Definitions

• biomechanics - application of the principles of mechanics / physics to biological organisms
• muscle action vs. function
  • action - motions produced by a muscle's shortening; described in reference to axes and planes of body
    • - determined by architecture of joint and position of muscle around it
    • - pure mechanics which can be inferred
  • function - how the organism chooses to use a muscle
    • - can involve positive, negative or non- work (see below)
• agonists (Gr., contestant)- muscles with an identical action; usually restricted to single axis or plane of reference
• antagonists (Gr., against + contestant; lit. enemy) - muscles with opposite action; usually restricted to single axis or plane of reference
• synergist (Gr., together + work) - muscles which act together to perform a function; can involve both agonists and antagonists
• work (W) - the mechanical definition
  • - occurs when a force moves its point of application
  • - e.g., muscles work by moving myosin heads along actin filament
  • - thus W = (F) (X), where
    • F= force (newtons; N)
    • X = distance moved (meters; m); can be positive or negative relative to line of action of force
  • - work is measured in joules [J = (N)(m)]
  • - muscles generate tension to perform positive, negative or non- work
    • - positive work - muscle shortens while generating tension (i.e., X > 0)
    • - negative work - muscle lengthens while generating tension (i.e., X < O)
    • - non-work - muscle generates tension without changing length (X=0)

• isometric and isotonic contractions
  • - limited to experimental conditions in which mechanical properties (either tension or change in length) of muscle are measured; i.e., not possible in vivo
  • - isometric contraction - muscle length is fixed and tension is measured
    • - used to generate length/tension curves (see below)
  • - isotonic contraction - muscle tension (load) is fixed and change in length (shortening) measured
    • - used to generate force (tension)/velocity curves (see below)

• sliding filament theory and length/tension curve (see Figure 1)
  • - theory proposed by biophysicist Jean Hanson (1919-73) and physiologist Hugh Esmor Huxley (1924- ) in 1954
  • - states that during contraction thin filaments slide past thick filaments with no change in the length of either type of filament
  • - force for producing sliding of thin filaments is generated by the cross-bridges (formed by myosin heads)
  • - theory predicts that force output will be proportional to the degree of overlap between thick and thin filaments or, more specifically, the number of cross-bridges formed

• biomechanical implications of the sliding filament theory:
  • 1.  for maximum force output (total tension) muscle should be positioned below its optimal length so that work (either positive or negative) will occur over peak of length/tension curve
  • 2.   muscles which produce the same action across a joint are typically arranged such that their optimal lengths occur at different joint positions thus permitting a nearly constant level of force output at all joint positions

• velocity-force curves (see Figure 2)
  • - generated from series of isotonic contractions
  • - force and velocity are inversely related such that at zero (0) velocity maximum force is generated, and at maximum velocity zero (0) force is generated
  • - power output = force x velocity (rate of doing work)
    • - measured in watts (1N x 1m/s)
    • - is maximized at about 30% of maximum force

• 1.   Force output is proportional to cross-sectional area (see Figure 3)
  • - specifically F = total CSA x Specific Tension of muscle (N/cm2)
  • - thus muscles that differ in length but have equal CSA generate equal amounts of force
• 2.   Excursion (distance a muscle can shorten) is proportional to fiber length (see Figure 4)
  • - maximum sarcomere excursion = 50% of resting length
  • - thus longer fibers will contract a greater distance
• 3.  Velocity (distance of shortening/unit of time) is proportional to fiber length (assuming equal load)
  • - muscles of different fiber length will contract to 50% in same amount of time
  • - since excursions distances differ but time is constant, velocity is greater in muscles with longer fibers

• Muscle architecture refers to arrangement and length of muscle fibers w/i a muscle
  • - variation in muscle architecture can affect:
    • (1) excursion (distance a muscle can contract)
    • (2) velocity
    • (3) force, and
    • (4) line of action
  • - variety of classification schemes exist; none perfect (except mine); many primarily descriptive
  • - functionally 3 general types: parallel, triangular and pinnate based on fiber arrangement (see Figure 5)
    • 1) triangular - muscle fibers radially arranged
      • -specialized for altering line of action assuming non-uniform distribution of motor units
    • 2) parallel - muscle fibers are arranged parallel to line of action (muscle pull)
      • - specialized for excursion and/or velocity
    • 3) pinnate - muscle fibers lie at an angle to line of action (muscle pull)
      • - specialized for force production
    • - N.B. Relationship between angle of pinnation (parallel fibers have an angle of pinnation = 0 degrees), fiber length and excursion is not simple; in fact in some situations pinnation actually can increase excursion

