sign in sign up
<<
Home , Therapeutic index

Drug Concentration and Therapeutic Response

Development Team

Principal Investigator Prof. Farhan J Ahmad Jamia Hamdard, New Delhi

Paper Coordinator Dr. Javed Ali Jamia Hamdard, New Delhi

Dr. Shadab Md. School of , Content Writer International Medical University (IMU), Kuala Lumpur, Malaysia

Dr. Sonal Gupta, KL Mehta Dayanand college, Content Reviewer Faridabad

Pharmaceutical Biopharmaceutics and sciences Concentration and Therapeutic Response 0

Drug Concentration and Therapeutic Response Drug Concentration and Therapeutic Response

Content

1. Introduction

2. /Concentration response relationship

3. Types of dose and response relationship

3.1.

3.2.

3.3. Selectivity

3.4. Affinity

4. Therapeutic Window

4.1. Therapeutic Index

5. The relationship between drug concentration and pharmacological effects in the whole

animal/human

6. Pharmacodynamic model

7. Onset and Duration of Action

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 1

Drug Concentration and Therapeutic Response I. Introduction

To produce therapeutic/beneficial effect or minor, major, serious and severe toxic effects,

interact with receptors, ion channels, membrane carriers or enzymes in the body; this is called

action of drug. The drug- interactions usually occur in the tissue

which is in equilibrium with the unbound drug (not bound to the plasma protein) present in the

plasma. Drugs bind and interact in a structurally specific manner with these protein receptors.

Activation of receptors in response to drug binding leads to activation of a second messenger

system, resulting in a physiological or biochemical response such as changes in intracellular

calcium concentrations leading to muscle contraction or relaxation. There are four main types of

receptor families

i. -gated ion channels

ii. G-protein-coupled receptors (GPCRs)

iii. Enzyme-linked receptors

iv. Intracellular receptors.

The most common receptors that are targets for drugs are the GPCRs; these are transmembrane

receptors linked to guanosine triphosphate binding proteins (G proteins) which activate second

messenger systems such as adenylyl cyclase (activated by, for example, β-adrenoceptors) or the

inositol triphosphate pathway (activated by, for example, α-adrenoceptors). A drug which binds

to a receptor having affinity, and produces a maximum effect is called a full

. A drug which binds to receptor, produces intermediate efficacy and produces

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 2

Drug Concentration and Therapeutic Response submaximal response is called as . Partial produce a therapeutic effect if

no agonist is present, but can act as antagonists in the presence of a full agonist. Pindolol (β

blocking agent) is a partial agonist, produces a smaller decrease in heart rate than that produced

by pure antagonists such as propranolol. Drugs which bind to receptor but do not have intrinsic

activity and have zero efficacy is called antagonist. Antagonists produce their effects by

counteracting the access of the natural transmitter (agonist) to the same receptor such as atropine

(Antagonist) vs acetylcholine (agonist) on muscarinic receptor. An is a molecule

that binds to the same site as an agonist but produce an opposite response (negative efficacy).

Currently there are several drugs such as haloperidol, chlorpromazine that have inverse agonist

activity at dopamine and serotonin receptors are used clinically.

Antagonists comprises of mainly two subcategories competitive and noncompetitive.

Competitive antagonists involve competition between antagonist and agonist and bind reversibly

to the same receptor site. Antagonist inhibitory effects for the same receptor can be overcome by

addition of a higher concentration of agonist. In the presence of competitive antagonist higher

agonist concentrations are needed to produce the same effect as in absence of antagonist. The

presence of a competitive antagonist causes a rightward shift of the dose response curve of the

agonist. The majority of clinically used drugs act as receptor antagonists are reversible

competitive antagonists. Agonist (Isoproterenol) and the antagonist (Propranolol) are good

example of competitive antagonist. Noncompetitive antagonists can bind irreversibly by covalent

bonds for the same receptor site as the agonist or bind to a different site of same receptor which

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 3

Drug Concentration and Therapeutic Response reduces the binding capability of the agonist by an allosteric mechanism. Due to irreversible

strong binding to receptor site, the effect of a noncompetitive antagonist cannot be reversed even

at high concentration of agonist, because the law of mass action does not apply. The primary

effect of noncompetitive antagonist causes rightward shift of dose response curve and reduction

in the maximal effect produced by the agonist.

