Faculty of Engineering – Department of Mechanical Engineering

Project 247

Role of Muscle Fatigue in Onset of Tibial Stress Fractures: Finite Element Analysis

Submitted by: Allon Messenberg, 037637188.

Submitted: June / 02 / 2002.

Project Supervisor: Dr. Amit Gefen.

Abstract

The human tibia is subjected to muscle loads and joint reactions. Abnormal transfer of these loads may lead to the development of stress fractures in the bone.

Abnormal cyclic loading, to which the tibia is subjected during intensive fatiguing gait, may cause an accumulation of microscopic damage, which deteriorates bone strength and stiffness, thus decreasing its mechanical performances. It is this microscopic damage, which triggers a bone remodeling response, a process that repairs the damage.

In situations where the damage accumulates at a rate greater than that of the body’s ability to repair this damage, the possibility of stress fracture occurrence exists.

This project focuses on the loading, to which the tibia is subjected during the push-off sub phase of the stance phase of gait.

The objective of this project was to assess the risk for stress fracture development, based on the stress distribution results, and attempt for understanding the role of the calf muscles, especially the Soleus, in minimization of this risk. This is of great importance to populations, such as athletes and military recruits, who often take part in physical activities which are more intensive than physiologically favorable, and who regularly continue their activities long after muscle fatigue has begun.

Using the “Visible Human” database, two dimensional digital slices of the tibia were selected. Utilizing a computer aided design (CAD) program (SolidWorks 2001, SolidWorks Corporation), a region of interest around the tibia was isolated in each slice and the relevant contours of cortical and trabecular bone were traced. The two dimensional contours were stacked in their corresponding anatomical spatial orientation, creating a three dimensional frame, upon which a three dimensional solid model of the tibia was reconstructed. The result was a three dimensional, anatomically consistent computer model of the tibia, which included both the cortical and trabecular bone components.

Using a finite element analysis software package, (Nastran 2001, MSC. Software Corporation), the model was meshed and analyzed as follows:

Adopting a widely accepted assumption for computational purposes, the model was assigned linear elastic properties, with the elasticity modulus for cortical and trabecular bone set as 18 GPa and 3 GPa, respectively. The appropriate loads and boundary conditions, consistent with the push-off sub phase of gait under normal loading conditions, were applied and the stress distribution throughout the tibia was calculated. The maximum compression stress was found to be -64 MPa and the maximum tension stress was found to be 2.5 MPa. These results clearly showed that stress levels, both compressive and tensile, throughout the tibia remained well below the ultimate limit. It was concluded, that, excluding the added effects of endocrine, nutritional and pathological factors, which may influence the rate at which the remodeling process can repair accumulating micro damage, the risk of stress fracture development under normal loading conditions is extremely low.

The model was then applied with the loads consistent with the onset of muscle fatigue, and the stress distribution throughout the model was again calculated. This analysis was performed over and again, with the appropriate loads, simulating the progression of muscle fatigue. The results showed two major effects:

• A rise in stress magnitudes, both compressive and tensile, as the muscle force output decreased.
• An enlargement of the regions which were exposed to these high stresses, as the muscle force output decreased.

It was concluded that the risk of stress fracture development, under muscle fatigue loading conditions, greatly increased as muscle fatigue progressed. This due to both the rise in stress levels, which being cyclically applied pose a serious threat of fatigue failure, and the enlargement of the stressed regions which greatly increase the probability of an area of pre-existing microdamage or stress concentration being exposed to the high stress magnitudes.

Based upon these results, the role of the soleus was concluded to be of vital importance in minimization of stress levels and distribution throughout the tibia, and thus, in minimization of the risk of stress fracture development.

In light of the above conclusions, several recommendations were made:

1. A training program which consists of gradual increments of physical intensity in order to promote both metabolic and aerobic performance, thus delaying the onset of muscle fatigue.
2. Minimization of the duration of physical activities after muscle fatigue has begun, thus minimizing the amount of accumulated microdamage.
3. Appropriate duration of rest between physical activities, allowing the body’s mechanism of bone microdamage repair to act efficiently.