0
Research Papers

Validation of an Empirical Damage Model for Aging and in Vivo Injury of the Murine Patellar Tendon

[+] Author and Article Information
Mark R. Buckley

e-mail: mbuck@upenn.edu

Andrew A. Dunkman

e-mail: andrew.dunkman@gmail.com

Katherine E. Reuther

e-mail: kreuther@seas.upenn.edu

Akash Kumar

e-mail: akkumar@seas.upenn.edu

Lydia Pathmanathan

e-mail: lydia.pathman@gmail.com

David P. Beason

e-mail: dpbeason@gmail.com
McKay Orthopaedic Research Laboratory,
424 Stemmler Hall,
36th Street and Hamilton Walk,
University of Pennsylvania,
Philadelphia, PA 19104

David E. Birk

Department of Molecular Pharmacology and Physiology,
Morsani College of Medicine,
University of South Florida,
12901 Bruce B. Downs Boulevard, MDC 8,
Tampa, FL 33612
e-mail: dbirk@health.usf.edu

Louis J. Soslowsky

McKay Orthopaedic Research Laboratory,
424 Stemmler Hall, 36th Street and Hamilton Walk, University of Pennsylvania,
Philadelphia,PA 19104
e-mail: soslowsk@upenn.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received August 25, 2012; final manuscript received January 25, 2012; accepted manuscript posted February 19, 2013; published online April 2, 2013. Assoc. Editor: Kenneth Fischer.

J Biomech Eng 135(4), 041005 (Apr 02, 2013) (7 pages) Paper No: BIO-12-1372; doi: 10.1115/1.4023700 History: Received August 25, 2012; Revised January 25, 2013; Accepted February 19, 2013

While useful models have been proposed to predict the mechanical impact of damage in tendon and other soft tissues, the applicability of these models for describing in vivo injury and age-related degeneration has not been investigated. Therefore, the objective of this study was to develop and validate a simple damage model to predict mechanical alterations in mouse patellar tendons after aging, injury, or healing. To characterize baseline properties, uninjured controls at age 150 days were cyclically loaded across three strain levels and five frequencies. For comparison, damage was induced in mature (120 day-old) mice through either injury or aging. Injured mice were sacrificed at three or six weeks after surgery, while aged mice were sacrificed at either 300 or 570 days old. Changes in mechanical properties (relative to baseline) in the three week post-injury group were assessed and used to develop an empirical damage model based on a simple damage parameter related to the equilibrium stress at a prescribed strain (6%). From the derived model, the viscoelastic properties of the 300 day-old, 570 day-old, and six week post-injury groups were accurately predicted. Across testing conditions, nearly all correlations between predicted and measured parameters were statistically significant and coefficients of determination ranged from R2 = 0.25 to 0.97. Results suggest that the proposed damage model could exploit simple in vivo mechanical measurements to predict how an injured or aged tendon will respond to complex physiological loading regimens.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Topics: Wounds , Tendons , Stress
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Stamped P150 mouse patellar tendon prepared for mechanical testing. The dark spots are Verhoeff's stain for optical tracking, which was not used in this study.

Grahic Jump Location
Fig. 2

(a) Strain and (b) stress versus time plots for a representative sample deformed at f = 1 Hz with an 8% strain offset. The solid black curves represent raw data, while the dashed lines represent sinusoidal fits. (c) The dynamic modulus |E*| is given by the ratio of the stress and strain amplitudes, while δ is computed from the phase difference between the stress and strain.

Grahic Jump Location
Fig. 3

Damage parameter D during (a) aging and (b) the injury response. In all aging and injured groups, D was significantly increased compared to baseline (P150 uninjured). Mean ± SD, (*) p < 0.05/3 versus P150 uninjured.

Grahic Jump Location
Fig. 4

Measured values of (a) |E*| and (b) tanδ plotted against (1 –D) < |E*|damaged > and (1 – D) < tanδdamaged > for mouse patellar tendons three weeks after injury at P120 tested at 4, 6, and 8% strain with f = 1 Hz. The dashed black lines represent power law fits of the acquired data. Relationships derived from these fits were used to predict |E*| and tanδ in other damage groups.

Grahic Jump Location
Fig. 5

Measured and predicted values of (a) |E*| and (b) tanδ for P300 mouse patellar tendons tested at f = 1 Hz. The solid black lines are not fits of experimental data, but represent the expected relationship between predicted and measured parameters (e.g., |E*|measured = |E*|predicted). Agreement between model and experiment was strong for the dynamic modulus |E*|, but weaker for tanδ. For |E*|, R2 = 0.90, 0.95, and 0.85 at 4%, 6%, and 8% strain, respectively. For tanδ, R2 = 0.54, 0.55, and 0.46 at 4%, 6%, and 8% strain, respectively. Results were similar at other frequencies (see Appendix).

Grahic Jump Location
Fig. 6

Measured and predicted values of (a) |E*| and (b) tanδ for P570 mouse patellar tendons tested at f = 1 Hz. The solid black lines are not fits of experimental data, but represent the expected relationship between predicted and measured parameters (e.g., |E*|measured = |E*|predicted). Agreement between model and experiment was evident for both parameters. For |E*|, R2 = 0.91, 0.80, and 0.42 at 4%, 6%, and 8% strain, respectively. For tanδ, R2 = 0.91, 0.85, and 0.91 at 4%, 6%, and 8% strain, respectively. Results were similar at other frequencies (see Appendix).

Grahic Jump Location
Fig. 7

Measured and predicted values of (a) |E*| and (b) tanδ for mouse patellar tendons six weeks after injury at P120 tested at f = 1 Hz. The solid black lines are not fits of experimental data, but represent the expected relationship between predicted and measured parameters (e.g., |E*|measured = |E*|predicted). Agreement between model and experiment was strong for the dynamic modulus |E*|, but weaker for tanδ. For |E*|, R2 = 0.83, 0.92, and 0.71 at 4%, 6%, and 8% strain, respectively. For tanδ, R2 = 0.25, 0.82, and 0.82 at 4%, 6% and 8% strain, respectively. Results were similar at other frequencies (see Appendix).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In