To contact FractalMed, please fill in this form and we will respond as soon as possible.

What is

Fractal dimension

A fractal is a geometric object whose basic structure, fragmented or apparently irregular is repeated at different scales. The term was suggested by the mathematician, Benoît Mandelbrot, in 1975. It comes from the Latin word, fractus, which means rough or fragmented.

Fractals are characterized by being a self-similar or self-resembling object when its parts have the same shape as the whole. However, fractals can be presented on different scales and may be slightly deformed.

Many natural structures are fractal types as the coast line, the snowflake or the brain surface. For instance, we can measure the fractal dimension of real objects: coast lines, clouds, trees, brain, etc. With these measurements we can compare objects from the real world with fractals generated by mathematical algorithms.

The key mathematical property of a genuinely fractal object is that its fractal metric dimension is a non-integer number

Therefore, fractal dimension is defined by counting the balls needed to cover the whole set or by counting the boxes of a grid that contain part of the set, when the dimensions of one or the other tend to zero, as for example the measurement of the coast of England.

Brocoli

Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since.

Snowflake

Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since.

Coast of England

Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since.

How fractal dimension of the brain can be analyzed and measured

Fractal dimension in the brain

Fractal dimension of the brain is a measurement that complements brain volumetric studies and seeks to obtain calculations and cut-off points enabling the neurologist to identify diseases and changes in their development

Fractal dimension measurements are more robust referring to technical problems resulting from the acquisition of magnetic resonance brain imaging. Although, this is a fact that is currently being investigated

Fractal dimension in the brain can be measured in several ways:

Based on 2D and 3D images. The 3D image is obtained by a reconstruction of high density 2D images.

We can measure the fractal dimension of the grey matter—cerebral cortex—or the white matter.

Based on the surface or the frame of the object. The study has more relevance in the white matter than in the grey one.

There are several ways and levels to analyze the fractal dimension of the brain.

Measuring the dimension of the brain surface or the interface between the grey and the white matter.

Collapsing the information of the voxels by creating a frame of the image and measuring its fractal dimension on it.

By using other brain measurements, such as the electroencephalography signal or any other type of signal obtained in medicine

What application has

Fractal dimension in the brain

In neurology, it is very significant to measure changes in brain volumes as a marker of brain damage. Brain diseases tend to cause a loss of brain tissue—atrophy—. However, its quantification is complex and limited:

By measuring the fractal dimension of the brain, we measure its complexity, and so any change in the fractal dimension reflects changes in the brain structure, as the ones caused by the diseases.

Fractal dimension of the brain will be modified in case of brain damages that alter the surface of the brain and change the pattern of gyrus.

At present, FractalMed transforms images into quantitative parameters of fractal geometry that present a good correlation with the early detection of Multiple Sclerosis.