Computational Investigation on the Biomechanical Responses ... · 29/08/2017 · (soliddisplacement)and (porepressure)inABAQUS( ). =− ∇ +∇→ =0, where istheunittensor,∇representsgradient,and→

Research ArticleComputational Investigation on the Biomechanical Responses ofthe Osteocytes to the Compressive Stimulus A Poroelastic Model

LipingWang 1 Jianghui Dong2 and Cory J Xian 1

1Sansom Institute for Health Research School of Pharmacy and Medical Sciences University of South AustraliaAdelaide SA 5001 Australia2School of Natural and Built Environments University of South Australia Adelaide SA 5095 Australia

Correspondence should be addressed to Cory J Xian coryxianunisaeduau

Received 29 August 2017 Revised 2 December 2017 Accepted 19 December 2017 Published 18 January 2018

Academic Editor Jiang Du

Copyright copy 2018 Liping Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Osteocytes the major type of bone cells embedded in the bone matrix and surrounded by the lacunar and canalicular systemcan serve as biomechanosensors and biomechanotranducers of the bone Theoretical analytical methods have been employed toinvestigate the biomechanical responses of osteocytes in vivo the poroelastic properties have not been taken into considerationin the three-dimensional (3D) finite element model In this study a 3D poroelastic idealized finite element model was developedand was used to predict biomechanical behaviours (maximal principal strain pore pressure and fluid velocity) of the osteocyte-lacunar-canalicular system under 150- 1000- 3000- and 5000-microstrain compressive loads respectively representing disusephysiological overuse and pathological overload loading stimuli The highest local strain pore pressure and fluid velocity werefound to be highest at the proximal region of cell processes These data suggest that the strain pore pressure and fluid velocityof the osteocyte-lacunar-canalicular system increase with the global loading and that the poroelastic material property affects thebiomechanical responses to the compressive stimulus This new model can be used to predict the mechanobiological behavioursof osteocytes under the four different compressive loadings and may provide an insight into the mechanisms of mechanosensationand mechanotransduction of the bone

1 Introduction

Bone is a dynamic biological structure that can adapt toits mechanical environment by changing its structure [1 2]The mechanical stimulation has now been recognized vitalfor regulating bone remodelling processes of bone formation(by bone-forming cells osteoblasts) and resorption (by bone-resorptive cells osteoclasts) and thus bone microstructurebone mass and bone strength [3] Osteocytes are seenas the main candidates for mechanosensory effects of thebone which are the most numerous bone cells (making upabout 90ndash95 [4 5] of all bone cells with osteoblasts andosteoclasts together only making up a total of up to 6 [6])

Osteocytes are known to regulate bone remodellingand are located within their lacunae surrounded by theperilacunar matrix (PCM) embedded in the bone matrix(extracellular matrix or ECM) Osteocytes are connectedto each other with slender cell processes located within

small tubes called the canaliculi within the bone matrixIt is believed that through this osteocyte cell body-cellprocess-lacunar-canalicular system the osteocytes are themechanosensorsmechanotranducers in bones which cansense the mechanical loadings and transduce them intobiochemical signals regulating bone remodelling [7ndash11]

To investigate bone tissue mechanosensingmechano-transduction and biomechanical behaviours of osteocytes anumber of researchers have studied the osteocyte-lacunar-canalicular system by theoretical analytical models Themathematical model has been a good tool to explain the phe-nomenon ofmechanotransduction in the lacunar-canalicularsystem [12] which is well accepted to be induced by flowmovement-like fluid shear stresses [13ndash19] Combined withmicrofocus computer tomography (mCT) the finite element(FE) modeling can be a biomechanical analysis tool to studybone [20] In addition the FE method can be used tosimulate bloodflow regeneration processes bone remodeling

HindawiBioMed Research InternationalVolume 2018 Article ID 4071356 16 pageshttpsdoiorg10115520184071356

