Basic Pharmacokinetics: IV Bolus

Question 1

Parenteral

Answer 1

Sterile preparation of drug(s) to be injected through one or more layers of skin or mucous membrane

Question 2

IntraVenous (IV) administration

Answer 2

the formulation is directly injected into a vein
ensures that ALL the dose enters systemic circulation.

Question 3

IV Bolus

Answer 3

the solution of the drug is directly injected into a vein via a syringe/needle (i.v. catheter) over a short period of time (seconds to few minutes).
gets a high concentration of the drug very fast
useful for emergency treatments
consider monitoring for toxicity (“a lot of drug in little time”) and irritation (“no dilution of the formulation at the injection site”).

Question 4

Which of the following ADME processes and events can occur following administration of an intravenous injection?

Answer 4

Distribution
Metabolism
Elimination
Disposition
Plasma binding
There is NO absorption in IV administration: there is only disposition

drug tissue -distribution- drug in systemic circulation -elimination into metabolism to metabolite or excretion to urine, sweat, saliva , bile

Question 5

IV Bolus administration: Plasma profiles

Answer 5

Distribution phase:
the decline in plasma levels is primarily determined by the distribution of the drug to the tissues.

Elimination (terminal) phase:
Equilibrium of distribution plasma-tissues is achieved
The decline in plasma levels is primarily due to loss of drug from the body.
The body “acts” as a “single container”.

Question 6

distribution phase

Answer 6

In some cases, the distribution phase is very short because the equilibrium of distribution plasma-tissues for the drug is achieved very fast.

When this occurs:
only the elimination phase is observed (unless very quick and early sampling is done)
we consider that the body acts a one-compartment from time 0.
we can use the one-compartment model

Question 7

The one-compartment model

Answer 7

The most frequently used despite its simplifications and assumptions.
The drug is assumed to rapidly (instantaneously!) distribute into an homogeneous fluid volume in the body
The simplest model: Only accounts for drug elimination

Question 8

The two-compartment model

Answer 8

The drug rapidly distributes to the central compartment (plasma and rapidly equilibrating tissues).
It takes some time to distribute to the peripheral compartment (deeper tissues).
The model will account for drug distribution and drug elimination

Question 9

Occam’s razor (Ockham’s razor)

Answer 9

Also known as law of economyorlaw of parsimony:
A principle stated by thescholasticphilosopherWillian of Ockham(1285–1347/49) that”pluralitas non est ponenda sine necessitate, “plurality should not be posited without necessity.”
The principle givesprecedenceto simplicity: of two competing theories, the simplerexplanationof an entity is to be preferred. The principle is also expressed as “Entities are not to be multiplied beyond necessity.
Briefly, the simplest explanation is usually the right one.

Question 10

The one-compartment model for IV Bolus Injection

Answer 10

More assumptions:
The volume of the compartment equals the volume of distribution of the drug
Elimination is a first-order process (k = rate constant) and
Elimination follows linear kinetics (no saturation of enzymes or transporters occurs)

elimination= metabolism + excretion

concentration = amount / volume

Question 11

The one-compartment model for IV Bolus InjectionElimination as a first order process

Answer 11

Elimination is a first-order process and k is the rate constant for the drug elimination.
The variation of A (amount of drug) in the compartment (body) with time is

lnA= ln A0- k x t

The rate of elimination (dA/dt) is directly proportional to the amount of drug present. The more drug present in the body, the faster it is eliminated

The proportionality constant (k) is the elimination rate constant (first-order rate constant).k has units of time-1

k= rate of elimination / A

k can be considered as the “fractional rate of drug removal”.
For example if k = 0.14h-1 for a drug; it means that:
14% of the drug in the body is removed every hour

Question 12

The one-compartment model for IV Bolus Injection. Concentration profiles

Answer 12

ln C= ln C0- k x t

Question 13

What do these equations mean? A = A0xe^-kt

Answer 13

Eq. 2 tells us how the amount of drug in the body (the compartment) evolves after an IV bolus injection:
At time 0, or time of the injection:
A = A0 = Dose

After the injection the amount of drug in the body (the compartment) declines exponentially due to the elimination (first order) process.
At any time “t” after the injection; the amount of drug in the body is given by Eq.2:
A = A0●e-kt

where: A is the amount of drug in the body at a time “t”
A0 is the dose injected
k is the elimination rate constant, and
t is the time elapsed since the injection.

