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 therapeutic index is the ratio of the median lethal dose (LD50, the dose that kills 50% of the animals) to the median effective dose (ME50, the dose that produces a therapeutic effect in 50% of the animals).
Large therapeutic index means that there is big difference between the lethal and the effective dose of the drug which indicates that the drug is relatively safe. Drugs with large therapeutic index usually have wide therapeutic range.
However, small therapeutic index means that there is small difference between the lethal and the effective dose of the drug which indicates that the drug is relatively not safe. Drugs with small therapeutic index usually have narrow therapeutic range.