Biomechanics

Biomechanics applies mechanics to living organisms, from the forces exerted by a muscle to the deformation of a biological cell. It connects geometry, motion, material response and biological activity. A bone supporting a load, blood moving through a vessel, and a muscle producing work are all mechanical systems, but their living components can remodel, consume chemical energy and change their properties.

A simple torque balance explains why an internal muscle force can greatly exceed an external load. In an idealized stationary forearm, suppose a downward load $W=20\mathrm{N}$ acts with perpendicular moment arm $r_W=0.30\mathrm{m}$ about the elbow and the balancing tendon force has muscle moment arm $r_m=0.030\mathrm{m}$. Neglect the forearm’s own gravitational weight and other muscles. Zero net torque requiresThese are perpendicular moment arms, not necessarily distances measured along the bone. Force balance also requires a joint reaction; the torque equation alone does not determine every internal force.

Geometry must also be separated from material behavior. A tendon with sectional area $20{\mathrm{mm}}^2$ carrying that illustrative $200\mathrm{N}$ has mean axial stress $10\mathrm{MPa}$. Its extension depends on its length, constitutive equation and loading history, not just the applied force. Measurements of stress against strain therefore answer a different question from measurements of force against extension. For a living specimen, hydration, temperature and the rate of deformation can all be controlled experimental variables.

An influential motivating experiment is Archibald Vivian Hill’s measurement of heat and work during muscle contraction. In his 1938 primary paper, a thermopile detected tiny temperature changes; an optically amplified galvanometer made the response fast enough to study shortening. Comparing contractions under different loads connected shortening speed, mechanical work and liberated heat. Such measurements constrain an active muscle model in a way that simply stretching a passive spring cannot.^[ref] The example captures a central aim of biomechanics: use measurable forces, motion and energy transfers to test how a biological mechanism works.