Drugs should be used to prevent, to cure and to diagnose diseases.
Pharmacology is the study of the actions, uses, mechanisms, and adverse effects of drugs.
Pharmacodynamics, Pharmacokinetics
Toxicology

Pharmacodynamics is the study of the biochemical and physiological effects of drugs and their mechanism of action

1. General classification of Drugs effects

A. Excitation is an increase or enhancement of mental activity by a drug. For example, stimulation of mental activity by caffeine.
Inhibition is a decrease of the function produced by a drug. For example, barbiturates induced sedative-hypnotic effect.

B. Direct Action refers to the action produced directly by a drug at the site of contact with drug. A direct action at one part can at times elicit effects on remote organs or tissues, which are designated as indirect action .

For example, norepinephrine constricts the blood vessels directly, increases blood pressure, It is the direct action. It reflexively decreases heart rate. That is the indirect action.

C. Selectivity : A drug is usually described by its most prominent effect or by the action thought to be the basis of that effect.
Cardiac glycosides mainly stimulate myocardium; diazepam inhibits central nervous system; streptomycin suppresses tubercle bacilli.

D. Therapeutic effect is the effect affecting the physiological and biochemical functions of the organisms and pathogenic processes.
It is used to prevent and treat diseases.

Etiological treatment means that the drug may eliminate the primary pathogenic factor and cure disease. Such as, antibiotics eliminate pathogenic organisms within body.

Symptomatic treatment means that the drug may improve the symptoms of disease, such as, use aspirin to treat high fever. In some critical condition, shock, convulsion, congestive heart failure, high fever, severe pain, symptomatic treatment is more urgent than etiological treatment.

E. adverse effect :
Any response to drug that is noxious and unintended and that occurs at doses used in man for prevention, diagnosis and therapy of a disease, or for the modification of physiological function.

Side effects of drugs are the effects which we do not want to have , but are nondeleterious, such as dry mouth with atropine which treat the spasm of intestine .

Toxic effects mean noxious effects induced by over dosage of drugs or accumulation of large amount of drugs.

They include acute toxicity which may damage the functions of circulatory system, respiratory system and nervous system, and chronic toxicity which may damage hepatic, renal, bone marrow and endocrine function.

Carcinogenesis, teratogenesis and mutagenesis belong to chronic toxicity.
Toxic effect are necessary prelude to avoidance of them or, if they occur, to rational and successful management of them.

Allergy is an adverse reaction that result from previous sensitization to a particular chemical or to one that is structurally similar. Such reactions are mediated by the immune system. The terms hypersensitivity and drug allergy are often used to describe the allergic state.

After effect : The effect still exists , after withdrawal of the drug, the drug concentration is below the threshold, such as, the patient feels hangover next morning, after taking barbiturates.

Secondary reaction : After long term of using broad spectrum antibiotics, due to the change of intestinal normal flora, the sensitive bacteria are abolished, then it appears the overgrowth of non-sensitivity bacteria such as staphylococcus and fungi, staphylococcus enteritis or candida infection (candidiasis) appears, This called secondary reaction.

Graded Dose- Response curve
As the dose administered to a single subject or isolated tissue is increased, the pharmacologic effect will also increase. At a certain dose, the effect will reach a maximum level.

Efficacy : The maximum effect of drug, E max is a measure of drug efficacy. Efficacy is also called intrinsic activity.

Potency : A comparative measure, refers to the different doses of two drugs that are needed to produced the same degree of effect. These two drugs have similar chemical structure and mechanisms of action. The lower the dose of drug effect, the higher the potency of drug.

Graded dose-response curve for three drugs
Efficacy and potency

B. Quantal Dose – Response Curve
1. A quantal response is an all –or – none response to a drug and relates to the frequency with which a specified dose of a drug produces a specified response in a population.

2. The quantal dose-response curve is a cumulative graph of the frequency distribution curve . The dose of drug required to produce a specified magnitude of effect in a large number of individual patients or experimental animals are plotted the cumulative frequency distribution of responses versus the log dose.

The specific quantal effect may be chosen on the basis of the clinic relevance (e.g. relief of headache or it may be in experimental animal). When these responses are summated, the resulting cumulative frequency distribution constitutes a quantal- dose-effect curve of the proportion or percentage of individuals who exhibit the effect plotted as a function of log dose.

