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Research Papers

# A Method for Predicting Collagen Fiber Realignment in Non-Planar Tissue Surfaces as Applied to Glenohumeral Capsule During Clinically Relevant Deformation

[+] Author and Article Information
Rouzbeh Amini

Department of Biomedical Engineering,
University of Akron,
260 S. Forge Street, ORLC Room 301,
Akron, OH 44325-0302
e-mail: ramini@uakron.edu

Carrie A. Voycheck

Department of Bioengineering,
University of Pittsburgh,
405 Center for Bioengineering,
300 Technology Drive,
Pittsburgh, PA 15219
e-mail: cvoycheck@gmail.com

Richard E. Debski

Department of Bioengineering,
University of Pittsburgh,
405 Center for Bioengineering,
300 Technology Drive,
Pittsburgh, PA 15219
e-mail: genesis1@pitt.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received April 4, 2013; final manuscript received October 30, 2013; accepted manuscript posted November 27, 2013; published online February 13, 2014. Assoc. Editor: Guy M. Genin.

J Biomech Eng 136(3), 031003 (Feb 13, 2014) (8 pages) Paper No: BIO-13-1173; doi: 10.1115/1.4026105 History: Received April 04, 2013; Revised October 30, 2013; Accepted November 27, 2013

## Abstract

Previously developed experimental methods to characterize micro-structural tissue changes under planar mechanical loading may not be applicable for clinically relevant cases. Such limitation stems from the fact that soft tissues, represented by two-dimensional surfaces, generally do not undergo planar deformations in vivo. To address the problem, a method was developed to directly predict changes in the collagen fiber distribution of nonplanar tissue surfaces following 3D deformation. Assuming that the collagen fiber distribution was known in the un-deformed configuration via experimental methods, changes in the fiber distribution were predicted using 3D deformation. As this method was solely based on kinematics and did not require solving the stress balance equations, the computational efforts were much reduced. In other words, with the assumption of affine deformation, the deformed collagen fiber distribution was calculated using only the deformation gradient tensor (obtained via an in-plane convective curvilinear coordinate system) and the associated un-deformed collagen fiber distribution. The new method was then applied to the glenohumeral capsule during simulated clinical exams. To quantify deformation, positional markers were attached to the capsule and their 3D coordinates were recorded in the reference position and three clinically relevant joint positions. Our results showed that at $60deg$ of external rotation, the glenoid side of the posterior axillary pouch had significant changes in fiber distribution in comparison to the other sub-regions. The larger degree of collagen fiber alignment on the glenoid side suggests that this region is more prone to injury. It also compares well with previous experimental and clinical studies indicating maximum principle strains to be greater on the glenoid compared to the humeral side. An advantage of the new method is that it can also be easily applied to map experimentally measured collagen fiber distribution (obtained via methods that require flattening of tissue) to their in vivo nonplanar configuration. Thus, the new method could be applied to many other nonplanar fibrous tissues such as the ocular shell, heart valves, and blood vessels.

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## Figures

Fig. 1

Schematic of a triangular element deformed from un-deformed configuration Ω0 to deformed configuration Ω1 via deformation tensor  01F. The covariant surface base vectors G1 and G2 as well as g1 and g2 are not necessarily orthogonal but they are expressed in terms of their components in an orthogonal coordinate system (i.e., (e1,e2,e3)) to take advantage of 3×3 matrix algebra.

Fig. 2

(a) Schematic of the volume differential element used to calculate dΘ, with t being the surface thickness, G1 being the covariant surface base vectors, N being the unit vector at angle Θ, dR being the differential position vector, dS being the differential arc length, and dA being the differential area vector. (b) The angle Θ in the un-deformed configuration was related to θ in the deformed configuration using the deformation of a normal vector N to n as described by Eqs. (21) and (22).

Fig. 3

Experimental Setup. Anterior (a) and inferior (b) views of a typical shoulder specimen. A 7 × 11 grid of strain markers were positioned on the tissue. The anteroinferior capsule was divided into six sub-regions: posterior axillary pouch glenoid side (PPG), posterior axillary pouch humeral side (PPH), anterior axillary pouch glenoid side (APG), anterior axillary pouch humeral side (APH), anterior band glenoid side (ABG), and anterior band humeral side (ABH). Note that the markers on the posterior band side were excluded from the final strain calculation.

Fig. 4

(a) Data points were generated on the surface of a unit sphere using matlab rand function. (b). Areal stretch after extension in x- and y-directions (x = 2X, y = 3Y, z = Z). Arrows show the direction of the major principal strain. (c) Main fiber direction μ (arrows) and normalized orientation index NOI (contour plots) in un-deformed configuration. (d) Main fiber direction μ and normalized orientation index NOI following axial extension (λx = 1.5).

Fig. 5

Maximum principle stretch and normalized orientation index NOI in each element for a representative anteroinferior capsule at (a) referential configuration, and (b)–(d) deformed configurations of 60 deg of abduction accompanied by (b) 0 deg, (c) 30 deg, and (d) 60 deg of external rotation. The arrows on each element show the direction of the maximum principle stretch. The black lines on the NOI contours separate the capsule sub-regions (b).

Fig. 6

Percent increase in normalized orientation index NOI of different capsule sub-region following 0 deg, 30 deg, and 60 deg of external rotation. The asterisks show the significant differences calculated from the Wilcoxon signed-ranks post hoc tests. Error bars are standard deviations.

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