Whole Bone Modeling Using Bone
Whole Bone Modeling Using Bone
Mineral Data
Mineral Data
or
or
Bones Are Not Amorphous Blobs
Bones Are Not Amorphous Blobs
Tho
m
as J. Beck
, Sc.D.
Tho
m
as J. Beck
, Sc.D.
The Johns Hopkins University
The Johns Hopkins University
School of Medicine
School of Medicine
The Fundamental problem
The Fundamental problem
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Bones get less dense as we age
Bones get less dense as we age
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Old people with low density bones
Old people with low density bones
fracture easily
fracture easily
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Space
Space
-
-
flight rapidly causes bones to
flight rapidly causes bones to
get less
dense
get less
dense
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Does space flight produce the same
Does space flight produce the same
effects on bone as aging?
effects on bone as aging?
The Human Femur
The Human Femur
Bone lo
ss causes
Bone lo
ss causes
fragility of proximal
fragility of proximal
(upper) end of femur
(upper) end of femur
Fractures are major cause
Fractures are major cause
of death (indirect) and
of death (indirect) and
disability in elderly
disability in elderly
Concern that space
Concern that space
-
-
flight
flight
might have similar
might have similar
conse
que
nces
conse
que
nces
Bone Dynamics
Bone Dynamics
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Bone is a dynamic tissue and is constantly
Bone is a dynamic tissue and is constantly
being
absorbed and rebuilt thro
ugho
ut life.
being
absorbed and rebuilt thro
ugho
ut life.
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Because bones get less dense with age
Because bones get less dense with age
physicians
inte
rpre
t this a
s
an imba
la
nc
e
physicians
inte
rpre
t this a
s
an imba
la
nc
e
between
between
resorptio
n
resorptio
n
and formation.
and formation.
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Old peo
p
le with low density bo
nes fracture
Old peo
p
le with low density bo
nes fracture
easily so it is assumed that bone density is a
easily so it is assumed that bone density is a
measure of likelihoo
d
o
f
fracture.
measure of likelihoo
d
o
f
fracture.
Current Bone “Density”Measurements
Current Bone “Density”Measurements
DXA Scan Image of Hip
DXA Scan Image of Hip
Digital image with all soft
tissues sub
t
racted and
only bone
mineral present
Pixel valu
es represent areal
mass in g/cm
2
Areal
mass is averaged over part
of region c
o
ntaining bone
(femoral neck region shown)
Result app
r
oximates volumetric
density and is called bone mineral de
nsity (BM
D
)
Femoral Neck BMD
Femoral Neck BMD
0
0.
2
0.
4
0.
6
0.
8 1
1.
2
1.
4
1.
6
20
40
60
80
100
A
g
e (
Y
ea
r
s
)
B M D ( g /cm
2
)
Looking at the details
Looking at the details
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Why do bon
e
s g
e
t l
e
ss d
e
nse as we ag
e?
Why do bon
e
s g
e
t l
e
ss d
e
nse as we ag
e?
barb2ne
barb2ne
Does this necessarily mean that bones are
Does this necessarily mean that bones are
ge
tting we
ake
r
?
ge
tting we
ake
r
?
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Why do astro
n
auts lose bone?
Why do astro
n
auts lose bone?
barb2ne
barb2ne
Are their bones getting weaker?
Are their bones getting weaker?
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Wh
at f
a
ctors are common b
e
t
w
een
ag
in
g
Wh
at f
a
ctors are common b
e
t
w
een
ag
in
g
an
d
an
d
microgravity
microgravity
and how do
they
differ?
and how do
they
differ?
Reduced Bone Str
e
ngth
Reduced Bone Str
e
ngth
is an Engine
ering Proble
m
is an Engine
ering Proble
m
Possible reasons:
Possible reasons:
1
.
The ma
te
rial is
le
s
s
able
to withs
t
a
nd
1
.
The ma
te
rial is
le
s
s
able
to withs
t
a
nd
loading stresses
loading stresses
Or
Or
2. The structure is altered to
increase lo
ading
2. The structure is altered to
increase lo
ading
stresses
stresses
Structure vs. Material Properties
Structure vs. Material Properties
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Evidence exists that bone material strength declines
Evidence exists that bone material strength declines
with age but effect disappears when corrected for
with age but effect disappears when corrected for
porosity
porosity
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No good evidence that space
No good evidence that space
-
-
flight influences
flight influences
material properties
material properties
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(no reliable way to measure
(no reliable way to measure
in vivo
in vivo
anyway)
anyway)
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W
ith
ou
t q
u
e
s
t
ion
W
ith
ou
t q
u
e
s
t
ion
bo
ne structure cha
n
ges wit
h
age
bo
ne structure cha
n
ges wit
h
age
and as a result of space
and as a result of space
-
-
flight
flight
An engineering perspective
An engineering perspective
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Long bones act as inefficient levers,
Long bones act as inefficient levers,
with a
c
tions due
to musc
le forc
es
with a
c
tions due
to musc
le forc
es
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Greatest
mech
an
ical stresses ar
e in
Greatest
mech
an
ical stresses ar
e in
bending
and torsion
bending
and torsion
Bending Stresses in Bones
Bending Stresses in Bones
At a given location, stress depends on:
At a given location, stress depends on:
1.