2 BioMed Research International

process and heat transfer and evaluate bone strength [21 22]McCreadie and Hollister (1997) were the first researchers tostudy the mechanical behaviours of lacunae and osteocytesby using an idealized 3D linearly isotropic material FE model[23] Bonivtch et al (2007) analysed the microstructuralresponses of the osteocyte lacuna by using a parametriclinearly isotropic material FE model [24] Sanz-Herrera etal (2008) developed the FE and the Voxel-FE models atthe macroscopic and microscopic scales [25] More recentlywith the development of computer and FE analysis softwarethe FE analysis has been widely applied to investigate thebiomechanical behaviours of osteocytes [26ndash29] 3D linearlyisotropic material FE models of osteocytes have been devel-oped including an idealized model and biorealistic (confo-cal image-derived) model [26] A linearly isotropic mate-rial 3D biorealistic osteocyte FE model was created basedon synchrotron X-ray phase nanotomography [30] Strainamplification analysis was conducted on an osteocyte understatic and cyclic loading using an idealized linearly isotropicmaterial 3D FE model [28] Based on quasi-3-dimensional(quasi-3D) cell microscopy a fluidndashstructure interaction FEmethod was used to study viscoelastic property [29] Thusthe FE model analysis is an effective alternative method forthe in vitro biomechanical studies [22]

Since nutrients and exchanges of metabolic products orbiochemical signals of osteocytes depend on the movementof interstitial fluid [31] basically nutrients are transportedby both fluid flow and diffusion within the bone [32ndash34]Reich et al (1990) [35] and Reich and Frangos (1991) [36]were the first to conduct fluid flow studies on bone cells inculture and they found that osteoblasts and endothelial cellshad similar responses to fluid shear stress excitation Smallmolecules (eg amino acids) can be diffusively transportedalone to the osteocytes [37] The solute transport occurredthrough the lacunar-canalicular system under cyclic loadingwhen the concentrations were different in the lacunar flowbetween the inward and outward [33] Goulet et al [32]used a homogeneous model and a vascularized model todemonstrate the bulk fluid movement and fluid exchangebetween the canals and the lacunocanalicular porosity Theprocess of the diffusional mixing was very fast and thenumerous osteocyte lacunae are used as mixing chambers[17] Osteocytes were proposed to be stimulated by relativelysmall fluid shear stresses acting on the membranes of theosteocytes [14] In addition since the passage of interstitialpore fluid adjacent to dendritic cell structure occurs in theporosity of the bone hierarchical microstructure interactionof fluid and the osteocyte-lacunar-canalicular system hasbeen regarded to play an important role in bone tissuemechanosensing andmechanotransductionThus it has beenrecognized that understanding the actual physics of flows inbone is important for the analyses of bone remodelling andthe bone hierarchical microstructure [38]

Poroelasticity is a well-developed theory for investigatingthe interaction of fluid and solid phases in a fluid-saturatedporousmedium [39ndash41] which has been an importantmeansapplied in research into bone and the osteocyte-lacunar-canalicular system [31 42ndash45] Based on the theory of poroe-lasticity the poroelastic properties include drained shear

modulus drained and undrained Poissonrsquos and Skemptonrsquoscoefficient and permeability coefficient [39 46 47] Thisporoelastic theorywas the firstmodel used to study the small-scale fluid mechanics within the lacunar-canalicular porosityusing Brinkmanrsquos equation (Darcyrsquos law and Stokes equation)Theporoelastic properties should be taken into account in thestudy of the osteocyte-lacunar-canalicular system [48 49] Acomputational model was developed to explore load-inducedfluid flow in bone as a mechanotransduction mechanismunder physiologically realistic loadingwith different frequen-cies [50] Subsequently a 2D anisotropic poroelastic modelwas used to study the local fluid flow characteristics in thevicinity of a single lacuna [19] More recently Nguyen et alstudied the mechanical behaviours of one single chondrocyteby using poroviscohyperelastic model [45]

