Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 451

Biochemical Toxicology

Spring 2010

Lecture Notes:: 23 February

© R. Paselk 2008
 
     
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Two Compartment Model

{Two compartment model overhead, Figure 3.4}

In this model the chemical does not distribute and equilibrate rapidly. Thus need additional compartments to model more closely. Often a two compartment model (a fast and a slow compartment) will approximate reality quite closely.

Again, for mathematical simplicity we will assume all processes are first-order. For the two compartments shown:

 

 Xperipheral = Xp
k21
k12

 

Xcentral = Xc
k10 

Where k10, k12, and k21 are first order rate constants, and the boxes represent the fast and slow compartments.

C(t) = Ae-alphat + Be-betat

where alpha & beta are apparent first-order decay constants and A & B are complex constants (see box below).

Box: Equations for the Two Compartment Model in Notes.

Xc(t) = Xo[{(alpha- k21)/(alpha -beta)}e-alphat + {(k21 -beta)/(alpha - beta)}e-betat]

Xp(t) = k12Xo/(alpha - beta) {e-alphat - e-betat}

where alpha & beta are apparent first-order decay constants (complex and multicomponent), k12 & k21 are first order rate constants describing intercompartmental transfer, and A & B are complex constants:

A = {Xo/Vc}{(alpha - k21)/(alpha - beta)}

B = {Xo/Vc}{(k21 -beta)/(alpha - beta)}

and Vc is the apparent volume of the central compartment.

For t >> 0

C(t) = Be-betat

This describes the post distributive phase, where beta is called the disposition rate constant. This occurs because the Ae-alphat term approachs zero rapidly compared to the other term.

So the two-compartment model reduces to a single compartment over the long term with t1/2 = 0.693/beta .

Chronic Ingestion

{overhead Figures 3.29, 3.30}

Time for Steady State (SS) depends on the elimination rate.

[SS] depends on both the Dose rate and the elimination rate as shown on Figure 3.29, p 54 & Figure 3.30, p 55 of Timbrell.

Multicomponent Models: the Example of PXB's in Rats

{overheads 3.7, 3.8, 3.10, 3.11}

Looked at two closely related models, each "monitoring" five different compartments: adipose, skin, muscle, liver, and blood.

In the first case rats were given single 0.6 mg/kg iv doses of PCB (6CB) and tissue concentrations were monitored for 100 hours. Initial high [blood] fell very quickly, as did the highly perfused muscle and liver tissues. Skin concentrations peaked at about 20 h, then gradually declined, while concentrations in adipose contnued to climb for the entire experiment. The predictions of the multicomponent model using blood, liver, gut lumen, muscle, skin, and fat matched very well.

In the second case rats were given single 1.0 mg/kg iv doses of PBB and tissue concentrations were monitored for 42 days. Initial high [blood] fell rapidly, reaching a nearly level (on a log plot) gentle slope by about 5 days, as did the highly perfused muscle and liver tissues. Skin concentrations peaked at about 3 days, then gradually declined, paralleling the previous tissues, but at 10-100 x's the concentration, while concentrations in adipose continued to climb for the entire experiment. The predictions of the modified multicomponent model using blood, liver, gut lumen, muscle, skin, and fat again matched well.

Let's go back to the Volume of Distribution.

Various body human compartments:

Volume of Distribution can then be expressed as:

VD = dose (mg)/plasma conc. (mg/L)

More rigorously, look at a plot of [plasma] vs. time, then (overhead Fig. 3.11 - plasma profile):

VD = dose/(k*Area)

where k is the elimination rate constant.

Alternatively,

VD = dose/Co

where Co = the ideal initial concentration found by extrapolating the descending leg of of the log [ ] vs. time curve to time = 0 (overhead Figure 3.13 - semilog plot of plasma conc.; Timbrell Fig 3.25, p 50).

 Box: pH effects on Distribution - Phenobarbital

Phenobarbital has a pKo = 7.2. Overdoses can be treated by shifting distribution with pH shifts. Thus if bicarbonate is given the phenobarbital will tend to shift into the plasma due to alkalosis, and then into the urine with the development of alkaline diuresis.

Assuming a pH of 7 in cell and plasma pH of 7.6, then the equilibrium distribution D is 100.6 = 4.

Excretion

Kidney: The major route of excretion for most compounds is the kidney.

Biliary Excretion: Larger, polar compounds are often preferentially excreted via the biliary system into the duodenum.

Other systems involved in excretion include the lungs (volatile substances), sweat, and milk (particularly for lipid soluble substances).


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Last modified 23 February 2010

© RA Paselk 2001