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: Φ pre < Φ post – relationship between Φ and duration of weightlessness 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 Applied LoadFailure Load Fracture Risk Φ = F applied F fail Aim 1: 3-segment model for locomotion ? Lagrangian formulation p 1 , τ 1 p 2 , τ 2 p 3 , τ 3 m 1 , I 1 m 2 , I 2 m 3 , I 3 v c3 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 c.m. acceleration via Jacobian Control Scheme (locomotion) Hip torque: PPD control Ankle & knee torque: Impedance control γ F F 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: u Earth =2 -6 m/s(He et al., 1991) u Mars = 2 - 4 m/s (Newman et al., 1994; Wickman & Luna, 1996) ? Leg stiffness: K leg = 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/s 2 ) ? Initial ankle angle: iteration until lowest point of hip trajectory occurs at x=0 (initial knee angle set to 5 deg) 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) 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) J o i n t A ngl e ( de g) ankle (Mars) ankle (Earth) knee (Earth) knee (Mars) hip (Earth) hip (Mars) 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) Tor que ( N - m ) ankle (Mars) ankle (Earth) knee (Earth) knee (Mars) hip (Earth) hip (Mars) 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) J o i n t Cont ac t For ce (N ) Total (Mars) Total (Earth) X (Earth) X (Mars) Y (Earth) Y (Mars) Hip Locus (50% Male) 0.0 0.2 0.4 0.6 0.8 1.0 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 X-location (m) Y - l o cat i o n (m ) Earth Mars 50th Percentile Male (Earth) 0 500 1,000 1,500 2,000 2,500 3,000 7 9 11 13 15 17 Kleg (kN/m) Peak For ce ( N ) 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 Pe ak For ce ( E BW ) u=2 u=3 u=4 u=5 u=6 Male (Earth) 0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 2 4567 Horizontal Velocity (m/s) P e a k For ce (N ) (5%) (50%) (95%) McMahon (1987) McMahon & Cheng (1990) Bergmann (1993) Bassey (1997) van den Bogert (1999) 13 Male (Mars) 0 500 1,000 1,500 2,000 2,500 3,000 .5.5.5.5.55 Horizontal Velocity (m/s) P e a k For ce ( N ) EVA (5%) EVA (50%) EVA (95%) IVA (5%) IVA (50%) IVA (95%) 011223344 Aim 1: ? 3-segment model based on that derived by van den Kroonenberg (1995) ? 5 degrees-of-freedom g Z X Z Y q 1 left side rear q 2 q 3 q 5 q 4 Hip Loading During Falls Control Scheme ? Ankle and knee: Impedance Control – Adjust (K p ) x and (K d ) x so that hip stays close to Y-Z plane – Adjust (K p ) z and (K d ) z so that body configuration at impact is close to that reported by van den Kroonenberg from kinematic studies ? Hip joints: PPD – Adjust control parameters to obtain appropriate trunk orientation at impact Variation of Parameters (Fall) ? Body Mass Properties (m, I) and Anthropometry: – Male and female, 5%, 50%, 95% – Values derived using GEBOD ? Gravity: Earth G = g, Mars G = 3/8 g (g = 9.807 m/s 2 ) ? Initial joint position and velocity values set to correspond with van den Kroonenberg (interpolated to get 50% values) ? Impact model – Stiffness: KEarth = 71 kN/m (Robinovitch, et al., 1991) KMars = 57 kN/m (20% less for space suit padding) – Damping: B = 923 N/m-s (damping ratio = 0.2, Robinovitch, et al., 1991) Joint Angle (50% Male — Earth) -80 -60 -40 -20 0 20 40 60 80 100 120 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time (s) Joi nt A ngl e ( deg) ankle X knee Y hip X hip Y ankle Y Joint Torque (50% Male — Earth) -300 -200 -100 0 100 200 300 400 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time (s) T o r q u e (N -m ) ankle Xknee Y hip X hip Y ankle Y Hip Force (50% Male — Earth) -2000 -1000 0 1000 2000 3000 4000 5000 6000 7000 8000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time (s) Im p a c t F o r c e (N ) 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 I m pact For ce ( B W ) Ftotal Fz Fy Fx Peak Impact Force vs Kgnd (Mars EVA) 0 1000 2000 3000 4000 5000 6000 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 Ground Impact Stiffness (kN/m) P e ak F o r ce ( N ) Male (50%) Female (50%) Hip Force during Impact (Male) 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 0 10 20 0 0 0 60 0 80 90 100 Percentile Pea k F o r c e ( N ) Earth Mars EVA Mars IVA Parkkari (1995) Robinovitch(1995) 345 7 Hip Force during Impact (Female) 