Effects of distal and proximal arm muscles fatigue on multi-joint movement organization

Abstract

To investigate the strategies developed by the central nervous system to compensate for fatigue in muscles, we studied the changes in the relative mechanical contribution of the joint torques in a multi-joint movement following an isometric exhaustion test. Eighteen male subjects performed throws, moving the arm in the horizontal plane, before and after two fatigue protocols. Muscular fatigue was induced either in the distal (extensor digitorum communis) or in the proximal (triceps brachii) agonist muscle of the arm. The kinematic, kinetic and electromyographic parameters of the movement were analysed. The subjects produced two different coordinations following the fatigue protocols. In the distal fatigue condition, the wrist angular velocity was maintained by decreasing elbow active torque. In the proximal fatigue condition, the compensatory strategy involved increasing the contribution of the wrist. In fact, the control of elbow and wrist was modified in order to compensate for the different mechanical effects.

Appendix I

Mean power frequency

$$ {\text{MPF}} = \frac{{{\int_0^\infty {f \cdot S(f)\,{\text{d}}f} }}} {{{\int_0^\infty {S(f)\,{\text{d}}f} }}}. $$

where f is the frequency; S(f) is the power of the spectrum defined by: S(f) = Re ² + Im ², in which Re and Im are, respectively, the real and the imaginary terms.

Elbow torques

$$ {\text{NT}} = \ifmmode\expandafter\ddot\else\expandafter\"\fi{\theta }_{2} \cdot I_{{\text{f}}} + I_{{\text{h}}} + {\left( {m_{{\text{h}}} \cdot l^{2}_{{\text{f}}} } \right)} + {\left( {m_{{\text{f}}} \cdot r^{2}_{{\text{f}}} } \right)} + {\left( {m_{{\text{h}}} \cdot r^{2}_{{\text{h}}} } \right)} + {\left( {2m_{{\text{h}}} \cdot l_{{\text{f}}} \cdot r_{{\text{h}}} \cdot \cos \theta _{3} } \right)} $$

$$ \begin{aligned} {\text{IT}} & = - \ifmmode\expandafter\ddot\else\expandafter\"\fi{\theta }_{1} \cdot I_{{\text{f}}} + I_{{\text{h}}} + {\left( {m_{{\text{h}}} \cdot l^{2}_{{\text{f}}} } \right)} + {\left( {m_{{\text{f}}} \cdot r^{2}_{{\text{f}}} } \right)} + {\left( {m_{{\text{h}}} \cdot r^{2}_{{\text{h}}} } \right)} \\ & \quad + {\left( {{\left( {m_{{\text{h}}} \cdot l_{{\text{u}}} \cdot l_{{\text{f}}} + m_{{\text{f}}} \cdot l_{{\text{u}}} \cdot r_{{\text{f}}} } \right)}\cos \theta _{2} + 2m_{{\text{h}}} \cdot l_{{\text{f}}} \cdot r_{{\text{h}}} \cdot \cos \theta _{3} + m_{{\text{h}}} \cdot l_{{\text{u}}} \cdot r_{{\text{h}}} \cdot \cos {\left( {\theta _{2} + \theta _{3} } \right)}} \right)} \\ & \quad - \ifmmode\expandafter\ddot\else\expandafter\"\fi{\theta }_{3} \cdot I_{{\text{h}}} + {\left( {m_{{\text{h}}} \cdot r^{2}_{{\text{h}}} } \right)} + m_{{\text{h}}} \cdot l_{{\text{f}}} \cdot r_{{\text{h}}} \cdot \cos \theta _{3} \\ & \quad - \ifmmode\expandafter\dot\else\expandafter\.\fi{\theta }^{2}_{1} \cdot {\left( {l_{{\text{u}}} \cdot {\left( {{\left( {m_{{\text{h}}} \cdot l_{{\text{f}}} + m_{{\text{f}}} \cdot r_{{\text{f}}} } \right)}\sin \theta _{2} + m_{{\text{h}}} \cdot r_{{\text{h}}} \cdot \sin {\left( {\theta _{2} + \theta _{3} } \right)}} \right)}} \right)} \\ & \quad + \ifmmode\expandafter\dot\else\expandafter\.\fi{\theta }^{2}_{3} \cdot {\left( {m_{{\text{h}}} \cdot l_{{\text{f}}} \cdot r_{{\text{h}}} \cdot \sin \theta _{3} } \right)} + \ifmmode\expandafter\dot\else\expandafter\.\fi{\theta }_{1} \cdot \ifmmode\expandafter\dot\else\expandafter\.\fi{\theta }_{3} \cdot {\left( {2m_{{\text{h}}} \cdot l_{{\text{f}}} \cdot r_{{\text{h}}} \cdot \sin \theta _{3} } \right)} + \ifmmode\expandafter\dot\else\expandafter\.\fi{\theta }_{2} \cdot \ifmmode\expandafter\dot\else\expandafter\.\fi{\theta }_{3} \cdot {\left( {2m_{{\text{h}}} \cdot l_{{\text{f}}} \cdot r_{{\text{h}}} \cdot \sin \theta _{3} } \right)} \\ \end{aligned} $$

