Drug delivery and pharmacokinetics term 2

what is the one-compartment model

• simplest possible representation of PK: drug goes in, drug goes out, no complications

• drug is injected IV as a bolus solution

• drug os then removed passively through the kidneys into the urine for excretion

• no metabolism, no protein binding, no sequestration by other tissues

what is the two-compartment model

• drug distributes form the central compartment of which plasma is a part

• to the peripheral compartment which is viewed as tissues

what is a major assumption of an IV bolus injection

at time=0, drug is completely and evenly distributed throughout the plasma

what are the main pharmacokinetics parameters

• volume of distribution

• clearance

• exposure

• mean residence time

• fraction of dose remaining

how to calculate conc. in IV bolus injection

C= amount/volume

how to calculate initial conc. of drug in the reservoir

C(0)=Dose/V

what is the rate of elimination in IV bolus injection

rate of elimination= Q x C x E= Q(C-Cout)

what is clearance

the volume of the fluid presented to the eliminating organ (extractor) that is effectively completely cleared of the drug per unit of time

how can you calculate the extraction ratio

• E= rate of elimination/ rate of presentation

• E= Q x (C-Cout)/Q x C= (C-Cout)/C

what is CL

• clearance

• the measured conc. entering the extractor (same as in the reservoir)

what are the units of CL

• ml/min or L/hr

• CL= Q x E

what does volume of distribution predict

the conc. for a given amount of drug in the body

what does clearance relate

relates the rate of elimination to the conc. in the systemic circulation- estimation of the rare of elimination at any conc.

what is the equation for the fractional rate of elimination, k

K= rate of elimination/ amount in reservoir= CL x C/A = CL x C/V xC= CL/V

what is another way of measuring the rate of elimination

• monitor the conc. in the reservoir

• rate of elimination= -dA/dt= Kelim x A

• since A= V x C equation can be transformed to: -dC/dt= Kelim x C

• using integration: C(t)= C(0) x e^-Kelim x t

• in linear form: lnC(t)= lnC(0) - kelim x t

what is K

the first order elimination constant

how should you calculate the half-life from an equation

• go back to the ln plot

• ln (plasma conc.)= -0.2tiem + 4.6053

• abbreviate time to t

• abbreviate plasma conc. at time t to Ct

• abbreviate initial plasma conc. to C0

• intercept= ln (initial plasma concentration.)= ln (C0)

• gradient= elimination constant

• ln2/ Kelim= t1/2

what are very important PK parameters that should be considered

• volume of distribution

• AUC (exposure)

• clearance

definition of volume of distribution

the total volume of fluid that the drug would occupy if the total amount of drug in the body was in solution at the same conc. it is in the plasma

what is Vd

• volume of distribution

• theoretical construct

• helps in comparing different drugs

• helps in manipulating PK equations

what is the equation for volume of distribution

• Vd= total amount n body/plasma conc. = dose/ plasma conc.

• units= L or L/kg

what does a low value of Vd mean

indicates tart the drug remains predominantly associated with the vascular system

what do intermediate values of Vd mean

indicate that the drug is distributed to other tissues

what does a very high Vd value mean

indicates that the drug is tightly bound to very specific tissues

how to determine if a patient has a greater exposure to the drug

• the process will be slower

• smaller Kelim

AUC

• exposure can be measured by AUC

• AUC may be calculated from graph or by integration of Ct

equation for the fraction of dose remaining

fraction of dose remaining= A(t)/dose= e^-kt

what is residence time

indicates how long drug molecules stay in the body

what is the mean residence time

the average time molecules of drug stay in the body

what is the pH partition hypothesis

only unionised nonpolar drugs penetrate the membrane and at equilibrium the conc. of unionised species is equal on both sides, but the total conc. may be very different

why may the total conc. in the pH partition hypothesis be very different

due to a different degree of ionisation

what is the pH in plasma water in the pH partition hypothesis

• 7.4

what is the pH in urine in the pH partition hypothesis

• 5.4

what are the only types of drugs that are capable of diffusing through cell membranes

unbound drugs

partition coefficient equation

conc. in oil/ conc. in water = solubility in oil/ solubility in water

what does log P=0 mean

equally soluble in both

what does log P=-ve mean

more soluble in water

what does log P=+ve mean

more soluble in oil

what do log P calculations ONLY consider

• un-ionised material

• more correct to discuss Log Papp and specific pH

what is Log Papp also known as

LogD

what is the equation for Papp

Papp= conc. unionised in oil/ (conc. un-ionised in water + conc. ionised in water)

