# How does Cmax decrease over time in human body? Use half life?

• freelooooo
In summary, the conversation discusses a scenario where a girl has tested positive for a banned substance in her system after using it 5 days ago. The substance has a half-life of 11 hours and initial values of Molar mass: 306.247 g mol-1, Tmax 2-4 hours, Cmax 363.3 ng / ml, and Half life: 11.21 hours. There is a discussion on how to calculate the ng/ml after 5 days at dosing 100mg, and the potential differences in concentration between someone weighing 80kg versus 100kg. The conversation also touches on the topic of pharmacokinetics and the possibility of the half-life not being constant over a long period of time
freelooooo
TL;DR Summary
Does Cmax decrease over time relative to the half life?
I'm interested in chemistry but it's all new for me and I'm just starting out. I tried to do some calculations but got stuck...

I was wondering, for example a supplement has the following values:

Molar mass: 306.247 g mol-1

Tmax 2-4 hours

Cmax 363.3 ng / ml

Half life: 11.21 hours

How do you calculate the ng / ml after 5 days at dosing 100mg? Since that 363 ng/ml is at the peak between 2-4 hours if I'm not mistaken?

If you use the half life calculation you get a value of ~0.097mg in the system but I assume that it differs per ml for how much someone weighs? Someone at 80kg is probably different then 100kg?

Welcome to PF.

jim mcnamara
berkeman said:
Welcome to PF.

Sorry, It was an article I read https://www.sportknowhowxl.nl/nieuw...dse-amateursporter-een-makkelijke-dopingprooi

it is saying the girl has used doping 5 days ago. The drug is not allowed in compeititon but she still got banned because there was some in the system. I tried to figure out how that works but got stuck with calculating what could be it.

It was very early for me so didnt read the second part correctly, but I've been trying to calculate it myself, see below. What I have been reading is a couple of studies and aditional websites

elimination of half life: https://www.sciencedirect.com/topic...s-and-molecular-biology/elimination-half-life
pharmacokinetics:
for blood volume: https://pubmed.ncbi.nlm.nih.gov/29873728/
the compound:

and this is my thought process:
If I'm not mistaken Cmax decreases with the same speed as the half-life so if you start with the 363.3 at the start.

Half-life 11h - Cmax 363.3
Monday: 363.3 - 181.5 ng/ml
Tuesday: 90.825 - 45.412 ng/ml
Wednesday: 22.706 - 11.353 ng/ml
Thursday: 5.676 - 2.838 ng/ml
Friday: 1.419 - 0.709 ng/mlCan also you calculate it also like this?:
Half-life 11h - dosage 100mg
Monday: 100 - 50 mg
Tuesday: 25 - 12.5 mg
Wednesday: 6.25 - 3.125 mg
Thursday: 1.562 - 0.7812 mg
Friday: 0.097 - 0.0488 mgAssume you have 6 liter blood, can you calculate it that way back to ng/ml?

0.0488 mg per 6 liter > (/6) > 0.00813 mg/l >(*1000) > 8.13 ng/ml

There is a big difference between Cmax ng/ml and the dosage ng/ml. Am I missing something? Or is that differences based on the test subject when they tested the Cmax of 363.3?

Of course there is lots of information missing but is the thinking process correct this way? And one small detail, are we always talking about mg/ml in your system or in your urine. Is that always the same or is there a delay?

Last edited:
If Tmax is 2-4 hours and you ask for 5 days (120 hours) you can probably safely ignore initial changes and assume initial concentration at t=0 to be 100 mg/body mass, then it is just an exponential decay with the given half life. Note that all data given are given as ranges, so at best you do calculations twice, assuming best/worst case scenario, and say "final concentration after five days should be somewhere between xxx and yyy".

And while that'll be better than nothing it won't be necessarily true. Half life of a drug doesn't have to be constant over long period of time, especially if it disappears due to some combination of metabolism and excretion.

berkeman said:
Welcome to PF.

Sorry, It was an article I read https://www.sportknowhowxl.nl/nieuw...dse-amateursporter-een-makkelijke-dopingprooi
it is saying the girl has used doping 5 days ago. The drug is not allowed in compeititon but she still got banned because there was some in the system. I tried to figure out how that works but got stuck with calculating what could be it.
Borek said:
If Tmax is 2-4 hours and you ask for 5 days (120 hours) you can probably safely ignore initial changes and assume initial concentration at t=0 to be 100 mg/body mass, then it is just an exponential decay with the given half life. Note that all data given are given as ranges, so at best you do calculations twice, assuming best/worst case scenario, and say "final concentration after five days should be somewhere between xxx and yyy".

And while that'll be better than nothing it won't be necessarily true. Half life of a drug doesn't have to be constant over long period of time, especially if it disappears due to some combination of metabolism and excretion.
That makes sense!

If I'm not mistaken Cmax decreases with the same speed as the half-life so if you start with the 363.3 at the start.

Half-life 11h
Monday: 363.3 - 181.5 ng/ml
Tuesday: 90.825 - 45.412 ng/ml
Wednesday: 22.706 - 11.353 ng/ml
Thursday: 5.676 - 2.838 ng/ml
Friday: 1.419 - 0.709 ng/ml

Can also you calculate it also like this?:
Half-life 11h - dosage 100mg
Monday: 100 - 50 mg
Tuesday: 25 - 12.5 mg
Wednesday: 6.25 - 3.125 mg
Thursday: 1.562 - 0.7812 mg
Friday: 0.097 - 0.0488 mg

Assume you have 6 liter blood, can you calculate it that way back to ng/ml?

0.0488 mg per 6 liter > (/6) > 0.00813 mg/l >(*1000) > 8.13 ng/ml

There is a big difference between Cmax ng/ml and the dosage ng/ml. Am I missing something? Or is that differences based on the test subject when they tested the Cmax of 363.3?

Of course there is lots of information missing but is the thinking process correct this way? And one small detail, are we always talking about mg/ml in your system or in your urine. Is that always the same or is there a delay?

Last edited:
Drugs dissolve in tissues and blood, so dividing by 6L is wrong - but if you divide by 60 kg of body mass (which is approx 60L), you will get very similar numbers.

## 1. How is Cmax affected by half-life in the human body?

The half-life of a drug refers to the amount of time it takes for the concentration of the drug in the body to decrease by half. As the drug is metabolized and eliminated from the body, its concentration (Cmax) will decrease over time in accordance with its half-life. The longer the half-life, the slower the decrease in Cmax.

## 2. What factors can influence the decrease of Cmax over time in the human body?

The decrease of Cmax over time can be influenced by a variety of factors such as the individual's metabolism and liver function, the route of administration, and the drug's chemical properties. Other factors such as age, weight, and overall health can also impact the rate of decrease.

## 3. Is there a general rule for how Cmax decreases over time in the human body?

There is no specific rule for how Cmax decreases over time in the human body as it can vary greatly depending on the drug and individual factors. However, in general, the concentration of a drug will decrease exponentially over time in accordance with its half-life.

## 4. Can the rate of decrease in Cmax be predicted using the half-life?

The half-life of a drug can give an estimate of the rate of decrease in Cmax over time, but it cannot accurately predict it. Other factors such as individual variability and drug interactions must also be taken into account.

## 5. How does the decrease in Cmax over time affect the effectiveness of a drug?

The decrease in Cmax over time can have a significant impact on the effectiveness of a drug. As the concentration of the drug decreases, it may no longer reach therapeutic levels in the body, resulting in a decrease in its effectiveness. This is why proper dosing and monitoring of drug levels is important to ensure optimal treatment outcomes.

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