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21 A mathematical model of human gait dynamics
176
Abstracts
Introduction Independent
interpolation
of missing 3D marker data is an accepted
practice
in
motion analysis. The results of independent interpolation conflict with the rigid body segment constraints. To address this conflict, a procedure for a segment based interpolation was presented previously’. This procedure has been expanded and integrated into the self contained software called Segment Based Interpolation this presentation is to describe the SBI software.
(SBI).
The purpose
of
Method Windows
The SBI software was written using Microsoft Visual Basic version 4.0 for on a Compaq 486 PC. IIe software uses a Vicon generated C3D data file, a
user defued
TXT file and data entered
software. 7he graphical user interface filtering options, minimum trajectory instructions file.
are then used to modify
into a graphical
user interface
to instruct
the
permits the users to enter the relevant file names, break size. and cwature constmin~. These the existing
C3D data fire or create a new C3D data
The SBI software processes only those uajecmties specified in the user defined .TXT or group file. The group file contains a definition for each segment of interest Each definition
consists
of three marker numbers
or landmark
labels that deftne the segment
The landmark labels are defmed in an optional formula file. The SBI software interprets the landmark formula and uses it in the segment based interpolation procedure. Once the segment definitions are loaded, the marker data is analyzed to determine the size and location of the traJectory breaks for each segment. Minor breaks are interpolated independently using a third order polynomial replace function. For major breaks, the software
compares
the segment based interpolation
parameters
to the
independent interpolation parameters, and uses the method that results in the smallest curvature. The SBI software then replaces the missing marker data and writes the results to a C3D tile. Results The SBl software automates the previously presented procedure for segment based interpolation. This make it a practical for clinical use. Validation of the SBI software in 1 clinical
setting will be presented.
Discussion The SBI software reduces
is flexible
the number of inaccuracies
development References I. Forstein
tool for interpolation inuoduced
of motion
by independent
interpolation.
Further
A Mathematical
Exploratory studies have just started that are designed to determine the clinical potential of our mathematictd model as a tool for evaluating therapeutic intervention strategies for improving gait mechanics and prosthesis design. Very preliminary results on 3 normal subjects and 2 amputees ( 1 AK and 1BK ) indicate that structural parameter sets exist that yield theoretical walking solutions that closely match experimental dynamic joint angle curves when compared by least squares error. Predicted optimal theoretical walks based upon maximizing mechanical energy efficiency show agreement to 2 place accoracy in nondimensionai units when comp&d with ex&imerttal-normals in the &tiables of s&p length, toe-off an4e and step frequency at self-selected speeds and at 2 and 3 mph. The optimal energetic walk was the nearest (smallest least square error) gait in the model gait space to the experimentallv observed gait in each subicct. When the number of decrees of freedom in the s&ight stancd leg (3 coo&d pendulum> model was increased to alTow the stance knee to bend during swing phase the stability of the model walk typically decreased by three orders of magnitude but the most mechanically energy efficient gait was slightly improved compared to the straight stance leg version of the model. This suggests that normal subjects can adequately control this “ore unstable gait and choose to do so because of the slight improvements in energy efficiency that ensues. .5,References Mochon
S. and McMahon
TA. (1980)Ballistic
Walking
J. Biomechanics
Vol 13.. 49-57.
Hatze H. (198 1) A Comprehensive Model for Human Motion Simulation and its Application to the Take-Off Phase of the Long Jump. I. Biomechanics Vol. 14, No. 3.. 135-142 Vol 4, Number
2: page 193,April
1996 The authors wish to acknowledge a Grant Award from St. Joseph’s Hospital and Medical Center(SJHMC) No. 9.98243 and The Kessler Foundation. Experiments on human subjects approved under Protocol R-171-95
ABSTRACT
HM tacker’,
ts and Dtscusy~n
data. The software
and testing will be presented.
