Concepts of Pharmacology - Half Life Calculation

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Transcript Concepts of Pharmacology - Half Life Calculation

Concepts of Pharmacology -

Half Life Calculation

-

C. M. Prada, MD July 12, 2006 1

• •

Pharmacokinetics = availability

- dosage and rate of administration - modes of transport – across biologic membranes; bound to proteins from plasma and tissues - blood flow to the site of action - extent and speed of the metabolic process of the drug - rate of the removal of the drug (and its metabolic products)

Pharmacodynamics = pharmacologic effect

(in relation with the plasma drug concentration) - cellular mechanisms of drug action - clinical evaluation of drug effects - biologic variability 2

Definition:

quantitative study of absorption, distribution, metabolism, and elimination of chemicals in the body, as well as the time course of these effects.

Summary:

- absorption - distribution - metabolism - elimination 3

• Concentration of a drug at its site of action is a fundamental determinant of its pharmacologic effects.

• Drugs are transported to and from their sites of action in the blood – because of that: the

concentration at the active site

is a function of the

concentration in the blood

• The change in drug concentration over time in the blood, at the site of action, and in other tissues is a result of complex interactions of multiple biologic factors with the physicochemical characteristics of the drug. 4

medicine movement

Pharmacokinetic Concepts: Rate Constants and Half-Lives

• • Disposition of most drugs follows

first-order kinetics

– a

constant fraction

of the drug is removed during a finite period of time.

• This fraction is equivalent to the

rate constant

of the process.

• Rate constants: • In when it is low.

; min • The absolute amount of drug removed is proportional to the concentration of the drug

first-order kinetics

-1 or h -1 , the rate of change of the concentration at any given time is proportional to the concentration present at that time.

• When the concentration is high, it will fall faster than

First-order kinetics

apply not only to elimination, but also to absorption and distribution.

Half-Lives

• • • The

rapidity

of pharmacokinetic processes is often described with

half-lives Half-Life

= the time required for the concentration to change by a factor of 2.

Half-Life

= the period of time required for the concentration or amount of drug in the body to be reduced to exactly one-half of a given concentration or amount.

Half-Life =

the time required for half the quantity of a drug or other substance deposited in a living organism to be metabolized or eliminated by normal biological processes. Also called

biological half-life

Zero-Order Elimination

approximately constant rate of elimination 8

First-Order Elimination

is concentration after time

C 0 k

is the initial concentration (

=0) is the elimination rate constant - first-order logarithmic process - that is, a

constant proportion

of the agent is eliminated

per unit time

(Birkett, 2002) Birkett DJ (2002).

Pharmacokinetics Made Easy

(Revised Edition). Sydney: McGraw-Hill Australia. ISBN 0-07-471072-9 .

First-Order Elimination (cont.)

dC 1). ------ = kC dt dC 2).

------ = k dt C 3).

ln C = - kt + D 4).

C = e D e -kt 5).

At time

t = 0: C = e D 6).

C 0 = e D

7). C

= C

e

-kt

At the time t = t1/2: C

(1/2)

= C

x 1/2 C

x 1/2 = C

e

-kt1/2

e

-kt1/2

= 1/2 - kt

1/2

= ln 1/2 = - ln 2 t

1/2

ln 2 = ------ k

C t = C 0 e -kt

The reduction of the quantity in terms of the number of half-lives elapsed :

t

1/2

ln 2 = ------ k

...

N 0 1 2 3 4 5 6 7

Number of half-lives elapsed

1/1 1/2 1/4 1/8 1/16 1/32 1/64 1/128

Fraction remaining As power of 2

1 / 2 0 1 / 2 1 1 / 2 2 1 / 2 3 1 / 2 4 1 / 2 5 1 / 2 6 1 / 2 7 ...

1 / 2

First-Order Elimination (cont.)

