03.09.2021

AGH student takes a step towards the application of brain biophysical models in diffusion-relaxometry imaging by using MRI


Dominika Ciupek, photography by Olga Kuśnieruk

Parameters of multi-compartment models in the transverse, sagittal and coronal planes: a) intraaxonal compartment volume fraction, b) fibre orientation dispersion index, c) intracellular compartment volume fraction, photo by Dominika Ciupek

Can biophysical models describing the structure of the brain be applied on a day-to-day basis in comprehensive imaging diagnostics, or will they remain only mathematical theories without practical use? Dominika Ciupek, the AGH student, is trying to answer the question. Her efforts were acknowledged by the Ministry of Education and Science and the student was awarded a grant as part of the "The Best of the Best! 4.0" programme.

Since the publication in 1973 by Paul Lauterbur of a work describing the method of generating images, giving the basis for magnetic resonance imaging (MRI), new diagnostic technologies employing the nuclear magnetic resonance are still developed in the medicine. The MRI technique is applied, in particular, when examining the brain. While the traditional MRI technique allows to obtain an image of the structure of an organ, modern solutions are far more advanced. One of them is diffusion-weighted imaging (DWI), which is used to denote differences in diffusion of water molecules. As a consequence of the natural obstacles they encounter in the brain tissue, their random movement becomes restricted and organised. We then say that it becomes anisotropic. The scanner "captures" all limitations and changes in diffusivity, and as a result thereof thanks to the data obtained by this method we know more about the tissue microstructure. It allows not only to diagnose injuries and pathological changes, but also learn about the natural aging processes of the brain.

Directional and biophysical models in brain imaging diagnostics

However, the method described above holds some limitations, as it does not provide clear information about the direction of the water molecules movement. The technology traditionally used for this purpose is diffusion tensor imaging (DTI). It allows to identify the direction in which the water molecules travel along the fibre tracts and to describe such process with quantitative measures. But it is not perfect, because the fibres arranged in a cross or a fan shape may distort the results of the measurements. Therefore, the use of advanced models is more frequently taken into considered, including biophysical models, which by using the language of mathematics, describe the structure of brain tissue in many dimensions.

– The application of biophysical models is the first step towards presenting the multi-compartment structure of the nervous tissue of the brain by means of quantitative indicators and factual interpretation of the obtained parameters. They thoroughly illustrate not only the diffusion within cells, but also describe the exchange of information at the extracellular level. Hence, we are able to find out if the properties of certain areas in the brain change as cause of progressive mental disorders, and to answer the question whether certain connections in the brain are broken due to the aging processes. The point is that in the literature at least a dozen of models representing the diffusion signal have been already described. When employing diffusion-relaxometry imaging, some of them may be the source of new, previously unknown information. Such information enables, then, a precise assessment of brain lesions with simultaneous consideration of relaxation and diffusion parameters. Now, it is the moment when we need to start to verify which models can be used in common brain imaging diagnostics, and which are just theoretical arguments – Tomasz Pięciak, DSc, explains, from the Faculty of Electronics, Automatics and Biomedical Engineering, Department of Biocybernetics and Biomedical Engineering and Escuela Técnica Superior de Ingenieros de Telecomunicación at Spanish Universidad de Valladolid.

For this to happen, irrespectively of the use of a given model in brain imaging diagnostics, it is necessary to fulfill the condition of the test repeatability. In other words, one should be sure that when the scanner uses identical settings of data acquisition, the same results for the specific parameters determined by the model will be obtained. What is more, from the point of everyday medical practice the time needed to obtain the results is equally important.

Research conducted by the AGH student

A step in this direction is the research conducted by Dominika Ciupek, the AGH student. The starting point for the research was the findings described in the engineering diploma thesis prepared under the supervision of Tomasz Pięciak, DSc. The author verified the possibilities of using biophysical models in imaging the white matter of the brain by diffusion-relaxometry, which is a genuinely innovative approach on a global scale. Before the results become a part of the daily routine in the medicine, it is necessary to answer the question what factors, apart from the factual changes in the tissue, may influence the obtained results.


The student showed that one of the key problems is the appropriate selection of data acquisition parameters and the use of a proper numerical optimisation method that allows to determine the desired parameters used for describing the tissue.

