Biexponential reactions are typical for various biological processes and occur almost as often as the first-order reactions. A great article titled, "Determination the rate constants of some biexponential reactions" by Bobrovnik explained some examples of reactions that are biexponential. One example is the initial compound A transforms first reversibly into intermediate compound B, which then irreversibly transforms into final product C. In the case of 6-fluoro-(18F)-L-dopa, I am not sure about its transformation, but I am guessing the amino acid is transforming into dopamine with an intermediate compound involved. I hope it helps giving you a very brief and basic introduction in pharmacokinetics. Let me know if you have a question.

Hi,

Pharmacometrics and pharmacokinetics is probably the most regulated discipline by Health Authorities. In case of half-life regulators define few different half lives related to elimination of drug molecules or therapeutic effect for example:

1) Physical half-life is the time needed for half of the population of atoms of a particular radioactive substance to disintegrate to another nuclear form (radiopharmaceuticals etc).

2) Elimination half-life (biological half-life) is the time needed for a human or animal to remove, by biological elimination, half of the amount of a substance that has been administered.)

3) Effective half-life is the time needed for a radionuclide in a human or animal to decrease its activity by half as a combined result of biological elimination and radioactive decay

see FDA reference below, 1,2 reflects PK and 3 reflect effects - PD

If its not described clearly how and what kind of half lives calculate Authors of publication then underestanding of the analysis coud be indeed dificult. But the proper understanding of elimination half life topics needs an explanation few additional topics:

Two different elimination half-lives (t1/2kel) were calculated based on the elimination phase for the same drug.

The problem is visible especially when LLOQ and or drug dosing are different in two experiments. For example, in a case when doses are equal but LLOQ for two experiments is different than in the study where LLOQ makes possible analysis only relatively high concentrations then in the PK curve some concentrations in the elimination phase are not visible. The last observed concentration is observed faster and sometimes a few points taken for Kel (elimination rate constant) analysis represent not exactly elimination but late distribution and finally, the t1/2kel value is shorter than should be (see my paper below about Kel validation). This is why some drugs PK analyzed 40 years ago with not such sophisticated methods like now very often show „shorter” t1/2kel.

Two t1/2kel are calculated from one PK profile (instead of one t1/2kel).

From my experience 99 % of such calculations express as „first”, half-life related to the distribution process and do not show what we define as the elimination phase. Such observations raise especially when people use very sensitive analytical methods and don't expect the elimination phase as long as they see it. Their analytical method allows the analysis of concentrations much longer, therefore the elimination phase becomes flat, which results in a long t1/2kel. Then, to link with earlier observations, they often calculate what they call the first half-life. However, this is just the end of the distribution phase.

The last group of problems is related to not optimized single dose study design.

The t1/2kel after a single dose could be calculated properly only if fits all basic rules (see the table in my paper below):

• Sampling points number from t0–tmax: >2–5
• Time of sampling from t0–tlast: tlast>tmax + 3 x t1/2kel
• Number of C–T for kel analysis: >3–4
• Minimum sampling points per subject: >12–18
• Minimum sampling time: Tlast> 3xt1/2kel
• Analytical method: LLOQ 3xt1/2kel

Article Leave-one-out Procedure in the Validation of Elimination Rat...

Article Comparison of bioequivalence study regulatory requirements f...

Article Pharmacokinetics definitions in regulatory documents: transf...

Guidance for Industry Developing Medical Imaging Drug and Biological Products https://www.fda.gov/media/71212/download

Of course, its still only the peak of the iceberg ..... :-)

Hope it helps,

Best regards

Tomasz

David Salehi Thank you for your answer.

First, I don't understand why they have reported the half-lives with a "50%" before the phrase. I mean "50 % with a half-life of 0.7 hours and 50 % with a half-life of 12 hours". The half-life has the meaning of 50% in itself. Is there an English language barrier as the writers are not native English speakers or is there something that I don't know?

Unfortunately, the article has not cited the sentence so that I can track down the numbers.

If the two have-lives are for the drug and its next metabolite, then please let me know if the following sentence is true: the 18F-DOPA has a half-life of 0.7 hour and the next metabolite (18F-dopamine) has a half-life of 12 hours.

Tomasz Grabowski

Thank you for your detailed answer.

Dear David Salehi and Tomasz Grabowski

I'll give you an update on what is the answer. The corresponding author kindly provided me with the French text that those sentences were translated from. The "half-life" proceeding the "50%" were translation errors. The drug is eliminated thoroughly within 13 hours. I will copy the French text and the Google Translate English version here.

"Elimination

La 6-fluoro-(18F)-L-dopa est éliminée selon une cinétique bi-exponentielle avec une demi-vie d’élimination biologique de 12 heures (67 - 94 %) et une demi-vie d’élimination physique de 1,7 à 3,9 heures (6 - 33 %). Ces deux demi-vies semblent dépendre de l’âge. L’activité de 18F est éliminée par les reins, 50% sont éliminés après 0,7 heure et 50% après 12 heures.

Demi-vie

Sur la base de ces données, un modèle biocinétique a été développé pour la 6-fluoro-(18F)-L-dopa. Selon ce modèle, 100 % de l’activité de 18F est distribuée de façon homogène dans le corps et éliminée par les reins avec des périodes biologiques d’1 heure (50 %) et de 12 heures (50 %). Ce modèle est considéré comme indépendant de l’âge."

Translation:

6-Fluoro-(18F)-L-dopa is eliminated according to bi-exponential kinetics with a biological elimination half-life of 12 hours (67 - 94%) and a physical elimination half-life of 1. 7 - 3.9 hours (6 - 33%). Both of these half-lives appear to be age-dependent. The 18F activity is eliminated by the kidneys, 50% is eliminated after 0.7 hours and 50% after 12 hours.

Based on these data, a biokinetic model was developed for 6-fluoro-(18F)-L-dopa. According to this model, 100% of the 18F activity is evenly distributed in the body and eliminated by the kidneys with biological periods of 1 hour (50%) and 12 hours (50%). This pattern is considered to be independent of age.

I hope it helps.

Thanks Delaram. I always try to avoid translated papers when I am not expert in the field. I highly recommend starting to read a book about Positron Emission Tomography and then reading articles. One suggestion is

Bailey, Dale L. Positron Emission Tomography : Basic Sciences. New York: Springer, 2005. Print. Good luck.

Advances in PET: The Latest in Instrumentation, Technology, and Clinical Practice 1st ed. 2020 Edition by Jun Zhang (Editor), Michael V. Knopp (Editor)

David Salehi Thank you for your recommendations. I will certainly have a look at them.

Jefry Winner G

The elimination half-life of a drug is a pharmacokinetic parameter that is defined as the time it takes for the concentration of the drug in the plasma or the total amount in the body to be reduced by 50%. In other words, after one half-life, the concentration of the drug in the body will be half of the starting dose.

With each additional half-life, proportionately less of the drug is eliminated. However, the time required for the drug to reach half of the original concentration remains constant.

In general, the effect of the drug is considered to have a negligible therapeutic effect after 4 half-lives, that is when only 6.25% of the original dose remains in the body. e.g.

In the event that a 100 milligram (mg) dose of an intravenous drug with a half-life of 15 minutes is administered, the following would be true:

• 15 minutes after the drug administration, 50 mg of the drug remains in the body.
• 30 minutes after the drug administration, 25 mg of the drug remains in the body.
• 45 minutes after the drug administration, 12.5 mg of the drug remains in the body.
• 1 hour after the drug administration, 6.25 mg of the drug remains in the body.
• 2 hours after the drug administration, 0.39 mg of the drug remains in the body.