M. et. al.. Gait and Posture.
Steady periodic solutions are generated for each gnt phase (swing, double support) by numericallv solvine Lamanne’s eouations of motion for a flexible number of skeletal segments
Model
of Human
Gait
Dynamics
TH Choi’. S Schenk’, B Gupta’, RP Narcessiat?. SA Sisto*, J Redling’.‘. P Engler I”, F Ghobad?, VK Mchterney’”
S Massood’.
lCe”ter for Applied Mathematics and Statistics, New Jersey Institute of Technology, University Heights, Newark NJ 07102-1982 2KessIer Institote for Rehabilitation, Inc. Pleasent Valley Way, West Orange, NJ 07102 3St. Josephs Medical Center, Dept. of Orthopedic Surgery and Sports Medicine. 703 Main St. Paterson, NJ 07503 lSeton Hall University, Depanment of Orthopaedics, School of Graduate Medical Education, South Orange N.J. 07079-2689 We present a highly idealized mathematical model of human walking that follows and extends the forward dvnamical solution aDorOaCh introduced bv Mochon and McMahon (1980 ) and Hatze(l98i). Our model can bz &d to identify bod~stroctore parameters such as segment lengths. “ass, “ass distribution. joint centers and joint viscosity from kinematic gait lab data. Without requiring additional kinematic data the model generates a complete ensemble of theoretical walks (gait space) all of which are consistent with a given subject’s structural parameters. Searches within the theoretically generated gait space are used to identify gaits that optimize model output parameters for a given smtctural pammeter set. For example. the model can be used to predict gaits that locally or globally optimize model out parameters such as mechanical energy efficiency, stabiity. muscular force generation. joint impact forces and range of motion. Constrained optimal solutions are osed to identify “best” gaits that are consistent with a given individual’s limitations in muscular force generation. range of joint motion, total mechanical energy output and neuromuscular woniination skills. A definition of gait stability is introduced that measures how difficult it is for the neuromuscular system to stab&e or control each theoretical steady gait. Model results are compared with experimentally observed walks to validate the signiticancc of the proposed definitions of gait efficiency and stability as underlying organizing principles in the selection of human gait. Finally, we indicate how the theory can be applied to gait training and prosthesis design.
Several
Factors Affect Knee Flexion in Swing Phase Steohen J. Pmzza, MST and Scott L. Delp, PhD’ iDepartment of Mechanical Engmeermg, Nonhwestem University, Evanston, IL 60201 *Departments of Biomedical Engineering and Physical Medicine & Rehabihtatlon, Northwestern University, Evanston. IL 60201 and Sensory Motor Performance Program, Rehabtlitatlon Institute of Chicago. Chicago. IL 6061 1 Introduction Manv persons with cerebral palsy walk with decreased range of knee motion. or stiff-knee gait. T% condition has comm&ly-been attributed to the kne&extending action of the rectus femoris. which freauentlv shows orolonxed and increased activation in uersons with stiff-knee gait (Perry, 1987): Fo; this reason, tie distal tendon of the rectus’femoris is sometimes transferred to the posterior side of the knee m an attempt to improve knee motion. Although this procedure is often successful. knee flexion does not ~“prove postoperatively in some patients. We believe that treatment outcomes are unpredictable because factors other than spastuty of the recta femoris may mhiblt knee flexion in some subjects. The purpose of this study was to identify the factors that contrlbute to knee flexion in normal swmg and to investigate how these factors are disrupted in strff-knee gait. We b&eve this “formation is needed to helo desien “ore effective treatments for stiff-knee gait. Analysis df the &tors that influence knee flexion most co&der the coupled dynamtcs of the swinging hmb. For example, the action of the rectus femoris is complex because the hip flexion moment It produces has the potential to “crease knee flexmn through dynamic coupling whde the knee extensmn moment It produces acts to decrease knee flexlon. These opposing mfluences cannot be examined usmg experimental measurements ofjoint angles or total joint moments. We therefore developed a mucle-actuated dynarmc simulation of the swing phase to examme the roles of the rectus femori? and of other determinants of knee flexion. We also performed a statlstlcal analysis using experimentally-measured gait kmematics to identify kmematic variables at toe-off that correlate wtth the level of knee flexion in swmg phase. Methodology Fwmuluriorr offhe compurer model. The lower extremity was represented by five segments
Abstracts
Introduction Independent
interpolation
of missing 3D marker data is an accepted
practice
in
motion analysis. The results of independent interpolation conflict with the rigid body segment constraints. To address this conflict, a procedure for a segment based interpolation was presented previously’. This procedure has been expanded and integrated into the self contained software called Segment Based Interpolation this presentation is to describe the SBI software.
