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A Microstructurally Motivated Model of the Mechanical Behavior of Tissue Engineered Blood Vessels

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Abstract

Mechanical models have potential to guide the development and use of engineered blood vessels as well as other engineered tissues. This paper presents a microstructurally motivated, pseudoelastic, mechanical model of the biaxial mechanics of engineered vessels in the physiologic pressure range. The model incorporates experimentally measured densities and alignments of engineered collagen. Specifically, these microstructural and associated mechanical inputs were measured directly from engineered blood vessels that were cultured over periods of 5–7.5 weeks. To the best of our knowledge, this is the first successful application of either a phenomenological or a microstructurally motivated mechanical model to engineered vascular tissues. Model development revealed the need to use novel theoretical configurations to describe the strain history of engineered vessels. The constitutive equations developed herein suggested that collagen remodeled between 5 and 7.5 weeks during a 7.5-week culture period. This remodeling led to strain energies for collagen that differed with alignment, which likely resulted from undulations that varied with alignment. Finally, biaxial data emphasized that axial extensions increase stresses in engineered vessels in the physiologic pressure range, thereby providing a guideline for surgical use: engineered vessels should be implanted at appropriate axial extension to minimize adverse stress responses.

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References

  1. American Heart Association. Biostatistical Fact Sheet: Cardiovascular Procedures. American Heart Association, 2002

  2. Armentano R. L., J. Levenson, J. G. Barra, E. I. Cabrera Fischer, G. J. Breitbart, R. H. Pichel, A. Simon. Assessment of elastin and collagen contribution to aortic elasticity in conscious dogs. Am. J. Physiol. 260, H1870–H1877, 1991

    PubMed  CAS  Google Scholar 

  3. Baek S., R. L. Gleason, K. R. Rajagopal, J. D. Humphrey. Theory of small on large: potential utility in computations of fluid–solid interactions in arteries. Comput. Meth. Appl. Mech. Eng. 196, 3070–3078, 2007. doi:10.1016/j.cma.2006.06.018

    Article  Google Scholar 

  4. Bank A. J., H. Wang, J. E. Holte, K. Mullen, R. Shammas, S. H. Kubo. Contribution of collagen, elastin, and smooth muscle to in vivo human brachial artery wall stress and elastic modulus. Circulation 94, 3263–3270, 1996

    PubMed  CAS  Google Scholar 

  5. Barra J. G., R. L. Armentano, J. Levenson, E. I. Fischer Cabrera, R. H. Pichel, A. Simon. Assessment of smooth muscle contribution to descending thoracic aortic elastic mechanics in conscious dogs. Circ. Res. 73, 1040–1050, 1993

    PubMed  CAS  Google Scholar 

  6. Chuong C. J., Y. C. Fung. On residual stress in arteries. J. Biomech. Eng. 108, 189–192, 1986

    PubMed  CAS  Google Scholar 

  7. Dahl S. L. M., C. Rhim, Y. C. Song, L. E. Niklason. Mechanical properties and compositions of tissue engineered and native arteries. Ann. Biomed. Eng. 35, 348–355, 2007. doi:10.1007/s10439-006-9226-1

    Article  PubMed  Google Scholar 

  8. Dahl S. L. M., M. E. Vaughn, L. E. Niklason. An ultrastructural analysis of collagen in tissue engineered arteries. Ann. Biomed. Eng. 35, 1749–1755, 2007. doi:10.1007/s10439-007-9340-8

    Article  PubMed  Google Scholar 

  9. Davies A. H., T. R. Magee, R. N. Baird, E. Sheffield, M. Horrocks. Vein compliance: a preoperative indicator of vein morphology and of veins at risk of vascular graft stenosis. Br. J. Surg. 79, 1019–1021, 1992. doi:10.1002/bjs.1800791011

    Article  PubMed  CAS  Google Scholar 

  10. Doehring T. C., E. O. Carew, I. Vesely. The effect of strain rate on the viscoelastic response of aortic valve tissue: a direct-fit approach. Ann. Biomed. Eng. 32, 223–232, 2004. doi:10.1023/B:ABME.0000012742.01261.b0

    Article  PubMed  Google Scholar 

  11. Downs J., H. R. Halperin, J. Humphrey, F. Yin. An improved video-based computer tracking system for soft biomaterials testing. IEEE Trans. Biomed. Eng. 37, 903–907, 1990. doi:10.1109/10.58600

    Article  PubMed  CAS  Google Scholar 

  12. Driessen N. J., W. Wilson, C. V. Bouten, F. P. Baaijens. A computational model for collagen fibre remodelling in the arterial wall. J. Theor. Biol. 226, 53–64, 2004. doi:10.1016/j.jtbi.2003.08.004

