Medical Engineering and Physics 39 (2017) 83–93

Contents lists available at ScienceDirect

Medical Engineering and Physics

journal homepage: www.elsevier.com/locate/medengphy

Biomechanical analysis of combining head-down tilt traction with

vibration for different grades of degeneration of the lumbar spine

Sicong Wang

a , Lizhen Wang

a , b , ∗, Yawei Wang

a , Chengfei Du

a , Ming Zhang

b , Yubo Fan

a , c , ∗

a Key Laboratory of Biomechanics and Mechanobiology, Ministry of Education, International Research Center for Implantable and Interventional Medical

Devices, School of Biological Science and Medical Engineering, Beihang University, 100191 Beijing, China b Interdisciplinary Division of Biomedical Engineering, the Hong Kong Polytechnic University, Hong Kong, China c National Research Center for Rehabilitation Technical Aids, 100176 Beijing, China

a r t i c l e i n f o

Article history:

Received 4 October 2015

Revised 31 August 2016

Accepted 23 October 2016

Keywords:

Head-down tilt (HDT) traction

Vibration

Degeneration

Lumbar spine

Finite element analysis (FEA)

a b s t r a c t

In recent years, a combination of traction and vibration therapy is usually used to alleviate low back pain

(LBP) in clinical settings. Combining head-down tilt (HDT) traction with vibration was demonstrated to be

efficacious for LBP patients in our previous study. However, the biomechanics of the lumbar spine during

this combined treatment is not well known and need quantitative analysis. In addition, LBP patients have

different grades of degeneration of the lumbar spinal structure, which are often age related. Selecting a

suitable rehabilitation therapy for different age groups of patients has been challenging. Therefore, a finite

element (FE) model of the L1–L5 lumbar spine and a vibration dynamic model are developed in this study

in order to investigate the biomechanical effects of the combination of HDT traction and vibration therapy

on the age-related degeneration of the lumbar spine. The decrease of intradiscal pressure is more effective

when vibration is combined with traction therapy. Moreover, the stresses on the discs are lower in the

“traction + vibration” mode than the “traction-only” mode. The stress concentration at the posterior part

of nucleus is mitigated after the vibration is combined. The disc deformations especially posterior disc

radial retraction is improved in the “traction + vibration” mode. These beneficial effects of this therapy

could help decompress the discs and spinal nerves and therefore relieve LBP. Simultaneously, patients

with grade 1 degeneration (approximately 41–50 years old) are able to achieve better results compared

with other age groups. This study could be used to provide a more effective LBP rehabilitation therapy.

© 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

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. Introduction

At some point in their lives, 85% of the population, especially

emales and those aged 40-80 years, will experience low back pain

LBP), which can induce decreased functional capacity of the spine,

uscle strength and endurance and other issues [1–4] . According

o a systematic review of global prevalence of LBP in 2012, the

ighest prevalence of LBP appears during middle age, which rep-

esents some of the most productive years of a person’s working

ife. This high prevalence of LBP may bring negative effects on eco-

omic conditions for individuals, families and industrial compa-

ies [2] . Research has indicated that LBP mainly results from the

rotrusion of intervertebral disc [5] . Moreover, the degeneration of

n intervertebral disc reportedly causes LBP as well [6] . Traction

eds were used to treat scoliosis, backaches and spinal deformi-

∗ Corresponding author at: School of Biological Science and Medical Engineering,

eihang University, No. 37, Xueyuan Road, Beijing 100191, China.

E-mail addresses: lizhenwang@buaa.edu.cn (L. Wang), yubofan@buaa.edu.cn

(Y. Fan).

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ttp://dx.doi.org/10.1016/j.medengphy.2016.10.004

350-4533/© 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

ies since the early 19th century. As one of the most common trac-

ion therapy devices, they act to relive LBP and recover joint func-

ions by decompressing discs or nerves by applying primary load

long the inferior-superior axis of the spine [7–9] . Meanwhile, low-

requency vibration was reported to be helpful for increasing the

ower limb strength, balance and muscular performance [10–12] . In

ecent years, traction and vibration have been commonly combined

o relieve LBP in clinical settings [13,14] . In our previous study,

lectromyography (EMG) of 30 patients was recorded to evaluate

he effect of the combination of traction and vibration therapy on

rector spinae. We concluded that combining head-down tilt (HDT)

raction (tilt angle: 20 °) with vibration (waveform: sinusoidal, am-

litude: 50 mm, footrest vibration frequency: 3.5 Hz, electrical mo-

or vibration frequency: 12 Hz at the same time, thus the working

ode of the spine combining bed we study in this research keeps

onsistent with what we reported before [15] ) could obtain better

ffects for the fatigue of lower muscle in LBP patients compared to

raction alone [15] . However, the biomechanism of combining HDT

raction and vibration therapy to relieve LBP is not clear now and

hould be quantitatively analyzed.

