Biomechanics Papers

Alexander 1983

If two creatures are DS, they are mechanically the same. Any measurement of time, length or mass on one creature can be applied to the other by using a scale factor.

h is usually leg length. Froude number is used to compare over speeds of locomotion as it is dimensionless

Can locomotion in animals be generalised using dynamic similarity and Froude numbers?

Yes - works best with cursorial mammals (typically >5kg) but works for bipeds/birds too

• Relative power output (  )
• Duty factor

• Weight proportional to volume of body assuming animals are similar densities.
• Stress = Weight/Area =  =[L]
• Stress scales with size
• At any given Froude number, larger animals will experience higher stresses
• If stress limitations are the same across animals, then large animals cannot attain higher Froude numbers and are limited in speed

Stride Length/Hip Height ratio is similar for individual groups of animals

Bullimore 2006

Relative stride length/duty factor at a given Froude number

RSL = stride length/leg length

Do animals change gait to minimise energetic cost of transport?

Yes, each gait has an optimum speed that minimises cost of transport

3 horses were ran on treadmills and they changed gaits on command. They used O₂ measurements to gauge metabolic cost

Hoyt 1982

• Bone lengths and diameters generally scale with geometrical similarity or 
• Bovidae scale with elastic similarity however

Biewener 1982

• Alexander 1979
• Biewener 1982

• They do a larger amount of 'manoeuvres'. Actions that have large accelerations or unpredictable moves that may incite very large stresses on their skeleton
• They accelerate harder when moving

• Bone orientation/curvature changes compared to the vector of peak ground force. (legs become more upright - r/R tie in)
• There exists an inverse relationship between duty factor and PGF (large animals share load between legs more of the time)
• There exists an inverse relationship between size and PGF

• Biewener 1989
• They become straighter and the animal stands more upright. (Rabbit vs Elephant)

• r = muscle contact point to ankle joint
• R = ankle joint to ground contact point (the point that reaction force acts through)

How does maximum running speed vary with body mass?

• MRS scales dynamically in mammals so that MRS ~ 
• Slight polynomial regression however - optimal mass for MRS is 119kg

Pollock 1994

Pollock 1994

• Is fast leg swinging metabolically costly? How much energy is used for fast leg swing during locomotion?
• Paper claims it is 30% of walking cost at 1.3m/s

• Participants put in aparatus that held their body up and were told to swing legs to the beat of a metronome. Frequency was adjusted to their preferred walking frequency. O₂ consumption was measured.
• Pendulum model used so that metabolic rate should be proportional to frequency⁴

• Force/Time
• Work

Short durations of force production increased metabolic cost. So swinging leg quickly increases cost of transport (link with muscle studies of red vs white muscle?)

What fraction of energetic cost of running is used for initiating then propagating leg swing?

Found to be about 20%

• Researchers felt they did not fully eliminate the need for muscle recruitment during leg swing but did not apply higher forces for risk of injuring participants. (so could be >20%)
• They felt their method added propulsive forces to the feet so overall metabolic rate was reduced anyway. (so could be <20%)

Runners were placed on treadmills (3m/s) and their feet were attached to cables. External swing assist (ESA) forces were applied to feet as a percentage of body weight (max 4%). Difference in O₂ consumption measured between normal/ESA running.

• What fraction of energetic cost of walking is used for leg swing?
• 10%

• Jesse used only external swing assist (ESA) forces on the feet which adds forward propulsion. Jinger applied a force to the waist of each participant and measured difference in O₂ consumption between waist force applied only and waist force/ESA applied. 
• Jesse felt not all muscle activation removed. Therefore, Jinger used a slower speed (3m/s -> 1.25ms)

The muscles recruited during running/walking in guinea fowl along with their aerobic limit is well documented. Therefore, blood flow rate through specific muscles could be measured to indicate metabolic cost during different phases of stride. This cannot be done in humans as muscle recruitment scheme is more complicated.

• Microspheres injected into left ventricle
• Distribution of spheres proportional to flow rate
• Count the number of spheres in a particular tissue and normalise against the total number of spheres flowing out of heart (which is checked periodically).

26%

• Muscles involved in locomotion confined to hind limbs - no division of labour between front/back legs
• Extensive EMG activity is documented so can partition their strides into swing/stance phases easily
• Aerobic limit is well defined
• Good treadmill runners. Repeatable O₂ vs speed curves

Is mechanical work a good predictor of cost of limb swing?

