unaccommodated lens. Assuming that the data shown in the Figure are representative, Strenk et al.'s data do not show that the lens is compressed in disaccommodation; on the contrary, they indicate that the lens behaves in an essentially incompressible manner. Stuart J. Judge and Harvey J. Burd University of Oxford, U.K. Reference Strenk SA, Strenk LM, Semmlow JL, DeMarco JK. Magnetic resonance imaging study of the effects of age and accommodation on the human lens cross-sectional area. Invest Ophthalmol Vis Sci. 2004;45:539-545. *In the sense used by Strenk et al., meaning taking the anterior and posterior area of the lens section, or rather hemisection, as that is all that is available in Figure 1. |
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Susan A. Strenk , Lawrence M. Strenk, John L. Semmlow
Send letter to journal:
sstrenk{at}wowway.com Susan A. Strenk, et al.
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Both Dr. Schachar and Drs. Judge and Burd argue that our findings on lens CSA do not support a conclusion that the lens material may be compressed with resting accommodation. Both arguments depend upon questionable assumptions and ignore the overwhelming weight of scientific data that reveal the lens to be a complex structure1 - the lens material contains water but this does not mean the lens material is water; the lens is a structured arrangement of interconnected cells, proteins and intracellular space. Modeling the lens as a water-filled Mylar balloon necessarily ignores the possibility of compression, thus greatly simplifying any mechanical modeling of the lens; unfortunately, it also ignores a wealth of scientific data on lens morphology, ultrastructure, recent in vitro MRI findings on the pressure induced syneretic response, and previous calculations of the Poisson ratio of the lens.1-7 Dr. Schachar ignores the internal structure of the lens and relies upon a bulk modulus value reported by Vaughan and Randall.8 This bulk modulus value was calculated from Brillouin scattering data obtained four days post mortem from a single, aged, human lens likely containing cataracts and is 3 x 109 N/m2, or six orders of magnitude greater than the Young's modulus calculated by Fisher9 in his groundbreaking work. Vaughan and Randall8 themselves are concerned by this large discrepancy and qualify their findings by noting, among other things, "[w]e should emphasise that our own values relate to a microscopic scale...smaller than recorded measurements of lens fibre width" and "[t]he implications of this work lie not so much at the opthalmological level as at the macromolecular." Dr. Schachar either ignores or misunderstands this critical distinction; Brillouin scattering measures parameters at a microscopic scale, while we report changes at a macroscopic scale. (As an example, the shear modulus of steel is approximately 1011 N/m2, yet certain steel springs can be easily compressed. This can be explained by noting that a small twisting strain occurs in a microscopic section of the spring, but integration over the entire spring leads to a large displacement on a macroscopic level. Similarly, small strains in the structure of the lens on a microscopic scale can lead to macroscopic changes in response to physiologic forces.) Dr. Schachar further ignores Vaughan and Randall's8 discussion of the varying structure of the lens due to the "high protein content of...lens tissues" and its positional dependence, as well as their reference to Fisher and Pettet's findings on the varying water content of the lens material (63.4% for the nucleus and 68.8% for the cortex). Dr. Schachar employs circular reasoning, assuming the lens is incompressible in order to prove that the lens is incompressible. Dr. Schachar's comments regarding the subjectivity/reproducibility of our measurements are disappointing. He takes our statements and (through selective underling of text) uses them to suggest that our analysis is qualitative. However, the very quote he uses states that the data is "quantitatively analysed" and, when the passage is read in its entirety, it details this quantitative analysis and reports that reproducibility measurements were obtained from scans collected on different days.10 Dr. Schachar ignores this as well as the repeatability results that have been peer-reviewed and published previously11 and in the manuscript under discussion.12 Moreover, our MRI measurements have been cross-validated with corresponding data from Scheimpflug, ultrasound and pachometry.13 The assertion by Drs. Judge and Burd that the change in CSA is accounted for solely by redistribution of the lens material without a change in lens volume is not true, neither in general nor for the specific case cited. In fact, it can only be true for one case: Dr/r = -DArea/Area. Unless this unique condition is satisfied, while redistribution of the lens material may occur, it cannot negate a volume change. This unique condition is satisfied only if one assumes an incompressible lens material. Drs. Judge and Burd attempt to determine the lens profiles and centroids for each accommodative state from the portions of lenses visible in Figure 1 (a reduced, reproduction, composite of two MRI images obtained from a single subject). Such imprecise methods necessarily introduce substantial error to subsequent volume calculations. Drs. Judge and Burd disregard these errors, calculate a negligible volume change (essentially satisfying the unique condition stated above), and conclude that any change in CSA must therefore be due to a change in the centroid location. They hold this conclusion to be true not only for the subject shown in Figure 1, but also for every subject in the study. Our own calculations reveal an 8.7% decrease in CSA and a 6.8% decrease in volume with resting accommodation for the subject represented in Figure 1. (Incidentally, the centroid is only 1.9% closer to the axis of revolution during the accommodative state for this subject.) Drs. Judge and Burd also note variations in signal intensity of the lens material in the MRI images and discuss re-setting the intensity to a uniform value. The MRI signal intensity variations within the lens are yet another indication that the lens material is not uniform and should not be modeled as a sack of incompressible fluid. Our data on the effect of age and accommodation on lens CSA support the conclusion that the lens material may be compressible and, in fact, compressed with resting accommodation when zonular tension is greatest. These findings support the Helmholtz theory of presbyopia and are consistent with published data on lens morphology, ultrastructure, in vitro MRI findings, and previous calculations of the Poisson ratio of the lens. Susan A. Strenk1,2 1Surgery/Bioengineering, Robert Wood Johnson Medical School, UMDNJ, Piscataway, New Jersey References 1. Bron AJ, Tripathi RC, Tripathi BJ. The lens. In: Wolff's Anatomy of the Eye and Orbit. 8th ed. London: Chapman & Hall; 1997:411-434. |
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