84 S. Wang et al. / Medical Engineering and Physics 39 (2017) 83–93

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In addition, LBP patients have different grades of degeneration

of the lumbar spinal structure, which are age related [ 16 , 17 ]. A new

term age-sensitivity has been introduced by Kurutz to describe the

elongation capacity decrease of 0.01–0.04 mm/year per year of ag-

ing [18] . Kurutz analyzed the age-sensitivity of time-related in vivo

deformability of human lumbar spine in centric tension. Kurutz re-

ported that, for degenerated lumbar segments in L3-S1, age sensi-

tivity was about −0.01 mm/year in the elastic phase and increased

to about −0.035 mm/year in the final viscoelastic phase [18] . The

patient’s age significantly influences the mechanical properties of

the lumbar spine units. We want to investigate the curative effect

of the combination of HDT traction and vibration therapy on dif-

ferent grades of degeneration of the lumbar spine. Selecting a suit-

able rehabilitation therapy for different age groups of LBP patients

remains a challenge. Therefore, different degeneration grades (0–4)

of the lumbar spine are introduced in this study.

Numerical simulation is one of the most effective and com-

monly used methods to quantitatively evaluate the effect of re-

habilitation therapy in terms of biomechanics [ 19 , 20 ]. Kurutz and

Oroszvary analyzed the biomechanical effects of weightbath hydro-

traction therapy for treating degenerative diseases of lumbar spine

using age-related degenerated finite element (FE) models (L1–L5)

[19] . They first time reported the deformations and stresses of in-

tervertebral discs in axial tension load during the weightbath hy-

drotraction therapy. Park et al. investigated the biomechanical ef-

fects of two-step traction therapy, which included global axial trac-

tion and local decompression, on the lumbar spine using a FE

model of the lumbar spine (L1–S1) [20] . They reported the de-

crease of the tensile stress on the fibers of the annulus fibrosus

and reduction in intradiscal pressure as well. The benefit of the

FE analysis approach is that it can provide the detailed stresses on

the fibers of annulus fibrosus and ligaments and detailed intradis-

cal pressure, because these values are difficult to measure in vivo

without damaging the soft tissues. Therefore, a three-dimensional

(3D) FE model of the lumbar spine (L1–L5), including five grades

of degeneration, is developed in this work for FE analysis.

The aim of this study is to investigate the biomechanism of

the combination of HDT traction and vibration therapy for reliev-

ing LBP. The changes of the intradiscal pressure, stresses of the in-

tervertebral discs, disc deformations and stresses of ligaments for

different grades of degeneration of the lumbar spine will be de-

termined during the traction and vibration combined therapy. The

results of this study could provide a theoretical basis for therapy

selection in future clinical practice.

2. Methods

2.1. Development of the FE model of the L1–L5 lumbar spine

The L1–L5 vertebrae was reconstructed in a medical image pro-

cessing software (Mimics 10.0, Materialise Technologies, Belgium)

based on CT images of a healthy 38 years old male (height: 175 cm,

weight: 68 Kg). The intervertebral discs were generated in a CAE

pre-processing software (Hypermesh 11.0; Altair Engineering Corp,

USA). Then, a 3D FE model of the L1–L5 lumbar spine was built

in the software of Abaqus 6.11-1 (HKS, Hibbit, Karlsson & Soren-

son Inc. USA). The lumbar spine model included five vertebrae

(L1–L5), four intervertebral discs and seven ligaments (interspinous

ligament (ISL), supraspinous ligament (SSL), anterior longitudinal

ligament (ALL), posterior longitudinal ligament (PLL), ligamentum

flavum (LF), capsular ligament (CL) and intermuscular transverse

ligament (ITL)). As shown in Fig. 1 a, a vertebra consisted of a ver-

tebral body and posterior elements; the vertebral body was made

up of bony endplate, cortical bone and cancellous bone. The cor-

tical bone was modeled as a 0.35 mm thick shell surrounding the

cancellous core. The thickness of the endplate was assumed to be

.5 mm. All components of the vertebra were modeled as hexahe-

ral solid elements. The facet joints were processed as nonlinear

ontact. The intervertebral disc was developed as a nucleus pul-

osus surrounded by an annulus fibrosus, and the nucleus pul-

osus was determined to be approximately 44% of the total disc

olume. The annulus fibrosus consisted of matrix (annulus ground

ubstance) and fibers. There were six layers of fibers surrounding

he annulus matrix. The nucleus and annulus matrix were modeled

s hexahedral solid elements. The annulus fibers were modeled as

russ elements which only experienced tension and arranged at an

ngle about ±30 ° from the endplates. The ligaments were devel-

ped using tension-only truss elements.

