Pharmacokinetics: basics

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

This is a diagram that shows the basic physiologic mechanisms of the kidney and the three steps involved in urine formation, namely filtration, reabsorption, secretion, and excretion.

 

 

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