Razvoj metoda matematičkog modeliranja u biologiji i medicini
Description: Although methods of mathematical modelling in biomedicine have been significantly developed so far still there are many problems that have to be addressed and solved mathematically. These problems are usually related to research for properties of a proposed mathematical model, to fitting a model to data and its validation and use in biomedicine. Since all of these stages in mathematical modelling are closely related to real data and understanding of the phenomena of interest we will particularly focus on three problems: modelling of avascular tumour spheroid growth, modelling of telomere shortening, and modelling and estimating correlation of telomere length/telomerase activity and spheroid growth rate. In modelling tumour spheroids growth we plan to obtain real data, fit diffusion processes of growth efficiently, select the most acceptable model and validate it. For this purpose we need to analyse properties of proposed estimators by methods of stochastic analysis and mathematical statistics, to use applied statistics methodology for fitting model to data and its validation, and to design and apply tests for model selection and for testing homogeneity of spheroids. In modelling telomere shortening we plan to determine and propose diffusion based models, analyse distributions of telomere extinction time and cells, and design statistical model for fitting the proposed process of telomere shortening. To do that we have to use methods of theory of random processes, stochastic analysis and mathematical statistics. Theorems that we plan to prove are improvements in the field of applied mathematics, particularly in application of random processes, mathematical and applied statistics. We expect that this research will have impacts on improving prediction models for cancer patients and applicability of tumour spheroids in personalized medicine, and in improving our understanding of cell aging processes.
Funder: Hrvatska Zaklada za Znanost
Funding type: grant
Funder scheme: DOK
Start date: 2022-04-04
End date: 2026-04-03
Investigator: Inga Urlić
Institution: University of Zagreb, Faculty of Science
Funded outputs count: 0
Funder award ID: DOK-2021-02-7662
OpenAlex ID: G968700136