×

A computational strategy for prestressing patient-specific biomechanical problems under finite deformation. (English) Zbl 1180.92009

Summary: In simulations of biomechanical structures the patient-specific geometry of the object of interest is very often reconstructed from in vivo medical imaging such as CT scans. Such geometries therefore represent a deformed configuration stressed by typical in vivo conditions. Commonly, such structures are considered stress free in simulations.
We present and compare two methods to introduce a physically meaningful stress/strain state to the obtained geometry for simulations in the finite strain regime and demonstrate the necessity of such prestressing techniques. One method is based on an inverse design analysis to calculate a stress-free reference configuration. The other method developed here is based on a modified updated Lagrangian formulation. The formulation of both methods is provided in detail and implementation issues are discussed. Applicability and accurateness of both approaches are compared and evaluated utilizing an analytical aorta model and fully three-dimensional patient-specific abdominal aortic aneurysm structures in the finite strain regime.

MSC:

92C10 Biomechanics
92C50 Medical applications (general)
74S30 Other numerical methods in solid mechanics (MSC2010)
92C55 Biomedical imaging and signal processing
68U20 Simulation (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Humphrey, Intracranial and abdominal aortic aneurysms: similarities, differences, and need for a new class of computational models, Annual Review of Biomedical Engineering 10 pp 221– (2008)
[2] Vorp, Biomechanics of abdominal aortic aneurysms, Journal of Biomechanics 40 pp 1887– (2007)
[3] Lasheras, The biomechanics of arterial aneurysms, Annual Review of Fluid Mechanics 39 pp 293– (2007) · Zbl 1296.76188
[4] Raghavan, Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability, Journal of Biomechanics 33 pp 475– (2000)
[5] Fillinger, Prediction of rupture risk in abdominal aortic aneurysm during observation: wall stress versus diameter, Journal of Vascular Surgery 37 pp 724– (2003)
[6] Fillinger, In vivo analysis of mechanical wall stress and abdominal aortic aneurysm rupture risk, Journal of Vascular Surgery 36 pp 589– (2002)
[7] Raghavan, Automated methodology for determination of stress distribution in human abdominal aortic aneurysm, Journal of Biomechanical Engineering 127 pp 868– (2005)
[8] Govindjee, Computational methods for inverse finite elastostatics, Computer Methods in Applied Mechanics and Engineering 136 pp 47– (1996) · Zbl 0918.73117
[9] Govindjee, Computational methods for inverse deformations in quasi-incompressible finite elasticity, International Journal for Numerical Methods in Engineering 43 pp 821– (1998) · Zbl 0937.74064
[10] Tezduyar, Arterial fluid mechanics modeling with the stabilized space-time fluid-structure interaction technique, International Journal for Numerical Methods in Fluids 57 pp 601– (2008) · Zbl 1230.76054
[11] Torii, Fluid-structure interaction modeling of a patient-specific cerebral aneurysm: influence of structural modeling, Computational Mechanics 43 pp 151– (2008) · Zbl 1169.74032
[12] Chadwick, Application of an energy-momentum tensor in elastostatics, Journal of Elasticity 5 pp 249– (1975) · Zbl 0328.73006
[13] Shield, Inverse deformation results in finite elasticity, Zeitschrift für Angewandte Mathematik und Physik 18 pp 381– (1967) · Zbl 0146.46103
[14] Lu, Inverse elastostatic stress analysis in pre-deformed biological structures: demonstration using abdominal aortic aneurysms, Journal of Biomechanics 40 pp 693– (2007)
[15] Lu, Inverse method of stress analysis for cerebral aneurysms, Biomechanics and Modelling in Mechanobiology 7 pp 477– (2008)
[16] Fachinotti, Finite element modelling of inverse design problems in large deformation anisotropic hyperelasticity, International Journal for Numerical Methods in Engineering 74 pp 894– (2008) · Zbl 1158.74369
[17] Holzapfel, Nonlinear Solid Mechanics (2000)
[18] Tezduyar, Sequentially-coupled arterial fluid-structure interaction (scafsi) technique, Computer Methods in Applied Mechanics and Engineering (2008) · Zbl 1229.74100 · doi:10.1186/1475-925X-6-38
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.