$$ {\text{MT}} = {\text{NT}} - {\text{IT}} $$

Wrist torques

$$ \begin{aligned} {\text{IT}} & = - \ifmmode\expandafter\ddot\else\expandafter\"\fi{\theta }_{1} \cdot {\left( {I_{{\text{h}}} + m_{{\text{h}}} \cdot r^{2}_{{\text{h}}} + m_{{\text{h}}} \cdot l_{{\text{f}}} \cdot r_{{\text{h}}} \cdot \cos \theta _{3} + m_{{\text{h}}} \cdot l_{{\text{u}}} \cdot r_{{\text{h}}} \cdot \cos {\left( {\theta _{2} + \theta _{3} } \right)}} \right)} \\ & \quad - \ifmmode\expandafter\ddot\else\expandafter\"\fi{\theta }_{2} \cdot {\left( {I_{{\text{h}}} + m_{{\text{h}}} \cdot r^{2}_{{\text{h}}} + m_{{\text{h}}} \cdot l_{{\text{f}}} \cdot r_{{\text{h}}} \cdot \cos \theta _{3} } \right)} \\ & \quad - \ifmmode\expandafter\dot\else\expandafter\.\fi{\theta }^{2}_{1} \cdot {\left( {m_{{\text{h}}} \cdot r_{{\text{h}}} \cdot {\left( {l_{{\text{f}}} \cdot \sin \theta _{3} + l_{{\text{u}}} \cdot \sin {\left( {\theta _{2} + \theta _{3} } \right)}} \right)}} \right)} \\ & \quad - \ifmmode\expandafter\dot\else\expandafter\.\fi{\theta }^{2}_{2} \cdot {\left( {m_{{\text{h}}} \cdot l_{{\text{f}}} \cdot r_{{\text{h}}} \cdot \sin \theta _{3} } \right)} - \ifmmode\expandafter\dot\else\expandafter\.\fi{\theta }_{1} \cdot \ifmmode\expandafter\dot\else\expandafter\.\fi{\theta }_{2} \cdot {\left( {2m_{{\text{h}}} \cdot l_{{\text{f}}} \cdot r_{{\text{h}}} \cdot \sin \theta _{3} } \right)} \\ \end{aligned} $$

$$ {\text{MT}} = {\text{NT}} - {\text{IT}} $$

where θ ₁ is the shoulder angle, θ ₂ is the elbow angle, θ ₃ is the wrist angle, I _i is the moment of inertia of the segment i, r _i is the radius of gyrations of the segment i, l _i is the length, m _i is the mass (i = u: upper arm, f: forearm, h: hand).