Zero-order input

The maximal effect in the models given above occurs later than the time when is reached since the drug produces an incremental effect, either inhibition of stimulation, provided the concentration remains above IC50 or SC50. How the response returns to its baseline after concentration decay is governed by the zero-order input rate and the rate... 

C(t) modeled according to two-compartment model with zero-order and first-order absorption Pharmacokinetic/pharmacodynamic relationship modeled using Hill model with first-order absorption. Modeled parameters matched experimental parameters when bicompartmental model with zero-order input was used. Linear PKs, anticlockwise hysteresis loop established for all doses studied. Apomorphine and growth hormone concentration predicted with good accuracy... 

An instructive example is the physiological variable serum creatinine. Creatinine is an endogenous metabolite formed from, and thus reflecting, muscle mass. Total body muscle mass is sufficiently constant to render measurement of serum creatinine useful for assessing actual renal function. The serum value of creatinine (R) is namely dependent on the continuous (zero-order) input of creatinine into the blood (A in) and its renal elimination rate, which is a first-order rate process (A out x ) In case of an extensive muscle breakdown, kin will temporarily increase. It may also be permanently low, for example in old age when muscle mass is reduced. Likewise, creatinine clearance may decrease for various reasons, described by a decrease in A out- An increase in creatinine clearance may occur as well, for example following recovery from renal disease. According to pharmacodynamic indirect response models. 

The system is shown in Fig. 21.7. It is described by two concentrations (state variables), CA and CB, by two zero-order input functions, JA and JB (input per volume and time), by two first-order output functions, kACA and kBCB (output per volume and time), and by the first-order transformations from A to B and vice versa. The inputs and outputs can be the sum of two or more processes, for instance, the sum of the input through different inlets and from the atmosphere (as in Eq. 21-7a), or the sum of the output at the outlet and by exchange to the atmosphere (as in Eq. 21-7b.). 

Sometimes, absorption can be described by sequential zero-order and Lrst-order absorption processes. Conceptually, if the Lrst-order rate constant is linked to the zero-order input, the model can be postulated as the consequence of dissolution-limited absorption (Garrigues et al., 1991 Holford et al., 1992). 

Zero-order input and one-compartment disposition (I0D1). This model and the I0D1 model only differ from the first model (IBD1) by the kinetic order of the input the disposition component remains the same. The compartmental box diagram is shown in Fig. 1.11. The differential... 

Figure 1.11 Zero-order input and one-compartment disposition box diagram.

Figure 1.12 shows the concentration profile plotted on Cartesian coordinates and semilog scales respectively. When a zero-order input has been left on for an amount of time equal to 3.3 to 5 half-lives, Cp is considered to be at steady state (90 and 96 percent of true steady state, respectively) and is designated as Cp ss. There is only one volume term, Vd, because the disposition is only one compartment. 

Zero-order input and one-compartment disposition (I0D1). The simplest case for achieving a drug plasma concentration between the MEC and MTC is to use a zero-order input. In Fig. 1.17, the six time points show time as measured in half-lives. At 3.3 half-lives, Cp is at approximately 90 percent of its true steady-state value at 5 half-lives, Cp is at approximately 96 percent of its true steady-state value. 

If drug had been administered in equally sized multiple intravenous bolus doses at equally spaced t time intervals (e.g., t = 6 h), then an accounting of accumulated drug between doses must be instituted. Figure 1.18, similar to the zero-order input, shows that repetitive instantaneous dosing will produce an average Cp profile similar to Fig. 1.17. 

Other transdermal systems give rates of release which are proportional to the square root of time. In order to model this behaviour it is possible to write a series of linear differential equations to describe transfer from the device and across the skin. However unlike the cases of first and zero order input, t1 2 input does not produce a simple analytical solution of the type given in equation (5). Plasma levels have therefore been calculated using a numerical approach and by solving the equations using the Runge-Kutta method. For GTN delivery, identical rate constants to... 

Scopolamine was the first drug to be marketed as a transdermal delivery system (Transderm-Scop) to alleviate the discomfort of motion sickness. After oral administration, scopolamine has a short duration of action because of a high first-pass effect. In addition, several side-effects are associated with the peak plasma levels obtained. Transderm-Scop is a reservoir system that incorporates two types of release mechanims a rapid, short-term release of drag from the adhesive layer, superimposed on an essentially zero-order input profile metered by the microporous membrane separating the reservoir from the skin surface. The scopolamine patch is able to maintain plasma levels in the therapeutic window for extended periods of time, delivering 0.5 mg over 3 days with few of the side-effects associated with (for example) oral administration. 

Assuming that zero-order input is acceptable for this drag, then ... 

Computations were carried through for values of 0.05 < 0 < 0.95 in increments of 0.05 unit, with C — 2, 3, 4, and 5. It was assumed that lateral interactions were due to attractive van der Waals-London dispersion forces, where the leading term in the energy expansion varies with distance as r-1/6 with R = V2 one finds C = C1/8. Calculations were also carried out in the Fowler-Guggenheim approximation this simply requires the determination of the zero-order inputs Po(a 0), Pj(b °K and P/P°. The results are exhibited in Figures 2 and 3 the broken curves refer to isotherms calculated according to Equations 22 and 23. 

When a drug is administered by constant intravenous administration, this zero-order input can be represented by a "step function." Derive the appropriate absorption function and convolute it with the disposition function to obtain the output function. 

A one-compartment model with first-order elimination was used to simulate unbound VPA concentrations. The two formulations differ only in the input function the ER formulation was accounted for through a zero-order input over 22 hours with 89% bioavailability. The DR formulation absorption was characterized by a 2h lag time (flag = 2h) followed by first-order absorption rate ka = 0.1 h ). The bioavailability F) of the DR preparation was assumed to be complete F = 1). 

Sometimes, two first-order absorption processes do not adequately describe the data and the absorption profiles are better described by a combination of first-order and zero-order processes (40, 56-59). Lag time may be added for each type of absorption, which then will determine whether the two processes are simultaneous or sequential. Moreover, if the first-order rate constant is finked to the zero-order input parameters, the model can be interpreted as the consequence of dissolution-limited absorption. The ordering of the processes (first-order absorption first, or zero-order absorption first) is usually empirical or data driven. Pathophysiology and/or physicochemical characteristics of the compound may help in deciding the order. 

Life Span Model Stimulatory Drug Effect and Zero-Order Input Model WinNonlin Code... 

D, dose F, bioavailability fr, fraction of dose undergoing first-order input in a dual absorption model K, zero-order input rate L and k, first-order absorption rate constants MAT, mean absorption time NV, normalized variance of Gaussian density function, t, nominal time ti g, duration of time-lag x, duration of rapid input in dual absorption model Ti f, duration of zero-order IV infusion T, modulus time. 

Often PK equations for common inputs such as first-order absorption zero-order input, or constant-rate infusions are derived from the differential equations describing the kinetics. LSA offers a very attractive alternative to such derivations that is more direct and does not require the use of differential equations or Laplace transforms. The LSA derivations can be done simply by elementary convolution operations (see Tables 16.1 and 16.2) in conjunction with the input-response convolution relationship between concentration, c(t), and the rate of input,/(t) ... 

It is common practice, in the hospital setting to infuse a drug at a constant rate (constant rate input or zero-order input). This method (Fig. 10.2) permits precise and readily controlled drug administration. 

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