Skip to main content

Advertisement

SpringerLink
Log in

Characterization of the Highly Nonlinear and Anisotropic Vascular Tissues from Experimental Inflation Data: A Validation Study Toward the Use of Clinical Data for In-Vivo Modeling and Analysis

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

Abstract

We study whether an inverse modeling approach is applicable for characterizing vascular tissue subjected to various levels of internal pressure and axial stretch that approximate in-vivo conditions. To compensate for the limitation of axial-displacement/pressure/diameter data typical of clinical data, which does not provide information about axial force, we propose to constrain the ratio of axial to circumferential elastic moduli to a typical range. Vessel wall constitutive behavior is modeled with a transversely isotropic hyperelastic equation that accounts for dispersed collagen fibers. A single-layer and a bi-layer approximation to vessel ultrastructure are examined, as is the possibility of obtaining the fiber orientation as part of the optimization. Characterization is validated against independent pipette-aspiration biaxial data on the same samples. It was found that the single-layer model based on homogeneous wall assumption could not reproduce the validation data. In contrast, the constrained bi-layer model was in excellent agreement with both types of experimental data. Due to covariance, estimations of fiber angle were slightly outside of the normal range, which can be resolved by predefining the angles to normal values. Our approach is relatively invariant to a constant or a variable axial response. We believe that it is suitable for in-vivo characterization.

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
FIGURE 7

Similar content being viewed by others

References

  1. Bathe K. J. (2005) ADINA System 8.3 Release Notes. ADINA R & D Inc, Watertown

    Google Scholar 

  2. Beller C. J., Labrosse M. R., Thubrikar M. J., Robicsek F. (2007) Finite element modeling of the thoracic aorta: including aortic root motion to evaluate the risk of aortic dissection. J. Med. Eng. Technol. 16:1–4

    Google Scholar 

  3. Beller C. J., Labrosse M. R., Thubrikar M. J., Robicsek F. (2004) Role of aortic root motion in the pathogenesis of aortic dissection. Circulation 109:763-769

    Article  PubMed  Google Scholar 

  4. Beller C. J., Labrosse M. R., Thubrikar M. J., Szabo G., Robicsek F., Hagl S. (2005) Increased aortic wall stress in aortic insufficiency: clinical data and computer model. Eur. J. Cardiothorac. Surg. 27:270–275

    Article  PubMed  Google Scholar 

  5. Beller C. J., Labrosse M. R., Thubrikar M. J., Szabo G., Robicsek F., Hagl S. (2005) Are there surgical implications to aortic root motion? J. Heart Valve Dis. 14:610–615

    PubMed  Google Scholar 

  6. Billiar K. L., Sacks M. S. (1997) A method to quantify the fiber kinematics of planar tissues under biaxial stretch. J. Biomech. 30:753–756

    Article  PubMed  CAS  Google Scholar 

  7. Bogren H. G., Buonocore M. H. (1999) 4D magnetic resonance velocity mapping of blood flow patterns in the aorta in young vs. elderly normal subjects. J. Magn. Reson. Imaging 10:861–869

    Article  PubMed  CAS  Google Scholar 

  8. Cacho F., Doblaré M., Holzapfel G. A. (2007) A procedure to simulate coronary artery bypass graft surgery. Med. Biol. Eng. Comput. 45:819–827

    Article  PubMed  Google Scholar 

  9. Chen H. Y., Einstein D. R., Chen K., Vesely I. (2005) Computational modeling of vascular clamping: a step toward simulating surgery. Conf. Proc. IEEE Eng. Med. Biol. Soc. 1:302–303

    PubMed  CAS  Google Scholar 

  10. Cook, R. D., Malkus, D. S., Plesha, M. E., and Witt, R. J. Basic elements. In: Concepts and Applications of Finite Element Analysis, 4th edn. New York: John Wiley & Sons, Inc., pp. 78–135.

