Heat of Liberation

Muscles and Heat
Dr. Maurissa D’Angelo
Muscle Heat
• Generates heat as contract
• Vitally important to maintaining body
• Most of heat from skeletal muscle
• Release excess heat to maintain temperature
Muscles and Heat
• Maintenance heat source
– Slow liberation of heat via resting muscle
– Unrelated to contraction, “background heat”
• Initial Heat
Liberated during contraction
Byproduct of chemistry of contractile process
– Activation heat, A: related to excitation-contraction coupling
– Shortening heat, ax: related to shortening of muscle
– Tension-time heat, f(P,t): related to cross-bridge turnover during time
when muscle is maintaining tension
• Recover heat – heat generated at end of contraction
Largely aerobic
Related primarily to oxidation of lactate
Liberated during relaxation (if muscle can relax without bearing load)
Degradation of potential energy of lifted load into heat (i.e. no longer
bearing load)
Initial Heat
• Extra heat – i.e. heat that exceeds maintenance heat,
liberated immediately following stimulus
• Occurs during:
– depolarization and repolarization of sarcolemma
– Release of activator calcium by sarcoplasmic recticulum
– Binding of calcium to troponin C
• Initial heat accompanies mechanical activity of
activated contractile proteins
• Because of heat modeling, Hill equation to predict
hyperbolic shape of force-velocity curve, define
chemical basis of muscular contraction
Isometric Contraction
• i.e. muscle isn’t shortening, not performing any
external work
• Heat
– Immediately after stimulation of muscle – activation
• Brief burst of heat prior to development of significant
– Following activation heat – slower rate heat
production along with development of tension
• Small
• Ignored for modeling and discussion (in this class)
Energy = (Work Produced) / (Free Energy of ATP)
Modeling Initial Heat
• DE = A + Wi (Activation Heat + Internal Work)
– Where DE is the change in external energy
– A is the heat of activation
– Wi is the internal work which takes place in isometrically
contracting muscle
• Even though ends of muscle are fixed, small amount of internal work
done by contractile elements
• Still have slight shape change in muscle, stretching
• DE = Q – W
– Energy in thermodynamic terms
– Q is the activation energy (plus small amount of heat liberated
during contraction)
– W is the internal work
Isotonic Contraction
• Muscle shortens while lifting constant load,
external work is performed
• Additional energy/heat present
• Total amount of heat liberated (ax)
– a: amount of heat liberated for each cm of
shortening (constant for given type of muscle)
– x: the distance the muscle shortens
– Shortening heat is therefore = a*x
Isotonic - Shortening Heat
• Shortening Heat = ax
– a is muscle specific
(units of force)
– x is the shortening
– DE = A + We + ax
(Energy Balance)
• A is Activation Heat
• We is External Work
• ax is Shortening Heat
– DE = Q + Px
• = Heat (A + ax) +
Work (Px)
Refined Equations
• Refined precision of measuring heat liberation
– Determined a (activation heat) is not constant
during isometric contractions at different loads
• Found proportional to developed tension
– Heat of shortening dependent on load
– Mommaerts separated heat of activation into two
components, A – true heat of activation and f(P,t)
– heat liberation which is a function of tension of
muscle (P) and length of time (t) tension is
Tension-Time Heat
• Isometric
– DE = A + Wi + f(P, t)
• Isotonic
– DE = A + We + ax + f(P, t)
• Where f(p, t) represents the heat liberated as a
function of both the muscle tension P and the
time duration t that the tension is exerted.
Hill’s Equation
“Characteristic Equation of Muscle”
• “Extra Energy”
• Let muscle lift a load P through a distance x.
• The energy generated as work W = Px
• The energy generated as Shortening Heat = ax
• Activation Heat A is omitted (not related to
• f(P, t) omitted for simplicity
• Extra Energy = Px + ax = (P + a) x
• Represents the total amount of extra energy liberated
by a muscle contracting under isotonic conditions.
“Extra Energy”
• Extra Energy Liberation = (P + a) x
Rate of Extra Energy Liberation = (P + a) dx/dt
• For an isometrically contracting muscle P = P0
and the Rate = 0 since there is no Work (x = 0)
nor is there any Shortening Heat (isometric).
• For an unloaded freely shortening muscle (P = 0)
the rate of energy release is a maximum.
“Extra Energy” - continued
• There is a direct linear proportionality for
– Rate of Extra Energy Released and the
– Difference between Max Load (P0) and
– the Actual Load (P), i.e. E (P0 - P)
• That is to say, the smaller the load, the greater
the rate of energy released.
– (P + a) v = (P0 - P) b
“Extra Energy” - continued
• (P + a) v = (P0 - P) b
• P v + a v = P0 b - P b
• P v + a v + P b + a b = P0 b + a b
• (P + a) v + (P + a) b = (P0 + a) b
Measuring Energy Cost via Heat
• Measure via direct and indirect calorimetry
• Direct – airtight insulated chamber
Person remains dormant or exercises
Humidified air provides oxygen
Chemical absorbents remove carbon dioxide
Heat produced picked up by stream of cold water
• Indirect – energy metabolism in body
– Oxygen dependent
– Measure oxygen consumption, calculate energy
– Measured via spirometer

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