The Palpable Prostate

Prostate cancer topics, links and more. Now at 200+ posts!

News: Health Day, Medical News Today, ScienceDaily, Urol Times, Urotoday, Zero Cancer Papers: Pubmed (all), Pubmed (Free only), Amedeo
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Reviews: Cochrane Summaries, PC Infolink Newsletters: PCRI, US Too General Medical Reviews: f1000, Health News Review
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Wednesday, June 22, 2016

Brachytherapy problem

In a perineal saturation biopsy, a brachytherapy-like grid of rectangular squares is spaced at s = 5mm. Biopsy samples are taken. The cancer will be assumed to be a disc, i.e. circle, of diameter d. It will be detected if  the disc intersects a vertex on the grid. What is the probability of detecting the cancer? of missing the cancer? Consider a disc of diameter d around each of the 4 corners of a particular square in the grid. (See accompanying diagram.)


One quarter of each of those discs lies in the particular square so the total area of those discs within that square divided by the area of the square is the probability of detection. (This assumes the probability distribution of the circle centers is uniform and assumes that the discs are not so large that they overlap.)

probability of detection of cancer 
= probability that the center of the cancer lies in one of the 4 quarter discs 
= (sum of 1/4 of the area of 4 discs of diameter d) / (area of one grid square) 
= 4 * 1/4 * (area of a disc of diameter d) / (area of one grid square) 
= (area of a circle of diameter d) / (area of one grid square) 
= (pi * (d^2)/4) / s^2
 
We used the fact that the area within a circle is pi*r^2 where r is its radius. This implies it equals pi * d^2/4 where d is its diameter. The above only works if the 4 quarter circles do not overlap and that is guaranteed if d is less than s. If d is greater than s then the quarter circles would overlap and adding their areas would represent double counting in the overlapping regions.

For a diameter of d = 2 mm we can compare the formula's result, 0.50265, with the result of a simulation, 0.4955, which generates 10,000 points uniformly on the square and counts the fraction of points lying within 2mm of a corner. To two decimal places both give 0.50 for d=2mm. Unlike the formula, the simulation is not restricted to the case where d is less than s. Both the formula and the simulation give the probability of detecting the 2mm cancer. The probability of missing the cancer is 1 minus the probability of detecting it.

1. Here is the calculation using the formula using d = 2 and s = 5:

(pi * (d^2)/4) / s^2 = (3.1415926 * 4^2/4) / 5^2 = 0.50265

2. Here is the the R code for the simulation again assuming d = 2 and s = 5. d as well as s and n (number of iterations) can be changed as needed. Run it by pasting the code into http://www.r-fiddle.org -- be sure to erase anything already in the r-fiddle text entry box first. You may need to press Run twice if the answer does not appear the first time. The answer that the R code simulation gives, 0.4955, equals the theoretical value of detection from the formula (0.5265) to two decimal places: The code below gives the probability of detection.

set.seed(123)
n <- 10000  # number of iterations in simulation
s <- 5 # length of side of a grid square
d <- 4  # diameter of each of the 4 discs centred at the 4 corners
r <- d/2
x <- runif(n, 0, s)
y <- runif(n, 0, s)
mean(x^2 + y^2 < r^2 | (s - x)^2 + y^2 < r^2 | x^2 + (s-y)^2 < r^2 | (s-x)^2 + (s-y)^2 < r^2)


Thanks to Don Morris for raising this problem.

Friday, June 3, 2016

Blog Updates for May 2016

June 3, 2016. In Metformin and Prostate Cancer we added: A May 2016 update by Sayyid and Fleshner [PMID: 27195314] [Full Free Text] reviews studies that show a decreased prostate cancer risk with metformin as well as beneficial effects for prostate cancer patients after treatment. Other recent work suggests benefit of combination therapy of metformin with statins, p53 stabilizers [PMID: 26900800], chemotherapy [PMID: 27118574].

Saturday, April 30, 2016

Blog Updates for April 2016

Note to readers. The Palpable Prostate Blog has now published over 200 blog posts -- this post is number 201.