1.
Properties of cross
Properties of cross
-
-
section
section
2.
2.
Bending Moments (moment arm
Bending Moments (moment arm
lengths and force magnitudes)
lengths and force magnitudes)
Bending stresses in cantilever beam
Bending stresses in cantilever beam
σσσσ
=
My
I
F
y
d
I = Cross-
sectional
Moment of Inertia
Compressi
ve
stress
Tensilestress
M = F x d
Maximum Bending Str
e
ss
Maximum Bending Str
e
ss
σ
max
=
y
My
I
=
M
Z
Sectio
n Modul
u
s predict
s
maximum stress (
Sectio
n Modul
u
s predict
s
maximum stress (
σσσσ
σσσσ
) on
) on
subperiosteal (outer) surface
subperiosteal (outer) surface
M = bending moment
M = bending moment
I = cross
I = cross
-
-
sectional moment of inertia
sectional moment of inertia
y = dista
n
ce from centroid
y = dista
n
ce from centroid
to surface
to surface
Z = secti
o
n modulus
Z = secti
o
n modulus
Structural Changes in Adulthood
Structural Changes in Adulthood
1.
1.
Bone material is continually being
Bone material is continually being
absorbed and reformed
absorbed and reformed
(remodeling).
(remodeling).
2.
2.
Bones adapt to changes in
Bones adapt to changes in
mechanical loading through life
mechanical loading through life
(modeling).
(modeling).
The Mechanism:
The Mechanism:
Skeletal Loa
d
ing a
nd Str
a
in Stimuli
Skeletal Loa
d
ing a
nd Str
a
in Stimuli
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Stresses cause loaded bones to
distort slig
htly
Stresses cause loaded bones to
distort slig
htly
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These minut
e chang
e
s in
sh
ap
e or dim
e
nsion
These minut
e chang
e
s in
sh
ap
e or dim
e
nsion
a
r
e s
t
ra
ins
a
r
e s
t
ra
ins
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Strains are detected at the cellular level
Strains are detected at the cellular level
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Bone is adapted to maintain a specific level
Bone is adapted to maintain a specific level
and frequency of daily
strain
and frequency of daily
strain
Frost’s
Frost’s
Mechanostat
Mechanostat
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Bone ad
ap
ts to keep
av
erag
e daily str
a
i
n
s w
i
t
h
i
n
Bone ad
ap
ts to keep
av
erag
e daily str
a
i
n
s w
i
t
h
i
n
a “norm
a
l
”
r
a
ng
e.
a “norm
a
l
”
r
a
ng
e.
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Strains abov
e rang
e cause new bone fo
rmatio
n
Strains abov
e rang
e cause new bone fo
rmatio
n
—
—
(modeling) to stimulate bones to get stronger.
(modeling) to stimulate bones to get stronger.
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Strains below rang
e cause bo
ne to be lost
Strains below rang
e cause bo
ne to be lost
–
–
(increased rates of remodeling) to stimulate
(increased rates of remodeling) to stimulate
bon
e
s t
o
get w
e
ak
er.
bon
e
s t
o
get w
e
ak
er.