Quantal dose – effect plots

Quantal dose – effect curve may also be used to generate information regarding the margin of safety to be expected from a particular drug used to produced a specified effect

ED
50
: The dose at which 50% of the individuals exhibit the specified quantal effect.
LD
50
: The dose at which 50% of the animals exhibit death.

Therapeutic index (TI) = LD
50
/ ED
50

Dose-response curve of effect and toxicity of A,B equal ED50 and LD50, toxicity B>A

A and B: to have same TI, difference slope

III. Receptor Theory and Drug Receptor
Interaction

Receptor . Macromolecular structure to which a drug binds in such a way as to initiate or modify a biological function.

D+R
K
1
K
2
DR
……E
Note: D: drug; R: receptor; DR: drug receptor complex; E: effect; K: rate constant.

A. Receptor Theory

1. Receptor occupation theory

When the receptors are occupied, the pharmacological effects will occur. The effects of drug are directly proportional to the numbers of receptors occupied.
Stephenson revised the opinion; it is not necessary to occupy all the receptors, when the maximal effect occurs.

Affinity : It is the tendency of a drug to form a combination with the receptors
Affinity = 1/K
D
; K
D
= dissociation constant

Intrinsic activity : Its inherent ability to produce an effect

Dissociation constant, K
D is a characteristic of the drug and of the receptor, it has the dimensions of concentration and is numerically equal to the concentration of drug required to occupy 50% of the sites of equilibrium (50% of the maximal effect. Minus log K
D is pD
2
= -log K
D
), which is called affinity index. The higher the affinity of the drug for the receptor, the lower will be K same time, the higher pD
2
D
, at the
, the stronger will be the effect of the drug.

A B
A: a, b, c (equal pD
2
, difference E max
)
B: a, b, c (equal E max
, difference pD
2
)

2 . Rate Theory : The response of a drug is the function of the rate of dissociation of drug receptor complex.

3. Two model theory : Receptors have to different conformation, activated conformation (R* ) and resting conformation (R ).
They may change to the other one. Activated form may combine with agonists, then may show its effect; resting conformation may combine with antagonist, which has no effect.

Ligand : chemical substances which can combine with receptors are called ligands, ligands include drug, hormones and neurotransmitters.

Spare receptors : For a highly active agonist with a high efficacy, the maximal response will be produced by a concentration that dose not occupy all receptors. The receptors remain unoccupied are termed spare receptors.

1. An agonist has high affinity to receptors and high intrinsic activity. An agonist is a drug that produces a pharmacological effect when it combine with receptors

An antagonist binds to the receptors to inhibit the action of an agonist, but initiate no effect themselves. Sometimes, the inhibition can be overcome by increasing the concentration of the agonist, ultimately achieving the same maximal effect.
Examples of pure antagonists are atropine and curare, which inhibit the effects of acetylcholine.

Partial agonists : They have agonistic activity but also have antagonistic activity

Pharmacological Antagonism occurs when an antagonist prevent an agonist from acting upon its receptors to produce an effect

1. Competitive antagonism : Competitive antagonists compete with agonists in a reversible fashion for the same receptor site. When the antagonist is present, the log dose-response curve is shifted to the right.
In the presence of a fixed concentration of agonist, increasing concentration of a competitive antagonist progressively inhibit the agonist response; high antagonist concentrations prevent response completely.

Non competitive antagonism : The noncompetitive antagonist binds irreversibly to the receptor site or to another site that inhibits the response to the agonist.
For example, drugs such as Verapamil and
Nifedipine prevent the influx of calcium ions through the cell membrane and thus block non-specifically the contraction of smooth muscle produced by other drugs.

Graded dose-response curve illustrating the effect of competitive antagonists

Graded dose-response curve illustrating the effect of non-competitive antagonists

D. Enhancement of drug effect

1. Additive drug effects occur if two drug with the same effect, when given together, produce an effect that is equal in magnitude to the sum of the effects when the drugs are given individually:
E
AB
= E
A
+ E
B

2. Synergism occurs if two drugs with the same effect, when given together, produce an effect that is greater in magnitude than the sum of the effects when the drugs are given individually.
E
AB
> E
A
+ E
B

3. Potentiation occurs if a drug lacking an effect of its own increases the effect of a second, active drug:
E
AB
> E
A
+ E
B

IV. Cellular Response of Receptor- Effector
Linkage.

Drugs or ligands combine with receptors induce a series of cellular responses and hence physiological or biochemical effects.
These are four types of cellular responses.

