ISPO 2001: Modeling in Gait

SY20: Modeling techniques in gait analysis

Yoshihira Ehara, The Kanagawa Rehabilitation Institute, Japan
Kenton Kaufman, The Mayo Clinic, USA
Chris Kirtley, Catholic University USA

Question	Variable	Posibilities	Modeling Tool	Assumptions & Limitations	Applications
Range of Motion, restricted motion, excessive motion	Joint Angles, Velocities	2D/3D, Helen Hayes, Cleveland, 6DoF joints	Link-segment model	Euler sequence dependence & gimbal lock	Pre/Post Assessment, documentation, outcome measures
Spasticity	Muscle-tendon lengths	Maximum & minimum averaged length	Deformable model, 3D reconstruction ± radiographic, MRI images	Muscle origin & insertion anthropometry, skin-bone artifact, muscle physiology	Planning treatment (e.g. surgery in Cerebral palsy)
Direction & magnitude of muscle activity	Joint Moment Electromyography	Flexor/extensor Ab/adductor In/external rotator	Inverse Dynamics (needs force platform) M_p = I.a - M_d + Rx_p(y_p - y_CoM) + Ry_p(x_CoM - x_p) + Rx_d(y_d - y_CoM) + Ry_d(x_CoM- x_d) where p=proximal; d=distal; CoM = center of mass; a = angular acceleration	Errors in joint center estimation, body segment parameters, error propagation	Identify weakness/spasticity, prosthetic alignment
Joint loading	Joint Force	Magnitude Direction	Inverse Dynamics Optimization	Lever arms, force compartmentalization	Endoprosthesis design, arthritis/walking aid assessment
Type of Contraction	Joint Power	Concentric Eccentric	Inverse Dynamics P = Mw where w = angular velocity	Filtering greatly affects peak amplitudes	Determine purpose of muscle activity (propulsion or braking)
Energy Transfer	Segmental Energies	Potential Linear kinetic Rotational kinetic	Segmental equations of motion	Body segment parameters	Prosthetics
Energy Consumption	Oxygen consumption, Physiological Cost (PCI)	Energy consumed (metabolic cost) Change in Heart Rate from resting	VO₂	Encumbrance of subject Confounding variables (anxiety)	Evaluation of Interventions (e.g. prostheticorthotic devices, surgery)
Efficiency	Joint Energies	Generation Absorption	Integration of Joint Powers	No co-contraction, friction, energy storage	Efficiency of prosthetic components
Direction of effort	Power Flow	Proximal Distal Absorbed	Passive & Active contributions to segmental power	Foot segment can be difficult to balance	Determining the role of muscle power bursts
Destination of effort, source of motion	Induced Acceleration	Ipsilateral joint Contralateral joint	Coupled Dynamics a = M^-1(q)t - M^-1C(q,w) - M^-1G(q)	Singularities due to problems in defining foot-floor interaction	Determine source of a given moment & control strategies available
Balance Control	Center of Pressure, Center of Mass, Base of Support	Postural Sway, anticipatory & reactive torques	Inverted Pendulum, Full body models, perturbation studies	Interpretation during locomotion	Falls in the Elderly, Quantification of Dysequilibrium
What if...?	Dynamic (Forward) Simulation	Computed Joint Motion Trajectories	Lagrange, Kane	Initial conditions, often 2D, assume trajectories	Influences on swing phase knee flexion.
Paraplegic Locomotion	Finite States Machines	Functional Electrical Stimulation (FES), conventional orthoses, hybrids	Rule base control, confusion matrices, accelerometers, force sensors, fuzzy logic, machine learning, neural networks	False positives & negative event detection	Neuroprostheses
Walking machines "I never satisfy myself unless I can make a mechanical model of a thing. If I can make a mechanical model I can understand it." (Lord Kelvin)	Balance, forward motion, energy consumption	Passive Walking, reflexes, springlike properties of muscles, tendons	Inverted Pendulum, series-elastic actuators, limit cycles, micro- gravity	Falling, instability	Test understanding, control hypotheses.