Bone
Bone
Remodeling
Remodeling
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Occurs mainly on
Occurs mainly on
internal
internal
bone surfaces
bone surfaces
throughout life
throughout life
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Rates are influenced by hormones and
Rates are influenced by hormones and
by skeletal loading
by skeletal loading
barb2ne
barb2ne
Increased loading
Increased loading
suppresses
suppresses
remodeling
remodeling
barb2ne
barb2ne
Decr
eased
lo
ad
i
n
g
Decr
eased
lo
ad
i
n
g
stimulates
stimulates
remodeling
remodeling
Bone
Bone
remodeling
remodeling
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Sk
el
et
al
lo
ad
ing
is dimi
nished i
n
t
h
e
Sk
el
et
al
lo
ad
ing
is dimi
nished i
n
t
h
e
e
l
de
rly re
la
tive to when the
y
were
stronge
r
e
l
de
rly re
la
tive to when the
y
were
stronge
r
an
d more act
i
v
e
an
d more act
i
v
e
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Space
Space
-
-
flight removes skeletal loading from
flight removes skeletal loading from
most of th
e b
o
d
y
(
excep
t u
p
p
e
r extremi
t
i
es)
most of th
e b
o
d
y
(
excep
t u
p
p
e
r extremi
t
i
es)
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Expect remodeling o
n
internal bone
Expect remodeling o
n
internal bone
surfaces to be stimulated in both cases
surfaces to be stimulated in both cases
Remodeling
Remodeling
in presence of load
in presence of load
Mechanical
Mechanical
Load
Load
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Bone is temporarily removed
Bone is temporarily removed
from internal surfaces
from internal surfaces
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Bendi
ng
strains i
n
crease on
Bendi
ng
strains i
n
crease on
external
external
surfaces
surfaces
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New
bo
ne is added to
external
New
bo
ne is added to
external
surfaces (modeli
n
g)
surfaces (modeli
n
g)
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Bone diameter increases to
Bone diameter increases to
compensate internal bone loss
compensate internal bone loss
Effects of normal modeling on bone density
Effects of normal modeling on bone density
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Le
ss
bone ne
eds
to be
adde
d to e
x
te
rnal
Le
ss
bone ne
eds
to be
adde
d to e
x
te
rnal
surface than removed from internal surface
surface than removed from internal surface
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Bone gets less dense because it is bigg
er in
Bone gets less dense because it is bigg
er in
diameter and because less bo
ne needed to
diameter and because less bo
ne needed to
maintain sectio
n modulus
maintain sectio
n modulus
Bone Modeling and Changing Load
Bone Modeling and Changing Load
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New bo
ne formation resulting from
New bo
ne formation resulting from
increased strain stimuli
increased strain stimuli
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Because long
bo
nes are mainly loading
Because long
bo
nes are mainly loading
in bending, maximum strains are on
in bending, maximum strains are on
the
the
outer
outer
surface
surface
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New bone formation (modeling)
New bone formation (modeling)
occurs o
n
t
h
e
occurs o
n
t
h
e
outer
outer
surface of
bo
ne
surface of
bo
ne
Adaptation to Increased
Loading
Adaptation to Increased
Loading
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Strains throug
hout the bone should increase.
Strains throug
hout the bone should increase.
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Rates of remodeling sho
u
ld decrease
Rates of remodeling sho
u
ld decrease
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May expect bo
ne to g
e
t bigg
er and cortex
May expect bo
ne to g
e
t bigg
er and cortex
thicker.
thicker.
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Sectio
n modulus sho
u
ld increase
Sectio
n modulus sho
u
ld increase
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Density may or may not increase depending
Density may or may not increase depending
on details of changes.
on details of changes.
Adaptation to Decreased Load
Adaptation to Decreased Load
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Strains decrease throug
h bo
ne
Strains decrease throug
h bo
ne
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Remod
e
lin
g i
n
creases from int
e
rnal
Remod
e
lin
g i
n
creases from int
e
rnal
surfaces
surfaces
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Bone
s
h
ould be
los
t
from inte
rnal
Bone
s
h
ould be
los
t
from inte
rnal
surfaces and cor
tices sh
oul
d
g
e
t
surfaces and cor
tices sh
oul
d
g
e
t
thinner
thinner
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Both sectio
n modulus and density
Both sectio
n modulus and density
shou
ld
decr
ease
shou
ld
decr
ease
Space
Space
-
-
Flight Effects
Flight Effects
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All loading will be absent (except that
All loading will be absent (except that
due to exercise countermeasures)
due to exercise countermeasures)
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Expect increased rates o
f
internal bo
ne
Expect increased rates o
f
internal bo
ne
loss
loss
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Expect no modeling
on outer surface
Expect no modeling
on outer surface
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Sectio
n modulus and density should
Sectio
n modulus and density should
decrease
decrease
Geometry from mass profiles
Geometry from mass profiles
using DXA Scanners
using DXA Scanners
01
2
3
4
Shaft Profile
Shaft Profile
Neck Pro
f
ile
Neck Pro
f
ile
Bone
BoneMassMass
(g/cm
(g/cm
22
)
)
Dista
n
ce (cm)
Dista
n
ce (cm)
01
2
3
4
Distance (cm)
5
Mass Projection of Shaft Cross
Mass Projection of Shaft Cross
-
-
Sectio
n
Sectio
n
W
∫
?
