Abstract

Computer simulations of musculoskeletal systems to date [1,2,3] use lumped inertial parameters for body segments which includes embedded muscle masses (see Current Generation of Biomechanical Models). In these simulations, muscles are massless actuators acting along their lines of action to drive these lumped inertial segments. Muscle forces show up in the equations of motion only as external forces, therefore the changing inertial properties of the muscle are not considered. For the next generation of musculoskeletal biomechanical models, a 3D muscle model which incorporates the acceleration of the muscle mass relative to the acceleration of the body segments needs to be developed.

To develop these revolutionary biomechanical models, there are several key steps which include:

	the construction of surface models
	the derivation of specific muscle morphological parameters from sectional images
	the construction of the 3D muscle model
	the incorporation of the muscle model into the overall equations of motion of the musculoskeletal system
	validation

This paper will address the first three steps and focuses on the lower extremity of the Visible Human male (VHM).

For surface modeling construction and derivation of morphological parameters, it is important for researchers to work with a standard set of data—the Visible Human dataset which features multiple imaging modalities and high resolution is the current "gold standard" for such an undertaking.

For surface modeling, non-uniform rational B-splines (NURBS) are used to define anatomical structures. The use of NURBS to define the muscle and tendon surfaces facilitates 3D deformations which allow for the changing properties of contracting muscle to be modeled. Since CT data is superior for the modeling of hard tissue specifically bone and is not perfectly registered with the cryosection (AS) image volume, a transform between the two volumes is needed. This transform has been developed using an affine transform model [4]. This allows the transformation of CT pixel space coordinates into AS millimeter space.

Muscle morphological parameters are needed for any muscle model. For a 3D muscle model, several specific parameters are necessary. These include muscle and tendon volumes, muscle line of action (tendon centroidal line), fascicle orientation and length, and inertial properties.

To create accurate surface models of muscle and tendon and to extract morphological data from the Visible Human data, it is necessary to use all three sectioning planes through the volume. Plate 1
and Plate 2 show the use of a sagittal plane view of the VHM volume to accurately segment the tendons of the rectus femoris muscle. A Quicktime movie shows surface models of the muscle body and tendons of the right rectus femoris muscles from the VHM data. Note the segmentation and models of the internal portions of the proximal tendon and the two heads of the proximal tendon.

Plate 3 shows the use of a frontal plane image to identify fat striations. These striations have been shown to run between and parallel to muscle fascicles and allows the prediction of fascicle orientation [5].

Plate 3 represents a projection of the fat striation onto the frontal plane. To calculate the true 3D orientation of a fascicle in the volume space requires two angles. These two angles can be calculated from the angle the fat striation projection makes with the horizontal axis in both the frontal and sagittal planes. A procedure has recently been developed to aid in calculating fascicle orientation. Within a segmented muscle volume, a thresholding algorithm isolates the fat striations and a volume render is produced yielding a 360 degree rotation about the vertical axis. Calculations are easily made from these isolated striations. An example Quicktime movie is shown for the vastus medialis.

Current work includes the formulation of the 3D muscle model. Key aspects of the 3D muscle model include: an activation dynamics model, a contraction dynamics model, passive characteristics of muscle tissue, and a deformation engine which deforms the surface model due to the physiological contraction state, maintains constant volume, and updates the inertial properties.

After the 3D muscle models are obtained for the major muscles of the lower extremity, they are then incorporated into the body segmental model (BSM) which includes the bone surface models and kinematic joint models. The dynamics of the overall system are obtained through a state variable formulation. These equations of motion are then forward integrated to simulate the system.