Choosing Model Parameters

Model parameters affect the behavior of the model. They can be altered and their effects measured by starting with a set of parameters, comparing the behavior of the model to either experimental results or an observed condition, then refining the parameters.

Sections:

• Joint Parameters
  • Hybrid III Crash Dummy Strength Scale Factor
  • Passive Stiffness/Damping
  • Passive Joint Limit Angles and Stiffness
  • Pgain/Dgain
• Soft Tissue Parameters - Trainable Muscles
  • Muscle-trained Driver Elements
• Soft Tissue Parameters - Hill-Type Muscles
  • Passive Element Properties
  • Contractile Element Properties
• Contact Force Parameters
• Motion Agent Parameters

Joint Parameters

The kinematic joints can be used in both a passive mode and active mode. Joint parameters include:

• Hybrid III Crash Dummy Strength Scale Factor
• Passive Stiffness/Damping
• Passive Joint Limit Angles and Stiffness
• Pgain/Dgain

Hybrid III Crash Dummy Strength Scale Factor

The joint torques generated using the Hybrid III crash dummy model are based on stiffness, damping and friction data measured at the Armstrong Aerospace Medical Research Laboratory, Wright Patterson Air Force Base [Kelps] from the mechanical Hybrid III [Foster, 77] crash dummy. This is a dummy model for the 50% human male. The non-linear stiffnesses are included in look-up table form for each of the three rotational degrees-of-freedom for each of the 18 joints in the human model.

Figure 1: Hybrid III joint torque curve form.

The data for the Hybrid III dummy typically be represented by the curve shown in Figure 1. This curve describes a small (or non-existent) stiffness throughout the normal operating range for a particular joint at a particular degree of freedom. The sharp inclines and declines of the curve are a result of the joint encountering hard-tissue (or soft tissues limitations) resistance that forces it to surpass the biological limit of the joint. It is within this range that injury occurs to the joint.

The joint torque data, derived from the Hybrid III crash dummy generally constructs a passive-response model for a kinematic rebound simulation -- essentially, a human being unaware of an impending crash. Altering the stiffness of the joints changes the slope of the curve in Figure 1. Typically this can be done by scaling the data based on the qualitative strength difference between the 50% male and the subject to be modeled. The Bungee Jump Tutorial illustrates the usage of this strength model and tuning the scaling parameter.

Passive Stiffness/Damping Parameters

The passive joints have two main functions: 1) to stabilize the model during the inverse dynamics simulation, and 2) to provide joint friction stiffness for a forward dynamics simulation.

The default values included in the panel are usually sufficient for stabilizing the model in an inverse-dynamics simulation. During the inverse-dynamics simulation the passive stiffness/damping parameters and the motion agent stiffnesses directly affect the model. For example, if the joint stiffnesses are set too radically, the motion agent stiffness may not be sufficient to move the body segments. Or conversely, if the motion agents are stiff and the joint stiffness/damping parameters are too small there may be too much oscillation during the simulation. Several tutorials illustrate the balancing of these parameters including: Dancing Tutorial, Walking Tutorial, and the Hip Replacement Tutorial.

As a rule of thumb (developed from many simulations over the years) a damping value that is 10% of the stiffness value is sufficient in most cases.

Passive Joint Limit Angles and Stiffness

Joint limit angles are rough estimates of the the angulation of the joint along a particular axis. The default values are based on the limits developed from the references listed at the bottom of this section.

The limiting stiffness is usually a high value to make sure the joint is not moved beyond its biological capabilities during the inverse-dynamics simulation.

Trained Driver Elements

The trained driver elements are PD-servo actuators which minimize the error between the desired instantaneous joint angle and the recorded model joint angle. This is accomplished by multiplying Pgain (or stiffness) times the error and Dgain (or damping) times the derivative of the error. Selecting these values can affect how well the model tracks the desired motion.

As a rule of thumb (developed from many simulations over the years) a Dgain value that is 10% of the Pgain is sufficient in most cases. See Dancing Tutorial for an example of using the PD-servo actuators.

