Help! Fluid geometry!

[C Elegans]

What is fluid geometry? Can somebody explain this to me in broad, general principal terms? All I know is that is is a mathematical model that can be used to anayse 3D volumes.

Sorry for posting this here, I've been searching the net for a suitable answer to my question, but what I've found is too detailed and applied, so I take a far shot and hope that somebody in our knowledgeble SYM-fauna knows what it is.

[Gruntboy]

Its the computation and mechanics of how fluids flow.

[frogus]

all I know is it involves The Square Root Of -1 a lot...

[C Elegans]

OK, so fluid geometry is just what it sounds like Thanks

Does anyone know how fluid geometry can be applied in order to analyse a volume that is not fluid?
Fluid geometry is supposed to be the next generation of methods for analysing neuroimaging data. It can also, if I understand things correctly, remove spatial distortions in the image, and improve the signal/noise ratio.

[Waverly]

Help me out a little, CE. What Grunt is describing is familiar to me as Fluid Dynamics. Fluid Geometry, as I understand it, is a term from Petrology, and has to do with porosity, wetting characteristics, and fluid distribution from a geological standpoint.

[Gruntboy]

You're right Waverly, about Petrology.

But it is also the measurement of fluid flow. Taking a quick look at the web, there are lots of sites using fluid geometry calculations for other things - computer modelling and art for example.

[frogus]

yeah...seems that the big application of whatever Fluid Biology is, is fractals. Chaos and infinity are involved too, as far as I can see.

[C Elegans]

@Grunt & Wave: When I searched the web earlier today, I found many sites that referred to applications of Fluid geometry in a lot of different contexts, both petrology, field theory and art, but without explaining what is actually is.

Fluid Mechanics/dynamics can obviously be used to solve problems in many areas. This is from Oxford reference online:

"Fluid dynamics is an important science used to solve many of the problems arising in aeronautical, chemical, mechanical, and civil engineering. It also enables many natural phenomena, such as the flight of birds, the swimming of fish, and the development of weather conditions, to be studied scientifically."

It must be something with the method that makes it suitable to use it not only for analysis of fluids, but also for other systems. I understand that it is used in biotechnics. The use in neuroimaging must AFAI understand, be connected to the mathematic modelling of the volume ie the brain. What I don't understand at all is how it is connected, and what you can do with Fluid geometry, what kind of problems can be solved in neuroimaging?

Quote:

posted by frogus yeah...seems that the big application of whatever Fluid Biology is, is fractals. Chaos and infinity are involved too, as far as I can see.

I have no idea. I saw something about fractals, geometry and petrology, and I also know fractals are used in biology but I have no idea how fractals connect to Fluid geometry - I'm not at all knowledgable about mathematical modelling, I only know the stuff I use myself.

[frogus]

mathematical modelling is just about translating algorithms (often those using infinite values and recursive or self-referential sentences) out of the formal system of maths (number theory) and into other formal systems which use visual symbols instead of numbers or letters say. I am not exactly sure how chaos is involved, and of course I know very little, and I feel as if this discussion might just be a bunch of people who know very little talking about what they know very little about...I am having trouble tracking down anything informative aswell. I guess it is just assumed that the only people who would want to know about fluid geometry are fluid geometricians...if anyone has a breakthrought though I am interested to hear it aswell...

[Lazarus]

You may (or may not) be in luck, C Elegans: I am a mechanical engineer, specializing in fluid flow and heat transfer. The other posts have got down fluid dynamics about right, but I, too, am at a loss as to how it relates to your field.

What is it that your end of the field is looking to explain? Flow of electrons through synapses? I could see how fluid flow might apply. Or maybe chemical composition and concentation throughout the brain? I could see how fluid diffusion analysis might apply there, too.

If you can give me a more accurate picture of what phenomenon you are trying to analyze, I may be able to give you a better answer.

[frogus]

at last...lovely! nice sig Laz...that's profound.

[C Elegans]

@Lazarus: Excellent! Maybe you can save my day

Quote:

Originally posted by Lazarus What is it that your end of the field is looking to explain? Flow of electrons through synapses? I could see how fluid flow might apply. Or maybe chemical composition and concentation throughout the brain? I could see how fluid diffusion analysis might apply there, too.