    Article  PubMed  CAS  Google Scholar 

  13. Fung Y. C., K. Fronek, P. Patitucci. Pseudoelasticity of arteries and the choice of its mathematical expression. Am. J. Physiol. 237, H620–H631, 1979

    PubMed  CAS  Google Scholar 

  14. Fung J. C., W. Liu, W. J. de Ruijter, H. Chen, C. K. Abbey, J. W. Sedat, D. A. Agard. Toward fully automated high-resolution electron tomography. J. Struct. Biol. 116, 181–189, 1996. doi:10.1006/jsbi.1996.0029

    Article  PubMed  CAS  Google Scholar 

  15. Hokanson J., S. Yazdani. A constitutive model of the artery with damage. Mech. Res. Commun. 24, 151–159, 1997. doi:10.1016/S0093-6413(97)00007-4

    Article  Google Scholar 

  16. Holzapfel G. A., T. C. Gasser, R. W. Ogden. A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elasticity 61, 1–48, 2000. doi:10.1023/A:1010835316564

    Article  Google Scholar 

  17. Holzapfel G. A., T. C. Gasser, R. W. Ogden. Comparison of a multi-layer structural model for arterial walls with a Fung-type model, and issues of material stability. J. Biomech. Eng. 126, 264–275, 2004. doi:10.1115/1.1695572

    Article  PubMed  Google Scholar 

  18. Hu J. J., T. W. Fossum, M. W. Miller, H. Xu, J. C. Liu, J. D. Humphrey. Biomechanics of the porcine basilar artery in hypertension. Ann. Biomed. Eng. 35, 19–29, 2007. doi:10.1007/s10439-006-9186-5

    Article  PubMed  CAS  Google Scholar 

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

    PubMed  CAS  Google Scholar 

  20. Humphrey J. D. Remodeling of a collagenous tissue at fixed lengths. J. Biomech. Eng. 121, 591–597, 1999. doi:10.1115/1.2800858

    Article  PubMed  CAS  Google Scholar 

  21. Humphrey J. D. Cardiovascular Solid Mechanics: Cells, Tissues, and Organs. New York: Springer, 2002

    Google Scholar 

  22. Humphrey J. D., F. C. P. Yin. A new constitutive formulation for characterizing the mechanical behavior of soft tissues. Biophys. J. 52, 563–570, 1987

    PubMed  CAS  Google Scholar 

  23. Jackson Z. S., A. I. Gotlieb, B. L. Langille. Wall tissue remodeling regulates longitudinal tension in arteries. Circ. Res. 90, 918–925, 2002. doi:10.1161/01.RES.0000016481.87703.CC

    Article  PubMed  CAS  Google Scholar 

  24. Lanir Y. A structural theory for the homogenous biaxial stress–strain relationships in flat collagenous tissues. J. Biomech. 12, 423–436, 1979. doi:10.1016/0021-9290(79)90027-7

    Article  PubMed  CAS  Google Scholar 

  25. Lanir Y. Constitutive equations for fibrous connective tissues. J. Biomech. 16, 1–12, 1983. doi:10.1016/0021-9290(83)90041-6

    Article  PubMed  CAS  Google Scholar 

  26. Lanir Y. Constitutive equations for the lung tissue. J. Biomech. Eng. 105, 374–380, 1983

    Article  PubMed  CAS  Google Scholar 

  27. Mayfield J. A., M. T. Caps, G. E. Reiber, C. Maynard, J. M. Czerniecki, B. J. Sangeorzan. Trends in peripheral vascular procedures in the veterans health administration, 1989–1998. J. Rehabil. Res. Dev. 38:347–356, 2001

    PubMed  CAS  Google Scholar 

  28. Mitchell S. L., L. E. Niklason. Requirements for growing tissue engineered vascular grafts. Cardiovasc. Pathol. 12, 59–64, 2003. doi:10.1016/S1054-8807(02)00183-7

    Article  PubMed  CAS  Google Scholar 

  29. Niklason L. E., J. Gao, W. M. Abbott, K. Hirschi, S. Houser, R. Marini, R. Langer. Functional arteries grown in vitro. Science 284, 489–493, 1999. doi:10.1126/science.284.5413.489

    Article  PubMed  CAS  Google Scholar 

  30. Piez, K. A. and R. C. Likins. The nature of collagen. In: Calcification in Biological Systems: A Symposium Presented at the Washington Meeting of the American Association for the Advancement of Science. December 29, 1958. Washington, D.C.: American Association for the Advancement of Science, 1960, pp. 411–420

