Bioequivalence and Bioavailability Forum

Hi BE-proff,

❝ Is it possible to detect cumulation of a substance using "classic" PK-parameters (AUC, Cmax, Tmax, etc)?

Not sure what you mean. According to the “Superposition Principle” linear pharmacokinetics could be tested by a comparison of AUC_0-τ (steady state) with AUC_0-∞ (single dose). Generally this is done in a study where after the single dose profile the drug is administered until steady state is reached.*


The comparison is done by a paired test – which assumes no period effects. I have never seen a crossover in 35 years… Would be a logistic nightmare.
If the 90% CI of AUC_0-τ/AUC_0-∞ is outside the acceptance range, nonlinear PK is proven. See also this lengthy thread.
The superposition principle is applicable to AUCs only (that’s why Friedrich Hartmut Dost called it “Gesetz der kor­res­pondierenden Flächen” – Law of Corresponding Areas back in 1953).
Comparisons of C_ss,max/C_max and t_ss,max–t_max are possible but of doubtful value.

❝ Maybe additional metrics to be calculated?

Whichever you might think of. A common one is the “Accumulation Index”:
   \(R=\frac{1}{1-2^\epsilon}\), where \(\epsilon=\tau/t_{^1/_2}\).
Phoenix/WinNonlin uses a different formula
   \(R=\frac{1}{1-\exp(-\lambda_\text{z}\cdot \tau)}\), which gives the same result (homework: why?).
\(\small{R}\) gives you an idea how much higher average concentrations in steady state are if compared to a single dose. Example: Half-life 12 h (\(\small{\lambda_\text{z}}\) 0.05776) and dosing interval 24 h \(\small{\Rightarrow R\;1.\dot{3}}\) (i.e., con­centrations in steady state will be ⅓ higher than after a single dose). If you decrease the dosing interval to \(\small{t_{\small{^1/_2}}}\), \(\small{R}\) will be 2.

I’m not a big fan of R since it might be difficult to obtain a reasonably good estimate of λ_z / t_½ in steady state. In the BE-context we don’t sample beyond τ. If you are interested in a good estimate of λ_z (e.g., in phase I studies of new drugs) you might sample longer.
Further­more, R is strictly valid only for the one-compartment model. For more compartments it is appro­xi­mate (since based on the elimination phase only).

---

• “True” steady state is reached at t = ∞. Too long for us mortals. However, most people are happy by ad­mi­nistering for five to seven half-lives. IIRC, only ANVISA requires ten half-lives.
   n   % ss
 1  50.00
 2  75.00
 3  87.50
 4  93.75
 5  96.88
 6  98.44
 7  99.22
 8  99.61
 9  99.80
10  99.90
11  99.95
12  99.98
13  99.99
  Formula: % ss = 100(1 – ½ⁿ )