Most prescription drugs are administered repeatedly for a limited duration (for acute illnesses) or for an extended period of time (for chronic conditions). As such, it is important to understand the pharmacokinetic behavior of drugs when they are administered according to repeat-dose regimens.

1. Medication Half Life Calculator

Single-Dose PK BehaviorFor the purpose of this discussion, we will use single-dose IV bolus administration as the starting point. Let’s assume we administer 500 mg of a drug into a hypothetical volume of 10 liters. Since the full IV bolus dose is administered at once, we will see an initial concentration of 50 mg/L (500 mg / 10 L of volume = 50 mg/L).The human body has evolved multiple mechanisms (, etc.) that allow for elimination of drugs and other substances. As a result, immediately following the initial bolus dose, drug concentrations will begin to decline.We frequently describe this decline in terms of half-life (the time required for concentration to decline by 50%). If our hypothetical drug has a half-life of 3 hours we would observe a concentration of 25 mg/L at three hours post-dose, a concentration of 12.5 mg/L at six hours post-dose, a concentration of 6.25 mg at 9 hours post-dose, etc. If no further doses are administered, the concentration will continue to decline by an additional 50% every 3 hours.

Superposition of Repeated DosesWhat if a second 500 mg dose is given at the 6-hour mark? For most drugs, the concentrations produced by this second dose would be comparable to concentrations produced by the first dose. However, at the 6-hour time point we still have 12.5 mg/L of drug remaining from the first dose, as described above.So, immediately following the second dose, we will have 12.5 mg/L remaining from the original dose, plus an additional 50 mg/L resulting from the dose that was just administered. This gives a combined observed concentration of 62.5 mg/L. Each additional 50 mg dose will produce concentrations comparable to the very first dose. However, the concentration we observe will be the sum of concentrations remaining from each prior dose combined with concentrations from the most recent dose.For example, a third dose delivered at the 12-hour time point will also produce an initial concentration of 50 mg/L. The concentration remaining from the second dose would be 12.5 mg/L, and the concentration remaining from the first dose would be 3.125 mg/L.

If we combine all of these concentrations, our observed concentration would be 50 mg/L + 12.5 mg/L + 3.125 mg/L ≈ 65.6 mg/L (an additive combination of concentrations from the first, second, and third doses).The process of adding concentrations from multiple doses to determine the observed concentrations is often referred to as the principle of superposition. The pattern of superposition described above assumes that each dose behaves approximately the same despite rising concentrations.It is important to note that simple, additive superposition is approximately true for very many drugs. However, superposition of exposures can become more complicated when the PK behavior of each dose changes as concentrations rise (e.g., drugs with saturable clearance, such as phenytoin). For the remainder of this discussion, we will stick with the simple, additive superposition scenario.

Reaching Steady StateSuccessive doses will result in increasing concentrations of the drug in the body until a plateau is reached. This plateau is called steady state. At steady state, the amount of drug administered on each dosing occasion is matched by an equivalent amount of drug leaving the body between each dose (rate in = rate out).At steady state, concentrations will rise and fall according to a repeating pattern as long as we continue to administer drug at the same dose level and with the same time period between doses. This repeated time period of dosing is often called the dosing interval and is abbreviated using the Greek letter tau (τ). Drug accumulation and attainment of steady state does not require IV bolus dosing. It is possible to observe a similar pattern of accumulation and attainment of steady state for virtually any route of administration.For most drugs, it takes roughly 5 half-lives to reach an approximate steady state.

It follows that, the time to steady state during a repeat-dose regimen is dictated by the half-life of the drug. Intuitively we might think that increasing the dose or giving doses more frequently would accelerate attainment of steady state.

However, neither of these changes will alter the speed at which steady state is achieved.Changing the dose or dosing interval will affect the concentrations achieved at steady state, but not the time required to achieve steady state. Some drugs have quite prolonged half-lives (days to weeks, or longer). For drugs with extended half-lives we may not be able to wait the necessary 5 half-lives to reach a desired steady state concentration.

When time is crucial (such as antibiotic use for critical-care patients), there is a method to achieve steady state more rapidly: the loading dose.A loading dose is an initial dose (or series of doses) intended to quickly achieve desired concentrations. A loading dose typically won’t achieve steady state on its own (that would take 5 half-lives).

However, once the desired concentrations are achieved with a loading dose, a repeat-dose (maintenance) regimen can be started at a lower dose level. If calculated correctly, this new maintenance regimen will maintain stable steady state exposure for the remaining duration of repeated drug administration. AUC and AccumulationFollowing a single dose, we can easily calculate the area under the concentration-time curve from zero to infinity (AUC 0-∞) as a measure of overall drug exposure. During repeat-dose administration we often calculate the AUC during a steady state dosing interval (AUC 0-τ) as a measure of overall drug exposure.

