RESULTS:

OBJECTIVE: Develop a phenomenological joint-space formulation of general human EE for various tasks that is validated by experimental gait data.

METHODS:

•Basal metabolic rate (BMR) - Mifflin-St.Jeor equation (in Watts):

•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:

•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

•Joint space phenomenological formulation of total metabolic EE (in W):

where

•The torque and angular velocity can and do have different signs depending on the activity metabolic cost associated with both positive and negative work

Dustyn Roberts and Joo H. Kim

Polytechnic Institute of New York University, Brooklyn, NY

REFERENCES: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.

BACKGROUND: 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.

ACKNOWLEDGEMENTS:This work was supported in part by a National Science Foundation Graduate Research Fellowship to Dustyn Roberts under Grant No. DGE-1104522.

DISCUSSION: 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.

RESULTS

A Phenomenological Human Energy Expenditure Model in Joint Space

BACKGROUND

OBJECTIVE

MODEL DERIVATION

DISCUSSION

ACKNOWLEDGEMENTS

REFERENCES

0.0485 9.99 6.25 4.92B M H A s

MODEL DESCRIPTION (CONTINUED):•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:

HEAT COEFFICIENT ESTIMATION

1 1 1 1

( ) ( ) ( ) + ( ) ( ) ( ) ( ) ( )

n n n n

i i ii i am i sl i i cc

i i i i

E t t q t h t h t q t Q t B t

if ( ) ( ) 0

= 1,..., if ( ) ( ) 0

sl i isl

sl i i

h t q th i n

h t q t

Parameter ValueBasal Metabolic Rate (W)

75

Average Active Metabolic Rate (W)

188

Average Total Metabolic Rate (W)

263

η+ 0.668η- 2.004 ham

hsl+

hsl-

0.10.2190.073

(2)

(1)

Estimation Results

Muscle Space

Joint Space(Generalized Coordinates)

muscle 1muscle 2

:::::::::

muscle p

joint 1joint 2

:::::

joint n

mapping

:::

muscle 3

• 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:

• Identification from First Law of Thermodynamics:

0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

x (m)

y (m

)

• Walking experiments [1] – estimation of heat coefficients and demonstration

Right

Left

stance

DS

RHC0%

LTO

28 36

62

55 62 70

70 96 104/36

DS

stance

SS1 SS2 DS

swing stance

DS SS1 SS2

swing

96

RTO

6256

RHC100%

LHC

RHO

LHO

( ) ( , ) | ( ) |ma t c q q t

sys totE Q W ( ) ( ) ( )metE t W t Q t

Total Human Energy Expenditure

Muscle Energy Consumption Basal Metabolic Energy Rate (BMR)

Muscle Work Active Muscle Heat

Activation Heat Maintenance Heat Shortening Heat Lengthening Heat

Food Water Air (O2)

Mass Loss (sweat, Air (CO2), etc.)

Resting Muscle Heat Brain/Liver/Kidney/Heart/etc.

Stored Energy

( ) ( ) (t) 1, 2,..., i i iW t t q i n

1

1 1( ) ( ) ( ) ( )u p

lower lowersagittal sagittal

E t s s W t W t B t

• Throwing simulation [6] – demonstration of general task example

Parameter (W) Value

Average Total Metabolic Rate 1278 (similar to cycle racing )

Peak Rate of Energy Expenditure 2830 (occurred at the release point)

Simulation Results