Table 1 showed the material properties of the healthy lum-

ar spine units. Linear elastic isotropic materials were used for

he vertebral body, posterior elements and endplates [21–23] . A

uid-like, isotropic, incompressible, elastic material was used for

he nucleus [ 19 , 24 ]. The annulus matrix was set to linear elas-

ic materials in both compression and tension state [ 19 , 24 ]. Lin-

ar elastic isotropic tension-only material was used for the annulus

bers, and the stiffness of the fibers increased outward to simulate

heir different types of radial variation and the contents of collagen

n fibers [ 19 , 21 , 25 ]. Linear elastic tension-only material was used

or ligaments [ 19 , 22 ]. The cross sectional area of each ligament in

able 1 was cited from published literatures [ 24 , 26 ]. The density

alues of L1–L5 units were listed in Table 1 to represent the mass

f the L1–L5, which were obtained from the literature [24] .

It was reported that the degeneration of intervertebral discs

ould result in LBP [6] . Meanwhile, the degeneration was corre-

ated with aging significantly [16–19] . Degeneration could gener-

lly induce changes of disc structure as aging, which was called

ge-related degeneration [ 19 , 25 ]. The age-related degeneration of

iscs was mainly reflected in the dehydration process, which led

o drier and harder components of nucleus [ 16 , 19 , 27 ]. Five grades

f degeneration were first introduced by Kurutz [19] . The changes

f the values of material properties were used to simulate the dif-

erent degeneration grades, and we obtained these values from the

iterature [19] . As described in Table 2 , the dehydrated state in the

ucleus was simulated by decreasing Poisson’s ratio; the harden-

ng process in the nucleus and annulus matrix was modeled by

ncreasing Young’s modulus. Only the tension material properties

ere used in our model because of the traction loading condi-

ion. Grade 0 (healthy) to 4 (fully degenerated) corresponded ap-

roximately to the following age ranges: < 40, 41–50, 51–60, 61–70

nd > 70 years, respectively ( Table 2 ). The correlation between five

rades of degeneration and five age groups was derived from re-

earch by Kurutz et al [18,19] .

.2. Spine combining bed working modes

The spine combining bed was designed for the treatment

f back pain combing traction and vibration. Fig. 1 b was the

chematic view of the spine combining bed. The bed plates of the

pine combining bed consisted of 1 fixed plate and 18 suspension

lates hanging on the edge of bed by flexible wires ( Fig. 1 b). The

uspension plates were highly moveable because of the flexible

ires. The only power source of this bed was the footrest, which

as controlled by an electrical motor (vibration frequency: 12 Hz).

he footrest could vibrate along X -axis. The waveform of the vibra-

ion was sinusoidal. The amplitude of the wave was 50 mm and the

ootrest vibration frequency was 3.5 Hz. In Fig. 1 a, the bed tilted

o 20 ° to keep the subject head-down position. The subject laid

upine on the bed with soles fixed on the vibration footrest via

andage. The traction load was exerted by the subject’s own body

eight when tile angle existed. When the footrest started vibrat-

ng, the feet of subjects would follow the movement of footrest

nd the other parts of the body would vibrate as well. When the

S. Wang et al. / Medical Engineering and Physics 39 (2017) 83–93 85

Fig. 1. Schematic of the experiment and the device. (a) The FE model of the L1–L5 lumbar spine including vertebra and intervertebral disc and the scheme of the experiment

procedure. (b) Schematic view of the spine combining bed and the properties of the vibration waveform.

Table 1

Material properties and element types of the healthy lumbar spine units.

Components Young’s modulus (MPa) Poisson’s ratio Cross-sectional area (mm

2 ) Density (t/mm

3 ) Type of element

Cortical bone 12,0 0 0 0.3 – 1.7 ×10 −9 Hexahedral

Cancellous bone 150 0.3 – 1.1 ×10 −9 Hexahedral

Posterior elements 3500 0.3 – 1.4 ×10 −9 Hexahedral

Endplate 100 0.4 – 1.2 ×10 −9 Hexahedral

Annulus matrix 4/0.4 ∗ 0.45 – 1.05 ×10 −9 Hexahedral

Annulus fibers 50 0/40 0/30 0 ∗∗ – – 1.0 ×10 −9 Truss

Nucleus 1/0.4 ∗ 0.499 – 1.02 ×10 −9 Hexahedral

ALL 8 ∗ 0.35 63.7 1.0 ×10 −9 Truss

PLL 10 ∗ 0.35 20 1.0 ×10 −9 Truss

ITL 5 ∗ 0.35 3.6 1.0 ×10 −9 Truss

CL 5 ∗ 0.35 60 1.0 ×10 −9 Truss

ISL 5 ∗ 0.35 40 1.0 ×10 −9 Truss

SSL 5 ∗ 0.35 30 1.0 ×10 −9 Truss

LF 5 ∗ 0.35 40 1.0 ×10 −9 Truss

∗ Tension. ∗∗ External/middle/internal fibers, tension.

Table 2

Material properties of different grades of degeneration of the lumbar spine FE model.

