eLFH - Pharmacokinetics Flashcards
Euler’s number ‘e’ description
Mathematical constant that describes the process where a variable increases or decreases at a rate that is proportional to its own magnitude
e value
2.718
Tear away function definition
Exponentially increasing functions
Example of tear away function
Bacterial growth
Examples of exponentially decreasing functions
Radioactive decay
Elimination of drug from body
Denitrogenation when pre-oxygenating
Water emptying from cylinder of water with tap at bottom
Asymptote
With exponentially decreasing functions, end state never quite reaches zero, but the curve gets ever closer to the x axis
This end state is called an asymptote
Use of logarithms in exponential graphs
Using logarithms converts curve to straight line graph when same log base as exponential is used
i.e. Natural logarithms are required for natural exponential processes as they relate to ‘e’
Natural logarithm definition
Logarithm with base of ‘e’ (2.718)
Exponential function vs Rectangular hyperbolic function
Both asymptote the x axis, but rectangular hyperbolic function also asymptotes y axis, whereas exponential function doesn’t
Exponential function models naturally occurring processes
Rectangular hyperbola is a section of a cone
Three constants that can be used to describe the exponential decay function
Rate constant (k)
Time constant (tau)
Half life (t1/2)
Rate constant (k) definition
Describes relationship between rate of decrease and the magnitude of the variable
I.e. k is ratio of the slope of the graph to its height
Units of rate constant ‘k’
In exponential processes that occur over time, units of k are always sec^-1
Time constant (tau) definition - 3 ways to describe it
1) Time required for a process to complete if it continued at its initial rate of fall (i.e. tangent to the graph at time = 0)
2) Time taken for the magnitude of the variable to fall to 37% of its initial value
3) Time to fall to 1/e of its original value
Half life definition
Time required for the magnitude of the variable to fall to one half of its original value
Half life must always be shorter than time constant by definition
Relationship between the three constants
Only need to know one of the constants to describe the shape of the graph
tau = 1 / k
k = 1 / tau
t1/2 = tau x 0.693
How much of process is complete after 3 time constants
94.9%
After 1 tau = 63% complete
After 2 tau = 63% + (63% of remaining 37%) = 86.3%
After 3 tau = 86.3% + (63% of remaining 13.7% = 94.9%
Single compartment model
Drug administered to the body becomes evenly distributed throughout a single hypothetical compartment which is the volume of distribution
Single compartment model is too simple to accurately model the kinetics of most drugs
Volume of distribution
Volume of theoretical compartments that a drug is distributed into
Used by TCI models
E.g. 100 mg of propofol in Vd of 20L equates to 5 microgram/ml
Example of drugs which follow a three compartment model
Propofol
Fentanyl
Three compartment model
Central compartment - Initial volume of distribution that is very small representing initial dispersal in the plasma
Shallow peripheral compartment - second compartment with perfusion rich organs including brain
Deep peripheral compartment - third and largest compartment with mostly fat redistribution of drug
Volume of distribution at a steady state (Vdss)
When drug is redistributed throughout all body tissues - Vdss is very large
Vdss = sum of all compartments
= 16 + 32 + 202
= 250 L in this example
3 definitions of clearance
1) Proportion of the compartment volume that flows in unit time
2) Mass of drug eliminated per unit time per unit drug concentration
3) At steady state, the dose rate (flow rate) divided by the steady state blood concentration
Conceptual way to think about clearance
Virtual flow of the volume of distribution
When a drug is cleared from the body by passage in the blood through an organ (e.g. liver or kidney) the volume that is completely cleared is the clearance
Drug clearance equations (3 of them)
Clearance = Drug infusion rate / Blood concentration
(in the steady state for this first equation)
or
Cl = k x Vd
or
Cl = Vd / tau
Units of clearance
L/min
or
L/kg/min
