6.1 Basic concepts
6.1.1 Viewpoints for analysis of biomechanical systems
Two outcomes are generally sought:
- Understand the motion (rigid body kinematics)
- This is typically musculoskeletal multi-body static/dynamic simulation
- Understand the stress, strain, and deformation
- This is typically finite element modeling
- The above are general categories. There are many variations!
To meet our objective as designers, we need the loads!
- Loads are necessary for determining load paths, stress, strain, and deformation
- Two methods can be used to obtain them
- Analysis of motion and calculation based on equilibrium
- Intelligent assumptions
- Typically both are required!
6.1.2 Typical elements in a rigid body model
- In the body-as-machine analogy, each body structure has a analog in the engineer’s toolkit
TABLE 2.1: Rigid Body Model Elements (@Bartel2006)
| Anatomic.Element | Model.Element |
|---|---|
| Bones or limb segments | Rigid links |
| Joints | Standard joints: spherical, revolute, cardan, etc. Rigid contact surfaces (kinematic constraints). Deformable contact surfaces (force constraints) |
| Muscles + tendons | Actuators |
| Nerves | Actuators + elastic + viscous elements |
| Ligaments + joint capsules | Controllers, Elastic or viscoelastic springs |
6.1.2.1 Bones
- Bones are deformable, however…
- bones are relatively rigid and can be modeled as rigid for certain purposes
- Example: musculoskelatal multibody dynamic simulation (AKA Link Dynamics Models)
6.1.2.2 Joints
- Joints act as kinematic constraints
- Kinematically can be described as:
- Articulating (knee, hip, shoulder, etc)
- Deforming (intervertebral discs in the spine, pubic symphysis)
- Joints have varying levels of complexity
6.1.3 Engineering perspective – simple joints
- Spherical (ball and socket) – hip and shoulder
- Revolute (hinge) – humero-ulnar joint
6.1.4 Engineering perspective – complex joints
- Many joints are complex
- Wrist
@Gray1918
6.1.5 Kinematics
@Seth2018
- Due to the complexity of joints, defining appropriate kinematics is
one of the major challenges of link dynamics problems
- Imaging studies allow direct (but limited) visualization of joint motion
- “Exact” motion can be established via kinematic study (precision?)
- We must use judgment in our kinematic assumptions with
respect to the desired outcome of the model
- Imprecise or inaccurate kinematics affects accuracy
- Reality recognizes that joints are flexible bodies which deform – modeling as a kinematic constraint may not be appropriate in all cases
6.1.6 Modeling of muscle/tendon/ligament
- Tendon and ligament have similar structure and load carrying
function
- They can be modeled in similar ways
- Alternatively, it is often easier to model muscle and tendon together as one structure
6.1.7 Muscle/tendon model
@Bartel2006
- We often choose to model muscle and tendon as a unit (circuit
analogy)
- Active control of a contractile element (neural stimulus)
- Elastic elements required in series and parallel (tendons, active and passive muscle tissue) – thus, energy storage
- Viscous (damping) element in parallel – thus, energy dissipation
- The parameters associated with these elements depend on:
- Muscle length and volume
- Speed of muscle contraction
- Etc
- Activation-contraction dynamics are complex – requires idealization (thus, error introduction!)
- Sometimes we first compute the link-dynamics problem and
back-calculate the required muscular response
- Could be used as calibration for future models. Use caution.
6.1.8 Ligaments and capsules
- Ligaments carry loads (obviously)
- Some ligaments are idealized as discrete cables (springs) or groups in series/parallel (collateral ligaments)
@Gray1918
- Some arrays of ligaments act more like membranes (interosseous membrane)
@Soubeyrand2007
6.1.9 Mechanical response of ligaments
- Ligaments have non-linear elastic behavior (followed by “plastic” deformation and failure)
- Small strains have very low forces (high compliance) – occasionally neglected in normal range of joint motion or modeled as linear spring
- Larger ligaments have varying “properties” through the cross section
- ie the ligamentous structures stiffen at different extensions
- May be appropriate to model as a set of parallel non-linear springs
6.1.10 Application of Link Dynamics Models
- A common task is to determine the forces/moments transmitted at
joints
- Typically in this context, bony deformation is not a concern (as so bone assumed to be rigid)
- Two types of external boundary conditions are possible:
- Kinematic constraints (constrained motion)
- Surface tractions (external forces/pressures)
Example:
- Typical Outputs
- Muscle/tendon/ligament forces
- Energy consumption, power output, work
- Joint reactions, loads, accelerations
- Floor and other external loads
- Range of motion, functional deficit due to injury
- Insights into overall functional mechanics
- Choice of how to include a boundary condition may depend on the
analysis
- Foot may not penetrate floor
- Floor imparts a force/moment on the foot
- In many cases, we can apply a statically equivalent load in place of a motion constraint (or vice-versa)
- Our assumptions must be appropriate for the goal of the model
6.1.11 Three types of solution are available for any problem
- Static analysis
- Fixed configuration – no motion allowed
- Quasi-static analysis
- A range of motion is considered (as an allowed configuration change – ie joint rotation)
- However, dynamics are ignored or inertia forces assumed to be constant
- Dynamic analysis
- Inertia in included