Month: November 2017

Pharmacokinetics – Distribution Series II – Rate of Drug Distribution

November 13, 2017 Biopharmaceutics, Pharmacokinetics No comments , , , ,

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.

Pharmacokinetics – Distribution Series

November 11, 2017 Pharmacodynamics, Pharmacokinetics, Uncategorized No comments , , , , , , , , ,

As a result of either direct systemic administration or absorption from an extravascular route, drug reaches the systemic circulation, where it very rapidly distributes throughout the entire volume of plasma water and is delivered to tissues around the body. Two aspects of drug distribution need to be considered: how radidly, and to what extent, the drug in the plasma gets taken up by the tissues. A lot of information on the rate of drug disribution can be obtained by observing the pattern of the changes in the plasma concentrations in the early period following drug administration. Information about the extent of drug distribution can be obtained by considering the value of the plasma concentration once distribution is complete. Thus, the plasma concentration constitutes a "window" for obtaining information on the distribution of the bulk of the drug in the body and how it changes over time.

Extent of Drug Distribution

A drug must reach its site of action to produce an effect. Generally, this involves only a very small amount of the overall drug in the body, and access to the site of action is generally a problem only if the site is located in a specialized area or space. The second important aspect of the extent of drug distribution is the relative distribution of a drug between plasma and the rest of the body. This affects the plasma concentration of the drug and is important because: 1) as discussed above, the plasma concentration is the "window" through which we are able to "see" the drug in the body. It is important to know how a measured plasma concentration is related to the total amount of drug in the body; 2) Drug is delivered to the organs of elimination via the blood. If a drug distributes extensively from the plasma to the tissues, the drug in the plasma will constitute only a small fraction of the drug in the body. Little drug will be delivered to the organs of elimination, and this will hamper elimination. Conversely, it a drug is very limited in its ability to distribute beyond the plasma, a greater fraction of the drug in the body will be physically located in the plasma. The organs of elimination will be well supplied with drug, and this will enhance the elimination processes.

Drug distribution to the tissues is driven primarily by the passive diffusion of free, unbound drug along its concentration gradient. Consider the administration of a single intravenous dose of a drug. In the early period after administration, the concentration of drug in the plasma is much higher than that in the tissues, and there is a net movement of drug from the plasma to the tissues; this period is known as the distribution phase. Eventually, a type of equilibrium is established between the tissues and plasma, at which point the ratio of the tissue to plasma concentration remains constant. At this time the distribution phase is complete and the tissue and plasma concentrations rise and fall in parallel; this period is known as the postdistribution phase. It should be noted that after a single dose, true equilibrium between the tissues and the plasma is not achieved in the postdistribution phase because the plasma concentration falls constinuously as drug is eliminated from the body. This breaks the equilibrium between the two and results in the redistribution of drug from the tissues to the plasma. Uptake and efflux transporters in certain tissues may also be involved in the distribution process and may enhance or limit a drug's distribution to specific tissues.

Physiologic Volumes

Three important physiological volumes – plasma water, extracellular fluid, and total body water, are shown in Figure 4.2. In the systemic circulation, drugs distribute throughout the volume of plasma water (about 3 L). Where a drug goes beyond this, including distribution to the cellular elements of the blood, depends on the physicochemical properties of the drug and the permeability characteristics of individual membranes.

The membranes of the capillary epithelial cells are generally very loose in nature and permit the paracellular passage of even polar and/or large drug molecules. Thus, most drugs are able to distribute throughout the volume of extracellular fluid, a volume of about 15 L. However, the capillary membranes of certain tissues, notably delicate tissues such as the central nervous system, the placenta, and the testes, have much more tightly knit membranes, which may limit the access of certain drugs, particularly large and/or polar drugs.

Once in the extracellular fluid, drugs are exposed to the individual cells of tissues. The ability of drugs to penetrate the membrane of these cells is dependent on a drug's physicochemical properties. Polar drugs and large molecular mass drugs will be unable to pass cell membranes by passive diffusion. However, polar drugs may enter cells if they are substrates for specialized uptake transporters. On the other hand, efflux transporters will restrict the distribution of their substrates. Small lipophilic drugs that can easily penetrate cell membranes can potentially distribute throughout the total body water, which is around 40 L.

