Monotonicity of the peak time in turnover models

Résume ́ xxxxxxxxxxxxxxxxxxxx Abstract We prove that in three of the classical turnover models in pharmacodynamics the time to maximal response increases with increasing drug dose when the concentration of the drug in the blood plasma decreases exponentially with time.

A Flexible Nonlinear Feedback System That Captures Diverse Patterns of Adaptation and Rebound

An important approach to modeling tolerance and adaptation employs feedback mechanisms in which the response to the drug generates a counter-regulating action which affects the response. In this paper we analyze a family of nonlinear feedback models which has recently proved effective in modeling tolerance phenomena such as have been observed with SSRI’s. We use dynamical systems methods to exhibit typical properties of the response-time course of these nonlinear models, such as overshoot and rebound, establish quantitive bounds and explore how these properties depend on the system and drug parameters. Our analysis is anchored in three specific in vivo data sets which involve different levels of pharmacokinetic complexity. Initial estimates for system (kin, kout, ktol ) and drug (EC50/IC50, Emax/Imax, n ) parameters are obtained on the basis of specific properties of the response-time course, identified in the context of exploratory (graphical) data analysis. Our analysis and the application of its results to the three concrete examples demonstrates the flexibility and potential of this family of feedback models

Feedback modeling of non-esterified fatty acids in rats after nicotinic acid infusions

A feedback model was developed to describe the tolerance and oscillatory rebound seen in non-esterified fatty acid (NEFA) plasma concentrations following intravenous infusions of nicotinic acid (NiAc) to male Sprague-Dawley rats. NiAc was administered as an intravenous infusion over 30 min (0, 1, 5 or 20 μmol kg−1 of body weight) or over 300 min (0, 5, 10 or 51 μmol kg−1 of body weight), to healthy rats (n = 63), and serial arterial blood samples were taken for measurement of NiAc and NEFA plasma concentrations. Data were analyzed using nonlinear mixed effects modeling (NONMEM). The disposition of NiAc was described by a two-compartment model with endogenous turnover rate and two parallel capacity-limited elimination processes. The plasma concentration of NiAc was driving NEFA (R) turnover via an inhibitory drug-mechanism function acting on the formation of NEFA. The NEFA turnover was described by a feedback model with a moderator distributed over a series of transit compartments, where the first compartment (M1) inhibited the formation of R and the last compartment (MN) stimulated the loss of R. All processes regulating plasma NEFA concentrations were assumed to be captured by the moderator function. The potency, IC50, of NiAc was 45 nmol L−1, the fractional turnover rate kout was 0.41 L mmol−1 min−1 and the turnover rate of moderator ktol was 0.027 min−1. A lower physiological limit of NEFA was modeled as a NiAc-independent release (kcap) of NEFA into plasma and was estimated to 0.032 mmol L−1 min−1. This model can be used to provide information about factors that determine the time-course of NEFA response following different modes, rates and routes of administration of NiAc. The proposed model may also serve as a preclinical tool for analyzing and simulating drug-induced changes in plasma NEFA concentrations after treatment with NiAc or NiAc analogues

Homoclinic orbits to a saddle-center in a fourth-order differential equation

AbstractWe study homoclinic orbits to a saddle-center of a fourth-order ordinary differential equation, which is invariant under the transformation x→−x, involving an eigenvalue parameter q and an odd, piece-wise, cubic-type nonlinearity. It is found that for a sequence of eigenvalues which tends to infinity, homoclinic orbits exist whose complexity increases as the eigenvalue becomes larger. These orbits are found to be embedded in branches of homoclinic orbits to periodic orbits as x→±∞