kinetics exam 2 Flashcards
A 10.2 mg dose of PAYNE-B-GORN is administered by IV bolus to a patient. A plot of the plasma concentrations assayed at different time points (vertical axis) against the corresponding times (horizontal axis) yielded a straight line on a regular metric graph sheet. PAYNE-B-GORN follows first-order elimination kinetics.
A
True
B
False
B
False
A 5.4 mg dose of SHARPMED is administered by IV bolus to a patient. A plot of the plasma concentrations assayed at different time points (vertical axis) against the corresponding times (horizontal axis) yielded a straight line on a semi-log graph sheet. SHARPMED probably follows first-order elimination kinetics.
A
True
B
False
True - this is the answer! straight line for semi-log is first order!
For a two-compartment linear model, drug concentration after t hours is given by Cp =Ae-at + Be-bt . In this, a is the rate constant for the elimination phase.
A
True
B
False
B
False - it is for the distributive phase
distributive phase is the alpha phase
elimination phase is the beta phase
Which of the following represents the elimination rate constant?
A
k10 - down arrow from the central compartment
B
k12 - arrow from central compartment to peripheral
C
k21 - arrow from peripheral to central compartment
A
k10 - down arrow from the central compartment
k12 & k21 are transfer constants
The Case for Extra Compartments
The presence of other compartments
- Different Blood flow rates to tissues
- Different permeability of drug into different tissues
- Uptake of drug from plasma compartment by tissues
- Binding of drug to tissues
Some Tissue Groupings
Highly perfused tissues include: kidney, hepatic-portal system, brain and heart.
- Poorly perfused tissues include adipose tissue, bone and hair
Two-Compartment Open Model
central compartment
k12–>
k21–>
peripheral compartment
k10 down arrow from the central compartment
Sometimes Observed Plasma Level-Time Curve
not a straight line but a bi-phasic (or 2 phase) plot
semi-log plot where there are two different slopes (slope 1 would be the distributive phase, slope 2 would be the elimination phase)
Phases of a Two-Compartment Model
distribution phase is the first slope
elimination phase is the second slope
distribution ie complete at the middle of the line
ONE-COMPARTMENT MODEL
drug is introduced intravenously
BEFORE DOSE - Large dose administered intravenously
AFTER DOSE - Instant thorough distribution throughout patient
TWO-COMPARTMENT MODEL
BEFORE DOSE - Large dose administered intravenously
RIGHT AFTER DOSE - Instant distribution
only in some organs
MUCH LATER AFTER DOSE - Later distribution throughout patient
-Two-Compartment Model: Phases
I - instant distribution
II - distributive equilibrium
III - elimination phase
DOSE TO BE ADMINISTERED
- central compartment to peripheral compartment
- not distribution yet
iNSTANT DISTRIBUTION IN FIRST COMPARTMENT ONLY
- some of the drug gets
moved to the peripheral while all of the drug is in the central compartment
- while some of the drug is being eliminated
DISTRIBUTION PHASE
- this is I
- some of the drug is in the peripheral compartment
- some more of the drug is in the eliminated
DISTRIBUTIVE EQUILIBRIUM
- more of the drug is in the peripheral compartment
- even more of the drug is being eliminated
Phases of a Two-Compartment Model: Distributive Phase
Distributive Phase: drug level in plasma declines and drug level in periphery rises, but net transfer from the central to the peripheral compartment
- Equilibrium: rate of drug entry into tissue equals the rate of exit
- Elimination (Beta) Phase:
drug levels in both compartments decrease in parallel
*rate of decrease slower than in distributive phase
*mimics a reversion to a one-compartment model
Two-Compartment Open Model
central compartment
k12–>
k21–>
peripheral compartment
k10 down arrow from the central compartment
graph of tissue and plasma levels
the plasma concentration is going down
because some of the drug is beginning to show up in the periphery tissue
then we reach distributive equilibrium and the drug in the plasma and tissue decrease in parallel
Rate and Hybrid Constants
when t is really large, we are down to one compartment and approaches zero
A = alpha phase which is the distribution phase
B = beta phase which is the elimination phase
Two Compartment Open Model: Some Important Equations
The hybrid constants α and β are the first-order rate constants for the distributive phase and the elimination phase respectively; they depend on the transfer constants k12 and k21:
k12 is movement from compart. 1 to 2
k21 is movement from compart. 2 to 1
a + b = k12 + k21 + k
ab = k21k
The intercepts A and B are constants but have no physiological significance
Example
A given drug used to treat Alzheimers follows first order (i.e. linear) 2-compartment pharmacokinetics. Values for a number of parameters for this drug have been documented. These numbers represent the micro constants for this drug. In order
to calculate the drug concentration after a single IV bolus dose these parameters need to be converted into values for the macro constants. The k and Vp for this drug in this patient are 0.223 hr-1 and 40.2 L, respectively. The k12 and k21 values this drug are 1.53 and 0.96 hr-1, respectively. Calculate the plasma concentration of
this drug 4 hours after a 25 mg, IV Bolus dose.
