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.
Help! Fluid geometry!
Help! Fluid geometry!
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.
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.
"There are in fact two things, science and opinion; the former begets knowledge, the latter ignorance." - Hippocrates
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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.
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.
"There are in fact two things, science and opinion; the former begets knowledge, the latter ignorance." - Hippocrates
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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.
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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.
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.
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@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?
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?
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.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.
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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...
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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.
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.
@Lazarus: Excellent! Maybe you can save my day
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.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.
"There are in fact two things, science and opinion; the former begets knowledge, the latter ignorance." - Hippocrates
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FEA
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.
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.
@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?
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
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@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.
-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.
1. yes
2. yes
3. yes
4. yes, noise comes both from specific binding (positrons emitting from neighbouring areas that also have high binding of the ligand) and from unspecific binding (positrons emitting from unwanted places such as proteins in the blood plasma, metabolites of the radioligand, etc). Furthermore, the PET technique in inself introduces more noise in the shape of distortion of shape of the 3D volume (ie the brain).
2. yes
3. yes
4. yes, noise comes both from specific binding (positrons emitting from neighbouring areas that also have high binding of the ligand) and from unspecific binding (positrons emitting from unwanted places such as proteins in the blood plasma, metabolites of the radioligand, etc). Furthermore, the PET technique in inself introduces more noise in the shape of distortion of shape of the 3D volume (ie the brain).
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OK, here's my take on it. If the problem occuring is in the collection of data and, incidentally, noise, neither fluid dynamics nor FEA will help. To refine THAT side of the process would be a task of a signals engineer.
However, if researchers are indeed looking to FEA and fluid dynamics to help resolve this difficulty, I would be inclined to think that they are trying to get around the problem of NOISE altogether, by BYPASSING that data collection process.
Let me again review FEA by using the example of heat transfer in a metal as a basis for further explanation. FEA is very, very good at taking a model of a piece of metal of any shape and telling us how heat will move through that object. It does this by first being "told" how heat moves in general through this metal. Once a computer has been given this basic information, very complex geometries of metal may be modelled, and heat transfer through them studied. The bonus here is that we (humans) no longer have to make a new real-world experiment for every different shape of metal we wish to examine. Instead, we just do it all on computer.
I would GUESS that this is what researchers are now trying to do with your subject. If they can get a better understanding of how this ligand is settling on various tissues, they can use this general information and finite element analysis for an infinite number of specific cases, without ever using a PET scan again.
Maybe.
While I am pretty good with my subject, I must admit I have never heard of it being applied to neuroscience. Let me know if this explanation seems to fit in with what you are seeing and hearing from your discipline. If so - great! If not, I will talk with one of my professors and see if they might have a better explanation.
However, if researchers are indeed looking to FEA and fluid dynamics to help resolve this difficulty, I would be inclined to think that they are trying to get around the problem of NOISE altogether, by BYPASSING that data collection process.
Let me again review FEA by using the example of heat transfer in a metal as a basis for further explanation. FEA is very, very good at taking a model of a piece of metal of any shape and telling us how heat will move through that object. It does this by first being "told" how heat moves in general through this metal. Once a computer has been given this basic information, very complex geometries of metal may be modelled, and heat transfer through them studied. The bonus here is that we (humans) no longer have to make a new real-world experiment for every different shape of metal we wish to examine. Instead, we just do it all on computer.
I would GUESS that this is what researchers are now trying to do with your subject. If they can get a better understanding of how this ligand is settling on various tissues, they can use this general information and finite element analysis for an infinite number of specific cases, without ever using a PET scan again.
Maybe.
Hm. Currently, we use several different filters to correct known distortions and "coloured" systematic noise. White noise is reduced with Wavelet analysis of the data. Furthermore, kinetic analysis is combined with the data, and the mathematic models used for this are based on knowledge of how a radioligand is behaving in the body and in different types of tissue. Maybe here is where FEA could be used? It would be great if it was possible to model every different radioligand without having to obtain a lot of PET scans at healthy people. Every receptor type we want to study requires its own specific radioligand, and for the serotonin system only there is 14 known receptors, for the dopamin 5, etc. There are hundreds of different receptor types, and all must be individually modelled before one can even start thinking about examining patients with various diseases.
Sunday 5th and Monday 6th, I'll be attending a method seminar where physics and modelling of PET is going to be discussed. That's why I asked you to reply before the 6th
Thanks a lot Lazarus for helping me out with this
Whereas my lab is world leading in creating new radioligands and making discoveries regarding brain functioning, we are certainly not in the front line when it comes to method development on the analysis and modelling side. Due to recent changes of cyclotron and new algoritms, we are currently in the process of evaluating and deciding what methods to use in the future, so a lot of discussion is going on, but nobody at my lab knows anything about this "fluid geometry" that is supposed to be the future for PET analysis
I'll post here again after the method seminar
Now, I am at least prepared to ask questions 
Sunday 5th and Monday 6th, I'll be attending a method seminar where physics and modelling of PET is going to be discussed. That's why I asked you to reply before the 6th
Thanks a lot Lazarus for helping me out with this
I'll post here again after the method seminar
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PET scans are used in our Cancer Network for some patients - its very expensive and relatively new. Clinicians seem to feel it gives them an advantage over CT scans, especially with hard-to-find cancers.
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@Grunt: PET scans are indeed better than CT and MRI to find certain types of cancers that are otherwise very difficult to find. I had a schoolmate who had an unusual type of pituary tumour. She became more and more ill, and she was almost beyond treatment when some smart neurologist figured they should do a PET scan on her. At the time, the cost of a PET scan was over $10 000, so it was not a common clinical practise. However, they found the tumour and it could be removed. She will be on a lot of medication for the rest of her life, but she survived, contrary to all other known patients with this type of tumours in Sweden.
I seem to recall you work at Wellcome, Grunt, is this correct? My institution (not me personally though) have a lot of collaboration with the Wellcome PET lab. It's on the neuroscience side only though. We also (and that include me) have a close collaboration with Hammersmith.
I seem to recall you work at Wellcome, Grunt, is this correct? My institution (not me personally though) have a lot of collaboration with the Wellcome PET lab. It's on the neuroscience side only though. We also (and that include me) have a close collaboration with Hammersmith.
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