Sajb 411952 969
Sajb 411952 969
Sajb 411952 969
*Corresponding author
Samir Zahaf
Email: zahafsamir1983@gmail.com
Abstract: The objective of this work is to study the effect of the backpack on the components of the spine system of a
child, know the effect of an eccentric load on the intervertebral discs, the creating a 3D model of the spine of child of 80
kg overall weight under the effect of three eccentric load (P2, P3, P4) plus P1 compression load and calculated by the
element method ends, For the boundary conditions we fixed the sacrum (Embedding the sacrum). We propose in this
section to draw up a comprehensive study of the distributions of stresses and normal elastic strain of Von Mises in the
intervertebral discs based on loads supported. The results show that the stress and strain of Von Mises are highest and
concentrated in four intervertebral discs (D1, D15, D16 and D17), which causes a problem that calls (herniated disc). We
concluded that the cause of the posterior load, a 350 mm lever arm with a 200N load present maximum Von Mises
stresses concentrated in four intervertebral discs (D1, D15, D16, D17), which justifies the distance between the load
which is the point of application of the load and the axis of the spine plays a very important role in increasing the
solicitation of the latter.
Keywords: Child; herniated discs; Lumbar-Thoracic; Intervertebral Discs; Finite Element; Biomechanics; Von Mises
Stress-Strain; Disc Degeneration
Fig-1: Normal disc (top). Herniated disc (bottom) shows the gel-filled nucleus escapes through a tear in the disc
annulus and compresses the spinal nerve [3]
Available online at http://saspublisher.com/sajb/ 952
Samir Zahaf et al., Sch. Acad. J. Biosci., Nov 2016; 4(11):952-969
It is the cause of symptoms when sciatic pain is up to a complete loss of feeling (anesthesia), loss
in back of the thigh, crural when pain is in front of the muscle strength or partial or complete paralysis or
thigh. It comprises variably pain in the lower limbs, sphincter disorders. continuously exerted, the pressure
defourmillements or tingling sensation (paraesthesia), of the herniated disc can cause irreversible damage [2].
the sensitivity to disturbance of sensation (dysesthesia)
Fig-2: Evolutionary forms of the herniated disc. (a) back pain. (b) - crack the annulus, (c) -progression the disc
material, (d) prolapse [4]. & www.espalda.org
Every year it is the same finding, Worse, their weight increases over the years
schoolchildren satchels or bags to back are too heavy from 6.5 kg in 1997 to 8 kg today in the best case. This
and can cause long-term back problems and deformities would amount to carry to an adult of 80 kg weight 17
of the spine that is to say students complain of back kg Yet the official circular of 2008 National Education
pain, shoulder pain, muscle pain, knee pain, pain in the clearly advocates that the weight of the backpack
neck, numbness pain, bad posture, poor balance and should not exceed 10% of the weight of the child, ie,
falls due at the port of a backpack overloaded view primary, about 2.5 kg ... we're off!! It is between 8 and
\"(Fig. 3) \" [5]. 15 years back is the most fragile, and scientific studies
Yet the official circular of 2008 National It is in this context daily, as well as family
Education clearly advocates that the weight of the education, the accumulation, repetition of these
backpack should not exceed 10% of the weight of the situations will cause joint damage, common causes such
child, either primary, about 2.5 kg ... we're off!! It is as scoliosis. This explains the fact that 67% of students
between 8 and 15 years back is the most fragile, and suffer from muscle tension, 50% of back pain, 24%
scientific studies have demonstrated imaging (MRI), the falling asleep during classes and 15% of pain in the
risk of joint damage and intervertebral disc are real [5]. shoulders [5]. The schoolbag defined as an eccentric
load \"(Fig. 3) \", the load represented by the mass (P4),
During this period of school age, the spine of in other words, this load created a moment of posterior
children is particularly rough ride. With their school bending which tends to bend the spine and causes a
bags too heavy, students are real porter, causing problem called lumbar disc herniation is the most
common cause of low back pain.
The diagram \"(Fig. 4) \" represents a child to We propose in this work to draw up a
age 10 years of overall specific weight 38 kg to wear a comprehensive study of stresses and strains in the spinal
backpack, backpack is the mass of 15 kg representing discs distributions based on supported loads. The results
the weight P4. show that the level of degeneration increased in all
intervertebral discs but concentrated in the four disks
The MRI study [6], alerts of this overweight D1, D15, D16 and D17.