History

Elftman
Bresler & Frankel
Paul
McMahon, Alexander
Winter
Zajac

Example Applications

Ankle function in normal locomotion

Variable	Results	Interpretation
Joint Angle		Approx. neutral at contact Dorsiflexes through stance Sudden plantarflexion at toe-off Rapid return to neutral
Joint Angular Velocity		High plantarflexor velocity at toe-off
Center of Pressure
Joint Moment		Small dorsiflexor moment on contact Rise in plantarflexor moment to a maximum in late stance
Foot Power
Shank Power
Joint Power		Small eccentric after contact Large burst of concentric power in late stance ("push-off")
Power Flow
Soleus Induced Acceleration
Gastroc Induced Acceleration

Clinical Case: #1. Right hemiparesis (cerebral palsy)

Weak & spastic (plantarflexed) ankle, with reduced push-off power

Bibliography

Kinematics

Davis, RB III, Ounpuu, S, Tyburski, D, and Gage, JR (1991). A gait data collection and reduction technique. Human Movement Sciences 10, 575-587.
Kepple TM, Arnold AS, Stanhope SJ, Siegel KL (1994) Measurement of musculoskeletal motion from surface landmarks: A three-dimensional computer graphics approach. Journal of Biomechanics 27(3):365-371.

Muscle lengths

Delp SL, Arnold AS< Speers RA & Moore C (1996) Hamstrings and psoas lengths during normal and crouch gait: implications for muscle-tendon surgery. J. Orthop. Res. 14: 144-151.
Thompson N, Baker R, Cosgrove A, Corry I & Graham H (1998) Muskuloskeletal modelling in determining the effect of botulinum toxin on the hamstrings of patients with crouch gait. Developmental Medicine and Child Neurology, ;40: 622-625
Szepannek, M., McDOWELL, B., Cosgrove, A.P., Baker, R. Which muscles have the most potential as internal rotators of the hip? Gait and Posture, 8, 71, 1998.
Eames, Niall W.A., Baker, R.J., Cosgrove, A.P.(1997) Defining gastrocnemius length in ambulant children.Gait and Posture,1(6): 9-17
N Eames, R Baker, A Cosgrove (1995) Estimating gastrocnemius length from joint rotation measurements, Gait & Posture 3 (4) pp. 277-278.
Eames N, Baker R, Hill N, Graham K, Taylor T & Cosgrove A 1999. The effect of botulinum toxin A on gastrocnemius length: magnitude and duration of response. Developmental Medicine & Child Neurology. 41 226-232.

Inverse Dynamics

Bresler, B. and Frankel, J. (1950). The forces and moments in the leg during level walking. Transactions of the ASME: 27-36.
Eng, J. and Winter, D. (1995). Kinetic analysis of the lower limbs during walking: What information can be gained from a three-dimensional model? Journal of Biomechanics, 28(6):753-758.
Scott, S. and Winter, D. (1993). Biomechanical model of the human foot: Kinematics and kinetics during the stance phase of walking. Journal of Biomechanics, 26(9):1091-1104.
Buczek FL, Kepple TM, Siegel KL, Stanhope SJ (1994) Translational and Rotational Joint Power Terms in a Six Degree-of-Freedom Model of the Normal Ankle Complex.Journal of Biomechanics 27(12):1447-1457

Balance Control

Kinnon, C. M. and Winter, D. (1993). Control of whole body balance in the frontal plane during human walking. Journal of Biomechanics, 26(6):633-644.
Agarwal, G., Berman, B., and Stark, L. (1970). Studies in postural control systems part i: Torque disturbance input. ieeetssc, 6-2:116-121.

