## Mean Residence Time (MRT): Understanding How Long Drug Molecules Stay in the Body

When I first began learning about pharmacokinetics, I was often confused by the mean residence time (MRT) parameter. I wasn’t really sure what it meant, how to interpret the value, and why it would ever be important. After many years of working with pharmacokinetic analysis, I still do not use MRT very often, but I now have a better appreciate of what it is telling me so that I can use it properly, if needed.

To discuss MRT, we need to change the conversation from the concentration of drug in the body at a given time to the residence time of individual molecules in the body. The idea behind calculating the mean residence time is that each molecule spends a different amount of time in the body, with some molecules lasting a very short amount of time and others lasting longer. You can plot the relative frequency of the residence time in the body, and it looks like a concentration-time curve.

Another way to look at MRT is to use a thought experiment. Imagine we could inject exactly 10 molecules of a drug into the blood stream, and then could measure when each molecule left the body. The data is presented below:

Molecule # Time in the body (min)
1 8.1
2 18.2
3 30.9
4 43.2
5 60.0
6 79.8
7 107.1
8 139.2
9 171.3
10 198.2

Note: Data from Parameters for Compartment-free Pharmacokinetics, Willi Cawello (Editor), 1999.

The half-life of the drug is the time to eliminate 50% of the drug in the body. In this case, the 5th molecule is eliminated at 60.0 minutes. The MRT is calculated by summing the total time in the body and dividing by the number of molecules, which is turns out to be 85.6 minutes. Thus MRT represents the average time a molecule stays in the body.

The generalized equation for an intravenous bolus injection is as follows: $MRT=\frac{\sum {N_i*t_i}}{\sum {N_i}}$
where ti is residence time and Ni is the number of molecules with a given residence time (or all molecules for the denominator).

We can assume that every molecule that enters the body will also leave the body. So we can substitute Dose for Ni using the following relationship: $\sum {N_i} = \int_0^{Dose} dA(t) = Dose$

Finally, for drugs with linear kinetics, the amount in the body is proportional to the concentration in plasma at all time points. By making these substitutions, we can arrive at the following for MRT calculations: $MRT= \frac{\int_0^{\infty} tC(t)dt}{\int_0^{\infty} C(t)dt} = \frac{AUMC}{AUC}$

where AUMC is the area under the first moment curve or the curve of concentration*time versus time.

The calculation is more complex if you have a route of administration other than IV bolus because you have to account for the time required for the drug to enter the body. This is often called the mean input time (MIT). In this situation, the following equation would be used: $MRT = \frac{AUMC}{AUC} - MIT$

There are many methods for estimating MIT depending on the type of dose administration.

So, why is MRT important? It can be used to estimate the average time a drug molecule spends in the body. It can also be used to help interpret the duration of effect for direct-acting molecules (e.g. blood pressure lowering agents). It should be noted that MRT is highly influenced by the measurements in the terminal phase. If there are inadequate samples to accurately estimate the terminal elimination rate constant, MRT estimates will be unreliable. 