Once the initial simple model of pain was constructed, Prof Darling and I began expanding the model. Critical to the development of the model were two constructs: Functionality and Compliance. These concepts would need to be integrated into the model in order to make it more complete.
To begin, we defined functionality as simply “the ability to get out of bed and do things”. The literature search demonstrated that there is a reciprocal relationship between functionality and pain (when functionality decreases, pain increases, and vice versa). In reality, the relationship between functionality and pain is far more complex, though the reciprocal relationship would suffice for the purposes of this model. In order to separate functionality and pain, the growth rates would always need to be inverses. This was accomplished by modifying the growth rates that went into the logistic growth equations.
As stated in the previous entry, modeling pain is not as simple as one logistic growth equation. The growth rate that affects changes in pain level is not a static number, but is influenced by compliance with certain factors that we believe influence pain levels. I have termed this collection of factors the MEDAL group, comprised of Medicine, Exercise, Diet, Attitude, and Lifestyle.
These 5 factors were scaled to a range of 0-4, to provide an accurate observation (0 = no compliance) and a 1-5 scale with a clear middle point. For this iteration of the model, the arithmetic average of the 5 factors was calculated and entered in as a Compliance term in the master capsule of the model. This Compliance term was then either subtracted from 2 (functionality) or had 2 subtracted from it (pain) in order to determine the growth rate used in the differential equation for either pain or functionality. As with before, I quickly learned that compliance is not as simple as an arithmetic average of its components.