Grades of age-related degeneration 0 (healthy) 1 2 3 4 (fully degenerated)

Age-classes (years) < 40 41–50 51–60 60–70 > 70

For tension

Nucleus

Young’s modulus 0.4 1.0 1.6 2.2 2.8

Poisson’s ratio 0.499 0.45 0.4 0.35 0.3

Annulus matrix

Young’s modulus 0.4 1.0 1.6 2.2 2.8

Poisson’s ratio 0.45 0.45 0.45 0.45 0.45

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ibration function worked and tile angle existed, the working

ode was called “traction + vibration” mode. When the footrest

as fixed and the tilt angle was 20 °, the working mode was called

traction-only” mode.

.3. Development of the vibration dynamic model

As shown in Fig. 2 a, we developed 5 mass points to represent

ifferent parts of the whole body. The five mass points included

eet, lower body, L5 bottom, L1 top and upper body mass point, re-

pectively. Our L1–L5 FE model was developed based on a healthy

8 years old male (height: 175 cm, weight: 68Kg). According to re-

orts by literatures and our subject’s height and body weight data,

e localized the mass center positions of different parts of the

ody [ 26 , 28 ]. The mass values, location information and the func-

ion of five mass points were listed in detail in Table 3.

For the connection between the five mass points, we used self-

efined Cartesian spring element developed in Abaqus software.

he springs we used were different from the normal springs which

nly supported axial elongation and shortening. The springs could

86 S. Wang et al. / Medical Engineering and Physics 39 (2017) 83–93

Table 3

The parameters of the mass points and springs used in the vibration dynamic model.

Mass point name Mass (Kg) Distance superior to the feet

point (mm)

Distance posterior to the center

of L2-L3 disc (mm)

Function in the vibration

dynamic model

Feet point 3 0 10 Vibration source

Lower body point 30 582 5 Inertia effect

L5 bottom point 0 982 1 Coupling to L5 bottom surface

L1 top point 0 1143 2 Coupling to L1 top surface

Upper body point 35 1443 −10 Inertia effect

Spring name Axial stiffness (N/mm) Bending stiffness (N/mm) Damping Available force

Spring 1 700 80 0.03 Fx, Fz

Spring 2 500 40 0.05 Fx, Fz

Spring 3 550 35 0.05 Fx, Fz

Fig. 2. The vibration dynamic model and the two working modes of the spine com-

bining bed. (a) Development of the vibration dynamic model, the boundary condi-

tions and loading conditions in the simulation procedure of the vibration. (b) Load-

ing conditions and boundary conditions in the “traction-only” working mode. (c)

Detailed locations definition with time in the “traction + vibration” working mode.

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transmit axial force and bending force as well. The springs had ax-

ial stiffness (Ezz), bending stiffness (Exx) and damping property.

The detailed parameters about spring 1 to 3 were listed in Table 3 .

The selected springs’ parameters were supported by a validation

process and we would explain it in detail in the validation results

part.

2.4. Simulation of vibration, boundary conditions and loading

conditions

Simulation of vibration: As shown in Fig. 2 a, to simulate the

vibration process, we applied a sinusoidal wave (frequency: 3.5 Hz,

amplitude: 50 mm) on the feet mass point.

Boundary conditions: As shown in Fig. 2 a, the feet point only

had X-direction freedom (UX). The Y and Z-direction freedoms (UY,

UZ) were fixed. And we also fixed the three rotation freedoms

(URX, URY, URZ) as well. As for the other four mass points (lower

body, L5 bottom, L1 top and upper body point), we set the X-

direction (UX) and Z-direction (UZ) freedoms to be free. The Y-

direction freedom (UY) and three rotation freedoms (URX, URY,

URZ) were fixed. The three springs could provide the bending force

Fx) and the axial force (Fz) but did not support Y-direction force

Fy).

Loading conditions: As shown in Fig. 2 a, we thought the upper

ody weight provided the main traction force at the head-down

osition. We applied a traction force (Ftraction) on the upper body

ass point. Because the tilt angle of the bed was 20 °, the traction

orce equation was written as: Ftraction = upper body weight ×sin

0 ° = 120 N. The direction of Ftraction was along Z -axis at the be-

inning timing of the vibration and kept consistent with the spring

′ s axial direction during the vibration. We admitted that the am-

litude of traction load would vary with different locations along

he longitudinal axis of the lumbar spine during vibration. But it

ould be difficult to quantify the traction load accurately at every

oment during vibration. So we simplified the traction load as a

onstant.

