23/10/2020

Pink October: Mathematics in the fight against breast cancer

Every year, during the month of October, thousands of people and institutions join the international Pink October campaign for an important cause: raising awareness about breast cancer through information on prevention and other aspects of the disease. Despite its widespread participation, the alert remains necessary. In 2020 alone, the National Cancer Institute (INCA) estimated 66,200 new cases of breast cancer in the country. With the pandemic and the need for social isolation, many examinations were not performed, worsening the situation.

Considered the "universal language of science," it's no surprise that mathematics is an important ally in the fight against the disease. Through computing, machine learning, or modeling, it underlies many diagnostic tools and studies on the effectiveness of breast cancer treatments.

According to a study published in January in the journal Nature , artificial intelligence software developed by researchers at Google Health and Imperial College London proved to be as efficient as two doctors working together in reading mammograms. This does not mean that the technology will replace doctors, but that it can alleviate the workload of these professionals, eliminating the need for double mammogram reading, speeding up diagnosis time and increasing the chances of a cure.

In a country like Brazil, where more than 70% of breast cancer cases are diagnosed at an advanced stage , implementations like this can be crucial to reversing the disease's trajectory.

At the Digital Signal and Image Processing Laboratory of the Brazilian Center for Physics Research (CBPF), mathematics, physics, and computer science came together to develop a technique that increased the number of detections of suspicious structures in mammography exams by 30%. The group's objective was to try to solve a common problem in the health field: the low quality of mammographic images.

“Mammographic images are typically difficult to visualize. The breast is basically made up of fat, and X-rays don't pay much attention to fat. These images often have very low contrast,” points out André Persechino, a doctoral student at CBPF who addressed the topic in his master's thesis.

To improve the analysis of this medical examination, the group applied the physical concept of diffusion, which states that, in a favorable environment, different concentrations of components tend to mix and homogenize, "like a drop of milk in a glass of water," exemplifies Persechino. Seeking to increase the contrast of digital mammography images, the group embarked on a complicated challenge of applied mathematics: performing reverse diffusion, transforming the initial blurred image into a sharper one.

To interpret a digital image as a physical system subject to diffusion, it was necessary to use an extensive mathematical framework and the non-linear diffusion equation. "It was equation from beginning to end. Objectively, a digital image is a matrix, a table of values. When we have a digital image on a computer, we use all the mathematical power of matrix algebra on it," comments the doctoral candidate.

Since each image presents unique characteristics, one of the biggest challenges of the project is to mathematically determine the computer's ability to identify which image structures should be highlighted and which should be homogenized. “In the field of artificial intelligence, for example, the 'holy grail' is finding patterns in the data. In our project, the great challenge is to discover patterns and syntactic structures in the images from the exams,” says Persechino.

Breast cancer, the leading cause of cancer mortality among women in Brazil, also affects men, although in a much smaller proportion, representing only 1% of all cases of the disease. The Ministry of Health offers treatment through the Unified Health System (SUS). Regular physical activity, a healthy diet, and maintaining a healthy body weight can prevent approximately 30% of breast cancer cases.

In addition to performing breast self-exams, the Ministry of Health recommends that women between 50 and 69 years of age undergo screening mammograms every two years. Early diagnosis allows for less aggressive treatment and can help reduce mortality from the disease. Taking care of yourself is essential!