using the equation for Papp what is the equation for log P app

Log Papp= LogP - log(1+10^(pH-pKa))

using the equation for log Papp what is the equation for log P

LogP= logPapp + log (1+ 10^(pH-pKa))

log P for oxytetracycline

-1.12

log P for caffeine

0.01

logP for morphine

0.15

logP for aspirin

1.19

logP for thiopentone

2.8

log P for methadone

3.9

log P for hydrocortisone

4.3

log P for amiodarone

6.7

gi tract oral absorption

• aqueous

• conc = C1

• static

plasma oral absorption

• aqueous

• conc= C2

• constantly moving

gi tract lining cell oral absorption

• lipid membrane with aqueous pore

• effective surface area = A

what is the equation for the rate of absorption

• rate of absorption = P x A x (C1-C2)

• P= partition coefficient

• A= effective surface area

• (C1-C2)= conc. gradient

generally what happens to permeability of a drug across the blood -brain barrier

• permeability of a drug increases with increasing lipophilicity

what drugs do not follow the rule of permeability across the blood-brain barrier

• vinblastine and vincristine

• permeability is lower than expected, due to in large their being substrates for the efflux transporter, P-glycoproteins

what process does passive facilitated diffusion speed up

the bidirectional process

example of a transporter in intestinal uptake

OATPs

exampple fo a transporter in intestinal efflux

• MDR1 (P-glycoprotein)

• BCRP

example of a transporter in hepatic uptake

OATPs

examples of transporters in hepatic efflux

MRP3

examples of transporters for biliary secretion

• MDR1

• MRP2

examples of transporters in renal uptake

OAT3

examples of transporters in renal secretion

• MDR1

• MRP2

examples of transporters in renal reabsorption

SVCT1

examples of transporters in brain uptake

LAT1

examples of transporters in Brain efflux

• MDR1

• BCRP

important factors to consider In drug distribution

• log P of a drug

• pKa pf a drug

• pH of aqueous environment

• relative size of aqueous compartment

• blood, CSF, vitreous humour

• relative blood flow to tissue

• proportion to body fat

• plasma protein binding

pH of plasma in ‘normal’ acidosis or alkalosis

may range from 7.2-7.5

pH of plasma in ‘severe’ acidosis or alkalosis

may range from 6.8-7.8

pH of interior of erythrocytes

7.2

pH of interior of muscle cells

6.9

pH of breast milk

6.8

what may be affected when a drug is ionisable

may affect amount of partitioning into lipid phase abdominal into the next aqueous compartment

total body of water in adult men including adipose tissue

approx 60%

total body of water in adult women including adipose tissue

approx. 50%

total body of water in neonates

approx. 75%

total body of water in adults excluding adipose tissue

approx. 66%

what are the 2 groups total water is divided into

• intracellular water

• extracellular water

what is the intracellular:extracellular water ration in adults

1: 0.5

what is the intracellular: extracellular water ration in infants

1: 1.5

what is the extracellular water volume in adults

approx. 15L

what is the plasma: extravascular fluid ratio in extracellular water

1:4

what is the blood: extravascular fluid in extracellular water

1:2

what is the cells: plasma ration in extracellular water

1:1.2

what is the blood volume in adult men and adult women

• men- 77mL/kg

• women- 65mL/kg

what is the blood volume in infants

80mL/kg

Blood- water, % tissue in body, overall % of body water

• 0.830

• 8.7

• 11

muscle- water, % tissue in body, overall % of body water

• 0.756

• 45.6

• 52

brain- water, % tissue in body, overall % of body water

• 0.748

• 2.2

• 2.5

skin- water, % tissue in body, overall % of body water

• 0.720

• 19.7

• 21.5

liver- water, % tissue in body, Overall % of body water

• 0.683

• 2.5

• 2.5

skeleton- water, % tissue in body, overall % of body water

• 0.220

• 17.4

• 6

adipose tissue- water, % tissue in body, overall % of body water

• 0.100

• varies

• varies

relative size of aqueous compartments

• assume the pH of each aqueous compartment is the same

• the conc. of the drug in each aqueous compartment will be the same

• the total amount of the drug in each aqueous compartment will be dependent on the relative size of the compartment

• need to consider the effect this has to drug action

adrenal glands- % tissue in body, blood flow, % of cardiac output

• 0.02

• 55

• 1

kidneys- % tissue in body, blood flow, % of cardiac output

• 0.4

• 4.5

• 24

thyroid gland- % tissue in body, blood flow, % of cardiac output

• 0.04

• 4.0

• 2

GI tract and liver- % tissue in body, blood flow, % of cardiac output

• 2

• 0.75

• 20