There are three other types of drug antagonism. Physiologic antagonism involves when one

drugs antagonises the action of other drug by acting on different receptors and mechanism.

Example: Acetylcholine (vasodilation) and norepinephrine (vasoconstriction) Chemical

antagonism involves when a one drug antagonises another drug by chemical interaction and

leads to a reduced response. Example: Interaction of positively charged drug protamine sulfate

which neutralises the effect of negatively charged drug heparin. Pharmacokinetic antagonism

occur when one drug suppressing or accelerating the effect of a second drug by change in

pharmacokinetics of drug such as increase/decrease in absorption, distribution, metabolism and

elimination. e.g. phenobarbital increases the metabolic degradation of anticoagulant .

Selectivity in drug action is associated to the structural specificity of drug binding to receptors.

Propranolol binds equally well to β1 and β2 adrenergic receptor, whereas metoprolol and atenolol

bind selectively antagonist at β1- adrenergic receptor. Salbutamol is a selective β2-adrenergic

receptor agonist and in this case, additional selectivity is achieved by inhaling the drug directly

to its site of action in the lungs.

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 4

Drug Concentration and Therapeutic Response II. Dose/Concentration response relationship

Regardless of how a drug effect occurs through binding or chemical interaction, the

concentration of the drug at the site of action controls the effect. However, the relationship

between response and concentration may be complex and is often nonlinear. Generally, when

discussing the drug action at the tissue level, we refer to drug ‘concentration’, while when

referring to drug action in the whole animal/person, we refer to the drug ‘dose’. When a drug is

administered to an animal or human, the relationship between the drug dose, regardless of route

used, and the drug concentration at the cellular level is even more complex.

The concept of the dose-response curve, or concentration-response curve is one of the most

important parts of . A dose-response curve describes the relationship between an

effect of a drug and the amount of drug given. Dose-response curves are essential to understand

the drug's safe and hazardous levels, so that the therapeutic index can be determined and dosing

guidelines can be created.

Dose-response curves are charted on an X-Y axis, with the drug dosage measured (usually in

milligrams, micrograms, or grams per kilogram of body-weight for oral exposures or milligrams

per cubic meter of ambient air for inhalation exposures) typically on the X axis and the response

to the medication typically on the Y-axis. When considering responses at the tissue level, the

quantity of drug is expressed as its concentration, usually expressed as a molar concentration,

although where the molecular weight is unknown we would express the concentration as

microgram/nanogram/ ml as appropriate. As the relationship between response and increasing

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 5

Drug Concentration and Therapeutic Response dose or concentration is best described by a logarithmic plot, dose-response curves (or

concentration-response curves) are graphed with the dose or concentration on a logarithmic scale

(X axis) as opposed to a linear scale; in such cases the curve is typically sigmoidal, with the

steepest portion in the middle (This is discussed in more detail in the final section of this module

see material under ‘The relationship between drug concentration and pharmacological effects in

the whole animal/human’)

When evaluating a dose-response curve (or concentration-response curve), one of the main

characteristics is a graded relationship between the response and the dose or concentration; this

means that as the amount of drug given is increased so is the response to the drug. There are

three phases of a dose-response curve (or concentration-response curve). First, the curve is flat as

the quantity of drug given is not sufficiently great to initiate a response. The first point along the

graph where a response above zero (or above the control response) is reached is usually referred

to as a threshold-dose. In the second phase, the curve steadily rises, with each increase in the

drug dose there is also an increased in response. At higher doses, undesired side effects appear

and grow stronger as the dose increases. The more potent a particular substance, the lower the

concentration or dose required to produce an effect. Finally, the curve plateaus at the top,

indicating that any further increases in drug dose will not produce any further increase response

to the drug (Figure 1). This grading of the dose response curve enables your healthcare provider

to tailor their prescription to the individual taking the drug.