A. Direct Regulation of Membrane
Permeability to Ions

After drug combine with receptors, the receptors are activated. This has effects on ion channel of membrane, changing ion flow across the transmembrane, generating membrane potential or changing intracellular ion concentration, that may induce physiological effect. Such as when cholinergic receptors are activated at neuromuscular junction, Na + influx will be increased.

B. Regulation via Intracellular Second
Messages:

After the receptors are activated, the second message C-AMP / C-GMP increases or decreases, phosphatidyl-inositol-4.5biphosphate(PIP
2
) decomposes to the second messagers inositol triphosphate ( IP
3
) and diacylglycerol ( DG ).

Effect of second message

C. Direct Modulation of Protein phosphorylation, such as insulin receptor

D: Regulation of DNA Transcription

Regulation of protein synthesis: it induces biochemical and physiological effect, such as steroid hormones.

Type of receptor – effector linkage
CR-receptor, G=G-protein; E=enzyme

V. Receptor Families and Their Transducer and Effector Molecules.

Receptor has ligand – binding domain and effctor domain.

A. Receptors as Enzymes

This class of receptor molecules mediates the first step in signaling by insulin, epidermal growth factor (EGF), platelet- derived growth factor
(PDGF), atrial natriuretic factor (ANF), transforming growth factor –
β
(TGF
β
), and many other topic hormones. These receptors are polypeptides consisting of an extracellular hormone binding domain and a cytoplasmic enzyme domain, which may be a protein tyrosine kinase, a serine kinase, or a guanylyl cyclase.

Catalytic activities:
Tyrosine kinase : growth factor receptors, neurotrophic factor receptors
Insulin, epidermal growth factor (EGF) receptors, platelet- derived growth factor
(PDGF) receptors

B: Multisubunit ligand-gated Ion Channels
Nicotinic Ach receptor
Glutamate receptor, GABA
A receptor
Glycine receptor, 5-HT
3 receptor

C. G-protein – Coupled Receptor Systems

G- protein – coupled receptors comprise many of the receptors, 5-HT receptors, opiate receptors, receptors for many peptides, purine receptors and many others, including the chemoreceptors involved in olfaction.

1. G protein coupled binding site.
They consist a single polypeptide chain of
400-500 residues. They all possess seven transmembrane - α helics. Both the extracellular amino terminus and the intracellular carboxyl terminus vary greatly in length and sequence. Agonists combine with the receptors.

2. G protein
G protein is the short term of guanine nucleotide – binding protein (also called
GTP-binding protein). The G proteins are bond to the inner face of plasma membrane.
They are heterotrimeric molecules (subunits are designated α,β andγ )

When the system in inactive, GDP is bond to the α subunit. An agonist – receptor complex facilitates GTP binding to the subunit in part by promoting the dissociation of bond GDP. Binding of GTP activates the α subunit, and the α–GTP subunit is then thought to dissociate from the
β, γ subunit and interact with a membrane bound effector.

There are two types of G-protein, one is excitatory G-protein (Gs) which stimulates adenylyl cyclase (AC) to increase cAMP.
Another is inhibitory G-protein (Gi) which inhibits AC and decrease cAMP

GDP-binding protein activation of effectors is regulated simultaneously by a GTPase cycle and α submit association / dissociation cycle. The GTP-liganded subunit activates some processes exclusively, and release of
β γ subunit, upon activation of Gα allows for regulation by
β γ subunit of shared or distinct effectors.

The regulatory cycles involved in G proteinmediated signal transduction.

3. Effectors.

D: Nucleus Receptors:
Regulation of transcription : Receptor for steroid hormones, thyroid hormone, retinoid are soluble DNA-binding proteins that regulate the transcription of specific genes.

VI. Relationship Between Regulatory
Mechanisms of Receptors and the
Pharmacological Action

Receptors are themselves subject to regulatory control, superstimulation or subnormal response may occur if the receptor activity or receptor numbers have been modified by up-or down regulation.
Such regulatory mechanisms are usually evident with chronic use of a agonist or an antagonist.

Receptor down regulation (desensitization) may follow continued stimulation of cells with agonists. Several mechanisms are possible (1) phosphorylation of the receptors, destruction of the receptors, relocalization, sequestiation (isolation of receptor); (2) decreased synthesis and number of receptors. For example, chronic use of isoprenaline for asthmatic patient the bronchial relaxation effect will be decreased.

