1. Muscle Generated Heat
Primary sources of liberated heat energy from skeletal muscle due to chemical processes:
Maintenance (Resting) - Slowly liberated background heat, unrelated to muscle contraction.
Recovery - Heat generated at the end of muscle contraction, related mainly to chemical reactions associated with energy production.
Initial - Liberated immediately after stimulation and throughout muscle contraction (tension).

2. Initial Heat Isometric Contractions - Activation Heat
Constant Length - No External Work
Isotonic Contractions - Shortening Heat
Constant Force (Load) - External Work
Tension-Time Heat

3. Initial Heat - Isometric
Two components:
Activation - Brief burst, immediately after stimulation.
Slower rate of heat production associated with the development of increasing tension.
DE = A + Wi (Activation Heat + Internal Work)
DE = Q - W

4. Initial Heat - Isotonic
In addition to external work (muscle shortening while lifting a constant load), additional heat is liberated due to the shortening process itself.
Note: This so called shortening heat is function of the shortening distance, but independent of the load. Although the amount of heat production is independent of the load, the rate of heat production decreases as the load increases.

5. Isotonic - Shortening Heat
Shortening Heat = ax
a is muscle specific (units of force)
x is the shortening distance
DE = A + We + ax
A is Activation Heat
We is External Work
ax is Shortening Heat
DE = Q + Px
= Heat (A + ax) + Work (Px)

6. Tension-Time Heat
Note: Early work of Hill (1930’s) was refined in the 1960’s with the advent of more precise measurements of heat.
Activation Heat was found to not be a constant for isometric contractions at various loads, but rather is proportional to the developed tension.
Shortening Heat however is a function of the load.

7. Tension-Time Heat continued
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.

8. 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 contraction)
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.

9. “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.

10. “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

11. “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

12. Hill’s Equation
(P + a) v + (P + a) b = (P0 + a) b