The steady state is the condition when the rate of drug administration is equal to the rate of drug elimination.

When the drug is administered as a constant rate IV infusion, there will be one steady state concentration as long as the rate of administration and the rate of elimination do not change.

When drug administration involves repeated doses, the drug concentration-time profile during each of the dosing intervals ( τ ) will be identical at steady state. This means that the maximum, the minimum, and the average concentrations during each dosing interval will be similar at steady state.

The idea is to transform the nonlinear Michaelis-Menten equation to a linear equation

This is equal to:

Rearrangement yields:

Dividing by F Cpss

This is an equation of a straight line. Plotting the dosing rate versus the total body clearance (dosing rate/Cpss) produces a straight line. The resulting line has a slope of -K_m and y-intercept equals V_max/F.

The slope of a straight line is the rate of change of the dependent variable (the variable plotted on the Y-axis) relative to the change of the independent variable (the variable plotted on the X-axis). A straight line has one slope (constant slope), however the slope of a curve is changing at different points on the curve.

The slope of a straight line is the rate of change of the dependent variable (the variable plotted on the Y-axis) relative to the change of the independent variable (the variable plotted on the X-axis). A straight line has one slope (constant slope), however the slope of a curve is changing at different points on the curve.

It is the Michaelis-Menten constant. It is a qualitative characteristic of how an enzyme interacts with the substrate and is independent of the enzyme concentration. K_m is equal to the substrate conc when the reaction rate is half its maximum value (1/2 V_max).

K_m has units of concentrations (amount/volume).

Conditions such as the presence of a competitive inhibitor can result in increasing K_m. This is because at any given drug conc the rate of drug metabolism is slower in presence of a competitive inhibitor compared to the rate in absence of the inhibitor.

In enzyme kinetics V_max is the maximum rate of the enzymatic reaction. For drug metabolism in vivo, V_max is the maximum rate of drug metabolism by a specific pathway.V_max has units of amount per time and can also have units of concentration per time.

The maximum rate of drug metabolism is dependent on the amount of enzyme available for drug metabolism via a specific pathway. Enzyme induction results in increasing the amount of the enzyme and V_max.

Diseases that affect the liver (the primary organ for drug metabolism) may result in decreasing the metabolic capacity for metabolic pathways and decreases V_max. Also, V_max may depend on the size of the patient. Children may have lower V_max compared to adults.