Continuum mechanics applied to living tissue: muscle force–length–velocity, bone stress/strain, joint kinematics, cardiovascular hemodynamics, gait. Bridge between physics and physiology; substrate of orthopaedics, sports science, and…
biomechanics
Hill muscle model
Contractile element (CE) in series with series-elastic (SE) and parallel to parallel-elastic (PE). Force–velocity relation (F + a)(v + b) =…
Sliding-filament mechanism
Actin thin filaments slide over myosin thick filaments via cyclic cross-bridge attachment–force-generation–detachment powered by ATP.…
Bone mechanics (Wolff's law)
Bone remodels architecture in response to mechanical loading: trabecular orientation aligns with principal stress trajectories (Wolff…
Cardiovascular hemodynamics
Poiseuille flow in vessels gives Q = πΔP r⁴/(8ηL); Windkessel model (RC circuit) captures aortic-compliance / peripheral-resistance pulse…
Gait analysis
Quantitative description of locomotion via stance/swing phases, ground-reaction forces (~1–2× body weight at heel strike), centre-of-mass…
Tissue mechanics (viscoelasticity)
Soft tissues (skin, tendon, arterial wall) exhibit stress-relaxation and creep modelled by generalised Maxwell or Kelvin–Voigt networks.…
Joint kinematics
Description of joint motion by rotations/translations in anatomical planes, ISB-standard Euler angles, and instantaneous centre of…
Bone stress–strain behaviour
Cortical bone: E ≈ 17 GPa (longitudinal), σ_yield ≈ 120 MPa (tension) / 170 MPa (compression); anisotropic and strain-rate-dependent.…
Huxley cross-bridge: dn/dt=f(x)(1−n)−g(x)·n; actin-myosin ATP-driven sliding kinetics
Huxley 1957 cross-bridge kinetics framework — the canonical two-state ODE model of actin-myosin interaction underlying all mechanistic…
Euler-Bernoulli beam: EI·d⁴w/dx⁴=q(x); σ=M·y/I; I_rect=b·h³/12
Euler-Bernoulli beam framework — the canonical 4th-order PDE model of slender-beam bending used throughout orthopaedic biomechanics for…
Pennation angle: F_tendon=F_fiber·cos(θ); L_t²=L_f²+L_a²+2·L_f·L_a·cos(θ)
Pennation-angle moment-arm geometry framework — the canonical triangle-closure model of muscle-fiber force projection onto the tendon axis…
Hill hyperbola: v(F)=b(F_max−F)/(F+a); v_max=b·F_max/a; F_opt=√(a(F_max+a))−a
Sympy-exact symbolic witness of the Hill force-velocity hyperbola canonical form and power-optimisation anchors. Setup: F (force), v…
Beam: I_rect=b·h³/12; σ_max=6·M/(b·h²); w_cant=P·L³/(3EI); P_cr=π²·EI/L²
Sympy-exact symbolic witness of the Euler-Bernoulli beam canonical identities for cross-section geometry, maximum bending stress,…
Pennation: F_t=F_f·cos(θ); F_t(0)=F_f; F_t(π/3)=F_f/2; L_t²=L_f²+L_a²+2L_fL_a·cos(θ)
Sympy-exact symbolic witness of pennation-angle force projection and tendon-fiber-aponeurosis triangle closure (law of cosines). Setup:…
Hill equation (1938)
A V Hill 1938 force-velocity hyperbola; modern Hill-type muscle-models + computational neuromechanics.
Mechanostat (Frost 1987)
H Frost 1987 mechanostat; modern Wolff law + osteoporosis + BMD imaging; clinical management.
Inverse dynamics (Zatsiorsky 1998)
V Zatsiorsky 1998 inverse-dynamics; modern motion-capture + opensim + clinical gait-analysis.
OFC (Todorov-Jordan 2002)
Todorov-Jordan 2002 OFC; modern motor-coordination minimum-intervention; computational basis.
Running economy (Margaria 1963)
R Margaria 1963 running-economy + spring-mass model; modern Hoogkamer 2018 super-shoes + 4% efficiency.
Hill 1938 detail
A V Hill 1938 (Nobel 1922) force-velocity F=(F_max - bv)/(v + a); modern cross-bridge Huxley 1957 + Pollard-Borisy 2003 actin.
Huxley cross-bridge (1957)
A F Huxley 1957 cross-bridge model; modern motor-protein nano-mechanics + isotonic / isometric force-Ca2+ regulation.
Inverse dynamics (Bresler 1950)
B Bresler 1950 inverse-dynamics; modern Vicon-3D-mocap + IMU-fusion + 3D-prosthetic-design lower-limb biomechanics.
Fung 1967
Y C Fung 1967 'biomechanics-of-soft-tissue'; modern strain-energy-density-function W(I1,I2,I3) + arterial-elastin model.
Spring-mass (Blickhan 1989)
R Blickhan 1989 spring-mass running model; modern Geyer SLIP biomechanics + bipedal-robotics ASIMO + Cassie ETH-Robotics.
Brain shear (Holbourn 1943)
A Holbourn 1943 brain rotational-shear-injury; modern DAI diffuse-axonal injury + helmet-design + 2024 CTE longitudinal NFL.