Nonlinear resonances of an idealized saccular aneurysm Articles uri icon

publication date

  • December 2017

start page

  • 154

end page

  • 166


  • 121

International Standard Serial Number (ISSN)

  • 0020-7225

Electronic International Standard Serial Number (EISSN)

  • 1879-2197


  • This paper investigates the occurrence of dynamic instabilities in idealized intracranial saccular aneurysms subjected to pulsatile blood flow and surrounded by cerebral spinal fluid. The problem has been approached extending the original 2D model of Shah and Humphrey (1999) to a 3D framework. The justification for using a 3D formulation arises from the works of Suzuki and Ohara (1978), MacDonald et al. (2000) and Costalat et al. (2011) who showed experimental evidences of intracranial aneurysms with a ratio between wall thickness and inner radius larger that 0.1. Two different material models have been used to describe the mechanical behaviour of the aneurysmal wall: Neo-Hookean and Mooney-Rivlin. To the authors' knowledge, for the first time in literature, the dynamic response of the aneurysm has been analysed using complete nonlinear resonance diagrams that have been obtained from a numerical procedure specifically designed for that purpose. Our numerical results show that, for a wide range of wall thicknesses and both constitutive models considered, the saccular aneurysms are dynamically stable within the range of frequencies associated to the normal heart rates, which confirms previous results of Shah and Humphrey (1999). On the other hand, our results also show that the geometric and material nonlinearities of the problem could bring closer than expected the resonance frequencies of the aneurysm to the frequencies of the pulsatile blood flow. (C) 2017 Elsevier Ltd. All rights reserved.


  • Mechanical Engineering
  • Medicine


  • intracranial aneurysm; finite elasticity; constitutive model; nonlinear resonances