3. Intro to Data
● Data comes from in vivo measurements conducted by Dr. Daley
○ Two individual fowls (blue and yellow)
○ Three trials (5cm, 7cm and level)
○ Two muscles recorded for each trail (LG, DF)
● Collected using
○ Sonomicrometry for the lengths
○ Tendon buckles for the forces
○ Implanted EMG for the activation
4. Model Description
Using the winding filament paradigm of muscle contraction, the following
vibrational model was derived by Petak and colleagues [3]. The below schematic is
the latest version of the wfm model v9.
5. Model Description: How it works
● Second-order differential equations are used to describe movement over time
● Displacement vectors (cm) and velocity vectors (cm/s) are found through
double integration of acceleration of the mass of the pulley
● Forces are described using the following equations
○ K*delta_x (Springs)
○ C*delta_v (Dashpots/Dampers)
○ Where K is a spring stiffness constant (N/cm), C is a damping rate constant (Ns/cm)
○ Delta_x is the displacement in position
○ Delta_v is the displacement in velocity
7. Methods
1. Transform raw EMG percent of activation
a. High-pass Butterworth filter
b. Rectificated
c. Low-pass Butterworth filter
d. Normalized to MVC
2. Activation time delay (23ms) incorporated into the model
3. General FL and FV incorporated into the model
4. Unknown physiological values estimated (i.e Lo, Po, Vo)
5. Force outputs multiplied by cos of the pennation angle
6. Hand tuning based on “after-flight” component analysis
7. Free-parameters optimized to the measured forces
8. Accuracy measured using R^2
8.
9. Activation time-delay incorporation
Fce = Po *[Fl(l)*Fv(v)*Act(i-d)]
Where i is the current data point, d is the activation delay in time steps, is the peak isometric force, l is
muscle fascicle length, v is the velocity of the contractile element, Fl is the force-length relationship
which is a function of l, the Fv is the force-velocity relationship which is a function of v, and Act which is
percentage of muscle activation between 0-.6.
10. General FL and FV
Where Lo is optimal length, Vo is optimal velocity, and where a,b,c and Afl are shape-factors.
Note that this force-velocity relationship uses three shape-factor which could be minized by using a
different set of equations.
11. “After-flight” Component Analysis
Each position, velocity, acceleration and force components of the current run is visually examined to
make sure it is performing properly.
12.
13. Figure 1: High-level flowchart of the optimization process where the free
parameters are tuned to minimize 1-R Squared. The EMG Normalizer is
the transformation function for the raw EMG signal
Optimization Process
22. Discussion
● Is this a science of curve fitting?
● And is wfm truly better than a
two-element Hill?
● And does this model truly describe
the winding filament hypothesis?
23. References
1. Daley, M., Voloshina, A. and Biewener, A. 2009. The role of intrinsic muscle mechanics in the
neuromuscular control of stable running in the guinea fowl. The Journal of Physiology. 587, 11 (2009),
2693–2707.
2. Lee, S.S. et al. 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.
3. Petak , J.L. PERFORMANCE TESTING OF A MUSCULOSKELETAL MODEL CONTROLLER FOR A ROBOTIC
PROSTHESIS.
