Comparison of human gastrocnemius forces predicted by Hill-type muscle models and estimated from ultrasound images

Abstract

Hill-type models are ubiquitous in the field of biomechanics, providing estimates of a muscle's force as a function of its activation state and its assumed force-length and force-velocity properties. However, despite their routine use, the accuracy with which Hill-type models predict the forces generated by muscles during submaximal, dynamic tasks remains largely unknown. This study compared human gastrocnemius forces predicted by Hill-type models with the forces estimated from ultrasound-based measures of tendon length changes and stiffness during cycling, over a range of loads and cadences. We tested both a traditional model, with one contractile element, and a differential model, with two contractile elements that accounted for independent contributions of slow and fast muscle fibres. Both models were driven by subject-specific, ultrasound-based measures of fascicle lengths, velocities and pennation angles and by activation patterns of slow and fast muscle fibres derived from surface electromyographic recordings. The models predicted, on average, 54% of the time-varying gastrocnemius forces estimated from the ultrasound-based methods. However, differences between predicted and estimated forces were smaller under low speed-high activation conditions, with models able to predict nearly 80% of the gastrocnemius force over a complete pedal cycle. Additionally, the predictions from the Hill-type muscle models tested here showed that a similar pattern of force production could be achieved for most conditions with and without accounting for the independent contributions of different muscle fibre types.

Keywords: B-mode ultrasound; Electromyography; Motor unit recruitment; Musculoskeletal simulation.

Fig. 1.

Approach for comparing lateral gastrocnemius (LG) and medial gastrocnemius (MG) forces during cycling estimated from ultrasound-based measures of tendon length changes and stiffness and predicted from Hill-type muscle models. (A) During the cycling protocol, subjects pedalled on a stationary bike while we measured tendon lengths from tracked ultrasound images of the LG and MG muscle–tendon junctions, fascicle lengths and pennation angles from ultrasound images of the LG and MG muscle bellies, and activation patterns derived from surface electromyography. A trigger from the ultrasound system was used to synchronize all data. Forces were estimated from the tracked ultrasound images of tendon length changes during cycling and tendon stiffness measured for each subject in an isometric protocol (Dick et al., 2016). (B) The experimentally determined fascicle lengths l_f, pennation angles β and normalized muscle activations for total (black), slow (red) and fast (blue) motor units were used as inputs for the muscle models. (C) We tested a traditional one-element Hill-type muscle model and additionally a two-element model that accounted for the independent contributions of slow and fast muscles fibres. Estimated forces from the ultrasound-based approach were compared with the forces predicted from the models for the LG and MG. CE, contractile element; PEE, parallel elastic element; β, pennation angle. Refer to Table 1 for definitions of all symbols.

Fig. 2.

Myoelectric intensity spectra reconstructed from the pooled frequency spectra (thin lines) and optimized wavelets (thick lines) for human LG (A) and MG (B). Low ­-frequency spectra are shown in red and high-frequency spectra in blue.

Fig. 3.

Time-varying force profiles for the LG (left) and MG (right) with pedalling condition for one representative subject. (A) Pedalling at 60 rpm cadence at 44 N m crank torque. (B) Pedalling at 100 rpm at 26 N m. Ultrasound-based estimates of force are represented in black, and predicted forces from the one-element model in grey and from the two-element model in red. Muscle forces F_m are normalized to the maximum isometric force F_max of either the LG or the MG.

Fig. 4.

Differential recruitment of slow and fast muscle fibres with pedalling condition for one representative subject. Raw EMG (grey) and total (black), slow (red) and fast (blue) intensity and activation traces for LG (A) and MG (B) when pedalling at 60 rpm at 44 N m (left panel) and 140 rpm at 13 N m (right panel). Vertical dashed lines show the timing of pedal top-dead-centre. These conditions have been chosen to highlight the differences in recruitment between slow and fast muscle fibres that can occur across the range of mechanical conditions tested here.

Fig. 5.

Sensitivity of one-element model predictions to force-velocity parameters in the LG (left) and MG (right). (A) Curvature of force–velocity relationship, α. (B) Maximum intrinsic speed, . Data points represent the mean±s.e. across all subjects (n=16). Different values of α and are shown using different shades of grey.