Unformatted text preview: Marinaz : Chapter 9 Enr/chmem Problem 20 AC’ILlVlTﬂ Via/n+5 Quinine
Malaria is a parasitic infection transmitted by mosquito bites, mainly in tropical areas of the
world. The disease has existed since ancient times, and currently there are hundreds of millions
of cases each year, with millions of deaths. Around 1630, Jesuits in Peru introduced the bark of
the cinchona tree to the West as the ﬁrst treatment for malaria. The drug quinine is the active
ingredient in the bark, and it is still used today. However, the concentration in the body of
quinine, and of most drugs, must be kept within certain parameters. If the concentration is too
low, the drug is ineffective. If the concentration is too high, toxic side effects can result.
Suppose you are a doctor who prescribes quinine for a 70 kg malaria patient. At 8 am each
day, she is to receive 50 mg of the drug.8 To be effective, the average concentration in the body
must be at least 0.4 mg/kg. However, concentrations above 3.0 mg/kg can be fatal. The halflife of quinine in the body is 11.5 hours. (a) What is the continuous rate of decay of quinine (in units of %/min)? (b) How much quinine is in the patient’s system just before and just after the ﬁrst day’s dose?
After the second day’s dose? (c) How much is in her system after a few more doses? After the nth dose? Explain what
happens in the long run. (d) Graph the concentration of the drug versus time showing what the steadystate looks like.
Find a formula for the repeating function. (e) What is the average (over time) of the concentration of quinine in the patient’s body? (f) Is this treatment both effective and safe? (g) Suppose instead that the patient were to receive two doses of 25 mg each day, one at 8 am
and one at 8 pm. Is this a safe and effective treatment? (h) Determine the average value of an exponentially decaying function between two points
(1:0,yo) and ($1,341). (i) Notice that the average concentration of quinine is the same for the 50 mg once per day and
25 mg twice per day treatments. Use part (h) to explain why. Would the average concentra
tion be the same for a 100 mg dose once every two days? (i) Suppose the original quinine regimen is stopped. How long after the last dose will the
amount of quinine be less than 10~10 times the patient’s body mass? 3This is a simpliﬁed model; actual treatments involve different drugs and more complicated dosage regimens. See, for
example, The Pharmacological Basis of Therapeutics, 9th Ed, ed. Joel G. Hardman, Alfred Goodman Gllman, and Lee E. Limbird, (New York: McGraw Hill, 1996). ...
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 Fall '08
 Bonner
 Calculus

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