Skip to main content
SpringerLink
Log in

Patient-Specific Wall Stress Analysis in Cerebral Aneurysms Using Inverse Shell Model

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

Stress analyses of patient-specific vascular structures commonly assume that the reconstructed in vivo configuration is stress free although it is in a pre-deformed state. We submit that this assumption can be obviated using an inverse approach, thus increasing accuracy of stress estimates. In this paper, we introduce an inverse approach of stress analysis for cerebral aneurysms modeled as nonlinear thin shell structures, and demonstrate the method using a patient-specific aneurysm. A lesion surface derived from medical images, which corresponds to the deformed configuration under the arterial pressure, is taken as the input. The wall stress in the given deformed configuration, together with the unstressed initial configuration, are predicted by solving the equilibrium equations as opposed to traditional approach where the deformed geometry is assumed stress free. This inverse approach also possesses a unique advantage, that is, for some lesions it enables us to predict the wall stress without accurate knowledge of the wall elastic property. In this study, we also investigate the sensitivity of the wall stress to material parameters. It is found that the in-plane component of the wall stress is indeed insensitive to the material model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

FIGURE 1
FIGURE 2
FIGURE 3
FIGURE 4
FIGURE 5
FIGURE 6

Similar content being viewed by others

References

  1. Brisman, J. L., J. K. Song, and D. W. Newell. Cerebral aneurysms. N. Engl. J. Med. 355:928–939, 2006.

    Article  CAS  PubMed  Google Scholar 

  2. David, G., and J. D. Humphrey. Further evidence for the dynamic stability of intracranial saccular aneurysms. J. Biomech. 36:1143–1150, 2003.

    Article  CAS  PubMed  Google Scholar 

  3. Elger, D. F., D. M. Blackketter, R. S. Budwig, and K. H. Johansen. The influence of shape on the stresses in model abdominal aortic aneurysms. J. Biomech. Eng. Trans. ASME 118:326–332, 1996.

    Article  CAS  Google Scholar 

  4. Humphrey, J. D., and P. B. Canham. Structure, mechanical properties, and mechanics of intracranial saccular aneurysms. J. Elast. 61:49–81, 2000.

    Article  Google Scholar 

  5. Humphrey, J. D., and S. K. Kyriacou. The use of laplace’s equation in aneurysms mechanics. Neurol. Res. 18:204–208, 1996.

    CAS  PubMed  Google Scholar 

  6. Humphrey, J. D., R. K. Strumpf, and F. C. P. Yin. Determination of a constitutive relation for passive myocardium. I. A new functional form. ASME J. Biomech. Eng. 112(3):333–339, 1990.

    Article  CAS  Google Scholar 

  7. Humphrey, J. D., R. K. Strumpf, and F. C. P. Yin. Determination of a constitutive relation for passive myocardium. II. Parameter-estimation. ASME J. Biomech. Eng. 112(3):340–346, 1990.

    Article  CAS  Google Scholar 

  8. Lu, J., and X. Zhao. Pointwise identification of elastic properties in nonlinear hyperelastic membranes. Part I: theoretical and computational developments. J. Appl. Mech. 76:061013/1–061013/10, 2009.

    Article  Google Scholar 

  9. Kim, H., K. B. Chandran, M. S. Sacks, and J. Lu. An experimentally derived stress resultant shell model for heart valve dynamic simulations. Ann. Biomed. Eng. 35(1):30–44, 2007.

    Article  PubMed  Google Scholar 

  10. Kim, H., J. Lu, M. S. Sacks, and K. B. Chandran. Dynamic simulation of bioprosthetic heart valves using a stress resultant shell model. Ann. Biomed. Eng. 36:262–275, 2008.

    Article  PubMed  Google Scholar 

  11. Kyriacou, S. K., and J. D. Humphrey. Influence of size, shape and properties on the mechanics of axisymmetric saccular aneurysms. J. Biomech. 29:1015–1022, 1996.

    Article  CAS  PubMed  Google Scholar 

  12. Lu, J., X. Zhou, and M. L. Raghavan. Computational method of inverse elastostatics for anisotropic hyperelastic solids. Int. J. Numer. Methods Eng. 69:1239–1261, 2007.

    Article  Google Scholar 

  13. Lu, J., X. Zhou, and M. L. Raghavan. Inverse elastostatic stress analysis in pre-deformed biological structures: demonstration using abdominal aortic aneurysm. J. Biomech. 40:693–696, 2007.

    Article  PubMed  Google Scholar 

  14. Lu, J., X. Zhou, and M. L. Raghavan. Inverse method of stress analysis for cerebral aneurysms. Biomech. Model. Mechanobiol. 7:477–486, 2008.

    Article  PubMed  Google Scholar 

  15. Ma, B., R. E. Harbaugh, and M. L. Raghavan. Three-dimensional geometrical characterization of cerebral aneurysms. Ann. Biomed. Eng. 32:264–273, 2004.