It's late at night and my thought is very blunt, so I'll post a more detailed description tomorrow. In short, I work with positron emission tomography (PET) as a brain imagining method. I do receptor studies where a radioligand (usually C11 + a ligand with affinity to the receptor we want to examine) is injected intravenously in a tracer dose. The positrons emitted are detected by the PET system, and backwards calculation of the emissions are used to reconstruct a 4D image (3D+time) of the distribution of the binding sites. The mathematic modelling of the reconstruction is what Fluid geometry is supposed to be applied to - this is much too brief, but I'll post more details about the specific problems tomorrow.

[Lazarus]

From everything you have described, I would assume that Finite Element Ananlysis (FEA) is in fact the modelling used for this application. Before I explain it (generally), I should point something out from one of your earlier posts: the web quote you include mentions bird flights, fish swimming, etc. I think (correct me if I am wrong) you have understood this quote to indicate that fluid dynamics looks at these discrete subjects in a macro aspect. That is, you may be thinking that fluid dynamics would be able to analyze bird migration, or some larger motion of birds. This is probably not what the site is indicating. Rather, fluid dynamics would examine how air flow around a bird would keep it in flight. In most cases, air is considered a fluid, and may be studied as such in such areas as aeronautics (that is until high speeds or temperatures make things go haywire).

Anyway. As to the brain and FEA. FEA is a way of breaking down lots of different phenomenon (heat flow, stress in structures, fluid flow, etc) into very, very small bits. You take a single "bit" of fluid, or steel, or whatever, and you (typically) do a kind of energy balance on it, so as to determine how it might effect the tiny little neighbor bits next to it (by transferring heat into them, or by transferring a stress into them, etc). Then you move from those neighbor bits, to THEIR neighbor bits, and so on, and so on.

FEA has lots of uses, and I could see how it could apply to your brain studies as well. If (correct me if I have misunderstood) you have some kind of tracer chemical floating around in a brain, and want to study how it moves about with FEA, you would start by studying how concentations of the chemical move in tissue (much like to use FEA for heat transfer, first it was necessary to directly study heat transfer in all sorts of materials). Once this information has been determined and fed into a computer, you could then throw all sorts of new models at the computer, and let it figure out how things will turn out.

Does that make sense? Does it seem to apply to what you are dealing with? Let me know.

[C Elegans]

@Lazarus: You are absolutely correct in your assumption of how I understood the quote about bird flights etc. Thanks for clearing that up.

Your explanation is very pedagogic, I think I understand most of it. We are indeed using a tracer chemical that floats around in the brain, and is supposed to bind to the receptor sites we want to study. Now, the problem is of course that all such ligands binds to a certain degree to other sites as well, not 100% to the receptor. Some amount of the ligand will bind to fat tissue, to proteins in the blood, etc. Thus, one of the major problems with PET technique is the signal to noise ratio, another problem is the partial volume effect ("bleeding" of signal between areas) that occurs when we study areas that are small relative to the scanner resolution. When positrons are emitted, the detectors registrate something as a hit according to certain set time and space parameters. Data of where and when all hits are produced, is calculated as to provide as a voxel-based volume of the brain + time, so that every voxel represent the number of decays (ie in our case events of positrons emitted) registrated in that voxel in this time frame. So the basis for our calculations of the "biological reality", ie the real concentration of radioligand bound to the right receptors is the decay values, and the current models we use is based on comparing every voxel to the neighbouring voxels + a reference region that is known to have no receptors of the type we want to study + comparison to blood plasma data as a 2nd reference.

A search on medline tells me you must be on the right track since FEA shows up as a method for analysing fMRI data. However, fMRI image analysis, like blood flow-PET, is based on analysis of movements of the compound through the brain, whereas receptor PET (as I do) images are based on values of decays, although the ligand is of course floating around. So unfortunately I still don't understand how FEA can be used in our case Could FEA be used also do enegy balancing on our voxels where the energy is in the form of positron emission?

[Lazarus]

@C Elegans: Let me check and see if I am understanding you.

-The actual DATA that you receive is from positron emmission?
-And this source of these emmissions is the tissue of the brain which you are attempting to study?
-And the tissues are emitting these positrons because you have traced them with some chemical (a ligand)?
-But a difficulty is arising in "noise" from neighboring tissues also attracting this ligand, and then also emitting positrons?

If I have all that correct, let me know, and I will revise and/or further explain what I believe may be the use of FEA.