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.)

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

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)

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

stability and flexibility? 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). 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

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

Compressive Follower Load

Sagittal Balance Change of the Cervical Spine

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 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)

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

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

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

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

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. 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)

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 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

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

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.

Tilt of L1 in the Sagittal Plane Upright Forward Flexed

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 -103.00 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) 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 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, 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 % Motion Change compared to Intact 30 8 Nm 6 Nm 0-1200 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)

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

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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<Anterior 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: 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

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

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

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

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