  31. Purslow P. P., T. J. Wess, D. W. Hukins. Collagen orientation and molecular spacing during creep and stress-relaxation in soft connective tissues. J. Exp. Biol. 201, 135–142, 1998

    PubMed  CAS  Google Scholar 

  32. Sacks M. S. Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar tissues. J. Biomech. Eng. 125, 280–287, 2003. doi:10.1115/1.1544508

    Article  PubMed  Google Scholar 

  33. Sacks M. S., D. B. Smith, E. D. Hiester. A small angle light scattering device for planar connective tissue microstructural analysis. Ann. Biomed. Eng. 25, 678–689, 1997. doi:10.1007/BF02684845

    Article  PubMed  CAS  Google Scholar 

  34. Solan A., S. Mitchell, M. Moses, L. Niklason. Effect of pulse rate on collagen deposition in the tissue-engineered blood vessel. Tissue Eng. 9, 579–586, 2003. doi:10.1089/107632703768247287

    Article  PubMed  CAS  Google Scholar 

  35. Stewart S. F., D. J. Lyman. Effects of a vascular graft/natural artery compliance mismatch on pulsatile flow. J. Biomech. 25, 297–310, 1992. doi:10.1016/0021-9290(92)90027-X

    Article  PubMed  CAS  Google Scholar 

  36. Taber L. A., J. D. Humphrey. Stress-modulated growth, residual stress, and vascular heterogeneity. J. Biomech. Eng. 123, 528–535, 2001. doi:10.1115/1.1412451

    Article  PubMed  CAS  Google Scholar 

  37. Vorp D. A., K. R. Rajagopal, P. J. Smolinski, H. S. Borovetz. Identification of elastic properties of homogeneous, orthotropic vascular segments in distension. J. Biomech. 28, 501–512, 1995. doi:10.1016/0021-9290(94)00012-S

    Article  PubMed  CAS  Google Scholar 

  38. Weizsacker H. W., J. G. Pinto. Isotropy and anisotropy of the arterial wall. J. Biomech. 21:477–487, 1988. doi:10.1016/0021-9290(88)90240-0

    Article  PubMed  CAS  Google Scholar 

  39. Wilson T. A. Mechanics of the pressure–volume curve of the lung. Ann. Biomed. Eng. 9, 439–449, 1981. doi:10.1007/BF02364762

    Article  PubMed  CAS  Google Scholar 

  40. Woessner J. F. The determination of hydroxyproline in tissue and protein samples containing small proportions of this amino acid. Arch. Biochem. Biophys. 93, 440–447, 1961. doi:10.1016/0003-9861(61)90291-0

    Article  PubMed  CAS  Google Scholar 

  41. Zulliger M. A., P. Fridez, K. Hayashi, N. Stergiopulos. A strain energy function for arteries accounting for wall composition and structure. J. Biomech. 37, 989–1000, 2004. doi:10.1016/j.jbiomech.2003.11.026

    Article  PubMed  Google Scholar 

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Acknowledgments

We thank NIH grants R01HL083895 (LEN), R01HL080415 (LEN and JDH), and R01HL64372 (JDH) for funding this study. We also thank the Duke Cancer Center Electron Microscopy Facility for preparing samples for transmission electron microscopy.

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Author notes

  1. Shannon L. M. Dahl

    Present address: Humacyte, Inc., PO Box 12695, Durham, NC, 27709, USA

  2. Laura E. Niklason

    Present address: Departments of Anesthesiology and Biomedical Engineering, Yale University, New Haven, CT, 06520, USA

Authors and Affiliations

  1. Department of Biomedical Engineering, Duke University, Durham, NC, 27708, USA

    Shannon L. M. Dahl, Megann E. Vaughn & Laura E. Niklason

  2. Department of Biomedical Engineering, Texas A&M University, College Station, TX, 77843, USA

    Jin-Jia Hu & Jay D. Humphrey

  3. Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Niels J. B. Driessen & Frank P. T. Baaijens

  4. Department of Anesthesiology, Duke University, Durham, NC, 27710, USA

    Laura E. Niklason

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  1. Shannon L. M. Dahl
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Correspondence to Shannon L. M. Dahl.

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Dahl, S.L.M., Vaughn, M.E., Hu, JJ. et al. A Microstructurally Motivated Model of the Mechanical Behavior of Tissue Engineered Blood Vessels. Ann Biomed Eng 36, 1782–1792 (2008). https://doi.org/10.1007/s10439-008-9554-4

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  • DOI: https://doi.org/10.1007/s10439-008-9554-4

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