However the material properties of the models in someof the previous studies [23 24 26 51] were assumedsolid in which the fluid or the interaction between fluidand solid matrix was ignored Although the poroelasticproperties were considered in some studies these modelswere theoretical models [42 47 52] or 2D FE models[19] In addition while foregoing FE models had focusedon the physiological compressive loading there has beenlittle attempt reported investigatingcomparing the effectsof disuse (150 microstrains) physiological (1000 micros-trains) overuse (3000 microstrains) and pathological over-load (5000 microstrains) compressive loads [53 54] onthe osteocyte-lacunar-canalicular system using FE modelanalyses In the current study an idealized 3D poroelasticFE model was developed to investigate the biomechanicalresponses of the osteocyte-lacunar-canalicular system whensubjected to four different compressive loads Since it hasbeen stated that in general the disuse load was under 200120583120576the physiological load was between 200 and 2500 120583120576 and theoveruse loading range was 2500ndash5000 120583120576 [53] consistentlythe osteocyte-lacunar-canalicular system FE model in thecurrent study was selected to be under the global compressiveloads of 150microstrains (disuse) 1000microstrains (physio-logical) 3000 microstrains (overuse) and 5000 microstrains(pathological overload) respectively Under these loads thefollowing three analyses were made (1) the distributionsof the maximum principal strains (2) the distributions ofthe maximum pore pressures and (3) the maximum fluidvelocities of the FE model

2 Materials and Methods

21 Geometry and a 3D Model of the Idealized Osteocyte-Lacunar-Canalicular System The osteocyte-lacunar-canalic-ular system was idealized as a 3D structure (Figure 1) Theosteocyte lacuna was described as a triaxial ellipsoid whichcan be expressed as follows [55]

(119909119897 )2 + ( 119910119898)

2 + (119911119899)2 = 1 (1)

where 119897 119898 and 119899 are the semiaxes of the osteocyte lacunain 119909 119910 and 119911 directions respectively 119909 119910 and 119911 are theminor major and intermediate axes of the osteocyte lacuna

BioMed Research International 3

y

x

z

O

(a) (b)

(c) (d) (e)

Figure 1 3-dimensional schematic representations of an idealized osteocyte-lacunar-canalicular system (a) A schematic diagram of anosteocyte lacuna where 119911 is the intermediate axis 119910 the major axis and 119909 the minor axis of the lacuna in the local coordinate systemSchematic diagrams of osteocyte lacuna and canaliculi showing (b) osteocyte cell body (green) with processes (blue) (c) in 119909-119910 plane (d) in119911-119910 plane and (e) in 119909-119911 plane

Table 1 Element numbers and element types of the finite elementmodel of the osteocyte-lacunar-canalicular system

Components Number of elements Element typeECM 77480 SolidPCM with canaliculi 7183 SolidOsteocyte cell body andprocesses 23205 Solid

Total 107868ECM extracellular matrix PCM perilacunar matrix

in the local coordinate system respectively (Figure 1(a)) Theidealized model is comprised of a number of parts that isECM PCM osteocyte cell body canaliculi and cell processes[28] (Figures 1 and 2 and Table 1)

The side length of each direction of the ECM cubeis 43 120583m for human [55] and is the outermost layer ofthe system which was modeled as an external solid layerconsisting of 77480 eight-node solid brick elements (Figure 2and Table 1)

Themiddle layer of the system is the PCMwith canaliculithat separates the ECM and the osteocyte cell body [2](Figure 3) Here it was modeled by two parts namely thePCM sim05ndash1 120583m thick layer [56] and the canaliculi straightcylindrical channels with a diameter of 025120583m [1 57] Hereboth the PCM and canaliculi are solid and consist of 7183eight-node brick elements in total (Table 1)

In this study the simulations were conducted using thesoftware ABAQUS 612 (SIMULIA Providence RI USA)to assume fully saturated media In the simulations only18 symmetry model was applied in the whole FE analysesbecause the model is symmetrical (Figure 2) Also theelements are eight-node C3D8R elements

22 Properties of Poroelastic Materials Applied in the Osteo-cyte-Lacunar-Canalicular System The material properties(isotropic material) used to represent the osteocyte-lacunar-canalicular system are listed in Table 2 In this study todevelop the model ECM PCM and osteocyte cell bodywere assumed to be poroelastic materials In the poroelasticconstitutive law the total stress (120590119879) acting at a point resultsfrom the combination of an effective stress (120590119864) and a pore


PCM

ECM

Osteocyte

Canaliculus

Processes

X Z

Y

Figure 2 One-eighth symmetry model applied in the 3-dimensional finite element meshing analyses of the idealized osteocyte-lacunar-canalicular system showing the geometric locations of extracellular matrix (ECM) perilacunarmatrix (PCM) osteocyte cell body canaliculiand cell processes