No. Muscle efficiency increased with speed so it is a non-linear relationship. Muscles also never worked at their accepted max efficiency - so that value can't be used either

Rubenson 2009

Horses are shown to store elastic energy in their muscles during a gallop in a 'catapult' system. This allows to generate much more force in a short time than normal muscle action

• Horse bicep is 0.4kg
• Using the rule that a muscle works at about 90W/kg, 50kg of muscle is required to achieve 4400W normally.

How does muscle use vary depending on environmental conditions?

Found that muscles can alter their functions depending on the operating conditions. Not necessarily linked to specific environments but more to difficulty of task for relative speeds.

• 
• Note: Clockwise is eccentric

• They are fundamentally similar! No evidence of any isometric muscle function - so no efficient movement.
• Therefore - noted that a duck's terrestrial ability is limited by the requirements of paddling. (aka non-optimised for either but at least capable of both)

Biewener 1999

• Muscles activate for lonnger periods on land
• Muscles activate at a greater intensity on land
• This is probably to counteract increased load bearing due to higher reaction forces

Rome 1988

They have a low max shortening velocity but act very efficiently and have low fatigue wear. They are used for slow, repetitive movements. E.g. Carp use them primarily at speeds of 0.2-0.4m/s

They have a high max shortening velocity but act inefficiently and suffer from fatigue. Used infrequently and only at times when maximal movements are necessary. E.g. Carp need these muscles for their startle response so they can escape quickly. Necessary for survival.

Daley 2003

Does output of individual muscles change in parallel with the demand for work on the body?

Yes - muscles adapt to the mechanical work required. They could lengthen to absorb force when going downhill. They could shorten to produce work for going uphill.

Humans are constrained by their ankle muscles at all locomotion speeds. They worked at their capacity in the study whereas other joints were not at capacity.

• Sports performance
• Rehabilitation for patients (e.g. cerebral palsy)
• Sports therapy

Which joints (for wallabies) are used to modulate mechanical power when changing speed?

Ankle joints have the greatest influence (89% of variation)

Work is produced somewhere else and transferred down the limb to the ankle. Work produced in the hip muscles is enacted at the end of the leg instead of being produced at the ankle directly.

McGowan 2005

Tendon elastic modulus. Animals must distort in shape to account for the fact that tendons have shared properties between animals.

• The limb moment arm between the peak ground force (PGF) and muscle tendon unit (MTU) in a limb changes length with animal size.
• E.g. larger animals have a lower ratio of MTU strain to PGF. Smaller animals have a higher ratio. (r/R in other papers)

The model could make instantaneous predictions of required work and rate of heat production for individual muscles. The mech. and thermal energy rates were combined to find metabolic power. Integrating by stride cycle time and summing all muscles found metabolic energy cost.

• preferred: 29%
• -20% preferred: 35%
• +20% preferred: 24%

Body mass >20kg

To use mechanical principles to generate a model that can predict max run speed and test its validity on living animals. 

Pretty alright model - 

Are there absolute limits to the speeds at which animals can run?

Tentatively yes. The model he uses shows a plateau but he has extrapolated a lot of data. Sudden advances in technology/understanding could invalidate the model

Population modelling. He assumes that by having larger and larger populations - by chance there ought to be better runners. He uses historical data to predict how run speed changes with population and extrapolates

• Thoroughbred horses are descended from the same 12-29 males and this is the only breed used. Lack of genetic diversity may mean a faster horse could be found outside this gene pool. 
• Dogs are less inbred but their morphology is very malleable (chihuahua to great dane). There could be a shape of dog that is yet to be bred for that could be faster than greyhounds

To make a theoretical basis to support the statistical model presented in Garland 1983 for an animal's max run speed vs their body mass.

• The mechanical model shows that stress is proportional to stride length.
• Large animals have larger stride length so experience more stress in their bones/tendons. 
• As larger animals approach stress limitations, stride length limitations are reached too.
• After some threshold of body mass, stress cannot be permitted to increase so stride length doesn't increase.
• V ~ stride frequency (which has a documented allometry of .
• Large animals get slower as they increase body mass.

• They are not restricted by maximum stress limitations as they do not approach the max stride length. 
• Allometry between body mass and top speed is positive for small animals.
• Suggested that limitation is power output averaged over the stride time

Horses operate at constant power and trade off metabolic work of forward locomotion for potential energy. Aka, they go slower up hill and faster downhill

Horses run fastest at level and get slower on both inclines and declines. They are limited by being quadrapeds