Chapter 3

Question 1

What is the one-compartment IV bolus model?
State the assumptions

Answer 1

The body is simplified and represented as a single box, into which the dose of the drug is deposited instantaneously.

Drug is assumed to distribute evenly and instantaneously throughout this compartment

Question 2

Outline the physiological basis for compartmental models.

Answer 2

Important to understand ADME of a compound and it allows us to make suggestions for the next stage of drug development. (Including dose selection, frequency of administration or decisions on formulation)

Compartmental pharmacokinetic models simplify complex human physiology by describing the concentration- time course of a drug with (relatively) simple mathematical equations.

Question 3

What is the relationship between drug amount, concentration, ke, Vd, and Cl in the IV bolus model?

Answer 3

Ke = Cl/Vd

This kind of model can be applied to a drug regardless of whether elimination occurs through hepatic metabolism or renal excretion (or any other means of elimination), provided that the elimination is a first- order process.

Question 4

What is a first order elimination process

Answer 4

A rate of elimination that is proportional to the amount of drug that is present.

relationship between drug concentration and elimination rate is

elimination rate = cl x cp (plasma concentration)

Question 5

relationship between drug concentration and elimination rate is

Answer 5

elimination rate = cl x cp (plasma concentration)

Question 6

relationship between elimination rate and amount of drug in the body is

Answer 6

elimination rate = Ke x Ab

Question 7

State the concentration-time equation for the one-compartment IV bolus model

Answer 7

C(t) = C(o)e -ket

Question 8

Half life equation

Answer 8

t1/2 = ln(2)/ke

Question 9

Derive the half-life equation

Question 10

What is a one-compartment IV bolus model

Answer 10

The one-compartment model is a basic pharmacokinetic model that assumes the body acts as a single, homogeneous unit where the drug distributes uniformly and instantaneously.

Question 11

State the assumptions of the one-compartment IV bolus model

Answer 11

Drug is assumed to distribute evenly and instantaneously throughout this compartment

The volume remains constant during the period under study

The compartment is assumed to receive the drug instantly at the time of the intravenous dose.

The compartment has a volume 𝑉1, which in a one-compartment model is equal to the volume of distribution (𝑉𝑑) of the drug.

Question 12

State the assumptions of the one-compartment IV bolus model

Answer 12

Instantaneous Distribution:
This single compartment is assumed to receive the drug instantly at the time of the intravenous dose.
The drug is assumed to distribute uniformly and instantaneously throughout the compartment as soon as it is administered.

First-Order Kinetics:
The absorption and elimination processes are assumed to follow first-order kinetics. This means that the rate of drug absorption into, and elimination from, the compartment is proportional to the drug concentration present at any given time. For instance, as the drug concentration decreases, the rate of elimination also decreases proportionally.
Elimination rate constant = 𝑘𝑒

Question 13

Define the elimination rate

Answer 13

fraction of drug eliminated per unit time (units are therefore h1).

Question 14

Define clearance

Answer 14

The volume of compartment cleared entirely of drug per unit time

Question 15

Explain the difference between the two methods:
Cl1<rnorm(mean=9.8, sd=2, n=4000)

and

Cl2<-9.8*exp(rnorm(mean=0, sd=0.3, n=4000))

(1 mark)

Answer 15

rnorm function generate 4000 random clearance values from a normal distribution.

The clearance values are symmetrically distributed around the mean of 9.8.
The distribution allows for negative values, which, although not physiologically plausible for clearance, can statistically appear due to the nature of the normal distribution, especially if the mean is close to zero and the standard deviation is relatively large.

exp and rnorm

This method uses the exp function applied to normally distributed values generated by rnorm.

The clearance values are log-normally distributed, meaning that the natural logarithm of these values is normally distributed.
This approach inherently restricts clearance values to be positive, aligning with the physiological reality where negative clearance values are not possible.
Clearance values are skewed to the right, typical for biological parameters where there is a lower boundary (zero), but potentially no upper boundary, reflecting a more realistic distribution for pharmacokinetic parameters.

Question 16

Explain rnorm() and exp and rnorm

Answer 16

rnorm function generates values from a normal distribution.

exp and rnorm generate log-normally distributed random variables from normally distributed data.

