Clinical Pharmacokinetics, Part 1

Contents

• Overview
• Uses of clinical pharmacokinetics
• Need for therapeutic drug monitoring (TDM)
• Relation between effect and serum drug concentration
• Fundamental hypothesis of pharmacokinetics and Toxicokinetics
• Therapeutic window
• Major pharmacokinectic compartments
• Use TDM for what kind of drugs
• Inter-individual variation
• Important pharmacokinetic variables
• Michaelis-Menton plot (Zero and First Order kinetics)
• Half-life defined on plot
• Clearance (CL) and Ke
• Volume of distribution (VD)
• Bioavailability
• IV Infusion - steady state
• Dose adjustment
• Loading dose
• One compartment model
• Two compartment model

Overview

• Why need "pharmacokinetics" and some general principles
• Important pharmacokinetic variables
• IV Constant Infusion
• Bolus & Multi-dose Regimens
• Two Major Approaches to Pharmacokinetic Analysis (Compartment models)
• 
• 

• picture

Why Need Pharmacokinetics and Some General Principles

Uses of Clinical Pharmacokinetics

• Therapeutic drug monitoring
  • Individualization
• Toxicity
  • Assess drug reactions
  • Diagnose toxicities

Need for TDM
(Therapeutic Drug Monitoring)

• Optimize/individualize dosage
  • Titration using measurement and computation to reduce "trial & error" approach
• Check for Compliance
  • Only 44% compliance in TB patients
  • Less than 60% in hypertensive patients

Relation Between Effect and Serum Drug Concentration

• Drug = Procainamide hydrochloride, an antiarrhythmic drug
• Effect = Premature ventricular contractions in human
• Note close correlation
  • Koch-Weser, 5th Int. Congr. Pcol & Future of Man

Procainamide

Fundamental Hypothesis

• Predictable relationship between
  
  plasma drug concentration
  
  and
  
  effect

Therapeutic Window

Major Pharmacokinetic Compartments

Use TDM for What Kinds of Drugs?

• Drugs with
  • Narrow safety margins
  • Effects not immediately obvious
  • Large inter-individual differences in pharmacokinetics

Inter-individual Variation

• Differences among individuals are greater for--
  • Dose --> Plasma drug concentration
• Than for --
  • Plasma drug concentration --> Effect

Important Pharmacokinetic Variables

Important Pharmacokinetic Variables

• First and Zero-order Kinetics (Michaelis-Menton plots)
• Half-life and Ke
• Clearance (CL)
• Volume of Distribution (Vd)
• Bioavailability (F)
• AUC (Area Under the Curve)

Michaelis-Menton Plot
First Order Kinetics

Michaelis-Menton Plot
Zero Order Kinetics

Half-life -- Defined on Plot

Clearance (CL) Usefulness

• CL is a measure of the rate at which drug is eliminated from the body
• It reflects function of organ(s) of elimination

Clearance Defined

• Definition
  • Virtual volume of measured body fluid (usually plasma) completely freed of drug per unit of time
• CLB = Sum of all clearances
  • CL(body) = CL(renal) + CL(liver) + ...

Extraction Ratio

Relating ER, CL, & Ke

• ER = constant if Flow, Vd, and renal function are constant.
• CL = Volume cleansed/min = 25 ml/min
  • If 0.5 of drug is removed and flow is 50 ml/min, then is equivalent to removing 100% of drug from 25 ml/min
• Ke = CL / Vd
  • i.e., Fraction of Vd cleansed/min
  • Note that this corresponds to fraction of drug removed/min!!!

Extraction Rate Limited vs.
Flow Rate Limited CL

• For Some Drugs changes in --
  • Organ function change CL very little
  • blood flow rates change CL much
• For Other Drugs changes in --
  • Organ function change CL much
  • Blood flow change CL very little
• For Still Others, changes in --
  • Both change CL significantly

Clearance and Ke

• CL= virtual volume of plasma completely freed of drug per unit time, (e.g., L/hr)
  • CL = Ke * Vd
• Ke = Fraction of Vd cleansed of drug per unit time and Fraction of drug removed per unit time (not shown here!) (e.g., n/hr )
  • Ke = CL/Vd
• Note: Same terms are in both equations

