kinetics exam 2

Question 1

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

Answer 1

B
False

Question 2

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

Answer 2

True - this is the answer! straight line for semi-log is first order!

Question 3

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

Answer 3

B
False - it is for the distributive phase

distributive phase is the alpha phase
elimination phase is the beta phase

Question 4

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

Answer 4

A
k10 - down arrow from the central compartment

k12 & k21 are transfer constants

Question 5

The Case for Extra Compartments

Answer 5

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

Question 6

Some Tissue Groupings

Answer 6

Highly perfused tissues include: kidney, hepatic-portal system, brain and heart.

• Poorly perfused tissues include adipose tissue, bone and hair

Question 7

Two-Compartment Open Model

Answer 7

central compartment
k12–>
k21–>
peripheral compartment

k10 down arrow from the central compartment

Question 8

Sometimes Observed Plasma Level-Time Curve

Answer 8

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)

Question 9

Phases of a Two-Compartment Model

Answer 9

distribution phase is the first slope

elimination phase is the second slope

distribution ie complete at the middle of the line

Question 10

ONE-COMPARTMENT MODEL

Answer 10

drug is introduced intravenously

BEFORE DOSE - Large dose administered intravenously

AFTER DOSE - Instant thorough distribution throughout patient

Question 11

TWO-COMPARTMENT MODEL

Answer 11

BEFORE DOSE - Large dose administered intravenously

RIGHT AFTER DOSE - Instant distribution
only in some organs

MUCH LATER AFTER DOSE - Later distribution throughout patient

Question 12

-Two-Compartment Model: Phases

Answer 12

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

Question 13

Phases of a Two-Compartment Model: Distributive Phase

Answer 13

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

Question 14

Two-Compartment Open Model

Answer 14

central compartment
k12–>
k21–>
peripheral compartment

k10 down arrow from the central compartment

Question 15

graph of tissue and plasma levels

Answer 15

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

Question 16

Rate and Hybrid Constants

Answer 16

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

Question 17

Two Compartment Open Model: Some Important Equations

Answer 17

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

Question 18

Example

Answer 18

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.

Question 19

Method of Residuals

Answer 19

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

Question 20

Method of Residuals II

Answer 20

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).

Question 21

Method of Residuals III

Answer 21

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

Question 22

curve with the WXYZ points

Answer 22

on the first line, there are the WXYZ

on the second line, there are the W’X’Y’Z’ points

Question 23

what does the central and peripheral compartments represent

lines on the graph

Answer 23

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

Question 24

method of residuals is used to

Answer 24

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

Question 25

Apparent Volumes of Distribution:
The Central Compartment

Answer 25

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

Question 26

Apparent Volumes of Distribution:
Steady State

Answer 26

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

Question 27

Apparent Volumes of Distribution: Extrapolated

Answer 27

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 .

Question 28

apparent Volumes of Distribution: By Area

Answer 28

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 

Question 29

Factors Determining the Number of Compartments

Answer 29

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

Question 30

Three-Compartment Open Model

Answer 30

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

Question 31

IV Bolus Two-Compartment Model: Elimination Rate Constant

Answer 31

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

Question 32

IV Bolus Two-Compartment Model: Clearance

Answer 32

• 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

Question 33

Apparent Volumes of Distribution: By Area II

Answer 33

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) .

Question 34

Apparent Volumes of Distribution: Significance

Answer 34

(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.

Question 35

Apparent Volumes of Distribution:
Peripheral Compartment

Answer 35

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)