question archive The dosage for Carboplatin chemotherapy drugs depends on several parameters of the particular drug as well as the age, weight, and sex of the patient
The dosage for Carboplatin chemotherapy drugs depends on several parameters of the particular drug as well as the age, weight, and sex of the patient
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The dosage for Carboplatin chemotherapy drugs depends on several parameters of the particular drug as well as the age, weight, and sex of the patient. For female patients, the formulas giving the dosage for such drugs are D = 0.85A(c + 25) and c = (140 − y) w/72x .
where A and x depend on which drug is used, D is the dosage in milligrams (mg), c is called the creatine clearance, y is the patient's age in years, and w is the patient's weight in kilograms (kg).
in this problem, look at a 40 year old patient and a drug with A = 2 and x = 5.
(a) Rewrite D as a function of c and c as a function of w using the values of A, x and y for this problem.
(b) Compute dD/dc
(c) Compute dc/dw
(d) Use the chain rule to compute dD/dw . Interpret the meaning of the derivative dD/dw .
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Answer:
a. D = 1.7c + 42.5 and c = 5w/18
b. dD/dc = 1.7
c. dc/dw = 5/18
d. dD/dw = 0.472.
Step-by-step explanation
Given D = 0.85A(c + 25) and c = (140 - y)w/72x
Question a
From the question, A = 2, y = 40 and x = 5
D = 0.85×2(c + 25)
D = 1.7(c + 25)
D = 1.7c + 42.5
and
c = (140 - 40)w/72×5
c = 100w/360
c = 5w/18
Question b
dD/dc = 1.7 (direct differentiation)
Question c
dc/dw = 5/18 (direct differentiation)
Question d
dD/dw = dD/dc × dc/dw
= 1.7 × 5/18
= 0.472
Hence, dD/dw is 0.472. This can be interpreted as: the product of the changes in dosage with respect to creatine clearance and the changes in creatine with respect to weight is 0.472.