In summary, drugs are able to pass through most of the capillary membranes in the body and distribute into a volume approximately equal to that of the extracellular fluid (about 15 L). The ability of a drug to distribute beyond this depends primarily on its physicochemical characteristics. Small, lipophilic drug molecules should penetrate biological membranes with ease and distribute throughout the total body water (about 40 L). A drug's distribution to specific tissues may be enhanced by uptake transporters. Conversely, efflux transporters will restrict the tissue distribution of their substrates. Total body water, about 40 L, represents the maximum volume into which a drug can distribute.

Tissue Binding and Plasma Protein Binding

Given that drug distribution is driven primarily by passive diffusion, it would be reasonable to assume that once distribution has occurred, the concentration of drug would be the same throughout its distribution volume. This is rarely the case because of tissue and plasma protein binding. Drugs frequently bind in a reversible manner to sites on proteins and other macromolecules in the plasma and tissues. At this time it is important to appreciate that bound drug cannot participate in the concentration gradient that drives the distribution process. The bound drug can be considered to be secreted away or hidden in tissue or plasma. Binding has a very important influence on a drug's distribution pattern. Consider a drug that binds extensively (90%) to the plasma proteins but does not bind to tissue macromolecules. In the plasma, 90% of the drug is bound and only 10% is free and able to diffuse to the tissues. At equilibrium, the unbound concentrations in the plasma and tissue will be the same, but the total concentration of drug in the plasma will be much higher than that in the tissues.

Plasma protein binding has the effect of limiting distribution and concentrating drug in the plasma. On the other hand, consider a drug that binds extensively to macromolecules in the tissues but does not bind to the plasma proteins. Assume that overall 90% of the drug in the tissue is bound and only 10% is free. As the distribution process occurs, a large fraction of the drug in the tissues will bind and be removed from participation in the diffusion gradient. As a result, more and more drug will distribute to the tissues. When distribution is complete, the unbound concentrations in the plasma and tissues wil be the same, but the total (bound plus free) average tissue concentration will be much larger than the plasma concentration. Tissue binding essentially draws drug from the plasma and concentrates it in the tissues. Drugs often bind to both the plasma proteins and tissue macromolecules. In this case the final distribution pattern will be determined by which is the dominant process.

Assessment of the Extent of Drug Distribution

Once distribution has gone to completion, the ratio of the total tissue concentration to the total plasma concentration remains constant. The actual tissue concentration (and the ratio) will vary from tissue to tisue, depending on the relative effects of tissue and plasma protein binding. It is not possible to measure individual tissue concentrations, and it is convenient to consider an overall average tissue concentration (Ct). The ratio of Ct to Cp will vary from drug to drug.

It is important to find a way to express a drug's distribution characteristics using a number or distribution parameter that can easily be estimated clinically. The ratio discussed above (Ct/Cp) expresses distribution but cannot be measured easily. Instead, we use the ratio of amount of drug in the body vs. plasma concentration at the same time to express a drug's distribution, that is, the apparent volume of distribution (Vd).

It is important to appreciate that the (apparent) volume of distribution is simply a ratio that has units of volume. It is not physiological volume and, despite its name, it is not the volume into which a drug distributes. The fact that drug A has a Vd value of 20 L does not mean that it distributes into a volume of 20 L, which is greater than extracellular fluid and less than the total body water.

The value of a drug's volume of distribution can be used to estimate the fraction of the drug in the body that is physically present in either the plasma or the tissues. The drug in the body (Ab) may be partitioned into drug in the plasma (Ap) and drug outside the plasma or in the tissues (At):

Ab = Ap + At

the fraction of the drug in the plasma,

fraction in plasma = Ap / Ab

After some algebra, we get

fraction in plasma = Vp / Vd

In a standard 70-kg adult male, Vp = 3 L:

fraction in plasma = 3 / Vd

The fraction of the drug in the body located in the tissues:

fraction in tissue = 1 – fraction in plasma = 1 – 3 / Vd

With this formula we can estimate the fraction of drug in plasma and in tissues, respectively.

