Aorta Mathematical Formula - Can someone help please

[themalteser]

Hi all,

I'm sure most of you are aware of the Cleveland Mathematical Formula, and it can be easily calculated if the circumference of the circle, say 4.4 is all the same all way round. However, if it's an oval, it can be a little bit more tricky, and I would appreciate if someone could help me with this.

In accordance with Cleveland, if the figure after calculation is greater than 10, than surgery is recommended. So, this is an example of someone with a 4.4cm x 4.4cm aortic dilation, height of 5'10".

So using Pi x radius squared to calculate cross sectional area:

4.4cm circumference = 2.2cm radius
Radius squared = 2.2*2.2 = 4.84
Pi x radius squared = 3.14*4.84 = 15.20

Cross sectional area divied by height in meters =
15.20 / 1.55 = 9.81 which is less than 10 therefore surgery not yet recommended.

(I saw an earlier post by skeptic49, and he calculated it to be 8.9 on a 4.5cm aortic dilation. Hopefully someone can explain this part.

But.

Here is example 2, and this is an oval shape dilation so it's 4.4 x 3.4 cm

First I'm calculating the circumference:

Square the long dimension and short dimension and add together=
a) (4.4 x 4.4) + (3.4 x 3.4) = 30.92

b) Divide the result of a by 2 = 30.92/2 = 15.46
c) Find square root of result b = 3.93
d) Multiply result c by pi = (3.93*3.14) = 12.35
e) circumference = 12.35 / 2 = 6.18
f) Radius = 6.18 /2 = 3.09

pi x radius squared / height in meteres
3.14 * (3.09 * 3.09) = 29.99
29.99/1.55 = 19.35

19.35 is way over 10!

I must be doing something wrong! Can someone please help me on this ?

Can't understand how I got point 1 wrong, and point 2 which is less figures than point 1, way higher!

Thank you

 

[LeakyUK]

1) Height in Metres is 1.78

2) I dont like the look of steps a & b. You would get closer if you divided by 4. The averageing logic looks wrong

square the average of the long and the short dim (4.4 + 3.4) / 2 = 3.9
so 1.95 * 1.95 * 3.14/1.78 = 6.7

I am not a mathematician so this result is for amusement only!

 

[themalteser]

Thanks Leakyuk, yours is so much better! So answer to A is 8.54 as it's a circle and answer to b is 6.7 as it's an oval shape. Makes more sense!

 

[normofthenorth]

Idon't understand a and b myself, and you don't need the circumference of an ellipse (=~oval) to get the area. You do need the two "radii", half the long axis "a", and half the short axis "b".
The area is Pi*ab, so just take your "Radius squared =
2.2*2.2 = 4.84" and substitute
2.2*1.7 = 3.74 and go from there. (1.7 = 3.4/2)

(If you prefer, there are several online area calculators for ellipses, but it's pretty simple.)

I get 7.58 as the "bottom line".

 

[heartman77]

Calculating for these numbers

Calculating for these numbers

How would the formula work out for a person with an aneurysm of 4.0 cm and being 5 ft 4 inches tall? Thanks for any help....

 

[themalteser]

Hi heartman, I get 7.63

 

[heartman77]

Themalteser.......thanks for the reply....how did u arrive at that....can you show the math.....Im reading and typing to you with a patch over one eye as my myasthenia gravis has flared up with a vengeance and im battling double vision. This is for a lady i met on a forum who has the same disease as me and whose Cat scan done to diagnose this disease showed an Aortic Aneurysm. I really appreciate it......thanks a lot....Michael

 

[normofthenorth]

Heartman, I think it's area in cm2 / height in m.
(I've discussed elsewhere whether or not that formula/model makes good sense. I don't think it does, but I'll do the math anyway.)
Area = Pi R-squared, so Pi times 2-squared or 4 Pi (12.566...).
Height in m = 5.33 feet / 3.25 feet/m = 1.64m
12.566.../1.64 = 7.6624... which is <<10.

Themalteser, I was taught in University to guesstimate my calculations before calculating them with total precision. It's partly a holdover from the old days of slide rules (when the "calculator" gave you the numbers, but not the position of the decimal point), but it still comes in handy as a "BS-detector" in the days of calculators and computers. You'd done the calculation with a circle of diameter 4.4, then you needed to do it for an oval (ellipse) that was 4.4 on one axis and 3.4 on the other. Well, one thing you know for sure is that the area has to be LESS than what you calculated for the circle, and you might guesstimate it as being about 1/4 less, like 3.4/4.4 as big. (That guesstimate actually leads directly to the correct formula and the right answer -- BONUS!!) Handy.

 

[heartman77]

Thanks so much

Thanks so much

NormoftheNorth......thanks so much...it was the area in Cm2....that was the part i was not clear on.....ill pass all this on to the lady who had asked me. I agree with you...not sure if the formula is all that accurate.....but ill let her make that decision. Thanks again so much for the help..........Michael