[Insight-users] Measuring tumor diameter

[Richard Beare]

So it sounds like the current working definition of tumor diameter
used by surgeons/medicos is the length of the longest straight line to
fit inside the tumour body, and that in practice this is usually
estimated using 2d slices.

In the ideal world you'd have a dataset of tumor images with diameter
estimates made by a variety of medicos against which you could compare
the various computational metrics - perhaps you have this.

There appears to be at least one major assumption/approximation that
medicos are willing to make with this sort of tumor - they are happy
with a single measure that basically assumes that the tumor is
approximately spherical.

So it seems to me that you have a number of alternatives. The first is
direct implementation of the manual estimation method you described.
As you say this will require computing something for all voxels on the
surface of the tumour, which is several thousand points, but I don't
think that will be prohibitively time consuming, at least compared to
actually segmenting the tumor well. There are a number of tricks that
might help speed things up.

Here are a few thoughts:

Computing the distance between all pairs of surface voxels is
feasible, but determining whether the intersecting line goes outside
the surface might be much more complex. Therefore an estimate of the
lower bound of distances that you are interested in would let you
avoid determining whether or not short lines fall outside the tumor. A
couple of estimation methods spring to mind - 1) measure the tumor
volume and determine the diameter of the equivalent sphere - any line
less than some significant fraction of this isn't of interest 2) Find
peaks in the euclidean distance transform, values of which represent
the radius of the biggest sphere that will fit inside the tumor - any
line less that a significant fraction of twice this value isn't of
interest. Then build a queue of voxel pairs sorted by distance between
them and check for valid line segments, starting with the longest
first. Stop when you find one that lies entirely within the tumor.

You could then compare performance of this sort of approach to the
other options that have been raised. At least this is a direct
translation of the current practice.

On Mon, Dec 22, 2008 at 9:34 AM, Andriy Fedorov <fedorov at bwh.harvard.edu> wrote:
> On Sun, Dec 21, 2008 at 11:20 AM, Steve M. Robbins <steve at sumost.ca> wrote:
>>> The approach I am currently considering is this:
>>>
>>> 1) go through the axial slices, find the one with the largest area
>>> 2) extract that slice contour
>>
>> This makes it seem like you have reduced the problem to 2D only.  Is
>> that desirable, or is that done due to convention (e.g. radiologists
>> traditionally look at stacks of 2D slices)?
>>
>
> Based on my discussion with a neurosurgeon, they usually look at 2D
> slices in AP/LR/IS directions, but also they may also look at oblique
> slices.
>
> To understand maximum diameter, as I understand it, imagine the
> contour of the tumor segmented in a 2d slice. Then take a set of
> segments connecting all possible combinations of the contour points.
> For each segment, subtract the subsegment which is outside tumor
> contour (this will happen only for concave shapes). The updated this
> way length of the longest segment will be the maximum diameter.
>
> I assume, one can take all combinations of surface points in 3d,
> instead of looking at a slice with the largest area, but this will be
> very time-consuming to walk along the segments connecting all possible
> pairs of points. I simplify the problem to develop an initial
> solution.
>
>>> 3) go through all possible combinations of the contour points, find
>>> the pair of most distant points, and take this as a diameter
>>
>> Here you are measuring using the normal Euclidean distance?  For
>> example, an "L" shape would have the two most distant points be the
>> end of the two legs and the diameter would join them to form a
>> right-angle triangle?
>>
>
> An "L" shape will have the maximum diameter equal to the length of the
> longer leg. With the diameter you suggest most of it will belong to
> the outside of the shape.
>
>>> 4) follow the line between the points in the previous step, and
>>> subtract the parts of the line that are outside the contour (this is
>>> how the tumor measurements are actually taken). This may change the
>>> measured diameter.
>>
>> I don't understand "subtract the parts of the line outside the contour".
>> In my "L" shape example, almost the entire line is outside; does that
>> mean you would say its diameter is zero?
>>
>
> The diameter defined this way will indeed be almost 0. This will not
> be the maximum diameter though.
>
>>> 5) repeat steps 3 and 4 until the maximum is found after taking into
>>> account diameter parts outside the countour
>>
>> Again, I'm not sure what this means.
>>
>> Naively, I might expect that you want to measure a longest distance
>> through the shape.  In the "L" example, this would be the sum of the
>> two legs.
>
> The diameter by definition should be measured along a line, you cannot
> sum up two legs...
>
>> I googled a bit but did not find any precise explanation of how to
>> measure a "tumour diameter".  Can you explain a bit?
>>
>
> I haven't found a precise definition either. Based on my
> understanding, the measure is very subjective, and it is basically
> what I described. Of course, it is not easy to visually identify the
> largest diameter.
>
> I hope I was able to clarify the problem for you a bit. If you find a
> better definition, please post...
>
> Thanks
>
> Andriy Fedorov
>
>
>
>> Thanks,
>> -Steve
>>
>>
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