Two drugs, Abraxane and Taxol, are both cancer treatments, yet have differing rates at which they leave a patient’s system. Using terminology from pha

nagasenaz 2020-11-26 Answered
Two drugs, Abraxane and Taxol, are both cancer treatments, yet have differing rates at which they leave a patient’s system. Using terminology from pharmacology, Abraxane leaves the system by so-called “first-order elimination”, which means that the concentration decreases at a constant percentage rate for each unit of time that passes. Taxol leaves the system by “zero-order elimination”, which means that the concentration decreases by a constant amount for each unit of time that passes.
(a) As soon as the infusion of Taxol is completed, the drug concentration in a patient’s blood is 1000 nanograms per milliliter (ngml). 12 hours later there is 50ngml left in the patient’s system. Use the data to construct an appropriate formula modeling the blood concentration of Taxol as a function of time after the infusion is completed.
(b) As soon as the infusion of Abraxane is completed, the drug concentration in a patient’s blood is 1000 nanograms per milliliter (ngml). 24 hours later there is 50ngml left in the patient’s system. Use the data to construct an appropriate formula modeling the blood concentration of Abraxane as a function of time after the infusion is completed.
(c) Find the long-term behavior of the function from part (b). Is this behavior meaningful in the context of the model?
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Cullen
Answered 2020-11-27 Author has 89 answers

(a)
Let T(t)−Amount of taxol in nanogram per mili litre present in the patient's blood at any time t in (hours) since infusion completely [Infusion completes at t=0] As T(t) taxol follow zero order elimination.
T(t)=m(t)+c, where m is a slope
at t=0T(t)=1000c=1000
and att=12T(12)=100
50=m×12+1000
m=79.16
Hence, T(t)=79.16t+1000
(b)
A(t)to Amount of Abraxane in ng/ml in patient's bloodat any time t in (hours) since infusion. As Abrasane follows Istorder elimination.
A(t)=P(θ)t
at t=0,A(t)=10001000=P(θ)0P=1000
Now,
A(t)=1000(θ)tAtt=24,A(t)=50
50=1000(θ)24
θ=(120)124θ=0.88265
Hence, A(t)=1000(0.8826)t
(c)
From the part (b): A(t)=1000(0.8826)t(1)
where,
A(t)= Amount of Abraxane in the patient's blood.
The equation (1) shows that the amount of Abraxane inpatient'sblood is exponentially decreasing in the patient'sblood.

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