### Alumni Laboratories

Visit the research laboratories of the alumni of Dr. Woo.

#### Board of Directors

Richard Debski, Ph.D. *President*

Caroline Wang, M.S. *Secretary*

Jamie Pfaeffle, M.D., Ph.D. *Treasurer*

Doug Boardman, M.D.

Thay Lee, Ph.D.

Patrick McMahon, M.D.

Karen Ohland, M.S.

Christos Papgeorgiou, M.D.

Masataka Sakane, M.D.

Sven Scheffler, M.D.

Jennifer Wayne, Ph.D.

# 2008 Erin McGurk Grant Recipient

**Carrie Voycheck, B.S.**

University of Pittsburgh

University of Pittsburgh

##### Comparison of Two Isotropic Hyperelastic Constitutive Models

for the Glenohumeral Capsule

Carrie with her advisor, Dr. Rich Debski

**Acknowledgement**

I would like to extend my sincere appreciation to ORLAC, especially Erin McGurk, for the financial support of this project. I am very honored to have received this award and genuinely grateful to Erin McGurk for providing this opportunity to female graduate students in musculoskeletal research. This grant enabled me to begin my Ph.D. thesis project - The Effect of Injury on the Material Properties of the Glenohumeral Capsule: A Finite Element Approach. I would also like to thank my advisor, Dr. Richard Debski for his continued guidance and support, as well as Dr. Jeffrey Weiss and Steve Maas for their contributions to this collaborative computational work. Finally, I would like to acknowledge the support of everyone at the Musculoskeletal Research Center.

**Final Report **

The glenohumeral capsule is subjected to complex loading during activities of daily living and frequently injured when dislocation occurs. However, clinical exams are not standardized to diagnose injury and poor patient outcomes occur following capsular repair procedures. Validated models of the glenohumeral capsule may be able to identify ways to improve these procedures. The material behavior of the glenohumeral capsule has been described with microstructural models (accounting for the response of each constituent) and phenomenological models (generalization of overall tissue behavior). In a previous study that used a phenomenological model, material symmetry of the capsule was found to be isotropic. However, the isotropic model could not predict tissue response to both tensile and shear elongations. We hypothesize that a microstructural model, incorporating the ground substance and randomly oriented collagen fibers, will better describe and predict the material behavior of the glenohumeral capsule than an isotropic phenomenological model. *The objective of this study was to compare the ability of phenomenological and microstructural models to describe and predict the material behavior of the axillary pouch in response to tensile and shear loading.*

A combined experimental-computational protocol was used to determine the material coefficients for phenomenological and microstructural constitutive models. Tissue samples from the axillary pouch were extracted from 5 shoulders (63±1 yr.). Two perpendicular tensile and shear elongations were applied to each tissue sample. Since the experimental tests produced inhomogeneous deformations, specimen-specific finite element models were used to predict the response of the tissue when represented with the two constitutive models. Boundary conditions from the experimental tests (geometry, clamp reaction force, applied elongation) were used to create finite element models of the tissue sample for each loading condition. The phenomenological model was based on isotropic hyperelastic strain energy. The microstructural model consisted of an isotropic matrix based on the neo-Hookean constitutive model that was embedded with collagen fibers. The fibers had a random distribution of orientation in the plane of the tissue, yielding an initially isotropic material symmetry that became anisotropic with deformation due to fiber realignment. Overall fiber stress was obtained by integration over the fiber angle distribution. Both models were used to describe the material behavior of each tissue sample. Optimized material coefficients for both constitutive models were determined for each specimen for the tensile longitudinal elongation using an inverse finite element optimization technique. These coefficients were then used to predict the response of the tissue to the other elongations. RMS errors were used to compare the optimized and predicted load-elongation curves to the experimental data.

Both the phenomenological and microstructural models were able to describe the experimental data for the tensile longitudinal elongation. The microstructural model provided a slightly better fit than the phenomenological model, with RMS errors between the experimental and optimized load-elongation curves always less than 1.2 N for the microstructural model and 1.7 N for the phenomenological model.

Both models provided similar predictions of the tensile transverse elongation (Fig. 1). However, the microstructural model was better at predicting the response to both shear elongations (Fig. 2). The average RMS errors between experimental and predicted load-elongation curves for the phenomenological model were 5.8 N (range: 1.5-11.0 N) for the tensile predictions and 36.3 N (range: 2.1-170.0 N) for the shear predictions. For the microstructural model, the average RMS errors were 5.5 N (range: 2.6-9.9 N) for the tensile predictions and 4.9 N (range: 2.3-17.5 N) for the shear predictions. ** Thus, when predicting the shear elongations, the microstructural model yielded RMS errors that were about 7 times less than the phenomenological model.** Predictions of shear behavior from the phenomenological model were consistently too stiff in comparison to the experimental measurements.

*Figure 1: A typical graph from one tissue sample: the optimized material coefficients from a tensile elongation were used to predict the response of the capsule to a perpendicular tensile elongation.*

*Figure 2: A representative graph from one tissue sample: the optimized coefficients from a tensile elongation were used to predict the response of the axillary pouch to a shear elongation.*

In this study, the microstructural model that incorporated the individual responses of the ground substance and collagen fibers provided better predictions for the material response of the glenohumeral capsule, thus supporting our hypothesis. Explicit representation of random fibers in the model provides a softer response to shear loading than the isotropic phenomenological model since collagen fibers can realign along the shear plane. ** Despite the initially isotropic material symmetry of the capsule resulting from the randomly oriented collagen fibers, surgeons may need to be conscious of the existence of the fibers during repair procedures.** The results of this study compare well with other studies that have modeled ligaments and tendons as fiber-reinforced composites. In the future, validated finite element models of the glenohumeral capsule can be further developed and then be used to simulate clinical examinations and surgical repairs on specific joint injures known to exist following dislocation in vivo.