(a)

0 02 04 06 08 1

05

1

Normalized time

Am

plitu

de

(b)

Figure 3 Conditions of compressive loading for the osteocyte-lacunar-canalicular system finite element model (a) Uniaxial compressiveloading (b) loading mode

Table 2 Properties of the poroelastic materials applied in the finite element model of the osteocyte-lacunar-canalicular system

Components of osteocyte lacunae Youngrsquos module Poissonrsquos ratio Permeability 1198960 (m2) Void ratio 1198900ECM 11GP [19] 038 [19] 10 times 10minus20 [58] 0053 [58]PCM with canaliculi 40 kPa [59 60] 04 [59 60] 4 times 10minus20 [59 60] 4 [59 60]Osteocyte cell body and processes 31 kPa [45 61] 035 [45 61] 06 times 10minus19 [45 61] 488 [59 60]ECM extracellular matrix PCM perilacunar matrix


pressure (119901) respectively carried out by the solid matrix andthe fluid phaseTheir relationship is shown in (2) In additionthe poroelastic formulation is based on the field variables 119906(solid displacement) and 119901 (pore pressure) in ABAQUS (3)

120590119879 = 120590119864 minus 119901119868 (2)

nabla119906 + nabla997888rarr119902 = 0 (3)

where 119868 is the unit tensornabla represents gradient and997888rarr119902 is fluidmass flow

The fluid mass flow 997888rarr119902 is relative to the pore pressure andcan be computed according to Darcyrsquos generalised law forflow through porous media and the calculated formula canbe expressed as follows

997888rarr119902 = minus119896nabla119901 (4)

The fluid flow can also be expressed as follows

997888rarr119902 = 997888rarrV times 119899119891 (5)

where 119896 is the permeability (which is assumed isotropic in thisstudy) nabla119901 is the gradient of pore pressure 997888rarrV is fluid velocityand 119899119891 is fluid volume fraction (porosity)

Material parameters involved in the poroelastic formula-tion are Youngrsquos modulus (119864) Poisson ratio (120592) porosity (119899119891)[which is related to the void ratio (119890) and can be expressedas (6) and (7)] and permeability (119896 unit of m2) The strain-dependent permeability with the exponential constitutive lawhas been developed [64ndash66] The permeability 119896 is assumedas the function of void ratio and may be expressed as (8)[67]This function can be implemented in ABAQUS softwarepackage

119899119891 = 119881fluid119881fluid + 119881solid =119881fluid119881total =

1198901 + 119890 (6)

119890 = 119881fluid119881solid =119881fluid119881total minus 119881solid =

1198991198911 minus 119899119891 (7)

119896 = 1198960 [119890 (1 + 1198900)1198900 (1 + 119890) ]2

exp [119872( 1 + 1198901 + 1198900 minus 1)] (8)

where119881fluid is the volume of void-space (such as fluids)119881solidis the volume of solids 119881total is the total or bulk volume 119890 isvoid ratio 1198960 is the initial permeability 1198900 is the initial voidratio and119872 is a constant and needs to be determined [68]

23 Boundary and Loading Conditions In order to investi-gate the biomechanical behaviours of the osteocyte-lacunar-canalicular system the compressive loadings were applied tothe 3D FE model In this study the displacements were usedas loadings rather than the forces In the current study theuniaxial ramped static loading was applied on the model

Uniaxial compressive loads were applied in the long boneaxis (Figure 3) with global displacement loads of compressiveloads applied respectively at 150 microstrains (disuse) 1000microstrains (physiological) 3000 microstrains (overuse)

Table 3 Strain amplification factor comparisons between this studyand previous studies

Sources MethodStrain

amplificationfactor

Present method FEM (poroelastic) 43[24] FEM (linearly isotropic) 314[62 63] In vitro measurement 399ndash1143

and 5000 microstrains (pathological overload) [53 62] Inorder to prevent any relative movements in all simulationsand to ensure the PCM attaching to the osteocyte andECM they were assumed being bonded perfectly Thus thedisplacement should be the same for the interface surfacesECM PCM and canaliculi and osteocyte cell body and pro-cesses were assumed being bonded perfectly Distributionsof the maximum principal strains of the osteocyte-lacunar-canalicular system FE model were simulated under thesedifferent loads

