Primjene diferencijalnih jednadžbi u biologiji

master's thesis

• Title (english): Applications of differential equations in biology
• Author: Mateja Pejić
• Mentor: Marko Erceg (mentor)
• Committee member: Marko Erceg (predsjednik povjerenstva)
• Committee member: Ilja Gogić (član povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Committee member: Tomislav Pejković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-07-18, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj rad istražuje poveznicu između matematike i neuroznanosti, s posebnim naglaskom na modeliranje električne aktivnosti neurona i srčanog tkiva.Razmatramo ključne matematičke modele, uključujući Hodgkin-Huxley (HH) i Fitzhugh-Nagumo (FHN) modele, koji opisuju aktivaciju neurona i generiranje akcijskih potencijala. Također, predstavljamo model volumenskog vodiča za srčano tkivo, istražujući kako se može primijeniti za razumijevanje širenja električnih signala u srcu. Rad uključuje i numeričke simulacije koje ilustriraju kako se ovi modeli mogu koristiti za analizu i predviđanje ponašanja podražljivih stanica.

Abstract (english)

This thesis explores the intersection of mathematics and neuroscience, with a particular focus on modeling the electrical activity of neurons and cardiac tissue. We delve into key mathematical models, including the Hodgkin-Huxley (HH) and Fitzhugh-Nagumo (FHN) models, which describe neuronal activation and the generation of action potentials. Additionally, we present a volume conductor model for heart tissue, examining how it can be applied to understand the propagation of electrical signals in the heart. The thesis also includes numerical simulations that illustrate how these models can be used for the analysis and prediction of the behavior of excitable cells.

• Keywords: neuroznanost; modeliranje električne aktivnosti neurona; srčano tkivo; Hodgkin-Huxley (HH); Fitzhugh-Nagumo (FHN)
• Language: croatian
• URN:NBN: urn:nbn:hr:217:941700
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-07-25 09:34:49