=
dA
x
x
I
c
x
)
(
∫
=
dA
A
Subperiosteal widthCross-sectio
nal area
Cross-sectional m
o
m
e
nt of inertia
Section Modulus
Properties measured from bone
Properties measured from bone
mass profiles
mass profiles
At all cross
At all cross
-
-
sectional regions:
sectional regions:
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BMD
BMD
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Subperiosteal Width
Subperiosteal Width
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Cross
Cross
-
-
Sectional Area (cortical bone
Sectional Area (cortical bone
eq
uiv
a
l
e
n
t
)
eq
uiv
a
l
e
n
t
)
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Sectio
n Modulus
Sectio
n Modulus
Need for a model of the cross
Need for a model of the cross
-
-
section
section
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Measur
ed
prop
erti
es d
o
n’t co
mpletel
y
Measur
ed
prop
erti
es d
o
n’t co
mpletel
y
describe the cross
describe the cross
-
-
section.
section.
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In absenc
e
of complete da
ta
(pic
ture
of
In absenc
e
of complete da
ta
(pic
ture
of
cross
cross
-
-
sectio
n) we need a model.
sectio
n) we need a model.
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Model assumes reasonable shape and has
Model assumes reasonable shape and has
geometry measured from DXA data.
geometry measured from DXA data.
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V
a
lidity de
pe
nds
on how well mode
l
V
a
lidity de
pe
nds
on how well mode
l
corresp
onds to
act
u
al cross
corresp
onds to
act
u
al cross
-
-
section.
section.
Properties modeled
Properties modeled
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Sh
ap
e o
f
cross
Sh
ap
e o
f
cross
-
-
section
section
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Proportion of trabecular and cortical
Proportion of trabecular and cortical
bone.
bone.
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En
docor
tical
d
i
ameter
En
docor
tical
d
i
ameter
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Cortical thicknesses
Cortical thicknesses
01
2
3
4
Measur
ed
Measur
ed
Bone Mass
Bone Mass
Profile
Profile
Distance (cm)
Cortical
Cortical
100% M
a
ss
100% M
a
ss
5
Modeled Shaft Cross
Modeled Shaft Cross
-
-
Section
Section
01
2
3
4
Measur
ed
Measur
ed
Bone Mass
Bone Mass
Profile
Profile
Distance (cm)
Distance (cm)
Trab
ecu
l
ar
Trab
ecu
l
ar
Cortical
Cortical
40% Mass
40% Mass
60% Mass
60% Mass
5
Modeled Neck Cross
Modeled Neck Cross
-
-
Section
Section
Some Examples:
Some Examples:
Study Populations:
Study Populations:
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National H
e
alth and N
u
trition Examination
National H
e
alth and N
u
trition Examination
Surv
e
y (NHAN
ES III)
Surv
e
y (NHAN
ES III)
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Study o
f
Study o
f
Osteoporotic
Osteoporotic
Fra
c
tures
(SOF)
Fra
c
tures
(SOF)
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Russian Cosmo
n
auts o
n
Mir Space Statio
n
Russian Cosmo
n
auts o
n
Mir Space Statio
n
NHANES III: A structural view of
NHANES III: A structural view of
normal aging in the hip
normal aging in the hip
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Cross
Cross
-
-
sectio
nal sample o
f
US po
pulatio
n
sectio
nal sample o
f
US po
pulatio
n
>14,000 hip DXA scans.
>14,000 hip DXA scans.
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White sub
White sub
-
-
sample including 2719 males
sample including 2719 males
an
d 2904 f
e
mal
e
s ag
e 20
an
d 2904 f
e
mal
e
s ag
e 20
-
-
90+.
90+.
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Data co
urtesy o
f
Dr. Anne Loo
k
er, US
Data co
urtesy o
f
Dr. Anne Loo
k
er, US
National Center for Health Statistics, and
National Center for Health Statistics, and
Dr. Heinz
Dr. Heinz
Wa
hne
r
Wa
hne
r
, Mayo Clinic
, Mayo Clinic
BMD and Section Modulus
BMD and Section Modulus
--
--
Males
Males
-4
0
%
-3
0
%
-2
0
%
-1
0
%
0%
10% 20%
