Interpolat​ion/Extrap​olation 3D Points

Hello

I have 5 markers (L1, L2, L3, L4, L5) all on the lumbar spine. L1 is missing.

From L2, L3, L4, L5 i have the x,y,z coordinates for 360frames. Is it possible to extrapolate the coordinates for L1?

The markers can be assumed to be equaly distributed.

Thank you!

[Walter Roberson]

Would the spine not be bending? If so then the markers might be equally distributed when the spine is straight, but what information is available to predict how the spine bent and took L1 with it?

[Walter Roberson]

Oliver responds:

I have the X,Y,Z coordinates of L5,L4,L3,L2 for 360frames. For this time we have the movement of the spine.

[Walter Roberson]

Oliver, please keep in mind that the volunteers here know MATLAB better than they know how the spine works, and especially we know MATLAB better than we know your experimental setup.

1) Are the 5 markers to be assumed to be on a single short part of the spine that is completely rigid and flat, like trying to predict where the "1" is on a wooden ruler when we know where "2", "3", "4", and "5" are?

2) Are the markers to be assumed to be on a segment of the spine that has a maximum bend from the other segments, and you are fine with getting back coordinates that are anywhere in the range of that maximum bend, or alternately getting back constraints on the range of positions where the L1 might be?

3) Are the markers to be assumed to be on a segment of the spine that moves in consistent ways, and that what is needed is to track the markers over time forward and backwards in order to figure out where the L1 must have been because the other markers on the spine would have moved differently if it had been elsewhere?

Option #1 is not difficult to implement and does not require knowledge of anything other than some easy geometry.

Option #2 is a bit more tricky but should not be too bad

Option #3 requires a lot more knowledge of spinal mechanics and would likely not be all that easy to implement.

[Oliver Kumar]

Hi, I think the best would be if I go back to the constraints on the rane of positions where L1 might be. All of my points L5, L4, L3, L2, L1, should have nearly the same X Y coordinates, they are only different in the Z Axys. The gap between the points can actually be assumed to be the same but it depends whether the spine is straight or bend. So the position of L1 has to depend on the differences from L5 to L4 to L3 to L2.

If I understood it right, the second part of your option 2 would be something like that?

Thanks for your help!

Oliver

[Star Strider]

If you also have T12, you can interpolate between T12 and L2. Otherwise (without seeing the radiograph and without knowing if this represents trauma or other abnormal anatomy), L1 could be crushed or simply absent. It’s not likely to have wandered far if it still exists.

[Oliver Kumar]

Yes I have T11. Could you please help me with the interpolation? Would it also be possible to extrapolate from L2 without the use of T11?

[Huy Le Van]

Hi. I am writting graduation thesis.Can you write code about lumbar spine pain ?(Guide)