1. One-compartment open model: Intravenous bolus administration
The one-compartment open model offers the simplest way to describe the process of drug distribution and elimination in the body.
This model assumes that the drug can enter or leave the body (i.e., the model is "open"), and the body acts like a single, uniform compartment.

2. Bolus
A dose of a substance given by injection for the purpose of rapidly achieving the needed therapeutic concentration in the bloodstream

3. The simplest route of drug administration from a modeling is a rapid intravenous injection (IV bolus).
The simplest kinetic model that describes drug disposition in the body is to consider that the drug is injected all at once into a box, or compartment,
and that the drug distributes instantaneously and homogenously throughout the compartment.
Drug elimination also occurs from the compartment immediately after injection.

4. PK model for a drug administered by rapid IV injection
DB = drug in body
VD = apparent volume of distribution
k = elimination rate constant.

5. Elimination Rate Constant
k is a first-order elimination rate constant with units of time-1
(eg, hr-1 or 1/hr).

6. Elimination Rate Constant
Total removal or elimination of the parent drug is effected by metabolism and excretion.
The elimination rate constant represents the sum of each of these processes:
k = km + ke (3.1)
where km = first-order rate process of metabolism
and ke = first-order rate process of excretion.
In such a case, each of these processes has its own first-order rate constant.

7. Elimination Rate Constant
Rate of elimination of drug in the body is a first-order process- depending on overall elimination rate constant, k and amount of drug in the body, DB, remaining at any given time, t.
(3.2)

8. Elimination Rate Constant
Integrating the rate equation
- DB= drug in the body at time t, and DB0= drug in body at t=0.
Equation 3.3.can also be expressed as:
(3.3)
(3.4)

9. Apparent volume of distribution
Each individual tissue in the body- may contain different concentration of drug- due to drug affinity for that tissue.
Conc. of drug in a tissue- reflects the vol. of fluid the drug is dissolved in.
Vol. of distribution- vol that must be considered in estimating the amount of drug in the body from the conc. of drug found in sampling compartment.

10. Apparent volume of distribution
The amount of drug in the body is not determined directly.
Blood sample is removed at periodic intervals and analyzed for its concentration of drug.
VD relates the concentration of drug in plasma (Cp) and the amount of drug in the body (DB), as in the following equation:

11. Apparent volume of distribution
Drug concentration in plasma is given by
where CP = concentration of drug in plasma at time t
we can write the equation

12. Calculation of Volume of distribution
The relationship between drug concentration, volume in which the drug is dissolved, and total amount of drug present is given by
where D = total amount of drug, V = total volume, and C = drug concentration.

13. Calculation of Volume of Distribution
In a one-compartment model,the VD is calculated with the equation:
it represents the instantaneous drug concentration (t = 0) after drug equilibration in the body

14. Calculation of Volume of Distribution

15. Calculation of Volume of Distribution
The dose of drug given by IV bolus represents the amount of drug in the body, DB, at t = 0.
Rate of drug elimination is given by
Replacing DB

16. Calculation of Volume of Distribution
Both k and VD are constants,
Integrated the equation
Small change in time (dt) results in small change in the amount of drug in the body, DB
Which is under the curve t=0 to t=

17. Calculation of Volume of Distribution
Integrating the equation
Upon rearrangement

18. Calculation of Volume of Distribution
The area between time intervals is the area of a trapezoid and can be calculated with the following formula:

19. Significance of the Apparent Volume of Distribution
The apparent volume of distribution is not a true physiologic volume. Most drugs have an apparent volume of distribution smaller than, or equal to, the body mass.
For some drugs, the volume of distribution may be several times the body mass.

20. Significance of the Apparent Volume of Distribution
Drugs with a large apparent VD are more concentrated in extravascular tissues and less concentrated intravascularly.
If a drug is highly bound to plasma proteins or remains in the vascular region, then CoP will be higher, resulting in a smaller
apparent VD. Consequently, binding of a drug to peripheral tissues or to plasma proteins will significantly affect VD.

21. Significance of the Apparent Volume of Distribution
The apparent VD is a volume term that can be expressed as a simple volume or in terms of percent of body weight.
In expressing the apparent VD in terms of percent body weight, a 1-L volume is assumed to be equal to the weight of 1 kg.
For example, if the VD is 3500 ml for a subject weighing 70 kg, the VD expressed as percent of body weight is