  11. Davis N. P., Han H. C., Wayman B., Vito R. (2005) Sustained axial loading lengthens arteries in organ culture. Ann. Biomed. Eng. 33:867–877

    Article  PubMed  Google Scholar 

  12. Ding Z., Friedman M. H. (2000) Dynamics of human coronary arterial motion and its potential role in coronary atherogenesis. J. Biomech. Eng. 122:488–492

    Article  PubMed  CAS  Google Scholar 

  13. Dobrin P. B. (1986) Biaxial anisotropy of dog carotid artery: estimation of circumferential elastic modulus. J. Biomech. 19:351–358

    Article  PubMed  CAS  Google Scholar 

  14. Draney M. T., Zarins C. K., Taylor C. A. (2005) Three-dimensional analysis of renal artery bending motion during respiration. J. Endovasc. Ther. 12:380–386

    Article  PubMed  Google Scholar 

  15. Einstein D. R., Freed A. D., Stander D., Stander N., Fata B., Vesely I. (2005) Inverse parameter fitting of biological tissues: a response surface approach. Ann. Biomed. Eng. 33:1819–1830

    Article  PubMed  Google Scholar 

  16. Freed A. D., Einstein D. R., Vesely I. (2005) Invariant formulation for dispersed transverse isotropy in aortic heart valves: an efficient means for modeling fiber splay. Biomech. Model. Mechanobiol. 4:100–117

    Article  PubMed  Google Scholar 

  17. Gasser T. C., Schulze-Bauer C. A., Holzapfel G. A. (2002) A three-dimensional finite element model for arterial clamping. J. Biomech. Eng. 124:355–363

    Article  PubMed  Google Scholar 

  18. Hassan T., Timofeev E. V., Saito T., Shimizu H., Ezura M., Tominaga T., Takahashi A., Takayama K. (2004) Computational replicas: anatomic reconstructions of cerebral vessels as volume numerical grids at three-dimensional angiography. AJNR Am. J. Neuroradiol. 25:1356–1365

    PubMed  Google Scholar 

  19. Hayashi K. (2004) Mechanical properties of soft tissues and arterial walls. In: Holzapfel G. A., Ogden R. W. (eds) Biomechanics of Soft Tissue in Cardiovascular Systems. Springer, Wien, New York, New York, pp. 15–64

    Google Scholar 

  20. Holzapfel G. A. (2006) Determination of material models for arterial walls from uniaxial extension tests and histological structure. J. Theor. Biol. 238:290–302

    PubMed  Google Scholar 

  21. Holzapfel G. A., Stadler M., Schulze-Bauer C. A. (2002) A layer-specific three-dimensional model for the simulation of balloon angioplasty using magnetic resonance imaging and mechanical testing. Ann. Biomed. Eng. 30:753–767

    Article  PubMed  Google Scholar 

  22. Honda T., Yano K., Matsuoka H., Hamada M., Hiwada K. (1994) Evaluation of aortic distensibility in patients with essential hypertension by using cine magnetic resonance imaging. Angiology 45:207–212

    Article  PubMed  CAS  Google Scholar 

  23. Humphrey J. D. (1995) Mechanics of the arterial wall: review and directions. Crit. Rev. Biomed. Eng. 23:1–162

    PubMed  CAS  Google Scholar 

  24. Humphrey J. D., Kang T., Sakarda P., Anjanappa M. (1993) Computer-aided vascular experimentation: a new electromechanical test system. Ann. Biomed. Eng. 21:33–43

    Article  PubMed  CAS  Google Scholar 

  25. Kaw, A. K. Macromechanical analysis of lamina. In: Mechanics of Composite Materials. Boca Raton: CRC Press, pp. 53–148, 1997

  26. Kozerke S., Scheidegger M. B., Pedersen E. M., Boesiger P. (1999) Heart motion adapted cine phase-contrast flow measurements through the aortic valve. Magn. Reson. Med. 42:970–978

    Article  PubMed  CAS  Google Scholar 

  27. L’Italien G. J., Chandrasekar N. R., Lamuraglia G. M., Pevec W. C., Dhara S., Warnock D. F., Abbott W. M. (1994) Biaxial elastic properties of rat arteries in vivo: influence of vascular wall cells on anisotropy. Am. J. Physiol. 267:574–579

    Google Scholar 

  28. Lanir Y., Fung Y. C. (1974) Two-dimensional mechanical properties of rabbit skin. I. Experimental system. J. Biomech. 7:29–34

