Force Velocity.ppt

First one is different
Decay at submaximal stimulations
Yield during dynamic motions
• During phases of constant velocity, force is not constant
• Two-stage elasticity
• “Push” fibers together faster than Vmax
– Brief period of 0 tension – Distinct recovery of tension
• dL-dt slope gives V0
V0
System elasticity
Isometric tension (●) V0 (o)
V0 depends on length
Apparent V0 rises sharply with passive tension. Elastic recoil? Lateral compression?
Apparent V0 falls below Ls=1.6 um.Thick filament-Z disk resistance?
• During whole movement
– W = P(DL); H=a(DL) (ie: energy = (P+a) DL)
– Time to move varies with P (nonlinear dW/dt, dH/dt)
– (P+a)DL/Dt empirically linear
• Length and velocity are not independent • Real motions follow trajectories
Troubles
• Instantaneous behavior from dynamic average
– Force to accelerate afterload – Force to move muscle’s own mass – Bath viscosity
• (P+a) V = b(P0-P)
b*P0
H=a(DL)
(P+a)V
b P0
Interpretator empirical hyperbola
– Internal viscosity (a V) – External power (P V)
• (P+a) V = b(P0-P)
– Work = Force * Distance; Heat measurable
• Extra heat of shortening
Different distances Same Speed
Same distance Different speeds
Heat released
Extra heat of shortening
Summary
• Isotonic shortening: hyperbolic force • Isotonic lengthening: catastrophic yield • Much of the behavior is viscoelastic
– Not P ≥ 0.8 P0 – Not t < 2 ms
– Sarcomere length control via laser – Simultaneous force measurement
Force transducer
Diffraction screen
Servo length control
Laser
Tension recovery after shortening
Fast tension transients
• Hill’s viscoelastic system is 1st order • Ford, Huxley & Julian, 1977
– Further refined spot follower – Low-impedance moving coil motor
Force Velocity
• Describe the force-velocity relationship • Explain the "extra heat of shortening" • Describe exceptions to the force-velocity
relationship
Near-zero loads
• Discontinuity in slope • Loads > P0
Edman 1988
Non-steady state forces
• Rack & Westbury 1974 • Whole muscle (distributed stimulation) • Triangular length changes
– P0; VVmax = bP0/a – V = b(P0-P)/(P+a); V = Vmax (1-P/P0)/(1+P/a)
• One ‘material property’ for muscle: a≈P0/4 • Convenient/accurate estimate for Vmax
• Whole muscle • Heat rate depends on length • Lengthening
Isotonic and isovelocity experiments
• Servo control
– Feed back some sensor data to match a control signal
– Nearly instant change in force, length, velocity without acceleration
• Largely confirm Hill’s results
Lutz & al., 2002
K.A. Paul Edman (1979)
• Single fibers
– (x-a)(y-b)=c – a, b are coordinates of asymptotes
Load (g)
Add some thermodynamics
• Conservation of energy
– Rubber band analogy: QW+H
– Friction analogy: W+f Q
Tension
Step size
100 ms
Fast stages
• Elastic recoil (short range stiffness)
– Linear – 6 nm/hs ~ 0.5% length change
• Rapid recovery
– Complex, up to ~1% length change
– Extrapolate linear relation vs hyperbola
Lengthening velocities
• Work done on muscle
– Directly stretch viscous elementgreater heat rate
– Negative work
• Sudden yield
Heat during overload
Heat during shortening Isometric heat
Overload heat - work
Catastrophic yield (68 g)
Length during overload (56 g)
Length-tension-velocity
– Edman, 1979 – Ford, Huxley & Simmons, 1977 – Rack & Westbury, 1969/74
Afterloaded contraction
• A. V. Hill
– Time to move fixed distance against known inertia
Position indicator
Counterweights (Inertia)
Magnetic release mechanism
Safety stops/timer
Muscle
Shortening velocity (cm/s)
Hyperbolic force-velocity
• Purely phenomenolocial/empirical
T0
T2 100 ms T1
Interpretation
• At least two sources of ‘viscosity’
– Fast & slow – In series
• “True” viscosity
– Velocity dependent process – Contrast: elastic element that relaxes
• Very small, very fast steps
– Crossbridge length – Chemical kinetics
Step response
• Instantaneous, elastic recoil • Rapid (2 ms), partial recovery • Slow (100 ms), complete recovery