A damage model for the percutaneous triple hemisection technique for tendo-achilles lengthening
Introduction
Although the percutaneous triple hemisection technique for tendo-achilles lengthening has been used for nearly 100 years (Hatt and Lamphier, 1947), the amount of tendon lengthening that occurs during the procedure remains difficult to predict. Many studies have shown the procedure to be relatively safe and effective (Costa et al., 2006, Hoffman and Nunley, 2006, Lee and Ko, 2005, Piriou et al., 2000, Redfern and Thordarson, 2008, Stauff et al., 2011). However, these studies also suggest that over-lengthening, or even full rupture of the tendon may occur, drastically reducing the patient׳s ability to walk. Therefore, accurate prediction of lengthening, as well as an enhanced understanding of the mechanisms of action in this procedure remain important topics to understand.
The difficulty in predicting lengthening is inherent in the procedure itself. It is performed by making three offset percutaneous cuts from the edge of the tendon to the approximate center of the tendon, followed by pulling the foot in dorsiflexion (Haro III and DiDomenico, 2007). When enough force is applied to the incised tendon, gaps are created at the locations of the incisions as the fibered sections slide relative to each other while being held together by a weakened extracellular matrix. Cadaver studies have shown that variations in the incisions made during the procedure drastically affect the overall amount of lengthening that occurs in the tendon (Hoefnagels et al., 2007). In some cases, the offset cuts are not sufficiently long to sever all of the connecting fibers, and those fibers must also weaken before any sliding takes place. Fig. 1 illustrates the lengthening process. Full rupture can occur if the matrix material becomes too weak to hold the sections of the tendon together. Since the biomechanics of the procedure are still unclear, mechanical results remain difficult to predict.
Because the weakened matrix material is responsible for holding the tendon pieces together, modeling this material behavior is important for predicting the success of the procedure. The behavior of weakened soft tissue for various other conditions, for both the matrix and fiber response, has been described through previously developed models that predict the behavior on a macroscopic scale (Calvo et al., 2007, Ehret and Itskov, 2009, Natali et al., 2005). Many of the models were developed using a non-linear continuum damage mechanics framework (Lemaitre, 1985) with the ability to describe irreversible effects (Simo, 1987, Simo and Ju, 1987a, Simo and Ju, 1987b). The purpose of this research was to develop a non-linear continuum damage mechanics model that describes the specific matrix and fiber damage that occurs during the percutaneous tendon lengthening procedure. Application of this model may help to better understand and predict the amount of lengthening that occurs during the procedure.
Section snippets
Description of the damage model
To the authors׳ knowledge, a damage model has never been applied to evaluate triple hemisection tendon lengthening. Our approach mimics that employed by others in modeling damage in fibered soft tissues (Calvo et al., 2007, Ehret and Itskov, 2009, Natali et al., 2005), with the significant change of utilizing a shear strain driven damage criteria. This section contains a summary of the specific damage model that was used for this research.
The constitutive behavior of tendons is commonly
Demonstration of the damage model
Two separate series of experimental tests were performed to quantify the matrix and fiber damage behavior of porcine Achilles tendon. Data from the experimental tests were used in conjunction with a system identification study to identify the optimized damage model parameters that best fit the experimental results. Included in this section are the experimental methods for both the matrix and fiber components along with comparisons between the experimental results and the numerical results from
Human tendon model
A hexahedral mesh (13,239 elements) of a human Achilles tendon was generated using TrueGrid (XYZ Scientific Applications, Inc., Livermore, CA). The anatomical geometry was constructed in Unigraphics NX (Siemens, Munich, Germany) based on published anatomical data (Koch and Tillmann, 1995). Three cuts were simulated in the tendon model by removing a single row of elements corresponding to the cut location and approximate scalpel blade width. The three cuts were spaced 25 mm apart and were made
Discussion
A phenomenological damage model was developed to represent the tissue weakening that occurs during a percutaneous triple hemisection technique for tendo-achilles lengthening. The model utilized both matrix and fiber damage and replicated the observed behavior of the tendon tissue during the surgical procedure. Matrix damage was triggered and evolved relative to shear strain. A terminal level of damage was utilized in order to mimic the observed behavior of the matrix material in shear sliding.
Conflict of interest statement
None.
Acknowledgments
Research funding for this work was provided by the National Science Foundation (CMMI-0952758).
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