 –Models assume that brain tissue is divided into different compartments. We can distinguish, e.g., the cerebrospinal fluid compartment, the extracellular compartment, and the intracellular compartment. They are represented by various mathematical equations. In the model equations, each of the tissue divisions is multiplied by appropriate fraction that represents such compartment in a small fragment of the brain – Dominika Ciupek describes. We need to translate our model equation into an objective function. Optimisation consists in finding solutions to functions for which its value will be closest to zero. Said solutions are the tissue parameters that are being sought.

Numerical analysis showed that the correctness of the established parameters has got a significant impact on the inversion time. It is the time between the radio pulses emitted by the scanner used during the test. With time the parameters designed for describing the tissue diffusivity and individual volume fractions indicated a variable tendency because the intensity of the magnetic resonance signal and domination of noise in the signal decreased. The aforementioned proves that the tested models can be used mainly when applying appropriately high inversion times.

A grant from the Ministry

The research being a part of the prepared thesis will be continued, because the project submitted for this purpose by the student "Multi-compartmental modelling of anisotropic white matter structures of the brain based on magnetic resonance diffusion-relaxometry imaging" has been chosen for funding by the Ministry of Education and Science under “The Best of the best! 4.0” programme. The programme supports talented students who, under the supervision of an experienced researcher, conduct research that is unique on a global scale. It allows the students to present their results at the most prestigious scientific congresses in the world.

As yet, I have used the data collected from healthy patients. Now, I would like to use synthetic data that would be generated by computer. Then a much larger range of inversion times may be employed than the six when writing the paper. Such a small amount of times does not allow to be fully convinced that it has got a significant impact on the described microstructural parameters – Dominika Ciupek says. She adds that by using a synthetic signal, one could also check the impact of other scanner settings on the correctness of the established parameters. A crucial within this respect may be, e.g., the echo time, that is, the time between the pulse sent by the scanner and the feedback signal. It would also allow to investigate whether more advanced biophysical models would be better at dealing with low inversion times.


While multi-compartment models are used in diffusion imaging, no one has used them extensively in diffusion-relaxometry imaging. We want to give a clear answer the question whether the step we have taken is correct and it indeed opens up new research and diagnostic perspectives in the field of neurodegenerative brain diseases, or we should take a step back and rethink the assumptions of the project from the beginning – Tomasz Pięciak, DSc, comments.

AGH – a university where talents are developed 

Dominika Ciupek became interested in the subject of digital signal processing and mathematical methods of MRI imaging when she attended the course conducted Tomasz Pięciak, DSc,  "Digital Signal Processing". – The doctor suggested that I should work on biophysical models. The more I read about it, the more I was fascinated with the possible applications – the student says.

Before she defended her engineering diploma thesis, her publication was accepted at the prestigious ISMRM & SMRT Annual Meeting & Exhibition in Vancouver. The publication was the result of a year and a half cooperation with scientists from Italy and Iran. Her paper was also awarded at the XXX National Conference of Student Research Groups "Man and his environment" in Kielce. The engineering diploma thesis prepared by Dominika Ciupek was highly assessed by an external reviewer from the NYU School of Medicine in New York.

The student is not the only person who notches up successes under the supervision of Tomasz Pięciak, DSc. To the successful group belongs also:

  • Anna Legierska (master's thesis "Super-resolution of diffusion magnetic resonance imaging data" awarded in the national competition "Young Innovative" organised by the Industrial Research Institute for Automation and Measurements, Warsaw 2019),
  • Jadwiga Piechota (master's thesis "Efficient implementation of an unloaded filter of non-local averages using an extended x86 instruction set" awarded in the national competition for the ABB Award for the best work in technical sciences, Krakow 2020),
  • Fabian Bogusz (master's thesis "Magnetic resonance diffusion imaging economical sampling for the needs of the assessment of the properties of the brain microstructure" won the 1st place in the “AGH Diamonds” competition for the best diploma thesis prepared at AGH in the category of theoretical works and 1st place in the 10th Competition for the Siemens Award for graduates in the field of Automatics and Robotics, Warsaw 2020).

The latter is currently continuing his research interests at doctoral studies.

– I have the pleasure to work with exceptionally talented and versatile female and male students. Their interdisciplinary approach to engineering sciences, natural sciences and the principles of medical sciences allows to deliver innovative works at the highest world level. What is more, I have given a lot of thought on the way of conducting research studies, the employment of which apparently works in this area – Tomasz Pięciak, DSc, says.