Relationship between the

elimination rate constant

and

half-life:

elim ln(Cpeak) - ln(Ctrough) = -------------------------------- t interval

t ½

= 0.693 /

elim

Half-life

is determined by clearance (CL) and volume of distribution (VD): Only for IV 17

Half-Life Calculation

• Directly from the corresponding

rate constants

: (ln 2) 0.693

t 1/2 = ---------- = ---------- k k Ex.: rate constant of 0.1 min -1 a half life of translates into 6.93 min.

Half – Life (cont.)

• • Half-Life of any

first-order kinetic

process can be calculated – ex.: drug

absorption

distribution

elimination First order

processes – asymptotically approach completion, because a constant fraction of the drug is removed per unit of time (not an absolute amount).

• The process will be

almost complete

after 5 (97%) …half-lives: 19

Half-Life Elimination (cont.)

• Repeated

equal doses

of a drug

more frequently than 5 elimination half-times

: result in drug being administered at a rate greater than its plasma clearance –

accumulation

in plasma. 21

Equations for Half Lives For a zero order reaction A products ,

t½ = [Ao] / 2k

For a first order reaction

t½ = 0.693 / k

rate = k: A products , rate = k[A]: For a second order reaction 2A products or A + B products (when [A] = [B]), rate = k[A] 2 :

t½ = 1 / k [Ao] http://www.chem.purdue.edu/gchelp/howtosolveit/Kinetics/Halflife.html

For a zero order reaction A products , rate = k:

For a first order reaction A products , rate = k[A]:

For a second order reaction 2A products or A + B products (when [A] = [B]), rate = k[A] 2 :

The Elimination Half-Time Limits

• Only in

single-compartment

models does it actually represent the time required for a drug to reach half of its initial concentration after administration • This is because in a

single-compartment

model

elimination

is the

only

process that can alter drug concentration • Intercompartmental distribution cannot occur because there are no other compartments for the drug to be distributed to and from • Most

drugs in Anesthesia

lipophilic

– therefore are more suited to

multicompartmental model

• In

multicompartmental models

, the

metabolism excretion

and of some intravenous anesthetic drugs may have

only minor contribution

concentration when to changes in plasma

compared with

intercompartmental distribution

the effects of 26

Drug Elimination

• Elimination = all the various processes that terminate the presence of a drug in the body.

• Processes: - metabolism - renal excretion - hepato-biliary excretion - pulmonary excretion (inhaled anesthetics mainly) - other: saliva, sweat, breast milk, tears.

Renal Excretion

• • Both

metabolically

changed and unchanged drugs

LMW substances

: filtered from blood through the Bowman membrane of the capsule • • • Some:

actively secreted Reabsorption in the tubule

: depending on the lipid solubility, degree of ionization, molecular shape, carrier mechanism (for some).

Weak acid

: best reabsorbed from an acidic urine.

• Important to know

if the drug is dependent

function or excretion.

renal

Hepatobiliary Excretion

• Drugs metabolites – excreted in the intestinal tract with the bile.

• Majority: reabsorbed into the blood and excreted through urine. (enterohepatic cycle).

• Poorly lipid-soluble organic compounds – at least three active transport mechanisms 29

Pulmonary Excretion

• Volatile anesthetics and anesthetic gases: in large part eliminated unchanged through the lung • The factors that determine uptake operate in reverse manner 30

Multicompartment Pharmacokinetics

• Instead of a single exponential process with one half-time, the pharmacokinetics are described by

2 or more exponential processes

– can calculate a half-time for each process: l 1, l 2, l 3, etc. (referred to as: a , b , g ).

• The

time 50%

for the

concentration to decrease

is dependent on the

preceding dosing history

and can

vary

with the

duration

by of

drug administration.

• The time to decrease plasma concentration by half is not equal with the time to remove half of the drug from the body -

terminal half-life.

Multicompartment Models

• 3 compartments: – Central = vascular bed – 2 nd = rapidly equilibrating, high perfusion (muscle) – 3 rd = large compartment – slow equilibrating, low perfusion (fat).

• 5 compartments: (isoflurane and sevoflurane measurements) – Central – Vessel-rich – Muscle group – 4 th compartment – The fat group 32

Context-Sensitive Half-Time

• Improved our understanding of anesthetic drug disposition; is clinically applicable.

