Pharmacology3(pharmacokinetics)

Chapter III Pharmacokinetics

DURGE RAJ GHALAN [email protected]

Learning Objectives 1. Describe the physicochemical factors that influence the absorption of drugs from enteral and parenteral routes of administration, their distribution within the body, metabolism (or biotransformation) and their routes and mechanism of excretion (ADME). Metabolism and Excretion are called Elimination

2. Explain how dose, bioavailability, rate of absorption, apparent volume of distribution, total clearance and elimination half-life affect the plasma concentrations of a drug after administration of a single dose. 3. Describe the factors that determine the time-course of systemic accumulation of a drug administered by infusion or multiple doses.

tissues

target of drug

binding and storage

sites of action

liver or extrahepatic biotransformation

Distribution Absorption sites of drug administration

free drug systemic circulation

Metabolism Excretion Metabolites

binding drug

Fig. 3-1 Schematic representation of the ADME process of a drug. Drug was absorbed from the sites of administration into the systemic circulation, in which they reversibly bind to albumin or other proteins. The bound drug is inactive, therefore it is limited its systemic distribution, metabolism and excretion. Only free drug is able to cross membrane to reach tissues, sites of drug action and be metabolized or excreted.

Transport Across Cell Membranes 1. Passive transport 2. Active transport 3. others: endocytosis or pinocytosis, facilitated diffusion, ion-pair transport

1. Passive transport a. Passage through lipid cell membrane by dissolution in membrane, simple diffusion and filtration. b. rate dependent on concentration gradient and lipid: water partition coefficient of drug. c. rate markedly higher for nonionized form of weak electrolyte because of its higher lipophilicity than the ionized form.

the characteristics of passive transport: a. no carrier requirement b. no energy requirement c. no saturability d. no competitive inhibition by cotransported compounds e. the concentration of the free drug is the same on both sides of the membrane at the steady state.

1. Therefore, the transmembrane distribution of a weak electrolyte is usually determined by its pKa and the pH gradient across the membrane. 2. The ratio of nonionized to ionized drug at each pH is easily calculated from the Herdersonhasselbalch equation.

Weak Electrolytes and Influence of pH Herderson-hasselbalch equation

pKa : pKa is the pH at which nonionized form of the drug is equal to ionized form of the drug. pKa of a drug is determined by the physicochemical property of the drug.

[X]

1000• [X]

A - + H+

HA plasma

pH = 7.4 Lipid mucosal barrier

(ion trapping)

gastric juice

pH = 2.4

HA [X]

weak acid

HA

nonionized

A - + H+

0.01• [X]

A - + H+

pKa=4.4

ionized

Fig.3-2 Lipid mucosal barrier acts as an ion trapping . Ion trapping is significant for many weak acid or base drugs. For example, when a weak acid drug (pKa=4.4) is dissolved in the gastric juice (pH=2.4), its concentration difference of ionized drug between both sides of lipid mucosal barrier is 100,000 times because the PH value of plasma is 7.4. Acidic drugs are well absorbed in the acidic medium of the stomach, however it is better for the absorptions of basic drugs in the alkaline medium of the small bowel.

Summary 1. More of a weak acid will be in the lipid-soluble form at acid pH, while more of a basic drug will be in the lipid-soluble form at alkaline pH. 2. This principle can be applied in the absorption, distribution and in the manipulation of drug excretion by the kidney.

Question ? Somebody was poisoned by overdose administration of Phenobarbital (weak acid), how to accelerate the excretion of the drug ? Sodium bicarbonate , alkaline urine ammonium chloride , acidic urine

2. Active transport a. Passage facilitated by an energy-dependent membrane carrier mechanism such that transport can occur against a concentration gradient. b. Passage characterized by the requirement of energy, saturability, selectivity and competitive inhibition by cotransported compounds. c. Transporters include the family of ATP-dependent proteins.

Absorption of Drugs 1. general determinants of absorption rate Lipid solubility, ionization, size of the molecule, and presence of a transport mechanism. Others like concentration gradient, blood flow, and surface area of absorption site.

2. routes of drug administration a. Oral (p.o.) ingestion 1) convenient route for administration of solid as well as liquid formulations. 2) first-pass elimination: absorbed drug passes via portal circulation through liver which may clear substantial fraction and thus decrease bioavailability.