N
e
ck BM
D
Sh
a
f
t
BM
D
Ne
c
k
se
c
t
ion
m
o
d
u
lu
s
S
h
a
f
t s
e
cti
o
n m
o
dul
us
20-29 30-39 40-49 50-59 60-69 70-79 80+
BMD and Section Modulus
BMD and Section Modulus
--
--
Females
Females
-
40%
-
30%
-
20%
-
10%
0%
10% 20%
Ne
c
k
B
M
D
S
h
a
ft BM
D
N
e
ck s
ecti
o
n
m
o
dul
us
S
h
a
ft s
ecti
o
n m
o
dul
us
20-29 30-39 40-49 50-59 60-69 70-79 80+
Subperiosteal
Subperiosteal
Widths
Widths
0% 2% 4% 6% 8%
10% 12% 14%
20-29
30-39
40-49
50-59
60-69
70-79
80+
Shaft
ma
le
s
Neck
ma
les
Shaft
F
e
ma
les
Neck
Fema
les
Youn
g Femur
Youn
g Femur
Aging Caus
es Internal Bone
Loss
Agin
g Femur
Agin
g Femur
Simultaneous Loading
Stimulates Ne
w
Bo
ne
Formation (Modeling)
Changes in Aging Long Bones
Changes in Aging Long Bones
View of Normal Aging Process
View of Normal Aging Process
Agin
g Bone
Agin
g Bone
Cross
Cross
-
-
Sec
t
ion
Sec
t
ion
Reduced BMD
Reduced BMD
But No
t Streng
th
But No
t Streng
th
Young Bone
Young Bone
Cross
Cross
-
-
Sec
t
ion
Sec
t
ion
Example:
Example:
can
can
compensate
compensate
for
for
10% loss in
10% loss in
BMD with < 1
BMD with < 1
mm increase in
mm increase in
outer diameter
outer diameter
Frost’s
Frost’s
Mechanostat
Mechanostat
Implies:
Implies:
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If skeletal loading is static
If skeletal loading is static
:
:
Bone strength should be maintained
Bone strength should be maintained
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If skeletal loading increases:
If skeletal loading increases:
Bone strength should improve
Bone strength should improve
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If skeletal loading decreases:
If skeletal loading decreases:
Bone strength should decline
Bone strength should decline
The Classic Hip Fracture Case
The Classic Hip Fracture Case
square6square6
An elderly woman who is:
An elderly woman who is:
barb4rightbarb4right
Physically inactive
Physically inactive
barb4rightbarb4right
Lo
w bo
dy weig
ht
Lo
w bo
dy weig
ht
barb4rightbarb4right
Reduced muscle m
a
ss
Reduced muscle m
a
ss
square6square6
Her skeletal loading is
Her skeletal loading is
considerably reduced from
considerably reduced from
levels when she was
levels when she was
younger and more active.
younger and more active.
square6square6
Longitudinal sample of white post
Longitudinal sample of white post
-
-
meno
pausal
meno
pausal
women ages > 65 at entry.
women ages > 65 at entry.
square6square6
Two hip scans averaging 3.6 years apart on 1876
Two hip scans averaging 3.6 years apart on 1876
subjects.
subjects.
square6square6
Subjects categorized by weight change:
Subjects categorized by weight change:
barb4rightbarb4right
Static (
Static (
+
+
1 kg of base
1 kg of base
-
-
line) N = 479
line) N = 479
barb4rightbarb4right
Gainers N = 654
Gainers N = 654
barb4rightbarb4right
Losers N = 743
Losers N = 743
square6square6
Data Courtesy of Drs. Steve Cummings and Katie Ston
e,
Data Courtesy of Drs. Steve Cummings and Katie Ston
e,
University of California at San Francisco
University of California at San Francisco
SOF: The Loading Hypothesis
SOF: The Loading Hypothesis
Femoral Neck Changes
Femoral Neck Changes
-5% -4% -3% -2% -1%
0% 1% 2% 3% 4% 5%
We
i
g
h
t
L
o
s
e
r
s
St
a
t
ic W
e
ig
ht
W
e
ig
ht
G
a
iner
s
B
M
D
S
e
c
t
i
o
n
M
o
dulus
ns
**
*
* p
<
.0002
*
*
Femoral Neck Changes
Femoral Neck Changes
-5% -4% -3% -2% -1%
0% 1% 2% 3% 4% 5%
We
i
g
h
t
L
o
s
e
r
s
St
a
t
ic
W
e
ig
h
t
W
e
ig
ht
G
a
ine
r
s
Subpe
r
.
W
i
dt
h
A
v
g
. C
o
r
t
. T
h
ic
k
n
e
s
s
**
*
**
**
**
*p
<
.
005
**p
<
.
0001
Increased
Increased
Load
Load
Constant Lo
ad
Constant Lo
ad
Stren
gth
Main
tai
n
ed
Stren
gth
Gained
Reduced Load
Reduced Load
Stren
gth
Lost
SOF Summary
SOF Summary
Same Subperiosteal Expansion In All Groups??
Same Subperiosteal Expansion In All Groups??
Bone Loss From Within Is
Bone Loss From Within Is
Load Dependent
Load Dependent
What If Loading Is Eliminated?
What If Loading Is Eliminated?
