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Dosing Rate Equation

Point of the equation




Intravenous Infusion Equation

Dosing Rate = CL x Css

where CL = Clearance Css = steady state concentration of the drug

The clinician wants to maintain a steady-state concentration of a drug within the therapeutic window, so he'll administer the drug at the same rate that it is eliminated.



Css = infusion rate



Clearance Equation


CL = rate of elimination



You'll want to add the clearance rates of different organs together in order to get the total clearance from the body


Do most drugs obey first order or zero order kinetics?

What does your choice for answer one look like on a graph where both the X (time) and Y (concentration of drug) axes are linear?

What about on a graph where Y axis is log concentration of drug and X axis is linear time?

Most drugs obey first order kinetics

A first order reaction is an exponential decay function on a linear graph

A straight line is obtained when the y-axis is log and the x-axis is linear


What does the slope of a first order reaction plotted on a log/linear graph represent?

It is the elimination rate of the drug. Because the elimination rate of the drug is equal to the slope of a linear curve, we can infer that a CONSTANT FRACTION of the drug is eliminated per unit of time. This also means that there is a half-life associated with first order reactions.


Describe elimination of a drug that follows first order kinetics

BUZZ WORD: Fraction. A CONSTANT FRACTION of the drug is eliminated per unit of time, so the absolute amount of drug removed will be concentration-dependent, and there will be a half-life associated with the elimination. There will be a plateau.


Half life in a first order reaction

The time it takes for the plasma concentration or the amount of drug in the body to be reduced by 50%. So on a graph, if your total administered concentration was 8 CCs (or whatever), find the time at which the concentration becomes 4 CCs in the blood, and that will be your half life. 


Volume of distribution: sometimes it describes a primary fluid compartment, and other times it has no relationship to how the drug is distributed in the body. If there were a correlation, though, list the main compartments and their volume

Plasma Volume: 4 Liters

Extracellular Fluid Volume: 12 Liters

Total Body Water: 40 Liters


Half Life Equation

T1/2 = (0.7)(Vd)



T1/2 = (0.7)



Dosing rate equation that accounts for an oral medication's bioavailability 


Explain the subtle change in the equation when a doctor is giving maintenance doses after administering a loading dose

F x Dosing Rate = CL x Css


F = bioavailability

CL = Clearance

Css = Steady State

Follow the same equation, except the question stem might say something like "target steady state" instead of just steady state. 


Equation that determines steady state concentrations after various dosing schedules AND accounts for bioavailability 

Css = (F x Dose)

           CL x T


T = the dosing interval

F = bioavailability 

Also notice that this equation is just a slight rearrangement from the equation that accounts for bioavailability, but not for a dosing schedule


What is the bioavailability of a drug administered by IV?



How many half lives does it take to reach a steady state?

5 half lives

The time to steady state is strictly dependent on half life. It does not matter how much medicine the doctor gives or how frequently he gives it. 


Loading Dose Equation and the reason for giving a loading dose

LD = (Css x Vd)



Loading doses are given when the doctor does not have time to wait for 5 half lives to achieve a therapeutic range (e.g. heart attacks). Loading doses can be dangerous due to the high concentrations that are achieved. The same equation is used regardless of whether you have a zero order or first order kinetic drug. 


Zero Order Kinetics

Zero order kinetics work like a Michaelis-Menten equation in that you'll have saturation of the enzyme metabolizing the drug, as well as Km, which is the dose that produces 50% of the maximal elimination rate. Vm is the maximum rate of the process. Example drugs are ethanol, aspirin, and heparin. 

BUZZ WORDS: Amount. The same AMOUNT of drug is metabolized regardless of the level of the drug. In addition, NO PLATEAU IS OBSERVED.


Volume of distribution equation

Vd = amt admin

        plasma conc



A drug has a half life of 24 hours. If administered every 12 hours, when will it reach steady state? When will it reach steady state if administered every 8 hours?

I do not know the numerical answers to these questions, but the principal is that steady state will be achieved at the same time, regardless of rate of administration. Recall that in first order kinetics, time to steady state is independent of dose or dose interval. It is strictly dependent on half life (plateau principle)


When discussing clearance, what is the most important limiting variable?

Blood flow to the organ is the limiting variable. 


Long-winded saturation kinetics (zero order kinetics) that I THINK I remember correctly from class: 

Assuming it takes one hour to metabolize a standard size drink: Scott, Tyler, Colby, and Stephanie go out to paint the town red after a test. Stephanie is clearly the over-zealous drinker of the group, so she naturally makes the poor choice to consume four standard size glasses of wine (5 oz) in four minutes at the beginning of the hour. Colby tries to keep up and manages to drink 3 standard size glasses of beer in about a half hour. Scott joins the debauchery and also drink 3 glasses of standard size beer in about 40 minutes. Finally, Tyler is milking old man status and claims he can only drink one beer before being absolutely off his face. Who metabolizes his drink fastest? Who gets to drive home two hours post-painting (bc Stephanie has gone and gotten sick on Tyler's trainers)?

Nobody metabolizes anything faster than anyone else. Each person takes an hour to metabolize one drink, so two hours later, Stephanie will still be wine-drunk and left with 10 oz of wine to muddle through. Colby and Scott will be nearly done - just one beer left to sort out, and Tyler will drive everyone home as soon as he finds his driving gloves and hat.