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Research Papers

On the Functional Role of Valve Interstitial Cell Stress Fibers: A Continuum Modeling Approach

[+] Author and Article Information
Yusuke Sakamoto, Rachel M. Buchanan

Center for Cardiovascular Simulation,
Institute for Computational
Engineering and Sciences,
Department of Biomedical Engineering,
The University of Texas at Austin,
Austin, TX 78712

Johannah Sanchez-Adams

Departments of Orthopaedic Surgery,
Duke University Medical Center,
Durham, NC 27710;
Departments of Biomedical Engineering,
Duke University Medical Center,
Durham, NC 27710

Farshid Guilak

Departments of Orthopaedic Surgery,
Washington University,
St. Louis, MO 63110;
Departments of Biomedical Engineering,
Washington University,
St. Louis, MO 63110;
Departments of Developmental Biology,
Washington University,
St. Louis, MO 63110

Michael S. Sacks

W. A. “Tex” Moncrief, Jr. Simulation-Based
Engineering Science Chair I
Center for Cardiovascular Simulation,
Institute for Computational
Engineering and Sciences,
Department of Biomedical Engineering,
The University of Texas at Austin,
Austin, TX 78712
e-mail: msacks@ices.utexas.edu

1Corresponding author.

Manuscript received August 12, 2016; final manuscript received December 12, 2016; published online January 19, 2017. Assoc. Editor: Victor H. Barocas.

J Biomech Eng 139(2), 021007 (Jan 19, 2017) (13 pages) Paper No: BIO-16-1340; doi: 10.1115/1.4035557 History: Received August 12, 2016; Revised December 12, 2016

The function of the heart valve interstitial cells (VICs) is intimately connected to heart valve tissue remodeling and repair, as well as the onset and progression of valvular pathological processes. There is yet only very limited knowledge and extant models for the complex three-dimensional VIC internal stress-bearing structures, the associated cell-level biomechanical behaviors, and how they change under varying activation levels. Importantly, VICs are known to exist and function within the highly dynamic valve tissue environment, including very high physiological loading rates. Yet we have no knowledge on how these factors affect VIC function. To this end, we extended our previous VIC computational continuum mechanics model (Sakamoto, et al., 2016, “On Intrinsic Stress Fiber Contractile Forces in Semilunar Heart Valve Interstitial Cells Using a Continuum Mixture Model,” J. Mech. Behav. Biomed. Mater., 54(244–258)). to incorporate realistic stress-fiber geometries, force-length relations (Hill model for active contraction), explicit α-smooth muscle actin (α-SMA) and F-actin expression levels, and strain rate. Novel micro-indentation measurements were then performed using cytochalasin D (CytoD), variable KCl molar concentrations, both alone and with transforming growth factor β1 (TGF-β1) (which emulates certain valvular pathological processes) to explore how α-SMA and F-actin expression levels influenced stress fiber responses under quasi-static and physiological loading rates. Simulation results indicated that both F-actin and α-SMA contributed substantially to stress fiber force generation, with the highest activation state (90 mM KCL + TGF-β1) inducing the largest α-SMA levels and associated force generation. Validation was performed by comparisons to traction force microscopy studies, which showed very good agreement. Interestingly, only in the highest activation state was strain rate sensitivity observed, which was captured successfully in the simulations. These unique findings demonstrated that only VICs with high levels of αSMA expression exhibited significant viscoelastic effects. Implications of this study include greater insight into the functional role of α-SMA and F-actin in VIC stress fiber function, and the potential for strain rate-dependent effects in pathological states where high levels of α-SMA occur, which appear to be unique to the valvular cellular in vivo microenvironment.

Copyright © 2017 by ASME
Topics: Fibers , Stress , Simulation
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References

Figures

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Fig. 1

(Top) Schematic of the microindentation experimental configuration. (Bottom) the VIC model computational domains, which consisted of three subdomains, Ωcyto, Ωnuc, and Ωind, representing the cytoplasm, nucleus, and rigid spherical indenter, respectively. The cytoplasm was considered as a solid mixture of basal cytoplasm (green network in the inset) and oriented stress fibers (black oriented lines in the inset). The basal cytoplasm was modeled as a nearly incompressible neo-Hookean material. The stress fibers were modeled as the ensemble of oriented fibers with passive elastic and active contractile responses with their orientation described by a continuum orientation distribution function. The substrate was not explicitly modeled as the no-slip boundary condition was prescribed on Γbottom. The contact between the indenter and VIC was modeled by no-penetration, no-slip contact boundary condition.

