Homework Help: Could really use some help with understanding a math model.

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.

 

26 views, but has anybody actually taken a look at it? =/

 

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 cuz it was considerably shorter than a few others, hehehe typical freshmen mindset =D)

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