.5. Locations definition during the vibration process

The detailed locations of the lumbar spine during vibration

ere described in Fig. 2 c. The red points on the sinusoidal curve

howed the feet trajectory along X -axis with time. The numbers 1–

1 corresponded to consecutive timings during the vibration pro-

ess. The 11 sub-figures matched different locations to the corre-

ponding 11 timings. The black arrows in each sub-figure repre-

ented the movement direction of the mass point. Because of the

nertia effect caused by human body weight, the movement of the

pper body point, L1 top point, L5 bottom point, lower body point

nd feet point lagged to the latter point one by one. We empha-

ized five locations for the following analysis. We chose the be-

inning position of vibration process as the initial location (1). We

hose the most distorted position of the lumbar spine (4 and 9)

s location II and location IV, respectively. We chose the similar

osition (6 and 11) to the initial position of the lumbar spine as

ocation III and V, respectively. Fig. 2 c was about describing the

traction + vibration” working mode. As a comparison, we depicted

he “traction-only” working mode in Fig. 2 b. The feet point was

xed and no vibration wave was applied on it. Only the traction

orce along Z -axis was applied on the upper body mass point. We

anted to compare the biomechanics of the lumbar spine at loca-

ion III and V in the “traction + vibration” working mode with that

t the location in the “traction-only” working mode to understand

he effectiveness of the combination of traction and vibration ther-

py for treating LBP.

. Results

.1. Validation results

.1.1. Validation of the FE model of the L1–L5 lumbar spine

The validation of the L1–L5 FE model was done by comparing

he calculated data by our model with the results from Renner’s re-

earch [29] . The range of motions of each segment under moment

S. Wang et al. / Medical Engineering and Physics 39 (2017) 83–93 87

Fig. 3. Validation of the FE model of the lumbar spine and validation of the vibration dynamic model. (a) Comparison of the range of motions and compression data of the

L1–L5 segments calculated by our FE model and the results provided by Renner et al. (b) The simulation data of the trajectory along X -axis of five mass points with time.

(c–f) Comparison of the trajectory along X -axis tracked by high speed camera in the experiments and the trajectory data along X -axis predicted by the dynamic model of

the lower body point, L5 bottom point, L1 top point and upper body point, respectively. (g) The simulation data of the trajectory along Y -axis of five mass points with time.

(h–k) Comparison of the trajectory along Y -axis tracked by high speed camera in the experiments and the trajectory data along Y -axis predicted by the dynamic model of

the lower body point, L5 bottom point, L1 top point and upper body point, respectively.

88 S. Wang et al. / Medical Engineering and Physics 39 (2017) 83–93

Table 4

Descriptive data for the subjects in the study.

Gender N Age (years) Mean ±SD Height (cm) Mean ±SD Body Weight (Kg) Mean ±SD

Male 15 22.5 ± 0.8 174.2 ± 3.1 68.6 ± 3.7

SD: Standard deviation

Fig. 4. The intradiscal pressure changes of L1–L5 discs for grade 0 (healthy) lumbar

spine during the vibration process in the “traction + vibration” mode. The intradiscal

pressure of all discs is higher at location II or IV than that at the initial location.

And the values for intradiscal pressure of all discs decrease at location III and V

compared to pressure at the initial location. The lowest values appear at location V

on L4-L5 disc.

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loading in three principal planes and the disc compression under

a follower load of 1200 N were calculated to compare with the ex-

perimental and simulated data reported by Renner et al [29] . The

loading conditions and boundary conditions were consistent with

the descriptions in the literature. As shown in Fig. 3 a, the calcu-

lated data by our FE model agrees well with the published experi-

mental and simulation data provided by Renner et al.

3.1.2. Validation of the vibration dynamic model

For validating our dynamic model, we did the experiments to

track the movements of different body parts during the vibration.

We chose 15 subjects whose body weight and height were close

to the male from whom we developed our FE model. The body

weight, height, gender and age data of the 15 subjects are showed

in Table 4 . In our experiments, we put markers on the subjects’

body surfaces. Four markers were put on lower body, L5 bottom,

L1 top and upper body depending on anatomic features, respec-

tively. The distances from these four markers to subjects’ feet are

consistent with the parameters in the dynamic model we have de-

veloped. We used high speed camera (400 frames per second) to

track the four markers’ moving trajectory during vibration. Then

we analyzed the kinetic data including the trajectory of these four

markers along X -axis and Z -axis.

Fig. 3 b shows the simulation data of five points’ trajectory along

X -axis. The vibration frequency decreases as the distance is further

away from feet point. And the vibration amplitude of these points

decreases as well when the distance from foot increases. The de-

crease of the vibration frequency and amplitude are caused by the

inertia effect of mass points and are affected by the bending stiff-

ness and the damping property of the springs as well. Fig. 3 c–f

shows the experiment data and simulation data of the trajectory

along X -axis of lower body point, L5 bottom point, L1 top point

and upper body point, respectively. By adjusting each spring’s ax-

ial stiffness, bending stiffness and damping parameters. Our simu-

lation data is in good agreement with the experimental data. Fig.

3 g shows the simulation data of five points’ trajectory along Z -

axis. The vibration amplitude decreases as the distance from feet

point increases but the vibration frequency does not change much.