Receptor up-regulation (supersensitivity) may follow continued use of antagonists (or denervation), usually synthesis of additional receptors. Up-regulation is connected with increase of sensitization for chronic use of in antagonist or having symptoms induced by withdraw of drugs, such as after chronic use of propranolol for hypertensive patient, suddenly stop to use it, it will induce rebound (increase of blood pressure)

VII. Mechanism of Action

A. Change the Physical and Chemical
Properties of the cellular Environment:
Antacid neutralizes gastric acid, IV mannitol induces diuretic effect (osmotic diuretic)

B. Interfere or Incorporate into Metabolic
Process: Sulfarages inhibit dihydrofolic synthetase, and interfere the synthesis of dihydrofolic acid, nucleic acid and protein.
Cholinesterase inhibitors increase the effect of Ach.

C. Influence of Biologic Membrane: antiarrhythmic drugs influence Na + , Ca 2+ , K + transport. Polymycin B, E can damage bacterial cytoplasmic membrane.

D. Influence Physiological Transmitters and hormones: Ephedrine enhances the release of NA from the adrenergic nerve endings.
Tolbutamide enhances the release of insulin and decreases the blood sugar concentration.

E: Influence of enzyme: omeprazole inhibit the Na + -K + ATPase of stomach to treat stomach ulcer

F: Influence of nucleic acid metabolism: nucleic acid metabolism of bacteria is influenced by antibiotics to abolished the life of bacteria.

F. Receptors.

Pharmacokinetics : That considers drug disposition and the way the body affects the drug with time i.e. the factors that determine its absorption, distribution, metabolism and excretion.
So, we know how rapidly and in what concentration and for how long the drug will appear at the target organ.

Drug transportation: In order to reach its site of action (receptor site), a drug have to traverse a succession of membranes
1. Passive diffusion : passive diffusion take place when a drug molecule moves from a region of relatively high to one of low concentration without requiring energy, carrier, saturation and competitive inhibition. Simple diffusion is major state of passive diffusion for drug transportation.

The rate of diffusion depend on the state, area and a concentration gradient of membrane. Nature of drug is key point to across the cell membrane. The drug which are small molecules (<200D), lipid solubility of drug, unionized form are easy to across the membrane.

Most drugs are either weak acid or bases.
Therefore, the pH of environment in which they dissolve, as well as the pKa of the drugs will be important in determining the fraction in unionized form that is in solution and able to diffuse across cell membrane.

The pKa of drug is define as the pH at which 50% of the molecules in solution are in the ionized form
Handerson – Hasselbalch equation
For an acid For a bases

Drugs exist in non-ionized and ionized forms. The non-ionized form of drugs are more lipid soluble and able to penetrate the cellular membrane, but ionized form of drugs are very difficult to penetrate the membrane. That is called ion trapping .

Weak acids (e.g. barbiturates) are more readily absorbed from the stomach than from other regions. Weak base drugs are more absorbed from the intestines than from stomach.

2. Active transport is a carrier – mediated process. This process require energy and proceed against a concentration gradient.
Such as methyldopa. The carriers of drug are selective and saturable in transport process. Like Probenecid blocks the active tubular secretion of Penicillin and hence prolong its action.

With facilitated diffusion , the transport process is selective and saturable, but the drug is not transferred against a concentration gradient. Such as absorption of glucose.

The mechanisms and disposition of drugs by the body.

Absorption : (1). Administration of gastrointestinal tract : most drugs are administered orally. The tablet and capsule need to be disintegration and dissolution, then that may be absorbed

The major portion of drug absorption is in small intestine, which has considerably greater absorptive surface, to wriggle slowly, particularly, pH = 7.4 (neutral)

Drugs that are administered orally and enter the portal circulation of liver and can be biotransformed by this organ prior to reaching the system circulation. This is called first pass elimination . Some drugs are reduced by first pass elimination. so the sublingual and rectum administration are recommended to avoid the first pass elimination

(2): Injection: Intravenous injection and intravenous infusion are administration which directly enter circulation and rapidly act in the body

(3): Other parenteral method. Such as intramuscular injection and subcutaneous injection are important method. The drugs via these methods are absorbed better, which are related to the temperature of site. massaging of the site where a drug has been administered increases the rate of absorption. Vasoconstrictive substance may prolong the absorption of drug.

