Chapter 3 Flashcards
What is the one-compartment IV bolus model?
State the assumptions
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
Outline the physiological basis for compartmental models.
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.
What is the relationship between drug amount, concentration, ke, Vd, and Cl in the IV bolus model?
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.
What is a first order elimination process
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)
relationship between drug concentration and elimination rate is
elimination rate = cl x cp (plasma concentration)
relationship between elimination rate and amount of drug in the body is
elimination rate = Ke x Ab
State the concentration-time equation for the one-compartment IV bolus model
C(t) = C(o)e -ket
Half life equation
t1/2 = ln(2)/ke
Derive the half-life equation
What is a one-compartment IV bolus model
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.
State the assumptions of the one-compartment IV bolus model
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 π1, which in a one-compartment model is equal to the volume of distribution (ππ) of the drug.
State the assumptions of the one-compartment IV bolus model
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 = ππ
Define the elimination rate
fraction of drug eliminated per unit time (units are therefore h1).
Define clearance
The volume of compartment cleared entirely of drug per unit time
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)
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.
Explain rnorm() and exp and rnorm
rnorm function generates values from a normal distribution.
exp and rnorm generate log-normally distributed random variables from normally distributed data.
one-compartment model oral absorption concentration equation:
C = (F.D.Ka)/(Vd (ka- ke )).(e^(-Ke t)-e^(-Ka t))
Explain why true drug clearance and volume of distribution cannot be estimated from data from a pharmacokinetic study of an orally administered drug:
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.
Concentration-time equation for the two-compartment IV bolus model:
C = Ae^(-Ξ±t)+Be^(-Ξ²t)
When using drug-data, πΌ is conventionally greater than π½ with Ae^(-Ξ±t) representing drug distribution and Be^(-Ξ²t) drug elimination in the majority of cases.
State the pk parameters in the two-compartment IV bolus model
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.
Volume of distribution in the two-compartment model
At time π‘ = 0
ππ = π1 = Dose/c0 = Dose/(A+B)
Volume of distribution steady state in the two compartment model
πππ π = π1 + π2
Inter-compartmental clearance (π)
Replaces π12 and π21 parameters.
π12π1 = π = π21π2
Define Primary pharmacokinetic parameters
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.
Define Secondary pharmacokinetic parameters
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)
State the secondary pharmacokinetic parameters
π‘1/2, ππ, π12 and π21.
these can all be derived from from πΆπ, ππ and π, using the equations. π΄ππΆ can be derived from πΆπ and π·ππ π. π΄, π΅, πππhπ and πππ‘π can be similarly derived.
State the Primary pharmacokinetic parameters for the one compartment model
Cl and Vd
State the Primary pharmacokinetic parameters for the two compartment model
Cl, Q, V1 and V2
State the rate constants for the one compartment model
Ke and VD
State the rate constants for the two compartment model
K10, K12, K21, V1 and V2
Model Parameterization:
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 drugβs 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.
Describe the two-compartment IV-bolus model
examples of what the two compartments may represent, the assumptions made in this model
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
state the primary pharmacokinetic parameters associated with the two-compartment IV-bolus model
Cl, V1, V2, Q
Explain why true drug clearance and volume of distribution cannot be estimated from data from a pharmacokinetic study of an orally administered drug
Without intravenous data, bio-availability cannot be estimated. PK parameters estimated from an oral study should therefore be referenced e.g. Cl/F
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
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
State the primary parameters associated with a two-compartment IV bolus model and the alternative rate constants
Cl, Q, v1, v2
alternatives: a (alpha), b (beta), k12, k21
Explain, with examples, what is meant by primary- versus secondary- pharmacokinetic parameters (4 marks)
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.
What is apparent volume of distribution
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
What is inter compartmental clearance
Q, is a parameter that replaces k12 and k21
Why is elimination modelled from the central compartment in the two-compartment model?
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.
When does the assumption of βmodelling elimination from the central compartment in the two-compartment modelβ NOT hold?
Give a drug example
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.
Give an example drug where elimination cannot be modelled from the central compartment
Muscle relaxant; atracurium.
It undergoes spontaneous degradation and ester hyrdolysis. These processes can occur in any tissue.
Explain βmodel parameterisationβ
In pharmacokinetic modelling, you will note that modellers may choose to βparameteriseβ (define) their model equations in terms of primary pharmacokinetic parameters or secondary pharmacokinetic parameters
Equation for inter compartmental clearance (Q)
K12V1 = Q = K21V2