Fig. 3 h–k presents the experiment data and simulation data of tra-

jectory along Z -axis of lower body point, L5 bottom point, L1 top

point and upper body point, respectively. The data calculated by

the dynamic model agrees well with the experimental data. Ac-

cordingly, this dynamic model could be considered as valid and

could be used to study the dynamic response of lumbar spine in

the “traction + vibration” working mode.

3.2. Intradiscal pressure on discs

The initial intradiscal pressure at each disc is assumed to be

zero in our dynamic model. Therefore, the values in Figs. 4 and 5

are only meaningful as relative values. Fig. 4 shows the intradiscal

pressure changes of four discs for grade 0 (healthy) lumbar spine

during vibration. Fig. 5 shows the effect of different grades of de-

generation of discs on the intradiscal pressure variation. Fig. 5 a–d

represents disc L1–L2, L2–L3, L3–L4 and L4–L5, respectively.

.3. Maximum von Mises stresses distributions on discs

Fig. 6 a shows the representative data of stresses distribution

n L3-L4 nucleus in two modes for the grade 0 (healthy) lum-

ar spine. The stresses of nucleus at location III and V in the

traction + vibration” mode are lower than the stresses in the

traction-only” mode. The maximum von Mises stresses on nu-

leus, annulus matrix and annulus fibers in the “traction + vibra-

ion” mode for grade 0 (healthy) people are shown in Fig. 6 b, c and

, respectively. The stresses on the fibers are higher than stresses

n annulus matrix and nucleus. Fig. 6 e–g show the effect of differ-

nt grades of degeneration of lumbar spine for the stresses on the

ucleus, annulus matrix and fibers, respectively.

.4. Disc deformations

Fig. 7 a–c show the changes of maximum disc longitudinal elon-

ation, maximum anterior disc radial retraction and maximum

osterior disc radial retraction of L1–L5 discs in the “traction + vi-

ration” mode for the grade 0 (healthy) people, respectively. Fig.

d–f show the effect of different grades of degeneration of lumbar

pine on the disc deformations in two modes.

.5. Maximum von Mises stresses on the ligaments

Fig. 8 a shows the changes of stresses on all ligaments in the

traction + vibration” mode for grade 0 (healthy) people. Fig. 8 b–

show the effect of different grades of degeneration of lumbar

pine on the stresses on ALL, PLL, LF, ISL, SSL, ITL and CL in the

wo working modes, respectively.

S. Wang et al. / Medical Engineering and Physics 39 (2017) 83–93 89

Fig. 5. Intradiscal pressure of L1–L5 discs at different grades of degeneration. (a–d) Effect of different grades of degeneration of the lumbar spine on the intradiscal pressure

variations in the two working modes for disc L1–L2, L2–L3, L3–L4 and L4–L5, respectively. The intradiscal pressure at location III and V in the “traction + vibration” mode is

compared with that in the “traction-only” mode. The intradiscal pressures in these two modes both decrease after traction. Moreover, the intradiscal pressure reduces more

in the “traction + vibration” mode than the “traction-only” mode for all discs. For different grades of degeneration, interestingly, the people at grade 1 obtain the greatest

intradiscal pressure decrease for all discs at location III or V in the “traction + vibration” mode.

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. Discussion

.1. Effect of vibration on the biomechanics of the lumbar spine

uring HDT traction

The intradiscal pressure of all discs both decrease at location

II and V in the “traction + vibration” mode and “traction-only”

ode. However, when the vibration is applied, the intradiscal

ressure decreases more in the “traction + vibration” mode, which

eans that the intradiscal pressure reduction is more effective

hen the traction therapy is combined with vibration. Sato et al.

nd Rohlmann et al. reported that the extra extension motions

ould increase the intradiscal pressure at discs [ 30 , 31 ]. Therefore,

he combination of vibration and traction therapy could help to

chieve better effect for reducing the intradiscal pressure and mit-

gating the stress concentration phenomenon caused by high in-

radiscal pressure. Moreover, the decrease of intradiscal pressure

s higher at location V than that at location III. And the decrease

f intradiscal pressure is higher for L1–L2 and L4–L5 than other

iscs. The minimum intradiscal pressure in the “traction + vibra-

ion” mode is −0.27 MPa at L1–L2 disc and −0.29 MPa at L4-L5

isc, which all appears at location V during vibration. This suggests

hat the therapy could have beneficial effects for patients with L1–

2 or L4–L5 disc damage.

The stresses on discs at location III and V in the “traction + vi-

ration” mode are lower than stresses in the “traction-only” mode.

he stress concentration phenomenon appeared at the posterior

art of nucleus in the “traction-only” mode is reduced after the

ibration is combined. Park et al. reported that the discs could be

amaged more easily by stress concentration because of the de-

eneration of lumbar spine units with aging which weakened the

isc [20] . Thus, the decrease of the stresses on the disc and re-

uction of stress concentration at the nucleus in the “traction + vi-

ration” mode could mitigate the risk of disc injury. In addi-

ion, the stresses on annulus fibers are much higher than stresses

n annulus matrix and nucleus during the vibration process. It

uggests that the fibers are stressed mostly to support the sta-

le status of discs during the vibration. Moreover, as shown in

ig. 6 a, the stresses are much higher at the lateral part of the

isc at location II or IV compared to other parts of the discs.

he distorted status of the lumbar spine at location II and IV

auses this very high stress level of the disc. Thus, this therapy

hould be cautious to be used for the patients with lateral disc

amage.

