Abstract
Physiological systems are often modelled by a set of compartments. Alternatively they can be described by the diffusion-convection-reaction equations governing distributed systems. The problem considered here is that of identifying a continuously changing input of some metabolite )tracee), endogenous to the system and hence inaccessible, when a nonlinear or time-varying component is also introduced into the loss parameter, as for example through feedback mechanisms. A tracer is used to determine the steady-state impulse response under time-invariant, linear conditions. A known input of tracer is also administered when the system is driven out of steady state. The integral equations developed utilize the predetermined impulse response, the measured concentrations of both tracer and tracee (output) in some region of the system to estimate the changing loss parameter and the unknown input in a continuous fashion.
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Radziuk, J. An integral equation approach to measuring turnover in nonsteady compartmental and distributed systems. Bltn Mathcal Biology 38, 679–693 (1976). https://doi.org/10.1007/BF02458642
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DOI: https://doi.org/10.1007/BF02458642