Two-Level Optimization Approach
Why Two Levels of Optimization Are Necessary
Optimization may be used to identify a system (or determine patient-specific joint
parameters) that best fit a 3D, 18 DOF lower-body model to an individual's movement
data. One level of optimization is necessary to establish the model's geometry. Given a
defined model, another level of optimization is required to position and orientate the
model's body segments. By formulating a two-level objective function to minimize 3D
marker coordinate errors, the two-level optimization results describe a lower-body model
that accurately represents experimental data.
Inner-Level Optimization
Given marker trajectory data, md, and a constant set of patient-specific model
parameters, p, the inner-level optimization (Figure 3-8, inner boxes) minimizes the 3D
marker coordinate errors, ec, between the model markers, mm, and the marker movement
data, md, (Equation 3-1) using a nonlinear least squares algorithm that adjusts the
generalized coordinates, q, of the model at each instance in time, t, (Figure 3-9), similar
to Lu and O'Connor (1999). In other words, the pose of the model is revised to match the
marker movement data at each time frame of the entire motion.
min e(q, p, t) = md(t) mm(q,p, t) (3-1)
At the first time instance, the algorithm is seeded with exact values for the 6
generalized coordinates of the pelvis, since the marker locations directly identify the
position and orientation of the pelvis coordinate system, and all remaining generalized
coordinates are seeded with values equal to zero. Given the joint motion is continuous,
each optimal generalized coordinate solution, including the pelvis generalized