The rate constant in pharmacokinetics is the same as the rate constant in chemical kinetics.  It relates the speed or rate of loss of a drug from a compartment with the concentration of that drug in the compartment.  Chapter 15 of your text reviews how to calculate the rate constant by using data obtained from the direct measurement of the concentration of the drug in blood or plasma.

The simplest case is for a one-compartment model after an IV bolus infusion.

Page 169 has the equation to be used.  Note that after a IV bolus injection the level of the drug in the blood or central compartment can only decline.  Thus the rate constant associated with this process is called the elimination rate constant to signify that it is the rate constant associated with the elimination of the drug from the central compartment.  That can be through urinary excretion or metabolism or being exhaled through the lungs (i.e. alcohol) etc.

As an example there is some data below.  Using the appropriate equations from the text solve for the elimination rate constant.

Nifedapine was administered to a patient 25 mg IV Bolus.  We will assume a normal adult of 70 Kg body weight.  The following data was obtained:
 
 
 

Time in Hours	Concentration in mcg/ml
2	139
4	65.6
6	31.1
8	14.6

 

 

Time (minutes)	Serum Concentration (picograms/ml)
3	380
10	280
20	170
30	130
40	100
50	70
60	50

If we stick with a one-compartment model we have added only one extra step.  The drug must be absorbed from the site of administration into the blood supply before it can be eliminated from the blood.  This requires that you separate the rate of absorption from the rate of elimination.  We can do that by using a technique called feathering.  Below are two sets of data for ampicillin.  You can use the system delineated on page 170 to obtain the elimination rate constant (ke) and the absorption rate constant (ka).

A 250 mg IV Bolus dose of ampicillin yields an AUC of 11 micrograms/ml hour

After a 500 mg dose the following blood levels were obtained:
 
 
 

Time ( Hours)	Serum Concentration (mcg/ml)	Serum Concentration (mcg/ml)
	Lederle	Bristol
0.5	0.37	0.38
1.0	1.97	1.91
1.5	2.83	2.49
2.0	3.15	3.11
3.0	2.73	2.79
4.0	1.86	1.95
6.0	0.43	0.49

The volume of distribution is not a real volume.  It is used to equate the concentration of the drug in the blood with the amount of drug in the central compartment.  Chapter 16 in your text discusses this concept.  Table 16-1 on page 181 has the equations which are used to calculate the volume of distribution (Vd).

For an IV bolus dose one compartment case we can simple determine the intercept value for the plasma (blood) level vs time curve.  This is called the Co value.  The relationship between Co and the Dose is the Vd.  Therefore Vd = D/Co

Use the examples above and calculate the Vd for Nifedapine and ANP

In order to determine the Vd for an oral dose you must know the fraction of the dose absorbed.  The determination of the the fraction of the dose absorbed not complicated but requires the determination of the Area Under the Curve (AUC) for both an IV bolus dose and the oral doses.  We will come back to that calculation after we discuss the determination of the AUC.

Clearance (Cl) is defined as the amount of plasma cleared or emptied of the drug per unit time.  It is directly related to the rate constant for elimination.

Clearance is composed of a number of methods for elimination of the drug from the plasma or blood supply.  Chapter 17 discusses the primary method which is through renal excretion.  Please review the anatomy and physiology of the kidney.

Note that equation 4 on page 193 demonstrates that we can determine the renal clearance by measurement of the drug as it appears in the urine.  This can be a function of filtration or secretion.  The portion of the renal clearance due to filtration is directly affected by the Glomerular Filtration rate which is estimated from the excretion of substances normally present in the urine like creatinine or inulin.  Another compound called p-Aminohippuric acid (PAH) is both passively filtered and actively secreted and can be used to estimate the active secretory function of the kidney.
The values for creatine clearance and PAH clearance can be used to adjust the dose for patient with impaired kidney function by a simple ratio between the normal value for the population and the value for that patient.
Table 17-6 gives a list of how these values change with a patient age.

Many drugs that are excreted unchanged in the urine have in the package insert a table that suggests changes in the dosage regimine for patients with impaired renal function.  Check it out.