This study describes a multidimensional 3D/lumped parameter（LP） model which contains appropriate inflow/outflow boundary conditions in order to model the entire human arterial trees. A new extensive LP model of the ...This study describes a multidimensional 3D/lumped parameter（LP） model which contains appropriate inflow/outflow boundary conditions in order to model the entire human arterial trees. A new extensive LP model of the entire arterial network（48 arteries） was developed including the effect of vessel diameter tapering and the parameterization of resistance, conductor and inductor variables. A computer aided-design（CAD） algorithm was proposed to effciently handle the coupling of two or more 3D models with the LP model, and substantially lessen the coupling processing time. Realistic boundary conditions and Navier-Stokes equations in healthy and stenosed models of carotid artery bifurcation（CAB） were used to investigate the unsteady Newtonian blood flow velocity distribution in the internal carotid artery（ICA）. The present simulation results agree well with previous experimental and numerical studies. The outcomes of a pure LP model and those of the coupled 3D healthy model were found to be nearly the same in both cases. Concerning the various analyzed 3D zones, the stenosis growth in the ICA was not found as a crucial factor in determining the absorbing boundary conditions.This paper demonstrates the advantages of coupling local and systemic models to comprehend physiological diseases of the cardiovascular system.展开更多
Based on some recent results for interlacing eigenvalue intervals from 1-parameter families of se- quences of eigenvalue inequalities, a new method is given to solving the index problem for Sturm-Liouville eigenvalues...Based on some recent results for interlacing eigenvalue intervals from 1-parameter families of se- quences of eigenvalue inequalities, a new method is given to solving the index problem for Sturm-Liouville eigenvalues for coupled self-adjoint boundary conditions in the regular case. The key is a new characteristic principle for indices for Sturm-Liouville eigenvalues. The algorithm corresponding on the characteristic princi- ple are discussed, and numerical examples are presented to illustrate the theoretical results and show that the algorithm is valid.展开更多
基金the Iranian National Science Foundation (INSF) for the financial support to this project (87040150)
文摘This study describes a multidimensional 3D/lumped parameter（LP） model which contains appropriate inflow/outflow boundary conditions in order to model the entire human arterial trees. A new extensive LP model of the entire arterial network（48 arteries） was developed including the effect of vessel diameter tapering and the parameterization of resistance, conductor and inductor variables. A computer aided-design（CAD） algorithm was proposed to effciently handle the coupling of two or more 3D models with the LP model, and substantially lessen the coupling processing time. Realistic boundary conditions and Navier-Stokes equations in healthy and stenosed models of carotid artery bifurcation（CAB） were used to investigate the unsteady Newtonian blood flow velocity distribution in the internal carotid artery（ICA）. The present simulation results agree well with previous experimental and numerical studies. The outcomes of a pure LP model and those of the coupled 3D healthy model were found to be nearly the same in both cases. Concerning the various analyzed 3D zones, the stenosis growth in the ICA was not found as a crucial factor in determining the absorbing boundary conditions.This paper demonstrates the advantages of coupling local and systemic models to comprehend physiological diseases of the cardiovascular system.
基金Supported by the National Natural Science Foundation of China(No.11361039 and 11161030)the Natural Science Foundation of Inner Mongolia Province,China(No.2013MS0116)
文摘Based on some recent results for interlacing eigenvalue intervals from 1-parameter families of se- quences of eigenvalue inequalities, a new method is given to solving the index problem for Sturm-Liouville eigenvalues for coupled self-adjoint boundary conditions in the regular case. The key is a new characteristic principle for indices for Sturm-Liouville eigenvalues. The algorithm corresponding on the characteristic princi- ple are discussed, and numerical examples are presented to illustrate the theoretical results and show that the algorithm is valid.
