A model of the factors affecting interstitial volume in oedema. Part III: Partial derivatives and integrals at...

The effects of the individual Factors controlling interstitial volume vary between the different steady-states. Partial derivatives of volume with respect to each Factor show only the effects near the steady-state. In passing from one steady-state to another, these partial derivatives vary greatly. The total effects of a Factor are those of the integral of the partial derivative from the initial steady-state to the final one. The simplest way to measure a Factor's total effect is by setting it to zero and observing the difference in tissue volume when the model is perturbed. Thus, to find the effect of proteolysis in lymphoedema, for example, let proteolysis = 0 and compare the final volume in lymphoedema with that when proteolysis is allowed to occur. While the effect of proteolysis is important in lymphoedema, it is of minimal importance in trauma or normal condition. It is again important if proteolysis is increased by benzo-pyrones. There is little correlation between a partial derivative at a steady-state and the integral of this from normal to the state. In low-to-moderate oedemas, many Factors influence the fluid volume. When this volume becomes very large, all Factors except tissue hydrostatic pressure decrease in importance. Tissue hydrostatic pressure can increase indefinitely and is the ultimate reason that oedemas do not increase without limit.