Quantitative dynamic models of arthritis progression in the rat

Abstract

Purpose: This comparison employs mathematical disease progression models to identify a rat model of arthritis with the least inter-animal variability and features lending to better study designs.

Methods: Arthritis was induced with either collagen (CIA) or mycobacterium (AIA) in either Lewis or Dark Agouti (DA) rats. Disease progression was monitored by paw edema and body weight. Models with production, loss, and feedback components were constructed and population analysis using NONMEM software was employed to identify inter-animal variability in the various disease progression parameters.

Results: Onset time was the only parameter different within all four groups (DA-AIA 11.5 days, DA-CIA 16.5 days, Lewis-AIA 11.9 days, Lewis-CIA 13.9 days). The loss-of-edema rate constant was 20% slower in DA (0.362 h(-1)) than Lewis (0.466 h(-1)) rats. Most models exhibited peak paw edema 20 days post-induction. Edema in CIA returned to 150% of the initial value after the disease peaked. DA rats displayed more severe overall responses.

Conclusions: No statistical differences between groups were observed for inter-animal variation in disease onset, progression and severity parameters. Onset time varies and should be noted in the design of future studies. DA rats may offer a more dynamic range of edema response than Lewis rats.

Fig. 1

Diagram for determination of paw swelling circumference. Each panel indicates paw (P) and ankle (A) measurement locations to determine the approximate circumferences on study day 20.

Fig. 2

Schematic of disease progression model components. The model is a modified basic indirect response model for the production and loss of paw or ankle swelling. The production component [k_in(t)] is both time dependent and inhibited by the degree of swelling to account for disease remission in the later portion of the time course. The loss component (k_out) is a first-order stationary rate constant.

Fig. 3

Arthritis disease progression as indicated by changes in paw swelling. Circles depict observed paw size relative to baseline values. The solid line is the population prediction for all points in each group, assuming no residual error. There are data from four rats (eight paws) in all plots except for the Lewis rats with CIA, n=2 (four paws).

Fig. 4

Arthritis disease progression model prediction of paw and ankle edema. Additional paw measurements were available from a time course of disease progression in 34 Lewis rats with CIA. Circles depict observed paw sizes. The solid line is the median prediction for each time point from a simulation of 10,000 rats, applying the model developed for Lewis rats with CIA. The shaded area is the 10th to 90th confidence interval.