Math

Q: How do you determine the volume of a hematoma (kidney, cyst)?

A: Physicians use the formula:

    volume = ½(abc) some use the formula 0.52(abc) see below

Note/Reference:

https://en.wikipedia.org/wiki/Ellipsoid

one of the most cited article in the first 100 years of radiology was based on determining the volume of the pituitary gland based on plain film measurements based on the above formula [DiChiro G, Nelson KB. Volume of sella turcica. AJR

1962;87:989-1 008]. On endocrine rounds in the 1980's housestaff would state the pituitary volume with 4 significant digits. (not really accurate since we are saying pi/3 is 1). 

Reference:

Kagetsu NJ. Inappropriate use of Significant Figures. AJR 157:645, 1991.

apparently AJR really liked this point. see

Mitchell CS. Appropriate use of Significant Figures AJR   169:597-8, 1997.

https://www.ajronline.org/doi/abs/10.2214/ajr.169.2.9242784

Q: Who cares about the volume of a hematoma?

A: Clinicians may make a decision to evacuate the hematoma based on its volume. 

http://www.ncbi.nlm.nih.gov/pubmed/8711791

Q: Does this over or underestimate the true volume?

A: Since the volume of a spherical ellipsoid is really (pi/3)(½(abc)), the above formula underestimates the "true" volume by about 5%. We are already assuming that the hematoma is a spherical elipsoid.

One can estimate the volume of a subdural hematoma with a similar equation. For the interested reader see: http://stroke.ahajournals.org/cgi/content/full/30/1/188

Q: The natural history of brain AVM is that the risk of hemorrhage is 1% per year. What is the risk of at least one hemorrhage in 5 years, 10 years, 30 years, n years.

A: Calculate the probability of no hemorrhage in 5 years

      p=(0.99)n

  so the probability of a hemorrhage in n years is 1-p or 1- (0.99)5

    p=(0.99)5 or 0.9510 so the risk of at least one hemorrhage is 4.9% or close to the estimate of 1% times 5 years

    For 10 years

    p=(0.99)10 or 0.9044 so the risk of at least one hemorrhage is 9.6% or close to the estimate of 1% times 10 years

    p=(0.99)30 or 0.7397 so the risk of at least one hemorrhage is 26% or somewhat less than estimate of 30% (1% times 30 years)

the general formula is risk of hemorhage over n years = 1-(0.99)n

Q: give an example of figuring odds in poker

A: similar logic can be used to figure out the odds of catching a flush in holdem with a four flush on the flop and two cards to go.

you should figure out the odds of not catching a flush first

(38/47)x(37/46)=0.65 so the odds of making the flush are 1-0.65 or 35%

http://www.gamblingteachers.com/holdem-suited-cards.html

http://en.wikipedia.org/wiki/Poker_probability_(Texas_hold_'em)