effect in the development of degenerative disc disease,
back pain and then herniated disc \ (Fig. 5) \". Fig. 5 shows two vertebrae of the spinal
column with an intervertebral disc under the effect of a
In this work, the simulation of the disc compound loading (compression P1 + bending moment
degeneration, based on a finite element model of the P4). The compressive load P1 creates an internal
spine depending on the mechanical properties were pressure in the nucleus, this pressure will there after
established ; the boundary condition has been applied in generate the disc degeneration or degenerative disc
the frontal plane to define restriction on movements of disease \"(Fig. 5)\" and \"(Fig. 7)\", as regards the
translation and rotation of the spine. forward flexion P4, if the load of the schoolbag
increases, automatically distance between the point of
load application and the axis of the spinal column
P1
Annulus fibrosus Compression
Bulge
Nucleus pulposus
P4
MATERIAL AND METHODS which allows the reconstitution of the vertebra, the
The objective of this study was to investigate ligament and bone using CAD programs.
the effects induced by an eccentric load of the backpack
on the back of a child, know the effect of an eccentric The result is a 3D geometric model including
load on the intervertebral discs, cortical bone, these three components will then be prepared for use in
cancellous bone, posterior bone, sacrum, basin, created finite element analyzes for the study of stresses and
a 3D model of spine, the total mass of person standing strains distribution in the system.
of specific global 80kg under the effect of three
eccentric loads (p2, p3, p4) plus a p1 compression load The steps for the execution of the 3D vertebra
and calculated by the finit element method, the model \"(Fig. 8) \" are as follow:
boundary conditions we fixed the sacrum (incorporation a) Draw cortical bone that is the upper hinge and the
of the sacrum) see \"(Fig. 4) \". lower hinge, then make the smoothing process; this
gives a solid body called the vertebral body.
The analysis of biomechanical problems b) Secondly, draw the posterior arch (blade with the
includes several steps. The first is to study the form to pedicle) with the spinous process.
define the geometrical configuration of the object, c) Finally we draw the transverse process.
Fig-9: Spine studied ; (a): Lateral (left) view. (b): dorsal view. (c): front view. (d): lateral (right) view
In static loading conditions, the model of the distribution in these disks as well as its supporting
reconstructed spine is used in an analysis for studying structures. The spine is reconstructed in 3D to study the
the role of the inter vertebral discs and the stress system dimensions (IVD - ligament-bone) \"(Fig. 10)\".
In order to define the boundary conditions, inter vertebral disk and ligament are treated as
restriction on movements of translation and rotation of perfectly bonded interfaces \"(Fig. 10)\".
the spine has been applied in the lower plane, and
defined as having zero displacements. Several charges Fig. 9 shows an isometric view of an explored
in the anterior direction were applied as follows: assembly of the spine and each component of the spine
The application of the load on the upper side of system is denoted by letters.
the thoracic vertebra TH1.
The fixed part applied to the body of the basin. Abbreviations
The interfaces between the different components D4: intervertebral disk upstairs four.
of the system of the spine, the cortical bone, the N4: nucleus in the intervertebral disc upstairs four.
D2: intervertebral disk upstairs two.
N4 : Nucleus Pulposus
Cortical Bone
Posterior Bone
D4 : Annulus fibrosus D4+ N4
Fig-11: 3D modeling thoracic vertebra L3, D4 disc of the lumbar spine (SOLIDWORKS 2016 software)
Basin
Ligament sacrotuberous
The selection of constitutive equations of the ligament is nonlinear viscoelastic as in previous studies
vertebral bone is defined as the part of the bone which [10]; a linear elastic model is chosen to represent this
carries the inter vertebral disc, composed of cortical behavior.
bone, cancellous bone, the posterior arch, with a
Young's modulus of about 12000 MPa. It is well known ANSYS WORKBENCH software was used for analyzing
that cortical bone has better load capacity than the this geometry and generate the most suitable mesh. For
cancellous bone. Cortical bone is considered as an the studied behavior, we used tetrahedral elements, type
isotropic material, and homogeneous linear elastic. Solid187 conforming to defined parametric surfaces
Table 1 shows the tensile strength of the structure interfaces \"(Fig. 13) \".
annulus fibrosis according to different authors. These
materials are anisotropic and non-linear elastic. The It is necessary to mesh the components of the
behavior of inter-transverse ligament and inter-spinous spine with small and confused elements to ensure
Available online at http://saspublisher.com/sajb/ 958
Samir Zahaf et al., Sch. Acad. J. Biosci., Nov 2016; 4(11):952-969
optimum accuracy of the results of stresses and strains appropriate to define the cortical and cancellous bone as
in the inter vertebral discs. homogeneous and isotropic. The magnitudes of 12000
MPa and 100 MPa (cortical and cancellous,
The material properties of the spine respectively) were observed in all studies by various
components were selected after a careful review of the researchers.
published literature Table 2; it was considered
Since physiologically the nucleus is fluid The posterior arch was modeled with tetrahedral
filled, the elements were assigned low stiffness values elements to 10 nodes contains (132464 elements,
(1MPa) and near incompressibility properties (Poissons 226389 nodes), the nucleus pulposus in the annulus
ratio of 0.499). Biologically, the annulus fibrosus is fibrosus were modeled with tetrahedral type elements
comprised of layers of collagen fibers, which attributes 10 nodes (26112 elements 42449 nodes), the annulus
to its non-homogenous characteristics. However, due to fibrosus were modeled with elements of type
limitations in modeling abilities, the annulus was tetrahedral to 10 nodes (114036 elements, 244800
defined as a homogenous structure with a magnitude of nodes).
