Transcript results - Force and Motion Foundation

A Phenomenological Human Energy Expenditure
Model in Joint Space
Dustyn Roberts and Joo H. Kim
Polytechnic Institute of New York University, Brooklyn, NY
BACKGROUND:
H
EAT COEFFICIENT
ESTIMATION
MODEL
DESCRIPTION
(CONTINUED):
Humans derive their energy from food, water, and air. This input energy
is transformed into the mechanical work of motion and the balance is
either stored or dissipated as thermal energy. Metabolic energy
expenditure (EE) is converted to mechanical work at the junction of
tendon and bone [1]. However, there are several losses and
inefficiencies that prevent direct transformation of metabolic energy to
mechanical work. The mechanical work at joints can be determined from
standard gait analysis and inverse dynamics procedures. Several existing
models that calculate metabolic EE based on output from Hill-type
muscle models [2] rely on geometric parameters that are often taken from
static cadaver studies [3]. Recent work [4] demonstrated the possibility of
calculating metabolic EE in joint space, which facilitates analysis and
simulations. By developing this capability in the joint space, vs. the
muscle space, we can solve for EE in any general motion when the
kinematic and kinetic data are known.
• Kinematic and kinetic gait data [1] were used to characterize the
physical activity in order to estimate the heat coefficients in EE model.
• To determine the whole body metabolic cost of gait based on the
sagittal plane lower body dataset used, the average metabolic EE rate
above BMR was estimated using an experimentally derived equation [5]
to determine acceptable scaling factors:


1
1
  B (t )
(2)
E1 (t )  su s p 
W
(
t
)

W
(
t
)




  lower 

 lower 

sagittal
 sagittal

RESULTS:
• Walking experiments [1] – estimation of heat coefficients and
demonstration
70
96 104/
36
LHC
LTO
OBJECTIVE:
DS
stance
Develop a phenomenological joint-space formulation of general human
EE for various tasks that is validated by experimental gait data.
DS
Left
swing
62
LHO
SS1
1
SS2
0.8
stance
stance
Right
56
y (m)
62
0.6
swing
0.4
DS
SS1
SS2
DS
0.2
RHO
RHC
0%
28
Muscle Space
• Resultant of multiple muscles
that contribute to a single
anatomical joint movement
 combination of kinematically
equivalent revolute joints
• The joint variables (angles)
serve as generalized
coordinates  joint space
• Muscle-induced actuator torque
and activation level:
Joint Space
muscle 1
muscle 2
muscle 3
:
:
:
:
:
:
:
:
:
muscle p
am (t )  c(q, q) |  (t ) |
(Generalized Coordinates)
mapping
:
:
:
joint 1
joint 2
:
:
:
:
:
joint n
• Identification from First Law of
Thermodynamics:
36
55
RTO
62
70
0
0.5
1
1.5
96
2
2.5
3
x (m)
Estimation Results
Parameter
Value
Basal Metabolic
75
Rate (W)
Average Active
188
Metabolic Rate (W)
Average Total
263
Metabolic Rate (W)
η+
0.668
η2.004
ham
0.1
hsl+
0.219
hsl0.073
Energy Expenditure as a Function of
Gait Cycle
750
BMR
Equation 1
Equation 2
500
250
0
0
20
40
60
% Gait Cycle
80
100
• Throwing simulation [6] – demonstration of general task example
E (t )   W (t )   Qmet (t )
Esys  Q  Wtot
RHC
100%
Energy Expenditure (W)
MODEL
DERIVATION
ETHODS
:
Food
Water
Parameter (W)
Simulation Results
Value
Average Total Metabolic Rate
Air (O2)
Total Human Energy Expenditure Stored Energy
1278 (similar to cycle
racing )
Peak Rate of Energy Expenditure 2830 (occurred at the
release point)
Muscle Energy Consumption Basal Metabolic Energy Rate (BMR) Mass Loss (sweat, Air (CO2), etc.)
Resting Muscle Heat Brain/Liver/Kidney/Heart/etc.
Muscle Work
Activation Heat
Active Muscle Heat
Maintenance Heat
Shortening Heat
DISCUSSION
ISCUSSION:
Lengthening Heat
• Basal metabolic rate (BMR) - Mifflin-St.Jeor equation (in Watts):
B  0.0485  9.99M  6.25H  4.92 A  s 
• Resultant actuator torque at each joint is the sum of the moments
created by both active and passive forces. The joint mechanical power
is due to the muscle-induced actuator torque:
Wi (t )   i (t )qi (t) i  1, 2,..., n 
A
ACKNOWLEDGEMENTS
CKNOWLEDGEMENTS:
• Heat released from active muscle = activation and maintenance heat
(dependent on muscle force independent of length changes) +
shortening and lengthening heat (dependent on the rate of change in
muscle length) + cocontraction heat
This work was supported in part by a National Science Foundation Graduate Research Fellowship
to Dustyn Roberts under Grant No. DGE-1104522.
• Joint space phenomenological formulation of total metabolic EE (in W):
n
n
n
n
i
E (t )    i (t )qi (t ) + ham
 i (t )   hsli  i (t )qi (t )   Qcci (t )  B(t )
i 1
i 1
i 1
hsl  if  i (t )qi (t )  0
where hsl = 
hsl  if  i (t )qi (t )  0
i 1
 i  1,..., n 
• The torque and angular velocity can and do have different signs
depending on the activity  metabolic cost associated with both
positive and negative work
The phenomenological model developed here shows a slightly different
EE profile than that derived from [1] although the average metabolic rate
is the same. This model is expected to more closely resemble the EE
profile of an actual subject based on physiologically derived terms. This
research represents the first step in developing a joint-space-based
human EE equation for general tasks. Improvements in coefficient
estimation and validation will be pursued in future work.
(1)
R
REFERENCES
EFERENCES:
1. D. A. Winter, Biomechanics and Motor Control of Human Movement, Wiley, 2009.
2. L. J. Bhargava, et al., “A Phenomenological Model for Estimating Metabolic Energy
Consumption in Muscle Contraction,” J Biomech, 37, n. 1, 81–88, Jan. 2004.
3. K. Manal, D. P. Roberts, and T. S. Buchanan, “Can Pennation Angles Be Predicted from EMGs
for the Primary Ankle Plantar and Dorsiflexors During Isometric Contractions?,” J Biomech, 41,
n. 11, 2492–2497, Aug. 2008.
4. J. H. Kim, J. Yang, and K. Abdel-Malek, “Planning Load-Effective Dynamic Motions of Highly
Articulated Human Model for Generic Tasks,” Robotica, 27, n. 5, 739–747, Sep. 2009.
5. P. G. Weyand, B. R. Smith, M. R. Puyau, and N. F. Butte, “The Mass-Specific Energy Cost of
Human Walking Is Set by Stature,” J Exp Biol, 213, n. 23, 3972–3979, Dec. 2010.
6. J. H. Kim, Y. Xiang, J. Yang, J. S. Arora, and K. Abdel-Malek, “Dynamic Motion Planning of
Overarm Throw for a Biped Human Multibody System,” Multibody Syst Dyn, 24, n. 1, pp.1–24,
Jun. 2010.