    Article  PubMed  CAS  Google Scholar 

  29. Lanir Y., Fung Y.C. (1974) Two-dimensional mechanical properties of rabbit skin. II. Experimental results. J. Biomech. 7:171–182

    Article  PubMed  CAS  Google Scholar 

  30. Lu X., Pandit A., Kassab G. S. (2004) Biaxial incremental homeostatic elastic moduli of coronary artery: two-layer model. Am. J. Physiol. Heart Circ. Physiol. 287:1663–1669

    Article  CAS  Google Scholar 

  31. Mercer J. L. (1969) Movement of the aortic annulus. Br. J. Radiol. 42:623–626

    Article  PubMed  CAS  Google Scholar 

  32. Migliavacca F., Pennati G., Di Martino E., Dubini G., Pietrabissa R. (2002) Pressure drops in a distensible model of end-to-side anastomosis in systemic-to-pulmonary shunts. Comput. Methods Biomech. Biomed. Engin. 5:243–248

    Article  PubMed  Google Scholar 

  33. Monos E., Raffai G., Contney S. J., Stekiel W. J., Cowley A. W. Jr. (2001) Axial stretching of extremity artery induces reversible hyperpolarization of smooth muscle cell membrane in vivo. Acta. Physiol. Hung. 88:197–206

    Article  PubMed  CAS  Google Scholar 

  34. Myers R. H., Montgomery D. C. (2002) Response Surface Methodology: Progress and Product Optimization Using Designed Experiments. Wiley, New York

    Google Scholar 

  35. Ohashi T., Abe H., Matsumoto T., Sato M. (2005) Pipette aspiration technique for the measurement of nonlinear and anisotropic mechanical properties of blood vessel walls under biaxial stretch. J. Biomech. 38:2248–2256

    Article  PubMed  Google Scholar 

  36. Roux W. J., Stander N., Haftka R. T. (1998) Response surface approximations for structural optimization. Int. J. Numer. Methods Eng. 42:517–534

    Article  Google Scholar 

  37. Sacks M. S. (2000) Biaxial mechanical evaluation of planar biological materials. J. Elast. 61:199–246

    Article  Google Scholar 

  38. Sacks M. S. (2003) Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues. J. Biomech. Eng. 125:280–287

    Article  PubMed  Google Scholar 

  39. Sacks M. S., Sun W. (2003) Multiaxial mechanical behavior of biological materials. Annu. Rev. Biomed. Eng. 5:251–284

    Article  PubMed  CAS  Google Scholar 

  40. Schulze-Bauer C. A., Holzapfel G. A. (2003) Determination of constitutive equations for human arteries from clinical data. J. Biomech. 36:165–169

    Article  PubMed  CAS  Google Scholar 

  41. Silver, F. H. Mechanical properties of connective tissues. In: Biological Materials: Structure, Mechanical Properties, and Modeling of Soft Tissues. New York: New York University Press, 1987, pp. 164–195

  42. Sipkema P., van der Linden P. J., Yin F. C. (2003) Effect of cyclic axial stretch of rat arteries on endothelial cytoskeletal morphology and vascular reactivity. J. Biomech. 36:653–659

    Article  PubMed  Google Scholar 

  43. Stander N., Craig K. J. (2002) On the robustness of a simple domain reduction scheme for simulation-based optimization. Eng. Comput. 19:431–450

    Article  Google Scholar 

  44. Stander N., Craig K. J., Müllerschön H., Reichert R. (2005) Material identification in structural optimization using response surfaces. Struct. Multidisc. Optim. 29:93–102

    Article  Google Scholar 

  45. Stander N., Roux W., Eggleston T., Craig K. (2004) LS-OPT User’s Manual: A Design Optimization and Probabilistic Analysis Tool for the Engineering Analyst. LSTC, Livermore

    Google Scholar 

  46. Steele B. N., Wan J., Ku J. P., Hughes T. J., Taylor C. A. (2003) In vivo validation of a one-dimensional finite-element method for predicting blood flow in cardiovascular bypass grafts. IEEE Trans. Biomed. Eng. 50:649–656

