In Vivo Loads on the Lumbar Spine

Standing and walking activities:
–
–

1000 N
Supine posture: ~250 N
Standing at ease: ~500 N
Lifting activities:
–
–
Lifting 10 Kg, back straight, knee bent:
Holding 5 Kg, arms extended:
>> 1000 N
1700 N
1900 N
(Nachemson 1987; Schultz 1987; McGill 1990; etc.)
In Vivo Loads on the Cervical Spine
EXERCISE LATERAL
SHEAR
(N)
Relaxed
Left Twist
Extension
Flexion
Left
Bending
0
33
0
0
125
A- P SHEAR
(N)
COMPRESSION (N)
2
70
135
31
93
122
778
1164
558
758
Moroney, et al., J. Orthop. Res. 6:713-720, 1988
Choi and Vanderby, ORS Abstract, 1997
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:
– Lateral bending:
– Axial rotation:
(White and Panjabi 1990)
–

12 - 17 degrees
6 - 16 degrees
2 - 4 degrees
Lumbar motion segments can withstand 3000 N 5000 N in compression without damage.
(Adams, Hutton, et al. 1982)
Ex Vivo Studies of the Lumbar Spine
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)
Neuromuscular
Control System
Spinal Column
Spinal Muscles
How to obtain spinal
stability and flexibility?
HYPOTHESIS

The resultant force in the spine must
be tangent to the curve of the spine
(it follows the curvature).
Curvature of the
Lumbar Spine
L1
Follower
Load
L2


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.
L3
L4
L5
Center of
Rotation
Compressive Follower Load
Compressive Follower Load
"Curve of the
Cervical Spine"
C2
C3
Center of Rotation
C4
Follower Load
C5
C6
Loading Cable
C7
Cable Guide
T1
T2
Cervical FSU Strength > 2000 N (450 pounds)
Compressive Follower Load
Sagittal Balance Change of the Cervical Spine
Sagittal Balance Change of the Cervical Spine
40
Sagittal Tilt of C2 (deg)
Vertical Load
Vertical Load
Neutral Posture
15 deg Flexed
30 deg Flexed
Follower Load
20
Follower Load
Neutral Posture
15 deg Flexed
30 deg Flexed
0
Follower Load
-20
Vertical Load
-40
0
50
100
150
200
Compressive Load (N)
250
Follower Load on the Lumbar Spine
Follower Load Path
Effect of Follower Load Path Variation
Effect of Follower Load Path Variation
Flexion / Extension Motions
L2-3
10
Rotation Angle (deg)
Rotation Angle (deg)
10
8

6
4
2
0
-2
-4
-6
-8
-10
L3-4

8
6
4
2
0
-2
-4
-6



-8
-6
-4

-8
-10
-8
-6
-4
-2
0
2
4
6
8
Applied Moment (Nm)
: p < 0.1
: p <0.05
-2
0
2
4
6
8
Applied Moment (Nm)
L4-5

L5-S1
10

10
Rotation Angle (deg)
Rotation Angle (deg)
No Follower Load
With Follower Load
8
6
4
2
0
-2
-4

-6

-8
-10

8
6
4
2
0
-2
-4
-6



-8
-10
-8
-6
-4
-2
0
2
4
6
8
Applied Moment (Nm)
-8
-6
-4
-2
0
2
4
6
8
Applied Moment (Nm)
Effect of Follower Load
Experimental results showed:
Significantly
No
increased stability
significant limitation of flexibility
(or segmental motion range)
Lumbar Spine Model
x
x
Muscle Force
Line of Action
L1
L2
L3
l5
L4
L5
l1
l2
l3
l4
y
y
Frontal Plane
Sagittal Plane
Nomenclature
x
M3
H3
F3
3
yo:
y n:
an:
n:
initial curvature of the spine
horizontal elastic deformation for the nth segment
initial horizontal distance from the origin at the nth node
horizontal elastic deformation at the nth node
EIn:
bending stiffness at the nth level
Fn:
 n:
muscle force on the the nth level
angle defining the line of action of the nth muscle
Pon:
Pn:
external vertical force on the nth level
Pon + Fnsin n (total vertical force)
Hn :
Mn :
external horizontal force on the nth level
external moment acting on the nth level
P3
y
Governing Equations for Follower Load
From the classic beam-column theory;
For Region n: ln+1  x  ln, n = 1, …, 5 (Note: l6 = 0)
n Pa
n P
n 1 P
n  H
n
Pi
Qi 
i i
i i
i
i
y 
yn  


