Drug clearance has units of mL/min.
Clearance_Total = Renal clearance (ke*Vd)+ Hepatic clearance (km*Vd) + Lung Clearance (kl*Vd) = (ke+km+kl)*Vd = k*Vd; e is for excreted; m is for metabolized and l is for lung.
Cp = plasma concentration
Elimination rate = Cp*Clearance_T
Clearance_Total = elimination rate/Cp= k*Vd
What does the volume of distribution mean? In clinical practice, what kinds of Vd can one expect to see?
Penicillin has a Clearance_T of 15 ml/min. Note that the elimination rate is a function of plasma concentration. If the Cp = 2 ug/mL, then the elimination rate is 30 ug/min.
Conversely, if you new what the clearance rate of penicillin was: i.e., 30 ug/min and you divide by the Cp, 2 ug/mL then you know what the clearance_T is 15 mL/min.
Cl * integral(0 to infinite) of Do/C(t) dt =integral(dDexcreted)
Clearance_Total = Do/AUC
Do =integral(0 to infinite) of Cp(t) dt (this is true iif Cl=1)
Renal_Clearance_rate = excretion rate/plasma concentration = dDu/dt / Cp = rate of urine flow * drug concentration in urine / plasma concentration = Qu * Cu / Cp
Renal_Clearance_rate = [filtration rate + secretion rate – reabsorption rate]/Cp
Inulin reference:
Clearance_drug /Clearance of inulin < 1 => The drug is partially reabsorbed
Clearance_drug /Clearance of inulin = 1 => The drug is filtered only
Clearance_drug /Clearance of inulin > 1 => The drug is actively secreted
Note that:
dDu/dt = ke*Vd*Cp = Clearance_renal_rate*Cp so Ke = Clearance_renal_rate/Vd
If the reabsorption fraction is fr then dDu/dt = Clearance_renal_rate(1-fr)*Cp
dDu/dt = Clearance_renal_rate*Cp
rearrange terms and
integrate from 0 to Du of dDu = Clearance_renal_rate*integral from 0 to t of Cp dt
[Du]0 to t = Clearance_renal_rate*[AUC]0 to t
As you plot the drug excreted at time t as a function of the AUC at time t then the slope is the Clearance_renal_rate.
Once can also state that:
[Du]0 to infinite = Clearance_renal_rate*[AUC]0 to infinite
The fraction excreted, fe, can be calculated by Du@infinite/(F*Do) = ke/k
Clearance_renal_rate = Clearance_Total*Du@infinite/(F*Do = fe*Clearance_Total = ke*Clearance_Total/k
Clearance_Total = F*Do/[AUC]0 to infinite
Clearance_Total = Infusion_rate/Concentration_steadystate