To prevent rigid bodymotion the symmetrical boundaryconditions were applied to the nodes on the opposing facesof the applied displacement loading and only 18 of thesymmetry model was used in the FE analyses Furthermorethe initial fluid pore pressure was assumed to be zero andimposed on the external surfaces of the model due to thelack of osmotic pressure in the osteocyte-lacunar-canalicularsystem [59]

3 Results

31 Validations of the Osteocyte-Lacunar-Canalicular SystemFE Model Distributions of the maximum principal strainsof the osteocyte-lacunar-canalicular system FE model werepredicted under global compressive loads of 150 microstrains(disuse) 1000 microstrains (physiological) 3000 micros-trains (overuse) and 5000 microstrains (pathological over-load) respectively The maximum principal strains of the FEmodel were found to be sim633 4272 12820 and 21528 micros-trains respectively The strain distribution of the modelunder the 1000-microstrain compressive loading is shownin Figure 4 The peak amplitudes of the cellular processeswere found higher than those of the ECM PCM and thecell body (Figure 4) Moreover the strain amplification factorof simulation was sim43 (Table 3) These findings are inagreement with those of the previous studies [2 24 6369] where the maximum strain amplification factors weremeasured to be sim75 in the in vitro measurement While 75was themaximum value of one of themany tested osteocytesthe average strain amplification factor was sim4 [63 69]

The maximum pore pressures on the cell and processeswere 898 7424 1759 and 2857 kPa when the model wassubjected to global compressive loads of 150 1000 3000and 5000 microstrains respectively Figure 5 shows the porepressure and distribution results of the FE model whenunder 1000-microstrain compression loading As shown thepredicted maximum pore pressure of the model occurs at 01


+4727+2727+2063+1400+1134+887+318minus279

(a)

+4727+2727+2063+1400+1134+887+318minus279

(b)

Figure 4 Strain distributions of finite element model under 1000-microstrain global loading (a) Perilacunar matrix and osteocyte (b)extracellular matrix

POR

t = Tt = 08Tt = 06Tt = 04T

t = 002T t = 01T t = 012T t = 02T

minus1146e minus 02minus3666e minus 03+4124e minus 03+1191e minus 02+1971e minus 02+2750e minus 02+3529e minus 02+4308e minus 02+5087e minus 02+5866e minus 02+6645e minus 02+7424e minus 02

minus1925e minus 02

(a)

POR


minus1925e minus 02

(b)

POR


minus1925e minus 02

(c)

Figure 5 Pore pressure distributions of the osteocyte-lacunar-canalicular system under 1000-microstrain compressive loading (a) Themaximum pore pressure when 119905 = 002 01 012 02 04 06 08 or 10119879 (total period of loading) (b) pore pressure distributions at canaliculiand perilacunar matrix when 119905 = 01119879 (c) pore pressure distributions in osteocyte and processes when 119905 = 01119879

of the total period of loading (01119879) and the maximum porepressure is located at the junction areas of canaliculi PCMand processes

Previously the maximum pore pressure of the corticalbone was found to be up to 250 kPa under 1MPa uniaxialstress [50] and the maximum hydraulic pressure of the

lacunar-canalicular system was up to 5MPa when an osteonwas subjected to 1Hz 1000 microstrain compression [15]Thus the predicted pore pressure values of our model (ie898 7424 1759 and 2857 kPa for the compressive loadsof 150 1000 3000 and 5000 microstrains respectively) arewithin the range of predicted values of these previous studies


FLVEL magnitude (Avg 75)+1819e minus 02+1668e minus 02+1516e minus 02+1365e minus 02+1213e minus 02+1061e minus 02+9097e minus 03+7581e minus 03+6065e minus 03+4549e minus 03+3033e minus 03+1516e minus 03+3075e minus 07

t = T

t = 01T t = 012Tt = 002T

t = 02T

(a)

FLVEL magnitude(Avg 75)

+1819e minus 02+1668e minus 02+1516e minus 02+1365e minus 02+1213e minus 02+1061e minus 02+9097e minus 03+7581e minus 03+6065e minus 03+4549e minus 03+3033e minus 03+1516e minus 03+3075e minus 07