(i.e., Space
(i.e., Space
-
-
Flight)
Flight)
Since lo
ading
stimulates subperiosteal
Since lo
ading
stimulates subperiosteal
modeling and co
ntrols rate internal
modeling and co
ntrols rate internal
remodeling
remodeling
head2right
head2right
Ac
ce
le
ra
te
d inte
rna
l
bone loss
Ac
ce
le
ra
te
d inte
rna
l
bone loss
head2right
head2right
No s
ubpe
r
ios
t
ea
l ex
pa
ns
ion
No s
ubpe
r
ios
t
ea
l ex
pa
ns
ion
head2right
head2right
Both BMD and bone
s
t
re
ngth should be
Both BMD and bone
s
t
re
ngth should be
re
duc
e
d
re
duc
e
d
Effects of Space
Effects of Space
-
-
Flight
Flight
square6
square6
Pre and post flig
ht hip data o
n
19 Russian
Pre and post flig
ht hip data o
n
19 Russian
Cosmonauts.
Cosmonauts.
square6
square6
Average of 178 (126
Average of 178 (126
-
-
312) days on Mir Space
312) days on Mir Space
Station.
Station.
square6
square6
Follow
Follow
-
-
up d
a
t
a
on 8 Co
smonau
ts (~1.5 y post
up d
a
t
a
on 8 Co
smonau
ts (~1.5 y post
flight)
flight)
square6square6
Data co
urtesy of Drs. A
d
ri
an Le
bla
n
c, Li
nda
Data co
urtesy of Drs. A
d
ri
an Le
bla
n
c, Li
nda
Shackelford, Vict
or Schnei
d
er and V.
Shackelford, Vict
or Schnei
d
er and V.
Ogano
v
Ogano
v
.
.
-10%
-8% -6% -4% -2%
0% 2%
B
M
D
S
ect
io
n
M
o
dul
us
Subpe
r
.
Wi
d
t
h
Co
r
t
.
T
h
i
c
kne
ss
Po
s
t
-
F
lig
h
t
Fo
llo
w
-
U
p
ns
ns
ns
**
**
**
*
*
p < 0.000
1
*p = 0.03
ns
*
Changes in Femoral Neck
Changes in Femoral Neck
Bone loss in space
Bone loss in space
-
-
flight
flight
Pre
Pre
-
-
Flight
Flight
Condition
Condition
Internal bone loss
Internal bone loss
without loading
without loading
stimul
us
stimul
us
No modeling
No modeling
ot
ot
outer surface
outer surface
Reduced BMD
Reduced BMD
and
and
reduced strength
reduced strength
Post-FlightCondition
So What do we know about bone loss?
So What do we know about bone loss?
square6
square6
Bones adapt to loading
conditio
ns, getting
Bones adapt to loading
conditio
ns, getting
strong
er
or weaker as lo
ad
d
e
man
d
s ch
ang
e
strong
er
or weaker as lo
ad
d
e
man
d
s ch
ang
e
square6
square6
Loss of bone do
esn’t necessarily mean loss of
Loss of bone do
esn’t necessarily mean loss of
strengt
h
strengt
h
--
--
bo
nes get mo
re mechanically
bo
nes get mo
re mechanically
efficient as we age
efficient as we age
square6
square6
The
home
os
ta
tic
e
n
dpoint that the body strive
s
The
home
os
ta
tic
e
n
dpoint that the body strive
s
to maintain is the sectio
n modulus
to maintain is the sectio
n modulus
square6
square6
Absence of load (space flight) removes
Absence of load (space flight) removes
s
timulus
for ada
p
tive
mode
ling, bone
s get
s
timulus
for ada
p
tive
mode
ling, bone
s get
weak
er as bon
e
is lost
weak
er as bon
e
is lost
Differences Between Fracture Cases
Differences Between Fracture Cases
and Contr
o
ls
and Contr
o
ls
square6
square6
121 hi
p fract
ure cases co
mpared to 4082
121 hi
p fract
ure cases co
mpared to 4082
contro
ls
contro
ls
square6
square6
Results adjusted for age, knee
Results adjusted for age, knee
-
-
height and
height and
weight
weight
% Differ
ences Between Fracture Cases and
% Differ
ences Between Fracture Cases and
Control
s
Control
s
Ag
e,
W
e
igh
t
&
Kn
ee H
e
ight
Ad
jus
t
ed
(p <
.
0
001)
Ag
e,
W
e
igh
t
&
Kn
ee H
e
ight
Ad
jus
t
ed
(p <
.
