Download Biomechanics Of Lifting And Lower Back Pain: Part 2

Biomechanics of Lifting and
Lower Back Pain: part 2
S.N. Robinovitch
Outline
• Spinal stability
• Shear forces
• Effect of abdominal pressure on
lifting mechanics
• Cantilever model of lifting
Forces on the lumbar spine
Moment due to applied
load
Erector Spinae Force
Disc shear force
(perpendicular to long axis
of vertebrae)
Disc compressive force
(parallel to long axis of
vertebrae)
Definition of stability
• Engineering definition of
stability: “system is in a state
of stable equilibrium if, for all
possible small displacements
from equilibrium, restoring
force arise which accelerate
the system back toward the
equilibrium position”
• Clinical definition of spinal
instability: “loss of the spine’s
ability to maintain its patterns
of displacement under
physiologic loads”
Effect of co-contraction on spinal
stability
•
•
Spine with ligaments but
no muscle will buckle
under 90 N force
Co-contracted muscles
act like cables to stabilize
the spine. Increasing the
force or stiffness in both
cables:
•
•
•
increases the load-carrying
capacity of the spine
Increases ability to
withstand perturbations
(surprise loads) from both
directions
Reduces risk for buckling
Shear Forces
• Shear forces act parallel to the
vertebral end plate and promote relative
sliding between vertebrae
• Shear forces at the L4-L5 arise from
(1) weight of the HAT, (2) hand forces (if
any), and (3) forces in muscles and
ligaments that connect to the spine
• If the erector spinae line of action is
parallel to the long axis of the vertebrae,
it does not contribute to disc shear force
• As the lumbar spine becomes fully
flexed, the contribution of ligaments to
the supportive moment increases.While
this increases spinal stability, it also
increases disc shear forces.
Shear force convention
• By convention, positive
shear (or “anterior shear”)
indicates a tendency for L4
to move forward on L5, as
when the trunk is flexed
forward (Figure A).
• Negative (or “posterior”)
shear indicates a tendency
for L4 to move backward on
L5, as when a person
pushes forward with their
hands (Figure B).
A
B
Shear force affects injury risk
1.00
0.80
Probability
In the Ontario Back
Pain Study, injured
workers had workloads
that involved:
• Higher peak hand
forces
• Higher peak L4-L5
shear forces
• Higher cumulative
moments (time
integrated)
• Higher peak trunk
velocities
0.60
0.40
0.20
0.00
0
500
1000
Peak Reaction Shear (N)
Norman et al, 1998
1500
Chaffin’s Cantilever Low-back Model
of Lifting
• Toppling moments due to
HAT weight and hand force
are balanced by supporting
moments from erector spinae
and abdominal pressure
• Includes abdominal
pressure, and allows that
long axis of L5/S1 may be
different than long axis of
torso.
• Related reading: Chaffin
and Andersson, Occupational
Biomechanics, Chapter 6:
Section 6.5.1
comp
axis
shear
axis
Governing equations: cantilever
Step 3.
model
Let
Step 1.
v
" M L 5 / S1 = 0 gives :
b * (mg) HAT + h(mg) load # D( FA ) # E ( Fm ) = 0.
Let
v
M
( L 5 / S1 ) external = b * (mg) HAT + h(mg) load
and
v
( M L 5 / S1 ) internal = #D( FA ) # E (Fm ).
assumed equal to 465 cm2 .
Note :1 mm Hg = 0.0133 N/cm2 = 133 Pa
!
Use E = 0.05 m and D = 0.11 m.
Step 2.
Define abdominal pressure PA (in mm Hg) as
v
depending on hip flexion and ( M L 5 / S1 ) external :
v
1.8
#4
PA = 10 [ 43 # 0.36 * (180 # $ H )](( M L 5 / S1 ) external )
where $ H is the included hip angle (knee hip - shoulder).
FA = PA * A
where A is the diaghram area,
Abdominal pressure
• Abdominal pressure (PA) is developed through
contraction of the diaphragm and abdominal
wall muscles.
• Abdominal pressure is higher in fast than slow
lifts.
• The internal force (FA) created by the
abdominal pressure is estimated using the
following two assumptions (Morris et. al., 1961)
• average diaphragm area (A) of 465 cm2
• a line of action parallel to the compressive
forces on the lumbar spine
Disc axes for compression and shear
• to calculate disc
compression and shear
force, the plane of L5/S1
must be determined.
• spinal curvature will
cause each intervertebral
joint to have unique
coordinate axes
• the longitudinal axis of
L5/S1 will differ from the
angle “T” of the torso
Sacral joint rotation
• Angle (!) between the plane of
L5/S1 and the horizontal is
assumed to depend on posture as
follows:
! = 40o + "
Where " depends on the included
knee angle “K” and the torso angle
“T” as follows:
" = -17.5 - 0.12T + 0.23K +
0.0012TK + 0.005T2 - 0.00075K2
• Alternatively, ! can be estimated
from spinal curvature
• For erect posture, ! ! 0 and ! !
40o
Sacral joint rotation (") scales with
torso and knee angle
• When the torso flexes beyond 20-30 deg, pelvis rotates
forward (cw) at a rate of 2 deg for each 3 deg of forward torso
flexion (T)
• When the knee flexes beyond 45 deg, pelvis rotates backward
(ccw) at a rate of 1 deg for each 3 deg of knee flexion (K)
Calculation of compression and
shear force
" F comp = 0 :
cos# ( mg) HAT + cos# ( mg) load
$FA + FM $ FC = 0
(Eqn 6.51)
" F shear = 0 :
sin # ( mg) HAT + sin # ( mg) load
$FS = 0
(Eqn 6.52)
Assumptions in the Cantilever Model
As discussed in Ch. 53 & 54, assumptions in this model
include:
1.2D analysis is valid
2.static (vs. dynamic) analysis is valid
3.ligament forces are negligible
4.single equivalent muscle for erector spinae
5.assumptions regarding muscle force direction and
moment arm
6.assumptions regarding abdominal pressure and surface
area
7.assumptions regarding orientation (rotation) of vertebral
joints