Drug in the body is located in either the plasma or the tissues. The amount of drug in either of these spaces is the product of the concentration of drug and the volume of the space. And because Ab = Ap + At, we get

Cp * Vd = Cp *Vp + Ct * Vt

where Cp is the plasma concentration of the drug, Vd the volume of distribution, and Vp the volume of plasma water, Ct the average tissue concentration of the drug, the Vt the overall volume of tissues that the drug distributes.

And because the unbound (free) drug concentration equals the total drug concentration multiplying fraction of unbound, while the unbound drug concentrations between plasma and tissues (extraceullar space) must be the same after reaching distribution equilibrium, we get,

Cp*fu = Ct * fut

After some algebra, we have

Vd = Vp + Vt * fu / fut

where fu is the fraction of unbound drug in plasma and fut is the fraction of unbound drug in tissues. This final equation shows that a drug's volume of distribution is dependent on both the volume into which a drug distributes and on tissue and plasma protein binding. It also shows that increased tissue binding (fut gets smaller) or decreased plasma protein binding (fu gets larger) will result in an increase in the volume of distribution. Also, if a drug binds to neither the plasma proteins (fu = 1) nor the tissues (fut = 1), its volume of distribution will be equal to that of the volume into which the drug distributes (physiologic volume).

Summary

  • Vd is a ratio that reflects a drug's relative distribution between the plasma and the rest of the body.
  • It is dependent on the volume into which a drug distributes and a drug's binding characteristics.
  • It is a constant for a drug under normal conditions.
  • Conditions that alter body volume may affect its value.
  • Altered tissue and/or protein binding may alter its value.
  • It provides information about a drug's distribution pattern. Large values indicate extensive distribution of a drug to the tissues.
  • It can be used to calculate the amount of drug in the body if a drug's plasma concentration is known.

Plasma Protein Binding

A very large number of therapeutic drugs bind to certain sites on the proteins in plasma to form drug-protein complexes. The binding process occurs very rapidly, it is completely reversible, and equilibrium is quickly established between the bound and unbound forms of a drug. If the unbound or free drug concentration falls due to distribution or drug elimination, bound drug dissociates rapidly to restore equilibrium. Clinically, although the total drug concentration is measured routinely, pharmacological and toxicological activity is thought to reside with the free unbound drug (Cpu). It is only this component of the drug that is thought to be able to diffuse across membranes to the drug's site of action and to interact with the receptor. Binding is usually expressed using the parameter fraction unbound (fu), and the unbound pharmacologically active component can be calculated:

Cpu = Cp * fu

The three primary plasma proteins combining drugs include albumin, 𝛼1-acid glycoprotein (AAG), and the lipoproteins. AAG is present in lower concentration than albumin and binds primarily neutral and basic drugs. It is referred to as an acute-phase reactant protein because its concentration increases in response to a variety of unrelated stressful conditions, such as cancer, inflammation, and acute myocardial infarction. Given that the unbound concentration is the clinical important fraction and that it is the total concentration that is routinely measured, it is important to know how and when the unbound fraction may change for a drug.

The binding of drug and plasma protein could be regarded as a drug and "receptor" interaction (occupation). So the pharmacodynamic Emax model could be used to describe this interacton mathematically. After some algebra modifications, we get

 

where PT is the serum concentration of plasma binding protein, Kd the equilibrium dissociation constant, and the Cpu the plasma concentration of unbound (free) drug.

At low concentrations, binding increases in direct proportion to an increase in the free drug (fu remains constant as Cpu increases, where Cpu < Kd). As the free drug concentration increases further, some saturation of the proteins occurs, and proportionally less drug can bind (fu will increase as Cpu increases further). Eventually, at high drug concentrations, all the binding sites on the protein are taken and binding cannot increase further.

The Changes of fu

  • Affinity

The affinity of the drug for the protein is the main determinant of fu. Affinity is expressed by Kd, which is a reciprocal form of affinity. As affinity increases, Kd gets smaller. Drugs with small Kd values bind extensively, whereas those with large Kd values will not bind extensively.

