Chapter 3

Pharmacokinetics

2

Drug Administration

Drug Concentration in

Systemic Circulation

Drug in Tissues of

Distribution

Drug Metabolism or Excretion

Drug Concentration at Site of Action

Pharmacologic Effect

Clinical Response

Toxicity Efficacy

Ph

arm

aco

kine

tics dose-concentration

Ph

arm

aco

dyn

am

ics concentration-effect

Distribution Elimination

Absorption

3

¨ Drug Transport¨ Process of Drug in vivo¨ Elimination Kinetics

4

Chapter 3

Section 1Drug Transport

5

Modes of Transport

1. Filtration

2. Simple diffusion

3. Carrier-mediated transport

1) Facilitated diffusion

2) Active transport

Passive transport

6

¨ Aqueous diffusion, Aqueous channel;

1. Filtration

¨ Hydrosoluble , driven by concentration gradient

7

1. Filtration

¨ Downhill movement.

Flux (molecules per unit time) =

Thickness

tcoefficientyPermeabiliAreaCC

21

8

Simple diffusion

¨ Lipid diffusion

¨ The most common transport for drug

9

2. Simple Diffusion, Passive Diffusion

¨ Ion trapping :– Nonionized form (uncharged) : low polarity,

hydrophobe, lipid soluble, permeation through membrane

– Ionized (charged) : high polarity, hydrophil, lipid unsoluble, unable permeation through membrane

10

Ionization of weak acid and weak bases¨ A weak acid is best defined as a neutral molecule that

can reversibly dissociate into an anion and a proton.

C8H7O2COOH C8H7O2COO- +H+

Neutral aspirin

Aspirin anion proton

11

Ionization of weak acid and weak bases¨ A drug that is a weak base can be defined as a neutral

molecule that can form cation by combining with a proton.

C12H11CIN3NH3 + C12H11CIN3NH2+H+

Pyrimethamine cation

Neutral pyrimethamine

Proton

12

pH & pKa determine the degree of dissociation of drug

¨ pH and pKa are important in determining the fraction in the un-ionized form.

¨ pKa : the pH at which 50% of the molecules in solution are in the ionized form.

13][

][10

][

][log

][

][log

][

]][[

HA

A

HA

ApKapH

HA

ApHpKa

HA

AHKa

AHHA

pKapH

Weak acid Weak base

][

][10

][

][log

][

][log

][

]][[

BH

B

BH

BpKapH

BH

BpHpKa

BH

BHKa

BHHB

pKapH

pH & pKa determine the degree of dissociation of drug

dissociation constant

14

¨ Henderson-Hasselbalch equation:

pHpKedUnprotonat

otonateda

)(

)(log

Pr

¨ The lower the pH relative to the pKa, the greater will be the fraction of drug in the protonated form.

¨ The protonated form of a weak acid is the neutral, more lipid-soluble form.

¨ The unprotonated form of a weak base is the neutral form.

16

Application of Henderson-Hasselbalch Equation

¨ Lipid-soluble form is reabsorbed by renal tubule¨ Weak acids are excreted faster in

urine;

weak bases are excreted faster in urine¨ Acidification: NH4Cl, Vc

¨ Alkalinization: NaHCO3, Acetazolamide( 乙酰唑胺）

alkaline acidic

17

Quiz¨ We orally administer a weak acid drug(A) with a pKa of 3.4.

Gut pH is 1.4, and blood pH is 7.4. Assume the drug crosses membranes by simple passive diffusion. Which of the following observations would be true?

A. Only the ionized form of drug, will be absorbed from the gut.

B. The drug will be hydrolyzed by reaction with HCl and so cannot be absorbed

C. The drug will not be absorbed unless we raise gastric pH to equal pKa, as might be done with an antacid

D. The drug would be absorbed, and at equilibrium the plasma concentration of the A- would be 10000 times than the plasma concentration of nonionized moiety(HA)

18

Carrier-mediated Active transport Facilitated transport

3. Carrier-Mediated Transport

19

3. Carrier-Mediated TransportTrans-membrane protein

– Selectivity/specificity– Saturation– Competitive inhibition

¨ Active transport– Against gradient– Energy required

¨ Facilitated transport– Down gradient– Energy free

20

Chapter 2

Section 2Process of Drug in vivo ：

Absorption, Distribution, Metabolism, Excretion

21

Ⅰ 、 Absorption

Process of drug leaving site of administration into systemic circulation.

