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Research Papers

Stress Analysis-Driven Design of Bilayered Scaffolds for Tissue-Engineered Vascular Grafts

[+] Author and Article Information
Jason M. Szafron

Department of Biomedical Engineering,
Yale University,
New Haven, CT 06520
e-mail: jason.szafron@yale.edu

Christopher K. Breuer

Tissue Engineering Program,
Nationwide Children's Hospital,
Columbus, OH 43215
e-mail: christopher.breuer@nationwidechildrens.org

Yadong Wang

Meinig School of Biomedical Engineering,
Cornell University,
Ithaca, NY 14853
e-mail: yw839@cornell.edu

Jay D. Humphrey

Fellow ASME
Department of Biomedical Engineering,
Yale University,
New Haven, CT 06520
e-mail: jay.humphrey@yale.edu

Manuscript received April 11, 2017; final manuscript received August 11, 2017; published online September 28, 2017. Assoc. Editor: Jeffrey Ruberti.

J Biomech Eng 139(12), 121008 (Sep 28, 2017) (10 pages) Paper No: BIO-17-1149; doi: 10.1115/1.4037856 History: Received April 11, 2017; Revised August 11, 2017

Continuing advances in the fabrication of scaffolds for tissue-engineered vascular grafts (TEVGs) are greatly expanding the scope of potential designs. Increasing recognition of the importance of local biomechanical cues for cell-mediated neotissue formation, neovessel growth, and subsequent remodeling is similarly influencing the design process. This study examines directly the potential effects of different combinations of key geometric and material properties of polymeric scaffolds on the initial mechanical state of an implanted graft into which cells are seeded or migrate. Toward this end, we developed a bilayered computational model that accounts for layer-specific thickness and stiffness as well as the potential to be residually stressed during fabrication or to swell during implantation. We found that, for realistic ranges of parameter values, the circumferential stress that would be presented to seeded or infiltrating cells is typically much lower than ideal, often by an order of magnitude. Indeed, accounting for layer-specific intrinsic swelling resulting from hydrophilicity or residual stresses not relieved via annealing revealed potentially large compressive stresses, which could lead to unintended cell phenotypes and associated maladaptive growth or, in extreme cases, graft failure. Metrics of global hemodynamics were also found to be inversely related to markers of a favorable local mechanobiological environment, suggesting a tradeoff in designs that seek mechanical homeostasis at a single scale. These findings highlight the importance of the initial mechanical state in tissue engineering scaffold design and the utility of computational modeling in reducing the experimental search space for future graft development and testing.

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Figures

Grahic Jump Location
Fig. 1

(a) Deformation to induce residual stresses, where Φo is the prescribed opening angle and Λ an associated axial stretch; (R,Θ,Z) are coordinates in the stress-free configuration and (ϱ,φ,ζ) are coordinates in the traction-free but residually stressed configuration. (b) Pressure-induced deformation where λ is a prescribed axial stretch; (r,θ,z) are coordinates in the residually stressed and loaded configuration. (c) Volumetric swelling constraint where υ* is a prescribed swelling ratio; (r*,θ*,z*) are coordinates in the swollen and loaded configuration.

Grahic Jump Location
Fig. 2

(a) List of fixed and varied parameters and their corresponding physical representations on the scaffold. (b) List of model outputs and their representations: (i) illustrative stresses that are calculated based in part on deformations in Fig. 1 and (ii) radial compliance and the method of calculation.

Grahic Jump Location
Fig. 3

Combinatorial parametric study of the effects of three scaffold parameters—normalized core shear modulus μc (subpanels i–iv), core thickness Hc (families of curves in each subpanel, with larger values denoted by darker curves and the local arrows), and varying sheath thickness Hs (abscissa for each subpanel)—on three important characteristics of scaffold behavior: (a) average core stress tcavg, (b) radial compliance Δri*/ΔP, and (c) diastolic radius ri*. Note the absence of core swelling and sheath residual stress.

Grahic Jump Location
Fig. 4

Similar to Fig. 3 except for different core swelling ratios υ* (i)–(iv) for a fixed core shear modulus. Each subpanel again varies core thickness Hc (represented by progressively darker shading on the curves and local arrows) and sheath thickness Hs (abscissa) and shows (a) average core stress tcavg, (b) radial compliance Δri*/ΔP, and (c) diastolic radius ri*. Note the absence of residual stress in the sheath.

Grahic Jump Location
Fig. 5

Changes in thickness ratio h/H (deformed/undeformed) for various values of core swelling υ* and sheath residual stress (prescribed by opening angles Φo) from (i)–(iii). Each subpanel shows changes as a function of increasing core thickness Hc (represented by darker shading on the plotted curves and local arrows) and varying sheath thickness Hs (along the abscissa) for (a) a control case with no swelling or residual stress, (b) varying core swelling (υ*), and (c) varying sheath residual stress (opening angles Φo).

Grahic Jump Location
Fig. 6

Similar to Figs. 3 and 4 except for different sheath opening angles Φo (i)–(iv) for a fixed core shear modulus. Each subpanel again varies core thickness Hc (represented by progressively darker shading on the curves and local arrows) and sheath thickness Hs (abscissa) and shows (a) average core stress tcavg, (b) radial compliance Δri*/ΔP, and (c) diastolic radius ri*. Note the absences of swelling of the core.

Grahic Jump Location
Fig. 7

Transmural values of circumferential stress for the core and the sheath, tθθc and tθθs, respectively, as a function of normalized radial position r*/ri* ; tθθc is represented by the leftmost portion of each curve while the section of the curve after the discontinuity represents tθθs. Subpanels (i)–(iv) show various combinations of core thickness Hc and sheath thickness Hs. Each panel shows a different parameter increasing using darkening curves: (a) normalized core shear modulus μc from 1 to 2, 5, and 10, (b) core swelling ratio υ* from 1 to 1.1, 1.2, and 1.4, (c) sheath opening angle Φo from 0 to 10 deg, 20 deg, and 40 deg. Note that μc=10 (normalized) was used for (b) and (c) to better visualize the effects of swelling and opening angle.

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