Question 17

one-compartment model oral absorption concentration equation:

Answer 17

C = (F.D.Ka)/(Vd (ka- ke )).(e^(-Ke t)-e^(-Ka t))

Question 19

Explain why true drug clearance and volume of distribution cannot be estimated from data from a pharmacokinetic study of an orally administered drug:

Answer 19

Estimating true drug clearance (CL) and volume of distribution (Vd) from pharmacokinetic studies of orally administered drugs is challenging due to the influence of bioavailability (F) and first-pass metabolism.

Since F is often unknown without intravenous comparison, true CL and Vd cannot be directly estimated from oral data alone. Additionally, the absorption process complicates the plasma concentration-time profiles, making it difficult to distinguish the effects of drug absorption from those of clearance and distribution.

Question 20

Concentration-time equation for the two-compartment IV bolus model:

Answer 20

C = Ae^(-αt)+Be^(-βt)

When using drug-data, 𝛼 is conventionally greater than 𝛽 with Ae^(-αt) representing drug distribution and Be^(-βt) drug elimination in the majority of cases.

Question 21

State the pk parameters in the two-compartment IV bolus model

Answer 21

Central Compartment (C1)
Peripheral Compartment (C2)

k12: The rate constant for drug movement from the central compartment to the peripheral compartment.
k21: The rate constant for drug movement from the peripheral compartment back to the central compartment.
k10 ( replaces ke) : The elimination rate constant, representing the rate at which the drug is cleared from the central compartment.

V1: Volume of distribution of the central compartment.
V2: Volume of distribution of the peripheral compartment.

Question 22

Volume of distribution in the two-compartment model

Answer 22

At time 𝑡 = 0
𝑉𝑑 = 𝑉1 = Dose/c0 = Dose/(A+B)

Question 23

Volume of distribution steady state in the two compartment model

Answer 23

𝑉𝑑𝑠𝑠 = 𝑉1 + 𝑉2

Question 24

Inter-compartmental clearance (𝑄)

Answer 24

Replaces 𝑘12 and 𝑘21 parameters.

𝑘12𝑉1 = 𝑄 = 𝑘21𝑉2

Question 25

Define Primary pharmacokinetic parameters

Answer 25

Primary pharmacokinetic parameters are dependent upon human physiology and drug physiochemical properties.

Primary PK parameters are directly derived from the drug concentration-time data without requiring complex calculations or assumptions about the pharmacokinetic model.
These parameters include:

Rate Constants
Clearance (CL)
Volume of Distribution (Vd)

These parameters are usually estimated directly from dose and concentration-time data using non-compartmental methods or initial estimates in compartmental modeling.

Question 26

Define Secondary pharmacokinetic parameters

Answer 26

Secondary pharmacokinetic parameters are derived from primary pharmacokinetic parameters

Secondary PK parameters are derived from primary parameters through mathematical relationships. They often provide more clinically relevant information but require more assumptions for their calculation. These parameters include:

Half-life
Area Under the Curve (AUC)

Question 27

State the secondary pharmacokinetic parameters

Answer 27

𝑡1/2, 𝑘𝑒, 𝑘12 and 𝑘21.
these can all be derived from from 𝐶𝑙, 𝑉𝑛 and 𝑄, using the equations. 𝐴𝑈𝐶 can be derived from 𝐶𝑙 and 𝐷𝑜𝑠𝑒. 𝐴, 𝐵, 𝑎𝑙𝑝h𝑎 and 𝑏𝑒𝑡𝑎 can be similarly derived.

Question 28

State the Primary pharmacokinetic parameters for the one compartment model

Answer 28

Cl and Vd

Question 29

State the Primary pharmacokinetic parameters for the two compartment model

Answer 29

Cl, Q, V1 and V2

Question 30

State the rate constants for the one compartment model

Answer 30

Ke and VD

Question 31

State the rate constants for the two compartment model

Answer 31

K10, K12, K21, V1 and V2

Question 32

Model Parameterization:

Answer 32

Parameterization of pharmacokinetic models involves defining a mathematical framework to describe the concentration-time data effectively. This can be in the form of:

Compartmental Models:
These include one-compartment, two-compartment, and multi-compartment models. Choosing the appropriate model depends on the complexity of the drug’s distribution and elimination kinetics. Model parameters typically include rate constants, volumes of distribution for each compartment, and clearances.

