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

Abstract

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 (M (1)) inhibited the formation of R and the last compartment (M ( N )) stimulated the loss of R. All processes regulating plasma NEFA concentrations were assumed to be captured by the moderator function. The potency, IC (50), of NiAc was 45 nmol L(-1), the fractional turnover rate k ( out ) was 0.41 L mmol(-1) min(-1) and the turnover rate of moderator k ( tol ) was 0.027 min(-1). A lower physiological limit of NEFA was modeled as a NiAc-independent release (k ( cap )) 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.

Fig. 1

Schematic illustration of the feedback model describing the NiAc-induced changes in NEFA. C _p and C _t denote the NiAc concentrations in plasma and the peripheral compartment. The NiAc disposition parameters are V _c, V _t, V _max1, K _m1, V _max2, K _m2, Cl _d, Inf, and Synt (definitions in Table 1). NEFA and denote the response and moderator compartments. The NEFA turnover parameters are R ₀, k _out, k _tol, k _cap, p, IC ₅₀ and γ (definitions in Table 2). I(C _p) is defined in Eq. 2. The number of moderator transit compartments N was 8. The solid and dashed lines represent fluxes and control processes, respectively

Fig. 2

Observed plasma NiAc concentration-time profiles during and after NiAc infusion. a 30 min infusion of vehicle (control), or NiAc 1, 5 or 20 μmol kg⁻¹ of body weight; b 300 min infusion of vehicle, or NiAc 5, 10 or 51 μmol kg⁻¹ of body weight. All infusions started at time t = 0 min

Fig. 3

Saturable elimination processes identified in the disposition of NiAc. The major clearance pathway up to a concentration of approximately 0.1 μmol L⁻¹ was high affinity (K _m1 = 0.00468 μmol L⁻¹, V _max1 = 0.0573 μmol min⁻¹ kg⁻¹). Below that concentration a second pathway (K _m2 = 16.6 μmol L⁻¹, V _max2 = 1.46 μmol min⁻¹ kg⁻¹) could be approximated to a first-order process. The two pathways contributed equally at concentrations around 1 μmol L⁻¹ and above that concentration the low affinity pathway became the major elimination process

Fig. 4

Representative model fits of NiAc plasma concentration-time data at different durations (30 min (left) and 300 min (right)) and rates of NiAc infusion. Solid and dashed lines represents individual and population fits, respectively. Infusion started at time t = 0 min. Plots of all individual regressions are available from the author upon request

Fig. 5

Goodness-of-fit plots for NiAc. Measured concentrations were plotted against population fitted concentrations (a) and individually fitted concentrations (b) on a logarithmic scale. Individually weighted residuals were plotted against time (c), and against individually fitted NiAc concentrations on a semi-logarithmic scale (d). Conditional weighted residuals were plotted against time (e), and against population fitted concentrations (f)

Fig. 6

Observed plasma NEFA concentration-time profiles during and after a a 30 min infusion of vehicle or NiAc (1, 5 or 20 μmol kg⁻¹ of body weight), and b a 300 min infusion of vehicle or NiAc (5, 10 or 51 μmol kg⁻¹ of body weight). The NEFA concentrations in each one of the control animals were stable but a large variability could be seen between the animals. All infusions started at time t = 0 min

Fig. 7

Representative model fits of NEFA plasma concentration-time data after different durations (30 min (left) and 300 min (right)) and rates of NiAc. Solid and dashed lines represent individual and population fits, respectively. Infusion started at time t = 0 min. Plots of all individual regressions are available from the author upon request

Fig. 8

Goodness-of-fit plots for NEFA. Measured concentrations were plotted against population fitted concentrations (a) and individually fitted concentrations (b) on a logarithmic scale. Individual weighted residuals were plotted against time (c), and against individually fitted NEFA concentrations on a semi-logarithmic scale (d). Conditional weighted residuals were plotted against time (e), and against population fitted concentrations (f)

Fig. 9

Simulated steady state plasma NiAc concentration versus plasma NEFA concentration (R _ss). The solid line represents the tolerant system according to Eq. 15, and the dashed line the non-tolerant system according to Eq. 17. The final parameter estimates from Table 2 were used to draw the two curves