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Gideon J. Zamba, Chris A. Johnson, Akim Adekpedjou, Michael Wall; Diffusion-Injection Model for Visual Change. Invest. Ophthalmol. Vis. Sci. 2012;53(14):176.
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The criteria used to determine visual field change have arbitrary decision rules with limited performance in clinical settings, and only modest agreement for direct comparisons of different analysis procedures. These criteria are far from fully reflecting the potential simultaneous time decay and spatial perturbation of locations in visual fields. In addition, their detection rates are questionable. We have developed a stochastic diffusion-injection model to estimate the distribution of time decay (loss) and space diffusion parameters. These parameters may be used as a gauge to identify subjects whose visual fields may be changing.
Two groups of subjects were evaluated. Ocular healthy (n=60) and glaucoma documented (n=120) subjects. To each cohort, we applied the stochastic partial differential equation (Whittle, 1963 & Heine 1955) to the longitudinal Space x Time data (52 locations in visual field, 10 visits). The data were collected at the glaucoma clinic at University of Iowa Department of Ophthalmology and Visual Sciences. The Size III SITA-Standard Automated Perimetry procedure was used. Our model is below in mod 1, where Y(l;t) the measurement during visit t(1-10) at location l(1-52). The model stipulates that the serial rate of change in Y equals the visual field spread around Y(diffusion with rate β) offset by a loss in Y(reaction or temporal decay α) up to a normal random error Δ(α,β>0).
The parameters are estimated as below in Table 1.
These parameters may be jointly used on a case-by-case basis to assess parameter variation in each subject relative to normal. Non-overlapping areas of the distributions do provide decision criteria for change. For glaucoma progression, various level of disease severity (mild to severe) should be studied to determine parameter trends as function of severity_thus taking a step toward an adequate quantification of ‘glaucoma visual field progression’.
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