References

• Engin, A.E., and Tumer, S.T. "Three-dimensional Kinematic Modeling of the Human Shoulder Complex." Journal of Biomechanical Engineering. 111:113-121. 1989
• F.C.T. Van der Helm. "A Standardized Protocol for Motion Recordings of the Shoulder." Conference of the International Shoulder Group. Masstritcht, Netherlands. 1997.
• Foster, J.K.; et al. "HYBRID III - A Biomechanically Based Crash Test Dummy." Proceedings of the 21st Stapp Car Crash Conf. 1977.
• H. Bao and P.Y. Willems. "On the Kinematic Modeling and the Parameter Estimation of the Human Shoulder." Journal of Biomechanics. 32(9):943-950. 1999
• H. Hatze. "A Three-dimensional Multivariate Model of Passive Human Joint Torques and Articular Boundaries." Clinical Biomechanics. 12:128-135. 1997
• Kelps, I.; et al. "Measurement of HYBRIDIII Dummy Properties and Analytical Simulation Data Base Development." Armstrong Aerospace Medical Research Laboratory Report no. AAMRL-TR-88-005.
• L. Herda, R. Urtasun, A.J. Hanson, and P. Fua. "An Automatic Method for Determining Quaternion Field Boundaries for Ball-and-Socket Joint Limits." International Journal of Robotics Research. 22(6):419-436. 2003
• R. Johnston and G. Smidt. "Measurement of Hip Joint Motion During Walking." Journal of Bone and Joint Surgery. 51(A):1083-1094. 1969
• T.B. Moeslund and E. Granum. "Pose Estimation of a Human Arm Using Kinematic Constraints." In Scandinavian Conference on Image Analysis. Bergen, Norway. 2001
• T. Kodek and M. Munich. "Identifying Shoulder and Elbow Passive Moments and Muscle Contributions." In International Conference on Intelligent Robots and Systems. 2002
• X. Wang, M. Maurin, F. Mazet, N. De Castro Maia, K. Voinot, J.P. Verriest, and M. Fayet. "Three-dimensional Modeling of the Motion Range of Axial Rotation of the Upper Arm." Journal of Biomechanics. 31(10):899-908. 1998

Soft Tissue Parameters - Trainable Muscle

Soft tissue parameters for muscles, tendons and ligaments include:

• pCSA = physiological cross sectional area
• M_stress= maximum tissue stress
• F_resting= resting load
• F_filter= force output filter %
• M_tone= overall muscle tone
• P_gain= proportional gain
• D_gain= derivative gain
• tendon/ligament strain stiffness/damping
• tendon/ligament preload/freelength

The muscle geometry data (pCSA) stored in LifeMOD™ was generated from a series of studies from [Schumacher]. In addition another source was consulted on human musculature anatomy by [Eycleshymer]. These sources, together with others listed in the reference section have provided detailed information on several muscles in various regions of the body and were used to compile the LifeMOD™ muscle geometry database. The data compiled has been scaled to a 1.70-m, 70 kg reference individual.

For model-specific data, the geometry data is scaled to the height, weight, gender and age using a built-in decision tree algorithm or allometric scaling [McMahon]. The pCSA can be further scaled using the overall muscle tone (M_tone) which directly scales the pCSA from 0 to 500%.

The upper limit of the muscle force (F_max) is generated by multiplying the pCSA for each muscle to a maximum tissue stress (M_stress) value derived from previous studies [Hatze].

Resting load (F_resting) is usually a nominal value to support the specific study. Good sources of resting loads for various ligaments are listed in the reference section.

Muscle Trained Driver Elements

The trained driver elements are PD-servo linear actuators that minimize the error between the desired shortening/lengthening patterns and the recorded model pattern for each muscle. This is accomplished by multiplying a Pgain (or stiffness) value by the error and a Dgain (or damping) times the derivative of the error. Selecting these values can affect how well the model records the desired motion.

As a rule of thumb (developed from many simulations over the years) a Dgain value that is 10% of the Pgain is sufficient in most cases.

The force is always tension-only and cannot exceed the upper limit of the muscle force (F_max) designated by the muscle geometry. The force is further affected by the force output filter percentage (F_filter). This value filters the force calculated for the muscle from 0% to 200% and affects the way muscle forces are calculated for instances of redundancy (multiple muscles contributing to the torque at the joint). Typically this value is used in a trial-and-error fashion by running successive simulations and observing the results (see Muscle Relocation Tutorial).

