Muscle-Tendon Length Initialization

Intro

Muscle-Tendon Length Initialization uses passive joint moment data to calibrate the optimal fiber length, tendon slack length, and maximum isometric force of muscles. This optimization is not a stand-alone tool, but it can be performed before Muscle-Tendon Personalization (MTP) and Neural Control Personalization (NCP) by including the length initialization settings with either of those tools.

It is strongly recommended to include Muscle-Tendon Length Initialization if using MTP. It may also be used with NCP if muscles that have not been personalized using MTP are included.

Inputs

• MTP inputs
• Passive moment data (optional)

Outputs

• Output is built into results of MTP (or NCP), no separate files

How it Works

Muscle-Tendon Length Initialization has two main methods, one of which requires passive moment data to be provided. MTP optimizes parameters used directly or indirectly in the following Hill-type muscle model force equation, using values defined in the table:

$$F_{muscle} = F_{max}[f_l(l_{m,norm})f_v(v_{m,norm})a + f_p(l_{m,norm})]$$

Value	Definition
$F_{max}$	maximum isometric force
$f_l()$	active force-length curve
$f_v()$	force-velocity curve
$f_p()$	passive force-length curve
$l_{m,norm}$	normalized fiber length
$v_{m,norm}$	normalized fiber velocity

Passive data are useful for calibrating length parameters because they remove activation dynamics from the equation. Without activations:

$$F_{muscle} = F_{max}[f_p(l_{m,norm})]$$

If passive moment data are provided, Length Initialization uses the above equation and adjusts optimal fiber length, tendon slack length, and optionally the maximum isometric force to match passive moments.

If no directory is given for passive moment data, Length Initialization will only use the muscle analysis results and dynamics provided for MTP or NCP and modify length parameters to minimize passive forces. This is a less accurate assumption than matching passive moment data, and it does not place a lower bound on normalized fiber length, so using passive data is strongly recommended.

Design Variables

MTLI can adjust the following design variables:

• Optimal fiber length scale factor (muscle-specific)
• Tendon slack length scale factor (muscle-specific)
• Maximum normalized fiber length (group- or muscle-specific)
  • Uses fiber length groups defined for either MTP or NCP. If a muscle is not included in any fiber length group, its maximum normalized fiber length is optimized individually
• Muscle tension (shared by all muscles)
  • Optional, used to scale maximum isometric force