• Advantage of pinnation / Disadvantage of parallel (see Figure 6)
  • - maximum force produced by a muscle is proportional to the sum of the cross-section of all its fibers
  • - for muscles of equal volume, more muscle fibers can be packed into a pinnate arrangement than a parallel arrangement
  • - since axis of contraction of muscle fibers not parallel to pull of muscle (line of action) some muscle force dissipated perpendicular to line of action
  • - thus force output = # of fibers x cosine of angle of insertion
  • - thus advantage of pinnation is to increase force output of a muscle by packing more fibers in a given volume of space

• Cost of pinnation / Advantage of parallel (see Figure 7)
  • - excursion = length a muscle fiber can contract; function of fiber length
  • - for muscles of equal length, pinnate muscles have decreased excursion relative to parallel
  • - max. sarcomere shortening = 50% of resting length; thus max. excursion of muscle = 50% of fiber length
  • - parallel fibers can shorten to their maximum
  • - pinnate fibers cannot shorten to their maximum w/o dislodging themselves from their tendons
  • - thus pinnate muscle has shorter excursion

• Muscles generate forces and skeletal elements apply these forces and thus serve a machines
  • - machine - device for transmitting forces from one point to another
  • - majority (but not all) of skeletal elements function as type of machine known as lever
  • - lever is a rigid bar (regardless of shape) which rotates about a fixed point (fulcrum)
  • - in levers forces work by creating rotational forces about the joints (fulcrum) known as moments; i.e.,
    • m = F x L, where
      • m = moment or torque
      • F = force; in this case muscle tension
      • L = Lever (or moment) arm; distance between force and fulcrum; lies perpendicular to line of action of force

• Lever systems are most easily analyzed under the conditions of equilibrium (see Figure 8)

• Force equilibrium: Fi x Li (in-torque) = Fo x Lo (out-torque)
  • - solving for Fo:
    • Fo = Fi x (Li/Lo)
  • - thus to maximize force-output of a lever system for a given muscle force (Fi):
    • 1) increase Li
    • 2) decrease Lo
  • - Li/Lo = lever advantage

• Velocity equilibrium: Vo x Li = Vi x Lo
  • - solving for Vo
    • Vo = Vi x (Lo/Li)
  • - thus to maximize velocity-output of a lever system for a given muscle velocity (Vi):
    • 1) decrease Li
    • 2) increase Lo
  • - Lo/Li = gear ratio

• Note that for a given muscle input (Fi) a muscle lever system can either:
  • a) maximize lever advantage (Li/Lo) and produce a stronger but slower force (Fo)
  • b) maximize gear ratio (Lo/Li) and produce a faster but weaker force (Vo)
  • - it cannot maximize both (inverse relationship)
  • - thus, there is a trade off between velocity and force in any lever system

• Quality of force production can be varied by using different types of muscle fibers
  • - vertebrate muscles can be broadly divided into slow and fast based upon speed of contraction
  • - slow fibers - specialized for prolonged tension generation
    • - typically generate small forces (due to small fiber CSA and low innervation ratio) at low metabolic cost (aerobic respiration)
    • - fatigue resistant due to high density of mitochondria and myoglobin
    • - 2 subtypes
      • 1) tonic - multi-terminal fibers; membrane cannot propagate an AP thus contraction is graded; limited to extra-ocular muscles in mammals
      • 2) slow twitch - single terminal fibers; widely distributed
  • - fast [twitch] fibers - specialized for generating tension rapidly
    • - typically generate larger forces (due to larger fiber CSA and high innervation ratio) at high metabolic cost (use both aerobic and anaerobic respiration)
    • - different sub-types (2A, 2B, 2X) differ in myosin isoforms and fatigue resistance

• Majority of muscles are of mixed fiber type composition being a combination of fast and slow fibers occurring in two arrangements
  • 1) mosaic - fast and slow fibers uniformly distributed
  • 2) compartmentalized - fiber types non-uniformly distributed into intramuscular compartments
  • - however, some muscles which are used for repetitive or constant tasks (e.g., posture) can be comprised nearly entirely of slow fibers
    • - e.g., soleus