What is first-pass effect? A drug that is absorbed from the stomach and intestine must first pass through the liver before it reaches the systemic circulation. If the drug is metabolized in the liver or excreted in the bile, some of the active drug will be inactivated or diverted before it can reach the general circulation and be distributed to its sites of action. If the metabolic or excretory capacity of the liver for the agent is great, bioavailability will be substantially decreased. That is so called first-pass effect.

3) Additional variables which may influence rate and extent of absorption include disintegration and dissolution of solids, acidity of gastric contents, gastric emptying rate, intraluminal biotransformation by host or bacterial enzymes, dietary contents, and presence of other drugs.

b. Parenteral Injection 1) Intravenous(i.v.) Injection: complete bioavailability; drugs only given in sterile solution; important when immediate effect required; increased risk of toxicity. 2) Subcutaneous(s.c.) and Intramuscular(i.m.) Administration: more extensive absorption of high molecular weight, polar molecules than by p.o. route; absorption rate can be manipulated by formation, e.g. rapid from aqueous solution, slow from suspension or solid pellet.

c. Pulmonary Inhalation 1) Rapid absorption of drugs in gaseous, vaporized or aerosol form. 2) Absorption of particulates depends on particle size which influences depth of entry in pulmonary tree.

d. Topical Application 1) Usually for local effect 2) Absorption through mucous membrane may be rapid 3) Absorption through skin generally slow; enhanced by increased lipophilicity, by damage to stratumcorneum, and by increased blood flow.

e. Sublingual Administration For example: Nitroglycerin f. Rectal Administration preclud

Distribution of Drugs A. Tissue difference in rates of uptake of drugs. 1) Blood flow: distribution occurs most rapidly into tissues with high blood flow (lungs, kidneys, liver, brain) and least rapidly in tissues with low flow (fat).

2) Capillary permeability: distribution rates relatively slower into CNS because of tight junction between capillary endothelial cells, endothelial cell efflux transporters, insignificant membrane aqueous pores, and juxtaposed glial cells around endothelium.interstitial

B. Differences in tissue/blood ratios at equilibrium 1) Dissolution of lipid-solution drugs in adipose tissue 2) Binding of drugs to intracellular sites 3) Plasma protein binding

Elimination of Drugs A. Biotransformation or metabolism 1) site of biotransformation liver (mainly) gastrointestinal tract, kidneys, lungs enzyme: cytochrome P450 (CYP) (in liver) others such as cholinesterase (AchE), and monoamine oxidase (MAO)

2) Major pathways of biotransformation a. Phase I: Oxidation Reduction Hydrolysis primary oxidative enzymes, the cytochrome P450s b. Phase II: Conjugation Reactions

phase Ⅰ

phase Ⅱ

Fig.3-3 The proportion of drugs metabolized by major phaseⅠand phaseⅡenzymes. The relative size of each pie section stands for the estimated percentage of phase I or phase II metabolism via different enzymes shown in the figure. In many cases, more than one enzyme is involved in a particular drug's metabolism.In this figure: CYP, cytochrome P450; GST, glutathione S-transferases; NAT, N-acetyltransferases; ST, sulfotransferases; TPMT, thiopurine methyltransferase; UGT, UDP-glucuronosyltransferases.

NADP+

NADPH

flavoprotein (reduce)

flavoprotein (oxidized)

P450

P450

Fe3+

RH2

RH2

Fe2+ O2

H2O P450

O2

Fe3+

P450

Fe2+

RH2

RH2

RHOH

(parent drug)

(oxidized product)

Fig.3-4 Cytochrome P450 cycle in drug oxidations. In the figure, O2: oxygen RH2: parent drug; RHOH: product.

Pro-drugs: pro-drugs are pharmacologically inactive compounds, are biotransformed to a therapeutic agent(or active drug).

