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Thread: gamma-function

  1. #16
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    Re: gamma-function




    Plug it in the formula in #9.

  2. The Following User Says Thank You to BGM For This Useful Post:

    pongtep (05-28-2013)

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    Re: gamma-function

    Thank you for your kindness.
    And I wonder about the Equation (7)/Figure 2 from this research
    https://docs.google.com/file/d/0Byxd...it?usp=sharing
    What is the max. slope for a given ymax and alpha?

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    Re: gamma-function

    I have take a look at the equation and it seems that it is exactly the same as the g(t) you posted. Not sure if the domain of g is restricted (but even in that case the maximum slope is still very easy to find from the information in #2)

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    Re: gamma-function

    Yes, I think so too. But my professor still asking "No. Again: What is the max. slope for a given ymax and alpha?" from https://docs.google.com/file/d/0Byxd...8xRmVDajg/edit
    So I don't understand about his question and I am confused about his objective. Because the maximum slope is still very easy to find from the information in #2.
    He told me this question is his previous research.
    Processes of drug distribution and dilution over time in biologic system can be described by different models - one of the simplest being the gamma-function. As you can see from the attached paper, the gamma function can be written as:

    g(t) = ymax * t^(alpha) * exp( alpha * (1-t))

    with ymax and alpha being constants of the biologic system, that can be estimated using Perfusion-CT.

    For one simple case of Perfusion estimation it's neccessary to calculate the maximum slope of g(t).

    That's why I'm asking you: With known ymax and alpha, what is the maximum slope of g(t) (with t>0)?
    Last edited by pongtep; 05-28-2013 at 04:14 AM.

  6. #20
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    Re: gamma-function

    I’m still searching for research papers that shows maximum slope of this method because this method has been using to solve the problem in many research papers.

  7. #21
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    Re: gamma-function

    Yes it is really confusing. Is the formula in #9 wrong?

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    Re: gamma-function

    Dr. Mark Madsen (author of this equation) send me email
    To find the maximum slope you would take the second derivative of the equation and set it to 0 and solve for t. That will give you the t value where the slope is maximal and then you can plug that t value into the equation to determine the maximal slope. Hope that helps,

  9. #23
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    Re: gamma-function

    So this is exactly what I did in #2. It makes me really confusing.

  10. #24
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    Re: gamma-function


    You carefully explain about this equation and Dr. Mark Madsen agreed with your result.

    It’s so perfect. I do appreciate your kindness.

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