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Home , ADME, Clearance (pharmacology), EC50, Maintenance dose, Pharmacodynamics, Volume of distribution

/ : Basic Principles for Internal Trainees

Hussain Mulla PhD Senior Clinical Researcher in Clinical / University Hospitals of Leicester Optimum ? What is ?

pharmacokinetics what = the body ADME does to & the pharmacology conc vs time

what pharmacodynamics the drug does to the body CLINICAL PHARMACOLOGY

Pharmacokinetics Pharmacodynamics

CL V Emax EC 50

Dose Concentration Effect A drug in the body: constantly undergoing change

How much? What’s happening? How much? How much?

What’s happening?

How much?

How much? What is Pharmacokinetics ?  Pharmakon = GK: “” Kinetics = “The temporal and spatial distribution of a substance in a system”  Quantitative description of changes in conc. of drug in body over time after dosing

single oral dose drug conc in body

time after dosing Dose to patient

Oral tablet Physiological Oral Drug influence on PK

First pass Hepatic Portal vein Gut

Liver Systemic Circulation Metabolism t of t A D M E drug

absorption & drug metabolism

drug +

excretion

drug + metabolites A D M E in a Patient Population drug Liver disease, renal failure, DDI GI motility / function affected by: absorption ,sepsis,surgery, efficacy drugs & drug

toxicity Liver failure, heart metabolism failure, infection, sepsis, hypoxia, co- Sepsis, ascites, hypoalbuminaemia, drug + metabolites hyper/hypovolaemia, CPB,ECMO Renal Failure, Billiary excretion disease, comedication, infection, sepsis

drug + metabolites Plasma Conc vs Time Profile

absorption rate > absorption rate = elimination rate elimination rate

1000 elimination rate > 750 absorption rate plasma drug 500 concentration 250

0 time after dosing Absorption DrugDrug AbsorptionInput

 Mode of drug administration influences the rate at which effective drug concentrations are achieved

 Drug Input  Dose Function of Dosage Form>>  >>Drug >> patient  Absorption Rate

 Drug Disposition  Function of Drug >>  , Elimination Rate constant patient>>Dosage Form  Half-life Distribution Drug Distribution

Kidneys

Fat etc.

Liver Factors influencing drug distribution

Drug Related • Ability to undergo passive diffusion • Transporters • Binding to macromolecules e.g. plasma proteins • Ion trapping

Patient Related • Blood perfusion rate of different tissues • the concentration of plasma proteins • haematocrit • body composition • tissue density • genetic variants of transporter proteins. Patterns of distribution Blood Tissues

Stays mainly in blood.

Distributes evenly.

Distributes strongly into tissue. Volume of distribution

A measure of the tendency of a drug to move out of the blood into the tissues.

Large volume of distribution indicates strong tendency to enter the tissues. Volume of distribution

Concentration = Dose Volume

D V = D/C V Volume of distribution

D = 50 mg C = 0.25 mg/L D V = D/C = 50mg / 0.25mg/L V = 200 Litres Volumes of distribution (In litres for average 70 Kg adult)

Small volume. Mainly stays  7 in plasma, little in tissues.  Gentamicin 16  35 Medium volume. Similar  150 concentrations in plasma and tissues  400  1,010 Large volume. Mainly in  Chloroquine 1,300 tissues, little in plasma . Theophylline target concentration

 What is required to rapidly achieve the target concentration of 10 mg/L? Theophylline: Loading Dose

 Loading Dose Amount = Vd . Target Concentration mcg = L . mcg/L 350mg = 35 L* 10mg/L

* 70kg adult Applications of Volume of Distribution

 Loading Dose Loading Dose = Vd . Target Concentration

 Half-life 0.69 x V T1/2 = CL

Clearance Clearance

 The fundamental drive for elimination of drug from the body

 Clearance is a measure of the efficiency with which a drug is irreversibly removed from the body

 Total body clearance is the sum of all elimination processes:  Metabolic + Renal + Biliary + Others

 Can be related to physiological processes  eg: Blood flow to the liver, Glomerular Rate  Thus enables predictions of effects on plasma and tissue concentrations in disease states Clearance - Metabolism

 change the drug to make it more “excretable”  Metabolism = removal of drug

 (CYP)  2D6; 3A4; 2C19......

 Conjugation  UDPG, Sulphate.....

