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HOPES AND FEARS
FOR THE FUTURE OF BIOMECHANICS
R. McNeill Alexander
School of Biology, University of Leeds
HOPES
HOPE
for a better understanding of:
the metabolic cost
of mechanical work
Energy Cost of Running
Full & Tu (1991) J Exp Biol 156:
215-231
Energy Cost of Flight
Alexander (1999) Energy for Animal Life. Oxford U P
Kram and Taylor’s hypothesis
Kram & Taylor (1990) Nature 346: 265-267
Metabolic power
is proportional to
force × Vmax
or to
body weight / foot contact time
Metabolic power × foot contact time / body weight
is constant
Roberts et al (1998) J Exp Biol 201: 2745
Cost coefficient =
metabolic rate × contact time / body weight
Various birds
Humans
Muscle Properties in Isotonic Contraction
Alexander (1997) J Theor Biol 184: 253-259
metabolic rate
(force * maximum shortening speed)
1
0.8
0.6
0.4
0.2
0
-0.4
-0.2
0
0.2
speed / maximum shortening speed
0.4
Metabolic rate/
(force×Vmax
cost of work
cost of force
Shortening rate/Vmax
metabolic rate ≈ cost of force + cost of work
Proximal muscles with short
tendons must lengthen and
shorten.
Distal muscles with long
tendons may contract
isometrically
metabolic rate
(force * maximum shortening speed)
1
0.8
This predicts duty factor, force pattern
and stride length quite well, for human
walking and running.
0.6
0.4
Minetti & Alexander (1997) 0.2
J Theor Biol 186: 467.
Sellers et al. (2003) J Exp Biol 206: 1127.
0
-0.4
-0.2
0
0.2
speed / maximum shortening speed
0.4
metabolic rate
(force * maximum shortening speed)
1
0.8
0.6
This applies to isotonic contractions,
not to work loops
0.4
0.2
0
-0.4
-0.2
0
0.2
speed / maximum shortening speed
0.4
HOPE
for the ability to measure:
forces in individual muscles
Recording muscle action
Activity
electromyography
Fascicle length changes sonomicrography
ultrasonic imaging
Tendon forces
tendon buckle
fibre optics
strain gauge on insertion
HOPE
for measurements of:
elastic savings
in proximal leg muscles
We know about savings here
How about savings here?
HOPE
for a better understanding of:
gait changes in birds and fish
If gravity is important
dynamic similarity is possible
only for systems moving with equal
Froude numbers,
(speed)2/(length × gravity).
A cat at 1 m/s has about the same
Froude number as a camel at 3 m/s.
The dynamic similarity hypothesis
Alexander & Jayes (1983) J. Zool. 201: 135-152.
The gaits of similar animals,
travelling with equal Froude numbers,
(speed)2/(hip height × gravity),
tend to be dynamically similar.
Froude numbers for gait changes:
gerbils, rats, coypu, cats, dogs, ferrets,
sheep, camels, rhinos, horses
from walk to trot (or pace) ≈ 0.5
from trot (or pace) to gallop ≈ 2.5
Gaits of birds and bats
Rayner (1986) Nature 321: 162 Spedding (2003) J Exp Biol 206: 2313
Vortex ring gait
used in slow flight
Continuous vortex gait
used in fast flight
Gait transition speeds
Rayner (1986) Nature 321: 162
Spedding (2003) J Exp Biol 206: 2313
Tobalske (1996) J Exp Biol 199: 263 Hedrick (2002) J Exp Biol 205: 1389
Thrush nightingale (span 26 cm) smooth transition
Noctule bat (span 34 cm) between 3 and 7 m/s
Turtle dove (span 44 cm) 7 m/s
Cockatiel (span 44 cm) 7 m/s
Magpie (span 57 cm) over 14 m/s
Pigeon (span 62 cm) 12 m/s
Gaits of swimming fish
Webb (1994) in Maddock Mechanics and Physiology of Animal Swimming
slow: median and paired fins, red muscle
faster: body, burst and coast, red muscle
faster: body, continuous, red muscle
faster: body, burst and coast, white muscle
fastest: body, continuous, white muscle
HOPE
for quantitative understanding of:
elastic mechanisms in
swimming and flight
A model of oscillatory movements:
insect or bird hovering
whale, fish or scallop swimming
Alexander (1997) J Theor Biol 184: 253-259
Fin or wing
Muscle
Tendon
Spring
force
distance
Willmott & Ellington (1997) J. Exp. Biol. 200: 2705
Manduca (hawkmoth) hovering
calculated aerodynamic power = 22 watts per kilogram
calculated inertial power
= 30 watts per kilogram
muscle power output with optimal elastic mechanism
22 watts per kilogram
muscle power output with no elastic mechanism
30 + (22/2) = 41 watts per kilogram positive power
and 19 watts per kilogram negative power
HOPE
for more knowledge of:
locomotion in natural habitats
HOPE
for quantitative understanding of:
the mechanics of accidents
that cause fractures
FEARS
FEAR
of excessively complex
models
A very simple model of jumping
Alexander (1990) Phil Trans Roy Soc B 329: 3
Seyfarth et al (2000) J Exp Biol 203: 741
The muscle has realistic
force/velocity properties, and is in
series with an elastic tendon
The model predicts the best run-up speed for a high- or
long-jumper, and the best angle for setting down the leg.
The Alexander/Seyfarth model of jumping has
three segments and one muscle.
The Pandy model of walking has 10 segments
and 54 muscles.
Pandy (2003) Phil Trans Roy Soc B 358: 1501
FEAR
of technical complexity
and
information overload
Methods for studying running
1975
film analysis
force plate
dissection
O2 consumption
treadmill
emg
2005
automatic 3D kinematics
telemetry
sonomicrography
ultrasonic imaging nmr
tendon buckles
microspheres
dynamic testing
work loops
Methods for studying swimming and flight
1975
film analysis
wind/water tunnel
dissection
emg
O2 consumption
2005
automatic 3D kinematics particle image velocimetry
telemetry
strain gauges
sonomicrography
ultrasonic imaging microspheres
work loops
Summary of hopes
•the metabolic cost of mechanical work
•forces in individual muscles
•elastic savings in proximal leg muscles
•gait changes in birds and fish
•elastic mechanisms in swimming and flight
•locomotion in natural habitats
•mechanics of accidents that cause fractures
Summary of fears
•excessively complex models
•technical complexity and information overload
The following are spare slides,
which I do not expect to use.
Optimum muscle speed parameter
Scallop
inertia forces low
Dolphin
Bee
Hummingbird
inertia forces high
Optimum compliance parameter
A simple model of a tubular bone
Currey & Alexander (1985) J Zool 206: 453
The model predicts the optimum ratio K of
internal diameter / external diameter
for strength with lightness
Optimum values of K for strength with lightness:
for impact strength 0.55
for yield strength
0.67
for stiffness
0.75
The Currey and Alexander model represents a bone as
a hollow cylinder
It could be represented instead by a finite element
model of a particular bone,