Post on 26-Dec-2015
In Vivo Loads on the Lumbar Spine
Standing and walking activities: 1000 N– Supine posture: ~250 N– Standing at ease: ~500 N
Lifting activities: >> 1000 N– Lifting 10 Kg, back straight, knee bent: 1700 N– Holding 5 Kg, arms extended: 1900 N
(Nachemson 1987; Schultz 1987; McGill 1990; etc.)
EXERCISE LATERAL
SHEAR (N)
A- P SHEAR (N)
COMPRESSION (N)
Relaxed 0 2 122 Left Twist 33 70 778 Extension 0 135 1164 Flexion 0 31 558
Left Bending
125 93 758
Moroney, et al., J. Orthop. Res. 6:713-720, 1988 Choi and Vanderby, ORS Abstract, 1997
In Vivo Loads on the Cervical Spine
Physiologic Spinal Motion
3-D Motion:- Flexion/Extension (Fig)- Right/Left Lateral Bending - Right/Left Axial Rotation
In normal condition, the spine should be flexible enough to allow these motions without pain and trunk collapse (Flexibility).
Physiologic Range of Motion
Biomechanical Functions of the Spine
Protect the spinal cord
Support the musculoskeletal torso
Provide motion for daily activities
Requirements for Normal Functions
Stability Stability + Flexibility
Ex vivo Studies of the Lumbar Spine
Range of Motion of the Lumbar Motion Segments:– Flexion/extension: 12 - 17 degrees– Lateral bending: 6 - 16 degrees– Axial rotation: 2 - 4 degrees
(White and Panjabi 1990)
Lumbar motion segments can withstand 3000 N - 5000 N in compression without damage.
(Adams, Hutton, et al. 1982)
P Without active muscles,
• When constrained to move in the frontal plane, lumbar spine specimens buckle at P < 100 N.
(Crisco and Panjabi, 1992)
• In the sagittal plane, a vertical compressive load induces bending moment and results in large curvature changes at relatively smaller loads. When exceeding the ROM, further loading can cause damage to the soft tissue or bony structure.
(Crisco et al., 1992)
Ex Vivo Studies of the Lumbar Spine
Spinal Column
Neuromuscular Control System
Spinal Muscles
How to obtain spinalstability and flexibility?
HYPOTHESIS
The resultant force in the spine must be tangent to the curve of the spine (it follows the curvature).
This resultant force (follower load) imposes no bending moments or shear forces to the spine.
As a result, the spine can support large compressive loads without losing range of motion.
L1
L2
L3
L4
L5
FollowerLoad
Center ofRotation
Curvature of the Lumbar Spine
Compressive Follower Load
Compressive Follower Load
C 2
C 3
C 4
C 5
C 6
C 7
T 1
T 2
"C u rv e o f th e C erv ica l S p in e"
C en te r o f R o ta tio n
F o llo w er L o ad
C 2
C 3
C 4
C 5
C 6
C 7
T 1
T 2
"C u rv e o f th e C erv ica l S p in e"
C en te r o f R o ta tio n
F o llo w er L o ad
Cervical FSU Strength > 2000 N (450 pounds)
Loading Cable
Cable Guide
Compressive Follower Load
Sagittal Balance Change of the Cervical Spine
C o m pressiv e L oad (N )
F ollow er L oad
F o llow er L oad
Vertica l L o ad
Vertica l L o ad
0 50 10 0 15 0 20 0 25 0
Sagi
ttal T
ilt o
f C
2 (d
eg)
-4 0
-2 0
0
20
40
Ve r t ic a l L o a dN e u tra l P o s tu re1 5 d e g F le x e d3 0 d e g F le x e d
