Author Topic: Formula for calculating tumor volume?  (Read 7706 times)

arcteryx

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Formula for calculating tumor volume?
« on: June 22, 2006, 04:39:00 am »
I was wondering if anybody knew the formula for calculating AN volume?  I understand this is important in calculating radiation dosage.

I read it might be something like: 4/3 * pi * L/2 * H/2 * W/2

(But that doesn't seem to make sense, since it would actually reduce the total volume if Length, Height, or Width were less than 2.)

HeadCase2

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Re: Formula for calculating tumor volume?
« Reply #1 on: June 22, 2006, 01:16:00 pm »
  Mathematically, the Volume calculation for an ellipsoid is v=(4/3)*pi*radius1*radius2*radius3, which is derived from the volume of a sphere v=(4/3)*pi*radius*radius*radius. But I couldn't tell you if this is how they calculate tumor volume for radiation therapy, they may have their own tweaks to the formula.  In your formula the /2 is to divide each diameter into a radius.  It would not matter if the length, height, or width were less than 2, mathematically it still works.
Regards,
 Rob
1.5 X 1.0 cm AN- left side
Retrosigmoid 2/9/06
Duke Univ. Hospital

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vjharris

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Re: Formula for calculating tumor volume?
« Reply #2 on: June 22, 2006, 08:54:54 pm »
  Mathematically, the Volume calculation for an ellipsoid is v=(4/3)*pi*radius1*radius2*radius3, which is derived from the volume of a sphere v=(4/3)*pi*radius*radius*radius. But I couldn't tell you if this is how they calculate tumor volume for radiation therapy, they may have their own tweaks to the formula.  In your formula the /2 is to divide each diameter into a radius.  It would not matter if the length, height, or width were less than 2, mathematically it still works.

Okay guys, it's bad enough I've got a brain tumor...don't make me do math, too!  ;) ;) ;)
2.2x2.37 right side meningioma or acoustic neuroma
Gamma Knife Dec 5, 2006

russ

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Re: Formula for calculating tumor volume?
« Reply #3 on: June 24, 2006, 09:38:51 am »
Hi
  Anyone...
  Going to factor in 360 meridians?
  Russ ( not a math major certainly! )

Windsong

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Re: Formula for calculating tumor volume?
« Reply #4 on: June 28, 2006, 06:10:32 pm »
i must be mathematically challenged...

i can't figure out how to do this using pi and 3 dimensions....

can someone please post and example in real figures that demonstrates how this is done...?

my efforts do not match end results... ???

thanks,
Windsong

HeadCase2

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Re: Formula for calculating tumor volume?
« Reply #5 on: June 29, 2006, 08:29:24 am »
Windsong,
  Here's an example.  If an AN was measured to be 1.5 cm x 1.0 cm x 0.8 cm, we can divide each "diameter" by 2 to convert them to radius measurements, giving 0.75 cm, 0.5 cm, and 0.4 cm.  We can plug these radii into the formula listed in the earlier note, using 3.1416 for the value of pi.
4/3 x 3.1416 x 0.75 cm x 0.5 cm x 0.4 cm = 0.62832 cubic cm.
  It should be noted that there is some error involved in measuring dimensions on MRIs, and trying to represent a complex shape as an ellipsoid.  I am not knowledable about radiation therapy, but the error involved is probably not significant in calculating radiation dosages.
Regards,
 Rob
PS: measuring ellipsoid dimensions is an interesting exercise, and involves tensor mathematics with eigen vectors, etc.  Tensor mathematics is used by scientists to descibe physical properties in the natural world, for example how a rock allows fluids to flow through it at different rates in differenet directions.
« Last Edit: August 07, 2006, 04:05:28 pm by HeadCase2 »
1.5 X 1.0 cm AN- left side
Retrosigmoid 2/9/06
Duke Univ. Hospital

GrogMeister of the PBW

arcteryx

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Re: Formula for calculating tumor volume?
« Reply #6 on: June 29, 2006, 04:59:49 pm »
This was the reason why doctors recommended against radiation for me (even though I would've preferred it).  You'll notice that as the two-dimensional size of the tumor increases, its volume (i.e., radiation required) is cubed.  So:

...for a 1cm AN, its volume is 0.52 cubic centimeters:
4/3 * 3.14 * 1cm/2 * 1cm/2 * 1cm/2 = 0.52cc

...for a 2cm AN, its volume is 4.18 cubic centimeters:
4/3 * 3.14 * 2cm/2 * 2cm/2 * 2cm/2 = 4.18cc

...for a 3cm CN, its volume is 14.12 cubic centimeters:
4/3 * 3.14 * 3cm/2 * 3cm/2 * 3cm/2 = 14.12cc

Windsong

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Re: Formula for calculating tumor volume?
« Reply #7 on: August 03, 2006, 09:33:41 pm »
Thank you.

That explains why when i tried all these numerous formulae for varius volume type things, i never could approximate a volume no. that made sense for my An.... but then I am not a mathemetician nor a physiscist nor a radiooncologist lol..... i think i'd leave these kinds of math calcs to them.....

best wishes,
Windsong




 


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