Title: Determination of patient-specific functional axes through two-level optimization
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Permanent Link: http://ufdc.ufl.edu/UF00094763/00001
 Material Information
Title: Determination of patient-specific functional axes through two-level optimization
Physical Description: Book
Language: English
Creator: Reinbolt, Jeffrey A.
Publisher: Reinbolt et al.
Place of Publication: Gainesville, Fla.
Copyright Date: 2003
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Bibliographic ID: UF00094763
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.


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Jeffrey A. Reinbolt (1), Jaco F. Schutte (2), Raphael T. Haftka (2),
Alan D. George (3), Kim H. Mitchell (4), and Benjamin J. Fregly (1, 2)

(1) Department of Biomedical Engineering
University of Florida
Gainesville, FL

(3) Department of Electrical & Computer Engineering
University of Florida
Gainesville, FL

Innovative patient-specific models and simulations would be
valuable for addressing problems in orthopedics and sports medicine,
as well as for evaluating and enhancing corrective surgical procedures
[1]. For example, a patient-specific dynamic model may be useful for
planning intended surgical parameters and predicting the outcome of
high tibial osteotomy (HTO). Development of an accurate inverse
dynamic model is a significant first step toward creating a predictive
patient-specific forward dynamic model. The precision of inverse
dynamic analyses is fundamentally associated with the accuracy of
kinematic model parameters such as segment lengths, joint positions,
and joint orientations.
Understandably, a model constructed of rigid links within a
multi-link chain [2] and simple mechanical approximations of joints
[3] will not precisely match the human anatomy and kinematics. The
model should provide the best possible assessment within the bounds
of the joint models selected [3]. Earlier studies describe optimization
methods to discover a set of model parameters for three-dimensional
(3D), 2 degree-of-freedom (DOF) models by decreasing the error
between the motion of the model and experimental data [3, 4]. In this
paper, we present a nested, or two-level, system identification
optimization approach to determine patient-specific joint parameters
that best fit an 18 DOF lower-body model to movement data.

A generic, parametric 3D full-body kinematic model was
constructed with Autolev as a 14 segment, 27 DOF linkage joined by a
set of gimbal, universal, and pin joints. Comparable to Pandy's [1]
model structure, three translational and three rotational DOFs express
the movement of the pelvis in 3D space and the remaining 13
segments comprise four open chains branching from the pelvis
segment. A static motion capture trial is used to create segment
coordinate systems and define dynamic marker locations in these
coordinate systems. A modified version of the Cleveland Clinic
marker set is used for this purpose. The locations and orientations of
the joints within the segment coordinate systems are described by 98

(2) Department of Mechanical & Aerospace Engineering
University of Florida
Gainesville, FL

(4) Orthopaedic Research Laboratory
The Biomotion Foundation
West Palm Beach, FL

patient-specific model parameters for the following joints: 3 DOF hip,
1 DOF knee, 2 DOF ankle, 3 DOF back, 2 DOF shoulder, and 1 DOF
elbow. The patient-specific parameters for each joint are defined in
two adjacent body segments (Figure 1). For example, the knee joint
axis is simultaneously established in the femur coordinate system and
the tibia coordinate system.

Figure 1. Schematic of a 1 DOF joint axis simultaneously
defined in two adjacent body segments and the geometric
constraints on the optimization of each of the 9 parameters.

Given dynamic motion capture data, the lower-level sub-
optimization (Figure 2, inner boxes) minimizes the 3D marker
coordinate errors between the model and the movement data using a

2003 Summer Bioengineering Conference, June 25-29, Sonesta Beach Resort in Key Biscayne, Florida

nonlinear least squares algorithm that adjusts the DOFs of the model at
each instance in time [2]. Initially, the algorithm is seeded with exact
values for the pelvis DOFs, since the marker locations directly identify
the position of the pelvis coordinate system, and all remaining DOFs
are seeded with values equal to zero. Given the joint motion is
continuous, each optimal DOF solution at a particular time instance is
used as the algorithm's seed for the subsequent time instance.
The upper-level global optimization minimizes the sum of the
squares of the 3D marker coordinate errors computed by the lower-
level algorithm throughout every time instance, or the entire joint
motion, by modifying the patient-specific model parameters. To
manage computational requirements, the upper-level optimization
employs a parallel version of the particle swarm algorithm operating
on a 20-processor network cluster; therefore, each is separately seeded
with a random set of initial patient-specific model parameter values.
The number of patient-specific model parameters adjusted throughout
each optimization are as follows: hip = 6 (all translations); knee = 9 (4
rotations, 5 translations); and ankle = 12 (5 rotations, 7 translations).

