It is the integral of the plasma concentration-time profile from time zero to time infinity.
It has units of mass-time/volume.
The area under the curve after an iv administration is dependent on the administered dose and the total body clearance.
The first-order renal excretion rate constant is the rate constant for the drug elimination by the kidney. The renal excretion rate constant is dependent on the renal clearance and the volume of distribution.
For cone-compartment model:
For two-compartment model:
This rate constant represents drug elimination by the kidney in the urine. The renal excretion rate constant cannot be bigger than the overall elimination rate constant (k). When the drug is excreted entirely through the kidney, the renal clearance will be equal the total body clearance and the renal excretion rate constant will be equal to the overall elimination rate constant.
The first-order renal excretion rate constant has units of time-1.