Geodesic
Simulation of nonlinear dynamics of Hamiltonian systems in biomechanics using computed tomography images
Matematičeskoe modelirovanie, Tome 26 (2014) no. 1, pp. 109-121

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Meshless method of the mathematical simulation of the dynamics of the three-dimensional nonlinearly deformed hyperelastic media, based on the Hamiltonian description of discrete classical mechanics and symplectic integration method for the solution on the temporary layer is developed. The comparative results of solution of model problem and the solution of the actual problem of biomechanics about the dynamics of the artificial valve of heart are represented.
Keywords: biomechanics, deformable media, finite deformation, point approximation, Hamiltonian description, symplectic integrator, mathematical simulation. 
@article{MM_2014_26_1_a8,
     author = {A. I. Nadaryshvili and V. A. Petushkov},
     title = {Simulation of nonlinear dynamics of {Hamiltonian} systems in biomechanics using computed tomography images},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {109--121},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2014_26_1_a8/}
}
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A. I. Nadaryshvili; V. A. Petushkov. Simulation of nonlinear dynamics of Hamiltonian systems in biomechanics using computed tomography images. Matematičeskoe modelirovanie, Tome 26 (2014) no. 1, pp. 109-121. http://geodesic.mathdoc.fr/item/MM_2014_26_1_a8/