Mathematics and breast cancer prevention

Few days ago I came across this sad and beautiful website:

The battle we didn't choose: my wife's battle with breast cancer (*)

Angelo Merendino is a photographer based in Cleveland. Angelo and his wife Jennifer's story is moving: love at first sight (at least from Angelo's side :)), soon culminated to a wedding in Central Park. After only 5 months, Jennifer finds out she has breast cancer. While they fought side by side, Angelo collected everyday amazing pictures of their daily difficult battle. Usually I do not get so impressed by pictures, but in this case I could really feel a hint of the everyday obstacles they had to face and I was deeply moved.

X-ray CT scans are a valuable alternative to mammography, as diagnostic methods to detect breast cancer and cancer in general. Problem is, several studies (**) highlighted a correlation between CT scans and risk of getting cancer. Irradiating a patient with X-rays increases their risk of getting cancer by a small percentage. At the end of the day, such small percentage is a someone out there.

This is why we focus our research on sparse tomography. Sparse indicates a situation where we have constraints and can get only few measurements. We could be able to get just few projections (for instance to limit the irradiation) or just from a limited angle instead of all around the person (or, in general, the object of study). The classical approach of FBP (filtered back projection) works poorly when you have a limited amount of data. We have developed and are still developing several alternative reconstruction algorithm to improve this. The algorithm I am currently working is an implementation of a modified version of the level set method. As an example of what such reconstruction technique can do with respect to FBP, see the following pictures (***):

Comparison of the reconstruction of the classical Shepp-Logan phantom scanned from full angle, only 10 projections. Left: the original phantom. Center: FBP reconstruction Right: level set method reconstruction.
Comparison of the reconstruction of the classical Shepp-Logan phantom scanned from full angle, only 10 projections.
Left: the original phantom.
Center: FBP reconstruction
Right: level set method reconstruction.
Comparison of the reconstruction of a knee specimen, scanned from full angle, only 10 projections. Left: the original phantom. Center: FBP reconstruction Right: level set method reconstruction.
Comparison of the reconstruction of a surgical C-arm device from a knee specimen, scanned from full angle, only 10 projections.
Left: sharp reconstruction.
Center: FBP reconstruction
Right: level set method reconstruction.

You can clearly see how much of an improvement this is. 10 is a very low number of projections compared to "usual", therefore small irradiation. During my recents work travelling, I met several medical physicists and found out there is still a long way to go to share such new techniques outside the mathematical world, even thought such research has been going on for about a decade.

My hope for the near future is to be able to develop new mathematical reconstruction techniques and to be able to spread them among the medical imaging community, in the hope of experimenting with real life situations. Stories like the one of Angelo and Jennifer are the fuel that keeps me going and my inner motivation. Thank you Angelo for having the courage and strength to share your story, as you can see it has a wide reach.

 

(*) The featured image of this post is part of Angelo Merendino's collection. Please check out also his foundation The Love You Share, dedicated to assisting breast cancer patients and their families.

(**) See for instance this study by American Medical Association (2009) and  this paper on JAMA (2007).

(***) You can learn more by reading Limited data X-Ray tomography using nonlinear evolution equations by V. Kolehmainen, M. Lassas, S. Siltanen.

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Paola Elefante

Technical Project Manager working in Supply Chain Management solutions at Relex Solutions Oy. Proud mother with the best husband ever. Shameless nerd&geek. Feminist. Undercover gourmet.

2 thoughts on “Mathematics and breast cancer prevention

  1. Breast cancer is a serious topic and it is alarming that victims of breast cancer is increasing each year. The treatment is not easy for those who suffered breast cancer. I think a lot of women should take care of themselves and have a breast cancer screening.

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