(b)



(c)

Figure 6 Fluid velocity distributions of the osteocyte-lacunar-canalicular system under the 1000-microstrain compressive loading (a) Fluidvelocities when 119905 = 002 01 012 02 and 10119879 where 119879 is the relative period of loading (b) fluid velocity distribution at canaliculi andperilacunar matrix when 119905 = 01119879 and (c) fluid velocity distribution at the osteocyte and processes

Themaximumfluid velocities of the FEmodel were foundto be 269 1819 5665 and 9798 120583ms when the model wassubjected to global compressive loads of 150 1000 3000and 5000 microstrains respectively Figure 6 displays thefluid velocities of the FE model under the 1000-microstraincompression load The fluid velocities changed only slightlyafter 119905 = 02119879 In a previous study the peak fluid flow velocityin canaliculi of the bone lacunar-canalicular system was sim60 120583ms under a surface strain of 400-microstrain loading[70] Recently Wang et al presented the range of fluid flowvelocity of 131ndash693120583ms under 298- and 510-microstrainloading [71] Compared to these experimental and theoreticalvelocity values our predictedmaximumfluid velocities of theFE model are within the reasonable and comparable ranges

32 Distributions of the Maximum Principal Strains Maxi-mum Pore Pressures andMaximum Fluid Velocities In orderto investigate the biomechanical responses of the cell body

and processes five points of the model in one straight linewere selected for analyses (Figure 7(a)) Because the geometryof the osteocyte-lacunar-canalicular model is symmetricalonly one process and 18 the cell body were analysed PointA is located at the end of the process which is near to theloading surface point B is near to the junction of the processand PCM point C is at the top of the cell body and near thejunction of the process and PCM point D is about themiddleof 18 cell body and point E is at the bottom of 18 cell body(Figure 7(a))

Detailed analyses of the maximum principal strains withloading time at these five different locations are shown inFigures 7(b)ndash7(e) when the model was subjected to differentcompressive loads As shown the strain value of point E isbigger than those of the other points in the steady state pointB has the oscillation in the early phase and point C has theoscillation in most phases of loading time and the values ofpoints A and D are smaller than those of other points In


A B C D

E

(a)

0 02 04 06 08 1Normalized time

Stra

in (u

m)

Point APoint BPoint C

Point DPoint E

minus50

0

50

100

150

200

250

300

350

400

450

Stra

in (u

m)

Point APoint D

0

5

10

15

20

25

30

35

40

02 04 06 08 10Normalized time

150 150

(b)

Stra

in (u

m)

Point APoint D

0

20

40

60

80

100

120

140

160


Stra

in (u

m)


Point DPoint E

0

500

1000

1500

2000

2500

3000

3500


1000 1000

(c)

Figure 7 Continued


Stra

in (u

m)

Point APoint D


0

100

200

300

400

500

600

700

Stra

in (u

m)


Point DPoint E

minus2000

0

2000

4000

6000

8000

10000

12000


3000 3000

(d)

Stra

in (u

m)

Point APoint D

0

200

400

600

800

1000

1200


Stra

in (u

m)


Point DPoint E


minus2000

0

2000

4000

6000

8000

10000

12000

14000

160005000 5000

(e)

Figure 7 Detailed analyses of the maximum principal strains versus loading time at different locations (a) of the osteocyte cell body and aprocess when under different compressive loads ((b) (c) (d) and (e) for 150 1000 3000 and 5000 microstrains respectively)

Figure 7 some oscillations occurred at point C which is at thetop of the cell body and near the junction of the cell processand perilacunar matrix (PCM) Being at the junction of thecell body process and PCM whose material properties weredifferent the responding displacementstrain of point C maythus oscillate under mechanical loads

Figure 8 shows results of detailed analyses of the porepressure distributions of the cell body and a process at thefive different locations (points A B C D and E) when theFE model was under the four different compressive loadingsAs shown the pore pressure of point B is larger than those ofthe other points and that at point A it is smallest among thesepoints