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 6

Drug Concentration and Therapeutic Response

Figure 1. Relationship of drug concentration to percentage effect on linear scale and log scale. (EC50 value: Concentration which produces 50% of the drug maximum response)

3. Types of dose and response relationship

A fixed dose administered to a range of individuals will produce a range of concentration

measurements due to pharmacokinetic variability among individuals. These concentrations will

also change over time. In addition to this a range of responses can be determined, both

therapeutic response and toxic effect. It is therefore common to consider concentration-effect

relationships rather than dose-response relationships. The concentration-response relationships

are of two type graded and quantal. A graded concentration response curve are plotted for

responses such as contraction of muscle are determined on a continuous scale. Graded response

curves relate the size of the dose to the intensity of response and hence used in characterizing the

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 7

Drug Concentration and Therapeutic Response actions of drugs. Therefore, the percentage of the group responding to increasing doses is

plotted, a sigmoidal dose-response or graded response curve is constructed. On the other hand,

when a drug is administered to the whole animal, certain types of responses may be all or none.

For example, before immunoassays were developed, the potency of insulin was determined by

administration to mice, where it caused convulsions due to a large reduction in the blood

glucose; in this case, convulsions either occurred or did not occur – this is termed a quantal

response and the relationship is defined as the percentage of animals showing the response and

the dose of the drug. The doses required to produce a specified quantal effect in an individual

population or experimental animals are log normally distributed. The cumulative frequency

distribution of such responses plotted against the log dose produces a gaussian curve.

Equilibrium (KD) are determined experimentally and is measured the

affinity of a drug for a receptor. The equilibrium dissociation constant of the receptor drug

complex, KD, is the ratio of rate constants for the reverse reaction (K2) and forward (k1)

reaction between the drug and receptor and the drug receptor complex. The concentration of a

drug at which receptor occupancy is half of maximum effect. Drugs with a low KD have high

affinity dissociate slowly from receptors. Drugs with a high KD having low affinity dissociate

rapidly from receptors.

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 8

Drug Concentration and Therapeutic Response 3.1. Potency

Potency refers to the amount of drug rrequired to produce a certain response. A drug which

produces a certain effect at 5 mg dosage is ten times more potent than a drug which produces the

same effect at 50 mg dosage. In other words, potency defines as the dose (ED50) or

concentration (EC50) of a drug required to produce 50% of the drugs maximum effect. Relative

potency is more important than absolute potency. EC50 or ED50 value are used to evaluate the

comparing the differences in drug potency. EC50 equals KD when there is a linear relationship

exist between response and receptor occupancy. Often, signal amplification occurs between

response and receptor occupancy which causes EC50 for response being much less (ie,

positioned to the left on the x -axis of the log dose response curve) than KD for receptor

occupancy.

Potency depends on both the efficiency with which drug receptor interaction is coupled to

response and affinity of a drug for its receptor. Potency is inversely related to the dose of drug

required to produce a therapeutic effect. Potency of drug is important in selecting dose of a drug.

Graded dose response curves provide information on the potency of drugs that is different from

the information derived from quantal dose response curves. In a quantal dose response

relationship, the ED50 is the dose at which 50% of individuals exhibit the specified quantal

effect.

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 9

Drug Concentration and Therapeutic Response

Figure 2. Graphical representation of the dose-response curves for a number of drugs (A, B, C and D) differ in their potency but have the same efficacy. In this figure drug A is more potent than drug B, C and D.