yo   

( i  x )   M i
i 1 EI n
i 1 EI n
i 1 EI n
i 1 EI n
i 1  EI n
i 1
EI n 
''
n
n
where
Pi  Poi  Fi sin i
y o ( i )   i
Qi  Fi cos i
y o ( i )  a i
i = 1,…, 5
Governing Equations for Follower Load
Boundary Conditions: fixed at the sacrum,
y5(0) = 0 and y5(0) = 0
Displacement and Slope Continuity Equations:
yi(li+1) = yi+1(li+1)
i = 1,…,4
yi(li+1) = yi+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
Ri = Resultant force at ith level
Ri need to be tangent to the curve to be a follower load.
L2
R2
L3
H2
H1
F1
Po1
Po2
Po1
R2
R1
R3
L4
L5
R1
at L2
at L1
L1
H1
F1
R4
R1
R5
Qi
(a n  a n 1 )  ( n   n 1 ) n Pi



i 1 EI n
i
1 EI n
 n   n 1
n
F2
n = 1,…, 5 (Note: a6 = 0, 6= 0, l6 = 0)
Model Response to Follower Load up to 1200 N
in Frontal Plane
Model Response to Follower Load up to 1200 N
In Frontal Plane
Po1 = 1040 N
L1
F1 = 163 N
L2
F2= 35.5 N
F3 = 27.2 N
R1=1159 N
R2=1177 N
=
L3
R3=1188 N
L4
F4 = 25.2 N
F5 = 29.5 N
0.2 m
R4=1197 N
L5
R5=1201 N
Model Responses In Frontal Plane
Po1 = 350 N
Po2 = Po3 = Po4 = Po5 = 50 N
Po1
L1
F1 = 51.9 N
L2
F2= 6.80 N
F3 = 6.74 N
R1=388 N
R2=441 N
=
L3
R3=494 N
L4
F4 = 8.23 N
F5 = 12.3 N
0.2 m
R4=546 N
L5
R5=598 N
Model Responses In Frontal Plane
Po1 = Po2 = Po3 = Po4 = Po5 = 110 N
Po1
L1
L2
F2= 6.74 N
R1=122 N
R2=236 N
=
F1 = 16.1 N
F3 = 6.74 N
L3
R3=346 N
L4
F4 = 3.04 N
F5 = 9.45 N
R4=457 N
L5
R5=569 N
0.2 m
Model responses vary with changes in external load distribution and muscle origin distance
as well.
Tilt of L1 in the Sagittal Plane
Upright
Forward
Flexed
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
286.00
Loading 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
5.27
Loading 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
Effect of Follower on Instrumentation
6 Nm
Decrease
8 Nm
Increase
% Motion Change compared to Intact
BAK
Threaded
cage
0-1200 N
30
20
10
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
Flexion
Extension
0
200
400
600
800
1000
Compressive Follower Preload (N)
1200
Role of Muscle Coactivation
?
Stability &
Flexibility
Postulations about Follower Load

Follower load path seems to be produced mostly by deep muscles.
–

Failure in making follower path may be the major source of various spinal
disorders.
–
–
–

Multifidus
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
Nomenclature
m
Fi  Muscle Forces (i = 1,…,m)
 ext
F j  External Forces (j = 1,…,n)
 jt
Fk  Joint Forces (k = 1,…,6)
 vt
rl  Position of the centroid of lth vertebra
(l = 1,…,5)
 vt
rl
Muscle Forces for Follower Load
Optimization to compute muscle forces producing Follower load
Object Function: minimization of summation of joint forces
6
6
jt
jt 
min  Fk and  M k 
k 1
 k 1

