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Peak drug levels in linear pharmaco kinetic systems 3. multi modal impulse responses in multi compartment systems



Peak drug levels in linear pharmaco kinetic systems 3. multi modal impulse responses in multi compartment systems



Bulletin of Mathematical Biology 44(5): 609-636



The unimodality of the impulse response was studied in compartmental systems, where the impulse response in any given compartment is the time course of the amount of diffusing substance in that compartment after an initial instantaneous injection of the substance into that or another compartment. In certain compartmental structures, with injection in certain compartments, the impulse response is always unimodal or monotonic in all compartments, regardless of the numerical values of the various transfer rate coefficients. Structures with this property are here named UM structures, and they include the familiar mammillary and catenary structures. The set of all UM structures is described. Structures which are not UM (NUM structures) are identified by showing that, by removal of certain connections and compartments according to certain rules, they can be reduced to small structures which can be shown to be NUM by numerical computation. Computations on 2 systems with bimodal impulse responses show that with constant infusions of a fixed amount of substance the peak level may increase paradoxically with decrease in the infusion rate over a certain range. This effect is extremely small.

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