Bolus and Infusion Kinetics

Explain the concepts of intravenous bolus and infusion kinetics. To describe the concepts of effect-site and context sensitive half time.

Continuous Infusions

Plasma concentrations of an IV infusion are influenced by:

• Distribution
• Metabolism
• Elimination

Onset of Continuous Rate Infusions

Without a loading dose, the concentration of drug infused at a constant increases in a negative exponential fashion:

• Plasma concentration initially rises rapidly
• Distribution into peripheral compartments is the main method for drugs to leave plasma
  This is because at the start of an infusion there is a large concentration gradient between plasma and peripheral compartments.
• Elimination becomes more important in prolonged infusions
  As peripheral compartments fill the concentration gradient between plasma and compartments falls, and redistribution becomes relatively less important.
• Steady state is achieved when concentrations in compartments are equal, and input is equivalent to clearance
  • Concentration at steady state is determined by the ratio of infusion rate to clearance: $C = {Infusion \ Rate \over Clearance}$
    • Therefore, at steady state with drugs with 100% bioavailability:
      $Infusion \ Rate = C_{target}.Cl$
    • For drugs given by a route with less than 100% bioavailability:
      $Route \ Dosing \ Rate = {Cld.C_{target} \over Bioavailability }$
    • If the dosing is given intermittently, then:
      $Dosing \ Rate = Dose.Dose \ Interval$
  • Volume of distribution at steady state is termed V_Dss and is the apparent volume into which a drug will disperse during a prolonged infusion, and is the sum of all compartment volumes in the model.

Continuous Rate Infusions with Bolus Dosing

As seen, above starting an infusion at the rate required to maintain steady state is inefficient:

• For any desired plasma concentration, it will take three time constants (4-5 half-lives) for a continuous infusion to reach this concentration
  • If the half-life is long, then achieving a therapeutic level will take some time
• A bolus dose aimed to fill the V_D will allow steady-state to be reached immediately: $Loading \ dose = V_D.C_{target}$

Stopping an Infusion

For a bi-exponential model (i.e. only one peripheral compartment), decline in plasma concentration can be modeled by the equation $C = Ae^{- \alpha t} + Be^{- \beta t}$. In this model:

• $\alpha$ is the time-constant for redistribution
• $\beta$ is the time-constant for terminal elimination
  (Provided the infusion has reached steady-state).
• Neither $\alpha$ or $\beta$ correspond to any individual rate constant

Factors affecting rate of offset of an infusion can be classified into pharmacokinetic, pharmacodynamic, and other drug factors:

• Pharmacokinetic factors
  • Distribution
    • V_D
      High V_D will decrease clearance from central compartment. Factors affecting V_D include:
      • Ionisation
        Ion trapping can cause drug to be sequestered.
      • Protein binding
      • Lipid solubility
        Affected by body fat.
    • Speed of distribution
      • CO
        Affects organ blood flow.
    • Redistribution
      During an infusion, peripheral compartments become saturated with drug. When an infusion ceases, drug is redistributed central compartment.
      • This is related to context-sensitive half time (see below)
  • Metabolism
    • Route of clearance
      • Organ-dependent
        • Organ failures
        • Extraction ratio
        • Organ blood flow
      • Organ-independent
      • Saturatable kinetics
        Zero-order kinetics.
    • Presence of active metabolites
  • Elimination
    Route of excretion of active drug or active metabolites.
    • Organ failures
• Pharmacodynamic Factors
  • Age
    • Sensitivity
      Dose required for effect and dose required for recovery.
  • Organ failures
  • Pregnancy
• Other drug factors
  • Pharmacokinetic interactions
    • Enzyme inhibition/induction
  • Pharmacodynamic interaction
    • Drug tolerances
      • Tachyphylaxis
  • Drug action
    Drugs which alter gene or receptor expression, or bind irreversibly (e.g. clopidogrel) may show ongoing effects even after the drug has left the system.

Context-Sensitive Half-Time

Context-sensitive half time is:

• Defined as the time for plasma concentration to fall to half of its value at the time of stopping an infusion
• A method to describe the variability in plasma concentrations after ceasing an infusion
  The "context" is the duration of infusion.
• Used because terminal elimination half-life has little clinical utility for predicting drug offset
  Half-lives are often misleading when discussing drug infusions.
• Dependent on:
  • Duration of infusion
    During an infusion, drugs distribute out of plasma into tissues. When the infusion ceases, drug is cleared from plasma and tissue drug redistributes back into plasma.
    • The longer an infusion, the more drug has distributed out of tissues, and the longer the redistribution phase
    • The longest context-sensitive half time occurs when an infusion is at steady-state
  • Redistribution
    The maximal CSHT reached depends on the:
    • V_Dss
      Drugs with a larger V_Dss have a longer CSHT, as only a small proportion of the drug in the body will be in plasma and able to be cleared.
    • Rate constant for elimination
      Drugs with a smaller rate constant for elimination have a longer CSHT.

Drugs with longer context-sensitive half-times will wear off less predictably.

• Remifentanil has little redistribution and a small Vd, and so has a very short context-insensitive half time
  It wears off reliably and quickly following cessation of infusion.

Context-Sensitive Decrement Time

• Describe the time it takes for a drug level to fall to a particular percentage of its starting value following cessation of an infusion
• They are used because the half-times do not describe mono-exponential decay
  i.e. The time taken for drug concentration to reach 25% of its starting value is not twice the context sensitive half-time.
• The context-sensitive half-time could also be described as the 50% context-sensitive decrement time

References

1. Peck TE, Hill SA. Pharmacology for Anaesthesia and Intensive Care. 4th Ed. Cambridge University Press. 2014.
2. Hill SA. Pharmacokinetics of Drug Infusions. Contin Educ Anaesth Crit Care Pain (2004) 4 (3): 76-80.