    Article  PubMed  Google Scholar 

  16. Ma, B., J. Lu, R. E. Harbaugh, and M. L. Raghavan. Nonlinear anisotropic stress analysis of anatomically realistic cerebral aneurysms. ASME J. Biomed. Eng. 129:88–99, 2007.

    Article  Google Scholar 

  17. Mirnajafi, A., J. Raymer, M. J. Scott, and M. S. Sacks. The effects of collagen fiber orientation on the flexural properties of pericardial heterograft biometerials. Biometerials 26:795–804, 2005.

    Article  CAS  Google Scholar 

  18. Naghdi, P. M. The theory of plates and shells. In: Handbuch der Physik, vol. VIa/2, edited by C. Truesdell. Berlin: Springer-Verlag, 1972, pp. 425–640.

    Google Scholar 

  19. Sacks, M. S. Biaxial mechanical evaluation of planar biological materials. J. Elast. 61:199–246, 2000.

    Article  Google Scholar 

  20. Schieck, B., W. Pietraszkiewicz, and H. Stumpf. Theory and numerical analysis of shells undergoing large elastic strains. Int. J. Solids Struct. 29:689–709, 1992.

    Article  Google Scholar 

  21. Seshaiyer, P., and J. D. Humphrey. A sub-domain inverse finite element characterization of hyperelastic membranes including soft tissues. J. Biomech. Eng. Trans. ASME 125:363–371, 2003.

    Article  Google Scholar 

  22. Seshaiyer, P., F. P. K. Hsu, A. D. Shah, S. K. Kyriacou, and J. D. Humphrey. Multiaxial mechanical behavior of human saccular aneurysms. Comput. Methods Biomed. Eng. 4:281–289, 2001.

    Article  Google Scholar 

  23. Shah, A. D., and J. D. Humphrey. Finite strain elastodynamics of intracranial saccular aneurysms. J. Biomech. 32:593–599, 1999.

    Article  CAS  PubMed  Google Scholar 

  24. Shah, A. D., J. L. Harris, S. K. Kyriacou, and J. D. Humphrey. Further roles of geometry and properties in the mechanics of saccular aneurysms. Comput. Methods Biomech. Biomed. Eng. 1:109–121, 1998.

    Google Scholar 

  25. Simmonds, J. G. The strain energy density of rubber-like shells. Int. J. Solids Struct. 21:67–77, 1985.

    Article  Google Scholar 

  26. Simo, J. C. On a stress resultant geometrically exact shell model. Part VII: shell intersections with 5/6-dof finite element formulations. Comput. Methods Appl. Mech. Eng. 108:319–339, 1993.

    Article  Google Scholar 

  27. Simo, J. C., and D. D. Fox. On a stress resultant geometrically exact shell model. Part I. Formulation and optimal parametrization. Comput. Methods Appl. Mech. Eng. 72(3):267–304, 1989.

    Article  Google Scholar 

  28. Simo, J. C., and D. D. Fox. On a stress resultant geometrically exact shell model. Part II: the linear theory; computational aspects. Comput. Methods Appl. Mech. Eng. 73:53–92, 1989.

    Article  Google Scholar 

  29. Simo, J. C., D. D. Fox, and M. S. Rifai. On a stress resultant geometrically exact shell model. Part III: computational aspects of the nonlinear-theory. Comput. Methods Appl. Mech. Eng. 79:21–70, 1990.

    Article  Google Scholar 

  30. Taylor, R. L. FEAP User Manual: v7.5. Technical Report. Berkeley: Department of Civil and Environmental Engineering, University of California, 2003.

  31. Zhao, X., X. Chen, and J. Lu. Pointwise identification of elastic properties in nonlinear hyperelastic membranes. Part II: experimental validation. J. Appl. Mech. 76:061014/1–061014/8, 2009.

    Article  CAS  Google Scholar 

  32. Zhou, X., and J. Lu. Inverse formulation for geometrically exact stress resultant shells. Int. J. Numer. Methods Eng. 74:1278–1302, 2008.

    Article  Google Scholar 

Download references

Acknowledgments

The work was funded by the National Science Foundation Grant CMS 03-48194 and the NIH(NHLBI) Grant 1R01HL083475-01A2. The supports are gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Center for Computer Aided Design, The University of Iowa, Iowa City, IA, 52242, USA

    Xianlian Zhou & Jia Lu

  2. Department of Biomedical Engineering, The University of Iowa, Iowa City, IA, 52242, USA

    Madhavan L. Raghavan

  3. Departments of Neurosurgery, and Engineering Science and Mechanics, Penn State University, Hershey, PA, 17033, USA

    Robert E. Harbaugh

Authors
  1. Xianlian Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Madhavan L. Raghavan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Robert E. Harbaugh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jia Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jia Lu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, X., Raghavan, M.L., Harbaugh, R.E. et al. Patient-Specific Wall Stress Analysis in Cerebral Aneurysms Using Inverse Shell Model. Ann Biomed Eng 38, 478–489 (2010). https://doi.org/10.1007/s10439-009-9839-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-009-9839-2

Keywords

Search

Navigation