9. 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: N
(Nachemson 1987; Schultz 1987; McGill 1990; etc.)

10. In Vivo Loads on the Cervical Spine
EXERCISE
LATERAL A -
P SHEAR
COMPRESSION (N)
SHEAR
(N)
(N)
Relaxed 2
122
Left Twist 33 70
778
Extension
135
1164
Flexion 31
558
Left
125 93
758
Bending
Moroney, et al.,
J. Orthop. Res.
6:713 -
720, 1988
Choi and Vanderby, ORS Abstract, 1997

11. 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).

12. Physiologic Range of Motion

13. Biomechanical Functions of the Spine
Protect the spinal cord
Support the musculoskeletal torso
Provide motion for daily activities

14. Requirements for Normal Functions
Stability
Stability + Flexibility

15. Ex vivo Studies of the Lumbar Spine
Range of Motion of the Lumbar Motion Segments:
Flexion/extension: degrees
Lateral bending: degrees
Axial rotation: degrees
(White and Panjabi 1990)
Lumbar motion segments can withstand 3000 N N in compression without damage.
(Adams, Hutton, et al. 1982)

16. Ex Vivo Studies of the Lumbar Spine
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) P

17. stability and flexibility?
Neuromuscular
Control System
Spinal Column
Spinal Muscles
How to obtain spinal
stability and flexibility?

18. 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.
Curvature of the
Lumbar Spine L1 L2
Follower
Load L3 L4
Center of
Rotation L5
Compressive Follower Load

19. Compressive Follower Load
Loading Cable
Cable Guide
Cervical FSU Strength > 2000 N (450 pounds)

20. Compressive Follower Load

21. Sagittal Balance Change of the Cervical Spine

22. Sagittal Balance Change of the Cervical Spine

23. Follower Load on the Lumbar Spine

24. Follower Load Path

25. Effect of Follower Load Path Variation

26. Effect of Follower Load Path Variation

28. Flexion / Extension Motions
No Follower Load
With Follower Load
L2-3
L3-4
-10 -8 -6 -4 -2 2 4 6 8 10
-10 -8 -6 -4 -2 2 4 6 8 10  
Rotation Angle (deg)
Rotation Angle (deg)     -8 -6 -4 -2 2 4 6 8 -8 -6 -4 -2 2 4 6 8
Applied Moment (Nm)
: p < 0.1
: p <0.05
Applied Moment (Nm)  
L4-5
L5-S1 
Rotation Angle (deg)
Rotation Angle (deg)      -8 -6 -4 -2 2 4 6 8 -8 -6 -4 -2 2 4 6 8
Applied Moment (Nm)
Applied Moment (Nm)

29. Effect of Follower Load
Experimental results showed:
Significantly increased stability
No significant limitation of flexibility (or segmental motion range)

31. Lumbar Spine Model x x y y Frontal Plane Sagittal Plane Muscle Force
Line of Action L1 L2 L3 l5 L4 l4 l3 L5 l2 l1 y y
Frontal Plane
Sagittal Plane

32. Nomenclature x yo: initial curvature of the spine
yn: horizontal elastic deformation for the nth segment
an: initial horizontal distance from the origin at the nth node
n: horizontal elastic deformation at the nth node
EIn: bending stiffness at the nth level
Fn: muscle force on the the nth level
n: angle defining the line of action of the nth muscle
Pon: external vertical force on the nth level
Pn: Pon + Fnsin n (total vertical force)
Hn: external horizontal force on the nth level
Mn: external moment acting on the nth level M3 H3 F3 P3 3 y

33. Governing Equations for Follower Load
From the classic beam-column theory;
For Region n: ln+1  x  ln, n = 1, …, 5 (Note: l6 = 0)
where
i = 1,…, 5

34. 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

35. 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

36. Constraints for Follower Load
Ri = Resultant force at ith level
Ri need to be tangent to the curve to be a follower load.
at L1
at L2 L1 H1 F1 H1 H2 L2 R1
Po1 R2
Po1
Po2 L3 R1 R2 R3 L4 F1 R4 R1 L5 R5 F2
n = 1,…, 5 (Note: a6 = 0, 6= 0, l6 = 0)

