INTRODUCTION
Before you begin to study Pharmacokinetics and the use of Compartment Models to understand the time line for drugs in the body you should review some basic Kinetics
In General Chemistry you were introduced to the chemical reaction.In Pharmaceutics I you were taught about the kinetics of chemical reactions.Lets review!
A chemical reaction is described as a process in one or more chemicals
undergo a change to produce one or more products.The
starting materials are called reactants.The
speed with which that happens is called the rate of the reaction and is
often represented mathematically as a differential expression.dc/dt
The rate of reaction is related to the amount of reactants by a simple equation.
dC/dt = -k[reactant one]n1 [reactant two]n2 …
[reactant ?]n?
In a simple case with just two reactants coming together to react the expression can be specifically written to fit that reaction.As an example you performed an experiment in PHA 311 where you followed the degradation of aspirin.The two reactants were aspirin and water.
dC/dt =-k [Aspirin] X [Water]
Please note that the minus sign can be located in front of the differential expression or on the right side of the expression.The concentration terms are in molar concentration units.
Since water is in such a high concentration when compared to aspirin it can be considered to be a constant and the C term will only refer to the molar concentration of Aspirin.The expression can be rewritten as
dC/dt = -k*[Aspirin]
It would be good to remind yourself of some of the key terms in understanding kinetics.
Rate of a reaction is the speed of the reaction
Rate constant is the k in the expression.It changes the proportionality between the rate and the concentration of the reactants into an equation.It is constant only for that reaction under the conditions specified
Order of a Reaction – Generally it has been found that the rate of the reaction is proportional to the sum of the exponents on the reactants of interest.Thus in our example the order in the general equation is n1 +n2+ …+n?.The order of the example when water is included would be 1+1 = 2 and when we ignore water the order would be one.When we know the true order of a reaction as we do in the hydrolysis of aspirin BUT we recognize that because of the large amount of water present is act like a different order we often call that pseudo order reaction.Thus the aspirin reaction is a true second order reaction but act like a first order or pseudo first order reaction.
REMEMBER that all our calculations and categorizations of a reaction are based on the reactants not the products.
Although the order of a reaction can be any number including fractional numbers the most common are whole digits (0,1,&2)
The equations that are used in conjunction with these reactions include the differential form, the integrated form and the half-life expression
Differential
FormIntegratedHalf
Life Expression
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The Unites are in molar concentration and common
units of time ( hours, minutes, seconds, yeas etc.)
There are also special cases of reactions that
involve other substances that are not reactants but facilitate or catalyze
the reaction. In biological
systems the most common catalyst is the enzyme. Enzyme
mediated reactions follow what is commonly called Michaelis-Menton Kinetics
after the two individuals who did the original work in the area.
Michaelis-Menton Kinetics has a unifying equation
listed below:
In this expression dC/dt is often replaced with V for velocity and Vmax is the maximum rate of the reaction. As you can see by simple substitution when C is much larger than Ka (called the Michaelis constant) the denominator is approximately equal to C and the equation becomes a Zero order equation. Conversely is Ka is much larger than C it becomes a first order equation with a rate constant equal to Vmax/Ka.
Compartment Models
Lets start with some definitions:
Compartment - One of the parts or spaces into which an area is subdivided. A separate section or chamber.
Model - A tentative description of a system or theory that accounts for all of its known properties.
Please turn to your text on page 157. Figure 14-1 is the simplest form of a compartment model of drug movement and distribution in the body.
We all understand that the body is made up of a number of organs and spaces. Each one of these could constitute a compartment and we would then determine the speed with which a drug moves between these compartments. BUT It is an unnecessary complication to have that many compartments when many act the same way. The blood is considered the central compartment. We add to this all the tissue, organs and spaces that are in rapid equilibrium with the blood. If there are a groups of tissues or organs which are in slow equilibrium with the blood they can be grouped into a tissue compartment. This is a two compartment model.
In class we will examine this and ascribe to each model the appropriate differential equations. Figure 14-3 & 14-4 Show the characteristics of each model and what should be expected when the time line for a drug in the body is examined.
It is possible to have more complicated models but they are not useful when we apply these principles to the adjustment of an individual patients dosage regimen.