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Pharmacokinetics – Distribution Series II – Rate of Drug Distribution

Figure 4.1 shows the plasma concentration and the typical tissue concentration profile after the administration of a drug by intravenous injection. It can be seen that during the distribution phase, the tissue concentration increases as the drug distributes to the tissue. Eventually, a type of equilibrium is reached, and following this, in the postdistribution phase, the tissue concentration falls in parallel with the plasma concentration.

Drug distribution is a two-stage process that consist of:

1.Delivery of the drug to the tissue by the blood

2.Diffusion or uptake of drug from the blood to the tissue

The overall rate of distribution is controlled by the slowest of these steps. The delivery of drug to the tissue is controlled by the specific blood flow to a given tissue. This is expressed as tissue perfusion, the volume of blood delivered per unit time (mL/min) per unit of tissue (g). Once at the tissue site, uptake or distribution from the blood is driven largely by the passive diffusion of drug across the epithelial membrane of the capillaries. Because most capillary membranes are very loose, drugs can usually diffuse from the plasma very easily. Consequently, in most cases, drug distribution is perfusion controlled. The rate of drug distribution will vary from one tissue to another, and generally, drugs will distribute fastest to the tissues that have the higher perfusion rates.

Perfusion-Controlled Drug Distribution

Drug is presented to the tissues in the arterial blood, and any uptake of drug by the tissue will result in a lower concentration of drug leaving the tissue in the venous blood. The amount of drug delivered to the tissue per unit time or rate of presentation of a drug to a tissue is given by

rate of presentation = Q * Ca

where Ca is the drug concentration in the arterial blood and Q is the blood flow to the tissue

rate drug leaves the tissue = Q * Cv

where Cv is the drug concentration in the venous blood

so, rate of up take = Q * (Ca – Cv) (remember the O2ER in oxygen delivery?)

When drug uptake is perfusion controlled, the tissue presents no barrier for drug uptake, and the intial rate of uptake will equal the rate of presentation:

initial rate of uptake = Q * Ca

Thus, it is a first-order process. The value of Ca will change continuously as distribution proceeds throughout the body and as drug is eliminated. When the distribution phase in a tissue is complete, the concentration of drug in the tissue will be in equilibrium with the concentration leaving the tissue (venous blood). The ratio of these concentrations is expressed using the tissue blood partition coefficient (Kp):

where Ct is the tissue concentration. The value of Kp will depend on the binding and the relative affinity of a drug for the blood and tissues. Tissue binding will promote a large value of Kp, whereas extensive binding to the plasma proteins will promote a small Kp.

Once the initial distribution phase is complete, the amount of drug in the tissue (At) at any time is

At = Ct * Vt = Kp * Cv * Vt

Distribution is a first-order process and that the rate of distribution may be expressed using the first-order rate constant for distribution (Kd). The physiological determinants of the rate constant for distribution are most easily identified by considering the redistribution process, which is governed by the same physiological factors and has the same rate constant as those for distribution.

If the drug concentration in arterial blood suddenly became zero; the

rate of redistribution = Kd * At = Kd * (Kp * Cv * Vt) = |Q * (Ca – Cv)| (where Ca = 0) = |Q * –Cv| = Q * Cv

Thus, 

Kd = Q / Vt / Kp, when Ca sudden became zero.

The first-order rate constant for distribution is equal to tissue perfusion divided by the tissue: blood partition coefficient and the corresponding distribution half-life is computed via dividing LN(2) (0.693) by Kd.

Summary

The time it takes for distribution to occur is dependnet on tissue perfusion. Generally, drug distribute to well-perfused tissues such as the lungs and major organs faster than they do to poorly perfused tissues such as resting muscle and skin.

The duration of the distribution phase is also dependent on Kp. If a drug has a high Kp value, it may take a long time to achieve equilibrium even if the tissue perfusion is relatively high. If on the other hand, a drug has a high Kp value in a tissue with low perfusion, it will require an extended period of drug exposure to reach equilibrium.

The amount of drug in tissue at equilibrium depends on Kp and on the size of the tissue. A drug may concentrate in a tissue (high Kp), but if the tissue is physically small, the total amount of drug present in the tissue will be low. The distribution of a drug to such a tissue may not have a strong impact on the plasma concentration of the drug.

Redistribution of a drug from the tissues back to the blood is controlled by exactly the same principles. Thus, redistribution take less time when Kp value is small and the perfusion is high, and will take a long time when the Kp is high and the perfusion is low.

Diffusion-Controlled Drug Distribution

The epithelial junctions in some tissues, such as the brain, placenta, and testes, are very tightly knit, and the diffusion of more polar and/or large drugs may proceed slowly. As a result, drug distribution in these tissues may be diffusion controlled. In this case, drug distribution will proceed more slowly for polar drugs than for more lipophilic drugs. It must be pointed out that not all drug distribution to these sites is diffusion controlled. For example, small lipophilic drugs such as the intravenous anesthetics can easily pass membranes by the transcellular route and display perfusion-controlled distribution to the brain.

Diffusion-controlled distribution may be expressed by Fick's law

rate of uptake = Pm * SAm * (Cpu – Ctu)

where Pm is the permeability of the drug through the membrane (cm/h), SAm the surface area of the membrane (cm2), Cpu the unbound drug concentration in the plasma (mg/mL), and Ctu the unbound concentration in the tissue (mg/mL).

Initially, the drug concentration in the tissue is very low, Cpu >> Ctu, so the equation may be written

rate of uptake = Pm * SAm * Cpu

which can be seen that under these circumstances, the rate of diffusion approximates a first-order process.

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