Tendons/Ligaments

Various data sources exist for ligament mechanical properties including [Woo], [Wilson], [Fung] and others listed in the reference section.

References

• Butler DL, Grood ES, Noyes FR. "Biomechanics of Ligaments and Tendons." Exer Sport Sci Rev. 6:125-181. 1978
• Cribb AM, Scott JE. "Tendon Respose to Tensile Stress: An Ultrastructural Investigation of Collagen-Proteoglycan Interactions in Stressed Tendons." Journal of Anatomy. 187:423–8. 1995
• Eycleshymer, A.C., & Shoemaker, D.M. A Cross-section Anatomy . New York: Appleton-Century-Crofts. 1970
• Fung YC. Biomechanics: Mechanical Properties of Living Tissues. New York: Springer-Verlag. 1993.
• Hatze, H. "Estimation of Myodynamics Parameter Values from Observations on Isometrically Contracting Muscle Groups." European Journal of Applied Physiology and Occupational Physiology. Vol 46. 325-338. 1981
• Hubbard RP, Chun KJ. "Mechanical Responses of Tendons to Repeated Extensions and Wait Periods." Journal of Biomechanical Engineering. 110:11–9. 1988.
• Hubbard, R.P., Soutas-Little, R.W. "Mechanical Properties of Human Tendon and Their Age Dependence." Journal of Biomechanical Engineering. 106:144-150. 1984
• Klein-Breteler, M.D., Spoor, C.W. and Van der Helm, F.C. "Measuring Muscle and Joint Geometry Parameters of a Shoulder for Modeling Purposes." Journal of Biomechanics. 32, 11, 1191-1197. 1999
• McMahon, T.A. Muscle, Reflexes, and Locomotion. Princeton, NJ: Princeton University Press. 1984
• Noyes, F.R. and Grood, E.S. "The Strength of the Anterior Cruciate Ligament in Humans and Rhesus Monkeys: Age-related and Species-related Changes." Journal of Bone and Joint Surgery. 58A(8), 1074-1082. 1976
• Peterson, R.H., Woo, S. L.-Y. "A New Methodology to Determine the Mechanical Properties of Ligaments at High Strain Values." Journal of Biomechanical Engineering. 108:365-367. 1986
• Pierrynowski, M.R., & Morrison, J.B. "Length and Velocity Patterns of the human Locomotor Muscles." D.A. Winter (Ed.). Biomechanics. P33-38. Champaign, IL. Human Kinetics. 1983
• Pierrynowski, M.R., & Morrison, J.B. "Estimating the Muscle Forces Generated in the Human Lower Extremity When Walking:Theoretical Aspects." Mathematical Biosciences. 75, 69-101. 1985
• Pierrynowski, M.R., & Morrison, J.B. "Estimating the Muscle Forces Generated in the Human Lower Extremity When Walking: A Physiological Solution." Mathematical Biosciences. 75, 43-68. 1985
• Provenzano, P., Lakes, R., Keenan, T., Vanderby Jr., R. Nonlinear Ligament Viscoelasticity. Ann Biomed Eng. 29:908–14. 2001
• Schumacher, G.lf. von, & Trommer, R. Die gegenseitige des Feucht- undTrockengewichtes und die fur die Bestimmung der Arbeit von Skelettmuskeln. Anatomlscher Anzeiger. 111, 175-188. 1962
• Schumacher;G.H. von & Wolff, E. Trockengewicht Querschnitt der menschlichen Skelettmuskulatur. Trockengewichte; Anatomischer Anzeiger. 118, 317-330. 1966
• Schumacher, G.H. von, & Wolff, E.. Trockengewicht und gischer Querschnitt der menschlichen Skelettmuskulatur. II. Physiologische Querschnitt. Anatomischer Anzeiger Bd. 119, 259-269. 1966
• Schumacher, G.H. von, & Wolff, E. J. Querschnitt dermenschlichen Skelettmuskulatur; Trockengewicht und physiologischen Querschnitt (schluB). Anatomischer Anzeiger Bd. 119, 270-283. 1966
• T. Kodek and M. Munich. "Identifying Shoulder and Elbow Passive Moments and Muscle Contributions." International Conference on Intelligent Robots and Systems. 2002
• Wilson, C.J. and Dahners, L.E. "An Examination of the Mechanisms of Ligament Contracture." Clinical Orthopaedics and Related Research. Vol 227, p286-291. 1988
• Woo, S.L-Y., Gomez, M.A., Woo, Y-K. and Akeson, W.H. "The Relationships of Immobilization and Exercise on Tissue Remodeling." Mechanical Properties of Tendons and Ligaments. Vol II. Biorheology. Vol 19(3), p397-408. 1982
• Woo, S.L-Y, Orlando, C.A., Gomez, M.A., Frank, C.B. and Akeson, W.H. Tensile "Properties of the Medial Collateral Ligament as a Function of Age." Journal of Orthopaedic Research. Vol 4(2), p133-141. 1986