4.2 MPa.
The gelatinous cartilage modeled with a
This was based on the modulus of the ground tetrahedral element to 10 nodes (87710 elements,
substance (4.2 MPa) and the collagen fibers reported in 160055 nodes). Finally, the different types of ligaments
the literature, taking into account the volume fraction of generated by a tetrahedral mesh to 10 nodes Table 3.
each component. The complete model of the spine
\"(Fig. 13)\" was realized by the SOLIDWORKS The diagram in \ "(Fig. 4) \" shows a person
SOFTWARE VERSION 2014 and was then transferred standing of specific global 80kg weight, the overall
to the software Calculates each element ends ANSYS mass (Head, Neck, Arm (left + right), Forearm (left +
16.2 WORKBENCHE generated the default mesh then right), hand (left + right)) is 13,4517kg to divided by
generated linear global custom mesh tetrahedra 10 the top surface of the thoracic vertebrae Th1
nodes conform to surface. representing the pressure P1, P2 load represents the
mass of the body superior Trunk is 12,768kg, the
The three views of spine model with distance between the point of application of the load
condensed mesh are shown in \"(Fig. 13)\". All element and axis (yy ') is 200 mm \ "(Fig. 14) \".
and node numbers are specified in Table 3.
The total mass of the lower trunk of the
Fig. 13 shows a complete model that consists human body is equal to 22 kg; represented by P3, the
of 1178694 elements and 2005025 nodes. Cortical bone distance between the point of application of the load
contains (644683 elements and 961810 nodes), and the axis (yy ') is 250 mm \ "(Fig. 14) \" P4
cancellous bone contains (164441 elements 244460 represents the maximum mass of the backpack is (20
nodes). kg), the distance between the point of load application
Table 3: Element and node numbers in the column vertebral system components
COMPONENT NODES ELEMENTS Thickness
Cortical Bone 961810 644683 3mm
Cancellous Bone 244460 164441 3mm
Posterior Bone 226389 132464 3mm
Cartilage endplates 160055 87710 3mm
Annulus Ground Substance 244800 114036 3mm
Nucleus Pulposus 42449 26112 3mm
Anterior Longitudinal Ligament 45798 24467 3mm
Posterior Longitudinal Ligament 14414 6607 3mm
Ligamentum Flavum 30226 13447 3mm
Transverse Ligament 285328 131648 3mm
Inter-Spinous Ligament 28968 13158 3mm
Supra-Spinous Ligament 17833 8279 3mm
Capsular ligament 51816 24072 3mm
Sacrotuberous Ligament 20878 10128 3mm
Sacroiliac posterior Ligament 5876 3280 3mm
Interosseouse Ligament 13756 8306 3mm
TOTAL 2005025 1178694 3mm
For the boundary conditions we fixed the sacrum of global stress state for each component of our model
(Embedding the sacrum) \"(Fig. 14) \". We propose in were presented.
this section to draw up a comprehensive study of the
distributions of stresses and elastic strain in the A quantitative analysis was performed based
intervertebral discs, the cortical bone, cancellous bone, on a scale of progressive visual colors predefined by the
the posterior arch, anterior longitudinal ligament and software used (ANSYS Workbench 16.5), ranging from
posterior according to the supported loads. Distributions dark blue to red.
Fig-15: Histogram of stress and strain in the spine for a load of 20kg
Fig-16: Distributions of stresses and strains in the thoracic vertebrae (Th3, Th4) for a load of 20kg
Fig-17: Distributions of stresses and strains in the thoracic vertebrae a load of 20kg
Fig-18: Histogram of stresses and strains in the DIV for a load of 20kg
We see in Fig (18) the intervertebral discs (D1, D15, (P1 compression + bending moment (P3)) has a contour
D16, D17) absorbed the maximum stresses that equal of maximum red part stresses in the disc D1 and we see
(6,9797MPa, 4,4374MPa, 4,7858MPa, 2,7365MPa), On in this figure the front part of the disc D1 is pulled and
the other hand the posterior loading presents of another compressed part, other hand figure (9) clearly
maximum strains concentrated in the intervertebral shows that the backpack is a repeated effort back into
discs (D1, D15, D16, D17) which are respectively equal everyday life ultimately cause disc problems,
to (1.7347, 1.0586, 1.1463, 0 66065) as mentioned in \ particularly at the lumbar region (lumbar disc
"(Fig. 19) \". Figure (9) shows that the mixed loading herniation).