F o llo w e r L o a dN e u tra l P o s tu re1 5 d e g F le x e d3 0 d e g F le x e d
C o m pressiv e L oad (N )
F ollow er L oad
F o llow er L oad
Vertica l L o ad
Vertica l L o ad
0 50 10 0 15 0 20 0 25 0
Sagi
ttal T
ilt o
f C
2 (d
eg)
-4 0
-2 0
0
20
40
Ve r t ic a l L o a dN e u tra l P o s tu re1 5 d e g F le x e d3 0 d e g F le x e d
F o llo w e r L o a dN e u tra l P o s tu re1 5 d e g F le x e d3 0 d e g F le x e d
Sagittal Balance Change of the Cervical Spine
Follower Load on the Lumbar Spine
Follower Load Path
Effect of Follower Load Path Variation
Effect of Follower Load Path Variation
Flexion / Extension MotionsL2-3
Applied Moment (Nm)
-8 -6 -4 -2 0 2 4 6 8
Ro
tati
on
An
gle
(d
eg
)L3-4
Applied Moment (Nm)
-8 -6 -4 -2 0 2 4 6 8
Ro
tati
on
An
gle
(d
eg
)
L4-5
Applied Moment (Nm)
-8 -6 -4 -2 0 2 4 6 8
Ro
tati
on
An
gle
(d
eg
)
-10
-8
-6
-4
-2
0
2
4
6
8
10
-10
-8
-6
-4
-2
0
2
4
6
8
10L5-S1
Applied Moment (Nm)
-8 -6 -4 -2 0 2 4 6 8
Ro
tati
on
An
gle
(d
eg
)
-10
-8
-6
-4
-2
0
2
4
6
8
10
-10
-8
-6
-4
-2
0
2
4
6
8
10
No Follower LoadWith Follower Load
: p < 0.1: p <0.05
Effect of Follower LoadExperimental results showed:
Significantly increased stability
No significant limitation of flexibility (or segmental motion range)
Lumbar Spine Model
y y
x x
Frontal Plane Sagittal Plane
L1
L2
L3
L4
L5
Muscle ForceLine of Action
Nomenclature
y
x yo: initial curvature of the spineyn: horizontal elastic deformation for the nth segmentan: initial horizontal distance from the origin at the nth noden: horizontal elastic deformation at the nth node
EIn: bending stiffness at the nth level
Fn: muscle force on the the nth leveln: angle defining the line of action of the nth muscle
Pon: external vertical force on the nth levelPn: Pon + Fnsin n (total vertical force)
Hn: external horizontal force on the nth levelMn: external moment acting on the nth level
F3
3
P3
H3
M3
Governing Equations for Follower Load
From the classic beam-column theory;
For Region n: ln+1 x ln, n = 1, …, 5 (Note: l6 = 0)
iiii sinFPoP
iii cosFQ iio a)(y iio )(y where
i = 1,…, 5
n
1iii
n
1i n
i
n
io
1n
1i n
in
1i n
iin
1i n
iin
n
1i n
i''n M)x(
EI
Q
EI
Hy
EI
P
EI
P
EI
aPy
EI
Py
Governing Equations for Follower Load
Boundary Conditions: fixed at the sacrum,y5(0) = 0 and y5(0) = 0
Displacement and Slope Continuity Equations:yi(li+1) = yi+1(li+1) i = 1,…,4yi(li+1) = yi+1(li+1) i = 1,…,4
Solution Procedures
20 unknowns for the elastic deformations, y1, y2, y3, y4, and y5:- 10 constants arising from 5 homogeneous solutions to 2nd-order
DE- 5 unknown elastic deformation values at 5 vertebral centroids (i)- 5 muscle forces (Fi)
15 Equations:- 5 differential equations- 2 boundary conditions- 8 displacement and slope continuity equations
5 more equations: - constraints on the muscle forces to produce follower load
Constraints for Follower Load
n
1i n
i
1nn
1nn1nnn
1i n
i
EI
P)()aa(
EI
Q
n = 1,…, 5 (Note: a6 = 0, 6= 0, l6 = 0)
R1
H1
R2
R3
R4
R5
L1
L2
L3
L4
L5
Po1
F1
F1
H1
Po1
R1
at L1
Ri = Resultant force at ith levelRi need to be tangent to the curve to be a follower load.