(SBI).
The purpose
of
Method Windows
The SBI software was written using Microsoft Visual Basic version 4.0 for on a Compaq 486 PC. IIe software uses a Vicon generated C3D data file, a
user defued
TXT file and data entered
software. 7he graphical user interface filtering options, minimum trajectory instructions file.
are then used to modify
into a graphical
user interface
to instruct
the
permits the users to enter the relevant file names, break size. and cwature constmin~. These the existing
C3D data fire or create a new C3D data
The SBI software processes only those uajecmties specified in the user defined .TXT or group file. The group file contains a definition for each segment of interest Each definition
consists
of three marker numbers
or landmark
labels that deftne the segment
The landmark labels are defmed in an optional formula file. The SBI software interprets the landmark formula and uses it in the segment based interpolation procedure. Once the segment definitions are loaded, the marker data is analyzed to determine the size and location of the traJectory breaks for each segment. Minor breaks are interpolated independently using a third order polynomial replace function. For major breaks, the software
compares
the segment based interpolation
parameters
to the
independent interpolation parameters, and uses the method that results in the smallest curvature. The SBI software then replaces the missing marker data and writes the results to a C3D tile. Results The SBl software automates the previously presented procedure for segment based interpolation. This make it a practical for clinical use. Validation of the SBI software in 1 clinical
setting will be presented.
Discussion The SBI software reduces
is flexible
the number of inaccuracies
development References I. Forstein
tool for interpolation inuoduced
of motion
by independent
interpolation.
Further
A Mathematical
Exploratory studies have just started that are designed to determine the clinical potential of our mathematictd model as a tool for evaluating therapeutic intervention strategies for improving gait mechanics and prosthesis design. Very preliminary results on 3 normal subjects and 2 amputees ( 1 AK and 1BK ) indicate that structural parameter sets exist that yield theoretical walking solutions that closely match experimental dynamic joint angle curves when compared by least squares error. Predicted optimal theoretical walks based upon maximizing mechanical energy efficiency show agreement to 2 place accoracy in nondimensionai units when comp&d with ex&imerttal-normals in the &tiables of s&p length, toe-off an4e and step frequency at self-selected speeds and at 2 and 3 mph. The optimal energetic walk was the nearest (smallest least square error) gait in the model gait space to the experimentallv observed gait in each subicct. When the number of decrees of freedom in the s&ight stancd leg (3 coo&d pendulum> model was increased to alTow the stance knee to bend during swing phase the stability of the model walk typically decreased by three orders of magnitude but the most mechanically energy efficient gait was slightly improved compared to the straight stance leg version of the model. This suggests that normal subjects can adequately control this “ore unstable gait and choose to do so because of the slight improvements in energy efficiency that ensues. .5,References Mochon
S. and McMahon
TA. (1980)Ballistic
Walking
J. Biomechanics
Vol 13.. 49-57.
Hatze H. (198 1) A Comprehensive Model for Human Motion Simulation and its Application to the Take-Off Phase of the Long Jump. I. Biomechanics Vol. 14, No. 3.. 135-142 Vol 4, Number
2: page 193,April
1996 The authors wish to acknowledge a Grant Award from St. Joseph’s Hospital and Medical Center(SJHMC) No. 9.98243 and The Kessler Foundation. Experiments on human subjects approved under Protocol R-171-95
ABSTRACT
HM tacker’,
ts and Dtscusy~n
data. The software
and testing will be presented.
