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?