Intro to Pharm and Tox Topics   

Absorption and Elimination

Lets assume that absorption is a first order process at the administration site where Ka is the absorption rate constant and Aa is the amount of drug at the administration site:

absorption = Ka Aa  

dAa  =  - Ka Aa
  dt

Meanwhile in the rest of the body both absorption and elimination determine concentration:

dAb  =  Ka Aa  - Kb Ab
 dt

Þ  Ab(t) = Ab(0) F Ka • (e^-Ket  - e^-Kat)
                    Ka - Ke                     

Þ  Cp(t) = Ab(0) F Ka • (e^-Ket  - e^-Kat)  
                  Vd(Ka - Ke) 

              = Cp(0) F Ka • (e^-Ket  - e^-Kat)  
                     Ka - Ke

A slowing drug loss from the absorption site delays the attainment and decreases the magnitude of peak plasma drug concentrations. In the set of graphs on the right, Case A illustrates how a faster absorption allows for a higher peak plasma concentration achieved faster than in cases B and C. In Case C, absorption limits elimination, so that plasma drug decline reflects absorption rather than elimination.

The administration route and formulation significantly modifies absorption for many drugs. A drug is usually absorbed much slower orally (PO) than intravenously (IV) or intramuscularly (IM). Different formulations of the drug can achieve intermediate absorption rates and peack plasma concentrations.

Elimination is usually a 1st order reaction, i.e. the rate of reaction is driven by the concentration of substrate:

elimination concentration amount

elimination  =   Cl  •  Cp  =   Ke  •  Ab

mg               =   mL • mg  =   1   •  mg
min                   min    mL     min

Were Cl is the clearance, Cp is the plasma concentration, Ke is the elimination rate constant and Ab is the amount in the whole body (i.e. amount of bolus or dose). Another important measure is the apparent volume of distribution Vd:

Cp  =   Ab  
           Vd       

Since:   Cl Cp   =   Ke Ab     then:    Cl   =   Ke
                 Vd             Vd                    Vd

The volume of distribution is an apparent (not real) volume, usually larger than total plasma volume (~ 3 L per 70 kg male) or total body fluids (~ 42 L per 70 kg male). This is due to the accumulation of drug in tissue other than plasma, while using Cp to assess volume. Drugs that have a large apparent Vd will have a low plasma concentration relative to total dose administered. Drugs that bind to tissue will reach a saturation point beyond which additional dosage remains as free drug.

Clearance and volume of distribution are independent variables in this system. Ke depends on Cl and Vd, not the other way around. These equations can be ploted over time:

dAb   =   - Ke Ab  
 dt

Þ  Ab(t) = Ab(0) e^(-Ket)

dCp   =   - Cl Cp  
 dt

Þ  Cp(t) = Cp(0) e^(-Ket)

If elimination follows 1st order kinetics, the half-life t1/2 is the time it takes Ab or Cp to decline by 50%:

0.5Cp(0) = Cp(0) e^(-Ket1/2)

ln [0.5Cp(0)] = ln [Cp(0)] - Ke t1/2

ln [0.5Cp(0)] - ln [Cp(0)] = - Ke t1/2

ln 0.5 = - Ke t1/2

-0.693 = - Ke t1/2  

Þ  t1/2   = 0.693/Ke

Þ  0.693   =  Cl  =  Ke
         t1/2          Vd

The elimination-over-time plot can also be logarithmic:

ln [Cp(0)] = ln [Cp(0)] - Ke t
     y         =       b     -   m x

The above equations apply if absorption and distribution occur immediatelly after administration, as may occur with IV injection. Non-immediate input as in by oral administration is complicated by an additional term: bioabailability (F), the fraction of administrered dose that makes it to the central compartment.

Continue to "Physiological Models " or take a quiz: [Q1].

Need more practice? Answer the review questions below.

Questions coming soon