Patellar-tendon transformation under changing muscle force

Abstract

To distinguish the effects of increasing muscle force and changing patellar-tendon mechanical response on tendon strain. In this article human muscle–tendon mechanics were examined for loading exposure, tendon geometry, force-range selection, adaptation timing and measurement reliability. Axial mechanics, an exponential force–strain relation and a common-shape adaptation function were evaluated analytically. Secant rigidity obeys Q_s = F/ϵ; its change therefore describes the force–strain relationship rather than independently establishing tissue adaptation. For F : 2000 → 2600 N, C : 1000 → 1200 N and β = 20, the calculated strain rises from 5.493% to 5.763%, a relative increase of 4.92%. Evaluating each force on both response curves separates the positive force contribution from the negative curve contribution. In a linear response, force and secant-rigidity ratios of 1.30 and 1.20 instead give an 8.33% strain increase. Equal eventual force and rigidity gains produce a temporary strain elevation when their common adaptation function advances faster for force. With 30% eventual gains and a threefold rigidity-to-force adaptation-time ratio, peak elevations are 10.63% for g(v) = 1 − e^−v and 19.39% for g(v) = 1 − e^−v2. Patellar-tendon transformation requires comparison of response curves at matched forces. Strain at the operating force is a separate deformation outcome. Reference preload, slope interval, anatomical segment and covariance among measurements determine whether the two comparisons can be interpreted consistently.