37. Model Response to Follower Load up to 1200 N in Frontal Plane

38. Model Response to Follower Load up to 1200 N
In Frontal Plane
Po1 = 1040 N L1
R1=1159 N L2
F1 = 163 N
F2= 35.5 N
R2=1177 N = L3
F3 = 27.2 N
R3=1188 N L4
R4=1197 N
F4 = 25.2 N L5
F5 = 29.5 N
R5=1201 N
0.2 m

39. Model Responses In Frontal Plane
Po2 = Po3 = Po4 = Po5 = 50 N
Po1 L1
R1=388 N L2
F1 = 51.9 N
F2= 6.80 N
R2=441 N = L3
F3 = 6.74 N
R3=494 N L4
R4=546 N
F4 = 8.23 N L5
F5 = 12.3 N
R5=598 N
0.2 m

40. Model Responses In Frontal Plane
Po1 = Po2 = Po3 = Po4 = Po5 = 110 N
Po1 L1
R1=122 N L2
F2= 6.74 N
R2=236 N = L3
F1 = 16.1 N
F3 = 6.74 N
R3=346 N L4
R4=457 N
F4 = 3.04 N L5
F5 = 9.45 N
R5=569 N
0.2 m
Model responses vary with changes in external load distribution and muscle origin distance as well.

41. Tilt of L1 in the Sagittal Plane
Upright
Forward
Flexed

42. Loading Conditions: Po1 = 350 N; Pok = 50 N (k = 2,…, 5)
Predicted Muscle Forces, Internal Compressive Forces (Muscle Origin = 10 cm)
With Follower Load
Without Follower Load
Muscle Force 1
0.00
Muscle Force 2
31.60
Muscle Force 3
58.30
Muscle Force 4
89.70
Muscle Force 5
77.60
Total Musc. Force (abs)
360.00
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)
286.00
Loading Conditions: Po1 = 350 N; Pok = 50 N (k = 2,…, 5)

43. 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
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)

44. By making a follower load path,
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.

45. Effect of Deviations from Follower Load Path

46. Effect of Follower on Instrumentation
% Motion Change compared to Intact 30
8 Nm
6 Nm N
BAK
Threaded
cage 20 10
-10
-20
Decrease Increase
-30
-40
-50
-60
Flexion
-70
Extension
-80
-90
200
400
600
800
1000
1200
Compressive Follower Preload (N)

47. Role of Muscle Coactivation?
Stability &
Flexibility

48. 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

49. Stability & Flexibility
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

50. Muscle Forces for Follower Load
Nomenclature
Muscle Forces (i = 1,…,m)
External Forces (j = 1,…,n)
Joint Forces (k = 1,…,6)
Position of the centroid of lth vertebra
(l = 1,…,5)

51. Muscle Forces for Follower Load
Optimization to compute muscle forces producing Follower load
Object Function: minimization of summation of joint forces
Equality Constraints:
Inequality Constraints:
Force Equilibrium: for l = 1,…,5
Moment Equilibrium: for l = 1,…,5
Follower Load: for l = 1,…,5

52. Spine Skeletal Model From T1 to Sacrum-Pelvis
<Posterior view> <Lateral view>

53. Total Muscles -214
<Anterior view> <Posterior view> <Sagittal view>

54. <Posterior view> <Lateral view>
Erector Spinae Group - 78 Iliocostalis (24), Longissimus (48), Spinalis (6)
<Posterior view> <Lateral view>

55. <Posterior view> <Lateral view>
Iliocostalis - 24
<Posterior view> <Lateral view>

56. <Posterior view> <Lateral view>
Longissimus - 48
<Posterior view> <Lateral view>

57. <Posterior view> <Lateral view>
Spinalis - 6
<Posterior view> <Lateral view>

58. <Posterior view> <Lateral view>
Transversospinalis Group - 94 Interspinales (12), Intertransversarii (20), Rotatores (22), Multifidus (40)
<Posterior view> <Lateral view>

59. <Posterior view> <Lateral view>
Interspinales - 12
<Posterior view> <Lateral view>