 Worry about:  Ontogeny and developmental differences  Genetic polymorphism  Active metabolites  Saturation leading to non-linearity  Drug interactions Clearance - Excretion  Urinary excretion (Renal Clearance)  3 processes  Glomerular filtration – first order for unbound drug  Tubular secretion – active and saturable  Reabsorption – first order for unionised drugs

 CL R = CL GF + CL TS – CL TR

 Biliary excretion  Usually active secretion via transporters  Some conjugates can be hydrolysed in the gut and the drug reabsorbed  enterohepatic re-circulation Clearance Classification

 Constant  Dose independent

 Concentration Dependent  Dose dependent

 Flow Dependent Clearance Classification

 Constant  First order, linear  Most metabolism  Glomerular filtration Clearance Classification

 Concentration Dependent  Mixed order, non-linear, Michaelis-Menten  Tubular secretion   Clearance Classification

 Flow Dependent  Organ Specific clearance  morphine Clearance rates of common drugs

 Very Rapid  GTN 150L/h  Plasma, liver, other tissues

 Rapid  Morphine 60L/h  Liver Clearance rates of common drugs

 Medium  Gentamicin 6L/h  Kidney

 9L/h  Kidney and liver  Slow  Theophylline 3L/h  Liver  Very Slow  Warfarin <3L/day  Liver Clearance

Rate of Drug Elimination = Clearance * Plasma Concentration Theophylline Target Concentration

 How can a target concentration of 15 mg/L be maintained? Theophylline: Continuous Infusion Rate

 At steady state  Rate Out = Rate In

 Hence

Rate In = CL. Target Concentration mg/kg/h = L/kg/h . mg/L 0.67 mg/kg/h = 0.044 L/kg/h* . 15 mg/L

*for a young adult Applications of clearance

 Maintenance Dose rate = CL. Target Concentration

 Half-life 0.69 x V T1/2 = CL

Half-life Half-Life t 1/2

t1/2 is constant over whole time curve 1000

750 t1/2 plasma drug 500 conc 250

0 time after dosing Half-Life t 1/2

 A drug’s half-life ( t1/2 ) is determined by  (i) its clearance ( CL ) &  (ii) its volume of distribution ( V )

0.693 * V CL t1/2 = ( Ke = ) CL V

0.693 t1/2 = Ke Half-Life t 1/2

V & CL affect t1/2 in opposite directions

 t1/2 increased by increase in V

 t1/2 decreased by increase in CL

However high CL does not necessarily mean short t1/2 ?:

 chloroquine : high CL but long t1/2  since high V is due to high lipid causing extensive binding to tissues Half-Life t 1/2

 Disease can decrease (increase) both volume of distribution and elimination processes involved in clearance (e.g. hepatic or renal failure)

 Because V & CL have opposing effects on t1/2 , a decrease in both still might result in no change in t1/2

 Half-life not good indicator of changes in CL Significance of Half-Life t 1/2

5 x t 1/2 steady state conc plasma drug conc

1

0.5 t1/2 0 drug effectively eliminated after ≈ time after dosing 5 half-lives Half-Lives t 1/2

Drug t1/2 (h) Neonates Children Morphine 6-12 2 6 3.5 Gentamicin 12 2-3 Digoxin 55-90 15-72 CLINICAL PHARMACOLOGY

Pharmacokinetics Pharmacodynamics

CL V Emax EC 50

Dose Concentration Effect Pharmacodynamics

 Science linking concentration and effect

 The two most important PD parameters of a drug are  Efficacy - Emax (maximum effect)  - EC50 (conc producing 50% of max effect)

 Drug Effects can be immediate, delayed, cumulative The PK-PD relationship

Midazolam

Sedation 100 Amnesia Response

0 EC50 65 ng/mL Plasma Concentration of Concentration and Effect

Emax 100 90

80

70

60

50 Effect 40

30

20

10

0 0 10 20 30 40 50 60 EC50 Concentration

N G Holford 2000 Sigmoid Emax model

 E= Drug Effect Emax . Conc Hill E = Hill Hill  Conc is the concentration EC 50 + Conc at the  Emax is the maximum drug effect

 EC 50 is the conc at 50% of Emax  Hill determies steepness Sigmoid Emax model

100

90

80

70 Hill=1

60 Hill=0.5 50 Hill=2 40 Response (%) Response 30 Hill=4

20 Hill=10

10

0 0 10 20 30 40 50 60 70 80 90 100

Concentration Applications of the Emax model

 Selection of an appropriate dosing interval depends on more than the PK half-life - the target concentration and it’s relation to the EC50 must be considered too.