    Article  PubMed  Google Scholar 

  47. Stefanadis C., Stratos C., Vlachopoulos C., Marakas S., Boudoulas H., Kallikazaros I., Tsiamis E., Toutouzas K., Sioros L., Toutouzas P. (1995) Pressure–diameter relation of the human aorta. A new method of determination by the application of a special ultrasonic dimension catheter. Circulation 92:2210–2219

    PubMed  CAS  Google Scholar 

  48. Sussman T., Bathe K. J. (1987) A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Comput. Struct. 26:357–409

    Article  Google Scholar 

  49. Takamizawa K., Hayashi K. (1987) Strain energy density function and uniform strain hypothesis for arterial mechanics. J. Biomech. 20:7–17

    Article  PubMed  CAS  Google Scholar 

  50. Tang D., Yang C., Kobayashi S., Ku D. N. (2001) Steady flow and wall compression in stenotic arteries: a three-dimensional thick-wall models with fluid-wall interactions. J. Biomech. Eng. 123:548–557

    Article  PubMed  CAS  Google Scholar 

  51. Tozzi P., Hayoz D., Oedman C., Mallabiabarrena I., Von Segesser L. K. (2001) Systolic axial artery length reduction: an overlooked phenomenon in vivo. Am. J. Physiol. Heart Circ. Physiol. 280:2300–2305

    Google Scholar 

  52. Van Loon P. (1977) Length-force and volume-pressure relationships of arteries. Biorheology 14:181–201

    PubMed  Google Scholar 

  53. von Maltzahn W. W., Warriyar R. G., Keitzer W. F. (1984) Experimental measurements of elastic properties of media and adventitia of bovine carotid arteries. J. Biomech. 17:839–847

    Article  Google Scholar 

  54. Vorp D. A., Severyn D. A. Steed D. L., Webster M. W. (1996) A device for the application of cyclic twist and extension on perfused vascular segments. Am. J. Physiol. 270:787–795

    Google Scholar 

  55. Weizsäcker H. W., Lambert H., Pascale K. (1983) Analysis of the passive mechanical properties of rat carotid arteries. J. Biomech. 16:703–715

    Article  PubMed  Google Scholar 

  56. Weizsäcker H. W., Pinto J. G. (1988) Isotropy and anisotropy of the arterial wall. J. Biomech. 21:477–487

    Article  PubMed  Google Scholar 

  57. Wikström J., Holmberg A., Johansson L., Löfberg A. M., Smedby O., Karacagil S., Ahlström H. (2000) Gadolinium-enhanced magnetic resonance angiography, digital subtraction angiography and duplex of the iliac arteries compared with intra-arterial pressure gradient measurements. Eur. J. Vasc. Endovasc. Surg. 19:516–523

    Article  PubMed  Google Scholar 

  58. Zhou J., Fung Y. C. (1997) The degree of nonlinearity and anisotropy of blood vessel elasticity. Proc. Natl. Acad. Sci. U.S.A. 94:14255–14260

    Article  PubMed  CAS  Google Scholar 

  59. Zhu H., Friedman M. H. (2003) Relationship between the dynamic geometry and wall thickness of a human coronary artery. Arterioscler. Thromb. Vasc. Biol. 23:2260–2265

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Dr. Ivan Vesely and the Heart Valve Research Laboratory at Childrens Hospital Los Angeles for their financial support and vision. Dr. Einstein’s contribution was supported by NIH-NHLBI 1 R01 HL077921-01A2.

Author information

Authors and Affiliations

  1. Department of Biomedical Engineering, University of Southern California, Los Angeles, CA, USA

    Kinon Chen

  2. Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA, USA

    Bahar Fata

  3. Biological Monitoring & Modeling, MS P7-56, Pacific Northwest National Laboratory, Richland, WA, USA

    Daniel R. Einstein

Authors
  1. Kinon Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bahar Fata
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel R. Einstein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kinon Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, K., Fata, B. & Einstein, D.R. Characterization of the Highly Nonlinear and Anisotropic Vascular Tissues from Experimental Inflation Data: A Validation Study Toward the Use of Clinical Data for In-Vivo Modeling and Analysis. Ann Biomed Eng 36, 1668–1680 (2008). https://doi.org/10.1007/s10439-008-9541-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-008-9541-9

Keywords

Search

Navigation