• Effect of

distribution

depends on the on

plasma drug conc.

varies in magnitude and direction over time -

drug concentration gradients

between various compartments.

- ex.: early part of the infusion of a lipophilic drug, the distributive factor decrease its plasma conc. as the drug is transported to the unsaturated peripheral tissues central circulation – later, after the infusion is discontinued: drug will re-enter in the 33

Context-Sensitive Half-Time (cont.)

• Def.:

context-sensitive half-time

describes the time required for the plasma drug concentration to decline by 50% after terminating an infusion of a particular drug.

•

Calculated

by using computer simulation of multicompartmental models of drug disposition: 34

Context-Sensitive Half-Time (cont.)

• • • Reflects the

combined effects

and

metabolism

distribution

on drug disposition • The data confirm the clinical impression that as the

infusion duration increases

, the

context sensitive half-time

of all drugs

increases

. This phenomenon is not described by the

elimination half-life

No relationship N.B.:

For a with the

Half-Life.

one-compartment model

sensitive half-life = elimination half-life.

: context 36

Context-Sensitive Half-Time (cont.)

• Compare

fentanyl sufentanil

(half life

462 min

.) and (half-life concentration.

577 min

.) – storage and release of fentanyl from the peripheral binding sites: delay the declines of plasma • Compare

propofol

• Because of : 1). and

thiopental

– comparable c-s h-t following a brief infusion only.

high metabolic clearance

of propofol and 2). relatively

slow rate of return to plasma

peripheral compartments.

of propofol from 37

Context-Sensitive Half-Time (cont.)

• •

Alfentanil

– studied for ambulatory techniques • Elimination half – life: 111 min.

• Small distribution volume – not significant in plasma decay after infusion

Sufentanil

– elimin. half – life: 577 min.

• Less context-sensitive half-time (for infusions up to 8 hours);

large volume of distribution

for

sufentail

• After termination of its infusion, the decay in plasma drug conc. is accelerated not only by

elimination

, but also by continuous

redistribution

into the peripheral compartments.

Context-Sensitive Half-Time and Time to Recovery

• Time to recovery depends on other additional factors: –

Plasma concentration below awakening

can be expected which – Awakening from anesthesia is a function of

effect-site concentration decay

–

Effect-site equilibration

equilibration between drug concentration in blood and the drug effect can be determined:

t1/2 ke0

– half-time of 39

1). Zero order pharmacokinetics

If there is one thing that separates pharmacology from other medical subjects, it is zero order pharmacokinetics! Salicylic acid is an example of a drug that behaves this way. What is drug elimination according to zero order kinetics?

A constant amount of drug is removed per unit of time.

This makes the rate of metabolism saturable, so that small changes in dose, can give dramatic changes in plasma concentration

2). A drug was given intravenously at a dose of 200mg. The initial concencentration in plasma (Co) was 10 µg/ml, and the Kel (elimination constant) was 0.02/h. Determine the plasma clearance (Clpl) and t1/2 for this drug. Distribution volume: Vd = dose/ Co = 200 mg / 10 mg/L = 20 L Cl pl = Vd x Kel = 20 L x 0.02/h = 0.4 L/h T1/2 = ln 2 / kel = 0.693 x 0.02 = 35 hours

The kinetic order of a reaction is determined by the exponent of the rate equation, n, in dc/dt = K C n :

Kinetic order

2 1 0

Equation

dc/dt = K C 2

Dependency on C

Exponential dc/dt = K C 1 or dc/dt = K C Linear dc/dt = K C 0 or dc/dt = K None 43

Saturable kinetics

usually follow

Michaelis-Menten equation

: dC/dt = [(dC/dt)m.C] / (Km + C) where (dc/dt)m is the maximum rate that a reaction can reach and Km is the Michaelis-Menton constant that corresponds to a concentartion at which the rate is 1/2 of the maximum.

When C is very small it can be ignored from denominator and reduces the above equation to: dC/dt = [(dC/dt)m.C] / Km or dC/dt = (dC/dt)m/Km.C.