Figure 2. Two-level optimization technique minimizing the
distance errors between kinematic model markers and
marker trajectory data to determine functional joint axes.

To evaluate the ability of this two-level optimization approach
(Figure 2) to calibrate the generic kinematic model to a particular
patient, we generated synthetic movement data for the ankle, knee, and
hip joints based on in vivo model parameters and movement data. We
then evaluated the optimization's ability to recover the original model
parameters used when generating the synthetic motions. For each
generated motion, the distal segment moved within the physiological
range-of-motion and exercised each DOF for the joint. The resulting
synthetic marker trajectories without noise were recorded. To simulate
skin movement artifacts, a continuous numerical noise model of the
form A sin (wt + y) was used and the equation variables were
randomly generated within the following bounds: amplitude A (0 to 1
cm); frequency w (0 to 25 rad/s), and phase angle y (0 to 2it) [5].

For synthetic motions without noise, each optimization precisely
recovered the original marker trajectories and model parameters to
within an arbitrarily tight convergence tolerance (i.e., le-12). For
synthetic motions with noise, the ability of the two-level approach to
determine the original marker trajectories and model parameters is
summarized in Table 1. The mean marker distance errors are
approximately 0.5 cm, which is of the same order of magnitude as the
selected random continuous noise model.

Synthetic Data Hip Knee Ankle
With Noise
Mean Marker
Mean Marker 4 61e-01 + 1 81e-01 510e-01 + 195e-01 506e-01 + 1 88e-01
Distance Error (cm)
Mean Rotational
Mean Rotational n/a 2 56e-01 + 8 20e-02 2 42e+00 + 1 03e+00
Parameter Error (deg)
Mean Translational
Mean Translational 1 74e-02 + 155e-02 8 90e-02 + 5 14e-02 3 45e-01 + 2 84e-01
Parameter Error (cm)

Table 1. Results of two-level optimization for synthetic data
with random continuous numerical noise to simulate skin
movement artifacts with maximum amplitude of 1 cm.

The main motivation for developing a 27 DOF patient-specific
computational model and a two-level optimization method to enhance
the lower-extremity portion is to predict the post-surgery peak knee
adduction moment in HTO patients [6]. The accuracy of prospective
dynamic optimizations made for a unique patient is determined in part
by the fitness of the underlying kinematic model. If the current model
cannot adequately reproduce experimental motion, the chosen joint
models may be modified. The two-level optimization method
satisfactorily reproduces patient-specific model parameters defining a
3D lower-extremity model that is well suited to a particular patient.

This study was funded by Whitaker Foundation and NIH National
Library of Medicine (R03 LM07332-01) grants to B.J.F.

1. Pandy, M.G., 2001, "Computer Modeling and Simulation of
Human Movement," Annual Reviews in Biomedical Engineering,
Vol. 3, pp. 245-273.
2. Lu, T.-W., and O'Connor, J.J., 1999, "Bone Position Estimation
from Skin Marker Coordinates Using Global Optimization with
Joint Constraints," Journal of Biomechanics, Vol. 32, pp. 129-
3. Sommer III, H.J., and Miller, N.R., 1980, "A Technique for
Kinematic Modeling of Anatomical Joints," Journal of
Biomechanical Engineering, Vol. 102, pp. 311-317.
4. Bogert, A.J. van den, Smith, G.D., and Nigg, B.M., 1994, "In
Vivo Determination of the Anatomical Axes of the Ankle Joint
Complex: An Optimization Approach," Journal of Biomechanics,
Vol. 27, pp. 1477-1488.
5. Cheze, L., Fregly, B.J., and Dimnet, J, 1995, "A Solidification
Procedure to Facilitate Kinematic Analyses Based on Video
System Data," Journal ofBiomechanics, Vol. 28, pp. 879-884.
6. Prodromos C.C., Andriacchi T.P., and Galante J.O., 1985, "A
Relationship Between Gait and Clinical Changes Following High
Tibial Osteotomy," Journal of Bone Joint Surgery (American),
Vol. 67, pp. 1188-1194.

2003 Summer Bioengineering Conference, June 25-29, Sonesta Beach Resort in Key Biscayne, Florida

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