Inequality Constraints:
Equality Constraints:
m
Fj  0
Force Equilibrium: for l = 1,…,5
6
F
k 1
m
k ,l
6
F
ext
k ,l
jt
l
F F
jt
l 1
0
k 1
Moment Equilibrium: for l = 1,…,5
 jt 6  jt
 m  m 6  ext  ext  jt  jt  jt
 rk ,l  Fk ,l   rk ,l  Fk ,l  rk ,l  Fl  rk ,l 1  Fl 1   M k  0
6
k 1
k 1
Follower Load: for l = 1,…,5
 jt  vt  vt
Fl //( rl 1  rl )
k 1
( j  1,..., m)
Spine Skeletal Model
From T1 to Sacrum-Pelvis
<Posterior view>
<Lateral view>
Total Muscles -214
<Anterior view>
<Posterior view>
<Sagittal view>
Erector Spinae Group - 78
Iliocostalis (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 - 94
Interspinales (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
Upper Body Weight : 350 N
1 = External Oblique Rib11 to Pel (-)
2 = Internal Oblique Rib11 to Pel (-)
3 = Longissimus – T10 to Sa
4 = Psoas Major – T12 to Fe (-)
5 = Quadratus Lumborum – Rib12 to Pel
6 = Rectus Obdominis - Rib6 to Pel (-)
7 = Spinalis Thoracis – T6 to L1
8 = Spinalis Thoracis – T5 to L2
9 = Interspinales - T12 to L1
10 = Intertransversarii – T12 to L1 lateral
11 = Rotatores - T12 to L1
12 = Rotatores – T12 to L2
W
M
FBD at T12
2-D Simulation of 64 Muscles
FBD at L1Downward muscles
13 = Longissimus – L1 to Sa
14 = Psoas Major – L1 to Fe (-)
15 = Quadratus Lumborum – L1 to Pel
16 = Multifidus – L1 to Sa F1
17 = Multifidus – L1 to Sa F2
18 = Multifidus – L1 to L5 F3
19 = Multifidus – L1 to L4 F4
20 = Interspinales – L1 to L2
21 = Intertransversarii – L1 to L2 lateral
22 = Rotatores – L1 to L2
23 = Rotatores – L1 to L3
Upward muscles
7 = 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
Downward muscles
24 = Longissimus - L2 to Sa
25 = Psoas Major – L2 to Fe (-)
26 = Quadratus Lumborum – L2 to Pel
27 = Multifidus – L2 to Sa F1
28 = Multifidus – L2 to Sa F2
29 = Multifidus – L2 to L5 F3
30 = Multifidus – L2 to Sa F4
31 = Interspinales – L2 to L3
32 = Intertransversarii – L2 to L3 lateral
33 = Rotatores – L2 to L3
34 = Rotatores – L2 to L4
Upward muscles
8 = 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 (-)
FBD at L2
2-D Simulation of 64 Muscles
Downward muscles
35 = Longissimus - L3 to Sa
36 = Psoas Major – L3 to Fe(-)
37 = Quadratus Lumborum – L3 to Pel
38 = Multifidus – L3 to Sa F1
39 = Multifidus – L3 to Sa F2
40 = Multifidus – L3 to Sa F3
41 = Multifidus – L3 to Sa F4
42 = Interspinales – L3 to L4
43 = Intertransversarii – L3 to L4 lateral
44 = Rotatores – L3 to L4
45 = Rotatores – L3 to L5
Upward muscles
31 = Interspinales – L3 to L2 (-)
32 = Intertransversarii – L3 to L2 lateral (-)
33 = Rotatores – L3 to L2 (-)
23 = Rotatores – L3 to L1 (-)
FBD at L3
2-D Simulation of 64 Muscles
Downward muscles
46 = Longissimus - L4 to Sa
47 = Psoas Major - L4 to Fe (-)
48 = Quadratus Lumborum - L4 to Pel
49 = Multifidus – L4 to Sa F1
50 = Multifidus – L4 to Sa F2
51 = Multifidus – L4 to Sa F3
52 = Multifidus – L4 to Sa F4
53 = Interspinales – L4 to L5
54 = Intertransversarii – L4 to L5 lateral
55 = Rotatores – L4 to L5
56 = Rotatores – L4 to Sa
