Analysis and application of smeared methodology in modelling of transport within deformable biological systems

[V. D. Simić]

146 str.

Osnovu svih vitalnih procesa u ljudskom organizmu predstavlja razmena mase, koja se paralelno odvija na nekoliko skala: od krvnih sudova ka unutrašnjosti ćelija i do organela unutar ćelija. Molekuli, kao što su kiseonik, produkti metaboličkih procesa, lekovi i slično, prolaze kroz različita okruženja- krv, međućelijski prostor unutrašnjost ćelija i unutrašnjost samih organela; kao i biološke barijere (zidovi krvnih sudova, membrane ćelija i organela). Ogroman broj aspekata transporta mase je i dalje nepoznat, pre svega biofizički mehanizmi transporta lekova u organizmu. Još jedan izazov u modeliranju ovih procesa, predstavlja kompleksnost kapilarne mreže, Poredeći nivoe u ljudskom organizmu, od reda veličine organa pa sve do kapilarnog nivoa, nije izvodljivo modelirati svaki pojedinačni kapilar u okviru računskog modela stoga jepoželjno imati razvijenu metodologiju upotrebljivu za praktičnu primenu. Osnovni cilj disertacije je predstavljanje, kreiranje i razvoj distribuirane (eng. smeared) metodologije, kompozitnog distribuiranog konačnog elementa (eng. Composite Smeared Finite Element- CSFE) kao i KTM (engl. Kojic Transport Model- KTM), razvijenog od strane akademika Miloša Kojića. Takođe, korišćenjem pratećih softvera za simuliranje različitih procesa u biološkim sistemima (difuzije, konvekcije, mehanike tkiva) kao rezultat, biće prikazane i različite vrste jednostavnih i složenih numeričkih modela koji služe za validaciju metodologije. Numerička metoda koja će biti korišćena je metoda konačnih elemenata (MKE) kao i softverski paket PAK (Program za Analizu Konstrukcija), u kome su implementirane sve jednačine prikazane u teorijskim proglavljima. Za vizualizaciju i analizu dobijenih rezultata koristiće se CADFIS (eng. Computer- Aided Design Fields and Solids) softver. Rezultat korišćenja ove metodologije je jedan novi koncept, sposoban da zameni modeliranje kompleksnih bioloških sistema i kapilarne mreže unutar njih, ekvivalentnim modelima koji su robusniji i nude ogromnu uštedu vremena prilikom modeliranja, kao i prilikom izvršavanja simulacija. Tačnost primenjene metodologije je još jedna velika prednost u odnosu na konvencionalne načine modeliranja, kao i korišćenje merljivih parametara.

One of the crucial processes in living organisms is mass transport, that occurrs simultaneously from blood vessels to tissues and– in the reverse– transport from organelles to blood vessels. Molecules, such as, oxygen, waste products of cell metabolism, drugs etc, are being transported throughout different barriers- blood, extracellular space, cell and organelle interior; as well as biological barriers (blood vessel wall, cell membranes and organelles). There are still many ascpects of mass transport procces that are not discovered, primarily biophysical drug transport mechanisms inside living organisms. Another challenge present during this modeling process is complexity of capillary network inside complex biological systems (i.e. organs and tumors). Comparing different scales in human organism, starting from organ level up to capillaries, due to complexity and heterogeneity of capillary systems, it is however not feasible to model in silico individual capillaries, hence there is a need for simplified and robust computational models that address mass transport in capillary–tissue systems for practical purposes. Main goal of this doctoral dissertation is introducing and development of smeared modeling concept, formulation of a new Composite Smeared Finite Element (CSFE) and Kojic Transport Models, defined by academician Milos Kojic. Also, using accompanied softwares for simulating different transport processes inside biological systems (diffusion, convection and tissue mechanics) as a result here will be presented different types of simple and complex numerical models used for validation and application of methodology. Numerical method used in this dissertation is finite element method as well as PAK software, in which are implemented all equations listed in theoretical chapters. Regarding visualization and analyzis of numerical results, we will use CAD FIS (Computer-Aided Design Fields and Solids) software package. Main result of using this methodology is a novel concept, capable to replace modeling of complex biological systems and capillary network within, equivalent (smeared) models, more robust which saves time during modeling process, as well as simulation execution. Accuracy of this methodology is another advantage of applied methodology, regarding conventional modeling processes, as well as usage of measurable parameters.

transport mase, distribuirani model, kompozitni konačni element, KT modeli

mass transport, smeared model, composite smeared finite element, КТ models

531(043.3); 602(043.3)

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