Soft Tissue Parameters - Hill Muscle

The Hill-type muscle is a combination of a passive element, F_PE and and contractile element, F_CE .

F_MUSCLE = F_CE + F_PE

Passive Element Properties F_PE

Contractile Element Properties F_CE

References

• Cole, G.K., et al. "Modeling of Force Production in Skeletal Muscle Undergoing Stretch." Journal of Biomechanics. Vol 29(8), p1091–1104. 1996.
• Deng, Y.C. Human Head/Neck/Upper-Torso Model Response to Dynamic Loading. PhD thesis. University of California. 1985.
• Magid, A., et al. " Myofibrils Bear Most of the Resting Tension in Frog Skeletal Muscle." Science. Vol 230, p1280–1282. 1985.
• Myers, B.S., Cervical Spine Muscle. Final Report F.2c, Duke University. 1998.
• Rack, P.M.H., et al. " The Effects of Length and Stimulus Rate on Tension in the Isometric Cat Soleus Muscle." Journal of Physiology.Vol 204, p443–460. 1969.
• Winters, J.M. et al. Multiple Muscle Systems: Biomechanics and Movement Organization. P69–93. Springer-Verlag. 1990.
• Winters, J.M. et al., "Estimated Mechanical Properties of Synergistic Muscles Involved in Movements of a Variety of Human Joints." Journal of Biomechanics. 21:1027–1041. 1988.

Contact Force Parameters

Parameters for contact forces available in LifeMOD™ include:

• Contact Stiffness
• Exponent
• Damping
• Full Damping Depth
• Mu Static Friction Coefficient
• Mu Dynamic Friction Coefficient
• Friction Transition Velocity
• Stiction Transition Velocity.

The contact force in LifeMOD™ allows for a generalized 3-D contact between any pair of geometric objects. For more technical information see the ADAMS/Solver documentation. The contact force supports:

• Multiple contacts
• Dynamic friction
• Contact between three-dimensional solid geometries

The contact force uses Parasolids, a geometry toolkit from Unigraphics, as the underlying geometry engine for three-dimensional contacts. Currently, the contact force supports Parasolids 11.1. The geometry engine is responsible for detecting contact between two geometries, locating the points of contact, and calculating the common forces at the contact points. Once the contact kinematics are known, contact forces, which are a function of the contact kinematics, are applied to the intersecting bodies.

Intermittent contact - characterized by contact for short periods of time. It is also known as impulsive contact. Two geometries approach each other, undergo a collision, and separate as a result of the contact. The collision generates an impulse, that affects the momentum of the colliding bodies. The simulation develops an estimate of the contact force by modeling the local deformation behavior of the contacting geometries. Energy loss during the collision is usually modeled as a damping force that is specified with a damping coefficient.

Intermittent contact is characterized by two distinct phases. The first is compression, where the bodies continue to approach each other even after contact occurs. The kinetic energy of the bodies is converted to potential and dissipation energy of the compressing contact material. When the entire kinetic energy is transformed, the potential energy stored in the material reverses the motion of the contacting bodies. Potential energy is transformed again to dissipation energy and kinetic energy. This is known as the decompression phase. It is important to note that energy losses due to dissipation occur in both phases.

Persistent contact - characterized by contact for relatively long periods of time such as the condyler contact in a knee joint. External forces acting between the two bodies serve to maintain continuous contact. Persistent contact is modeled as a nonlinear spring-damper; the stiffness models the elasticity of the surfaces of contact, and the damping models the dissipation of energy. Two bodies are said to be in persistent contact when the separation velocity, after a collision event, is close to zero. The bodies, therefore, cannot separate after the contact.

