Could really use some help with understanding a math model.

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In summary, the conversation is about an undergrad college student seeking help with a biomathematics paper on a mathematical model for Dynamic Starvation in humans. The student has emailed the authors of the paper with questions and is struggling to understand the energy balance equation and how to apply it in a mathematical graphing program. The student is seeking assistance from the forum but has not followed the proper guidelines in asking for help.
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Here is the deal (I'll try to keep this short).
I'm an undergrad freshmen math major and I'm taking an Intro Biology class in which we have to present a paper. I have two other group members who have done zero work and I'm not even sure if they will read the paper (but I'll handle that later).
The paper is about a mathematical model for Dynamic Starvation in humans. It's a short, fast and easy read: http://www.springerlink.com/content/y38rh4l710vu3621/fulltext.pdf (please, don't be scared off by the 17 pages, it's really quick to read).

Anyway, I tried e-mailing the authors of the paper with my questions, so I"ll just reproduce the e-mail:
"First, allow me a short introduction.
I'm a freshmen in college, currently enrolled in a Biomathematics program and had to write a summary on a biomathematics paper, and I chose yours. I thought I understood it perfectly well, even having fairly limited mathematical background (in fact, I learned a lot just by reading you paper), but one thing stumped me. Sorry if this is a littel long, but I want to be accurate when talking about other people's work.

You guys developed teh energy balance equation from some (mostly valid) assumptions:

(LambdaF)(dF/dT) + (LambdaM)(dM/dT) = -[C + k(L + M)]

And then you initially defined dF/dT = (1/LambdaF)[F/(M+F)](-[C + k(L + M)]) and dM/dT = (1/LambdaM)[M/(M+F)](-[C + k(L + M)]), which makes the left side equal the right side. So far so good.
But we also noted that F(t) changes also due to conversion to ketone bodies, so dF/dT = -r(K)F + (1/LambdaF)[F/(M+F)](-[C + k(L + M)]).
However, that makes the left side not equal to the right by a difference of (LambdaF)-r(K)F.

I tried to play around with the equation, even adding dK/dT to the left side of it, and pulling the brain's energy requirent from 'C' on the right side. I can make the sides equal, but I'm essentially a) Playing with an equation that I did not develope and b) doing something that probably is not accurate.

I guess what I'm trying to ask is the following: once we have our rates of changes dF/dT, dM/dT, dK/dT defined; what becomes of the energy balance equation?

Also, I have recently purchased a mathematical graphing program (MatLab), and would like to apply the equations to myself and my family for the sake of getting some cool graphs for the presentation. But I'm fairly puzzled on what equations exactly you guys graphed for each graph (again, I'm not certain of what to use for the energy balance equation)."

Please, I've been at it for awhile--trust me, I'm too arrogant to ask for assistance most of the time, but I'm reallys tuck and any help is appreciated.

Thanks in advance.
 
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  • #2
26 views, but has anybody actually taken a look at it? =/
 
  • #3
end3r7 said:
26 views, but has anybody actually taken a look at it? =/

Maybe because you have not adhered to the forum rules: you must show your work, and state the question exactly before you will receive help. Note that, you haven't given a page number, or equation number or anything! By the way, I wouldn't say that emailing the authors of the paper was the correct way to proceed with such a problem.

Also, I wouldn't hold your breath on someone having the time to read a paper, understand what you're having trouble with and then explain it to you. Since a teacher has asked you to present this paper, could you not ask her/him for help? Presumably s/he knows about this paper!

That said;

end3r7 said:
Here is the deal (I'll try to keep this short).
I'm an undergrad freshmen math major and I'm taking an Intro Biology class in which we have to present a paper. I have two other group members who have done zero work and I'm not even sure if they will read the paper (but I'll handle that later).
The paper is about a mathematical model for Dynamic Starvation in humans. It's a short, fast and easy read: http://www.springerlink.com/content/y38rh4l710vu3621/fulltext.pdf (please, don't be scared off by the 17 pages, it's really quick to read).

Anyway, I tried e-mailing the authors of the paper with my questions, so I"ll just reproduce the e-mail:
"First, allow me a short introduction.
I'm a freshmen in college, currently enrolled in a Biomathematics program and had to write a summary on a biomathematics paper, and I chose yours. I thought I understood it perfectly well, even having fairly limited mathematical background (in fact, I learned a lot just by reading you paper), but one thing stumped me. Sorry if this is a littel long, but I want to be accurate when talking about other people's work.

You guys developed teh energy balance equation from some (mostly valid) assumptions:

(LambdaF)(dF/dT) + (LambdaM)(dM/dT) = -[C + k(L + M)]

And then you initially defined dF/dT = (1/LambdaF)[F/(M+F)](-[C + k(L + M)]) and dM/dT = (1/LambdaM)[M/(M+F)](-[C + k(L + M)]), which makes the left side equal the right side.

Are you sure about that? It looks to me like you will get a factor of M+F on the right hand side.
 
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  • #4
cristo, this is hardly a standard question, and it's hard for me to do more than I did. I did in fact "show" my work, but if what you want is for me to scan my annotations or upload my powerpoint presentation so far, I can do that too. Please, no one assume that I didn't do any work on this, I have... lots.

Also, I cannot understand your last remark. If we replace the dF/dT and dM/dT wtihout accounting for Ketone production, we arrive at an identity: -[C + k(L + F)] = -[C + k(L + F)]. (It was L+F, not L+M, sorry. But that doesn't change the situation anyway). And that seems to make sense, but once we do account for Ketone production, we pick up an extra term on the left. But whether the ride side is changed or not was not explicitily said. (Pages 33-34)

Oh, and before I forget, we got to choose our papers (I didn't exact, my group members did because it was considerably shorter than a few others, hehehe typical freshmen mindset =D)

But yea, thanks for answering the topic anyway. I'm the middle child so I already have a complex of being ignore hehehe =P =)
 

1. What is a math model?

A math model is a simplified representation of a real-life situation or problem using mathematical equations and symbols. It helps us understand and analyze complex systems and make predictions about their behavior.

2. Why do we use math models?

Math models are used to gain a better understanding of real-world phenomena and make informed decisions. They allow us to test different scenarios and predict the outcomes of certain situations without having to physically carry out experiments.

3. How do you create a math model?

To create a math model, you first need to identify the variables and parameters that are relevant to the situation. Then, you use mathematical equations and symbols to represent the relationships between these variables. The model is then tested and refined to best fit the real-life scenario.

4. What are some common types of math models?

Some common types of math models include linear models, exponential models, and statistical models. Other types include differential equations, network models, and optimization models.

5. What are the limitations of math models?

Math models may have limitations due to simplifications and assumptions made about the real-life situation. They may not accurately represent every aspect of the system and can result in incorrect predictions if the model is not properly constructed or tested.

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