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