Impact Force algorithm - The contact force employs an impact force algorithm. The general form of the impact force function is then determined by:

Fn = k * (g**e) + Step (g, 0, 0, dmax, cmax)dg/dt

where:

• g represents the penetration of one geometry into another.
• dg/dt is the penetration velocity at the contact point.
• e is a positive real value denoting the force exponent.
• dmax is a positive real value specifying the boundary penetration to apply the maximum damping coefficient cmax. (see Figure 2 for damping effect)

Figure 2: Contact damping coefficient relation to penetration as illustrated by
Step (g, 0, 0, dmax, cmax)

Contact Friction Force Calculation - The contact force uses a relatively simple velocity-based friction model for contacts. Specifying the frictional behavior is optional. Figure 3 shows how the coefficient of friction varies with slip velocity.

Figure 3: Relationship of friction coefficient to slip velocity

Human-Environment Contact Properties

Various sources exist for contact between body segments and various objects. [SAE] is a good source for general human segment to car interior properties. Many data sources exist for foot/floor contact [Aerts], [Bennett] and others listed in the reference section.

Internal Contact properties

Internal contact properties include contact in joints such as the knee joint (see Total Knee Replacement Tutorial). Many data sources exist for articular contact such as [Li] and [Walker]. A good source for general contact and frictional properties between various materials is listed in [Avalllone].

References

• Aerts, P., Ker, R.F., De Clercq, D., Ilsley, D.W., Alexander, R.M. "The Mechanical Properties of the Human Heel Pad: A Paradox Re-solved." Journal of Biomechanics. Vol 28, p1299-1308. 1995
• Avallone, E.A. Marks' Standard Handbook for Mechanical Engineers. McGraw-Hill. 2004
• Bennett, M.B., Ker, R.F. "The Mechanical Properties of the Human Subcalcaneal Fat Pad in Compression." Journal of Anatomy. 131-138. 1990
• De Clercq, D., Aerts, P., Kunnen, M. "The Mechanical Characteristics of the Human Heel Pad During Foot Strike in Running: And In-Vivo Cineradiographic Study." Journal of Biomechanics. Vol 27, p1213-1222. 1994.
• Decraemer W.R., Maes M.A., Van Huyse V.J.. "A Nonlinear Vicsoelastic Constitutive Equation for Soft Biological Tissues Based Upon a Structure Model." Journal of Biomechanics. Vol 13, p559-564. 1980
• Demiray H., Vito R.P. "Large Deformation Analysis on Soft Biomaterial." International Journal of Engineering Science. Vol 14, p789-793. 1976
• Gilchrist, L.A., Winter, D.A. "A Two-Part, Viscoelastic Foot Model for Use in Gait Simulations." Journal of Biomechanics. Vol 29, p795-798. 1996
• Guler, H.C., Berme, N., Sheldon, R. " A Viscoelastic Sphere Model for the Representation of Plantar Soft Tissue During Simulations." Journal of Biomechanics. Vol 31, p847-853. 1998
• Jorgensen, U., Larsen, E., Varmarken, J.E. "The HPC Device: A Method to Quantify the Heel Pad Shock Absorbency." Foot & Ankle. Vol 10, p93-98. 1989
• Ker, R.F., Bennet, M.B., Alexander, R.M., Kester, R.C. "Foot Strike and the Properties of the Human Heel Pad." Proceedings of the Institution of Mechanical Engineering 203 Part H. 191-196. 1989
• Kinoshita, H., Ogawa, T., Kuzuhara, K., Ikuta, K. "In Vivo Examination of the Dynamic Properties of the Human Heel Pad." International Journal of Sports Medicine. Vol 14, p312-319. 1993
• Li, J.T., Armstrong, C.G., Mow, V.C. "The Effect of Strain Rate on the Mechanical Properties of Articular Cartilage in Tension." ASME Biom3ech Symposium. Vol 56, p117-120. 1983
• Nordin, M., Frankel V.H. "Biomechanics of Tissues and Structures of the Musculskeletal System. In Lea, Febringer (ed) Basic Biomechanics of the Musculskeletal System. Philadelphia. 1989
• Scott, S.H., Winter, D.A. "Biomechanical Model of the Human Foot: Kinematics and Kinetics During the Stance Phase of Walking." Journal of Biomechanics. Vol 26, p1091-1104. 1993
• (SAE) Society of Automotive Engineers. "Human Tolerance to Impact Conditions as Related to Motor Vehicle Design." SAE Information Report no. J885. 1986.
• Walker P.S. "Bearing Surface Design in Total Knee Replacement." Engineering Medicine. Vol 17, p149. 1988

