Pharmacokinetics

Pharmacokinetics describes how the body affects a specific xenobiotic/chemical after administration through the mechanisms of absorption and distribution, as well as the metabolic changes of the substance in the body (e.g. by metabolic enzymes such as cytochrome P450 or glucuronosyltransferase enzymes), and the effects and routes of excretion of the metabolites of the drug. Pharmacokinetic properties of chemicals are affected by the route of administration and the dose of administered drug. These may affect the absorption rate.

Metrics

The following are the most commonly measured pharmacokinetic metrics: The units of the dose in the table are expressed in moles (mol) and molar (M). To express the metrics of the table in units of mass, instead of Amount of substance, simply replace 'mol' with 'g' and 'M' with 'g/dm3'. Similarly, other units in the table may be expressed in units of an equivalent dimension by scaling.

Pharmacokinetic metrics

Characteristic	Description	Symbol	Unit	Formula	Worked example value
Dose	Amount of drug administered.	$D$	$\mathrm {mol}$	N/A (Design parameter)	500 mmol
Dosing interval	Time interval between drug dose administrations.	$\tau$	$\mathrm {h}$	N/A (Design parameter)	24 h
Maximum serum concentration	The peak plasma concentration of a drug after administration.	$C_{\text{max}}$	$\mathrm {mmol/L}$	N/A (Direct measurement)	60.9 mmol/L
Minimum time for Cmax	Minimum time taken to reach Cmax.	$t_{\text{max}}$	$\mathrm {h}$	N/A (Direct measurement)	3.9 h
Minimum plasma concentration	The lowest (trough) concentration that a drug reaches before the next dose is administered.	$C_{{\text{min}},{\text{ss}}}$	$\mathrm {mmol/L}$	$C_{min}={\frac {SFDk_{a}}{V_{d}(k_{a}-k)}}\times \{{\frac {e^{-k_{e}\tau }}{1-e^{-k_{e}\tau }}}-{\frac {e^{-k_{a}\tau }}{1-e^{-k_{a}\tau }}}\}$	27.7 mmol/L
Average plasma concentration	The average plasma concentration of a drug over the dosing interval in steady state.	$C_{{\text{av}},{\text{ss}}}$	$\mathrm {h\times mmol/L}$	${\frac {AUC_{\tau ,{\text{ss}}}}{\tau }}$	55.0 h×mmol/L
Volume of distribution	The apparent volume in which a drug is distributed (i.e., the parameter relating drug concentration in plasma to drug amount in the body).	$V_{\text{d}}$	$\mathrm {L}$	${\frac {D}{C_{0}}}$	6.0 L
Concentration	Amount of drug in a given volume of plasma.	$C_{0},C_{\text{ss}}$	$\mathrm {mmol/L}$	${\frac {D}{V_{\text{d}}}}$	83.3 mmol/L
Absorption half-life	The time required for 50% of a given dose of drug to be absorbed into the systemic circulation.	$t_{{\frac {1}{2}}a}$	$\mathrm {h}$	${\frac {\ln(2)}{k_{\text{a}}}}$	1.0 h
Absorption rate constant	The rate at which a drug enters into the body for oral and other extravascular routes.	$k_{\text{a}}$	$\mathrm {h} ^{-1}$	${\frac {\ln(2)}{t_{{\frac {1}{2}}a}}}$	0.693 h−1
Elimination half-‍life	The time required for the concentration of the drug to reach half of its original value.	$t_{{\frac {1}{2}}b}$	$\mathrm {h}$	${\frac {\ln(2)}{k_{\text{e}}}}$	12 h
Elimination rate constant	The rate at which a drug is removed from the body.	$k_{\text{e}}$	$\mathrm {h} ^{-1}$	${\frac {\ln(2)}{t_{{\frac {1}{2}}b}}}={\frac {CL}{V_{\text{d}}}}$	0.0578 h−1
Infusion rate	Rate of infusion required to balance elimination.	$k_{\text{in}}$	$\mathrm {mol/h}$	$C_{\text{ss}}\cdot CL$	50 mmol/h
Area under the curve	The integral of the concentration-time curve (after a single dose or in steady state).	$AUC_{0-\infty }$	$\mathrm {M} \cdot \mathrm {s}$	$\int _{0}^{\infty }C\,\mathrm {d} t$	1,320 h×mmol/L
		$AUC_{\tau ,{\text{ss}}}$	$\mathrm {M} \cdot \mathrm {s}$	$\int _{t}^{t+\tau }C\,\mathrm {d} t$
Clearance	The volume of plasma cleared of the drug per unit time.	$CL$	$\mathrm {m} ^{3}/\mathrm {s}$	$V_{\text{d}}\cdot k_{\text{e}}={\frac {D}{AUC}}$	0.38 L/h
Bioavailability	The systemically available fraction of a drug.	$f$	Unitless	${\frac {AUC_{\text{po}}\cdot D_{\text{iv}}}{AUC_{\text{iv}}\cdot D_{\text{po}}}}$	0.8
Fluctuation	Peak–trough fluctuation within one dosing interval at steady state.	$\%PTF$	$\%$	$100{\frac {C_{{\text{max}},{\text{ss}}}-C_{{\text{min}},{\text{ss}}}}{C_{{\text{av}},{\text{ss}}}}}$ where $C_{{\text{av}},{\text{ss}}}={\frac {AUC_{\tau ,{\text{ss}}}}{\tau }}$	41.8%

See Also

• Wikipedia article