The Approach to Model Building
Having completed our discussion of the basic concepts of mechanism-based modeling and provided a few simple examples of population dynamics models related to the immune system, we are now ready to return to the problem of subcutaneous insulin absorption.
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The Approach to Model Building Jakob L. Laugesen and Erik Mosekilde
Structure generates behavior. Broadly speaking, the feedback structure of a system determines the dynamics it can display. Close the loop and watch dynamics unfold.
3.1 Flow Diagram for the Subcutaneous Absorption of Insulin Having completed our discussion of the basic concepts of mechanism-based modeling and provided a few simple examples of population dynamics models related to the immune system, we are now ready to return to the problem of subcutaneous insulin absorption. We recall that the data presented in Chap. 1 led us to the following dynamical hypotheses that seem to explain the slow initial absorption rate, the separate volume and concentration effects, and the characteristic tail phenomenon observed at low concentrations [22, 23]: • Insulin is present at the subcutaneous injection site in three different forms: Hexameric, dimeric and bound insulin. Only the dimeric form is absorbed into the blood. • At high insulin concentrations, the chemical balance between dimeric and hexameric insulin is shifted towards the hexameric form, and the fractional absorption rate is therefore relatively small. As the insulin concentration in the depot decreases, due to absorption or to diffusive spreading, the balance is shifted towards the dimeric form, and the observed absorption rate increases.
J.L. Laugesen E. Mosekilde () Department of Physics, Technical University of Denmark, Fysikvej 309, DK-2800 Lyngby, Denmark e-mail: [email protected]; [email protected] E. Mosekilde et al. (eds.), Biosimulation in Biomedical Research, Health Care and Drug Development, DOI 10.1007/978-3-7091-0418-7 3, © Springer-Verlag/Wien 2012
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J.L. Laugesen and E. Mosekilde
• For large injected volumes, diffusion of insulin in the tissue has little effect on the spreading of the depot. For the smallest injection volumes, on the other hand, the insulin molecules can rapidly spread over distances comparable to the radius of the depot, and the resulting reduction in the insulin concentration shifts the balance towards dimeric insulin, hence speeding up the absorption process. • Finally, at low concentrations a notable fraction of insulin is bound in the tissue, and the absorption rate is limited by the rate at which insulin is released from the bound state. Alternative hypotheses are possible as well. In particular, one could think of other types of biochemical processes in the subcutaneous tissue, or one could consider a process of self-inhibition by which the administered insulin solution through interaction with the tissue caused a temporary reduction of the blood perfusion at the injection site, thus lowering the rate of absorption. The pharmaceutical industry takes great care to avoid such effects, e.g. by using isotonic insulin solutions, and in the cases where reactions are observed, they usually show up as a temporary reddening of the skin, indicating an increased blood supply. It is interesting to note that, although most of the results displ
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