Wed20October0612PM 10

An infusion of fentanyl is administered by intravenous infusion to a patient.

Mu receptor occupancy (y-axis) is measured using positron emission tomography (PET) and is charted graphically against the dose of fentanyl (x-axis).

Which of the following transformations occur when values on the x-axis are converted to logarithms?

(Please select 1 option)

Straight line to exponential curve

Wash-in exponential curve to a straight line

Sigmoid curve to a straight line (Hill plot)

Rectangular hyperbola to sigmoid curve Correct

Wash-out exponential curve to a straight line

Explanation

Knowledge of mathematical relationships is explored in the Primary FRCA examination.

A dose response curve of a pure agonist for the mu opioid (MOP) receptor is a classic example of a rectangular hyperbola. When the x-axis is converted to a logarithmic scale the relationship between the now log dose (x-axis) and response (y-axis) becomes sigmoid in shape.

Another example of a rectangular hyperbola is reaction velocity plotted against substrate concentration ('simple' enzyme reaction; Michaelis-Menten kinetics)

V0 = Vmax [S]

Km + [S]

Where Km is the Michaelis constant, Vmax is the maximum velocity and [S] is the substrate concentration.

Further transformation results in a straight line when log [response/1 - response] against log dose (Hill plot). The slope of a Hill plot should equal +1 if a ligand binds competitively and reversibly.

With a wash-out or wash-in exponential relationship when a value (y) is measured against time (t) a straight line with a gradient (k or -k respectively) results from a logarithmic transformation of the y-axis.

A straight line to exponential curve is mathematically incorrect.

Answer Statistics

1

19%

2

26%

3

24%

4

27%

5

6%

Times answered: 238