3.2. Efficacy

Efficacy or intrinsic activity is the ability of the drug to produce a maximal response when it

binds to the receptor. Conformational changes in receptors because of drug occupancy activate

physiologic events and biochemical that characterize the drug response. In some tissues, agonists

demonstrating high efficacy even when only a small portion of the receptors is occupied.

Difference in drug efficacy can be evaluated by looking at maximal response produced by

different drug. Agonists can also differ in terms of their efficacy. Figure 3 represent four agonists

that differ in their relative efficacy but have same potency. Drug A is the most efficacious, and

Drug D the least efficacious. Drugs B and C that bind to a receptor, but produce less than

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 10

Drug Concentration and Therapeutic Response maximal response are called partial agonists. Figure 4 showed Drug X has greater efficacy per

dosing equivalent and is thus more potent than drug Y or Z. Drugs X and Z have equal efficacy,

indicated by their maximal response (ceiling effect). Drug Y is more potent than drug Z, but its

maximal efficacy is lower.

Figure 3. Graphical representation of dose-response curve for four agonists that differ in efficacy but have same potency. In this figure, Drug A is more efficacious than drug B, C and D.

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 11

Drug Concentration and Therapeutic Response

Figure 4. Showed comparison of dose-response curves in relation to potency and efficacy

3.3. Selectivity refers to a drug’s ability to preferentially produce a particular effect and is

associated to the structural specificity of drug binding to receptors site. Selectivity of drug action

relates to the number of different mechanisms involved. Examples of selective drugs include

cimetidine (an H2-), atropine (a muscarinic receptor antagonist) and

salbutamol (a β2-adrenoceptor agonist). Cyclooxygenase-2 (COX-2) preferential NSAIDs

demonstrate partial specificity for COX-2, the inducible enzyme formed at sites of inflammation.

By comparison, COX-2 selective NSAIDs are without significant effect on COX-1, the

constitutive enzyme that performs a range of physiologic functions. Nonselective drugs result in

drug effects through several mechanisms of action. For example, chlorpromazine causes

blockade of D2-dopamine receptors, α-adrenergic receptors, and muscarinic receptors. Lack of

receptor selectivity is one cause of side effects; for example, chlorpromazine may cause a dry

mouth by blocking muscarinic receptors in the doses used to treat schizophrenia.

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 12

Drug Concentration and Therapeutic Response 3.4. Affinity of a drug for a receptor describes how tenaciously drug binds to the receptor. The

chemical forces in drug-receptor interactions involved are van der Waal forces, electrostatic

forces and the forces associated with hydrophobic bonds and hydrogen bonds. Variation in the

strength of these forces determines the degree of dissociation and association of the drug and the

receptor. Covalent binding of fluoroquinolones drug acting on bacteria to receptor leads to

formation of an irreversible link is an example of affinity of drug to receptor.

4. Therapeutic Window

The optimal design of a therapeutic dosage regimen is generally established on the basis of

systemic exposure-responses relationships, with the aim of achieving a desired safety–efficacy

balance for a given drug. Therapeutic window (TW), which is typically considered as the

therapeutic range of drug’s plasma concentration associated with safe effective treatment, is an

important parameter in efforts to attain this equilibrium (1). Drugs with a good therapeutic

window are effective in a range of doses that produces therapeutic responses without causing any

significant toxic side effect in patients. The therapeutic window is the ratio of the maximum safe

concentration (MSC) to the minimum effective concentrations (MEC). The concentration of drug

should always lies in between MSC and MEC in order to provide risk free therapeutic success. If

any drug exceeds the MSC then it will surely produce adverse effects; if the drug is unable to

achieve the MEC, this will result in therapeutic failure. The therapeutic window is also termed as

the safety window and can be quantified by the therapeutic index.

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 13

Drug Concentration and Therapeutic Response

Figure 5: Therapeutic window

4.1. Therapeutic Index (TI):

Therapeutic index (TI) describes a relationship between the doses of a drug that causes lethal or

toxic effects with the dose that causes therapeutic effects. It is also referred to as the therapeutic

ratio.

