Mechanical work as an indirect measure of subjective costs influencing human movement

Abstract

To descend a flight of stairs, would you rather walk or fall? Falling seems to have some obvious disadvantages such as the risk of pain or injury. But the preferred strategy of walking also entails a cost for the use of active muscles to perform negative work. The amount and distribution of work a person chooses to perform may, therefore, reflect a subjective valuation of the trade-offs between active muscle effort and other costs, such as pain. Here we use a simple jump landing experiment to quantify the work humans prefer to perform to dissipate the energy of landing. We found that healthy normal subjects (N = 8) preferred a strategy that involved performing 37% more negative work than minimally necessary (P<0.001) across a range of landing heights. This then required additional positive work to return to standing rest posture, highlighting the cost of this preference. Subjects were also able to modulate the amount of landing work, and its distribution between active and passive tissues. When instructed to land softly, they performed 76% more work than necessary (P<0.001), with a higher proportion from active muscles (89% vs. 84%, P<0.001). Stiff-legged landings, performed by one subject for demonstration, exhibited close to the minimum of work, with more of it performed passively through soft tissue deformations (at least 30% in stiff landings vs. 16% preferred). During jump landings, humans appear not to minimize muscle work, but instead choose to perform a consistent amount of extra work, presumably to avoid other subjective costs. The degree to which work is not minimized may indirectly quantify the relative valuation of costs that are otherwise difficult to measure.

Figure 1. Total mechanical power vs. time for vertical jumping and landing.

Subjects jumped vertically, landed and returned to rest. Representative trial demonstrates phases of a jump: Counter-Movement, Push-off, Aerial, Collision and Recovery, defined by zero-crossings of center-of-mass (COM) power. Landing is represented by the Collision and Recovery phases. Total power was estimated as the sum of COM power (due to motion of the COM) and Peripheral power (due to motion relative to the COM). Net landing height was defined as the displacement between maximum aerial height of the COM and standing rest posture.

Figure 2. Total landing work: plotted (A) as a function of net landing height and (B) relative to minimum possible work for each landing phase and strategy.

The theoretically minimum amount of landing work possible was defined as the change in potential energy from peak aerial height to standing rest (dashed line). Stiff landings achieved very close to this theoretical minimum. During Preferred landings, subjects performed 37% more Collision work than the minimum, necessitating additional positive Recovery work. Soft landings were even more extreme, with subjects performing about 76% more negative work than necessary. All relative work amounts were significantly different from each other (P<0.001).

Figure 3. Mechanical power estimates.

(A) Total power was estimated as the sum of center-of-mass (COM) power (due to motion of the COM) and Peripheral power (due to motion relative to the COM). (B) Joint power represents net contributions from muscle-tendon acting about the joints (ankle, knee, hip, lumbosacral), based on standard inverse dynamics. (C) Soft Tissue power is defined as the Total power minus the Joint power (see Text S1 for more details on calculations). Soft Tissue power was close to zero in most phases of the jump, except during Collision (immediately after touchdown), when it exhibited regions of negative, then positive power.

Figure 4. Collision and Push-off work, and contributions from passive soft tissues to Total work during Preferred landing.

Total and Soft Tissue work are plotted as a function of net landing height for (A) Collision and (C) Push-off (N = 8). Passive contributions were computed as the ratio of linear regression slopes (B _SoftT/B _Tot) for (B) Collision and (D) Push-off, yielding asymptotic proportions of 16% and −2%, respectively (shown as dashed lines). Soft Tissues therefore contributed substantially to Collision, but not to Push-off. For low net landing heights, the Soft Tissue contribution to Collision appeared to be greater than the asymptote (deviation shown as gray dotted line). That deviation appears consistent with heelstrike Collisions during walking, which are similar in magnitude to landings of about 3 cm and have Soft Tissue contributions of about 60%, as estimated previously .

Figure 5. Collision work, contributions from passive soft tissues during Soft and Stiff landing.

(A) Soft landings exhibited a significant increase in magnitude of Total work and a significant decrease in magnitude of Soft Tissue work during Collision, causing (B) a reduction in Soft Tissue contributions from the Preferred 16% to 10.6%. Stiff landings had the opposite effect, reducing Total Collision work and increasing Soft Tissue Collision work, with the overall effect of substantially increasing the proportion of Collision performed passively.

Figure 6. Soft Tissue work after touchdown in Preferred landing.

Positive Soft Tissue work immediately following the negative Collision work suggests an elastic rebound of passive tissues. For all landing conditions, the magnitude of positive Soft Tissue work after landing was about 20–30% of the negative work.