  • Free drug concentration

Because the therapeutic plasma concentrations of most drugs are much less than their Kd values, binding is able to increase in proportion to increases in the total concentration: fu remains constant over therapeutic plasma concentrations. There are, however, a few drugs that have therapeutic plasma concentrations that are around the range of their Kd values. These drugs, which tend to be drugs that have very high therapeutic plasma concentrations, include valproic acid and salicylates, both of which bind to albumin, and disopyramide, which binds to AAG. The binding of these drugs uses a substantial amount of protein, and as a result they display concentration-dependent binding. As the drug concentration increases, some degree of saturation is observed, and the fraction unbound gets larger.

  • Plasma binding protein concentration

As predicted by the law of mass action, changes in the protein concentration will produce changes in the degree of binding. In the case of AAG, increases in the concentration are more common. Physiological stress caused by myocardial infarction, cancer, and surgery can lead to four- to fivefold increases in the AAG concentration. Lipoprotein concentrations vary widely in the population. They can decrease as a result of diet and therapy with HMG-CoA reductase inhibitors (statins), and increase due to alcoholism and diabetes mellitus.

  • Displacement

The binding of one drug may displace a second drug from its binding site. This displacement occurs because two drugs compete for a limited number of binding sites on the protein. Not surprisingly, displacers tend to be those drugs that achieve high concentrations in the plasma, use up a lot of protein, and display concentration-dependent binding.

  • Renal and hepatic disease

The binding of drugs to ablumin is often decreased in patients with severe renal disease. This appears to be the result of both decreased albumin levels and the accumulation of compounds that are normally eliminated, which may alter the affinity of drugs for albumin and/or compete for binding sites. The binding of several acidic drugs, including phenytoin and valproic acid, is reduced in severe renal disease. Plasma protein binding may also be reduced in hepatic disease.

Clinical Consequences of Changes in Plasma Protein Binding

Changes in fu as a result of altered protein concentration or displacement will result in a change in the fraction of the total drug that is unbound. Two issues need to be addressed when considering the clinical consequences of this: the potential changes in the unbound drug concentration at the site of action, and the interpretation and evaluation of the routinely measured total plasma concentrations.

When binding decreases, the pharmacologically active unbound component increases, and in theory, the response or toxicity could increase. However, the clinical consequences of altered plasma protein binding are minimized by two factors: 1) increased elimination and 2) little change in drug concentrations outside the plasma.

In many cases, only the unbound drug is accessible to the organs of elimination. This is known as restrictive elimination because elimination is restricted by protein binding and is limited to the unbound drug. For drugs display restrictive clearance, the increase in the unbound concentration that occurs when binding decreases results in an increase in elimination of the drug. The increase in elimination is usually proportional to the increase in unbound concentration. As a result, the unbound drug concentration in the plasma eventually falls to exactly the same value as that before the change in binding. In other words, the increase in the unbound concentration is canceled out by increased elimination.

The time it takes for the unbound concentration to return to its normal level is determined by the rate of elimination of the drug (the elimination half-life). If the drug is eliminated rapidly, the unbound concentration returns to its original level quickly. If the drug is eliminated slowly, it takes a long time for the unbound concentration to return to its original level. The time it takes to return can be important for drugs that have a narrow therapeutic index.

The plasma comprises a relative small physiological volume (3 L). Even when plasma protein binding is extensive, the fraction of the drug in the body that is located in the plasma is much less than that in the tissues. As a result, when the fraction unbound increases, the extra drug that distributes to the tissue is often very small in comparison to the amount of drug already present. This is particularly the case for drugs that have large volumes of distribution, where the majority of the drug in the body is in the tissues and only a very small fraction resides in the plasma.

Interpreting Cp

In clinical practice, drug therapy may be monitored by ensuring that plasma concentrations lie within the therapeutic range. The therapeutic range of a drug is expressed most conveniently in terms of concentration routinely measured, the total plasma concentration (Cp). But since the unbound concentration is the pharmacologically active component, the therapeutic range should more correctly be expressed in terms of this unbound concentration. Formulas have been developed for some drugs that will convert a measured plasma concentration of a drug to the value that it would be if the protein concentration were normal. We can prove the below formula with algebra modification.

 (when plasma drug concentration << Kd)