Two Compartment Model

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.

• First, the central, rapid equilibration, compartment is taken to be the blood and highly perfused tissues and organs such as liver and kidney.
• Second, a slow equilibration compartment is taken to be peripheral tissues which are relatively poorly perfused (muscle, fat, etc.)

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

C(t) = Ae^-t + Be^-t

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

For t >> 0

C(t) = Be^-t

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

So the two-compartment model reduces to a single compartment over the long term with t_1/2 = 0.693/ .

Chronic Ingestion

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

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:

• Plasma water (about 3L)
• Interstitial water (about 11 L)
• Intracellular water (about 36 L)

Volume of Distribution can then be expressed as:

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

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

V_D = dose/(k*Area)

where k is the elimination rate constant.

Alternatively,

V_D = dose/C_o

where C_o = 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.

• Blood flow through the kidney represents 25% of cardiac output - very highly perfused organ!
• Passive glomerular filtration: filtrate (MW < 70,000 MW) passes into tubule.
  • Resorption of lipid soluble compounds may take place in the tubule.
  • Concentrations of compounds in the filtrate approximate [unbound] in plasma.
  • Fates of compounds in filtrate determined by lipid solubility, therefore urine pH is important factor in excretion.
    • bases secreted better if urine acidic
    • acids secreted better if urine is basic
• Passive diffusion into the tubule can also occur.
  • Organic acids and bases appear to exchange by diffusion processes in the proximal convoluted tubule.
• Active tubular secretion. This is important for charged compounds

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

• Usually need to have a MW > 300 for this system to be effective.
• Generally active processes are specific for acids, bases or neutral compounds.
• Charged compounds will not be resorbed from the intestinal lumen and so will be lost with feces.
• Can get intestinal resorption however if the excreted conjugated compound is hydrolyzed or metabolized to give a non-polar entity by intestinal flora.

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

Last modified 23 February 2010

© RA Paselk 2001