# About Trabecular Spacing and Trabecular Separation

Dear Mr mdoube;

As we know, while having data about Tb.Sp ; we choose “spacing” option in measuring Trabecular Thickness…
My question is, if our gained data of “Tb. Sp” is trabecular spacing or trabecular separation…

Trabecular Separation(Tb. Sp) = 1/Tb.N - Tb.Th
Trabecular Spacing (Tb. Spac) = 1/Tb.N

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Dear Ersague,

In my opinion Tb.N is not a very useful measurement, especially if you have 3D images (e.g. from X-ray microtomography). The reason is that to calculate Tb.N the algorithm must assume an underlying 3D geometry, which may or may not be correct. It’s also ambiguous - some people use Tb.N as measured from 2D images and others use it measured from 3D images.

Tb.Sp as implemented by BoneJ is the Local Thickness of the marrow space in between trabeculae. The Tb.Sp at a point in the structure is defined by the diameter of the largest sphere that fits within the marrow space and that contains the point. Spheres are fitted directly. The mean Tb.Sp number reported is an arithmetic mean of the pointwise Tb.Sp values. It’s actually just the same process as Tb.Th but applied on the background phase of the input image.

Best regards,

Michael

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Hi Michael,

After reading many replies from you, I have to admit that you are really an expert in this area. So my question is can we get Tb.N. using ImageJ, or can we calculate Tb.N. based on the results that we get using ImageJ. Many thanks.

Alex

Yes: some people calculate it as (BV/TV)/Tb.Th. Others use 1/(Tb.Th + Tb.Sp); this is how Tb.N is calculated by Bruker’s CTAn, for example. So there is no need to do anything apart from a simple calculation using thickness results.

Because Tb.N is fundamentally not independent from other parameters, and relies on a geometric model assumption, I much prefer to use Conn.D, which is a topological count of ‘handles’. Care must be taken with Conn.D because it can count small loops of noise as handles, so make sure your data are clean and smooth, and you have run Purify, prior to a Conn.D measurement.

Hi Michael,

Thank you so much for your quick response. After checking the literature, especially the guideline of ASBMR 2010 for reporting results of bone microarchitechture, it’s recommanded to report Tb.Th, Tb.Sp and Tb.N. based on 3D calculations, namely using a sphere-fitting method. Cuz using 2D methods to calculate these meansures, we have to assume a geometric structure, either rodlike or platelike, and these highly idealized models are considered two ends of a spectrum, where the real architecture is a mixture of both rods and plates. And in the 3D model, the formula to calculate Tb.N. is Tb.N=1/(Tb.Th + Tb.Sp), you are correct.Thats my understanding of this parameter.

Best,

Alex

One more point, if we wanna use 2D model to calculate Tb.N., it’s based on the geometric assumptions, Tb.N.=(BV/TV)/Tb.Th is based on parallel plate model, Tb.N.=Sqr((4/PI)*(BV/TV))/Tb.Dm is based on cylinder rod model. Am I right?

Alex

Michael,

Recently I have been trying to use BoneJ to analyze trabecular spacing, as I have in the past.

While I choose trabecular spacing for the results table, the only result it is able to show is thickness. After reading through the old Google forum I waited several hours to see if it was maybe playing catchup with the output, but it never showed up. It also is unable to output Trabecular number.

I’ve combed through all of the buttons looking to see if it is an option that I have checked that has caused trabecular spacing to go away but can’t find anything.

I’m using a Mac.
OS Sierra 10.12.6
FIJI is up to date
BoneJ is 1.4.2

Mimi

It’s probably that the spacing in your image is quite big and that there is lots of contact between background and the sides of the stack. BoneJ treats the outside as continuous rather than the image stack having ‘walls’ that stop growth of the spheres that do the fitting. That means the spheres just keep on growing and never hit the sides. You can try to speed it up by downsampling your image (Image > Scale, enter values < 1), or by putting some “walls” of foreground on the sides.

Thanks Michael,

I cropped down the Thresholded TIFF stack and was able to get a spacing number after about 1/2 hour. The number values for mean and max were extraordinarily high. Discussed more below.

