**1. Introduction**

The human motor system benefits from remarkable muscular redundancies: A motor task is normally performed with the simultaneous involvement of more muscles than strictly necessary. Furthermore, this same task may be performed in multiple ways, with different muscle combinations. From the mechanical viewpoint the musculoskeletal system is indeterminate, whereby the number of unknown muscle forces exceeds the number of available equations. We address in this Chapter the biomechanics of the lower limbs in longdistance running under conditions of developing fatigue. In long-distance running the running speed may result in more than 300 foot-strikes per leg per kilometer. Each such foot-strike evokes an impact loading that results in a vertical shock impulse transmitted upwards through the body and carries with it the potential for injuries in the bone and joint tissues.

Fatigue, or stress, fractures occur in bones in response to repetitive stresses over multiple cycles, when the body's ability to adapt is exceeded [1,2]. An important factor which affects the incidence of bone stress injury, is exposure to abrupt changes in the bone loading [1], and consequent alteration in the strain distribution [3] with insufficient recovery periods [4]. Other factors include footwear, terrain and intensity of activity or training [1].

Two of the major factors responsible for impulse attenuation at foot- or heel-strike are the shock absorption capacity of the active muscle in the lower limbs, and the cushioning effect of the foot heel-pad tissue. In previous reports we have shown that in long distance running the impact shock load on the lower limbs increases with progressing fatigue [5-8]. One additional question is whether, as a result of fatigue, an imbalance between the activities of the plantar and dorsi flexor muscles of the ankle develops. Such an imbalance would compromise the protective action provided by the muscles to the shank [9-11].

© 2012 Mizrahi and Daily, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### 154 Injury and Skeletal Biomechanics

The goal of this research was to characterize the heel-strike shock propagation and attenuation in running by means of a biomechanical model, and to examine changes taking place as a result of running fatigue.

Modeling the Foot-Strike Event in Running Fatigue via Mechanical Impedances 155

(3)

*x x v m/s i i i* (0) 0 ; (0) 1 , 1,2,3,4 <sup>0</sup> (2)

<sup>2</sup> **g** 9.81 / *m s*

These values rely on reported landing velocities between -0.8 m/s to -1.2 m/s for running speeds of 3.5 m/s (comparable to the speeds of this study), while wearing various types of

The above masses are expressible in terms of the total body mass from anthropometric data

4 123

masses *mj*, information about the rise time of the peak acceleration can be obtained.

1 ( ) 0.839

From the simultaneous recording of the foot ground reaction forces and accelerations on the

**Figure 1.** Lumped model including 4 masses connected by elastic stiffnesses with parallel dampings. The masses *m*j (*j* = 1..4) represent, respectively, the foot + shoe, the shank, the thigh and the rest of the body (including the non-supporting leg). Each of the stiffness *k*j and damping *c*j (*j* = 1..4) represent, respectively, the lumped effects of the heel-pad + sole, the ankle joint, the knee joint and the hip joint.

*m mmm m*

1 2 3

0.0465 0.100

0.0145

*m m m m m m*

and gravitational acceleration

running shoes [21-23].

[24].
