In Vivo Loads on the Lumbar Spine l Standing and walking activities:1000 N – Supine posture: ~250 N – Standing at ease: ~500 N l Lifting

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


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


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




Total Musc. Force (abs) 360.00 0.00

Compressive Force 1 159.00 55.60





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



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)


Iliocostalis - 24


Longissimus - 48


Spinalis - 6


Transversospinalis Group - 94Interspinales (12), Intertransversarii (20),

Rotatores (22), Multifidus (40)


Interspinales - 12


Intertransversarii - 20


Rotatores - 22


Multifidus - 40


Internal & External Oblique - 12


Psoas Major – 12

<Anterior view> <Lateral view>

Quadratus Lumborum – 10


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


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


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 (-)


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 (-)


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 (-)


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 (-)


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_L5_L1_F3_R 0


Interspinales_L2_L1_R 74.48

Intertransversarii_L2_L1_La_R 69.64

Rotatores_L2_L1_R 53.81


Joint Force at L1-L2 815.32

2-D Simulation of 64 Muscles: Solutions at L2-L3 and L3-L4 Joints


PsoasMajor_Fe_L2_R 23.00






Interspinales_L3_L2_R 0

Intertransversarii_L3_L2_La_R 0





PsoasMajor_Fe_L3_R 9.72







Intertransversarii_L4_L3_La_R 78.60


Rotatores_L5_L3_R 0


2-D Simulation of 64 Muscles: Solutions at L4-L5 and L5-S`1 Joints

Longissimus_Sa_L4_R 43.92








Intertransversarii_L5_L4_La_R 0


Rotatores_Sa_L4_R 0


Longissimus_Sa_L5_R 2.70





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

Documents

In Vivo Loads on the Lumbar Spine l Standing and walking activities:1000 N – Supine posture: ~250 N – Standing at ease: ~500 N l Lifting