F2
H2
Po2
R2
at L2
R1
Model Response to Follower Load up to 1200 Nin Frontal Plane
Model Response to Follower Load up to 1200 NIn Frontal Plane
Po1 = 1040 N
F1 = 163 NL2
L3
L4
L5
R1=1159 N
R2=1177 N
R3=1188 N
R4=1197 N
R5=1201 N
L1
F2= 35.5 N
F3 = 27.2 N
F4 = 25.2 N
F5 = 29.5 N
0.2 m
=
Model Responses In Frontal Plane
Po1
F1 = 51.9 NL2
L3
L4
L5
R1=388 N
R2=441 N
R3=494 N
R4=546 N
R5=598 N
L1
F2= 6.80 N
F3 = 6.74 N
F4 = 8.23 N
F5 = 12.3 N
0.2 m
=
Po1 = 350 NPo2 = Po3 = Po4 = Po5 = 50 N
Model Responses In Frontal Plane
Po1
F1 = 16.1 N
L2
L3
L4
L5
R1=122 N
R2=236 N
R3=346 N
R4=457 N
R5=569 N
L1
F2= 6.74 N
F3 = 6.74 N
F4 = 3.04 N
F5 = 9.45 N
0.2 m
=
Po1 = Po2 = Po3 = Po4 = Po5 = 110 N
Model responses vary with changes in external load distribution and muscle origin distance as well.
Tilt of L1 in the Sagittal Plane
Upright ForwardFlexed
Predicted Muscle Forces, Internal Compressive Forces (Muscle Origin = 10 cm)
With Follower Load Without Follower Load
Muscle Force 1 -103.00 0.00
Muscle Force 2 31.60 0.00
Muscle Force 3 58.30 0.00
Muscle Force 4 89.70 0.00
Muscle Force 5 77.60 0.00
Total Musc. Force (abs) 360.00 0.00
Compressive Force 1 159.00 55.60
Compressive Force 2 180.00 58.50
Compressive Force 3 220.00 60.00
Compressive Force 4 287.00 57.90
Compressive Force 5 339.00 53.60
Total Comp. Force(abs) 1185.00 286.00Loading Conditions: Po1 = 350 N; Pok = 50 N (k = 2,…, 5)
Predicted Internal Shear Forces and Moments(Muscle Origin = 10 cm)
With Follower Load Without Follower Load
Shear Force 1 0.43 22.60
Shear Force 2 -0.99 13.40
Shear Force 3 0.07 -0.10
Shear Force 4 0.35 -15.80
Shear Force 5 0.00 -26.9
Total Shear Force (abs) 1.84 78.8
Moment 1 0.06 0.514
Moment 2 0.23 1.39
Moment 3 0.12 1.64
Moment 4 0.43 1.35
Moment 5 0.18 0.38
Total Moment (abs) 1.02 5.27Loading Conditions: Po1 = 350 N; Pok = 50 N (k = 2,…, 5)
By making a follower load path,
Muscle co-activation can significantly reduce
the shear forces and moments,
while increasing
the compressive force
in the spine.
Effect of Deviations from Follower Load Path
8 Nm 6 Nm
0-1200 N
BAK Threaded cage
Compressive Follower Preload (N)
0 200 400 600 800 1000 1200
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
20
30
Flexion
Extension
Dec
reas
e
Incr
ease
Effect of Follower on Instrumentation
% Motion Change compared to Intact
Role of Muscle Coactivation
Stability &
Flexibility
?
Postulations about Follower Load
Follower load path seems to be produced mostly by deep muscles.– Multifidus
Failure in making follower path may be the major source of various spinal disorders.
– Deformities: Scoliosis, Spondylolisthesis, kyphosis– Degenerative diseases: disc degeneration, facet OA, etc.– Adverse effect of spinal fusion and instrumentation at the adjacent level
Re-establishment of failed follower load mechanism may be most important in the treatment of spinal disorders.
– Deep muscle strengthening
Future Studies
Find if the spine is under the compressive follower load in vivo and, if so, how the follower load is produced in vivo.
– Development of mathematical model should be helpful.
Can the Back Muscles Create Follower Load In-vivo?
