Drug Absorption: Proportional to Amount Present at Time t

  • Thread starter Shaybay92
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In summary: This is correct, now you just have two constants and two constraints on them: D(0) and D(4 hours).But the rate of absorption is the amount absorbed over time? D represents the amount left, so it would have to be d(50-D)/dt? Because 50-amount left = amount absorbedYes, that's right.
  • #1
Shaybay92
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Homework Statement


The rate at which a particular drug is absorbed by the body is proportional to the amount of the drug present (D) at any time t. If 50mL is initially administered to a patient and 50% remains after 4 hours, find

A) D as a function of t.

The Attempt at a Solution



I'm confused as we have to make D=the amount present (not yet absorbed)

This means that it would be:

d(50-D)/dt [tex]\alpha[/tex] D

Is this correct, in that the rate of absorption is Amount absorbed/time, so 50mL-D = amount absorbed?

By doing this, I integrate and just get Ae^kt = D
 
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  • #2
Shaybay92 said:
I'm confused as we have to make D=the amount present (not yet absorbed)

This means that it would be:

d(50-D)/dt [tex]\alpha[/tex] D

This is correct. I'd only write dD/dt though.


Shaybay92 said:
By doing this, I integrate and just get Ae^kt = D

Correct as well, now you just have two constants and two constraints on them: D(0) and D(4 hours).
 
  • #3
But the rate of absorption is the amount absorbed over time? D represents the amount left, so it would have to be d(50-D)/dt? Because 50-amount left = amount absorbed
 
  • #4
That's right, but you can certainly show that d(50-D)/dt = -dD/dt. What was your question again? :p
 
  • #5
How does d(50-D)/dt turn into -dD/dt?
 
  • #6
Differentiation is linear, so that d(50-D)/dt = d 50 /dt - dD/dt. Differentiation of a constant gives zero.
 
  • #7
Thankyou!
 
  • #8
i don't think you need the 50 at all to formulate the differntial equation

the statement
The rate at which a particular drug is absorbed by the body is proportional to the amount of the drug present (D)

is enough to give you the differential equation
[tex]\frac{dD(t)}{dt} = -kD(t) [/tex]
for some as yet undetermined constant k

integrate, then use the given values to find the constants
assume an initial value
[tex]D(0) = d [/tex]
value at time = 4hrs
[tex]D(4) = d/2 [/tex]
 

What is drug absorption proportional to amount present at time t?

Drug absorption proportional to amount present at time t refers to the relationship between the amount of a drug present in the body at a specific time (t) and the rate at which it is absorbed into the bloodstream. This means that the higher the amount of drug present, the faster it will be absorbed.

How does drug absorption proportional to amount present at time t affect drug effectiveness?

The rate of drug absorption can have a significant impact on the effectiveness of a drug. If the drug is absorbed quickly, it can reach therapeutic levels faster and have a more immediate effect. However, if absorption is slow, it may take longer for the drug to reach therapeutic levels and have a delayed effect.

What factors influence drug absorption proportional to amount present at time t?

There are several factors that can affect the rate of drug absorption, including the drug's chemical properties, formulation, route of administration, and individual patient factors such as age, weight, and health status. Additionally, food and other medications can also impact drug absorption.

Can drug absorption proportional to amount present at time t be controlled?

While there are certain factors that can influence drug absorption, the rate at which a drug is absorbed is primarily determined by the drug itself and cannot be controlled by the patient. However, healthcare professionals can adjust the dosage, formulation, or route of administration to achieve the desired rate of absorption.

How does drug absorption proportional to amount present at time t differ from drug distribution?

Drug absorption proportional to amount present at time t refers to the process of a drug entering the bloodstream from the site of administration. Drug distribution, on the other hand, refers to the movement of a drug throughout the body once it is in the bloodstream. While drug absorption is influenced by factors such as concentration and formulation, drug distribution is affected by factors such as blood flow, tissue permeability, and binding to proteins in the blood.

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