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Important parameters in the Fish Tank 3 : Mean Residence Time and Protein Binding

Important parameters in the Fish Tank 3 : Mean Residence Time and Protein Binding
Another way to explore the exposure of drug to the body is with the mean residence time. The mean residence time is the average time that a drug molecule stays in the body. It’s shown by the equation MRT equals 1 over K. Now, it’s interesting to take a closer look at how the MRT relates mathematically. It represents the point at which 36.8 of percent of the drug is still remaining in the body. The reason this holds true. Remember we said that e to the minus KT is the percent remaining. Now since MRT equals 1 over K, when the time is equal to the MRT, we can substitute 1 over K for T in the e to the minus 8 KT equation.
Such that it equals e to the minus 1, which is always 0.368. So what this tells us? It’s that when the time is equal to the mean residence time 63.2% of the drug that was in the body has been eliminated and 36.8% of the drug is remaining. It might seem strange that much more of the drug has already been eliminated when we reached the mean residence time, the average time for a drug molecule to remain in the body. But keep in mind that when the sermon concentration is greater, the rate of elimination is also greater. So we would expect more drug to be eliminated during the first half of a drug molecules residence in the body.
Then the second half in terms of the overall drug in the body, we know that area under the curve equals the concentration at time zero divided by K and area under the curve therefore since MRT equals one over K, area under the curve can also be represented by the equation concentration at time 0 times MRT. This is illustrated in the in the graph shown the “Green rectangle” is what results when we multiply the concentration at time 0 times the mean residence time which for this drug with a k’ of 0.25 1 over K is 4.
So the mean residence time is 4 hours What that tells us is that the area under the curve that’s shown during those four hours from the concentration at time 0 is 30 milligram hours per liter, which is the same area under the curve that we would get for the blue curve for the entire duration of drug elimination Just as an easier way of representing the area under the curve for that mean residence time. Now let’s pause the video for another question. Area under the curve increases when the dose is increased. That’s a true statement. It increases when dose is increased. B is also true.
It increases when clearance decreases remember the equation is area under the curve equal dose divided by clearance. Area under the curve is the same after one dose as it is between multiple doses . This is also a true statement. It’s independent of the dosing interval. But it depends on the dose and as long as the dose does not change the dosing interval can change and the area under the curve between doses will be the same. So the answer to this question is E, all of the above, A, B and C. Now, let’s take a look at protein binding, which can also influence serum concentrations.
The fu is the fraction unbound which represents the fraction of the concentration of unbound drug divided by the total concentration of drug . If fu increases, the fraction unbound of drug increases which means that the protein binding of the drug decreases. We can say that clearance will increase the distribution or the volume of the drug will increase and the pharmacologic effect will increase. So protein binding affects many aspects of drug action in the body and also the pharmacokinetics of the drug in the body. Now keep in mind that this only matters if the drug is more than 80% protein bound. Otherwise, fraction unbound changes are not clinically significant.
The reason that proteins have such impact on the clearance and the volume of distribution, and the pharmacologic effect of the drug is that proteins are extremely large molecules when the protein is attached to the drug it impairs the ability of the drug to be eliminated from the blood and thereby preventing elimination. It blocks the drug from attaching to drug receptors so it impacts the pharmacologic effect of the drug and it prevents the drug from crossing membranes so it impacts the volume of distribution of the drug. All of these occur because proteins are so large in comparison to the size of most drug molecules. Now let’s take a closer look at how protein binding affects clearance.
Protein can be thought of as protecting fish from being trapped by the net. Okay if I am catching fish in a net. Okay it’s easy to catch an unbound fish in the net as I pull it through the fish tank. However, when that fish is bound to a protein molecule the protein is so large that it prevents the net from capturing the fish. So in effect, protein protects fish from being cleared, from being eliminated from the blood. So if the protein is attached to the drug molecule, that’s protected if the protein is then detached and the drug molecule is unbound as part of the fraction unbound, the drug is then able to be cleared.
So the higher the percentage of drug that is not bound to protein the greater the clearance of that drug regardless of the size of the net. This means that fraction unbound provides less protection. So it causes the drug clearance to be increased.

Prof. Brown illustrates the definition of Mean Residence Time (MRT) in this video. MRT is a measure of drug exposure over time.

He also explains that under some conditions, protein binding will affect clearance (CL), volume of distribution, and pharmacologic effect. We will learn the detail in the next video.

The brain exercise this time is about the relationship between AUC, clearance (CL), and the dose. Do you have any questions? Feel free to leave them below.


Prof. Daniel L. Brown

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Clinical Pharmacokinetics: Dosing and Monitoring

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