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TECHNICAL PAPERS: Soft Tissue

# The Relation Between Collagen Fibril Kinematics and Mechanical Properties in the Mitral Valve Anterior Leaflet

[+] Author and Article Information
Jun Liao, Jonathan Grashow

Engineered Tissue Mechanics Laboratory, Department of Bioengineering, and the McGowan Institute for Regenerative Medicine, University of Pittsburgh, Pittsburgh, PA 15219

Lin Yang

National Synchrotron Light Source (NSLS), Brookhaven National Laboratory, Upton, NY 11973

Michael S. Sacks1

Engineered Tissue Mechanics Laboratory, Department of Bioengineering, and the McGowan Institute for Regenerative Medicine, University of Pittsburgh, Pittsburgh, PA 15219msacks@pitt.edu

1

Corresponding author.

J Biomech Eng 129(1), 78-87 (Jun 24, 2006) (10 pages) doi:10.1115/1.2401186 History: Received November 27, 2005; Revised June 24, 2006

## Abstract

We have recently demonstrated that the mitral valve anterior leaflet (MVAL) exhibited minimal hysteresis, no strain rate sensitivity, stress relaxation but not creep (Grashow, 2006, Ann Biomed Eng., 34(2), pp. 315–325;Grashow, 2006, Ann Biomed. Eng., 34(10), pp. 1509–1518). However, the underlying structural basis for this unique quasi-elastic mechanical behavior is presently unknown. As collagen is the major structural component of the MVAL, we investigated the relation between collagen fibril kinematics (rotation and stretch) and tissue-level mechanical properties in the MVAL under biaxial loading using small angle X-ray scattering. A novel device was developed and utilized to perform simultaneous measurements of tissue level forces and strain under a planar biaxial loading state. Collagen fibril D-period strain $(εD)$ and the fibrillar angular distribution were measured under equibiaxial tension, creep, and stress relaxation to a peak tension of $90N∕m$. Results indicated that, under equibiaxial tension, collagen fibril straining did not initiate until the end of the nonlinear region of the tissue-level stress-strain curve. At higher tissue tension levels, $εD$ increased linearly with increasing tension. Changes in the angular distribution of the collagen fibrils mainly occurred in the tissue toe region. Using $εD$, the tangent modulus of collagen fibrils was estimated to be $95.5±25.5MPa$, which was $∼27$ times higher than the tissue tensile tangent modulus of $3.58±1.83MPa$. In creep tests performed at $90N∕m$ equibiaxial tension for $60min$, both tissue strain and $εD$ remained constant with no observable changes over the test length. In contrast, in stress relaxation tests performed for $90min$$εD$ was found to rapidly decrease in the first $10min$ followed by a slower decay rate for the remainder of the test. Using a single exponential model, the time constant for the reduction in collagen fibril strain was $8.3min$, which was smaller than the tissue-level stress relaxation time constants of 22.0 and $16.9min$ in the circumferential and radial directions, respectively. Moreover, there was no change in the fibril angular distribution under both creep and stress relaxation over the test period. Our results suggest that (1) the MVAL collagen fibrils do not exhibit intrinsic viscoelastic behavior, (2) tissue relaxation results from the removal of stress from the fibrils, possibly by a slipping mechanism modulated by noncollagenous components (e.g. proteoglycans), and (3) the lack of creep but the occurrence of stress relaxation suggests a “load-locking” behavior under maintained loading conditions. These unique mechanical characteristics are likely necessary for normal valvular function.

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## Figures

Figure 1

Biaxial stretch device custom made for the synchrotron SAXS beamline. Labels: (1) specimen chamber, (2) guide shaft, (3) lead screw, (4) tissue holder, (5) submersible load cell, (6) concave stage, (7) suture, (8) tissue in PBS solution, (9) small X-ray window, (10) motor, and (11) PBS solution guiding tube. Inset image: the photo of biaxial stretching device on synchrotron SAXS beamline (X21 endstation at the NSLS).

Figure 2

(a) Typical SAXS pattern from the mitral valve anterior leaflet. (b) A schematic of SAXS data analysis showing the specimen aligned with its preferred circumferential direction aligned to the horizontal direction (x axis). The actual fibril preferred direction, Φp, was referred to the x′ axis. A ring that enclosed the brightest fifth order diffraction ring was used to capture the angular distribution of scattering intensity. Here, Φ was the angle with respect to x axis. (c) The resulting angular distribution of the scattering data was fit by a Gaussian distribution well (r2=0.994).

Figure 3

(a) Relationship between collagen fibrillar D-period strain (εD) and applied equibiaxial tissue tension. Also shown in (b) the corresponding equibiaxial tension-areal strain at the tissue level. Data presented as mean±SEM.

Figure 4

The relationship between stress, collagen fibril D-period strain (εD) and tissue strain along the fibril preferred direction. Here the tensile modulus of the MVAL collagen fibrils was found to be 95.5±25.5MPa along the preferred fibril direction, with the tissue tensile modulus 3.58±1.83MPa. Data presented as mean±SEM.

Figure 5

(a) Collagen fibril D-period strain (εD) and (b) tissue areal strain versus time during creep tests, where both demonstrated no detectable change in strain. Data presented as mean±SEM.

Figure 6

(a) Biaxial stress relaxation of mitral valve and (b) D-period strain (εD) in the stress relaxation process. Data presented as mean±SEM.

Figure 7

Representative angular distribution of collagen fibrils in biaxial (a) stretch, (b) creep, and (c) stress relaxation. Here, a peak value of 90N∕m equibiaxial tension was maintained during the creep tests and 90N∕m equibiaxial tension was also used as the initial stress level for stress relaxation. Note that the distribution curves were shifted upwards for clarity.

Figure 8

Overall preferred direction and NOI of collagen fibrils in biaxial (a) stretch, (b) creep, and (c) stress relaxation. 90N∕m equibiaxial tension was maintained in creeping procedure. 90N∕m equibiaxial tension was also used as the initial load in stress relaxation.

Figure 9

A schematic demonstrated how fibril angular distribution is affected by the uncrimping of collagen fibers: (a) crimping collagen fibers, (b) angular distribution of collagen fibrils of crimp configuration, (c) crimp structure of collagen fibers under load-free condition, (d) straightened collagen fibers, (e) angular distribution of collagen fibrils of straight configuration, and (f) straightened collagen fibers under 90N∕m equibiaxial loading. Picrosirius red staining was used for histological sections.

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