M. et. al.. Gait and Posture.
Steady periodic solutions are generated for each gnt phase (swing, double support) by numericallv solvine Lamanne’s eouations of motion for a flexible number of skeletal segments
Model
of Human
Gait
Dynamics
TH Choi’. S Schenk’, B Gupta’, RP Narcessiat?. SA Sisto*, J Redling’.‘. P Engler I”, F Ghobad?, VK Mchterney’”
S Massood’.
lCe”ter for Applied Mathematics and Statistics, New Jersey Institute of Technology, University Heights, Newark NJ 07102-1982 2KessIer Institote for Rehabilitation, Inc. Pleasent Valley Way, West Orange, NJ 07102 3St. Josephs Medical Center, Dept. of Orthopedic Surgery and Sports Medicine. 703 Main St. Paterson, NJ 07503 lSeton Hall University, Depanment of Orthopaedics, School of Graduate Medical Education, South Orange N.J. 07079-2689 We present a highly idealized mathematical model of human walking that follows and extends the forward dvnamical solution aDorOaCh introduced bv Mochon and McMahon (1980 ) and Hatze(l98i). Our model can bz &d to identify bod~stroctore parameters such as segment lengths. “ass, “ass distribution. joint centers and joint viscosity from kinematic gait lab data. Without requiring additional kinematic data the model generates a complete ensemble of theoretical walks (gait space) all of which are consistent with a given subject’s structural parameters. Searches within the theoretically generated gait space are used to identify gaits that optimize model output parameters for a given smtctural pammeter set. For example. the model can be used to predict gaits that locally or globally optimize model out parameters such as mechanical energy efficiency, stabiity. muscular force generation. joint impact forces and range of motion. Constrained optimal solutions are osed to identify “best” gaits that are consistent with a given individual’s limitations in muscular force generation. range of joint motion, total mechanical energy output and neuromuscular woniination skills. A definition of gait stability is introduced that measures how difficult it is for the neuromuscular system to stab&e or control each theoretical steady gait. Model results are compared with experimentally observed walks to validate the signiticancc of the proposed definitions of gait efficiency and stability as underlying organizing principles in the selection of human gait. Finally, we indicate how the theory can be applied to gait training and prosthesis design.
Several
Factors Affect Knee Flexion in Swing Phase Steohen J. Pmzza, MST and Scott L. Delp, PhD’ iDepartment of Mechanical Engmeermg, Nonhwestem University, Evanston, IL 60201 *Departments of Biomedical Engineering and Physical Medicine & Rehabihtatlon, Northwestern University, Evanston. IL 60201 and Sensory Motor Performance Program, Rehabtlitatlon Institute of Chicago. Chicago. IL 6061 1 Introduction Manv persons with cerebral palsy walk with decreased range of knee motion. or stiff-knee gait. T% condition has comm&ly-been attributed to the kne&extending action of the rectus femoris. which freauentlv shows orolonxed and increased activation in uersons with stiff-knee gait (Perry, 1987): Fo; this reason, tie distal tendon of the rectus’femoris is sometimes transferred to the posterior side of the knee m an attempt to improve knee motion. Although this procedure is often successful. knee flexion does not ~“prove postoperatively in some patients. We believe that treatment outcomes are unpredictable because factors other than spastuty of the recta femoris may mhiblt knee flexion in some subjects. The purpose of this study was to identify the factors that contrlbute to knee flexion in normal swmg and to investigate how these factors are disrupted in strff-knee gait. We b&eve this “formation is needed to helo desien “ore effective treatments for stiff-knee gait. Analysis df the &tors that influence knee flexion most co&der the coupled dynamtcs of the swinging hmb. For example, the action of the rectus femoris is complex because the hip flexion moment It produces has the potential to “crease knee flexmn through dynamic coupling whde the knee extensmn moment It produces acts to decrease knee flexlon. These opposing mfluences cannot be examined usmg experimental measurements ofjoint angles or total joint moments. We therefore developed a mucle-actuated dynarmc simulation of the swing phase to examme the roles of the rectus femori? and of other determinants of knee flexion. We also performed a statlstlcal analysis using experimentally-measured gait kmematics to identify kmematic variables at toe-off that correlate wtth the level of knee flexion in swmg phase. Methodology Fwmuluriorr offhe compurer model. The lower extremity was represented by five segments