This study evaluated the accuracy of one-element and two-element Hill-type muscle models in predicting the forces of the medial and lateral gastrocnemius muscles in walking and running goats. Goat muscle and tendon data were collected using implanted EMG electrodes, sonomicrometry crystals, and tendon force transducers during various locomotive behaviors. A novel two-element model that accounts for fast and slow motor units provided more accurate predictions of in vivo and in situ muscle forces than a traditional one-element model. However, both models have limitations such as assumptions of independence between activation and force-length/velocity properties.

1. Accuracy of gastrocnemius muscles forces in
walking and running goats predicted by
one-element and two-element Hill-type models
Author: Lee, S. S
Published: Sep. 2013
Presenter: Christopher D. Whitney

2. Introduction
● Hill-type muscle models are commonly used to predict muscle forces
● However, they are not very accurate during relevant movements (i.e. walking,
running, etc.)
● This study evaluates a novel two element Hill-type model
○ Inspired by the different muscle fiber types (e.g ‘fast’ and ‘slow’)

3. Methods
● Data collection
○ Goats were trained to walk, trot and gallop on a motorized treadmill
○ Lateral and medial gastrocnemius were instrumented w/
■ Implanted EMG electrodes to measure activation
■ Sonomicrometry crystals to measure fascicle length (resolution 0.3 μm)
■ “E”-shaped tendon buckles to measure tendon forces
○ Recorded in-vivo during 15-20 strides during different conditions (e.g walking,
trotting, galloping) at 5000 Hz
○ Force–length and force-velocity relationships were calculated in-situ

4. Methods (Cont.)
● Data processing
○ Motor recruitment signals for slow and fast fiber types were identified through a wavelet
optimization [2]
○ Transfer function were derived for the whole muscle as well as the slower and faster motor units
(see below)
○ Constants were identified for the different motor units and were determined from in-situ data
pooled from the six goats.
Constants

5. Muscle Model
Active-FL Passive FL Pennation AngleScaling FactorTotal Force

6. Are you ready for the schematic?

8. Results

12. Results
● In-vivo forces yielded r2
values (0.26-0.51)
● In-situ forces yielded r2
values (0.8–0.95)
● Two-element model more accurately than the one-element model under in situ
and in vivo conditions

13. Limitations

14. Limitations
● Assumption that activation, force–length, and force–velocity properties are
independent
● Failure to account for history-dependent effects
● Time resolution errors in the Gauss filter applied during the wavelet analysis
● Exclusion of tendon in the model

15. Questions?
Thoughts?

16. References
1. Lee, S.S., Arnold, A.S., Miara, M. de B., Biewener, A.A. and Wakeling, J.M. 2013. Accuracy
of gastrocnemius muscles forces in walking and running goats predicted by
one-element and two-element Hill-type models. Journal of biomechanics. 46, 13 (Sep.
2013), 2288–95.
2. Lee, S.S., Miara, M. de B., Arnold, A.S., Biewener, A.A. and Wakeling, J.M. 2011. EMG
analysis tuned for determining the timing and level of activation in different motor units.
Journal of electromyography and kinesiology : official journal of the International Society of
Electrophysiological Kinesiology. 21, 4 (Aug. 2011), 557–65.