0
001)
-1
5%
-1
0%
-5%
0% 5%
10
%
15
%
20
%
BMD
C
S
A
Wid
t
h
S
ec
tio
n
M
o
dul
us
Mea
n
Co
rt
e
x
Bu
c
k
lin
g
ra
t
i
o
Vi
si
t
2
Vi
si
t
4
Bending in a Thick
Bending in a Thick
-
-
Walled Tube
Walled Tube
Crack p
r
opag
at
es from out
e
r su
rface
Crack p
r
opag
at
es from out
e
r su
rface
Sectio
n modulus predicts strength
Sectio
n modulus predicts strength
Bending in a Thin
Bending in a Thin
-
-
Walled Tube
Walled Tube
Folds inward on inner surface(crumpling or lo
cal buckling)
Sectio
n Modulus Overestimates Streng
th
Defining Thin
Defining Thin
-
-
Walled tubes
Walled tubes
Buckling Ratio =
r
r
t
t
Buckling considered for ratios > 10 in hollow tubesFor trabecular fil
l
ed volumes (femoral neck) cri
t
ical
value unknown but probably higher
Local Buckling In the Femoral Neck
Local Buckling In the Femoral Neck
square6
square6
How thin does the cortex need to be?
How thin does the cortex need to be?
barb2ne
barb2ne
At
visit
4 aft
e
r adju
stment for ag
e an
d
At
visit
4 aft
e
r adju
stment for ag
e an
d
body
si
ze, cases av
erag
ed 24.3
body
si
ze, cases av
erag
ed 24.3
vs
vs
20.6 in
20.6 in
contro
ls (18% higher).
contro
ls (18% higher).
Overall Conclusions:
Overall Conclusions:
square6
square6
Depending on skeletal loading, geometric
Depending on skeletal loading, geometric
changes may compensate for net bone loss.
changes may compensate for net bone loss.
square6
square6
Structural adaptation appears to be the case
Structural adaptation appears to be the case
for most post
for most post
-
-
meno
pausal women
meno
pausal women
–
–
inde
ed
inde
ed
most do
not fracture.
most do
not fracture.
square6
square6
Progression toward fragility may actually be
Progression toward fragility may actually be
a
a
consequence
consequence
of the adaptation to reduced
of the adaptation to reduced
loading as fo
llo
ws:
loading as fo
llo
ws:
But what about elderly hip fractures?
But what about elderly hip fractures?
square6
square6
Why do th
ey fractur
e if bon
e
is ad
ap
ti
n
g
Why do th
ey fractur
e if bon
e
is ad
ap
ti
n
g
to their loading
?
to their loading
?
square6
square6
One would expect that bone have some
One would expect that bone have some
margin for overload.
margin for overload.
square6
square6
Could bones fail in o
t
her than pure
Could bones fail in o
t
her than pure
bending
?
bending
?
Evidence from Hip Fracture Cases
Evidence from Hip Fracture Cases
square6
square6
57 h
i
p fr
act
u
re cases co
mpared to 125
57 h
i
p fr
act
u
re cases co
mpared to 125
random contro
ls
random contro
ls
square6
square6
Results adjusted for age
Results adjusted for age
square6
square6
With and witho
u
t adjustment for
With and witho
u
t adjustment for
weig
ht
(
C
ases w
e
re li
ght
e
r on
av
erag
e)
weig
ht
(
C
ases w
e
re li
ght
e
r on
av
erag
e)
square6
square6
SOF data co
urtesy of Dr. Stev
en
SOF data co
urtesy of Dr. Stev
en
Cummings, analysis by Dr. Katie
Cummings, analysis by Dr. Katie
Sto
n
e
Sto
n
e
SOF Hip Fracture Cases
SOF Hip Fracture Cases
Relative to Random Controls
Relative to Random Controls
-2
0%
-1
5%
-1
0%
-5%
0% 5%
BMDBMD
Section Section
ModulusModulus
Subper
i
os
teal
Subper
i
os
teal
Wid
t
h
Wid
t
h
Cor
t
i
c
a
l
Cor
t
i
c
a
l
ThicknessThickness
Progress Toward Fragility
Progress Toward Fragility
square6
square6
Sk
el
et
al
lo
ad
ing
is r
e
d
u
ced
Sk
el
et
al
lo
ad
ing
is r
e
d
u
ced
square6
square6
Mechanostat accelerates
Mechanostat accelerates
barb2nebarb2ne
Endocortical resorption
Endocortical resorption
barb2nebarb2ne
Subperiosteal expansion?
Subperiosteal expansion?
square6
square6
Sectio
n modulus adapts to reduced lo
ad but
Sectio
n modulus adapts to reduced lo
ad but
square6
square6
Cortex thins to point w
h
ere failure o
ccurs not
Cortex thins to point w
h
ere failure o
ccurs not
in pure bending
(perhaps in
in pure bending
(perhaps in
lo
cal buckling??)
lo
cal buckling??)
Bending in a Thick
Bending in a Thick
-
-
Walled Tube
Walled Tube
Crack p
r
opag
at
es from out
e
r su
rface
Crack p
r
opag
at
es from out
e
r su
rface
Sectio
n modulus predicts strength
Sectio
n modulus predicts strength
Bending in a Thin
Bending in a Thin
-
-
Walled Tube
Walled Tube
Folds inward on inner surface(crumpling or lo
cal buckling)
Sectio
n Modulus Overestimates Streng
th
Questions About Local Buckling
Questions About Local Bucklingsquare6square6
When does this transition occur?
