In the analysis of extra-vascular plasma
concentration-time profiles, the disentanglement of influences from disposition and
absorption rate influences is often challenging. This can be particularly true when
absorption is considerably slower than disposition, that is, in a "flip-flop" system. The purpose of this communication is to
define a pharmacokinetic flip-flop system (in a linear
system) and characterize some of its properties.

The well-known Wagner-Nelson equation (1)
characterizing drug absorption in the presence of monoexponential disposition can be
rearranged as follows:

where *Vz *is the terminal exponential volume of distribution, *K* is the terminal disposition rate constant once drug
absorption is complete (best determined from *IV* dosing), *C* is the plasma
concentration at time t and D C is the change in plasma
concentration over the time interval D t. In
Eq. 1, it is best to utilize *C* at the time corresponding to the midpoint of *(D C/D t)*. In those situations where *KC >> (D C/D t),* which serves as a definition
of a pharmacokinetic "flip-flop" system, Equation 1 simplifies to:

where *(V**z)(K) *is
clearance *(CL).* Equation 2 indicates that under these
conditions, rate of absorption approximates rate of elimination. When this is observed,
which can exist during many or most segments of a plasma concentration-time profile,
regardless of complexity, the pharmacokinetic profile is in a state of
"flip-flop," viz., rate of absorption approximates rate of elimination. In a
simplified sense, a "flip-flop" exists when rate of absorption is the
rate-limiting step in the sequential/parallel processes of drug absorption, distribution
and elimination. The "trap" commonly fallen into is that the terminal
exponential phase half-life following extra-vascular dosing is mistakenly thought to
exemplify terminal drug disposition, when in fact it characterizes terminal exponential
drug absorption half-life. The "trick" that can be applied is simply to
recognize that in a "flip-flop" model, the plasma concentration-time profile
tends to closely parallel rate of absorption. This provides a simple and effective way to
visualize the shape of the rate of absorption profile, without the necessity of
deconvolution, e.g., Wagner’s modification of the Loo-Riegelman equation (2).

**Figure 1.
Recombinant human growth hormone (GH) mean semilogarithmic
plasma concentration-time profiles (3) following: an intravenous bolus
injection of 0.2 mg/kg doses to 4 dogs (theoretical profile based on mean parameters from
biexponential curve-fits); and a profile following subcutaneous administration of 0.7
mg/kg doses in a poloxamer gel formulation administered to 4 dogs. Rate of absorption was
calculated by Wagner’s modification of the Loo-Riegelman equation (2). The
multiplication of rate of absorption by a factor of 5 was selected to deliberately
position the rate of absorption profile close the plasma concentration-time profile, thus
facilitating comparison of the two functions.**

Figure 1 illustrates a "flip-flop"
pharmacokinetic system. Note the rapidity of intravenous growth hormone (GH) disposition
compared to the profile following subcutaneous dosing of the gel formulation. GH
intravenous disposition is biexponential, with disposition half-lives of 0.0687 and 0.574
hours. The more rapid exponential term virtually completely disappears after about ten
half-lives (0.687 hours), after which intravenous disposition becomes monoexponential.
Additionally and more importantly, Equation 1 is applicable to extravascular plasma
concentration-time profiles after 0.687 hours, since the only significant influences
impacting the GH plasma concentration-time profile derive from absorption and terminal
exponential disposition processes. Applying Equation 1 to plasma concentration-time data
for the subcutaneous formulation at 48 and 72 hours, *DC/D*t = 0.0375 ng/mL/hour. At the midpoint of this time period (60
hours), (K)(C) = 4.55 ng/mL/hr. Since *KC >> DC/Dt,* rate of absorption » rate of
elimination, and a "flip-flop" condition exits. Even though this was established
using absorption phase, terminal exponential data, the "flip-flop" condition
exists throughout most of the profile, since the downward slope of the profile from the
gel formulation never approaches the steepness of the plasma concentration-time function
following IV doses. As noted above ("trick"), the plasma concentration-time
profile from the gel formulation closely mirrors the rate of absorption profile. This
provides an easy way to access the shape of an absorption rate profile in a
"flip-flop" model.

**
**References

**
**
- Wagner J G; Nelson E. Kinetic analysis of blood
levels and urinary excretion in the absorptive phase after single doses of drug. J Pharm
Sci, 53:1392-1403, 1964.
- Wagner J G. Pharmacokinetic absorption plots from oral data alone or
oral/intravenous data and an exact Loo-Riegelman equation. J Pharm Sci, 72:838-842, 1983.
- Katakam M; Ravis W R; Golden D L; Banga A K. Controlled release of human
growth hormone following subcutaneous administration in dogs. Int J Pharm, 152:53-58,
1997.

**Corresponding author**:
Harold Boxenbaum, Arishel Inc., 14621 Settlers Landing Way, North Potomac, Maryland,
20878-4305, USA, email:shelbyb@ix.netcom.com

**Keywords:** Pharmacokinetic,
Flip-Flop, Growth Hormone

JPPS Contents

**Published by the Canadian Society for
Pharmaceutical Sciences.**