Motion Agent Parameters

The parameters available for the motion agents include:

• Individual motion agent weights
• Translational stiffness/damping
• Rotational stiffness/damping
• Linear conversion
• Angular conversion
• Time Offset

Motion Agents as Motion Influencers

LifeMOD™ provides several ways for the user to affect the way the motion agents influence the behavior of the model during the inverse-dynamics simulation.

The motion agent (Figure 5) is composed of a part which tracks the MOCAP data and a spring attachment to the body segment. The spring attachments between the motion agent and attachment location of the model affect the motion of the model. For example, if the springs in the motion agents at the feet were much stiffer than those throughout the body, the feet will match the MOCAP data closer that the rest of the segments (see Figure 5). This method serves well to match the MOCAP data to the model since during the inverse-dynamics simulation the model will not surpass joint limits and will react to contact with objects and the ground.

Figure 4: Offsets between the MOCAP data locations and the segment attachment locations

Figure 5: Motion Agent configuration

LifeMOD™ provides several ways to modify motion agents and affect the body motion during the inverse-dynamics simulation. First, there is a globally translational stiffness/damping coefficient which is applied to all motion agents present on the model. There is also a rotational stiffness/damping coefficient for those motion agent sets which include orientation data in addition to location data.

Another method of modifying the contribution of the motion agents to the motion of the model is to modify the individual motion agent weights. This is done in the Walking Tutorial, for example. In some cases the optical marker is occluded from the set due to shadowing from other body segments. If this occurs, this marker can be turned off by setting the weighting factor to 0.

Keep in mind how closely the model needs to track the data when selecting global stiffness/damping properties and motion agent weights. There may be cases when the model does not need to follow the MOCAP data as closely as in other situations.

Tuning the parameters during the inverse-dynamics simulation minimizes the offsets between the motion agents (MOCAP marker locations) and the locations on the model.

There are some cases where a different set of global stiffness/damping properties are used for the equilibrium simulation than for the inverse-dynamics simulation. When the model is a fair distance from the data point cloud, the spring force should be reduced avoid producing excessive loading. After the model is equilibrated, higher stiffness values may be implemented for the inverse-dynamics simulation.

Data Considerations

LifeMOD™ provides the capability to select a window of data from the MOCAP data source. This is used when the user is only concerned with a portion of the entire recorded cycle. See Walking Tutorial for an example of using a data window.

Also, if not done at the data collection stage, there may be a need to filter the motion data if it is excessively noisy. LifeMOD™ provides a Butterworth filter to smooth the data.

References

• Gavrila, D. "The Visual Analysis of Human Movement: A Survey." Computer Vision and Image Understanding. 73(1). 1999
• Hilton, A., Beresford, D., Gentils, T., Smith, R., and Sun, W. "Virtual People: Capturing Human Models to Populate Virtual Worlds." In Computer Animation Conference, Geneva, Switzerland. 1999
• Kakadiaris, I., and Metaxas, D. "3D Human Body Model Acquisition from Multiple Views." International Journal of Computer Vision. Vol 30(3), p191–218. 1998
• Moeslund, T., and Granum, E. "A Survey of Computer Vision- Based Human Motion Capture." Computer Vision and Image Understanding. 81(3). 2001
• Plankers, R. and Fua, P. "Articulated Soft Objects for Multi-View Shape and Motion Capture." IEEE Transactions on Pattern Analysis and Machine Intelligence. 2003
• Plankers, R. and Fua, P. "Articulated Soft Objects for Video-based Body Modeling." In International Conference on Computer Vision. p394-401. Vancouver, Canada. 2001
• Plankers, R. and Fua, P. "Tracking and Modeling People in Video Sequences." Computer Vision and Image Understanding. 81(3). 2001