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Editors Selection IGR 9-4

Structure and function: Structural and functional measures compared

Comment by Douglas Anderson on:

20023 A framework for comparing structural and functional measures of glaucomatous damage, Hood DC; Kardon RH, Progress in Retinal and Eye Research, 2007; 26: 688-710

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As glaucoma first develops it some-times appears that quite a number of retinal ganglion cells (and their axons) disappear before visual function is af-fected. Is there a sufficient excess of neural connections that absolutely no function disappears when the fi rst neu-rons die? Or, do existing tests recognize the loss of structural elements while the visual function remains within normal range (even if different from the previous level in that individual)? Hood and Kardon's (1280) data came from individuals who had both retinal nerve fiber layer (RNFL) thickness estimates by optical coherence tomography (OCT) and visual threshold estimates with the Swedish Interactive Thresholding Algorithm (SITA standard). The subjects included some with glaucoma, some with ischemic optic neuropathy, and some without ocular disease. The authors explore various possible mathematical relationships between structure and function, noting various complexities in the relationship.

For example, RNFL thickness measurements include glia and other elements in addition to axons. Also, visual thresholds are measured in logarithmic units (decibels), while thickness is measured in linear units (micrometers). The analysis is convincing that most likely the loss of ganglion cells (and their axons) is accompanied from the very start of disease by a loss of visual function.

The loss of ganglion cells (and their axons) is accompanied from the very start of disease by a loss of visual function

However, the measured values may fall outside the normal range for structure before the lower limits of normal visual function is reached, though sometimes it is the other way around. Secondly, the relationship between structure (number of axons) and visual threshold appears to be linear, provided the visual function is converted to linear units instead of decibels. There is a residual RNFL thickness, however, because of non-axonal tissue in this layer, which remains when all axons are lost. Others have found that the relationship is linear if both axes are in decibels. These relationships are not the same unless the slope of the log-log plot (in decibels) has a slope of 1.0, which it doesn't. Some fine tuning of the models may bring them into accord, as the relationships may depend on location within the visual field (which the authors indeed found) as well as other variables. The authors also point out some noise is introduced into the measurements by blood vessels, and indeed all structure or function estimates are imperfect with current technology. They showed only a weak correlation coefficient for the relationship between structure and function in normal eyes and suspect that the rather tight relationship between structure and function in disease does not extend into the normal range. However, any correlation would be difficult to show when the range of measurements for visual threshold is small compared to the measurement reproducibility in decibels. It seems (to me) possible that the sloping curved relationship observed when RNFL is plotted against function in decibels in those with disease may fit the data in the normal range just as well as the straight line with shallow slope assumed if there is little change in RNFL over the normal range of visual thresholds. This may seem a minor point of interest mainly to basic psychophysics, but could become of practical import in clinical evaluation if a way is found to know and take into account that an individual started out with higher than average number of axons and visual threshold, so that low normal values represent a loss from baseline in that individual, even though such values appear in some individuals without disease. The authors look to the future, pointing out that the rigorous mathematical approach they illustrate could be used to compare the power and usefulness of any two of the many diagnostic tests now emerging, including comparison of two structural tests or two functional tests. The discussion is rich in reference to the data and mathematical models of others. There is more food for thought and investigation than can be summarized here, and the serious scholar must read the article in its entirety.

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