Question 14

What do these equations mean? C = C0 x e^-kt

Answer 14

Eq. 4 tells us how the concentration of drug in the body evolves after an IV bolus injection:
At time 0, or time of the injection
C = C0 = A0 / V = Dose / V

After the injection, the drug concentration declines exponentially due to the elimination (first order) process.
At any time “t”; the drug concentration in the body is given by equation 4:
C = C0●e-kt

where:
C is the concentration at a time “t”
C0 is the concentration at time 0 and C0=D/V
k is the elimination rate constant, and
t is the time elapsed since the injection

Question 15

V is used for

Answer 15

The apparent volumen of distribution (V) is the (apparent) volume into which a drug distributes in the body at equilibrium.

V is the “apparent” volume having a given Cplasma of the drug required to account for all the drug in the body.
V = Abody/Cplasma

In other words, V is the volume that multiplied by Cplasma =  Abody

V is used for:
relating A and Cp
estimating the dose required to achieve a given concentration “Crequired”:
Bolus Dose = V * Crequired

Question 16

C0

Answer 16

is the plasma concentration that results from instantaneous distribution of the dose into the volume of distribution (V).

Question 17

Estimating the volume of distribution with IV bolus data

Answer 17

𝑉(𝑣𝑜𝑙𝑢𝑚𝑒)=(𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑑𝑟𝑢𝑔 𝑖𝑛 𝑡ℎ𝑒 𝑏𝑜𝑑𝑦 (𝑚𝑎𝑠𝑠))/(𝐷𝑟𝑢𝑔 𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 𝑝𝑙𝑎𝑠𝑚𝑎 (𝑚𝑎𝑠𝑠/𝑣𝑜𝑙𝑢𝑚𝑒)
Calculation of V requires:
that the equilibrium of distribution achieved
knowing the amount of drug in the body (Abody) and the drug concentration (Cplasma) at the same time.
In our model:
Equilibrium attained from t = 0. As in the one-compartment distribution is “instantaneous”
There is one time point for which A and Cp are known: At time 0:
A = A0 = dose
Cp = C0 (we can find C0 by extrapolation)
Thus: 𝑉(𝑣𝑜𝑙𝑢𝑚𝑒)=(𝐷𝑜𝑠𝑒 (𝑚𝑎𝑠𝑠))/(𝐶_0 (𝑚𝑎𝑠𝑠/𝑣𝑜𝑙𝑢𝑚𝑒)
C0 is the plasma concentration that results from instantaneous distribution of the dose into the volume of distribution (V).

Question 18

Clearance (Cl)

Answer 18

Clearance is the proportionality factor relating the rate of drug elimination (dA/dt) to the plasma drug concentration:

Following an IV bolus injection, the drug concentration evolves as described by:

So, the elimination rate of the drug following an IV bolus injection will be given by:

Following IV bolus administration, the elimination rate of the drug declines exponentially with time.

Question 19

Elimination half-life

Answer 19

The elimination half-life, t1/2 is the time required for the drug concentration (and for the amount of drug) in the body to fall by one-half

The elimination half-life (t1/2) is a very handy and popular! pharmacokinetic parameter.
The half-life of a drug can be used for quick predictions about:
How quickly the drug concentration will decline in plasma
How quickly the amount of drug in the body will decline
Time to reach the steady-state in an IV infusion (see next lectures on this topic))
Time to reach the steady-state in multiple doses regimen

Question 20

Area Under the Curve (AUC)

Answer 20

In pharmacokinetics, the area under the “plasma concentration – time” can be used for:
express the “body exposure” to the drug as a linkto therapeutic and toxic response
to determine the clearance of a drug
to estimate the bioavailability of an extravascular formulation
to assess the bioequivalence (compare bioavailability)of two formulations (see later lectures)

The AUC0- = area under the “plasma concentration – time”
curve from t = 0 to t =  following IV bolus administration of a
drug the PK of which are well described by the one-compartmental
model is given by the expression:

Question 21

Applications of Area Under the Curve (AUC)

Answer 21

AUC is very frequently used to estimate the clearance of a drug:

This is the preferred method to estimate clearance because it is model independent.
That is, getting Cl through AUC and D is always correct, no matter whether the PK of the drug are:
linear or not, and
well-described or not by the one compartment model.
In contrast, the expression Cl = kxV is only appropriate when the PK of drug are linear and well-described by the one-compartment model.
AUC is obtained from the experimental data.
The manual estimation of AUC is shown next, but normally “software” is used.