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Fig. 2

Three-dimensional orientation of the stress fibers and specification of adhesion regions. The stress fiber orientation distribution functions were defined on local 2D planes, whose normal vector depends on the position within the VIC. On the top surface, the plane normal corresponds to the surface normal of the VIC (without y-component). On the bottom surface, we defined adhesion regions, which span from the cell tip to the 1/6 of the cell length toward the center. In the adhesion regions, the plane normal is defined 45 deg from the bottom surface. In the nonadhesion region, the plane normal corresponds to the surface normal of the ellipsoid directly above (without y-component). Once we defined the plane normal for top and bottom surfaces, we calculated the plane normal inside the VIC by linearly interpolating the top and bottom normal vectors. Thus, moving from the bottom to top surfaces of the VIC, the plane normal transitions smoothly. The preferred orientation of the fibers (θp) corresponds to the x-direction.

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Fig. 3

The actual simulation geometry and mesh. The simulation was carried out in the quarter-domain by utilizing symmetry. The mesh was refined around the indenter-VIC contact region.

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Fig. 4

Normalized expression levels of F-actin (left) and α-SMA (right). The expression levels were normalized to the CytoD group. TGF-β and/or KCl treatments induced higher levels of F-actin, whereas only the T90 group exhibited an increase in α-SMA, but (∼5 fold).

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Fig. 5

The stress fiber orientation histograms and corresponding fits of the constrained von-Mises distribution for CytoD (left) and C5 (right) groups. The angle θ = 0 represents the preferred direction of the fiber (θp).

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Fig. 6

Indentation force versus depth curves for CytoD, C5, C90, and T5 groups for slow (2 μm/s) and fast (12 μm/s) indentation speeds. Red curves represent the indentation depth averaged over the same force with error bars representing one standard error. Blue curves represent the indentation depth versus force obtained from the simulations with best fit parameters. None of these groups exhibited strain rate sensitivity.

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Fig. 7

Indentation force versus depth curves for T90 group for slow (left, 2 μm/s) and fast (center, 12 μm/s) indentation speeds. Red curves represent the indentation depth averaged over the same force with error bars representing one standard error. Blue curves represent the indentation depth versus force obtained from the simulations with best fit parameters. Only T90 group exhibited significant strain rate sensitivity, which was captured by our model, as more easily in the model results (right).

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Fig. 8

Total shear modulus of the stress fibers (μsftot), contraction strength of the stress fibers (f0), and total viscosity of the stress fibers (ηsftot) obtained from the parameter estimations. The expression levels of α-SMA contribute significantly to the contraction strength (f0) as well as strain sensitivity (ηsftot) of the stress fibers within VICs.

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Fig. 9

Computed contributions of the F-actin and α-SMA to the maximum contraction strength for each group. The stacked green/blue columns represent the estimated maximum contraction strength values (f0,estimated) calculated by fitting Eq. (13) to the f0 values. F-actin contributed to the contraction strength up to a certain point when the VICs were activated in T5 and C90 groups. However, almost all of the increase in contraction strength in T90 group to C90 group was due to α-SMA contribution.

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Fig. 10

Parametric study: effect of the length-tension parameter values (ε0) to the estimated maximum contraction strength (f0) values. The ε0 values used were 0.01, 0.1, 1.0, and 10.0. Slight increase in the estimated f0 values was observed as ε0 value decrease. However, the f0 values are relatively unaffected by ε0 values.

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Fig. 11

Traction field on the bottom of the VIC with f0 = 1200 Pa calculated from the simulation. Tractions are concentrated around the adhesion region. The VIC pulls the substrate one-dimensionally toward the center.

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Fig. 12

Total force exerted by a VIC calculated from the tangential traction on the bottom of the VIC by Eq. (14). The total forces are 71.8 nN, 86.6 nN, 142.6 nN, and 158.5 nN for C5, C90, T5, and T90 groups, respectively. Relative increase of the total force from the C5 to T5 group was ∼2.0 fold.

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Fig. 13

(a) Schematic of the stretch of a VIC inside mitral valve and corresponding fiber stretch during valve closing. Assuming that NAR corresponds to the cell aspect ratio as well as representative fiber length, we simulated the 1D fiber stretch and calculated the stress. (b) Stretch and stretch rate of the 1D fiber computed from the NAR of VICs within mitral valve during systolic valve closure [55].

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Fig. 14

One-dimensional stress within stress fibers during systolic closure of mitral valve. The stress generated within stress fibers was greatly different due to different passive elastic, active contractile, and viscous stresses within the fibers. Only T90 group exhibited significant effect of viscous effect, which peaked around 0.12 s.

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Fig. 15

Stress calculated from the simulation of 1D fiber stretch at its peak strain rate (Fig. 13(b)), with the stress from each component determined at the point of peak strain rate (t = 0.08). Passive elastic response explains the most of increase in the stress from normal state (C5 group) and it activated states (T5 and C90 groups). The enhancement in active contractile and especially the viscous responses explain the further increase in the stress in highest activation state (T90 group). Collectively, these results suggest that incorporated αSMA is intrinsically viscoelastic.

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