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 0 1020 0 0506070 0 010 Percentile P eak F o rce ( N ) Earth Mars EVA) Mars IVA van den Kroonenberg - dynam (1995) van den Kroonenberg - exper (1996) 34 89 * Fall impact forces reduced by 15% to account for soft tissue attenuation (Robinovitch et al., 1997) Applied Force Summary ( Male & Female 50%) 0 1000 2000 3000 4000 5000 6000 7000 Male Run Female Run Male Fall* Female Fall* A ppli e d For c e ( N ) Earth Mars IVA Mars EVA Finite Element Analysis QCT scans and NIH Image Extract contours Stack contours to define geometry 3-D Finite Element Model Define element material properties Extract density distribution (trabecular area) Methods: NIH Image Resliced Sections Outlines Femur Model Results: Failure Analysis Validation Trabecular bone specimens in torsion Similar results, r 2 =0.86 in bending y = 0.98x + 0.03 r 2 = 0.89 0 0.4 0.8 1.2 1.6 2.0 2.4 0 0.4 0.8 1.2 1.6 2.0 2.4 FEA Ultimate Torque, Nm Exp. Ultim ate Torque, Nm Y rotation = +21 deg Z rotation = +15 deg Y rotation = +10 deg Element Material Properties Cancellous elements [Ashman et al., 1989]: E = (2.84 x 10 3 )ρ 1.07 Cortical elements [Snyder and Schneider, 1991]: E = 21,910ρ - 23,500 Poisson’s ratio: ν = 0.3 for all elements Method of Increasing Endosteal Diameter For each curve defining endosteal boundary: ? Determine centroid ? Calculate average radius ? Calculate magnitude of point displacement (JHU results) ? Direction of displacement found by bisecting angle defined by adjacent points Muscle Strength Loss in Spaceflight ? Start with Earth-normal muscle magnitudes and directions: for mid-stance [Cheal et al.,1992] : Mag (BW) X (med-lat) Y (post-ant) Z (dist-prox) Gluteus medius 0.80 -0.67 0.18 0.72 Gluteus minimus 0.30 -0.78 0.21 0.59 Iliopsoas 1.30 -0.10 0.73 0.68 ? Reduce muscle strength with duration of weightlessness: – 40% lower at 6 months, 60% lower at 12 months, based on lit. ? 21% lower peak activated force 17 day flight [Widrick et al., 1999] ? 120 days of HDT bed rest [Koryak, 1999] : – 44% / 33% (M/F) decline in isometric max. voluntary contraction (MVC) – 36% / 11% (M/F) decline in isometric twitch contraction (Pt) – 34% / 24% (M/F) decline in tetanic contraction force (Po) ? Maximal explosive power (MEP) reduced to 67% after 31 days, and to 45% after 180 days of space flight [Antonutto et al., 1999] Failure Analysis Algorithm No Yes ABAQUS User Subroutine Update ε, σ FE Model Increment Displacement Calculate Strains and Reaction Forces Calculate ε max (prin), ε min (prin) Reduce Modulus End Node Failure? Model Failure? Yes No Node Failure: Maximum Principle Strain > 0.8% (tension) Minimum Principle Strain < -1.1% (compression) Model Failure: Reaction Force undergoes two successive decrements with increasing displacement Mid-s tance Lo ading (Pre- and Po s t-Flig ht) 0 1000 2000 3000 4000 5000 6000 7000 0 0.5 1 1.5 2 2.5 3 Z Displacement (mm) R e a c t i o n F o r ce ( N ) 0 months (muscles) 0 months (no muscles) 12 months Fall Configuration Loading (Pre- and Pos t-flight) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 X Displacement (mm) R e a c ti o n Fo rc e (N ) 0 months 12 months 0 1000 2000 3000 4000 5000 6000 7000 8000 -2 0 2 8 10 12 14 Duration of Weightlessness (months) Fa ilure Loa d ( N ) Male Run Female Run Male Fall Female Fall Courtney - Fall (1994, 1995) Bouxsein - Fall (1994) Beck - Stance (1990) Run Fall 64 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 Run (Earth,0) Run (Earth, 12) Run (Mars IVA, 12) Run (Mars EVA, 12) Fall (Earth, 0) Fall (Earth, 12) Fall (Mars IVA, 12) Fall (Mars EVA, 12) Fa c t or o f R i s k f o r Fr a c t u r e Male 50% Female 50% Conclusions ? Fall impact carries higher risk of fracture under all circumstances. ? Risk of fracture during locomotion is significantly greater for Mars EVA compared to Earth-normal and Earth-return. Reducing space suit mass is important. ? Muscles contribution during mid-stance is critical. ? Contrary to popular belief, risk of fracture during a fall on Mars (both IVA and EVA) is decreased compared to Earth- normal (lower gravity, spacesuit padding for EVA). FOR values are still close to 1.0, though, especially for males. ? Greatest risk to astronauts is from a fall occurring right after return from a long-duration mission. Use hip pads temporarily?