Non-compartmental Analysis (NCA): This approach does not assume any specific compartmental structure and is used to calculate parameters like AUC, t1/2, t 1/2 , CL, and Vd directly from plasma drug concentration-time data.

Question 33

Describe the two-compartment IV-bolus model
examples of what the two compartments may represent, the assumptions made in this model

Answer 33

In the two compartment model IV-bolus model, the body is simplified and represented as a two boxes. These boxes may represent a central compartment (e.g. the circulation and high water-content tissues) and a peripheral compartment (e.g. fat). Drug is deposited (usually) in the central compartment and is usually removed from the central compartment through an elimination process (a simplification for metabolic and excretion pathways) (3 marks for any reasonable description)

Assumptions: Drug administered instantaneously; Drug distributes evenly and instantaneously; volume remains constant during the period of study (2 marks)

May state that elimination is a first-order process but this is not a necessary assumption No additional marks for this point

Clearance, inter-compartmental clearance, volume of each compartment are the primary parameters associated with this model (2 marks)
Cl, V1, V2, Q

Question 34

state the primary pharmacokinetic parameters associated with the two-compartment IV-bolus model

Answer 34

Cl, V1, V2, Q

Question 35

Explain why true drug clearance and volume of distribution cannot be estimated from data from a pharmacokinetic study of an orally administered drug

Answer 35

Without intravenous data, bio-availability cannot be estimated. PK parameters estimated from an oral study should therefore be referenced e.g. Cl/F

Question 36

true drug clearance and volume of distribution cannot be estimated from data from a pharmacokinetic study of an orally administered drug. Explain why this does not apply to elimination half-life

Answer 36

Calculation of t1/2 involves ratio v/cl, which cancels out the F reference or definition of elimination half-life is time taken to half drug concentration in elimination phase. bio-availability no longer relevant as all absorption has occurred

Question 37

State the primary parameters associated with a two-compartment IV bolus model and the alternative rate constants

Answer 37

Cl, Q, v1, v2

alternatives: a (alpha), b (beta), k12, k21

Question 38

Explain, with examples, what is meant by primary- versus secondary- pharmacokinetic parameters (4 marks)

Answer 38

Primary pharmacokinetic parameters are dependent upon human physiology and drug physiochemical properties. V_d and Cl are primary pharmacokinetic parameters. inter-compartmental clearance, Q, is also a primary pharmacokinetic parameter.

Secondary pharmacokinetic parameters are derived from primary pharmacokinetic parameters. t_{1/2}, k_e, k_{12} and k_{21} can all be derived from Cl, V_n and Q, AUC can be derived from Cl and Dose.
A, B, alpha and beta can be similarly derived.

Question 39

What is apparent volume of distribution

Answer 39

The theoretical volume of fluid required to dilute the amount of drug present in the body to achieve the same concentration as that measures in the plasma

Question 40

What is inter compartmental clearance

Answer 40

Q, is a parameter that replaces k12 and k21

Question 41

Why is elimination modelled from the central compartment in the two-compartment model?

Answer 41

For most drugs metabolism/Excretion is hepatic or renal. Therefore, it is reasonable to model elimination from compartment 1. As compartment 1 is usually modelled as the plasma.

Question 42

When does the assumption of ‘modelling elimination from the central compartment in the two-compartment model’ NOT hold?

Give a drug example

Answer 42

For drugs that undergo degradation that is independent of the renal and hepatic systems. As the central compartment is usually modelled as the plasma.

Muscle relaxant; atracurium undergoes spontaneous degradation and ester hyrdolysis. These processes can occur in any tissue.

Question 43

Give an example drug where elimination cannot be modelled from the central compartment

Answer 43

Muscle relaxant; atracurium.

It undergoes spontaneous degradation and ester hyrdolysis. These processes can occur in any tissue.

Question 44

Explain ‘model parameterisation’

Answer 44

In pharmacokinetic modelling, you will note that modellers may choose to ‘parameterise’ (define) their model equations in terms of primary pharmacokinetic parameters or secondary pharmacokinetic parameters

Question 45

Equation for inter compartmental clearance (Q)

Answer 45

K12V1 = Q = K21V2