Muscle Modeling in Biomechanics Tuesday, October 29, 2013.

Muscle Modeling in Biomechanics

Tuesday, October 29, 2013

Models

• Hill’s Muscle model• Musculoskeletal model

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Hill’s Muscle Model

• Representation of the muscle mechanical response• Represents muscle behavior rather than structure• Three element model

– Contractile Component (CC)– Series Elastic Component (SEC)– Parallel Elastic Component (PEC)


Contractile Component (CC)

• Active tension of skeletal muscle• Magnitude of the CC force depends on its mechanical

characteristics which can be expressed in four separate relationships– Stimulation-activation (SA), force-activation (FA),

force velocity (FV), and force-length (FL) • Active force of the CC comes from the force generated

by the actin and myosin cross-bridges at the sarcomere level


Stimulation-Activation

• How the nervous system signal is related to the muscle’s intrinsic force capability

• Stimulation: alpha motor neuron motor unit action potential that travel across muscle fibers travel to SR release calcium

• Activation activates actin-myosin complex• How much activation is produced for a given input of

stimulation?– Placed on relative percentages fro modelling

percentages – linear



• When motor unit is activated, there is a time delay between the onset of neural action potential and the activation at the crossbridge level

• 2 components– Motor unit action potential to SR– Length of time of the calcium ions to be released and

attach to thin filaments• Deactivation process

– Calcium reabsorption


Force-Activation

• Direct and linear relationship– 10%, 20%, or 50% activation represents 10%, 20%,

or 50% force, respectively

*Conceptual*independent from any specific kinematic


Force-Velocity

(P + a)(v + b) = (P₀ + a)b• P = Muscle Force• P0 = Max Isometric Force• v = Contraction Velocity• a =Coefficient of shortening heat• b = a* v0 /P0

• v0 = Max velocity (F=0)

*constants are muscle and species specific*for isometric and concentric


Force-Velocity


Force-Length

• Isometric force production is greatest at intermediate CC lengths and declines as the CC lengthens or shortens


CC Properties Combined

• CNS initiates process by sending stimulation signal to muscle

• Causes activation according to stimulation-activation properties previously discussed

• CNS modifies stimulation, thus activation, thus force capability

• CNS indirectly controls force-length(through SA and FA)• Force control depends on force-velocity and force-length

relationship which is more complex


CC Properties Combined


Series Elastic Component

• Passive elastic elements in series with the CC • Tendons and aponeurosis contribute to SEC component

– Tendons joins the muscle fibers to the skeleton– Aponeurosis connects external tendon to muscle

fibers, and connective elements within the muscles fibers (z-lines)

• Represents the tendon and the intrinsic elasticity of the myofilaments


Series Elastic Component

• Elastic behavior is described by its force-extension (FΔL) relationship

• Low force low stiffness• Higher force stiffer and unit increases in force produce

less extension


Parallel Elastic Component (PEC)

• Resistance of the passive muscle to an external force across an inactive, passive muscle

• Correlated with the fascia that surrounds the outside and separates muscle fibers into compartments (epimysium, perimysium, and endomysium)

• Similar FΔL relationship to SEC


Parallel Elastic Component (PEC)

• Plays a role in active force production• Active force is a summation of CC + PEC force

associated with isometric length of the muscle


Component interaction (active force)

• Use simplified Hill model that omits PEC• Use in vivo experiments to determine response during

twitch (short duration stimuli) and tetanus stimulation (greater duration stimuli)


Component interaction (active force)


General CC-SEC interactions

• Muscle length = CC length + SEC length– Isometric, muscle length is constant, thus inverse

relation between the CC and SEC• Muscle velocity = CC velocity + SEC velocity

– Isometric, muscle velocity equals zero, thus CC and SEC have equal but opposite velocities during isometric situations

• These hold true for all muscle contractions (isometric and dynamic

• Strength of the 2-component Hill model is that it allows estimation of CC length and velocity during active force production


Muscle model Algorithm

• Implement Hill-type models in several ways through different algorithms

• Can create an algorithms using the model parameters for particular muscles (FL information, a and b dynamic constants, SEC elasticity)

• Can then be applied to a musculoskeletal model as information on multiple muscle is available during contraction


Musculoskeletal Model

• Representation of the entire movement system to estimate the muscle forces during a motion sequence

• Information gathered from the Hill-type models can be used to create musculoskeletal models in addition to information obtained from body segments characteristics as well as inverse and forward dynamics in order to allow thorough analysis of human movement

• Resultant joint moments are mathematically associated with the unknown forces produced by the individual muscles.– These forces can be estimated with a

musculoskeletal muscle that uses a Hill model to represent each specific muscle



• Relation between a given muscle force and a given joint moment is dictated by the geometrical relation between the muscle’s position and the center of rotation of the joint in question

• Muscle force output is determined in part by the stimulation is receives from the CNS



• These models can be created from multiple sources of information– Joint/skeletal geometry

• Cadaver studies and imaging techniques• Information or direction of force application by

determining origin and insertion– Muscle Architecture

• Pennation angle– Direction fibers are orientated

• Cross-sectional area– Arrangement of sarcomeres– Number of fibers in parallel


Control Models

• Multiple ways to create control models of the CNS signal for comparison purposes– Electromyographical models

• Surface and indwelling electrodes– Theoretical control models

• Uses theoretical information about the CNS to create a model

– Optimization model• Hybrid model• Use a combination of methods and theories to

create the most accurate model (imaging, EMG, inverse dynamics)


Conclusion

• Hill Model– CC, SEC, PEC

• Use these relationships and apply them to more general musculoskeletal models

• Makes it possible for thorough and reliable assumptions for various human movements

• Keep in mind, there are specific limitations to each model


References

Robertson, D. G. E. (Ed.). (2004). Research methods in biomechanics. Human Kinetics.

Robertson, D. G. E. (2nd Ed.). (2013). Research methods in biomechanics. Human Kinetics.


Muscle Modeling in Biomechanics Tuesday, October 29, 2013.

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