¨ Inhalation¨ Intranasal¨ Intravenous Infusions, Intravenous Injections, Intravenous¨ Mucosal¨ Ophthalmic¨ Oral ¨ Buccal¨ Sublingual¨ Rectal¨ Topical

22

Buccal/Sublingual

¨ absorbed though oral mucus membranes in mouth – buccal = cheek– sublingual (SL) = under tongue

First pass elimination (first pass metabolism, first pass effect )

¨ pass through liver before reaching circulation

¨ undergo metabolism by liver

24

Bioavailability

Bioavailability refers to the extent and rate at which the drug enters systemic circulation, thereby accessing the site of action.

If the drug is given by extravascular administration, less than 100% of a dose reach the systemic circulation.

25

Bioavailability (F)

F = 100% A

D

F = AUC P.O

AUC I.V

p.o

i.V

AUC (area under the curve): The area under the plasma drug concentration-time curve , reflects the actual body exposure to drug after administration of a dose of the drug and is expressed in mg*h/L . It is directly proportional to the total amount of drug in the patient's blood.

Routes of Administration, Bioavailability, and General Characteristics.

Route Bioavailability(%) Characteristics

Intravenous (IV) 100 (by definition) Most rapid onset

Intramuscular (IM)

75 to ≤ 100 Large volumes often feasible; may be painful

Subcutaneous (SC) 75 to ≤ 100 Smaller volumes than IM; may be painful

Oral (PO) 5 to < 100 Most convenient; first-pass effect may be significant

Rectal (PR) 30 to < 100 Less first-pass effect than oral

Inhalation 5 to < 100 Often very rapid onset

Transdermal 80 to ≤ 100 Usually very slow absorption; used for lack of first-pass effect; prolonged duration of action

27

Ⅱ 、 Distribution

Drug goes to organs and tissue from circulation via its permeation

Dependent on its solubility, the rate of blood flow to the tissues, and the binding of drug molecules to plasma proteins

28

1. Plasma protein binding

¨ Free drug Bound drug

][

][

][

][

thenprotein, plasma ofamount totalis If

][

]][[

drug bound is DP drug free is

DK

D

P

DP

P

KDP

PD

D

DPPD

DT

T

D

，

29

¨ Unbound drug = active ¨ Reversible equilibrium¨ Saturable: albumin, most common protein to bind

drugs ¨ Nonspecific & competitive

Drug and Drug (especially, drug of high binding rate): phenylbutazone + warfarin

Drug and Endogenetic substance: billirubin

30

+B drug ：

98%

Free A drug: 1%A drug: 99%

plasma protein

Free A drug: 2%

Effect increase, even toxicity

31

Distribution

Body’s barriers : Blood-brain barrier (BBB) : 1. Tight junction between endothelial cells

2. Astrocyte surrounding the endothelial cells

Placental-barrier Blood-eye-barrier

血脑屏障 (Blood-brain barrier, BBB)

由毛细血管壁和 N 胶质细胞构成

33

Ⅲ 、 Metabolism, Biotransformation Sites of biotransformation

– liver– Others: GIT, kidneys, brain, & plasma

34

Results of metabolism :

1.transform into inactive substance;

2.inactive drug (pro-drug) → active metabolite; Codein morphine

3.active drug → other active substance; Phenylbutazone( 保泰松 ) and oxyphenbutazone （羟基保泰

松） Diazepam ( 安定 ) and oxazepam （去甲羟基安定） Carbamazepine ( 卡马西平 ) and 10, 11-epoxide carbamazepine

（环氧卡马西平）

4. transformed into toxicant. Isoniazid → acetyl isoniazid

35

Steps of Metabolism

¨ Phase Ⅰ– oxidation, reduction and hydrolysis

¨ Phase Ⅱ– Conjugation with endogenous

compounds(glucuronic acid , glycine, sulfuric acid)

36

matabolism

Phase I Phase II

Drug

Drug inactivaed

activityor

bound

Drug

Lipophilic Hydrophilic

Excretionbound

bound

37

Metabolism Enzyme

¨ Specific enzymes– cholinesterase, monoamine oxidase (MAO), etc.

¨ Non-specific enzymes– hepatocyte microsomal enzymes (cytochrome P450

enzyme system, CYP 450).