Figure 9 presents results of detailed analyses of the fluidvelocities of different locations (points A B C D and E) of

cell body and a process when the model was under differentcompressive loadings Fluid velocity of point B is larger thanthose of the other points in the steady state In the earlyresponse phase the fluid velocity of point A appears inoscillation and then reaches a value in the steady state PointA is in distal end of the process The fluid velocity of point Ais more sensitive than other points during the ramp increase

4 Discussion

It is now widely believed that fluid that flows through theosteocyte-lacunar-canalicular system can affect and controlthe bone adaptation since when the osteocytes are stimulatedby fluid stress they can produce biological signals that guidethe recruitmentactivity of osteoclasts andor osteoblasts on


0

1

2

3

4

5

6

7

8


Point DPoint E

minus1

Pore

pre

ssur

e (kP

a)


150

(a)Po

re p

ress

ure (

kPa)


Point DPoint E


minus10

0

10

20

30

40

50

60

70

1000

(b)

Pore

pre

ssur

e (kP

a)


Point DPoint E


minus20

0

20

40

60

80

100

120

140

160

3000

(c)

Pore

pre

ssur

e (kP

a)


Point DPoint E

minus50

0

50

100

150

200

250


5000

(d)

Figure 8 Detailed analyses of pore pressures versus loading time at different locations (defined in Figure 7(a)) of the osteocyte cell body and aprocess when the systemwas under different compressive loads ((a) (b) (c) and (d) for 150 1000 3000 and 5000microstrains respectively)

the surface of the bone [47] Thus the fluid embodiedin osteocyte-lacunar-canalicular system is vital for the sys-tem to regulate bone remodelling [72] Previously variousmodels including the FE analysis model have been used tostudy biomechanical behaviours of the osteocyte-lacunar-canalicular system However these previous studies have nottaken the poroelastic properties into the FE model analysisThe current study has developed a FEmodel with one triaxiallacunar osteocyte ellipsoid and by using a 3D poroelasticmodel under four different compressive loads investigatedthe biomechanical responses (strain pore pressure andfluid velocity) of the osteocyte-lacunar-canalicular systemIt is now known that different biomechanical responses

can be produced by different mechanical stimulations [3]including the tensile loading when the bone is bended orpulled away from itself and the compressive loading causedby the force pushing the bone together (eg the animalrsquosweight in the axial load component) [73] Among thesethe compressive load has been widely studied in osteocytesby using the FE analysis method [24 26ndash28] Althoughseveral analyses of the strain amplification in osteocytesusing the poroelastic models have been reported [18 74 75]these studies had focused on theoretical models and therelative contribution of strain amplification has not beenreported with 3D poroelastic FE models that are subjectedto mechanical loading-like strains In the current study four


Flui

d ve

loci

ty (u

ms

)


0

0005

001

0015

002

0025

003

Point APoint B

Point CPoint D

Point E

150

(a)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035


Point APoint B

Point CPoint D

Point E

1000

(b)

Flui

d ve

loci

ty (u

ms

)


0

01

02

03

04

05

06

07

08

09

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025


Point CPoint D

Point EPoint APoint B

Point CPoint D

Point E

3000 3000

(c)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035

Point CPoint D

Point E


Flui

d ve

loci

ty (u

ms

)

Point APoint B

Point CPoint D

Point E


002040608

112141618

25000 5000

(d)

Figure 9 Detailed analyses of fluid velocities versus loading time at different locations (defined in Figure 7(a)) of the osteocyte cell body and aprocess when the systemwas under different compressive loads ((a) (b) (c) and (d) for 150 1000 3000 and 5000microstrains respectively)


different degrees of compressive strain loads were applied toour 3D poroelastic FEmodel to investigate the biomechanicalresponses of the osteocyte-lacunar-canalicular system that isunder 150 microstrains (disuse) 1000 microstrains (physio-logical) 3000 microstrains (overuse) and 5000 microstrains(pathological overload) respectively

