The method of administering a drug can have a strong influence on the drug concentration

If time, t, is in hours and concentration, C, is in ng/ml, the drug concentration curve for a drug is given by C = 12.4te0.2t. (a) Graph this curve. (b) How many hours does it take for the drug to reach its peak concentration? What is the concentration at that time? (c) If the minimum effective concentration is 10 ng/ml, during what time period is the drug effective? (d) Complications can arise whenever the level of the drug is above 4 ng/ml. How long must a patient wait before being safe from complications?

Let b = 1, and graph C = atebt using different values for a. Explain the effect of the parameter a.

If t is in hours, the drug concentration curve for a drug is given by C = 17.2te0.4t ng/ml. The minimum effective concentration is 10 ng/ml. (a) If the second dose of the drug is to be administered when the first dose becomes ineffective, when should the second dose be given? (b) If you want the onset of effectiveness of the second dose to coincide with termination of effectiveness of the first dose, when should the second dose be given?

Figure 4.92 shows drug concentration curves for anhydrous ampicillin for newborn babies and adults.21 Discuss the differences between newborns and adults in the absorption of this drug. 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 Adults Newborns t (hours) drug concentration (g/ml) Figure 4.92

Absorption of different forms of the antibiotic erythromycin may be increased, decreased, delayed or not affected by food. Figure 4.93 shows the drug concentration levels of erythromycin in healthy, fasting human volunteers who received single oral doses of 500 mg erythromycin tablets, together with either large (250 ml) or small (20 ml) accompanying volumes of water.22 Discuss the effect of the water on the concentration of erythromycin in the blood. How are the peak concentration and the time to reach peak concentration affected? When does the effect of the volume of water wear off? 2 4 6 8 10 12 0.5 1 1.5 2 2.5 3 250 ml water 20 ml water t (hours) concentration of erythromycin (g/ml) Figure 4.93

Hydrocodone bitartrate is a cough suppressant usually administered in a 10 mg oral dose. The peak concentration of the drug in the blood occurs 1.3 hours after consumption and the peak concentration is 23.6 ng/ml. Draw the drug concentration curve for hydrocodone bitartrate.

Figure 4.82 shows the concentration of nicotine in the blood during and after smoking a cigarette. Figure 4.94 shows the concentration of nicotine in the blood during and after using chewing tobacco or nicotine gum. (The chewing occurred during the first 30 minutes and the experimental data shown represent the average values for ten patients.)23 Compare the three nicotine concentration curves (for cigarettes, chewing tobacco and nicotine gum) in terms of peak concentration, the time until peak concentration, and the rate at which the nicotine is eliminated from the bloodstream.

If t is in minutes since the drug was administered, the concentration, C(t) in ng/ml, of a drug in a patients bloodstream is given by C(t) = 20te0.03t. (a) How long does it take for the drug to reach peak concentration? What is the peak concentration? (b) What is the concentration of the drug in the body after 15 minutes? After an hour? (c) If the minimum effective concentration is 10 ng/ml, when should the next dose be administered?

For time t 0, the function C = atebt with positive constants a and b gives the concentration, C, of a drug in the body. Figure 4.95 shows the maximum concentration reached (in nanograms per milliliter, ng/ml) after a 10 mg dose of the cough medicine hydrocodone bitartrate. Find the values of a and b. 1.3 23.6 t (hours) C (ng/ml) Figure 4.95

This problem shows how a surge can be modeled with a difference of exponential decay functions. (a) Using graphs of et and e2t, explain why the graph of f(t) = ete2t has the shape of a surge. (b) Find the critical point and inflection point of f.

Figure 4.96 shows the plasma levels of canrenone in a healthy volunteer after a single oral dose of spironolactone given on a fasting stomach and together with a standardized breakfast. (Spironolactone is a diuretic agent that is partially converted into canrenone in the body.)24 Discuss the effect of food on peak concentration and time to reach peak concentration. Is the effect of the food strongest during the first 8 hours, or after 8 hours? 2 4 6 8 24 100 200 300 400 t (hours) concentration of canrenone (ng/ml) Standardized breakfast Fasting stomach Figure 4.96

The method of administering a drug can have a strong influence on the drug concentration curve. Figure 4.97 shows drug concentration curves for penicillin following various routes of administration. Three milligrams per kilogram of body weight were dissolved in water and administered intravenously (IV), intramuscularly (IM), subcutaneously (SC), and orally (PO). The same quantity of penicillin dissolved in oil was administered intramuscularly (P-IM). The minimum effective concentration (MEC) is labeled on the graph.25 (a) Which method reaches peak concentration the fastest? The slowest? (b) Which method has the largest peak concentration? The smallest? (c) Which method wears off the fastest? The slowest? (d) Which method has the longest effective duration? The shortest? (e) When penicillin is administered orally, for approximately what time interval is it effective? 6 12 18 24 0.01 0.05 0.1 0.5 1 5 10 MEC IV IM PO SC P-IM t (hours) concentration of penicillin in serum (g/ml) Figure 4.97

Figure 4.98 shows drug concentration curves after oral administration of 0.5 mg of four digoxin products. All the tablets met current USP standards of potency, disintegration time, and dissolution rate.26 (a) Discuss differences and similarities in the peak concentration and the time to reach peak concentration. (b) Give possible values for minimum effective concentration and maximum safe concentration that would make Product C or Product D the preferred drug. (c) Give possible values for minimum effective concentration and maximum safe concentration that would make Product A the preferred drug. 1 2 3 4 5 0.5 1 1.5 A B C D t (hours) concentration Figure 4.98

Figure 4.99 shows a graph of the percentage of drug dissolved against time for four tetracycline products A, B, C, and D. Figure 4.100 shows the drug concentration curves for the same four tetracycline products.27 Discuss the effect of dissolution rate on peak concentration and time to reach peak concentration.