1. ## 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)

3. ## Re: gamma-function

And I wonder about the Equation (7)/Figure 2 from this research
What is the max. slope for a given ymax and alpha?

4. ## Re: gamma-function

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

5. ## 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)?

6. ## 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. ## Re: gamma-function

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

8. ## 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. ## Re: gamma-function

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

10. ## Re: gamma-function

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

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