Ribbons and groups: a thin rod theory for catheters and filaments: Ribbons and groups: A thin rod theory for catheters and filaments
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| Názov: | Ribbons and groups: a thin rod theory for catheters and filaments: Ribbons and groups: A thin rod theory for catheters and filaments |
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| Autori: | Lawton, W., Raghavan, R., Ranjan, S.R., Viswanathan, R. |
| Prispievatelia: | MATHEMATICS, CENTRE FOR INFORMATION ENHANCED MEDICINE |
| Zdroj: | Journal of Physics A: Mathematical and General. 32:1709-1735 |
| Informácie o vydavateľovi: | IOP Publishing, 1999. |
| Rok vydania: | 1999 |
| Predmety: | 0209 industrial biotechnology, Finite element methods applied to problems in solid mechanics, catheter navigation, 0206 medical engineering, Biophysics, 02 engineering and technology, network of blood vessels, Special subfields of solid mechanics, rotation group, thin rod equations, Rods (beams, columns, shafts, arches, rings, etc.), wall potential, perturbation theory |
| Popis: | Summary: We use the rotation group and its algebra to provide a novel description of deformations of special Cosserat rods or thin rods that have negligible shear. Our treatment was motivated by the problem of the simulation of catheter navigation in a network of blood vessels, where this description is directly useful. In this context, we derive the Euler differential equations that characterize equilibrium configurations of stretch-free thin rods. We apply perturbation methods, used in time-dependent quantum theory, to the thin rod equations to describe incremental deformations of partially constrained rods. Further, our formalism leads naturally to a new and efficient finite element method valid for arbitrary deformations of thin rods with negligible stretch. Associated computational algorithms are developed and applied to the simulation of catheter motion inside an artery network. |
| Druh dokumentu: | Article |
| Popis súboru: | application/xml |
| ISSN: | 1361-6447 0305-4470 |
| DOI: | 10.1088/0305-4470/32/9/017 |
| Prístupová URL adresa: | https://ui.adsabs.harvard.edu/abs/1999JPhA...32.1709L/abstract |
| Prístupové číslo: | edsair.doi.dedup.....09cab8176c4fa6f21bf7dc5f9133ef26 |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | Summary: We use the rotation group and its algebra to provide a novel description of deformations of special Cosserat rods or thin rods that have negligible shear. Our treatment was motivated by the problem of the simulation of catheter navigation in a network of blood vessels, where this description is directly useful. In this context, we derive the Euler differential equations that characterize equilibrium configurations of stretch-free thin rods. We apply perturbation methods, used in time-dependent quantum theory, to the thin rod equations to describe incremental deformations of partially constrained rods. Further, our formalism leads naturally to a new and efficient finite element method valid for arbitrary deformations of thin rods with negligible stretch. Associated computational algorithms are developed and applied to the simulation of catheter motion inside an artery network. |
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| ISSN: | 13616447 03054470 |
| DOI: | 10.1088/0305-4470/32/9/017 |