– These isozymes involved in Phase I reactions.– If binds to carbon monoxide , spectrum with a maximum at

450 nm

38

CYP1A1/2CYP1B1

CYP2A6

CYP2B6

CYP2E1

CYP3A4/5/7

CYP2C19

CYP2C9CYP2C8

Non-CYP enzymes

CYP 2D6

39

Characteristic of hepatic drug enzyme

¨ low selectivity¨ great variability¨ enzyme activity is liable to be influenced by

outside factors.– enzyme inducer– enzyme inhibitor

40

General inducers:

苯妥英 phenytoin 、奎尼丁 quinidine 、利福平rifampicin 、卡马西平 carbamazepine 、灰黄霉素griseofulvin 、巴比妥类 barbiturates （苯巴比妥为最） 、 甲丙氨酯 meprobamate ，格鲁米特 glutethimide 、保泰松 butazodine 、 chronic alcoholic intoxication 慢性酒精中毒

General inbibitors:

酮康唑 Ketoconazole 、西咪替丁 cimetidine 、异烟肼 isoniazide 、红霉素 erythrocin 、磺胺 sulfonamide 、氯霉素 chloramphenicol ，柚子汁 grapefruit juice ， acute alcoholic intoxication 乙醇急性中毒者

环孢素伊曲康唑

利福平

麦芽汁

42

Ⅳ 、 Excretion

¨ Drug or metabolite → emunctory( 排泄器官 ) or secretory( 分泌器官 )→ outside of body

¨ Excetion organ: – kidney – bile duct – intestinal tract – salivary gland( 唾液腺 ) – galactophore( 乳腺 ) – sudoriferous gland( 汗腺 ) – lung

43

Excretion

¨ Renal excretion: glomerular filtration, active tubule secretion, passive tubule reabsorption.

2. 胃肠道：胆汁 - 粪便途径

Liver

Gut

Feces excretion

Portal vein

Bile duct

胆汁排泄(biliary excretion)

和肝肠循环(Enterohepatic

recycling)

45

Chapter 2

Elimination Kinetics

46

Kinetic process

¨ 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:

This rate process is called N grade rate process. where K is rate constant, Minus of right-sideness denotes reduction of drug concentration.

)0( NKCdt

dc N

First order elimination kinetics

n = 1 dC/dt = - kC

Zero order elimination kinetics n = 0 dC/dt = -k

dC/dt = - kCn

k ： Rate constant for elimination

Log

Un

its o

f D

rug

Time

n=0n=1

n=0

n=1

Un

its o

f D

rug

Rate of elimination is proportional to C. t ½ is a constant

Rate of elimination is independent to C. t ½ is variable

T1/2: The time it takes for the [drug] in the body to be reduced by 50%

48

Zero-order Kinetics First-order Kinetics

Contant Rate Process Rate is proportional to the drug concentration

dC/dt = -K0 dC/dt = - KC

t1/2 =0.5C0/K0 , depends on initial drug concentration

t1/2 =0.693/K , independent and is a constant value

Most drugs Ethanol, phenytoin, aspirin

Capacity-limited elimination, carrier based processes after saturation

Not linked with carriers or unsarurable if linked with carriers

Comparison

Compartment Model房室模型

Section 4

One compartment model一室模型

¨ Considers the body to be a single compartment. A drug is absorbed , immediately distributed, and subsequently eliminated by metabolism and excretion.

D

D

DKa

Ke

Two compartment model二室模型¨ Central compartment ： plasma, heart, lung,

kidney, endocrine system, et al ¨ Peripheral compartment ： muscle, fat

tissue, bone, et al¨ Most drugs are transported with two

compartment model

D D DKa

D

K12

K21Ke 或K10

Central compartment

Peripheral compartmentDistribution

Two compartment model

53

Chapter 2

Section 5Important Parameters in

Pharmacokinetics

54

1. Volume of distribution,Vd

Vd ＝ D ／ C0

D for total dose of drugC for concentration in plasma―C0 equilibrium of distribution

Vd: theoretical volume that the total amount of administered drug would have to occupy (if it were uniformly distributed), to provide the same concentration as it currently is in blood plasma.Vd relates the amount of drug in the body to [C] of drug in blood or plasma

55

Understand the drug distribution in the body ：

• Vd≈5L indicates in the plasma ，• Vd≈30-40L in the total body fluid ， • Vd ＞ 40L in the tissue and organs ， • Vd ＞ 100L in the specific organ or big range

tissues ， e.g thyroid , Skeleton, adipose tissue

Needed to calculate a loading dose ：D=Vd×C

significances ：

70kg person

42L Body fluid

56

2. Clearance, CL

otherliverkidneysystem

otherother

liverliver

kidneykidney

RE

RE

RE

L/h)or ml/min ((RE)n eliminatio of Rate

CLCLCLCLC

CL

CCL

CCL

CCL

― Definition: volume of blood which is cleared off a drug per unit of time

Calculations ：1. Cl is constant in first-order kinetics

CL ＝ KeVd

AKRE eCRECl /

CAVd /

CAKeCl /

dVKeCl

Reasoning:

Calculations ：2. CL ＝ A / AUC （ A for total drug in body, = dose ）

Reasoning:

AUC

A

AUC

CVVKCL

AUC

CK

K

CAUC

VKC

CVK

C

AK

C

RECL

CVAC

AV

AKRE

dde

ee

dedee

dd

e

First-order Elimination Kinetics (linear kinetics)

as

Definition: The time it takes for the [drug] in the body to be reduced by 50%

Half-life, T1/2

dVKeCl

Cl

Vdt 693.02/1

Constant repeated administration of drugs Steady-state concentration

Aim to let MTC>Css>MEC

Css-max < MTC

Css-min > MEC

RATE IN = RATE OUT

61

Additive amount of eliminated drug T1/2 1 2 3 4 5

50 25 12.5 6.25 3.125

50 25 12.5 6.25

50 25 12.5

50 25

50sum 50 75 87.5 93.5 96.5

62

时间 ( 半衰期 )

MTC

MEC

Dru

g C

once

ntra

tion

(ug/

ml)

Css is proportional to dose and dosing interval

时间 ( 半衰期 )

MTC

MEC

63Css = AUCss/ τ

64

Chapter 2

Section 6Dosage design and Optimization

65

1. target concentration

Steady-state concentrion （ Css ）

Css-max < MTC

Css-min > MEC

66

Maintenance dose (MD) To maintain SS , the dosing rate must equal to

the rate of elimination. That is dosing rate = rate of elimination

TC : Target concentration

MD= CL×TC×Dosing interval

67

Loading Dose ¨ Loading dose is dose required to achieve a specific

plasma drug concentration level immediately with a single administration.

mm

tt

m

K

mL

K

mL

mK

LL

DD

e

D

e

DD

te

DD

DFeDFDF

e

e

e

2

21

111

1

2/12/1

2ln

2/1

时，当

即每隔一个 t1/2 给药一次时，负荷量为维持量的 2 倍。

首剂加倍

69

The target concentration strategy

1. Choose the target concentration, TC.2. Predict volume of distribution (Vd) and clearance (CL) based

on standard population values with adjustments for factors such as weight and renal function.

3. Give a loading dose or maintenance dose calculated from TC, Vd, and CL.

4. Measure the patient's response and drug concentration.5. Revise Vd and/or CL based on the measured concentration.6. Repeat steps 3–5, adjusting the predicted dose to achieve TC.¨

Important Pharmacokinetics Calculations

¨ Single-Dose Equations– Volume of distribution (Vd):

– Half-life (t1/2):

¨ Multiple Doses or Infusion Rate Equations– Loading dose (LD):– Maintenance dose (MD):

CL

Vt

C

DV

d

d

7.02/1

0

F

CCLMD

F

CVLD

CCLk

ss

pd

ss

0

Brian is a 15 yr old patient who has been admitted to the hospital with a severe case of bacterial septicemia caused by a gram-negative organism that has been determined to be sensitive to Gentamycin. Gentamycin’s Vd=20 L. What i.v. loading dose would you give Brian to rapidly achieve a therapeutic plasma level of 5 mg/L?

A. 20 mg B. 25 mg C. 50 mg D. 100 mg E. 250 mgD

72

¨ The following graph shows the elimination time course obtained after giving a 320 mg dose of a drug by both i.v. & oral routes. From the data shown, calculate the drugs elimination clearance. You may need to use a calculator.

A. 0.6 L/hrB. 1.75 L/hrC. 10 L/hr D. 32 L/hr E. 36 L/hr

AIM get Cl,

1st to Calculate Vd,

Vd ＝ D ／ C0

Vd ＝ 320mg/32ug/ml=10L

2nd to get t1/2

t1/2=4h

Cl=0.693×10L/4h=1.75L/h

2/1

693.0t

VdCl

This formula can be used to calculate both Vd, t1/2 & Cl after giving a single drug dose

74

Your pediatric patient is suffering from a bacterial infection & requires maintenance dosing with gentamicin. Gentamicin’s elimination clearance is 5.0 L/hr. What maintenance i.v. dose of gentamicin should you give every 8 hours to maintain an average steady-state plasma level of 5 ug/ml?

A. 25 mg B. 50 mg C. 100 mg D. 200 mg

Original question from USMLE

D

The end