Energetics

Elftman H (1939) Forces & energy changes in the leg during walking. Am. J Physiol. 125: 339-356.
Winter, D.A. (1983). Energy generation and absorption at the ankle and knee during fast, natural, and slow cadences. Clinical Orthopedics and Related Research, 175, 147-154.
Siegel KL, Kepple TM, Caldwell GE (1996) Improved agreement of foot segmental power and rate of energy change during gait: Inclusion of distal power terms and use of three-dimensional models. Journal of Biomechanics 29(6):823-827.
Siegel, K., Kepple, T., & Caldwell, G. (1996) "Improved Agreement of Foot Segmental Power and Rate of Energy During Gait: Inclusion of Distal Power Terms and use of 3D models." Journal of Biomechanics, 29, 823-827.

Induced Acceleration

Zajac FE and Gordon ME(1989) Determining muscle's force and action in multi-articular movement. In: Pandolf, K. (ed.) Exerc Sport Sci Revs. Baltimore: Williams & Wilkins, vol. 17: 187-230
Zajac FE (1989) Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. In Bourne, J.R. (ed.): CRC Critical Rev in Biomed Eng. Boca Raton: CRC Press, vol. 17 (#4), 359-411
Kepple, T. Siegel , K., & Stanhope, S. (1997) "The use of two foot-floor models to examine the role of the ankle plantar flexors in the forward acceleration of normal gait." Gait and Posture, 5, 172-173.

Forward Simulation

Onyshko, S. and Winter, D. (1980). A mathematical model for the dynamics of human locomotion. Journal of Biomechanics, 13:361-368.
Delp SL, Loan JP, Hoy MG, Zajac FE, Topp EL & Rosen JM (1990) An interactive graphics-based model of the lower extremity to study orthopedic surgical procedures. IEEE Trans. Biomed. Eng. 37(8):757-767.
Delp SL & Loan JP (1995) A software system to develop and analyze models of musculoskeletal structures. Computers in Biology & Medicine 25:21-34.
Riewald SA & Delp SL (1997) The action of the rectus femoris muscle following distal tendon transfer: does it generate a knee flexion moment? Dev. Med. & Child Neurol. 29: 153-158.

Finite State Machines

B.Andrews, R.Barnett, G.Phillips, C.Kirkwood, N.Donaldson, D.Rushton, T.Perkins, Rule-Base control of a hybrid FES orthosis for assisting paraplegic locomotion, Automedica,11:175-199 (1989)
S.Ng, H.Chizeck, A fuzzy logic gait event detector for FES using Firmware Transitional Logic, Proc. IEEE EMBS 10th Ann.Conf.1562-1563
B.Heller, P.Veltink, N.Rijkhoff, W.Rutten, B.Andrews,Reconstructing muscle activation during normal walking: A comparison of symbolic and connectionist machine learning techniques, Biol. Cybern. 69:327-335 (1993)
A.Kostov, B. Andrews, D. Popovic, R. Stein, W. Armstrong, Machine Learning in Control of Functional Electrical Stimulation Systems for Locomotion, IEEE Trans. Biomed. Eng. 42:6:541-551 (1995)

Walking Machines

McMahon T (1984) Muscles, Reflexes and Locomotion
Ruiina (1998) The Simplest Walking Model: Stability, Complexity, and Scaling. ASME Journal of Biomechanical Engineering, Vol. 120 No. 2 pp. 281 - 288.
Coleman, M, Ruina, A (1998) Physical Review Letters April Vol 80, Issue 16 pp. 3658 - 3661.
McGeer, T. (1990) Passive dynamic walking, International Journal of Robotics Research, Vol. 9, No., 2: 62-82.
Kuo, A. D. (1999) Stabilization of lateral motion in passive dynamic walking, International Journal of Robotics Research, Vol. 18, No. 9, pp. 917-930.
Chaillet, N., Abba, G., and Ostertag, E. (1994). Double dynamic modelling and computed-torque control of a biped robot. In IEEE International Conference on Intelligent Robots and Systems, volume 3, pages 2007-2014, Munich.
He, J., Kram, R., McMahon, T., 1991. Mechanics of running under simulated low gravity., J. Applied Phsiology, 71(3):863-870.