# pharmacokinetics

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Objectives
Understand the concepts of bioavailability, volume of distribution, half-life and clearance of drugs
Understand how to calculate the pharmacokinetic properties of drugs and the inter-relationship
Understand how pharmacokinetic principles are applied to clinical situations

Supplemental Reading: The Pharmacological Basis of Therapeutics, 12th edition, Chapter 2, pages 17-39. Katzung & Trevor’s Pharmacology Examination & Board Review, 10th ed., Chapter 3

Clinical Pharmacokinetics
Deals with relationship of drug dose and conc of drug in body over time
Important relationship between drug dosage, pharmacokinetic processes, and pharmacological response with respect to plasma drug concentration (Cp)
Bioavailability, volume of distribution, t1/2 life, and clearance are pharmacokinetic factors used to calculate dosing regimens

BIOAVAILABILITY or F Value (Fraction absorbed)
Expressed as ratio: F (0-1) that compares any adm route with IV adm
F can be expressed as a percentage, % Bioavailability = F x 100
Presence of food and other drugs can significantly change bioavailability
Area under the curve (AUC) analysis used to determine F
F = AUC (area under blood concentration curve) PO (any route)/AUC IV
Actual drug amount absorbed = Dose x F
Dose=Actual drug amount absorbed/F

AUC
amount under curve – 60% of route available vs 100% from intravenous route

Problem
Patient receives 100 mg of a drug IV. Oral bioavailability of drug is 25%. How much would have to be administered orally in order to provide the same pharmacologic effect.

New Dosage = Amount absorbed from old dosage / F of new dosage form
(100 mg/25%=100mg/0.25=400 mg)

pharmacokinetics
concentration of drug in plasma

pharmacodynamics
concentration of drug associated with effect

anything intravenously
100% fraction absorbed
anything given another path will have lower fraction

distribution
drug in tissues of distribution

elimination
drug metabolized or excreted
related:
clearance express in L/hr
half-life

PROBLEM 2
Elderly patient has difficulty swallowing large capsule, needs to switch to liquid form of drug. Capsule contained 200 mg drug with F= 0.60. If F of liquid is 0.80, how many drug mgs of liquid form are needed?

New Dosage = Amount absorbed from old dosage / F of new dosage form
((200 mg X 0.6)/0.8=150 mg)

DRUG DISTRIBUTION
Vd = Amount drug in body (DxF) / Cp0
(Note: Cp0 is plasma conc. @ time 0, determined from drug elimination curve)
Vd = 1000 mg / 250 mg /L plasma , adm IV
Vd = 1000 mg / 10 mg /L plasma, adm IV
LD = Vd x Cp (IV administration); for PO adm must divide by F value

DXF/Cp0
Dose times fraction absorbed/ concentration

concentration vs time
can determine cp0
can determine half life
etc.

problem 3
1. The following data were available from a 70 kg patient given a 100 mg dose of metoprolol, administered orally:

Bioavailability=50%; plasma concentration =150 g/L , Calculate the volume of distribution

Vd = D x F / Cp
= 100 mg x 0.5 / (150 ug/l)
= 50 mg / (0.150 mg/l)
= 333 liters

questions will be for this exam
calculation based

Problem 4
Calculate an oral loading dose of digoxin for a 70 kg man which would produce a plasma level of 1.5 g/L. ( F=0.62; Vd=7.3 L/kg).

Vd = 7.3 L/kg x 70 kg =511L
LD = Vd x Cp / F (need F when not IV)
= 511L x (1.5 ug/L) / 0.62
=766.5 ug / 0.62
= 1236 ug or 1.24 mg (PO)

Pharmacokinetic Rate Reactions
Particularily applies to enzymatic drug biotransformation (drug metabolism)
First Order – change in pharmacokinetic rate reaction proportional to dosage; drugs have a fixed T1/2, most drugs
Zero Order – change in pharmacokinetic rate reactions not proportional to dosage; drugs have no fixed T1/2 (eg, alcohol). These drugs in overdose accumulate faster to significantly raise Cp

T 1/2
Only first order reaction have fixed T 1/2
T 1/2 is the time required to change the amount of drug in the body by one-half during elimination, not the duration of action
*T1/2 = 0.7 / k (0.7: natural log of 2; k= elim. rate constant)*
Determine k from elimination rate curve

ONE- COMPARTMENT MODEL
Body viewed as single compartment based on drug distribution
*Drug conc in different tissues not equal, but at equilibrium and proportional to Cp*
Drug conc in different tissues varies proportionately as Cp changes
*Characteristic of drugs that are predominantly water soluble*

TWO-COMPARTMENT MODEL
Body viewed as 2 compartments based on distribution, blood flow, lipid solubility
Central compartment – high blood flow, blood, brain, lungs, heart, liver, kidney
Peripheral compartment – low blood flow, tissues with inc % fat (skin, muscle, adipose); destination of lipid soluble drugs with large Vd
Drugs always enter exit central compartment.

illustration of what happens when drug is in central compartment

one/two compart models
if you look at one compartment model, you don’t appreciate and you will underestimate the plasma concentration
one compartment shows 16… 2nd compartment shows 31

CLEARANCE
money slide
Rate at which drug is cleared from body, defined as volume of fluid (plasma) from which drug is removed in given time eg. mls / min or liters/hr
CL = Vd x ke or CL = Vd x 0.7 / t 1/2
Rearrange for T1/2 = Vd x 0.7 / CL
CL has inverse relationship with T1/2
Vd and T1/2 have a proportional relationship

Applies to drugs whose elimination depends on renal clearance
Adjustment based on ratio of patients creatinine clearance vs normal creatinine clearance (100-120 ml/min)
*Corrected dose= normal dose x ratio (patients creatinine clearance / 100 ml/min)*

PLATEAU PRINCIPLE – CPSS
Applies only to drugs following first order
Dosage and dosage interval must remain constant when determining Cpss
Plateau or Cpss is a function of T 1/2
Calculation of maintenance dose or dosage interval for CPSS
*Maintenance dose x F/T=CPSS x CL (T:dosing interval)*
Maintenance dose=CPSS x CL x T / F
CPSS = Dose x F / (CL x T)

related to elimination half-life time
after 5 dosages

accumulation + elimination
0
1 – 50
2 – 75
3- 87.5
4 – 93.75
5- 96.88

practice problems remind
Drug absorption/distribution:
Vd = Amount drug in body (DxF) Cp0 (Note: Cp0 is plasma conc. @ time 0, determined from drug elimination curve)
LD = Vd x Ther.Cp / F (need F when not IV)
Maintenance dose = CL x CPSS x T / F
CPSS = Dose x F / (CL x T)
3. Drug elimination:
T1/2 = 0.7 / k (k= elim. rate const)
T1/2 = Vd x 0.7 / CL
CL = Vd x 0.7 / t ½
4. Always keep unit consistent throughout the calculation.

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