Hence the rate becomes dependent upon a constant, [(dC/dt)m / Km], and C, and the kinetics change to a first order. On the other hand during the time when C is very high, Km becomes negligible and the equation reduces to: dC/dt = (dC/dt)m.C / C Now C can be cancelled from both nominator and denominator to give:

i.e.,

dC/dt = (dC/dt)m the rate depends only upon a constant but not upon concentration. From then on the reaction proceeds according to zero order kinetics. Between these two extremes the order of the reaction is a mixture of first and zero kinetics.

Concentration dependency of the kinetic order of saturable reaction.

www.pharmacy.ualberta.ca/pharm415/orderof.htm

Michaelis Menten Equation

The Michaelis Menten process is somewhat more complicated with a maximum rate (velocity, Vm) and a Michaelis constant (Km) and the amount or concentration remaining. 46

Half-Lives for Some Common Drugs

• Narcan (Naloxone): plasma half-life: - adult: 64 ±12 min; neonate: 3.1 ± 0.5 hours • Fentanyl: half-life: 2 – 9 hours • Morphine: terminal half-life: 1.5 – 4.5 hours • Midazolam: elimination half-life: 1.8 – 6.4 hours • Flumazenil (Romazicon): distribution half-life: 7 – 15 min.; terminal half–life: 41 – 79 min 47

Codeine Fentanyl Hydrocodone Hydromorphone Levorphanol Meperidineæ

Drug Duration 4–6 h 1–2 h 4–8 h 4–5 h 6–8 h 2–4 h Half-life 3 h 1.5–6 h 3.3–4.5 h 2–3 h 12–16 h 3–4 h Route IM/IV/SC PO IM/IV PO IM/IV/SC PO IM/IV/SC PO IM/IV/SC PO Equianalgesic Dosage 120 mg 200 mg

0.1 - 0.2 mg

20-30 mg 1.3–1.5 mg 7.5 mg 2 mg 4 mg 75 mg 300 mg

Methadone Morphine Oxycodone Oxymorphone æ

4–6 h 3–6 h 4–6 h 3–6 h 15–30 h 1.5–3 h NA NA IM/IV/SC PO IM/IV/SC PO PO IM/IV/SC 1-10 mg§ Medline Short term: 5-10mg Chronic use: 1-4 mg (2 mg)

2 - 20 mg§ Medline Short term use: 20 mg Chronic dosing: 2 4 mg (3mg)

10 mg

30–60 mg#

15-30 mg (20 mg) 1 mg

Important Update: Opana™ and Opana ER™ (oxymorphone immediate release and oxymorphone extended release tablets) have been approved by the FDA. Propoxyphene *

4–6 h 6–12 h PO PO 10 mg 130-200 mg * Propoxyphene HCL: 130mg; Napsylate: 200mg. Not recommended for chronic pain management and therefore not available in program above.

# §:

Acute dosing (opiate naive): 60mg. Chronic dosing: 30 mg.

Many equianalgesic tables underestimate methadone potency - more studies are needed. Parenteral: Program utilizes 10mg for short-term dosing and 2 mg for chronic dosing. Oral: Program utilizes 20mg for short-term dosing and 3 mg for chronic dosing.

Meperidine should be used for acute dosing only and not used for chronic pain management (meperidine has a short half-life and a toxic metabolite: normeperidine). Its use should also be avoided in patients with renal insufficiency, CHF, hepatic insufficiency, and the elderly because of the potential for toxicity due to accumulation of the metabolite normeperidine. Seizures, confusion, tremors, or mood alterations may be seen. http://www.globalrph.com/narcoticonv.htm

= 1 + 1/1! + 1/2! + 1/3! +…… e is the limit of (1 + 1/n)n as n tends to infinity e = 2.718281828459045235

Euler 49

Disclaimer

• This is a compilation intended only for the personal use of the MHMC residents, and not for publication • For the bibliographic sources, please send an e-mail to: [email protected]

Concepts of Pharmacology - Half Life Calculation

Transcript Concepts of Pharmacology - Half Life Calculation