Mathematically you can calculate TI by following way;

Therapeutic Index: LD50/ED50

or

Therapeutic Index: TD50/ED50

Lethal Dose (LD50): the dose required to produce death in 50% of the population). LD values

always refer for animal studies. Lethal doses in humans are hardly calculated.

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 14

Drug Concentration and Therapeutic Response Toxic Dose (TD50): dose required to produce toxic effect in 50% of the individuals.

ED50 is the quantity of a drug that can produce desired therapeutic effects in 50% of the

population. Such types of studies are usually conducted in animal models or patients.

Note: EC50: the drug concentration producing 50% of a maximal effect– used for in vitro studies

only.

Figure 6. Graphical representation of dose-response relationships for producing therapeutic and toxic effects.

Drugs having a wider therapeutic window are safer in comparison to those having low

therapeutic window because minor modification in the dose of such drugs (aspirin,

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 15

Drug Concentration and Therapeutic Response acetaminophen) will not produce toxic effects. Some drugs (for example, , ,

) have a narrow therapeutic window resulting frequently in in therapeutic doses.

Increasing the dose of a drug with a narrow therapeutic window increases the probability of

toxicity. A drug having a TI of 2 or less than 2 would be relatively narrow therapeutic window.

For some drugs, such as cancer chemotherapeutic agents, the therapeutic effect cannot be

achieved without toxicity because the doses required, for example, to kill cancer cells, may also

affect some other rapidly multiplying cells such as those in the skin, bone marrow and

gastrointestinal tract.

The concept of TW can be expressed more precisely in a philosophical manner using a

therapeutic utility curve. Figure 7 shows the weighted probabilities of the various responses

plotted against the logarithm of plasma concentration. By algebraic summing the weighted

possibilities of each response, a curve representing the chance of net therapeutic effects versus

the systemic exposure, or simply a therapeutic utility curve can be obtained. Any range of

plasma concentration, with its corresponding therapeutic utility equal to or higher than the pre-

set values, is defined as the systemic exposure associated with therapeutic success, which is also

known as the TW of the drug. However, owning to the subjective nature of therapeutic utility

curve, the width of TW largely depends on the pre-set value of the therapeutic utility and the

assigned relative weightings of each response.

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 16

Drug Concentration and Therapeutic Response

Figure 7 shows a schematic diagram of the therapeutic utility curve.

The concept of TW based on systemic exposure is depicted in Figure 6. A therapeutic failure is

principally associated with systemic concentration below or above the TW, owing to the absence

of adequate efficacy and the inability of having adequate efficacy without toxicity respectively.

A successful therapy, or an effective therapy with minimal adverse effects, is more likely to be

achieved if the plasma concentration falls within the TW. However, therapeutic and adverse

responses of drug often correlate poorly with plasma concentration, thus adding further

complexity to TW determination. Development of is one classic example of poor

correlation; here, repeated drug exposure leads to the loss of response despite maintenance of

plasma concentration. Another example is the contribution of active metabolites to drug

response, whereby the measurement of plasma concentration of parent drug alone is insufficient

to establish the correlation. It is difficult to correlate the systemic exposure of effective single-

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 17

Drug Concentration and Therapeutic Response dose therapy with its therapeutic effect, for example morphine (to alleviate acute pain) and

nitroglycerin (to relieve angina pectoris). Occasionally, the response to certain drugs may relate

more closely to the duration and dose of therapy, instead of the plasma concentration.

Furthermore, time delays in drug effects can also complicate the relationship between systemic

exposure and response.

Table 1: Therapeutic window of selected drugs, where concentrations above the

therapeutic range will cause toxicity.