3) factors affecting drug metabolism a. genetic variation b. disease factors c. age and sex d. environmental determinants inhibition of drug metabolism, and induction of drug metabolism

Induction of CYP: Up-regulate the enzyme e.g. Barbiphenyl ( 苯巴比妥 ) induce CYP decrease drug concentration tolerance( 耐受性 ) Inhibition of CYP: Down-regulate the enzyme

B. Excretion 1) routes of excretion a. Urine (renal excretion) b. Biliary and Fecal Excretion c. Breath (pulmonary excretion) d. Minor routes: sweat, saliva, tears, reproductive fluids, breast milk

1. renal excretion 1) glomerular filtration ( 肾小球滤过 ) 2) passive tubule reabsorption ( 肾小管被动重吸收 ) 3) active tubule secretion ( 肾小管主动分泌 )

1) glomerular filtration ： Molecular Weight (MW) <20,000

2) passive tubule reabsorption a. passive transport b. pH-dependent: reabsorption of weak electrolytes is dependent on urinary pH( raising the pH promotes excretion of acids, impairs excretion of bases).

3) active tubule secretion active transport carrier-mediated weak acid carrier, and weak base carrier competitive inhibition by cotransported compounds

weak acid drugs: probenecid, penicillin, indomethacin, acetazolamide, aspirin, furosemide, cefaloridine, methotrexate, sulfinpyrazone, salicylic acid, thiazides.

weak base drugs: amiloride, morphine, 5-HT, histamine, quinine, dopamine, pethidine, tolazoline, triamterene, mepacrine

Time Course of Plasma Concentrations A. Relationship between plasma concentration and drug effect minimum effective concentration, latency, duration of effect, time and magnitude of peak effect

MEC for adverse response

drug concentration

peak concentration

therapeutic dosage window intensity duration of effect

MEC for desired response

onset of effect area under the curve ， AUC latency

time

Fig. 3-5 The blood drug concentration-time curve of a single dosage administered extravenously. MEC: minimal effect concentration.

open one compartment model D0

central compartment

D0

open two compartment model central compartment

k1 2 k2 1

peripheral compartment

ke

ke

logC

logC e -k -α /2.30

03 .3 /2

-β

/2.3

03

3

t

t

Fig.3-6 Schematic representation of the compartment models and their concentration curves. In the two open compartment model, the central compartment consists of intravascular fluid and highly perfused tissues , including heart, liver, brain, lung and kidney.

B. Time-course of plasma concentrations for a single dose 1. Case with highly rapid absorption relative to elimination a. Single compartment model 1) First-order kinetics (elimination)

d c dt = −K eC Ke (elimination rate constant): fraction eliminated per unit time

(first-order kinetics) C

C t = C0e

logC

− ket

logC t = logC 0 −

1 ket 2.303

t

Fig. 3-7 Concentration-time curve and logarithm concentration-time curve of the first-order kinetics.

t

First-order kinetics (elimination) 1. Elimination rate from plasma is proportional to plasma concentration 2. Plasma half-life (t1/2=0.693/ke) is constant and independent of dose. 3. Most drugs in the body were eliminated by firstorder kinetics.

2) zero-order kinetics (elimination)

d C dt = −KC

0

C

0

＝1

d C dt = −K

zero-order kinetics C

C t = C 0 − K⋅ t

logC

t

Fig.3-8 Concentration-time curve and logarithm concentrationtime curve of the zero-order kinetics.

t

zero-order kinetics (elimination) 1. Elimination rate is constant. 2. Plasma half-life (t1/2 =C/2ke) is not a constant and is dose-dependent. 3. few drugs such as phenytoin, salicylic acid and ethanol, when used in large dose, were eliminated by zero-order elimination. While the plasma concentration decrease, the zero-order elimination transfer to the first-order elimination.

Pharmacokinetic parameters Most drugs in the body obey first-order elimination 1 C = C e(5) logC = logC − k t t

0

− ket

t

C

0

2.303

e

logC

(6)

t

log Ct= Ｙ， log C0=a ， -ke / 2.303=b ， t 为 X， Ｙ＝ a ＋ b X equation

t

from the pharmacokinetic experiment, 1. we can detect Ct. 2. then, we calculate C0 and Ke 3. and then, we can get the following pharmacokinetic parameters

A. apparent volume of distribution (Vd)

Vd = D 0 C 0 = D C

1. fluid compartments of 70-kg subject in liters and percent of body weight: plasma volume 3 L, blood volume 5.5 L, extracellular water 12 L, total body water 42 L. 2. Vd ＝ 5L, drug distribute in plasma ； Vd ＝ 10~20L, drug distribute in extracellular ； Vd ＝ 40L ， drug distribute in total body water; Vd ＝ 100~200L, drug distribute in tissue.