When does this transition occur?
square6
square6
How thin does the cortex need to
How thin does the cortex need to
be?
be?
square6
square6
What is the role of trabecular bone
What is the role of trabecular bone
in prevention of local buckling?
in prevention of local buckling?
square6
square6
Can this effect be measured with
Can this effect be measured with
DXA data?
DXA data?
Caveats
Caveats
square6
square6
Structural geometry can be measured with
Structural geometry can be measured with
current DXA scanners but not very well
current DXA scanners but not very well
square6
square6
Small changes in dimensions are
Small changes in dimensions are
structurally important, but can’t be
structurally important, but can’t be
reliably measured with current DXA
reliably measured with current DXA
scanners
scanners
DXA Clinical Prototype
DXA Clinical Prototype
Under Construction
Under Construction
Current DXA Scanner mass profiles
Current DXA Scanner mass profiles
01
2
3
4
Shaft Profile
Shaft Profile
Neck Pro
f
ile
Neck Pro
f
ile
Bone
BoneMassMass
(g/cm
(g/cm
22
)
)
Dista
n
ce (cm)
Dista
n
ce (cm)
Homework
Homework
square6
square6
Much we don’t know but yo
u can speculate
Much we don’t know but yo
u can speculate
on, based on results of simple simulations
on, based on results of simple simulations
square6
square6
Simulations can employ
kno
wn effects o
n
Simulations can employ
kno
wn effects o
n
bone from measured data
bone from measured data
Using Simulations of Bone Adaptation
Using Simulations of Bone Adaptation
square6
square6
Simulate
fe
mora
l s
h
a
f
t a
s
a
right c
y
lindric
a
l
Simulate
fe
mora
l s
h
a
f
t a
s
a
right c
y
lindric
a
l
hollow tube
subje
c
te
d to be
nding:
hollow tube
subje
c
te
d to be
nding:
barb2nebarb2ne
Changing rates of remodeling
Changing rates of remodeling
barb2nebarb2ne
Changing load
Changing load
barb2nebarb2ne
Changing both load and rates of remodeling
Changing both load and rates of remodeling
square6
square6
Examin
e effects on BM
D, sect
i
o
n mod
u
lu
s an
d
Examin
e effects on BM
D, sect
i
o
n mod
u
lu
s an
d
bon
e
di
amet
er
bon
e
di
amet
er
Assumptions:
Assumptions:
square6
square6
Moment arms are constant in
Moment arms are constant in
ad
ul
tho
o
d, ch
an
ges in
cr
oss
ad
ul
tho
o
d, ch
an
ges in
cr
oss
-
-
sectional
sectional
dimensions and load magnitudes only
dimensions and load magnitudes only
square6
square6
Sectio
n modulus chang
e
s linearly with
Sectio
n modulus chang
e
s linearly with
load magnitude
load magnitude
square6
square6
Remodeling changes inner radius of
Remodeling changes inner radius of
tub
u
l
a
r bon
e
(can i
n
cr
ease or
d
e
crease
tub
u
l
a
r bon
e
(can i
n
cr
ease or
d
e
crease
we will assume only increase).
we will assume only increase).
Example 1:
Example 1:
square6
square6
Remodeling with consistent skeletal
Remodeling with consistent skeletal
loading
loading
square6
square6
Remodeling removes bone from inner
Remodeling removes bone from inner
surface (increases inner radius) at a
surface (increases inner radius) at a
c
e
rta
i
n ra
te
c
e
rta
i
n ra
te
square6
square6
Wha
t
inc
r
e
a
s
e
in oute
r ra
dius will
Wha
t
inc
r
e
a
s
e
in oute
r ra
dius will
result in a constant section modulus?
result in a constant section modulus?
Geometry of hollow tube
Geometry of hollow tube
I =
π
4
(r
o
4
-r
i
4
)
A =
π
(r
o
4
-r
i
4
)
BMD =
A
ρρρρ
m
2r
o
ρρρρ
m
= effectiv
e
m
ineral
density of solid bone
( use~1.05 g/cm
3
)
Starting dimensions
Starting dimensions
For young 25 y/o adult male r
o
= 1.67 cm
r
i
= 1.16 cm
For young 25 y/o adult female r
o
= 1.47 cm
r
i
= 0.97 cm
Remodeling
Remodeling
square6
square6
Assume
Assume
r
r
i
i
Increases at constant
Increases at constant
rate
rate
square6
square6
Measured data suggest
Measured data suggest
increase of .004 cm/y
increase of .004 cm/y
in males
in males