Drug Therapeutic Range (µg/mL) Therapeutic range (µmol/L)

Amikacin 15 - 25 25.62 - 42.70

Carbamazepine 5 - 12 21.16 - 50.80

Cyclosporine 0.1 - 0.4 0.08 - 0.33

Digoxin 0.0008 - 0.002 0.00102 - 0.00256

Gentamicin 5 - 10 10.45 - 20.90

Imipramine 0.15 - 0.3 0.53 - 1.07

Lidocaine 1.5 - 5.0 6.40 - 21.34

Quinidine 2 - 5 6.16 - 15.41

Tacrolimus 0.005 - 0.015 0.004 - 0.025

Theophylline 10 - 20 55.50 - 111.00

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 18

Drug Concentration and Therapeutic Response 5. The relationship between drug concentration and pharmacological effects in the whole

animal/human

In pharmacology, relationships between drug dose and response are described using models

based on classical receptor theory. Dose-response curves are constructed by measuring a

response (e.g. contraction of a muscle) at different doses. In , a fixed dose

administered to a range of individuals will produce a range of concentration measurements due

to individual pharmacokinetic variability; different individuals absorb, metabolise and excrete

drugs at different rates, with drug concentrations in the body changing over time. It is therefore

common to consider “concentration-effect” relationships rather than dose-response relationships.

In clinical practice, some drugs may be administered at doses that are at the top of the dose-

response curve. In such cases, increasing the dose will not improve response but may increase

the likelihood of toxicity. In contrast, sometimes it is not possible to reach the top of the

concentration-effect curve due to unacceptable toxicity. In such cases, simpler concentration-

effect models, such as linear or log linear models may be adequate to describe the relationship

between drug concentration and effect. There are conditions in which the drug concentration not

a good sign of therapeutic response. These include:-

i. Drugs used at concentrations which give a maximum effect.

ii. Hit and run drugs; some drugs act irreversibly e.g. the effect of aspirin on

cyclooxygenase in platelets or the MAO inhibitors. Termination of these effects relies on

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 19

Drug Concentration and Therapeutic Response synthesis of new platelets or MAO, so that there is no evident relationship between drug

concentration and effect.

iii. Delayed distribution. There are some drug which is slowly distributed at the site of drug

action. The best example is digoxin. Digoxin drug concentrations after an administration

showed a smaller therapeutic response due to delayed distribution. However, after some

time period when drug concentration fall due to redistribution to the site of action, the

therapeutic response increases as compared to initial higher concentration.

iv. The wrong effect can be measured. For example, after the first dose as the warfarin

concentration decreases, the effect of warfarin on prothrombin time increases. The rate of

onset of effect is determined by the rate of fall of existing clotting factors. As we know

that the direct effect of warfarin is on the rate of synthesis of clotting factor. If this is

measured directly than warfarin concentration corelates well with the therapeutic

response.

v. (Acute tolerance) develops. Drug therapeutic effectiveness decreases with

continued use of drug is called tolerance. Amphetamine or are good examples.

Drug concentrations after a single dose cause a greater therapeutic effect than the same

concentrations used at later time causes less therapeutic effect.

6. Pharmacodynamic (PD) models

Pharmacodynamic models describe the relationship between drug concentration at the site of

action and the effect. PD models use data derived from plasma drug concentration vs. time

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 20

Drug Concentration and Therapeutic Response profile and from the time course of pharmacological effect to predict the pharmacodynamics of

the drug. There are various direct and indirect PD model. In this module, we have explained only

direct PD models. The characteristics of direct models are:-.

i. the drug has a direct effect,

ii. The action of the drug is rapid and

iii. there is a rapid equilibrium of the drug between its site of action and the sampled

biological fluids.

6.1. Linear Concentration-Effect Model

This model assumes that there is a direct linear relationship between the drug concentration and

the effect. For example, linear relationships have been observed when the fall in blood pressure

is plotted against the plasma concentration of a calcium antagonist. Note that the effect could be

an increase or a decrease in a measurement, for example, a calcium antagonist may increase

heart rate whereas a beta blocker reduces heart rate.