3. we can predict characteristic of drug from Vd. e.g. high Vd, high lipid solubility, distribute in tissue, eliminate very slowly. 4. the plasma half-life(t1/2) of a drug is directly proportional to Vd, and inversely proportional to total clearance (Cl) ; for a given Cl, the higher the Vd, the longer the t1/2. CL = Ke ⋅ Vd

t1/2=0.693/k e

B. Plasma clearance, (CL)

CL = Ke ⋅ Vd CL = C0 ⋅V d AUC = D 0 AUC

Vd & Cl 1. CL total ＝ CL hepatic ＋ CL renal ＋ CL others 2. Vd of a drug is determined by physicochemical characteristic of the drug. 3. CL total Ke CL = Ke ⋅ Vd

C. Plasma half-life(t1/2) The half-life( t1/2) is the time it takes for the plasma concentration or the amount of drug in the body to be reduced by 50%.

t1/2 ， Ct ／ C0=1/2

1) First-order kinetics, one compartment model

d c dt = −K eC C t=C 0/2

C t = C0e

− ket

t1/2=0.693/ke

Plasma half-life (t1/2=0.693/ke) is constant and independent of dose. (11)

Table 3-2 The Relationship between the Rest Dose ( or Accumulation Dose) and the t1/2 for Medication a First-order Kinetics Elimination Drug number of t1/2

after a single iv rest amount dose

iv

100%×(1/2)0 ＝ 100%

0%

100%

1

100%×(1/2)1 ＝ 50%

50%

150%

2

100%×(1/2)2 ＝ 25%

75%

175%

3

100%×(1/2)3 ＝ 12.5%

87.5%

187.5%

4

100%×(1/2)4 ＝ 6.25%

93.8%

193.8%

5

100%×(1/2)5 ＝ 3.12%

96.9%

196.9%

6

100%×(1/2)6 ＝ 1.56%

98.4%

198.4%

∞

100%×(1/2)∞≈0%

100%

200%

regular medication: every t1/2 interval give a single dose rest dose before iv accumulation dose after iv

2) zero-order kinetics, one compartment model

d C dt = −K

C t = C 0 − K⋅ t

Ct=C0/2 时， t1/2 ＝C0/2ke Plasma half-life (t1/2 =C/2ke) is not a constant and is dose-dependent.

Bioavailability (F, 生物利 用 度

)

bioavailability The amount of the drug that reaches the systemic circulation can be expressed as a fraction of the dose absorbed (F). This fraction is often called bioavailability.

Bioavailability (F) is determined experimentally by measuring AUC of dosage form of drug given by one route and comparing it to AUC of same dose of drug under conditions of complete absorption, i.e. given i.v. AUC: Area under plasma concentration

Bioavailability (F)

F £½

F £½

AUC(ev)

¡Á100£¥

AUC(iv)

AUC(test)

¡Á100%

AUC(standard)

CmaxA

increase risk of toxicity

MEC for adverse response

plasma drug concentration

CmaxB CmaxC

MEC for desired response

C B A TmaxA

TmaxB

TmaxC

time

Fig. 3-9 The theoretical plasma concentrations resulting over a period of time after the oral administration of three different formulations of the same dose of the same drug. Each drug has a different speed of absorption but has the same AUC.

First-order elimination and multiple dose

1 dose / t1/2

2.0 dose

峰浓度 (Cssmax)

2 dose/t1/2 after 1dose/t1/2

2.0

1.5 • 1.5Fig. 3-11 Schematic representation of fundamental pharmacokinitic relationships for repeated administration of drugs. In the figure: (A) a drug is adiminstered in one dose at interval of t1/2 , and (B) a drug is given in two 1.0 1.0 doses firstly and then added in one dose谷浓度 at intervals of t1/2. 1.44t1/2dose iv after iv drip Iv drip (Cssmin) 0.5 0.5

0

1

2

3

4

5

(A)

6

t1/2 0

1

2

t1/2

(B)

Fig. 3-10 Schematic representation of fundamental pharmacokinetic relationships for repeated administration of drugs. In the figure: (A) a drug is administered in one dose at interval of t1/2 , and (B) a drug is given in two doses firstly and then added in one dose at intervals of t1/2.