# Chapter 8

## Bioavailability Parameters, ka and F

### Absorption Rate Constant, ka

Figure 8.4.1 Linear Plot of Cp versus Time with ka = 3, 0.6, or 0.125 hr-1

Click on the figure to view the interactive graph

Before going on to calculate the parameters ka, kel, and F from data provided we can look at the effect different values of F and ka have on the plasma concentration versus time curve. As ka changes from 3, 0.6 to 0.125 hr-1 the time of peak concentration changes to 1, 2.75 and 6.25 hour. Notice that with higher values of ka the peak plasma concentrations are higher and earlier.

### Extent of Absorption or Bioavailability, F

Figure 8.4.2 Linear Plot of Cp versus Time with F = 1, 0.66, or 0.33

Click on the figure to view the interactive graph

Changing F values is equivalent to changing the dose. Thus the higher the F value the higher the concentration values at each time point. Since the values of kel and ka are unchanged the time of peak plasma concentration is unchanged.

Thus, tpeak = 1, 1, and 1 hour. The same in each case.

### Some items to consider

Item 1. A drug which undergoes extensive metabolism, with a high extraction ratio, may be subject to significant first-pass metabolism. In a healthy subject this would mean that the drug availability (F value) could be significantly lower than 1. In a patient with significant liver disease the first-pass metabolism could be reduced leading to a higher F value and more drug reaching the blood stream.

Consider a drug with the parameter values in healthy subjects: F = 0.1; V = 766 L; kel = 0.105 hr-1; ka = 3.0 hr-1; CL = 74 L/hr. Plot a concentration versus time curve after an oral dose of 192 mg. Contrast this with the results obtained with the same dose given to a patient with severe cirrhosis. Use the parameter values: F = 1.0; V = 777 L; kel = 0.080 hr-1; ka = 3.0 hr-1; CL = 62 L/hr. Explore the problem as a Plot - Interactive graph. Pentikainen et al., 1978.

Item 2. A drug which undergoes extensive metabolism, with a relatively high extraction ratio, may be subject to significant first-pass metabolism. In a healthy subject this would mean that the drug availability (F value) could be significantly lower than 1. In a patient with significant liver disease the first-pass metabolism could be reduced leading to a higher F value and more drug reaching the blood stream. Other pharmacokinetic changes may modify this effect.

Consider a drug with the parameter values in healthy subjects: F = 0.30; V = 290 L; kel = 0.173 hr-1; ka = 3.0 hr-1; CL = 860 ml/min. Plot a concentration versus time curve after an oral dose of 80 mg. Contrast this with the results obtained with the same dose given to a patient with severe cirrhosis. Use the parameter values: F = 0.42; V = 380 L; kel = 0.063 hr-1; ka = 3.0 hr-1; CL = 580 ml/min. Explore the problem as a Plot - Interactive graph. Wood et al., 1978.

Item 3. A drug with poor solubility has been marketed for some time. Peak drug concentrations after a single 0.5 mg (500 mcg) dose were approximately 0.8 ng/ml (mcg/L). Drug intoxication was traced back to a change in dosage form formulation. Measured bioavailability went from approximately 30% to 75%.

Consider a drug with the parameter values in original product: F = 0.30; V = 180 L; kel = 0.023 hr-1; ka = 5.0 hr-1; CL = 69 ml/min. Plot a concentration versus time curve after an oral dose of 500 mcg (0.5 mg). Contrast this with the results obtained with the same dose but with the new formulation. Use the parameter values: F = 0.75; V = 180 L; kel = 0.023 hr-1; ka = 5.0 hr-1; CL = 69 ml/min. Explore the problem as a Plot - Interactive graph. Danon et al., 1977.

Item 4. In this Chapter we have assumed that the absorption process is uncomplicated and can be represented as a single first order process. Occasionally an additional process may be necessary. With sustained release products an additional dissolution step may be necessary.

A drug was administered as an IV injection, and oral solution and two tablet formulations (one rapid and the other a slow release tablet). A dissolution step was included to model the two tablet formulations. Parameters values included kel = 0.077 hr-1,V = 81.3 L, ka = 0.113 hr-1. The two tablet formulations required kd = 0405 hr-1 or 0.0261 hr-1. The dose were 25000 mg (Dose1 IV bolus), 20300 mg (Dose2 Oral solution), 19000 mg (Dose3 Oral rapid release tablet) and 21600 mg (Dose3 Oral slow release tablet). Simulate the concentration versus time curves after each dose. Bevill et al., 1977. Explore the problem as a Plot - Interactive graph.

Try graphing linear or semi-log plots of drug concentration after a single oral dose.
References
• Pentikainen, P.J., Neuvonen, P.J., Torpila, S. and Syvalahti, E. 1978 Effect of Cirrhosis of the Liver on the Pharmacokinetics of Chlormethiazole, Br. Med. J., 2, 861-3.
• Wood, A.J.J., Kornhauser, D.M., Wilkinson, G.R., Shand, D.G. and Branch, R.A. 1978 The influence of cirrhosis on steady-state blood concentrations of unbound propranolol after oral administration, Clin. Pharmacokin., 3, 478-487 through Benet, L.Z., Massoud, N., and Gambertoglio, J.G. 1984. Pharmacokinetic Basis for Drug Treatment, Raven Press
• Danon, A., et al. 1977 An outbreak of digoxin intoxication, Clin. Pharmacol. Ther., 21, 643 through Gibaldi, M. 1984 Biopharmaceutics and Clinical Pharmacokinetics, 3rd ed., Lea & Febiger
• Bevill, R.F., Dittert, L.W. and Bourne, D.W.A. 1977 Disposition of Sulfonamides in Food-Producing Animals IV: Pharmacokinetics of Sulfamethazine in Cattle following Administration of an Intravenous Dose and Three Oral Dosage Forms, J. Pharm. Sci., 66, 619-23
• Heading, R.C., Nimmo, J., Prescott, L.F. and Tothill, P. 1973. The dependence of paracetamol absorption on the rate of gastric emptying, Br. J. Pharmacol., 47, 415-421
• Barr, W.H. 1969 Factors involved in the assessment of systemic or biologic availability of drug products, Drug Inform. Bull., 3, 27-45

Student Objectives for this Chapter