Medication Half Life Calculator

Interestingly, if clearance remains constant for a drug (no change in CL with increasing concentrations), AUC 0-τ at steady state will be identical to the AUC 0-∞ following single-dose administration.This equivalence assumes that the dose level administered as a single dose is identical to the dose level administered in the repeat-dose regimen. This AUC equivalence proves useful in terms of calculating PK parameters. For example, following a single IV bolus dose, we can calculate CL using the following expression: CL = Dose/ AUC 0-∞. AUC equivalence allows us to estimate CL using steady state AUC 0-τ: CL = Dose/ AUC 0-τ. The latter clearance estimate is frequently termed steady state clearance (CL,ss). ConclusionsMost drugs will deviate from the ideal accumulation pattern described above to some extent. However, understanding the principle of superposition allows for reasonable predictions of repeat-dose PK behavior for a very large number of drugs.

This becomes particularly useful when progressing from single-dose studies to repeat-dose studies for the first time during drug development. This knowledge also enables us to design repeat-dose regimens that efficiently and reliably achieve desired concentrations within a clinically-acceptable time frame.Have more questions about designing single-dose vs. Related Articles.

Recently I made an Excel spreadsheet that lets you calculate the amount of any given drug that's in your body, given its half life. The spreadsheet is designed to be useful in figuring out how long to spend tapering off drugs. It is designed to answer questions such as:'I want to taper off Lexapro, which has a half-life of 14 days. I just cut my dose in half. How many days should I wait until cutting my dose in half again?' I am not a doctor, this is not medical advice and following it will probably kill you, etc.)You can download this table here:Delete the Megafileupload from the beginning of the filename or else Excel won't let you open the file.Here is an explanation of what all the columns mean and how to use the spreadsheet:Half Life: Replace the default (14) with the half-life of the drug you want to taper off. This can be any number of days.Elimination Constant: There is no need to change anything here, it will update automatically when you change the half-life.

This represents K in the following article: K in the following article:Temp data (see instructions): This is generated from automatically based on the half-life you enter. See the next section for what to do here.Amount left in body: This is NOT UPDATED AUTOMATICALLY. In order to update this column, copy cells B2-B366. Then paste by value into column C. To do this highlight cells C2-C366 with your mouse, then right click and select Paste Special. Then select Values. This allows you to reverse sort the data, which you should now do.

Highlight cells C2-C366, then go to the data menu and click on sort. Then click on continue with current selection. Then click descending.What this shows you is the amount of the drug left in your body after X days. For example, if you take 5mg of Lexapro on day 1 (14 day half life) then on day 14 you would have 2.5mg of Lexapro from that day left in your body. The sum of all the numbers in this column is the total amount of the drug in your body, assuming you have been taking the same amount of the drug every day for a year.Taper Curve: Cell D2 is the total amount of drug X in your body assuming you have been taking the same amount every day indefinitely.

So for example, if you have been taking 1mg of Lexapro per day (Half life 14 days) then the total amount of Lexapro in your body would stabilize at 20.7mg after a couple months. Cell D3 is the total amount of the drug in your body after your first day of halving the drug. The rest of this column shows how the amount of the drug in your body declines after halving your dose, until the total amount of the drug in your body eventually settles at an equilibrium. (This equilibrium is obviously half the amount it used to be on your original dose.)Percent Complete: This shows how close your body is to having the new equilibrium amount of the drug in it after halving the dose.

On day 1 the percentage is 200%, because you haven't yet halved your dose. After this it gets closer and closer to 100%, which is the equilibrium for your new dose.Graph: I think this should be updated automatically. It's just a visualization of how quickly your body reaches its new equilibrium after halving your dosage.NOTE: In practice this spreadsheet is mostly useful for drugs with half-lives of at least a few days.

This is because there are two factors at work with tapering off a drug: The amount of a given substance in your body, and the rate at which your brain can adapt to the reductions in that substance. With drugs with very long half-lives, like many SSRIs, if you halve your dose then the amount of the drug in your system will be gradually falling for several weeks before eventually leveling out. This rate of decline is slow enough that your brain chemistry will adapt as the amount of the drug in your system is gradually falling. Thus the most important thing is to know how much of the drug is in your system, so that you know when to halve your dose again.However, with drugs like benzos that have very short half-lives, when you halve your dose it will only take a couple of days before you reach a new equilibrium in the amount of drug in your body.

This is much too fast for your brain chemistry to catch up. Because of this you will either want to shave tiny amounts off your pill for a couple months, or else halve your dose and then stay there for a while. Obviously this isn't very much information to go on, which is why I said that this spreadsheet won't be very useful for drugs with short half-lives. (However, this spreadsheet may still have some value for calculating the risk of drug interactions, assuming I didn't mess anything up.).