Results 1 to 3 of 3

Math Help - modelling drug in body

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    7

    Exclamation modelling drug in body

    Could someone please help me urgently?
    The problem is: 130 micrograms of thyroxine is needed in her bloodstream. Her doctor prescribed one 100 microgram ,thyroxine tablet to be taken every day. If the half-time of thyroxine is 6.7 days, either justify that the uptake of thyroxine by the body and clearance through the liver fits a model similar to that for renal clearance stated above, or modify the mathematical model (do not alter the dosage or prescribe other drugs) so that it fits the given conditions.


    I know already that to model the renal clearance, it would be a geometric progression with each term having exponential decay:
    so
    amount in body = De^(-0.10nT) + De^(-0.10 (n-1)T) +De^(-0.10 (n-2)T) +......+ D
    because k = -0.10 So this is a geometric progression, defining variables: T = time interval between intakes, D = initial dose, n = nth number of dosage
    But I know it is not as simple as this becasue this only modesl the renal clearance and not the absorption of the drug by the body. Could you please help me out? I don't know what I can do to the model to make it fit those numbers (100 per dose , resulting in 130 all the time in the body)

    I also don't understand how you can find the long term amount of drug in the body using the initial dosages using a spreadsheet. If possible could you explain to me how you set out the spreadsheet? Becasue what I did to find the long-term saturation level was to take the sum to inifinity of the terms of that geometric progression.


    This problem is quite urgentso appreciate ANY feedback!! Could yopu please help me out with the developemtns of the model to fit those numbers?

    -thank you kindly!!!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    You cannot build a decent model with the given information. Still required are:

    1) Time to maximum serum concentration, and
    2) Absorption effectiveness.

    I could not fine the time to maximum serum concnetration right off, but the absorption effectiveness of synthroid is an astoundingly broad 40%-80%! Maybe I'm just not looking, but that strikes me as a massively broad range. No wonder recommended administration requires a slow start. One would not want to assume 40% if you're going to get 80%.

    Having said that:

    Change in Concentration = Dosage*Effectiveness*(Function of Absorption Rate)*(Function of Clearance Rate)

    So far, you have two of the four pieces for a basic model.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by linyen416 View Post
    Could someone please help me urgently?
    The problem is: 130 micrograms of thyroxine is needed in her bloodstream. Her doctor prescribed one 100 microgram ,thyroxine tablet to be taken every day. If the half-time of thyroxine is 6.7 days, either justify that the uptake of thyroxine by the body and clearance through the liver fits a model similar to that for renal clearance stated above, or modify the mathematical model (do not alter the dosage or prescribe other drugs) so that it fits the given conditions.
    There is something funny going on here, with a daily dose the steady state blood load will be about 10.17 times the daily dose uptake. Thus to get a blood load of 130 micrograms would imply an uptake of about 12.8%, which seems low.

    (This assumes that the half time in the blood is 6.7 days)

    My medication which has a similar half-time is usually taken once or twice a week :- depending on the level of fluctuation in blood concentartion that is acceptable. A daily dose with this half-time implies a very tight control on the blood concentration

    RonL
    Last edited by CaptainBlack; August 13th 2008 at 02:53 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Drug Dosage Modeling
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: August 2nd 2012, 11:40 AM
  2. drug calculation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 13th 2011, 08:35 AM
  3. Drug brand prob
    Posted in the Statistics Forum
    Replies: 1
    Last Post: November 12th 2009, 11:10 PM
  4. Drug Absorption
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: September 4th 2009, 09:07 PM
  5. decay rate of drug
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: July 12th 2009, 07:22 PM

Search Tags


/mathhelpforum @mathhelpforum