(4): Special method: such as intra-artery, local anesthetics were also used in order to avoid the side effect of body. Administration of respiration tract: Aerosol vaporize the drug solution into small particle (5µm), so it may be absorbed through the capillaries which adhere to the pneumoaheolus face, but the face area is larger and the blood volume of lung is rich. Such as aerosol of isoprenaline is used to treat asthma

Transdermal administration : the lipophilic drugs may pass through the skin, so it is absorbed slowly, such as, toxicosis of pesticide, and Transderm-nitro (nitroglycerin) and Nifedipine are used to prevent the angina from attack.

Drug distribution

The drug has the plasma protein binding after the drug enters the circulation. Nonbinding drugs are called free drugs. More acidic drugs are bound to albumin, more basic drugs are bound to α
1 acid glucoprotein. Less drugs are bound to globulin.
The state of binding similar to receptor binding of drug . The percent protein binding is very important, because the part does not exert any pharmacological effects, but has a store form in plasma.

Plasma protein binding is a reversible process, that is influenced by DP, D, and K
D of plasma. The binding site of protein are not unlimited and subject to saturation. The percent protein binding of drugs varies dramatically. Drugs may alter the protein binding of other agents. Such as, only a slight displacement of a highly bound drug like bishydroxycoumarin can oral anticoagulant by phenvlbutazone, can cause serious haemorrhage.
Because only 1% of anticoagulant is free, and additional displacement of 1% increase its effect by 100%.

The rate of distribution of drug from blood to tissue depend on the blood volume of organs. The more blood volume the organ has, the faster the amount of drug diffused.
Then there is a redistribution in some organs. e.g. Thiopental is lipophilic drug, and it diffuses into brain more quickly, then, redistribute to the fat and other tissues.

The concentration of drug at target organ should be measured through the concentration of plasma. So the effect of the drug may be estimated at target organ.

The pKa and pH are other key points.
Generally, weak base drugs penetrate the cellular membrane facilely when the toxicity of weak acid drug take place, the basic substance should be used to alkalify the blood in order to transfer the acid drugs out of the cells

Blood-Brain Barrier : Drug can enter the brain from circulation by pass through the blood-brain barrier. This boundary consist of several membranes, including those of capillary wall, the glial cells closely surrounding the capillary, and neuron. Such a structure limit the entry of many drugs into the brain.

Some drugs may be modified to avoid the centre nervous system reaction. Such as
Atropine methyl-atropine. Haloperidol
N-n-butyl haloperidol iodide

The placental barrier is membrane separating fetal blood from maternal blood in intervillous space. It resembles the capillary, and almost all drugs may penetrate the placental barrier. During pregnancy, the drugs which affect fetal developing should be contraindicated.

Drug Biotransformation

Drug is a xenobiotic. Before being excreted from body, most drugs are metabolized. A small number of drug exist in their fully ionized form. More lipid-soluble drugs are metabolized by the liver. The goal of metabolism is to produce metabolites that are polar, or charged, and can be eliminated by the body.

Using two general sets of reaction, called phase I and phase II . Phase I metabolic reaction include oxidation, reduction and hydrolysis . Phase II reaction involve conjugation . During phase I , most drugs are inactivated pharmacologically, a few drugs become more active and toxic in nature.
Phase II result in the drug being more hydrophilic and thus more easily excreted from the body.

The hepatic cytochrome P450 is the most important enzyme ( hepatic drug enzyme ). It consist of more than 70 enzymes. A drug substrate binds to cytochrome P450, then the complex acquired two hydrogen ions, a molecular oxygen from NADPH and cytochrome b undergoes hydroxylation by O, the another O bind the two H + to H
2
RH + NADPH + O
2
O.
+2 H
+
5 and the drug
ROH + NADP+ H
2
O
The enzyme system is called mixed function oxidases or monooxygenase

Enzyme activation and inhibition. Some drugs are able to increase the activity of certain isoenzyme forms of cytochrome P450 and thus increase their own metabolism, as well as that of other drugs.
So that it may enhance the tolerance of drugs for the body. Such as phenobarbital. In contrast, some drugs inhibit cytochrome P450 activity and therefore increase their own activity as well as that of other drugs, like cimetidine.

In cytochrome P450 system, CYP3 and
CYP2c play a significant role, that related to the metabolism of many drugs. 30-50% of drugs are metabolised by CYPA4 which is the member of CYP3.

