Clinical Pharmacokinetics: Pharmacokinetic "Tools" (Constants)
Definition
Volume of fluid that would be necessary to contain the amount of drug in the body at a uniform concentration equal to that in plasma.
Assumes the body is a single homogeneous fluid compartment and the drug is evenly distributed
volume of distribution MAY OR MAY NOT match a physiologic space
volume of distribution may exceed the actual volume of the body
volume of distribution RARELY smaller than ECF (e.g. immunoglobulins - though they reach (non-bloodstream) ECF evenentually, it's often VERY slow).
Accurately predicts the plasma concentration that results when a certain amount of drug is present in the body.
Application
Defines concentration following one intravenous dose.
Roughly describes tissue penetration
Large volumes of distribution = good tissue penetration
Small volumes = poor tissue penetration.
Calculation
Volume of distribution = (Amount in Body) / (Concentration in Plasma)
Sample Problem
An Excel Spreadsheet that lets you "what if" with Volume of Distribution: http://cpharm.vetmed.vt.edu/vm8784/KINETICS/distrib.xls
Definition
Time for elimination of one half of the total amount in the body
Time required to decrease the plasma concentration by one half.
(mean the same thing, because the volume of distribution is the ratio between these two - see previous equation).
Application
Residues
Estimate the time necessary for complete (nearly) removal of the drug from the body
At 5 x T1/2, 97 % is eliminated.
At 10 x T1/2, 99 %+ has been eliminated
Limitations (won't be correct when...)
Drug sequestered in one or more tissues by covalent binding (small fraction of drug)
Drug metabolites may contribute to the residues
Expected half-life is altered by diseased in a particular patient
Half-life of elimination does not control residue
slow absorption tends to residues for most sustained release products
Approach to Steady State
Steady state plasma concentration (peak, average, and trough) are identical at all time points following each administered dose.
5 X T1/2 to reach 97% of steady state concentrations
Predicts time at which effect will no longer increase
Either starting treatment or upon altering dose and interval
Digoxin (T1/2 in the dog = 40 hours)
Maximum effects of digoxin may appear as late as 8 days after therapy is initiated.
Loading dose: the first dose of a drug, when a large dose (compared to the maintenance dose) is given to bring the drug in the body to the steady state amount.
Dose interval / half-life - determines need for loading dose
Example: Sulfadimethoxine (Albon) - labeled dose = 55 mg/kg PO, IV, or SQ initially, then 27.5 mg/kg once daily thereafter.
Used for sulfonamides with long half-lives
Not used with digoxin (therapeutic index too narrow)
Sample Problem
View the Half-Life Spreadsheet at http://cpharm.vetmed.vt.edu/vm8784/KINETICS/elim.xls
Definition
The rate constants of elimination are used with equations 1 - 3 to determine the rate of elimination of the drug from the blood stream.
Determination
One compartment λz = negative slope ln conc. versus time curve
Two compartment λz = negative slope of the terminal phase of ln conc. versus time plots
Application
Determine concentration at some time = t after dose
Determine clearance (see clearance)
Determines the half-life of elimination (half-life and elimination rate constants are really just two ways to say the same thing).
Definition
Classic (physiologic): total clearance is the volume of blood cleared of the drug by the various elimination processes (metabolism and excretion) per unit time. For the "drug" creatinine:
Clr = glomerular filtration rate
Clearance is a product of blood flow through the organs of elimination and the efficiency of extraction (the fraction of the blood flow is cleared during a given time period). This is "what's happening" in the body.
Mathematical (drugs and modeling): Clearance - a proportionality constant between the rate of drug and average plasma concentration (Cpave) such that:
Cpave = (rate of drug administration) / (Clearance)
Application
The most consistent pharmacokinetic descriptor
Between individuals of the same species
Between individual with the same disease
Central to the Application of pharmacokinetics
Average concentration prediction
Dose rate determinations
Adjustment of dosage (diseases or drug interactions)
If clearance and the desired average plasma concentration are known dosage rates can be calculated directly.
Determine patient drug clearance indirectly. (See Therapeutic Monitoring of Digoxin at http://cpharm.vetmed.vt.edu/vm8784/KINETICS/digoxin.htm).
Rate of administration directly related to "altered" clearance
Constant intravenous infusion - Cpave is the actual concentration at steady state equilibrium.
Intermittent forms of therapy - other constants must be used to describe peaks and troughs, but the average concentration (our usual target) is controlled only by dose rate and clearance.
Absorption rate constant (Ka) describes the rate of drug movement (oral, im, sc) into the circulatory system from the GI tract or injection site.
Rapid absorption may decrease total duration of effect (drug available for elimination earlier)
Rapid absorption leads to higher peak concentrations
Slow absorption may improve drug performance provided that therapeutic concentrations are reached and bioavailability is not compromised.
Formulation Factors
Concentration, tablet de-aggregation, dissolution rate, and volume
Patient Factors
Disease - integrity of membranes, blood flow, and tissue pH
Concurrent drug administration
Definition
F is the value assigned to drug bioavailability. The fraction of a dose absorbed (F) is the direct measure of the extent of drug absorption.
Absolute F for a non-intravenous route is determined by comparing the Area Under the Curve (AUC) of the concentration vs. time curve, for an intravenous dose to that for the non-intravenous route.
Relative F for two non-intravenous doses is determined by comparing the AUC's for the two doses. Drug products have equal bioavailability if the F for a single dose is the same.
Pharmacokinetic factors
The rate of elimination and distribution are the same for any dose form or route of administration. They have no effect on the difference in AUC for two routes of adminstration.
rate of absorption
Definition
Formulations are said to be equally BIOAVAILABLE if the amounts of drug reaching the systemic circulation following administration are the same.
The areas under the concentration versus time curves are the same but they MIGHT OR MIGHT NOT be the same shape.
Definition
Formulations are said to be BIOEQUIVALENT if the nature and extent of therapeutic and toxic effects are equal following the administration of equal doses.
Bioequivalence and bioavailability are used to compare two different formulations or routes of administration of a drug.
EQUAL BIOAVAILABILITY DOES NOT ASSURE BIOEQUIVALENCE
Therapeutic effect is controlled by the magnitude and duration of plasma concentrations the same peak and trough concentrations occurred at the same time. (concentration versus time curves ARE the same magnitude and shape.