90 S. Wang et al. / Medical Engineering and Physics 39 (2017) 83–93

Fig. 6. Maximum von Mises stresses on L1–L5 discs. (a) Representative stresses distributions on the L3-L4 nucleus in the two working modes for the grade 0 (healthy)

lumbar spine. The stresses of nucleus at location III and V in the “traction + vibration” mode are lower than the stresses in the “traction-only” mode. The maximum Mises

stresses appear at location II and IV because of the most distorted status of the lumbar spine during vibration. The maximum stress of nucleus at location II appears at the

left side of nucleus, which is determined by the lumbar spine moving direction. (b–d) Changes of maximum von Mises stresses on nucleus, annulus matrix and annulus

fibers of all discs for grade 0 (healthy) lumbar spine in the “traction + vibration” mode, respectively. The stresses on the fibers are higher than stresses on annulus matrix

and nucleus. (e–g) Effect of different grades of degeneration of the lumbar spine on the stresses on nucleus, annulus matrix and annulus fibers in the two working modes,

respectively. The stresses on nucleus, annulus matrix and fibers at location III and V in the “traction + vibration” mode decrease compared to the “traction-only” mode. The

stresses of nucleus and matrix at location III or V obtain the lowest values at grade 1 but the stress of fibers reaches peak at grade 1.

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As shown in Fig. 7 , the disc deformations improve after the vi-

bration is combined with traction. The posterior radial retraction

of discs is higher than the anterior disc radial retraction. Deen et

al. reported the posterior disc protrusion at L5-S1 by axial trac-

tion therapy [32] . The pure axial traction therapy did not pro-

vide disc longitudinal elongation or disc posterior radial retraction

as predicted. However, the results calculated by our model show

that the posterior radial retraction and anterior radial retraction

both increase after the combination of vibration and traction ther-

apy, especially for the posterior part of discs. The beneficial effect

of the posterior disc radial retraction suggests that this therapy

could be better for the patients with posterior disc protrusion. The

“traction + vibration” mode of the therapy could avoid the possible

disc bulging induced by pure axial traction load.

For ligaments, the stresses reach peak values at locations II and

IV in the “traction + vibration” mode. Because of the higher stresses

values on ALL, PLL and CL, these three ligaments are discussed in

detail in this study. Iida et al. reported that increase of the stress

n the PLL induced the detachment of the nucleus pulposus from

he spinal nerve root on the posterior disc [33] . Thus, the increases

f stresses on PLL might have beneficial effect for the posterior disc

adial retraction. Sharma et al. concluded that the increase of stress

n the ALL protected against excessive rotation and motion of the

iscs on the anterior part [34] . This suggests that the increases of

tresses on ALL from our results could contribute to preventing the

isc protrusion in the anterior direction. CLs locate inside the artic-

lar capsule and exhibit a significant relationship with the articu-

ar joint’s motion. CLs play major roles in rotational stability of the

rticular joint in extension. The increase of stress on CLs indicates

n increased extension rotation among the facet joints during vi-

ration. SSL and ISL are most susceptible to failure during flexion

ecause they play the major stabilizing roles in flexion [34] . The

ncreases of stresses on the ISL and SSL indicate an increased flex-

on of the spine during the vibration. In summary, the increases

f stresses on PLL and ALL might help to prevent excessive disc

ulging in the posterior or anterior direction. However, there are

S. Wang et al. / Medical Engineering and Physics 39 (2017) 83–93 91

Fig. 7. Maximum disc deformations of L1–L5 discs. (a–c) Changes of maximum disc longitudinal elongations, anterior disc radial retractions and posterior disc radial retrac-

tions of the L1–L5 discs for grade 0 (healthy) lumbar spine in the “traction + vibration” mode, respectively. The values of disc radial retraction are higher at the posterior

part of disc than the anterior part. Generally, the disc deformations of L1–L2 and L4-L5 are larger than other two discs. (d–f) Effect of different grades of degeneration of the

lumbar spine on the disc deformations including disc longitudinal elongations, anterior disc radial retractions and posterior disc radial retractions in the two working modes,

respectively. The disc deformations at location III and IV in the “traction + vibration” mode are larger than that in the “traction-only” mode. Both the longitudinal elongation

of discs and radial retraction of discs are highest at grade 1. And the disc deformation values gradually decrease from grade 1 to 4.

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ome defects of this vibration-induced stress increase at location II

nd IV in this therapy. The failure strength of ligaments decrease

ith aging [33] . Thus, the stress increase would increase the risk

f ligaments damage for the elderly people.

