Distinguish active tension, passive tension and external work

1. Identify the structure and functional question

Muscle force can include active crossbridge contribution and passive resistance from stretched elastic structures. Length changes the arrangement of contractile and connective components, so force is not determined by activation alone. The same total force can combine active and passive terms in different proportions.

2. Connect architecture, mechanism and assumptions

An isometric boundary holds whole-muscle length fixed; a concentric action shortens an active muscle and an eccentric action lengthens it under load. These terms do not automatically specify constant force. Internal sarcomere and tendon lengths can change while the total preparation length stays fixed, so the level at which length is measured matters.

The original isometric curve stipulates capacity A(L)=max(0,1−((L−1)/0.5)²). Active force is 100uA(L) for activation u, and passive force is 200max(0,L−1)². Both are invented normalized functions. They show an active optimum and a rising passive term without claiming a universal measured force–length curve.

External shortening work is zero when external length does not change, but ATP consumption and heat generation need not be zero. The model does not compute energy efficiency, fatigue or shortening velocity. A comparison must report active/passive contributions and the mechanical boundary rather than inferring metabolic silence from lack of motion.

3. Reconstruct the original worked case

At L=1.2 and activation 0.5, active capacity is 0.84, active force 42 and passive force 8, giving total 50 units. At zero activation the passive 8 remains. The externally held length gives zero shortening work, not necessarily zero biochemical energy use.

4. Predict and investigate

Predict first: Can force remain when activation is zero, and can ATP be used when the preparation does not shorten?

Compare activation 0 and 0.5 at L=1.2, then compare lengths 0.8 and 1.2 at the same activation. Separate the symmetric active capacity from the asymmetric passive term.

5. Transfer to a changed mechanism or boundary

Apply the mechanism to a changed boundary

At L=1.4 and activation 0.25, calculate active capacity, active force, passive force and total.

Retain the first response, units, uncertainty and any prior feedback exposure in the notebook before comparing this public explanation.

Compare a worked response

Capacity is 1−0.8²=0.36; active force 9, passive force 32 and total 41. This is a supplied isometric model, not an estimate of a person’s muscle function.

6. Retain a bounded functional explanation

Preserve first predictions, settings, complete quantities and an independent observation that could reject the explanation in the Anatomy and Physiology course workspace. Public feedback and invented models are not clinical evaluation, supervised specimen work or independently assessed reasoning. No physical exercise, temperature exposure, electrical stimulation, personal measurements or treatment is requested.

Supporting anatomical mechanism, checked 30 October 2026. Original teaching prose, numerical packets, schematic diagrams and exercises; no real physiological measurement or injury threshold is inferred.