Fig-19: Distributions of stresses and strains in the DIV for a load of 20kg
L1
Anterior
L2
L3
Posterior
L4
Von Mises strain D1
L5
Anterior S1
Posterior
Fig-20: Distributions of stresses and strains in the intervertebral disc D1 for a load of 20kg
Fig (20) shows that the mixed loading (P1 regarding the spinal nerve compressed by the two discs
compression + bending moment (P3)) has a contour of (D1, D2) and the pressure causes intense pain radiating
maximum stresses red part in the disc D1 and we see in throughout the leg, the path of pain follows closely the
this figure the front part of the disc D1 is pulled and path of the nerve. In extreme cases, this results in partial
another compressed part, other hand \ "(Fig. 20) \" or complete paralysis of the leg.
clearly shows that the backpack is a repeated effort to
back into everyday life ultimately cause disc problems, A load applied to the upper surface of the
particularly at the lumbar region (lumbar disc thoracic vertebra TH1 of the spinal column causes a
herniation). high concentration of normal maximum von Mises
stresses in the anterior and posterior part of the cortical
We see in Fig 21 that the backpack it's a very bone (S1, Th12, Th5, Th1) (parts by red) this is
dangerous loading and with time creates pain in the 1st, indicated in \ "(Fig. 22) \".
2nd intervertebral disc and causes sciatica or cruralgia,
Fig-21: Images of a girl 17 years old suffering back pain so severe, she was unable to walk. TDM spine
lumbosacral axial section (a, b) and sagittal reconstruction (c) showing a double HD L4-L5 and L5-S1 (d)
Standard radiography spine profile lumbosacral showing a pinch last intervertebral disc L5-S1
Fig-22: MRI of the lumbar sacral spine of a 16-year-old boy showing: (a) MRI weighted sagittal sequence T1, T2,
(b) weighted axial T2, (c) showing a herniated disc L5-S1 posterolateral left side and migrated down
Fig-23: Histogram of stresses and deformations in the cortical bone for load of 20kg
On the other hand, \ "(Fig. 22) \" shows that the relative to the other components of the system of the
maximum von Mises stresses in the cortical bone (S1, spine.
Th12, Th5, Th1) are equal to (40,069MPa, 140.15 MPa
223.82 MPa 496, 69 MPa) as compared to other Fig (25) shows a histogram of the stresses and
components of the system of the spine see \ "(Fig. 24) strains Von put supported by the cancellous bone and it
\". is noted that the maximum stress is concentrated in the
cancellous bone of the thoracic vertebra Th1 as shown
A loading of the posterior backpack applied on in \ "(Fig. 26) \".
the upper surface of the thoracic vertebra TH1 of the
spinal column causes a high concentration of maximum The posterior load \ "(Fig. 3) \" shows clearly
normal strains in the anterior part of the thoracic that the stresses and strains of Von Mises are
vertebra Th (red part) this is mentioned in \ "(Fig. 23) concentrated in the two cancellous bone (Th1, Th5) and
\", with regard to the said vertebra supported Von strain are respectively equal to (4.6282Mpa, 5.7386MPa) and
value set which are equal to (0,041791mm / mm) (0.049594, 0.057685) this is mentioned in the (Fig 26)
Fig-24 : Distributions of stresses and strains in the cortical bone for load of 20kg
Fig-25: Histogram of stresses and strains in the cancellous bone with a load of 20kg
Fig-26: Distributions of stresses and strains in the cancellous bone with a load of 20kg
Fig-27: Histogram of stresses and strains in the posterior arch for a load of 20kg
Fig-28: Distributions of stresses and strains in the posterior arch for a load of 20kg
The posterior loading of the backpack with a 0.21719, 0.16183, 0.21867, 0.21867) compared to other
350mm lever shown that increased stresses and strains components of the system spine. We see in Figure 18
of Von Mises illustrated in the face of upper and lower the role of the basin to transmit the load to the lower
articulation of the posterior arch of the thoracic part of the human body and absorbation stresses and
vertebrae (Th3, Th4, Th5, Th6, Th7) (red outline) \ strain of Von mises bets (red outline), we note that the
"(Fig. 27) \", on the other hand \ "(Fig. 28) \"shows two bodies (basin, sacrum) supported stresses and
clearly legend stress and strain of Von Mises put in the normal elastic deformations which are equal to
thoracic region (Th3, Th4, Th5, Th6, Th7) are (46,069MPa, 28,201MPa) and (0.012947, 0.0187)
respectively equal to ( 995,68MPa, 754,61MPa, relative to the other components of the system of the
467,09MPa, 483,08MPa, 369,65MPa) and (0.29194, spine.
Anterior Anterior
Posterior Posterior
Anterior Anterior
Posterior Posterior
Fig-29: Distributions of stresses and strains in the basin and sacrum for a load of 20kg
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