Introduction to Veterinary Pharmacokinetics:

Pharmacokinetic Modeling

Drug Distribution

Volume of Distribution (Vz - also Vd)

The volume of fluid that "appears" to contain the amount of drug in the body (based on the plasma concentration).
  • Partially determines the relationship between dose and plasma concentration
  • Defines the volume of fluid that must be processed by organs of elimination
  • Roughly describes "tissue penetration"
  • May not equal an actual physiologic space.

Units

  • Liters or milliliters describing whole animal
  • Liters/kg or milliliters/kg
100 mg of a drug is added to a 10 liter fish tank filled with water.  A sample is taken after equillibrium is reached.  The chemical properties of the drug determine whether it stays in the water or sticks to the glass.
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Representative (theoretical) volumes of distribution. Initial estimate of body water is 1 liter/kilogram (l/kg).
Scenario Physiologic Space Volume of distribution
Drug distributed only to plasma water Blood volume = 7% of body weight
Plasma water = 55% of blood volume
1 l/kg x 0.07 x 0.55 = 0.0385 liters/kg
Drug distributed evenly in extracellular fluid only Extracellular fluid volume = 25% of body weight
1 l/kg x 0.25 = 0.25 liters/kg
Drug distributed evenly extracellular + intracellular fluid only Intracellular fluid volume = 40% of body weight
1 lg/kg x (0.25 + 0.40) = 0.65 liters/kg
Drug distributed evenly in extracellular fluid and concentrated 3x in intracellular fluid Extracellular fluid volume + 3x intracellular fluid volume
1 l/kg x (0.35 + (3 x 0.4)) = 1.45 liters/kg

Drug Elimination

Total Clearance (Clt)

The volume of plasma water cleared of the drug during a specified time period.
  • Organ clearance is the result of the flow (Q) through the organ and the efficiency of extraction (E):
    Clearance = Q x E
  • Total body clearance (Clt) is the sum of all organ clearances
    Clt (total) = Clh (hepatic) + Clr (renal) + Clp (pulmonary) 
  • The relationship between clearance and the volume controls how quickly the drug is removed from the body.

Units:

  • Volume / unit time  (l/hr, l/min, ml/hr etc) describing whole animal
  • Volume / kilogram / unit time  (l/kg/hr, ml/kg/min etc.)
A stylized representation of hepatic clearance. Note that extraction efficiency remains constant for both the initial condition and 30 minutes later. 10% of the drug molecules entering the liver are converted to metabolite.

Rate constant of elimination (λz)

A direct answer to the question "How fast are drug concentrations falling?", λz is the slope of the natural log plot of the drug concentration versus time profile. It's related to clearance in that it's also the fraction of the volume of distribution cleared per unit time.

  • "Produced" by the relationship between the volume of distribution and the total clearance:
    λz = Clt ÷ Vz
  • Determined from the slope of the "elimination portion" of the drug concentration vs time profile (curve).

Units

  • /hr, /min, hr-1, min-1

Although the amount eliminated from the body is less and less for each time interval, the FRACTION of the amount eliminated during each interval is constant. This is demonstrated by the semi-log plot.

Semi-logarithmic plot of hypothetical plasma concentration vs. time profile. Note that while this base10 log plot shows a straight line, the slope can only be calculated using natural logs.

Elimination half-life (T1/2)

The time for elimination of one half of the total amount in the body.

Units

  • Hours or minutes

Application(s)

Tissue Residues

  • At 5 x T1/2 97% has been eliminated
  • Make sure you use the longest half-life
    • Metabolites may be more important than the drug
    • Extremely slow absorption from injection site may be the primary cause of residues.

Approach to steady state

  • Steady state exists when defined plasma concentrations (peak, average, trough) are identical following each administered dose during chronic therapy.
  • At 5 x T1/2 concentrations are 97% of steady state values no matter what the dose and interval.
    • For digoxin, maximum effects of digoxin may appear a week after therapy is initiated, for phenobarbital it can be two weeks.
  • Loading doses may be recommended when dose intervals are (relatively) short and half-lives are (relatively) long.
Approach to steady state. A stylized example in that the dose interval equals the drug half-life.

Absorption

Absorption rate constant (ka)

The absorption rate constant describes the rate of drug movement (oral, IM, SC, etc.) from the dose to the circulatory system. In combination with other factors, ka determines the time required to reach the peak concentration (Cmax) following a dose of drug and the peak drug concentration.

Units

  • /hr, /min, hr-1, min-1

Fraction of dose absorbed (F)

When a drug is administered by any route OTHER than IV, it is rare that the entire dose is absorbed

  • Oral - Destroyed in GI tract, passes out in feces before it is absorbed, binds to ingesta, etc.
  • IM - Hydrolysis of drug in tissue, drug binding to injection site, abcess formation, etc.

Units

  • Either percentage of dose or fraction of the dose (59% = 0.59)

Application

    The fraction of the dose absorbed determines a drug's bioavailability (how much gets into the blood stream).  Bioavailability is a common measure used to compare two different drug formulations (tablets vs. elixir) or to compare products sold by two different manufacturers (trade name drugs vs. generics).

Bioavailability and Bioequivalence

Two drug products are bioequivalent if the nature and extent of therapeutic and toxic effects are equal following administration

Although similar and related, equal bioavailability (F) does not guarantee bioequivalence.

Two dose forms of the same drug are depicted. These two dose forms have equal fractions absorbed and equal rate constants of absorption. They are equally bioavailabile and they are bioequivalent.

Two dose forms of the same drug are depicted. These two dose forms have equal fractions absorbed but very different rate constants of absorption. These two dose forms have equal bioavailability but they are not bioequivalent.