Cytochrome P-450 transformation (oxidation)

Cytochrome P-450 transformation (reduction)

Phase II reactions are conjugation reaction:
To combine a glucuronic acid , sulfuric acid, or glycine with the drug to make it more polar, the high polar drugs can then be excreted by kidney.

Excretion of Drugs
Drugs are excreted from the body in variety of ways.
Excretion can occur by kidneys into urine. That is most important routes for the drug excretion. Some drugs in the blood pass into the glomerulor filtrate . Drugs can excreted in free forms (water-soluble substances). Nonionized lipid- soluble drugs may be reabsorbed by tubule. Some drug may transported into the lumen of the tubule by either of two transport mechanism. One transport mechanism deal with acidic molecules, the other with basic molecules.

Competition between drugs that share the same transport mechanism may occur, in which case the excretion of these drugs will be reduced. Probenecid is a drug that was designed to compete with penicillin for excretion and therefore increase the duration of action of penicillin.
Toxicity with acid drug can be treated by alkalifying which makes the urine more alkaline, this ionizes substance and renders it less prone to re-absorption. In contrast, basic drugs is same reason for their toxicity.

Renal disease will affect the excretion of certain drugs which may prolong the effect of these drugs. Such as cardiac glycosides administration.

Modify the urine of pH to treat toxicity.

Drugs are also excreted from the body by the bile, faeces and by the lungs into exhaled air. Drugs may leave the body through breast milk and sweat.

The excretion of the drugs from bile posses three transport channels, i.e. acid, base and neutrality channels. Some drugs conjugated are excreted into bile and subsequently released into the intestines where they are hydrolysted back to parent compound and reabsorbed ( hepatoenteral circulation ). This effect of circulation prolongs the action of drugs, but in hepatocholangiostomy, the stay time of drugs in plasma which is excreted by bile may be shorten.

The change course of drug concentration with time (time- concentration relationship)

The relationship is described by time-Concentration curve

The ascending limb of curve is considered to be a general reflection of the rate of drug absorption. The peak concentration ( Cmax ) express same speed between absorbing and eliminating course. The time to reach the peak concentration of the drug is Tpeak . The descending limb of the concentration- time curve is a general indication of the rate elimination of the drug from the body. The time of overeffect concentration is effective period. The concentration in blood by one-half is called elimination half life.

The area under the concentration-time curve : AUC
It described the relative dose of drug that enter the circulation. AUC is an indication of bioavailability.

Bioavailability is the amount and speed of drug that is absorbed after administration by route X compare with the amount and speed of drug that is absorbed after intravenous
(IV) administration. X is any route of drug administration other than IV.

F = A / D *100%
D: Dose of drug A: dose of entering circulation
Absolute F=AUC ( oral) / AUC ( iv) *100%
Relative F=AUC (test) / AUC (standard) *100%
Standard drug compared with test drug to get the rate of absorption.

The bioavailability of different drugs is assessed by an evaluation of parameters
The peak concentration; The time to reach the peak concentration; The area under the concentration-time curve
The extent to which the bioavailability of one preparation form differs from that of another must be evaluated.

Bioavailability of three form preparations

Drug elimination kinetics is the eliminating course of plasma or blood concentration of drug with its distribution, metabolism and excretion. It is expressed by mathematics equation: dc / dt = -k*C n
C: plasma concentration(dose/volume) ; A: dose of plasma volume; k: rate constant

First-order kinetics : drug disappear from plasma by process that are concentration dependent. The higher of drug concentration is, the more the drug elimination in unit time is. The elimination is in percentage course: n=1 dc / dt = k e lnC t
= ln C
0
– k e
*C t
1 C t
=C
0 e -ket to convert from nature log to base 10 log units
Log C t
= log C
0
– k e
/ 2.303*t t = log C
0
/ C t
* 2.303/k e

When C t
= 1/2C
0 t
½
= log2 * 2.303/k e
= 0.301* 2.303/k e
= 0.693/k e the half life is 0.693/k e
. The half life is the period of the required for the concentration of drug to decrease by one half .
The half life is constant and related to k e for drugs in first order kinetics, and not related with plasma concentration ( C).
K e
: the fraction change in drug concentration per unit of time
K e
= 0.5 h -1 , t
1/2
= 1.39h

A t
=A
0 e0.693*n =A
0
(1/2) n When n=5, A t
= 3% . after 5 half life of a drug, the drug are almost eliminated

When a drug is given at dosing interval that is equal to its elimination half life, the steady state will be achieved in 5 half life.

