**3.2. Surface generation**

Possible translations and rotations relative to the inertial system can be realized through the implementation of appropriate joint types. If a model is composed of two or more rigid bodies, they are connected by a massless joint. The joints provide certain DoF. Depending on the

**1.** allows bodies or a body and a reference frame to be connected to each other with no DoF,

Furthermore, it is possible that forces and torques can be transferred between two body markers, which are generally located on different bodies, by a so-called force element. The type of interaction depends on the implemented force law. According to [19], the DoF of a model are determined by a number of independent state variables, which characterize the movement of the body. Furthermore, the movement of the MBS system depends on the inertial properties of its bodies, masses, inertia tensors, and its centers of gravity. The kinematics of the model is defined by a system of coupled differential equations. These equations of motion give the relation between motion and forces. For this reason, they can be solved in two ways: the forward or direct dynamics and the inverse dynamics. In the case of forward dynamics, the movement is determined by known internal forces or torques, whereas the reconstruction of the internal forces or torques from movements and external forces, like the gravity, is called

It should be noted that the presented modeling styles MBS and FE can be used independently

The aim of our biomechanical computer modeling is to consider the characteristics of a musculoskeletal system through the use of knowledge from the fields of mechanics, anatomy, and physiology in the model in an appropriate manner, in order to obtain as accurately as possible a realistic simulation of the biomechanical behavior of the system. In the following, various application examples of a lumbar spine model that takes all spinal structures with their

The MBS models of the lumbar spine consist of vertebrae L1–L5, os sacrum and os ilium. These bony parts are connected by joints with appropriate DoF and ligament structures, which are attached to characteristic points of the skeletal parts. The facet joints are realized as threedimensional (3D) contact areas, so that the acting contact forces avoid the penetration of two corresponding joint surfaces. All the individual structures are modeled with specific material

definition of joint type, the joint

32 Numerical Simulation - From Brain Imaging to Turbulent Flows

inverse dynamics [20].

**3. MBS lumbar spine models**

**3.1. Structure of the spine model**

**2.** provides free movement to the body, with six DoF,

of each other, but can also be combined with each other.

specific material properties into account are presented.

properties in order to simulate their realistic mechanical behavior.

**3.** applies kinematic excitations to a body, as a rheonomic joint.

The 3D surface models of the vertebral bodies are based on computed tomography (CT) data sets of artificial vertebrae of Europeans. These data sets are generated through the use of segmentation and visualization plugins to visualize the data sets and make them available for simulation as Computer Aided Design (CAD) data sets (**Figure 3**) [21, 22].

**Figure 3.** Surface generation through segmentation (left) and visualization (right) plugins [29].