Clearance -- Tidbits

• CL = constant when plasma drug concentration ([drug]p) is less than that which "saturates" the elimination system(s)
• CL = variable when [drug]p is at or near the Vmax of elimination process(es)
• CL often changes with disease and stage of disease

Volume of Distribution (Vd) Usefulness

• The major usefulness of Vd is as a variable in pharmacokinetic computations
• Vd has no anatomic correlate
• Vd assumes drug is uniformly distributed throughout the volume indicated. This assumption is seldom warranted

Volume of Distribution (Vd) Definition

Vd -- Tidbits

• Virtual space
  • not specifically identifiable as an anatomic space
  • Does not imply equal drug concentration throughout the body
• Changes with --
  • physiologic status, e.g., pregnancy
  • disease and disease state, e.g., changes in protein binding

Vd -- Types

• Vd(extrap)
  • extrapolated from plot of Cp vs time
• Vd(ss)
  • more complicated!
• Others
• Don't all give the same answer. Tendency today is to use Vd(ss) where possible

Determining Vd(extrap)

• Fluid measure usually plasma
• Usually measure TOTAL DRUG
• Measuring FREE DRUG better, but not perfect indicator of drug at site of action
• May exceed Total Body Water!

Bioavailability (F) -- Usefulness

• Bioavailability (F) is multiplied by the dose given to determine the TRUE DOSE
• It accounts for loss prior to drug reaching the central circulation

Bioavailability (F) -- Definition

• Definition
  • Fraction of administered drug that reaches the systemic circulation
• Dose calculation example
  • Recommended dose = 20 mg/Kg
  • F = 0.5
  • True dose = Recommended dose / F
  • True dose = (20 mg/Kg) / 0.5 = 40 mg/Kg

Bioavailability (F) -- Tidbits

• Use systemic circulation because --
  • it is EASY to sample
  • it is in contact with all body tissues
• Not 100% because of drug loss through --
  • elimination prior to reaching central systemic plasma
  • Binding of drug to tissue components thus preventing absorption

Bioavailability (F) -- Sites of Loss

• Example -- PO Adm.
  • Penicillin G, 1000 IU
    • 90% destroyed in stomach so only 10% reaches systemic circulation
  • Other drugs
    • propranolol -- extensive inactivation in liver

Bioavailability (F) -- Determination

• Look-up in reference
• Measure: Compare exposure by desired route to IV, which is defined as 1.0.
• Exposure i.e., integral of drug concentration and time plot (AUC)

IV Constant Infusion

IV Infusion to Steady State
"Accumulation"

• IV infusion at constant rate causes drug concentration to rise until it plateaus at the steady state
• Css = Concentration of drug at steady state plateau

IV Infusion
Time To Steady State

• Time to reach steady state concentration during constant IV infusion is determined by elimination rate!
• Examples
  • 50% Css = 1 half-life
  • 75% Css = 2 half-lives
  • 87.5% Css = 3 half-lives
  • 93.75% Css = 4 half-lives
  • 96.87% Css = 5 half-lives
  Infusion -- Cp Rise and Fall
  If elimination is first-order, i.e., absolute amount elminated each unit of time varies with Cp, then the rise and fall of Cp are vertically inverted images with time courses dependent on elimination half-life

IV Infusion -- Initial Dose Rate

• Look up values in literature
• Population (desired / predicted) values
  • Css = 30 mg/L
  • CL = 0.33 L/hr
• Predicted DR = Css x CL
  • 30 mg/L x 0.33 L/hr = 10 mg/hr

IV Infusion -- Adjust Dose

• Initial Dose Rate
  • 10 mg/hr
• Css
  • Measured = 20 mg/L
  • Desired = 30 mg/L
• Use simple proportion
  • New Dose Rate = Initial Rate * (Desired Css / Measured Css)
  • New Infusion Rate = 15 mg/hr

IV Infusion -- Adjust Dose
Estimate Patient's CL from data?

