There are three steps involved in this verification. Scroll down to view each in turn.
Step One. Determine if there is a consistent dose-response for all durable fibers taken together. The model predicts that all durable fibers (those that do not dissolve in the animal's lifetime) produce the same disease incidence at the same dose, where "dose" is here taken to be the total number of fibers potentially inhaled by the animal during the study. (It is the airborne fiber concentration times the animal minute volume times the time they were exposed.) The data for several different types of durable fibers, each administered at several different concentrations for differing lengths of time (all shown with black squares appear to lie along the same S-shaped curve. Averaging these durable fiber data produces the red curve with the indicated vertical error bars. | |
The fact that all of these points lie near the same curve is significant because it suggests that twice the concentration for half the time yields the same dose and therefore the same response. | |
Step Two. Now the data for the less durable fibers are added to the graph as blue X symbols, without adjusting the dose for the short time that these fibers remain in the lung. These non-durable fiber results do not fall on the red curve of the durable fibers and produce significantly less disease incidence than the durable fibers at the same dose. It is this difference in disease incidence that the predictive model seeks to explain. | |
Step Three. Now the dose of the non-durable fibers is adjusted according to the predictions of the model. The mathematical formula for adjustment can be expressed simply as "twice the dissolution rate is like half the dose". This animation flips back and forth between the unadjusted dose, as in Step Two above, and the adjusted dose that takes dissolution rate into account. With dose adjusted according to the model, the blue squares of the non-durable fibers fall on the red curve too. | |
Apparently, this model can be used to predict the incidence of fibrosis following chronic inhalation for a fiber of any given dissolution rate administered at any concentration for any length of time within this range. |