The initial and final eccentricities of the LDFs along the superior, inferior, and temporal (
Figs. 2C–E) meridians show a wide range of disease progression rates across
ABCA4-RD patients studied. Progression rate tended to be higher for patients first examined at earlier ages compared with those first examined at later ages (
Fig. 4A, symbols). In addition, there appeared to be a tendency for those with relatively smaller lesions at first visit (
Fig. 4A, red symbols) to expand slower compared with those with relatively larger lesions (
Fig. 4A, green symbols) at any given age. Along the nasal meridian, the progression rate of the outer nasal LDF also appeared to be higher for patients first examined at earlier ages. To mathematically model the progression data a formula with exponential and linear components was considered
where
LDF1 and
LDF2 are the eccentricities (in degrees) of the LDF at the first and second time points, respectively,
AGE1 and
AGE2 (in years) are the ages at first and second time points, respectively,
k1,
k2,
k3, and
k4 are parameters. The term in curly brackets defines the rate of expansion of LDF (in °/y). All available serial data along superior, inferior, and temporal meridians (symbols in
Fig. 4A) were used with a least squares fitting algorithm (Excel Solver; Microsoft Office 2013, Redmond, WA, USA) to estimate a single set of four model parameters as:
k1 = −0.095 °/y,
k2 = 25.25 °/y,
k3 = 0.18 yrs
−1, and
k4 = 0.049 °/y. The use of the more limited data from the outer nasal boundary resulted in a different set of model parameters as:
k1 = 0.61 °/y,
k2 = 4.41 °/y,
k3 = 0.06 yrs
−1, and
k4 = 0.008 °/y. Family of curves produced by the model (
Fig. 4A, lines) appear to describe the data well.