I was unable to use the Image>Scale parameters to further constrain my data. The error is that an 8-bit binary image is required. My stack is 8-bit so I’m not sure what is going wrong.

Using the Image>Scale constraint to limit the space would be exceedingly useful for me not just because of processing time. I’ve included two pictures of the bone I am scanning - I would like to exclude the marrow cavity. The marrow cavity is open to the space surrounding the bone in the stack so I need to make sure that that isn’t being included as Tb. Sp. By my calculations capping the max Tb. Sp. at about .5 mm would be adequate to exclude the surrounding space and the marrow cavity, but I’m not sure how to circumvent the 8-bit image notice that I’m getting.

Mimi

I see little point in reporting Tb.N at all because it is totally derived from Tb.Th and Tb.Sp. Use Conn.D instead, because it measures the number of loops of bone directly.

@Mimi_Sammarco this image looks poorly suited to Tb.Sp measurement, which expects a volume filled with trabeculae. Here, the algorithm will attempt to fill all the non-bone space with spheres, which is pretty much the marrow cavity and the space outside the bone. If you want to continue this discussion, please take it to its own thread.

Hi Michael,

Seeing that both Tb.Th and Tb.Sp are measured by the diameter of the largest sphere that fits within that space would you consider the two parameters fully independent from each other, or since they are measuring (to some extent) the inverse of one another, that they have some shared component (some dependency between them)?

Thanks
Meir

Yes and no and maybe.

Yes because without any a priori information about the structure, you don’t know if there is a relationship between Tb.Th and Tb.Sp. You could have thin sparse struts or thick densely packed struts, or anything in between, or the opposite (thick/sparse or thin/dense). At this point you could make a fair assumption of independence between Tb.Th and Tb.Sp.

No because once you know something about your structure the assumption of independence is less strong. If for example you have a baseline measurement of Tb.Th and Tb.Sp and then you are measuring the anabolic effect of exercise or the catabolic effect of disuse, you can expect that trabecular thickening will be accompanied by a concomitant reduction in space between trabeculae (and vice versa).

Maybe because even in the case where you have a baseline structure, the way the bone actually responds, and the way the spheres are fitted and averaged, may be unintuitive, or challenge your conceptual model. For example perforated plates, with the dominant Tb.Sp component measuring the space between plates, may thicken by filling up the perforations first, or the parts of the rod-like trabeculae that thicken (giving Tb.Th) might not be the same parts that limit the spheres in the marrow space that give Tb.Sp.

So, you don’t really know until you measure and then check how related the variables are in your data with a statistical test of correlation.

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Thank you for your prompt answer. But wouldn’t a statistical test of correlation look only for a linear correlation? I’m not sure that the correlation between Tb.Th and Tb.Sp is linear.

I know you stated in the past that you don’t think Tb.N is very informative but I can see a range of changes for each variable (Tb.Th and Tb.Sp) with two end points. At one end we have a change in Tb.Th that is compensated by an inverse change in Tb.N and thus Tb.Sp stays constant and at the other end we have a change in Tb.Sp that is compensated by an inverse change in Tb.N and thus Tb.Th stays constant (obviously these two extreme cases are very rare in nature, if they even exist). In between these 2 hypothetical extremes all interactions between Tb.Th and Tb.Sp are possible and I don’t believe that this correlation is linear. However I do think that at each point along this range their is an interaction between Tb.Th and Tb.Sp and thus I don’t think that they are ever truly independent.

I would love to hear your thoughts on the matter.

No. I intentionally left out the word ‘linear’, because you can choose what model you use to fit to the data (even Excel lets you fit power, exponential, polynomial functions to your data, and provides an R²). You can also do non-parametric fitting e.g. Spearman’s ρ.

My point about Tb.N is that as a derived term it can’t be independent of both Tb.Th and Tb.Sp. If you want to know how many trabeculae there are (if there is even such a thing as a single trabecula) then a measure that does something completely different, such as Conn.D, should be used instead.

There are a few papers around that measure the interactions among the different parameters, which show (to paraphrase) that BV/TV is the most important independent predictor of mechanical behaviour, followed by anisotropy. The others are either not very independent from BV/TV or don’t explain much of the mechanical behaviour by themselves.