Method of Residuals
The distribution phase is more rapid than the elimination phase i.e. α > β
* Thus as Ae-αt approaches zero, Be^-βt will still have a value so the last equation becomes:
Cp = Be^-Bt
ie.
log Cp = -(Bt./2.3) + log B
Method of Residuals II
β may be obtained from the slope of a semilog plot of Plasma level against time
Also, by extrapolating the beta phase line on the semilog plot, B can be obtained
A line representing the distribution phase is i.e. α is obtained from the slope of the C – C ’ against time plot
obtained by subtracting points (C ’) on thep
extrapolated beta line from the corresponding original observed data points (Cp).
Method of Residuals III
We can find beta by finding the slope of the elimination line
the distribution phase is the first slope and the elimination phase is the second slope
curve with the WXYZ points
on the first line, there are the WXYZ
on the second line, there are the W’X’Y’Z’ points
what does the central and peripheral compartments represent
lines on the graph
central: kidneys, heart, brain
peripheral: outer limbs
with two compartment model we do not get a straight line but a 2 phase line
with a one compartment model we get a straight line
method of residuals is used to
determine the intercepts
B is the elimination graph extrapolated (or brought to) the y axis
line from the WXYZ points are drawn down to the axis and that is the W’X’Y’Z’
those points connected to the x axis are time points so these are tw, tx, ty, tz
so those are the time values
so if you take
W - W’ = tw
X - X’ = tx
Y - Y’ = ty
Z - Z’ = tz
so if you connect those lines it would intersect the y axis at A
Apparent Volumes of Distribution:
The Central Compartment
Volume of the central compartment Vp (or Vi, the initial volume of distribution) is usually > 3 L (the average adult’s plasma fluid volume) i.e. distribution occurs outside the vascular pool
- C = Ae-αt + Be-βt
- Also: Vp = D0/ k[AUC]0
Apparent Volumes of Distribution:
Steady State
Dt = total amount of drug in tissues;
* Dp = total in the central compartment
* The apparent volume of drug at steady state is given by the total amount of drug in the body divided by the plasma concentration at steady state:
(VD)ss = (Dp + Dt)/ Cp
i.e. (VD)ss = Vp + (k12/k21)Vp
Apparent Volumes of Distribution: Extrapolated
Obtained from the beta phase intercept of the plasma level-time curve
NB: A change in drug distribution results in a change in Vp and therefore a change in (VD)exp .
apparent Volumes of Distribution: By Area
Similar to Vp calculation except that b is used instead of the overall elimination rate constant k:
This is easier to determine practically than (VD)ss
(VD ) clearance
Factors Determining the Number of Compartments
Assay sensitivity i.e. ability to detect low concentrations
- Number of samples collected i.e. inappropriate sampling intervals
- Route of administration
- Rate of drug absorption
- Total time for blood sampling
Three-Compartment Open Model
Often the data gathered indicates the presence of a third compartment representing tightly bound drug in tissues OR poorly perfused tissue such as bone and fat.
Level of Blood Perfusion:
Central Compartment > Tissue Compartment > Deep Tissue Compartment
follows a mammillary model
IV Bolus Two-Compartment Model: Elimination Rate Constant
k has to do with drug elimination from the central compartment
β has to do with drug elimination after the distribution is almost done i.e. the beta phase, and is affected both by the movement of the drug in to and out of the tissue compartment
β is therefore a hybrid constant β< k
IV Bolus Two-Compartment Model: Clearance
- Recall the model-independent method:
If the [AUC]0 is underestimated, the Cl value gets
inflated
* To avoid this for a two-compartment model, a
model dependent method: Cl = (VD)β
Apparent Volumes of Distribution: By Area II
The expected decline in b in case of renal impairment could be masked if there is rapid redistribution between the plasma and the tissue. A change in k could account for the change in (VD) .
Apparent Volumes of Distribution: Significance
(VD)exp > (VD)ss (VD) > Vp
* (VD) is more affected by the dynamics of the elimination phase whereas (VD)ss is a more accurate reflection of the general distribution of the drug.
* For the purpose of modeling, assumed to be independent of clearance and other parameters
* In reality factors such as drug binding, metabolism and uptake affect more than one parameter, rendering them not truly independent e.g. volume of distribution is not truly independent of clearance as depicted in models.
Apparent Volumes of Distribution:
Peripheral Compartment
The apparent volume of the tissue compartment
Vt = Vpk12/ k21
Is an estimate of average drug build-up in body
tissues (recall drug concentration will vary from tissue to tissue, or even between tissue samples)
* Amount of drug in tissue may (Dt) be more relevant to pharmacodynamic activity than the amount in the plasma:
Dt = (k12Dp0/(a - b)) (e-βt – e-αt)