.2. Effect of different grades of degeneration on the biomechanics of

he lumbar spine during the combination of traction and vibration

herapy

With increasing age, the degenerated discs express two prop-

rties, including loss of incompressibility and being harder of nu-

leus. The higher Young’s modulus of the nucleus and annulus

atrix means greater hardening and stiffening with the grade

ncrease. Simultaneously, the lower Poisson’s ratio of the nu-

leus represents a dehydrated state (decreasing incompressibility)

18 , 19 ]. Kurutz et al. reported that those aged 40 to 45 year old

ad the most vulnerable discs [18] . Schmidt et al. found that discs

n moderate degeneration grade were easy to have protrusion and

hen pressed on spinal nerves, thus caused back pain [35] . As the

ata shown in Figs. 5 –7 , the decrease of intradiscal pressure for

ll discs, the decrease of stresses on nucleus and annulus matrix,

nd the increase of disc deformations all has the greatest effect

t grade 1 compared to other grades. Thus the data predicted by

ur model suggests that the people in the group with grade 1 de-

eneration, who have the higher risk of disc damage and higher

ossibility of disc protrusion, are able to achieve better treatment

uring the combination of traction and vibration therapy.

.3. Limitations of this study

There are some limitations in this study. First, elastic materi-

ls were used to simulate the property of intervertebral discs and

he Poisson’s ratio was used to measure the compressibility of nu-

leus because we introduced five grades of degeneration of the

isc. We obtained the material properties of five grades degener-

ted lumbar spine from Kurutz’s research [19] . To our knowledge,

here are no other materials used for these five grades of degen-

ration of lumbar spine except elastic materials in published lit-

ratures till now. Second, while we accept that the traction load

rovided by body weight varies at different locations during vibra-

ion, it would be difficult to specify the traction load accurately at

very moment during the vibration process. Third, the viscoelas-

ic property of the human tissue was neglected in our model. The

reeping phase was not analyzed during the combination of trac-

ion and vibration therapy. Fourth, the muscle was not considered

nd the L5-S1 segment and pelvis were not included in the current

odel.

. Conclusion

A FE model of the L1–L5 lumbar spine is developed in this

tudy to investigate the biomechanical effects of combining HDT

raction and vibration therapy on age-related degenerated lumbar

pine. We find that the decrease of intradiscal pressure is more ef-

ective when vibration was combined with traction therapy. More-

ver, the stresses on the discs are lower in the “traction + vibra-

ion” mode than the “traction-only” mode. The stress concentra-

ion at the posterior part of nucleus is mitigated after the vibration

s combined. The disc deformations especially posterior disc radial

etraction is improved in the “traction + vibration” mode compared

o the “traction-only” mode. These beneficial effects of this therapy

ould help decompress the discs and spinal nerves and therefore

elieve LBP. In addition, grade 1 people (41–50 years old) are able

92 S. Wang et al. / Medical Engineering and Physics 39 (2017) 83–93

Fig. 8. Maximum von Mises stresses on ligaments. (a) Changes of the maximum

von Mises stresses on all ligaments for grade 0 (healthy) lumbar spine during vi-

bration process in the “traction + vibration” mode. The stresses on PLL, CL and ALL

are larger than the stresses on other ligaments and the values of PLL stress are the

highest among all ligaments. The maximum stresses of all ligaments reach their

peak values either at location II or IV. (b–h) Effect of different grades of degenera-

tion of the lumbar spine on the stresses on ALL, PLL, LF, ISL, SSL, ITL and CL in the

two working modes, respectively. The stresses on all ligaments reduce at location III

and V in the “traction + vibration” mode compared to the stresses in the “traction-

only” mode. The stresses on all ligaments do not change much when the grades

change.

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to achieve better treatment compared to other age groups. The re-

sults of this study could be used to provide a more effective LBP

rehabilitation therapy that combines traction and vibration instead

of traditional axial traction therapy.

Funding

This work was supported by grants from National Natural

Science Foundation of China ( 11 120 101 001, 11 572 029, 11 421 202,

11 322 223, 11 272 273 ), Doctor Program of Ministry of Education of

China ( 2 013 110 213 004 ), National Science & Technology Pillar Pro-

gram ( 2012BAI18B07 ), 111 Project (B13003), Jilin Province North

Star Spine Combing Co., Ltd. Training Programme for Young &

Middle-Aged Excellent Talents From Fujian Province Department

f Public Health (2013-ZQN-ZD-19). The sponsor had no role in

ny aspect of the study, including data collection and analysis,

anuscript preparation, or authorization for publication.

thical approval

This study was approved by the Science and Ethics Committee

f School of Biological Science and Medical Engineering in Beihang

niversity, China (Approval ID: 20,160,401).

onflict of interest

None declared.

cknowledgment

We thank Pin Xiang in Beihang University for the help to de-

elop the model and kind suggestions of the experiment design.

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