Bioavailability is where the marketing hides

A colleague forwarded me a product page in June with one phrase highlighted: up to ten times more absorbable. I asked her to find me the area under the curve comparison. There was none, naturally, and the sentence is not a lie in any sense you could take to a regulator. It is a ratio with the denominator removed.

What the word means

Bioavailability, written $F$, is the fraction of an administered dose that reaches the systemic circulation unchanged. Two consequences follow at once. It belongs to a dose, a formulation, a route and a population, not to a molecule. And it is defined by an area, never by a peak.

The area sits under the plasma concentration against time curve, and you obtain it with trapezoids, the least glamorous arithmetic in pharmacology:

${AUC}_{0-t}={\sum }_{i=1}^n\frac{C_{i-1}+C_i}{2}(t_i-t_{i-1})$

def auc_trapezoid(times, concentrations):
    """Linear trapezoidal AUC from paired sample times and plasma concentrations."""
    if len(times) != len(concentrations) or len(times) < 2:
        raise ValueError(
            "times and concentrations must be the same length and contain at least "
            f"2 points; got {len(times)} and {len(concentrations)}"
        )
    return sum(
        (concentrations[i - 1] + concentrations[i]) / 2 * (times[i] - times[i - 1])
        for i in range(1, len(times))
    )

That is the entire method. Everything difficult about bioavailability lives in the sampling schedule and the assay, not in the integral.

Absolute against relative

Absolute bioavailability compares an oral curve with an intravenous curve, because intravenous is the one route where $F=1$ by construction:

$F_{abs}=\frac{{AUC}_{po}/D_{po}}{{AUC}_{iv}/D_{iv}}$

Relative bioavailability compares two formulations neither of which is intravenous:

$F_{rel}=\frac{{AUC}_{test}/D_{test}}{{AUC}_{ref}/D_{ref}}$

Note the dose normalisation in both. Drop it and you can manufacture whatever ratio you were hoping for, which is trick one below.

Without an intravenous arm there is no absolute bioavailability. A supplement study cannot produce one. So when a page states a percentage and names no reference product, it has either done a relative comparison and hidden the reference, or it has done nothing.

The reason $F$ sits well under 1 for most oral drugs is loss in series: incomplete uptake across the gut wall, then metabolism inside the enterocyte, then metabolism in the liver before anything reaches the systemic circulation.

$F=f_{abs}\cdot (1-E_G)\cdot (1-E_H)$

with $E_G$ and $E_H$ the gut and hepatic extraction ratios. Three multiplied fractions. A compound can be taken up from the gut almost completely and still show an $F$ of 0.05 because the liver removes the rest on first pass. Which is why absorbable is the wrong word for the claim being made: it names one of the three terms and quietly ignores the other two.

The shape of the curve is not the size of the dose

Numbers below are illustrative, invented for teaching, no product implied.

Formulation	$C_{\max }$ (mg/L)	$t_{\max }$ (h)	AUC 0 to 24 h (mg·h/L)
A	1.20	3.0	8.4
B	1.68	1.0	8.5

B peaks 40% higher and gets there three times sooner. The same quantity of drug entered the circulation. Plot only the first two hours and B looks like a different product; compute the ratio of the areas and you get 1.01. Faster is what you want in an analgesic and precisely what you do not want in anything with a concentration dependent adverse effect. Faster is not more.

Five ways to claim ten times without measuring an area

1. Compare unequal amounts of the active. 100 mg of elemental magnesium against 100 mg of magnesium citrate is 100 mg against roughly 16 mg. Your six-fold is banked before anyone swallows anything.
2. Report the peak, or one early timepoint, and describe it as absorption.
3. Measure something adjacent: mineral dissolved in a vessel, transport across a Caco-2 monolayer, or urinary output of a metabolite the two formulations do not generate in equal proportion.
4. Divide by something close to zero. Relative bioavailability is a ratio, and if the reference area sits at the assay's lower limit of quantification, the ratio is a statement about your instrument rather than about absorption.
5. Run a dissolution test and write it up in the vocabulary of absorption.

Working out what your instrument can and cannot see, before believing what it appears to show, is the whole discipline. @dust/limiting-magnitude-from-first-principles does this for a telescope and the logic transfers without modification.

One that is real, worked through

Shoba and colleagues, Planta Medica 1998, on piperine and curcumin. This paper is where most black pepper claims eventually terminate, and it repays reading rather than citing.

Design: ten healthy men aged 20 to 26, randomised crossover, two week washout, a single 2 g oral dose of curcumin with or without 20 mg of piperine. Two withdrew for non-medical reasons, so the analysis rests on eight.

Results in the human arm. Curcumin alone gave a measured $C_{\max }$ of 0.006 plus or minus 0.005 µg/mL at one hour, and the paper states that serum levels were either very low or undetectable at most timepoints in most subjects. With piperine, $C_{\max }$ was 0.18 plus or minus 0.16 µg/mL at 45 minutes, back to zero by three hours. The reference area was computed by the trapezoidal method as 0.004, printed in the paper with the unit µg/mL, which cannot be the unit of an area. Relative bioavailability with piperine: 2000%.

So: trick four, in print, in 1998, cited a few thousand times since. The 2000% is arithmetically defensible and informationally almost empty, because a twenty-fold increase over a baseline that the assay could not see is a statement about the assay. There was no intravenous arm, so no absolute bioavailability exists anywhere in the paper. There was no clinical endpoint of any kind. Two of the six authors were at the company that manufactures the piperine extract, and the test article was prepared there.

The rat arm is quieter and more revealing. Area under the curve rose from 2.36 to 3.64 µg·h/mL, a difference the authors report as not statistically significant, and the paper still puts relative bioavailability at 154%.

I am not claiming piperine does nothing to curcumin glucuronidation. It very probably does something. I am claiming that a ratio computed against a baseline the assay could not see gives you no grounds to expect anything in a patient, and that a quarter of a century of packaging rests on that one sentence.

What a dissolution result is worth

A dissolution test tells you a formulation releases its contents into a defined medium at a defined rate. That is a real quality control measurement and a poor surrogate for absorption, because the vessel contains no gut wall, no transporters, no CYP3A4, no bile, no motility and no lunch.

Regulators do sometimes accept dissolution in place of a human study, and the conditions attached show exactly how narrow the inference is. A biowaiver wants an immediate release solid oral form, a drug highly soluble across the physiological pH range, permeability either high or at least characterised, dissolution that is very rapid (at least 85% in 15 minutes for the poorly permeable class), profile similarity against a named reference product, and excipients that do not themselves alter absorption. Every one of those clauses is load bearing. A bench result on a proprietary blend, against no reference product, satisfies none of them.

What I want before I believe a comparative absorption claim is not exotic: a human study, two formulations at equimolar doses of the active, randomised crossover with a washout, a sampling schedule long enough to catch the tail, area under the curve as the prespecified primary outcome, a confidence interval on the ratio, and the assay's lower limit of quantification stated so I can check whether the reference was measurable at all. That is a first year study design. Its absence is not an oversight.