UNAM creates a tool to classify tumors

The mathematical tool known as Discrete compactness It was initially used to characterize the volcanoes of the Valley of Mexico, however, it has been very useful in medical areas, it can be applied for classification of tcervical uterus , measure the urinary bladder and analyze changes in brain structures.

Created by the Mexican researcher Ernesto Bribiesca Correa, from the Research Institute in Applied Mathematics and Systems (IIMAS) of the UNAM , Discrete compactness serves, in addition to helping in the classification of tumors , to know how compact an object is in its normal state or if it has changed its shape, size or structure.

At present, through it, the compactness of Cervical tumors to know its size, if the disease has spread to other organs, as well as to determine its dispersion.

To know how compact an object is with Dr. Bribiesca's tool, first you must obtain the digital image of it and then measure the number of times that the sides of the cells (also known as pixels or pixels) are touched. , that is, the perimeter of contact, thanks to which it is possible to characterize the objects or know if they suffer modifications.

Dr. Bribiesca explained that until a few years ago, thanks to the measure of classic compactness (which has as an important feature the relationship between the perimeter and the area), it is simple to know the compactness of a simple object such as a triangle, a circle, a square or a cube.

However, the problem arose when it wanted to be calculated in some complex object (with tortuous perimeters), such as a volcano, a tumor or the human brain.

With the equation of discrete compactness, Dr. Bribiesca Correa achieved that the perimeter of an object is no longer its main reference, but its interior, so that supported by digital images of objects, it counts the number of sides that are touched between yes the cells. Thus, an object is less compact, the less contact there is between its cells, and the more compact it is between them.

This measure (which could be considered in the future as a global standard for measuring the compactness of a digital object), is a contribution to the science of mathematics worldwide.

The specialist collaborates with a group of researchers from the University of Leipzig , in Germany, composed of doctors, oncologists and gynecologists who have used the discrete compactness for the classification of Cervical tumors.

"This mathematical tool is only a parameter, an auxiliary one for the expert, from which he can know the structure of the tumors and, at a certain moment, make decisions about how to treat them. "
Bribiesca Correa also collaborated with a group of researchers from the Autonomous Metropolitan University-Iztapalapa (UAM-I) to classify brain images.

With the classification obtained, through the discrete compactness, it has been seen that the enveloping surface of a brain structure changes in relation to its volume when the organ has been affected by some conditions, such as Alzheimer's disease.

It is important to note that this tool is used in Denmark to calculate the shape and compactness of the urinary bladder in older adults; in France it was used for the classification of tumors whose surfaces are very corrugated, and in Canada they use this equation to measure the compactness of soils.