Stability & Flexibility
Muscle Forces for Follower Load
miF
Muscle Forces (i = 1,…,m)
extjF
jtkF
External Forces (j = 1,…,n)
Joint Forces (k = 1,…,6)
Nomenclature
vtlr
Position of the centroid of lth vertebra (l = 1,…,5)
vtlr
Muscle Forces for Follower Load
Optimization to compute muscle forces producing Follower load
Object Function: minimization of summation of joint forces
6
1k
jtk
6
1k
jtk MF andmin
Equality Constraints:
Force Equilibrium: for l = 1,…,5
Follower Load: for l = 1,…,5
01
6
1
,,
jt
l
jt
l
k
ext
lk
m
lk FFFF6
1k
Moment Equilibrium: for l = 1,…,5
06
111,,
6
1,,,,
k
jtk
jtl
jtlk
jtl
jtlk
k
extlk
extlk
mlk
mlk MFrFrFrFr
6
1k
)//( 1vt
lvt
ljt
l rrF
Inequality Constraints:
0mjF
),...,1( mj
Spine Skeletal ModelFrom T1 to Sacrum-Pelvis
<Posterior view> <Lateral view>
Total Muscles -214
<Anterior view> <Posterior view> <Sagittal view>
Erector Spinae Group - 78Iliocostalis (24), Longissimus (48), Spinalis (6)
<Posterior view> <Lateral view>
Iliocostalis - 24
<Posterior view> <Lateral view>
Longissimus - 48
<Posterior view> <Lateral view>
Spinalis - 6
<Posterior view> <Lateral view>
Transversospinalis Group - 94Interspinales (12), Intertransversarii (20),
Rotatores (22), Multifidus (40)
<Posterior view> <Lateral view>
Interspinales - 12
<Posterior view> <Lateral view>
Intertransversarii - 20
<Posterior view> <Lateral view>
Rotatores - 22
<Posterior view> <Lateral view>
Multifidus - 40
<Posterior view> <Lateral view>
Internal & External Oblique - 12
<Posterior view> <Lateral view>
Psoas Major – 12
<Anterior view> <Lateral view>
Quadratus Lumborum – 10
<Posterior view> <Lateral view>
Rectus Obdominis – 8
<Anterior view> <Lateral view>
2-D Simulation of 64 Muscles
1 = External Oblique Rib11 to Pel (-)2 = Internal Oblique Rib11 to Pel (-)3 = Longissimus – T10 to Sa4 = Psoas Major – T12 to Fe (-)5 = Quadratus Lumborum – Rib12 to Pel6 = Rectus Obdominis - Rib6 to Pel (-) 7 = Spinalis Thoracis – T6 to L18 = Spinalis Thoracis – T5 to L29 = Interspinales - T12 to L110 = Intertransversarii – T12 to L1 lateral11 = Rotatores - T12 to L112 = Rotatores – T12 to L2
Upper Body Weight : 350 N
FBD at T12
WM
2-D Simulation of 64 Muscles
FBD at L1Downward muscles13 = Longissimus – L1 to Sa14 = Psoas Major – L1 to Fe (-)15 = Quadratus Lumborum – L1 to Pel16 = Multifidus – L1 to Sa F117 = Multifidus – L1 to Sa F218 = Multifidus – L1 to L5 F319 = Multifidus – L1 to L4 F420 = Interspinales – L1 to L221 = Intertransversarii – L1 to L2 lateral22 = Rotatores – L1 to L223 = Rotatores – L1 to L3
Upward muscles7 = Spinalis Thoracis – L1 to T6 (-)9 = Interspinales – L1 to T12 (-)10 = Intertransversarii – L1 to T12 lateral (-)11 = Rotatores – L1 to T12 (-)
FBD at L1
2-D Simulation of 64 Muscles
FBD at L2
Downward muscles24 = Longissimus - L2 to Sa25 = Psoas Major – L2 to Fe (-)26 = Quadratus Lumborum – L2 to Pel27 = Multifidus – L2 to Sa F128 = Multifidus – L2 to Sa F229 = Multifidus – L2 to L5 F330 = Multifidus – L2 to Sa F431 = Interspinales – L2 to L332 = Intertransversarii – L2 to L3 lateral33 = Rotatores – L2 to L334 = Rotatores – L2 to L4