• Infused 10 mg/hr and produced 20 mg/L concentration in plasma
• CL = DR / Css
  • (10 mg/hr) / (20 mg/L) = 0.5 L/hr
  Note: CL predicted by population (literature) was 0.33 L/hr, slower than found in this patient, therefore, had to adjust dose to higher amount

IV Infusion -- Dose Adjustment Complications

• Real life slightly more complicated than the example
• Must account for
  • Formula weight of drug as supplied vs the Molecular weight of drug as measured
  • May need to give "loading dose" to produce concentration equivalent to Css faster

Load Dose -- Simple Approach

• Needed population/literature estimates
  • Css(desired)
  • Vd (note if is for "std 70 kg person" or "per kg"
• Loading dose = Css(desired) * Vd(predicted)
  • In earlier example --
    • Css(desired) = 30 mg/L & Vd(predicted) = 21L:
    • Dose(loading) (mg) = Css (mg/L) * Vd (L)
    • Dose(loading) = 630 mg

-----------------------------------------------------------------------------------------------

Bolus
&
Multi-Dose Regimens

Multi-Dose Regimens --
Additional Considerations

Two Major Approaches To Pharmacokinetics

• Model Dependent
  • One compartment model
  • Two compartment model
  • Three compartment model
  • etc.
• Model Independent
  • Dosing rate = Clearance * Css

One Compartment Model -- Diagram

One Compartment Model -- Assumptions

• Instant mixing in body (relative to other process rates and time of first measurement of drug concentration)

One Compartment Model -- Plot

Cp(t) = A * e-(Ke * t)

One Compartment Model -- Formula

• A = 0-time intercept of line drawn through data points
• Ke = negative slope of line
• t = time elapsed
• e = base of natural logs
• Cp(t) = Plasma drug concentration at time = "t"

Two Compartment Model -- Diagram

Two-Compartment Model Assumptions

• Instant mixing in each compartment (relative to other process rates and frequency of measurement)
• Input and output from central compartment

Two Compartment Model -- Plot

Two Compartment Model -- Formula

Cp(t) = A * e-(a * t) + B * e-(b * t)

Multi-Dose -- Similarities to Constant Infusion

Multi-Dose Adjust -- Css(ave)

Multi-Dose -- Use Which Css??
Css(min)!

Multi-Dose Adjust -- What about the Peak?

• If peak concentration is too high, could produce toxicity
• Must be concerned about degree of oscillation in dose schedule
• If route is other than IV, the degree of oscillation will always be less than predicted by calculation of Css(max) and (min)

Effect of Regimen on Oscillation

• If dose interval (T) = elimination half-life, then Peak is 2x Trough!
• Increased T, increases oscillation
• Decreased T, decreases oscillation toward that of IV infusion.
• Calculation of oscillation requires ability to estimate peak and trough at SS.

Estimation of Css(max) -- PEAK

• Css(max) = (F*D/Vd) * { 1 / [1- e(-Ke * T) ] }
  
• Note similarity to --
  
  Cp(t) = Cp(0) * Accumulation factor
  
• Terms:
• F = Bioavailability Vd = vol distr. (L)
• D = Dose (mg) T = Dose interval (hr)
• Ke = Elimination rate (1/hr) e= base natural log

Estimating Css(min)

• First estimate Css(max) using appropriate equation

Then use old standby for predicting Cp(t), but now "t" is defined as "T", the dose interval.

Css(min) = Css(max) * e(-ke * T)

• Similar to --
  
  Cp(t) = Cp(0) * e(-ke * t)

Determining Dose Interval (T)

• Refer to literature recommendations
• Make "T" something easy for patient / staff to comply with, e.g., q1d, q12h, q8h, q6h
• Keep "T" as long as possible consistent with reasonable oscillation
• Do multiple computations of Peak and Trough with various "Doses" and "T" to obtain appropriate regimen
• First recommendations will be close to literature values, but after have "MEASURED" Cp from patient, may be very different

Determining Dose Rate for Oral Dose forms, e.g., Tablets

• Using liquid dose forms has theoretical advantage of allowing "continuously variable" dosing.
• In practice, this is true only for injections
• For oral dose forms, nearly always some step function, e.g., teaspoon, tablespoon, for liquids
• For tablets, manufacturers prepare range of weights appropriate for most patients, e.g., 5 mg, 25 mg, 50 mg, 100 mg, etc.
• NOTE: In many cases, the drug is a small percentage of a tablets weight

Sample Calculation using Theophylline for Asthmatic

• Patient
• Drug
• Pharmacokinetic data
• IV Infusion
• Oral Dosage Regimen
• Oscillation
• Loading Dose

Multi-Dose