E.g. Beta blockers ACE inhibitors - half life of hours but administered once daily Emax model

Conc Effect Emax . Conc E = 0 0 EC 50 + Conc EC20 0.25 20 EC50 1 50 2 67 3 75 EC80 4 80 5 83 6 86 7 88 8 89 9 90 10 91 EMAX 99 99

N G Holford 2000 Theophylline Pharmacodynamics 60

50

40

FEV 1 (% normal) 30

20 Emax = 63% EC = 10 mg/L 10 50

0 0 5 10 15 20 25 30 Theophylline [mg/L] Mitenko & Ogilvie NEJM 289:600-3, 1973 Time course of Drug Effect

 How long does the drug effect last?

 Is there a half-life for effect?

 What is the relevance of EC50? What is the T 1/2 ?

Time Plasma Concentration (mg/L) Effect 0 50

6 25

12 12.5

18 6.25

24 3.18

30 1.59

36 0.80

42 0.40

N G Holford 2000 What is the T 1/2 ? Time Plasma Concentration (mg/L) Effect 0 50 94 6 25 89 12 12.5 80 18 6.25 67 24 3.18 50 30 1.59 33 36 0.80 20 42 0.40 10

The time course of the drug concentration, cannot in itself predict the time course or magnitude of drug effect. N G Holford 2000 Response is schedule dependent Peak Concentration = EC50 Midazolam Bolus Dose for Sedation 80 60

70 50 EC 50 60 40 50 Midazolam PK

40 Midazolam PD 30

30 20 20 Sedative Response (%) 10 10 Plasma (mcg/L) Concentration

0 0 0 2 4 6 8 10 12

Time (h)

Bolus dose 200mcg/kg Peak Concentration = 10 x EC50

Midazolam Bolus Dose for Sedation 800 100

90 700 Midazolam PK 80 600 Midazolam PD 70 500 60

400 50

40 300

30 Sedative Response (%) 200 Plasma (mcg/L) Concentration 20 100 10 EC 50 0 0 0 2 4 6 8 10 12

Time (h) Bolus dose 2000 mcg/kg Peak Concentration = 100 x EC50 Midazolam Bolus Dose for Sedation 8000 120

7000 100 6000 80 5000

4000 60 Midazolam PK

3000 Midazolam PD 40 Sedative Response (%) 2000 Plasma (mcg/L) Concentration 20 1000

EC 50 0 0 0 2 4 6 8 10 12

Time (h) Virtually no drug but Bolus dose 20000 mcg/kg still 70% response Disappearance of Drug Effect

 Exponential

 Conc < EC 20  Proportional to concentration e.g. midazolam t 1/2 = 1 h, 50% loss of effect per hour  Generally not useful for a sustained therapeutic effect (need to increase dose)  Linear

 EC 80 > Conc > EC 20  Proportional to time e.g. 10% drop in sedation level per hour  Can’t happen for steep curves (because the middle isn’t very wide)  Flat  Conc > EC80  Almost independent  A common scenario – a large dose is given for duration of effect.  “Time above threshold” models  The “too high” plasma concentrations may be an unnecessary risk Duration of Response

Doubling the Midazolam Bolus Dose for Sedation 140

120

100

Midazolam PK 200mcg 80 EC 50 Midazolam PK 400 mcg 60

40

20 Plasma (mcg/L) Concentration

0 0 1 2 3 4 5 6 7 8

Time (h) Duration of Response Doubling the Midazolam Bolus Dose for Sedation 140 70

120 60

One Half-Life 100 50 Midazolam PK 200mcg

Midazolam PK 400mcg 80 40 EC 50 Midazolam PD 200mcg 60 Midazolam PD 400mcg 30

40 20 Sedative Response (%)

20 10 Plasma (mcg/L) Concentration

0 0 0 1 2 3 4 5 6 7 8

Time (h) Clinical Pharmacology in the patient population

Pharmacokinetics Pharmacodynamics

Age, Wt, Liver Function Age , Disease, Co-meds, Renal Failure, Heart failure, etc…. GI function,CL Surgery,V infection, sepsis, hypoxia, Emax EC 50 hypothermia, DDI Genetics, CPB, ECMO etc…. Dose Concentration Effect Summary

 Clearance (CL) and Volume of Distribution (Vd) are the most important Pharmacokinetic Parameters

 Efficacy (Emax) and Potency (EC50) are the most important Pharmacodynamic Parameters

 An understanding of these parameters and their relationship (PK-PD) is of paramount importance in optimising doses for children

 In the patient population, many factors can affect the PK and/or the PD