Fig 1.
A simplified cell population model.
The lens epithelium consists of a single layer of lens epithelial cells (LECs) located in the anterior subcapsular region. The central zone (CZ), germinative zone (GZ), transitional zone (TZ) and meridional rows (MR) compose the lens epithelium. LECs in the GZ around the equator divide, migrate posteriorly, and differentiate into elongated lens fiber cells (LFCs). Newly formed LFCs surround existing cortical LFCs and become more internalized, culminating in production of highly ordered, tightly packed mature nuclear LFCs. These processes are simplified here, where cell migration is assumed to occur once a year.
Table 1.
Parameters used in a cell population model.
Fig 2.
A schematic diagram outlining a model for spontaneous cataractogenesis.
(A) Modeling of processes leading to manifestations of cataract predicated on the level of Damage that accumulates in lens epithelial cells. On one hand, upon cell division, the level of Damage decreases due to repair. On the other hand, when the level of Damage continues to exceed 1, posterior subcapsular or cortical cataracts appear at the onset time assigned to individual cells. (B) Lifelong assignment of Damage. Damage is randomly assigned to each individual person for every decade of life. The panel exemplifies two persons assigned with different levels of Damage as a function of age in years.
Fig 3.
Determination of the optimal values of the model parameters for reproduction of the Beaver Dam Eye Study (BDES) data.
(A) Changes in the residual sum of squares (RSS) from the BDES data [32] as a function of onset time. The means and standard deviations (SDs) of the onset time (mOnset and sdOnset, respectively) were calculated at five year intervals each for 40–150 years and 30–80 years in 300 lenses, where the level of mean Damage (mDamage) was set as 0.07–0.16 at 0.01 intervals (the data shown here for mDamage of 0.11). Then, the RSS vs the BDES data was calculated. (B) Changes in the RSS as a function of onset time. mOnset and sdOnset were calculated at two year intervals in 1500 lenses, where mDamage was set as 0.09–0.14 at 0.01 intervals (the data shown here for mDamage of 0.11). Then, the RSS vs the BDES data was calculated. These ranges of onset time were selected from the low RSS area in panel A. (C) Changes in the RSS as a function of mDamage. The grids were added onto the result in panel B, and the means and SDs of RSS in top 10 grids with low RSS were plotted at each mDamage. (D) Comparison of the cataract incidence between the calculated data and the observed BDES data. Simulations were conducted for 3000 lenses at mOnset of 89 years, sdOnset of 56 years, and mDamage of 0.11. Red and green circles show the BDES data for PSC and cortical cataracts, respectively. Red and green dotted lines show the calculated data for PSC and cortical cataracts, respectively. The calculated data are presented as means and 95% confidence intervals (CIs).
Fig 4.
Changes in the simulation results by parameter values.
(A) Comparison of the cataract incidence between the calculated data and the Beaver Dam Eye Study (BDES) data [32], when the standard deviations (SDs) of Damage (sdDamage) are set as 0.0, 0.2, 0.4 or 0.6 each multiplied by mDamage. (B) Comparison of the cataract incidence between the calculated data and the BDES data, when Repair is changed from 0.4 to 1.0 at 0.2 intervals. Red and green circles show the BDES data for posterior subcapsular (PSC) and cortical cataracts, respectively. Red and green dotted lines show the calculated data for PSC and cortical cataracts, respectively. The calculated data represent means and 95% confidence intervals (CIs). For parameter determinations made in Fig 3 and S1–S3 Figs, sdDamage of 0.2 × mDamage and Repair of 1 were used.
Fig 5.
The simulation of cataract onset time after ionizing radiation Damage (DamageRadiation).
The simulated onset time for posterior subcapsular (PSC) cataracts following exposure at age 30, 40, 50 and 60 years as a function of DamageRadiation (in an arbitrary unit) is shown in box-and-whisker plots in panels (A), (B), (C) and (D), respectively. The box indicates the inter-quartile range containing middle 50% of the data. The horizontal line within the box, and the vertical line (whisker) beyond the box hinges indicate the median value, and the data within 1.5 times the inter-quartile range, respectively. Red dots indicate the means.
Fig 6.
Comparison of the cataract onset time between the Merriam and Focht data [34] and the simulated data.
The simulated onset time for posterior subcapsular (PSC) cataracts following exposure at age 30, 40, 50 and 60 years as a function of dose assuming ionizing radiation Damage (DamageRadiation) of 0.1/Gy is shown in panels (A), (B), (C) and (D), respectively. The Merriam and Focht data shown as blue circles are for all corresponding data in those at age ≥30 years at the time of exposure in groups 1 and 2. For the calculated data, red solid lines indicate the median values, and blue dotted lines indicate the first and third quartiles (i.e., the 25th and 75th percentile).
Fig 7.
Changes in the cataract incidence following lifetime chronic exposure.
Exposures were assumed to occur at age 0–80 years at a constant dose rate that gives a lifetime cumulative dose of 0, 0.1, 1 and 10 Gy at age 80 years. Cataract incidence following such lifetime chronic exposure to 0, 0.1, 1 and 10 Gy is shown in panels (A), (B), (C) and (D), respectively. Red and green circles show the BDES data for posterior subcapsular (PSC) and cortical cataracts, respectively. Red and green dotted lines show the calculated data for PSC and cortical cataracts, respectively.