Finite strain elastodynamics of intracranial saccular aneurysms

Shah, Aamir S.; Humphrey, Jay D.

doi:10.1016/s0021-9290(99)00030-5

Cited by 73 publications

(81 citation statements)

References 25 publications

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“…For this sub-class, however, one can prove analytically that lesions described by either Fung or Skalak-Tozeren-Zarda-Chien (STZC) type stress-strain relations cannot exhibit a limit point instability (23,106,107); this is in contrast to rubber-like spherical membranes, which typically exhibit limit points (22). Because static instabilities tend to organize dynamic instabilities, it was not surprising that one can also show both analytically (given small perturbations about various equilibria) and numerically (using methods of nonlinear dynamics and a Runge-Kutta solution of a new nonlinear differential equation of the elastodynamics) that nearly spherical lesions tend to be dynamically stable (107,108). Hence, at least for this sub-class of ISAs, and probably more generally, neither quasi-static nor dynamic instabilities appear to be responsible for enlargement.…”

Section: Prior Biomechanical Analyses Intracranial Saccular Aneurysm mentioning

confidence: 99%

Intracranial and Abdominal Aortic Aneurysms: Similarities, Differences, and Need for a New Class of Computational Models

Humphrey

Taylor

2008

Annu. Rev. Biomed. Eng.

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266

237

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Intracranial and abdominal aortic aneurysms result from different underlying disease processes and exhibit different rupture potentials, yet they share many histopathological and biomechanical characteristics. Moreover, as in other vascular diseases, hemodynamics and wall mechanics play important roles in the natural history and possible treatment of these two types of lesions. The goals of this review are twofold: first, to contrast the biology and mechanics of intracranial and abdominal aortic aneurysms to emphasize that separate advances in our understanding of each disease can aid in our understanding of the other disease, and second, to suggest that research on the biomechanics of aneurysms must embrace a new paradigm for analysis. That is, past biomechanical studies have provided tremendous insight but have progressed along separate lines, focusing on either the hemodynamics or the wall mechanics. We submit that that there is a pressing need to couple in a new way the separate advances in vascular biology, medical imaging, and computational biofluid and biosolid mechanics to understand better the mechanobiology, pathophysiology, and treatment of these lesions, which continue to be responsible for significant morbidity and mortality. We shall refer to this needed new class of computational tools as Fluid-Solid-Growth (FSG) Models.

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Section: Prior Biomechanical Analyses Intracranial Saccular Aneurysm mentioning

confidence: 99%

Intracranial and Abdominal Aortic Aneurysms: Similarities, Differences, and Need for a New Class of Computational Models

Humphrey

Taylor

2008

Annu. Rev. Biomed. Eng.

Self Cite

266

237

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“…Recently, interest in the strain distribution in inflating membranes has extended to human pathology, e.g., aneurysms. 2,3 However, investigations of the strain distribution in membranes are rare, 4 and studies of crack growth in biaxial deformation yield conflicting conclusions. 5,6 The present study was motivated by the development of an inflated rubber disk as an ejection system for torpedoes on US Navy Virginia-class submarines.…”

Section: Introductionmentioning

confidence: 99%

Strains in an Inflated Rubber Sheet

Mott

Roland

Hassan

2003

Rubber Chemistry and Technology

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A technique to measure the strain distribution of an inflated membrane is described, and applied to natural rubber inflated to pole biaxial strains of 12%, 26%, and 33%. The radial strain was found to be nearly constant over the entire surface, while the circumferential strain falls to zero at the edge. Thus, biaxial deformation is limited to a narrow region in the vicinity of the pole. These results are quite different from (the very limited) data published previously. The stressstrain behavior was also measured in uniaxial tension, and the strain distribution of the inflated membrane calculated using finite elements. The experiment results and the modeling were in good agreement.

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“…The blood pressure is modeled using finite Fourier series since we consider the behavior to be pulsatile [10,17,18]:…”

Section: Model Of the Blood Pressurementioning

confidence: 99%

“…Different groups of researchers had identified the elastodynamics of the arterial wall interaction with the blood flow to be the main reason for the rupture of an aneurysm [7][8][9]. A coupled fluid-structure model to understand the elastodynamics better was later studied more extensively [10][11][12][13]. These models introduced mathematical models of increasing complexity for intracranial saccular aneurysms that described the coupled interaction between blood, arterial wall, and cerebral spinal fluid (CSF).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics and Analysis of Intracranial Saccular Aneurysms with Growth and Remodeling

Badgaish

Lin

Seshaiyer

2016

Journal of Nonlinear Dynamics

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A new mathematical model for the interaction of blood flow with the arterial wall surrounded by cerebral spinal fluid is developed with applications to intracranial saccular aneurysms. The blood pressure acting on the inner arterial wall is modeled via a Fourier series, the arterial wall is modeled as a spring-mass system incorporating growth and remodeling, and the surrounding cerebral spinal fluid is modeled via a simplified one-dimensional compressible Euler equation with inviscid flow and negligible nonlinear effects. The resulting nonlinear coupled fluid-structure interaction problem is analyzed and a perturbation technique is employed to derive the first-order approximation solution to the system. An analytical solution is also derived for the linearized version of the problem using Laplace transforms. The solutions are validated against related work from the literature and the results suggest the biological significance of the inclusion of the growth and remodeling effects on the rupture of intracranial aneurysms.

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Finite strain elastodynamics of intracranial saccular aneurysms

Cited by 73 publications

References 25 publications

Intracranial and Abdominal Aortic Aneurysms: Similarities, Differences, and Need for a New Class of Computational Models

Intracranial and Abdominal Aortic Aneurysms: Similarities, Differences, and Need for a New Class of Computational Models

Strains in an Inflated Rubber Sheet

Nonlinear Dynamics and Analysis of Intracranial Saccular Aneurysms with Growth and Remodeling

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