Clinical Pharmacokinetics
Part 2

Medical Pharmacology

1994

G.L. Coppoc

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)

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