Key Formulas

The following formulas and definitions should be understood so well that they are essentially memorized. You should be able to use them in solving problems. Consult other portions of these notes for details and qualifications of these terms and formulas.

Major Pharmacokinetic Parameters
Vd -- Volume of distribution Ke -- Elimination rate constant and t1/2 -- elimination half-life CL -- Clearance F -- Bioavailability

Formulas for Estimating and Adjusting Dose Rate
Dose Rate = Desired C(ss) * CL (mg/h) = (mg/L) (L/h)*
Adjusted Dose Rate = Initial Dose Rate * (Desired C(ss) / Measured C(ss))
Note that C(ss) will usually be expressed as concentration in plasma (Cp(ss)). The concentration can be a peak, mean, or trough value. "Desired" and "Measured" must be in the same terms, i.e., both peak, mean, or trough. In most practical clinical pharmacokinetics, the "trough" (sample taken when the next dose is given) is the most accurate value.

Formulas for Estimating and Adjusting Dose Rate

Dose Rate = Desired C(ss) * CL
(mg/h) = (mg/L) * (L/h)

Adjusted Dose Rate = Initial Dose Rate * (Desired C(ss) / Measured C(ss))

Note that C(ss) will usually be expressed as concentration in plasma (Cp(ss)).
The concentration can be a peak, mean, or trough value. "Desired" and "Measured" must be in the same terms, i.e., both peak, mean, or trough. In most practical clinical pharmacokinetics, the "trough" (sample taken when the next dose is given) is the most accurate value.

Formulas for Estimating Concentration
When Amount of Drug in Body Can Be Estimated*

Cp = Amount of Drug in Body / Vd
(mg/L) = mg / L

	Amount of Drug in Body / Kg
Cp =	--------------------------------------
	Vd / Kg

mg/L = (mg/Kg) / (L/Kg)

*Amount of drug in the body at "zero time" is the dose for a single, rapidly absorbed drug with a bioavailability of 100%. This can be used to obtain an estimate of Cp(0).

Note that the preceding formula can be rearranged to provide an estimate of the amount of drug in the body, a loading dose (DL), or a volume of distribution (Vd). You should be comfortable in using it in all of its forms.

Estimation of Concentration at "Zero Time"
Cp(0) = (F * D) / Vd mg/L = (fraction * mg) / L
*This estimate is reasonably valid for rapidly absorbed drugs. Note that Dose (D) and Vd can also be expressed in terms of body mass, i.e., mg/Kg and L/Kg.

Estimation of Concentration at "Zero Time"

Cp(0) = (F * D) / Vd

mg/L = (fraction * mg) / L

*This estimate is reasonably valid for rapidly absorbed drugs.
Note that Dose (D) and Vd can also be expressed in terms of body mass, i.e., mg/Kg and L/Kg.

Estimation of Concentration at a Specified Time
After Administration of Drug*
Cp(t) = Cp(0) * e^{-(Ke * t)} (mg/L) at time "t" = (mg/L) @ time "0" frcn remaining at time "t"*
Can also be used to estimate concentration at a specified time after a known* concentration. Replace the Cp(0) with Cp(known).

Estimation of Concentration at a Specified Time
After Administration of Drug*

Cp(t) = Cp(0) * e^{-(Ke
* t)}

(mg/L) at time "t" = (mg/L) @ time "0" * frcn remaining at time "t"

*Can also be used to estimate concentration at a specified time after a known concentration. Replace the Cp(0) with Cp(known).

Relationship Between Clearance and Elimination Rate*
Ke = CL / Vd frcn/h = (L/h) / L
*Be sure you can rearrange this formula to obtain Vd or CL for use when the other values are known.

Relationship Between Clearance and Elimination Rate*

Ke = CL / Vd

frcn/h = (L/h) / L

*Be sure you can rearrange this formula to obtain Vd or CL for use when the other values are known.

Relationship Between Elimination Rate and Half-Life*
Ke = 0.693 / half-life frcn/h) = 0.693 / h
*Be able to rearrange this formula to find half-life