Upward muscles8 = Spinalis Thoracis – L2 to T5 (-)20 = Interspinales – L2 to L1 (-)21 = Intertransversarii – L2 to L1 lateral (-)22 = Rotatores – L2 to L1 (-)12 = Rotatores – L2 to T12 (-)
2-D Simulation of 64 Muscles
FBD at L3
Downward muscles35 = Longissimus - L3 to Sa 36 = Psoas Major – L3 to Fe(-)37 = Quadratus Lumborum – L3 to Pel38 = Multifidus – L3 to Sa F139 = Multifidus – L3 to Sa F240 = Multifidus – L3 to Sa F341 = Multifidus – L3 to Sa F442 = Interspinales – L3 to L443 = Intertransversarii – L3 to L4 lateral44 = Rotatores – L3 to L445 = Rotatores – L3 to L5
Upward muscles31 = Interspinales – L3 to L2 (-)32 = Intertransversarii – L3 to L2 lateral (-)33 = Rotatores – L3 to L2 (-)23 = Rotatores – L3 to L1 (-)
2-D Simulation of 64 Muscles
FBD at L4
Downward muscles46 = Longissimus - L4 to Sa47 = Psoas Major - L4 to Fe (-)48 = Quadratus Lumborum - L4 to Pel49 = Multifidus – L4 to Sa F150 = Multifidus – L4 to Sa F251 = Multifidus – L4 to Sa F352 = Multifidus – L4 to Sa F453 = Interspinales – L4 to L554 = Intertransversarii – L4 to L5 lateral55 = Rotatores – L4 to L556 = Rotatores – L4 to Sa
Upward muscles19 = Multifidus – L4 to L1 F4 (-)42 = Interspinales – L4 to L3 (-)43 = Intertransversarii – L4 to L3 lateral (-)44 = Rotatores – L4 to L3 *34 = Rotatores – L4 to L3 (-)
2-D Simulation of 64 Muscles
FBD at L5
Downward muscles57 = Longissimus – L5 to Sa 58 = Psoas Major – L5 to Fe (-)59 = Multifidus – L5 to Sa F160 = Multifidus – L5 to Sa F261 = Multifidus – L5 to Sa F362 = Multifidus – L5 to Sa F463 = Interspinales – L5 to Sa64 = Rotatores – L5 to Sa
Upward muscles18 = Multifidus – L5 to L1 F3 (-)29 = Multifidus – L5 to L2 F3 (-)53 = Interspinales- L5 to L4 (-)54= Intertransversarii – L5 to L4 lateral (-)55 = Rotatores – L5 to L4 *45 = Rotatores – L5 to L3 (-)
2-D Simulation of 64 Muscles
FBD at Sacrum
Cost Functions:1) Sum of the Norm of Joint Force Vectors2) Sum of the Norm of Joint Moment Vectors
Equality Constraints (18):1) 12 Force Equilibrium Eqs2) 6 Moment Equilibrium Eqs3) 6 Directions of Joint Force Vectors in
Follower
Inequality Constraints:1) Magnitude of 64 Muscle Forces ≥ 0.0
Solver:Linear Opimization (Simplex Method on Matlab)
2-D Simulation of 64 Muscles: Solutions at T12-L1 and L1-L2 Joints
External_Ob_Pel_Rib11_R 0
Internal_Ob_Pel_Rib11_R 0
Longissimus_Sa_T10_R 0
PsoasMajor_Fe_T12_R 0
QuadratusLum_Pel_Rib12_R 0
Rec_Obdominis_Pel_Rib6_R 116.52
SpinalisTho_L1_T6_R 232.54
SpinalisTho_L2_T5_R 0
Interspinales_L1_T12_R 0.0001
Intertransversarii_L1_T12_La_R 0
Rotatores_L1_T12_R 143.41
Rotatores_L2_T12_R 0
Joint Force at T12-L1 815.32
Longissimus_Sa_L1_R 0
PsoasMajor_Fe_L1_R 0
QuadratusLum_Pel_L1_R 0
Multifidus_Sa_L1_F1_R 0
Multifidus_Sa_L1_F2_R 0
Multifidus_L5_L1_F3_R 0
Multifidus_L4_L1_F4_R 0
Interspinales_L2_L1_R 74.48
Intertransversarii_L2_L1_La_R 69.64
Rotatores_L2_L1_R 53.81
Rotatores_L3_L1_R 174.85
Joint Force at L1-L2 815.32
