《太空生物工程与生命支撑》（英文版）modeling alterations

Principal Aim To assess the strength changes, and associated change in fracture risk, due to structural alterations in the proximal femora of astronauts experiencing long- term weightlessness 3-D FEA has not yet applied to bone loss in astronauts Greatly increased risk of fracture upon return to Earth and possibly even under strenuous loading in space or on the moon or Mars Calculate change in factor of risk() op= actual load / predicted failure load hypothesis:Φpe<Φpot relationship between g and duration of weightlessness

Principal Aim To assess the strength changes, and associated change in fracture risk, due to structural alterations in the proximal femora of astronauts experiencing long￾term weightlessness. • 3-D FEA has not yet applied to bone loss in astronauts – Greatly increased risk of fracture upon return to Earth and possibly even under strenuous loading in space or on the moon or Mars. • Calculate change in factor of risk (Φ) – Φ = actual load / predicted failure load – hypothesis: Φpre < Φpost – relationship between Φ and duration of weightlessness

Research Plan 36y.0 Space Flight△ 3-segment models Male Incr. endost diam locomotion (3 dof) CT Red trabec. mass fall impact (5 dof) DXA Red. musc. strength Gender Adjustable Equations of Motion Finite Lagrangian Element Gravity Level Kane's method Model Earth(g), Mars(3/8g) Fracture Risk Failure load F Applied Load F

Research Plan Adjustable Finite Element Model 3-segment models: • locomotion (3 dof) • fall impact (5 dof) Gender 36 y.o. Male • CT • DXA Space Flight ∆: Incr. endost. diam. Red. trabec. mass Red. musc. strength Gravity Level Earth (g), Mars (3/8g) Equations of Motion: • Lagrangian • Kane’s method Failure Load Applied Load Fracture Risk Φ = Fapplied Ffail

Aim 1: Hip Loading During Locomotion 3-segment model for locomotion Lagrangian formulation P2, t

Aim 1: 3-segment model for locomotion • Lagrangian formulation p1, τ1 p2, τ2 p3, τ3 m1, I1 m2, I2 m3, I3 vc3 g y x Hip Loading During Locomotion

Solution of Equations for Locomotion Initial joint velocity from hip/seg. 3 Calc joint acceleration at each time step Integrate to get velocity and position values Hip force from cm acceleration via Jacobian

Solution of Equations for Locomotion Initial joint velocity from hip/seg. 3 Calc. joint acceleration at each time step Integrate to get velocity and position values Hip force from c.m. acceleration via Jacobian

Control Scheme(locomotion) Hip torque PPD control F Ankle knee torque Y Impedance control F

Control Scheme (locomotion) Hip torque: PPD control Ankle & knee torque: Impedance control γ FF x F y Y X

Variation of Parameters(Locomotion) Body Mass Properties(m, I)and Anthropometrics Male and female. 5%.50%.95% Values derived using GEBOD Horizontal velocity eArth=2-6 m/s(He et al., 1991) UMars=2-4 m/s (Newman et al., 1994; Wickman& Luna, 1996) Leg stiffness Ken =9-15 kN/m(He et al, 1991; Farley& Gonzalez, 1996; Viale et al., 1998) Gravity Earth G=g, Mars G= 3/8g(g=9.807 m/s2) Initial ankle angle: iteration until lowest point of hip trajectory occurs at x=0 (initial knee angle set to 5 deg)

Variation of Parameters (Locomotion) • Body Mass Properties (m, I) and Anthropometrics: Male and female, 5%, 50%, 95% Values derived using GEBOD • Horizontal velocity: uEarth = 2 - 6 m/s (He et al., 1991) uMars = 2 - 4 m/s (Newman et al., 1994; Wickman & Luna, 1996) • Leg stiffness: Kleg = 9 - 15 kN/m (He et al., 1991; Farley & Gonzalez, 1996; Viale et al., 1998) • Gravity: Earth G = g, Mars G = 3/8 g (g = 9.807 m/s2) • Initial ankle angle: iteration until lowest point of hip trajectory occurs at x=0 (initial knee angle set to 5 deg)

1.2 806 -0.8-0.6-04-0.2 0.4 0.6 Position(m)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Position (m) dt Position (m)

Joint Position (50% Male) ankle(Earth) 120 ankle(Mars) p hip(Earth) knee(Earth) knee( Mars) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Time(s)

Joint Position (50% Male) 0 20 40 60 80 100 120 140 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Time (s) Joint Angle (deg) ankle (Mars) ankle (Earth) knee (Earth) knee (Mars) hip (Earth) hip (Mars)

Joint Torque(50% Male) 400 knee(Mars) knee(Earth) hip( Mars) hip(Earth) 100 200 ankle(Earth) 400 ankle(Mars) 0. 0.10 12 Time(s)

Joint Torque (50% Male) -500 -400 -300 -200 -100 0 100 200 300 400 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Time (s) Torque (N-m) ankle (Mars) ankle (Earth) knee (Earth) knee (Mars) hip (Earth) hip (Mars)

Hip Force(50% Male) 2500 2000 1500 Total (Earth) 之1000 Total(Mars) 500 500 X(Earth) 1000 X(Mars) -1500 Y(Earth) 2000 Y(Mars) 2500 0.00 0.04 0.06 0.08 0.10 0.14 Time(s)

Hip Force (50% Male) -2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Time (s) Joint Contact Force (N) Total (Mars) Total (Earth) X (Earth) X (Mars) Y (Earth) Y (Mars)