60. <Posterior view> <Lateral view>
Intertransversarii - 20
<Posterior view> <Lateral view>

61. <Posterior view> <Lateral view>
Rotatores - 22
<Posterior view> <Lateral view>

62. <Posterior view> <Lateral view>
Multifidus - 40
<Posterior view> <Lateral view>

63. Internal & External Oblique - 12
<Posterior view> <Lateral view>

64. <Anterior view> <Lateral view>
Psoas Major – 12
<Anterior view> <Lateral view>

65. <Posterior view> <Lateral view>
Quadratus Lumborum – 10
<Posterior view> <Lateral view>

66. <Anterior view> <Lateral view>
Rectus Obdominis – 8
<Anterior view> <Lateral view>

67. 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

68. 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

69. 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

70. 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

71. 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

72. 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

73. 2-D Simulation of 64 Muscles
Cost Functions:
Sum of the Norm of Joint Force Vectors
Sum of the Norm of Joint Moment Vectors
Equality Constraints (18):
12 Force Equilibrium Eqs
6 Moment Equilibrium Eqs
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

74. 2-D Simulation of 64 Muscles: Solutions at T12-L1 and L1-L2 Joints
External_Ob_Pel_Rib11_R
Internal_Ob_Pel_Rib11_R
Longissimus_Sa_T10_R
PsoasMajor_Fe_T12_R
QuadratusLum_Pel_Rib12_R
Rec_Obdominis_Pel_Rib6_R
116.52
SpinalisTho_L1_T6_R
232.54
SpinalisTho_L2_T5_R
Interspinales_L1_T12_R
0.0001
Intertransversarii_L1_T12_La_R
Rotatores_L1_T12_R
143.41
Rotatores_L2_T12_R
Joint Force at T12-L1
815.32
Longissimus_Sa_L1_R
PsoasMajor_Fe_L1_R
QuadratusLum_Pel_L1_R
Multifidus_Sa_L1_F1_R
Multifidus_Sa_L1_F2_R
Multifidus_L5_L1_F3_R
Multifidus_L4_L1_F4_R
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

75. 2-D Simulation of 64 Muscles: Solutions at L2-L3 and L3-L4 Joints
Longissimus_Sa_L2_R
PsoasMajor_Fe_L2_R
23.00
QuadratusLum_Pel_L2_R
Multifidus_Sa_L2_F1_R
Multifidus_Sa_L2_F2_R
Multifidus_L5_L2_F3_R
Multifidus_Sa_L2_F4_R
Interspinales_L3_L2_R
Intertransversarii_L3_L2_La_R
Rotatores_L3_L2_R
72.80
Rotatores_L4_L2_R
90.22
Joint Force at L2-L3
815.32
Longissimus_Sa_L3_R
PsoasMajor_Fe_L3_R
9.72
QuadratusLum_Pel_L3_R
Multifidus_Sa_L3_F1_R
Multifidus_Sa_L3_F2_R
Multifidus_Sa_L3_F3_R
Multifidus_Sa_L3_F4_R
Interspinales_L4_L3_R
Intertransversarii_L4_L3_La_R
78.60
Rotatores_L4_L3_R
156.19
Rotatores_L5_L3_R
Joint Force at L3-L4
815.32

76. 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
QuadratusLum_Pel_L4_R
Multifidus_Sa_L4_F1_R
Multifidus_Sa_L4_F2_R
Multifidus_Sa_L4_F3_R
Multifidus_Sa_L4_F4_R
Interspinales_L5_L4_R
Intertransversarii_L5_L4_La_R
Rotatores_L5_L4_R
284.38
Rotatores_Sa_L4_R
Joint Force at L4-L5
815.32
Longissimus_Sa_L5_R
2.70
PsoasMajor_Fe_L5_R
Multifidus_Sa_L5_F1_R
Multifidus_Sa_L5_F2_R
Multifidus_Sa_L5_F3_R
Multifidus_Sa_L5_F4_R
376.66
Interspinales_Sa_L5_R
Rotatores_Sa_L5_R
Joint Force at L5-S1
846.95

77. 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.

78. 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.

79. 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

80. 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