Muscle and joint elastic properties during elbow flexion in Duchenne muscular dystrophy

Abstract

1. Maximal voluntary contraction (MVC), series elastic stiffness and total joint stiffness during elbow flexion were investigated in healthy boys and in boys with Duchenne muscular dystrophy (DMD) in order to assess changes in mechanical properties induced by the disease. 2. Two methods were used to perform stiffness measurements: (i) the application of sinusoidal perturbations to the joint during flexion efforts, allowing the calculation of total joint stiffness; (ii) the use of quick-release movements of the elbow, which had previously been maintained in isometric contraction, allowing the calculation of series elastic stiffness. In each case, stiffness was linearly related to torque, leading to the calculation of a normalized stiffness index as the slope of this stiffness-torque relationship. 3. As expected, mean MVC was found to be much higher for healthy boys (20.02 +/- 5.20 N m) than for DMD patients (3.09 +/- 2.44 N m). Furthermore, the results showed that it was possible to characterize healthy and DMD children by virtue of the mechanical properties measured. Mean series elastic stiffness index was higher for DMD children (142.55 +/- 136.58 rad(-1)) than for healthy subjects (4.39 +/- 2.53 rad(-1)). The same holds for mean total joint stiffness index: 43.68 +/- 67.58 rad(-1) for DMD children and 2.26 +/- 0.70 rad(-1) for healthy subjects. In addition, increases in stiffness were more marked in DMD patients exhibiting high levels of muscle weakness. 4. These changes are interpreted in terms of the adaptation of the properties of the muscles and joint involved, i.e. muscle fibres, tendons, peri- and intra-articular structures.

Figure 1

Elbow ergometer

Figure 2. Typical raw data for quick-released movement

A, healthy subject; B, DMD patient. Changes in acceleration (Δθ‘’) and position (Δθ) were calculated during the first 30 ms after release.

Figure 3. Typical raw data for sinusoidal perturbation test

A, healthy subject; B, DMD patient. Position-to-torque amplitude ratio (a/b) and position-to-torque difference in phase (φ) were calculated for each imposed frequency.

Figure 4. Typical series elastic stiffness-torque and inertia-torque relationships

Stiffness (▴) and inertia (▴) for a DMD patient. Stiffness (▪) and inertia (□) for a healthy subject.

Figure 5. Global series elastic stiffness-torque relationship for DMD patients

A clear dissociation of the population is observed. •, linear relationship for DMD patients with test scores < 5 (r²= 0.70, SI_QR= 138.36 rad⁻¹). ○, linear relationship for DMD patients with test scores ≥ 5 (r²= 0.46, SI_QR= 3.41 rad⁻¹).

Figure 6. Global series elastic stiffness-torque relationship for healthy subjects

r²= 0.61, global SI_QR= 3.85 rad⁻¹.

Figure 7. Typical total joint stiffness-torque and inertia-torque relationships

Stiffness (▴) and inertia (▵) for a DMD patient. Stiffness (▪) and inertia (□) for a healthy subject.

Figure 8. Bode diagrams

A, typical compliance and phase diagrams for healthy subjects. The compliance curve shows a peak in the resonant frequency followed by a linear decrease with a slope of -40 dB decade⁻¹ (r²= 0.95). B, typical compliance and phase diagrams for DMD patients. Resonant frequency shifted towards lower frequencies, leading to truncated diagrams (r²= 0.90).

Figure 9. Simulated Bode diagrams from the second-order model obtained by virtue of experimental data for a DMD patient and a healthy subject working at low torque

A, compliance diagram; B, phase diagram. □, experimental data for a DMD patient exerting a mean torque of 0.95 N m (r²= 0.99). ○, experimental data for a healthy subject exerting a mean torque of 1.14 N m (r²= 0.97). Simulated data in the 1-50 Hz frequency range are shown for a DMD patient (dotted line) and a healthy subject (continuous line).

Figure 10. Global total joint stiffness-torque relationship for DMD patients

No obvious global relationship is observed whereas a linear relationship can be observed for DMD patients with test scores ≥ 5 (○; r²= 0.32, SI_SP= 3.78 rad⁻¹). •, DMD patients with test scores < 5.

Figure 11. Global total joint stiffness-torque relationship for healthy subjects

r²= 0.67, global SI_SP= 2.74 rad⁻¹.