C L(plasma clearance) is defined as the sum of clearance of all the organs (liver, kidney and so on). It is the volume of fluid cleared of a drug per unit time. CL of drug is different from the elimination rate which is rate of removal of drug in weight per unit time, but they are related as shown in the equation CL= k e
* V
D

V
D
(apparent volume of distribution) is defined as the volume of fluid into which a drug appears to distribute with concentration equal to that of plasma, or the volume of fluid necessary to dissolve the drug and yield the same concentration as that found in plasma
V
D
= dose administration / initial apparent plasma concentration

The volume of distribution is hypothetical apparent volume, but not a real volume. It gives a rough accounting of where a drug goes in the body, if you have a feel for the various body fluid compartments and their size. In addition, it can be used to calculate the dose of drug needed to achieve a desired plasma concentration.

Such as, some drugs have a volume of distribution that exceeds body weight, in which case tissue binding is occurring
(bone, fat, nucleic acid and so on)

V d
= A / C
0
d

CL = k e
* V
D
CL = A / AUC
= 0.693 / t
1/2
* V
D
When patient suffer from the damage of kidney or liver, the CL is decreased for drugs. The dose should be adjusted

Zero – order kinetics: drugs that saturate routs of elimination disappear from plasma in non-concentration-dependent manner.
Many drugs will show zero-order kinetics at high dose of toxic concentration.

dC/dt = -KC
0
= -K, C t
C t
/ C
0
=1/2, t = t
1/2
= C
0
-K t
, when slope = -K, t
1/2
C
0
=C
0
- k t1/2
, t
1/2
=0.5* C
0
/k
So, for drugs with zero-order kinetics, a constant amount of drug is lost per unit time.
The half life is not constant for zero-order reaction, but depend on the concentration. Drugs is eliminated at same speed, such as at alcohol toxicity state.

In clinic, the treatment need in a therapeutic level of drug. For a drug displaying firstorder kinetics, at first, the plasma level will be low and infusion rate will be greater than elimination rate, so, the drug will accumulate until the amount administered per unit time is equal to the amount eliminated per unit time

C ss
= RE / CL= RA / CL = D m
/ τ/ CL
= D m
/ τ / K e
*V
D
D m
= maintenance doses, τ = interval time
The time needed to reach steady state depends on the t
1/2
, K e
, V
D and CL , but not the speed of administration. The speed of administration determines the level of C ss
.

Intravenous infusion of drug get the steady state of plasma smoothly. With repeated dosing the concentration fluctuates between
C max and C min
. The longer the interval time is , the bigger the fluctuation is.

Time-concentration curve of intravenous infusion

If the C max is desired higher or lower, the rate of administration is adjusted, but after the 5 half lives, the new C ss is achieved.

Sometime, the patient can not wait for the therapeutic effect to occur. In this condition, a loading dose is used. Load dose is a single large dose of a drug that is used to raise the plasma concentration to a therapeutic level more quickly than usually occur through repeated smaller dose

A ss
A ss
= D m
+ A ss e -ket , D
= loading dose
1
= A ss
= D m
/ (1-e -ket )
At beginning, the 1.44 times of infusion dose which is dosage of first half life time, should be intravenous injected , and it may reach the C ss once. at
When interval time is t
1/2 be given at first time
, the double dose should
Except t
1/2 is much longer or shorter, zero – order kinetics, half dose at half life interval and double dose at first time are necessary to get a desired effect and less side effects

Compartment model
One compartment model : The body is a single compartment . With this single compartment, a drug is absorbed, immediately distribute (e.g. by intravenous injection). This situation expresses itself graphically as a straight line when the log plasma concentration is plotted against the time after IV dose

the log plasma concentration is plotted against the time after IV dose with the one-compartment model

Two compartment model
The distribution of drug between the peripheral compartment. (Such as , muscle , skin and fat depots) and central compartment (such as brain, heart, liver and kidney). Because of the rich blood volume of central compartment organs, the drug firstly enter the central compartment, then enter the peripheral compartment.

C = A e
–αt
+ B e
–βt
An early, rapid, α-phase , which represent the redistribution of the drug to the peripheral compartment and a modest component of elimination. An later, slow, β –phase, which is combination of elimination and return of drug form to peripheral compartment to the central compartment in which the drug distribution rapidly.

Time-concentration curve of two compartment