Introduction to Biomechanics



Introduction to Biomechanics

|Assigned Reading: |   |Jenkins:   pp. 17-30. |

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Definitions

• biomechanics - application of the principles of mechanics / physics to biological organisms

• muscle action vs. function

o 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

o 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

o - occurs when a force moves its point of application

o - e.g., muscles work by moving myosin heads along actin filament

o - 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

o - work is measured in joules [J = (N)(m)]

o - 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)

Some Physiology (gag!)

• isometric and isotonic contractions

o - limited to experimental conditions in which mechanical properties (either tension or change in length) of muscle are measured; i.e., not possible in vivo

o - isometric contraction - muscle length is fixed and tension is measured

▪ - used to generate length/tension curves (see below)

o - 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

o - theory proposed by biophysicist Jean Hanson (1919-73) and physiologist Hugh Esmor Huxley (1924- ) in 1954

o - states that during contraction thin filaments slide past thick filaments with no change in the length of either type of filament

o - force for producing sliding of thin filaments is generated by the cross-bridges (formed by myosin heads)

o - 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:

o 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

o 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

o - generated from series of isotonic contractions

o - 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

o - power output = force x velocity (rate of doing work)

▪ - measured in watts (1N x 1m/s)

▪ - is maximized at about 30% of maximum force

Preliminary concepts

• 1.   Force output is proportional to cross-sectional area

o - specifically F = total CSA x Specific Tension of muscle (N/cm2)

o - 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

o - maximum sarcomere excursion = 50% of resting length

o - thus longer fibers will contract a greater distance

• 3.  Velocity (distance of shortening/unit of time) is proportional to fiber length (assuming equal load)

o - muscles of different fiber length will contract to 50% in same amount of time

o - since excursions distances differ but time is constant, velocity is greater in muscles with longer fibers

Muscle Architecture

• Muscle architecture refers to arrangement and length of muscle fibers w/i a muscle

o - variation in muscle architecture can affect:

▪ (1) excursion (distance a muscle can contract)

▪ (2) velocity

▪ (3) force, and

▪ (4) line of action

o - variety of classification schemes exist; none perfect (except mine); many primarily descriptive

o - functionally 3 general types: parallel, triangular and pinnate based on fiber arrangement

▪ 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

o - maximum force produced by a muscle is proportional to the sum of the cross-section of all its fibers

o - for muscles of equal volume, more muscle fibers can be packed into a pinnate arrangement than a parallel arrangement

o - 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

o - thus force output = # of fibers x cosine of angle of insertion

o - 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

o - excursion = length a muscle fiber can contract; function of fiber length

o - for muscles of equal length, pinnate muscles have decreased excursion relative to parallel

o - max. sarcomere shortening = 50% of resting length; thus max. excursion of muscle = 50% of fiber length

o - parallel fibers can shorten to their maximum

o - pinnate fibers cannot shorten to their maximum w/o dislodging themselves from their tendons

o - thus pinnate muscle has shorter excursion

Lever mechanics

• Muscles generate forces and skeletal elements apply these forces and thus serve a machines

o - machine - device for transmitting forces from one point to another

o - majority (but not all) of skeletal elements function as type of machine known as lever

o - lever is a rigid bar (regardless of shape) which rotates about a fixed point (fulcrum)

o - 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 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

o 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)

o - it cannot maximize both (inverse relationship)

o - thus, there is a trade off between velocity and force in any lever system

Muscle fiber types

• Quality of force production can be varied by using different types of muscle fibers

o - vertebrate muscles can be broadly divided into slow and fast based upon speed of contraction

o - 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

o - 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

o - 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

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