E=S.C +E0

where E is the drug response, S is the slope, C is the concentration of drug and E0 is the base

response level without drug

6.2. Log-Linear Concentration-Effect Model

The improvised version of this model, log-linear model is expressed as E=S. log C +E0, showing

that the drug response is directly proportional to the log of the concentration of drug. However,

as described earlier, as drug concentration increases the response reaches a maximum above

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 21

Drug Concentration and Therapeutic Response which there is no further increase in response to further increases in dose. Hence, the models are

only valid within certain ranges of drug concentration; the drug response has to be within the

range 20-80% of the maximum effect.

Figure 8: Graph of response against concentration with log linear portion

6.3. Emax Concentration-Effect Model The Emax model provides a better description of the true nature of the relationship between drug concentration and effect. It can be seen that concentrations of the test drug are increased further,

the increase in response is very small as the effect reaches Emax. E0, the maximum possible

effect (Emax), and the drug concentration producing half

maximal effect (EC50)

E=

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 22

Drug Concentration and Therapeutic Response

6.4. Sigmoidal Emax Concentration-Effect Model A further extension of the Emax model is the “Sigmoidal” Emax model (“Hill equation”), which

contains an additional parameter gamma (γ) is the slope factor of curve to describe the

“steepness” of the concentration-effect curve. This more general equation allows concentration-

effect profiles to vary in shape as seen in figure 9. A steep slope, with γ >1 implies that a small

change in concentration will produce a large change in effect. At the extreme, it is sometimes

reported as an “all or none” response (see profile for γ = 5). A shallow slope indicates that a large

change in concentration will be required to achieve a change in effect. This is often referred to as

a “flat” dose-response relationship (see profile for γ = 0.5). However, “flat” concentration-effect

relationships also occur if the maximum effect has already been reached, e.g.

bendroflumethiazide dose and blood pressure reduction. In that example, an increase in dose has

no effect on the therapeutic response but increases the likelihood of toxic effects.

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 23

Drug Concentration and Therapeutic Response

Figure 9. Sigmoidal E-max model (Hill equation)

In many cases, there is no simple clinical response measurement, such as blood pressure, that can

be directly related to drug concentration. In addition, responses after a single dose may differ

from those observed at steady state (e.g. “first dose effect” of ACE inhibitors). For antibiotics,

anti-cancer drugs and immunosuppressants, “response” may be a clinical parameter, such as

temperature or white cell count, or a percentage probability of clinical success or failure, such as

resolution of the infection, tumour response, tissue rejection or toxicity. Some responses may be

all or none – i.e. death or survival, whereas others may be graded, such as the severity of toxicity

to an anticancer drug.

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 24

Drug Concentration and Therapeutic Response

7. Onset and Duration of Action

A rapid equilibration between drug plasma concentration and its site of action coupled to a rapid onset

and offset of effect will produce an effect-time profile that mimics the drug concentration-time profile.

However, for many drugs there is a delay in such equilibration. The factor which influences duration of

drug action are amount of drug (dose size) and the rate of removal of drug from site of action.

Alternatively the pharmacological response may depend on a time-dependent induction or inhibition of a

biochemical or receptor process. In these cases, the maximum effect does not occur at the time of the

maximum concentration but lags behind. For example, if an antibiotic is given by IV bolus injection to

treat a deep-seated tissue infection, the maximum drug concentration will occur at the time of the

injection. However, it still has to distribute to the tissues and then into the organism to exert its effect on

cell wall or protein synthesis. The onset and duration of the response to warfarin depends both on the

pharmacokinetics of warfarin itself and of the clotting factors. These delays lead to a lag between peak

blood concentration and the peak effect.

Pharmaceutical Biopharmaceutics and Pharmacokinetics sciences Drug Concentration and Therapeutic Response 25