2-D Simulation of 64 Muscles: Solutions at L2-L3 and L3-L4 Joints
Longissimus_Sa_L2_R 0
PsoasMajor_Fe_L2_R 23.00
QuadratusLum_Pel_L2_R 0
Multifidus_Sa_L2_F1_R 0
Multifidus_Sa_L2_F2_R 0
Multifidus_L5_L2_F3_R 0
Multifidus_Sa_L2_F4_R 0
Interspinales_L3_L2_R 0
Intertransversarii_L3_L2_La_R 0
Rotatores_L3_L2_R 72.80
Rotatores_L4_L2_R 90.22
Joint Force at L2-L3 815.32
Longissimus_Sa_L3_R 0
PsoasMajor_Fe_L3_R 9.72
QuadratusLum_Pel_L3_R 0
Multifidus_Sa_L3_F1_R 0
Multifidus_Sa_L3_F2_R 0
Multifidus_Sa_L3_F3_R 0
Multifidus_Sa_L3_F4_R 0
Interspinales_L4_L3_R 0
Intertransversarii_L4_L3_La_R 78.60
Rotatores_L4_L3_R 156.19
Rotatores_L5_L3_R 0
Joint Force at L3-L4 815.32
2-D Simulation of 64 Muscles: Solutions at L4-L5 and L5-S`1 Joints
Longissimus_Sa_L4_R 43.92
PsoasMajor_Fe_L4_R 0
QuadratusLum_Pel_L4_R 0
Multifidus_Sa_L4_F1_R 0
Multifidus_Sa_L4_F2_R 0
Multifidus_Sa_L4_F3_R 0
Multifidus_Sa_L4_F4_R 0
Interspinales_L5_L4_R 0
Intertransversarii_L5_L4_La_R 0
Rotatores_L5_L4_R 284.38
Rotatores_Sa_L4_R 0
Joint Force at L4-L5 815.32
Longissimus_Sa_L5_R 2.70
PsoasMajor_Fe_L5_R 0
Multifidus_Sa_L5_F1_R 0
Multifidus_Sa_L5_F2_R 0
Multifidus_Sa_L5_F3_R 0
Multifidus_Sa_L5_F4_R 376.66
Interspinales_Sa_L5_R 0
Rotatores_Sa_L5_R 0
Joint Force at L5-S1 846.95
Result from Minimizing Moment Only
Similar patterns of muscle activation:– Minimal forces from long muscles– Significant forces in short muscles
Increasing joint follower load up to 1300 N
Solution is likely to be unique within the design space.
Discussion of Follower Load Potential static equilibrium for creating follower load in
quiet standing posture was simulated in 2-D without considering the joint stiffness.
– Further studies required for 3-D and other postures.
Parametric trials showed that the solution can vary sensitively to muscle orientations and external loading conditions.
– Instantaneous equilibrium
Back muscles can create a follower load in the lumbar spine in vivo.
Short segmental muscles play a significant role in creating follower load.
Future Studies
Investigate the biomechanical behaviors of the spine under various loading combinations of the follower loads and externally applied loads
– Altered follower load path may change the biomechanical response of the spine significantly and cause spinal disorders.
– Factors that may alter the follower load path:
• Local stiffness (or flexibility) changes in the spine due to the local disease, degeneration, injury and/or surgical interventions
• Abnormal neuromuscular control system
• Types of external loads or physiological activities
Future Studies Investigate the muscle abnormality in relation to spinal disorders
– MRI
Develop animal models for the study of follower load– Blocking nerve endings for muscle control
Effect of follower load on the spinal implants– More severe condition to spinal implant survival and greater need for load shearing in pedicle
screw instrumentation– Favorable condition for using cages and artificial discs
Develop new muscle strengthening methods