April 30, 2016 in Metformin and protate cancer we added: A number of investigations have concluded that metformin acts by blocking the glucose cancer cells need and in the absence of glucose they will turn to glutamanine and leucine. They hypothesize that interfering with glutamine and leucine uptake might synergistically work with metformin. Note that glutamine is a non-essential amino acid (i.e. the body can produce it itself) so simply lowering the intake of glutamine-containing foods might not be effective. [PMID: 23687346] [Free full text] [PMID: 26550231] [Full free text] [PMID: 24052625] [Full free text]

Thursday, March 31, 2016

Blog Updates for March 2016

March 31. In Choosing a Surgeon - Part I. Considerations, Choosing a Surgeon - Part I we added: Incidentally it has also been found that it is also true that radiation at high volume centers have better outcomes. See [PMID: 26972640] .

Thursday, February 25, 2016

Blog Updates for Feburary 2016

Feb 25, 2016. In Prostate Cancer Calculators we added this calculator: Probability of Recurrence, Potency and Continence after Laprascopic (LRP) Surgery Based on 500 LRP surgery patients of Christopher Eden this calculator accepts PSA and stage and displays the percentage of patients who were cancer-free, the percentage who regained potency and the percentage who regained continence after surgery. It also displays a table of data for all patients fitting the input parameters. The data is based on a follow up of 12 - 36 months with an average follow up of 13.5 months. The site links to a paper that provides more background detail. See theprostateclinic .

Feb 25, 2016. In Prostate Cancer Calculators we added this calculator in the Memorial Sloan Kettering section: Life Expectancy:As described and linked to in this prostatecancerinfo review "to use the tool, you will first be asked a number of questions about your health, your age, and your diagnosis with prostate cancer, and then those data are used to project your risk of death from prostate cancer and from other causes at 10 and 15 years after diagnosis.

Tuesday, January 5, 2016

Metformin and prostate cancer

[Updated June 21, 2016]

A 2014 article in the Journal of the National Cancer Institute by Azvolinksy [PMID: 24511112] [Full Free Text] and a 2014 article by Fleshner in the Canadian Urological Association Journal [PMID: 25243043] [Full Free Text] discuss observational studies on diabetic prostate cancer patients which have shown reduced risk of death from prostate cancer as well as reduced all cause mortality among those taking the widely used inexpensive diabetes drug, metformin. A May 2016 update by Sayyid and Fleshner [PMID: 27195314] [Full Free Text] reviews studies that show a decreased prostate cancer risk with metformin as well as beneficial effects for prostate cancer patients after treatment. Other recent work suggests benefit from combination therapy of metformin with statins, p53 stabilizers [PMID: 26900800], chemotherapy [PMID: 27118574].

An undated overview by Peter Wehrwein speculates that the biological mechanism may be the lowering of insulin, lowering of blood sugar output of the liver or via interruption of signalling pathways. A number of investigations have concluded that metformin acts by blocking the glucose cancer cells need and in the absence of glucose they will turn to glutamanine and leucine. They hypothesize that interfering with glutamine and leucine might synergistically work with metformin. Note that glutamine is a non-essential amino acid (i.e. the body can produce it itself) so simply lowering the intake of glutamine-containing foods might not be effective. [PMID: 23687346] [Free full text] [PMID: 26550231] [Full free text] [PMID: 24052625] [Full free text].

A 2015 meta-analysis by Wu et al found that the risk of developing prostate cancer (as opposed to the risk of death for those who have prostate cancer) is unaffected by metformin.

Confirmation of these results in diabetics and non-diabetics through randomized clinical trails is underway. See: [ClincialTrials.gov]

A video on metformin and prostate cancer by oncologist Dr. Charles (Snuffy) Myers can be viewed here: How + When to Use Metformin.

Monday, November 30, 2015

From Pilot to System Solution

It seems that so much is known in medicine and health care that is not widely enough applied. The video below of the keynote talk by Dr. Danielle Martin at the Health Quality Transformation 2015 conference focused on health care in Ontario notes that "less than 40% of health improvement projects successfully expand beyond the early group of adopters who first bring them to life" and discusses how innovation can move from pilot to system-wide application.

It discusses the concepts of spread and scale:

- Spread is about innovations diffusing to other teams or organizations, one at a time, as successive teams learn of the successful innovation and individually decide to adopt it.

- Scale is about large scale structural change involving policies that are implemented all at once across an entire region. It requires significant resources and political capital.

She discusses the application of these concepts and many associated issues and examples.