Upward muscles
19 = 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 (-)
FBD at L4
2-D Simulation of 64 Muscles
Downward muscles
57 = Longissimus – L5 to Sa
58 = Psoas Major – L5 to Fe (-)
59 = Multifidus – L5 to Sa F1
60 = Multifidus – L5 to Sa F2
61 = Multifidus – L5 to Sa F3
62 = Multifidus – L5 to Sa F4
63 = Interspinales – L5 to Sa
64 = Rotatores – L5 to Sa
Upward muscles
18 = 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 (-)
FBD at L5
2-D Simulation of 64 Muscles
Cost Functions:
1) Sum of the Norm of Joint Force Vectors
2) Sum of the Norm of Joint Moment Vectors
Equality Constraints (18):
1) 12 Force Equilibrium Eqs
2) 6 Moment Equilibrium Eqs
3) 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)
FBD at Sacrum
2-D Simulation of 64 Muscles:
Solutions at T12-L1 and L1-L2 Joints
External_Ob_Pel_Rib11_R
0
Longissimus_Sa_L1_R
0
Internal_Ob_Pel_Rib11_R
0
PsoasMajor_Fe_L1_R
0
Longissimus_Sa_T10_R
0
QuadratusLum_Pel_L1_R
0
PsoasMajor_Fe_T12_R
0
Multifidus_Sa_L1_F1_R
0
QuadratusLum_Pel_Rib12_R
0
Multifidus_Sa_L1_F2_R
0
Rec_Obdominis_Pel_Rib6_R
116.52
Multifidus_L5_L1_F3_R
0
SpinalisTho_L1_T6_R
232.54
Multifidus_L4_L1_F4_R
0
SpinalisTho_L2_T5_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
Interspinales_L1_T12_R
Intertransversarii_L1_T12_La_R
0.0001
0
Rotatores_L1_T12_R
143.41
Rotatores_L2_T12_R
0
Joint Force at T12-L1
815.32
2-D Simulation of 64 Muscles:
Solutions at L2-L3 and L3-L4 Joints
Longissimus_Sa_L2_R
PsoasMajor_Fe_L2_R
0
23.00
Longissimus_Sa_L3_R
PsoasMajor_Fe_L3_R
0
9.72
QuadratusLum_Pel_L2_R
0
QuadratusLum_Pel_L3_R
0
Multifidus_Sa_L2_F1_R
0
Multifidus_Sa_L3_F1_R
0
Multifidus_Sa_L2_F2_R
0
Multifidus_Sa_L3_F2_R
0
Multifidus_L5_L2_F3_R
0
Multifidus_Sa_L3_F3_R
0
Multifidus_Sa_L2_F4_R
0
Multifidus_Sa_L3_F4_R
0
Interspinales_L3_L2_R
0
Interspinales_L4_L3_R
0
Intertransversarii_L3_L2_La_R
0
Intertransversarii_L4_L3_La_R
78.60
Rotatores_L3_L2_R
72.80
Rotatores_L4_L3_R
156.19
Rotatores_L4_L2_R
90.22
Rotatores_L5_L3_R
0
Joint Force at L2-L3
815.32
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
Longissimus_Sa_L5_R
Multifidus_Sa_L4_F2_R
0
PsoasMajor_Fe_L5_R
0
Multifidus_Sa_L4_F3_R
0
Multifidus_Sa_L5_F1_R
0
Multifidus_Sa_L4_F4_R
0
Multifidus_Sa_L5_F2_R
0
Interspinales_L5_L4_R
0
Multifidus_Sa_L5_F3_R
0
Intertransversarii_L5_L4_La_R
0
Multifidus_Sa_L5_F4_R
376.66
Rotatores_L5_L4_R
284.38
Interspinales_Sa_L5_R
0
Rotatores_Sa_L4_R
0
Rotatores_Sa_L5_R
0
Joint Force at L4-L5
815.32
Joint Force at L5-S1
2.70
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.
–

Parametric trials showed that the solution can vary
sensitively to muscle orientations and external loading
conditions.
–


Further studies required for 3-D and other postures.
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
–

Develop animal models for the study of follower load
–

Blocking nerve endings for muscle control
Effect of follower load on the spinal implants
–
–

MRI
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