Urinary system, as a thermodynamic system

[student85]

Homework Statement

I was given the hard task of matematically modeling the human urinary system. I have to keep into account all the things going on. We CAN NOT model the bladder as being a sphere. So that is the main problem. It has the shape of an onion more or less. And it reduces and increases its volume depending on the amount of urine present. The approx. volume of the bladder is 400 cm3.
Basically what I'm looking for are ideas on how to model the bladder as a sistem, as the farthest we've gone is modeling spherical and cilindrical systems.
I don't know if this is more appropiate for the math section as what I am looking for is basically math and not a lot science terms.

Any help is DEEPLY appreciated.

 

[denverdoc]

does it include the kidneys, from a thermodynamic point of view this would add considerable complexity? If not things are much simpler. Urine flows from the kidneys where it is formed--it has a large range of osmolarity depending on the state of water balance and the health of the kidneys as well as any medications which might influence function such as a diuretic(this concentration has thermodynamic implications)--through the two ureters into the bladder. The bladder itself is composed of smooth muscle whose tension depends on the volume--if a sphere were used this would be a simple matter of applying LaPlace eqn relating tension and radius like a balloon. The state of tension will determine the energy consumption of the muscle itself. There is also the sphincter itself which is under the influence of the autonomic nervous system. Relaxation of this muscle is a voluntary event in most cases. Finally during urination, material is lost from the system in the form of fluid at a temperature nearly that of the core itself (37C). This implies a heat loss, and at least compared to water, a more concentrated substance. These are the notions off the top of my head.
Helpful?

 

[student85]

Thanks a lot denverdoc.
My main consern now is that I can not consider the bladder a sphere, the teacher told us that clearly. So I'm thinking of many things, like rotating a parabola around the y-axis, and perhaps using the solid as the shape of the bladder, but I don't know what function exactly I should use.