The simulation results of our poroelastic FE modelunder the compressive loads were found to be in goodagreement with the previous results [24 26 30 63 69 76]For example our predicted maximum principal strain wassim12820 microstrains under 3000-microstrain compressiveload and the corresponding result from Verbruggen etal (2012) was sim6600ndash12600 microstrains [26] In additionBonivtch et al (2007) predicted the local strain was sim4000ndash6000 microstrains for the osteocyte lacuna under a2000-microstrain compressive load [24] Thus the predictedresults from our poroelastic FE model are consistent withdata from the literature Since there is no validation data forthe idealized model in the existing literature our predictedresult for the 5000-microstrain compressive load cannot becompared A study indicated that the maximum principalstrain was 5-fold higher than the global strain load [76] Ina recent biorealistic osteocyte model study the local strainamplification factors were up to 10 and up to 70 in the ECMand in the osteocytes respectively and the peak amplitude ofthis model was 50000ndash70000 microstrains under the 1000-microstrain global compression [30] Data from the currentstudy indicates that the strain amplification factors onlychanged very slightly with the different global loads appliedsuggesting the strain amplification factor is not sensitive tothe global loads

Pore fluid pressure occurred when the osteocyte-lacunar-canalicular system is subjected to loads [42] The osteocyte-lacunar-canalicular system is a high-fluid-pressure domainbecause the pore size of the system is very small leadingto a slow decay of a pressure pulse [31] The current studyhas computed the pore fluid pressure distributions in theosteocyte cell body and processes under the compressiveloadings applied The maximum pore fluid pressures of cellbody and processes were found to be 898 7424 1759 and2857 kPawhen under 150 1000 3000 and 5000microstrainsrespectively Previously a modest pore fluid pressure inthe lacuna was found to be sim93 kPa when under a 100-microstrain compressive load [19] and the maximal porefluid pressuremagnitudewassim086 858 and 8535 kPawhenthe permeability was 10minus18 10minus19 and 10minus20m2 respectively[42] In addition maximum pore pressure was up to 250 kPawhen the cortical bone was subjected to 1Mpa uniaxialstress [50] and the maximum hydraulic pressure of lacunar-canalicular system was up to 5MPa when an osteon wasunder 1000-microstrain compression at 1Hz frequency [15]Our predicted results of pore fluid pressure are thus consis-tent with the findings of these previous studies In additionthese data suggest that the pore pressure increases with theincreasing global loading

Furthermore using the present model fluid velocity wasalso predicted and simulation was conducted for fluid flowwithin the osteocyte-lacunar-canalicular system in situ In

our model the maximum fluid velocities were 269 18195665 and 9798 120583ms under 150 1000 3000 and 5000microstrains respectively suggesting that the fluid velocityincreases with the increasing global loading Fluid velocityis another important characteristic of the response of anosteocyte to the mechanical loading stimuli since fluidmovement within the lacunar-canalicular system caused bymechanical loading can cause small deformations of bonedeliver nutrients to and remove wastes from the osteocytes[77] and the small fluid shear stress acting on PCM andthe osteocyte processes can regulate the lacunar-canalicularsystem [14]

Moreover the distributions of the strain pore pressureand fluid velocity of five selected points in the cell and aprocess were investigated over the whole loading time periodand under different degrees of compressive loading It wasfound that the values of these parameters increased firstlyand reached the peak values at about the 01119879 followedby declining and finally reaching the steady states Overallthese trends of changes are coincident with the mode ofloadingwith the load increasing starting from the initial pointand reaching the highest load at 01119879 Furthermore amongthe selected locations analysed the proximal side (near tothe cell) of a process was found to bear the highest localstrain pore pressure and fluid velocity In addition amongthe various degrees of loads applied it was found that thedegrees of biomechanical responses increasewithmechanicalloads In other words the local strain pore pressure andfluid velocity of the cell and a process increase with theglobal loading Because the loading time and the ramp timewere kept the same the high compressive loading occurredwith sharper loading ramps and causedmuch higher velocitypressure and principal strains peaks

In the current study the poroelasticmaterial propertywasapplied in all simulations The osteocyte-lacunar-canalicularsystem is considered to be fully saturated having only a solidmatrix phase and a fluid phase with no air voids and itconsists of the fluid spaces surrounding the osteocytes andtheir processes In most previous studies the porosity ofosteocyte-lacunar-canalicular system was assumed to be 005[39 47 72 78] However in some studies the values werevariable being as low as 0023 inman [79] 0042 in dogs [80]and even 0007 in mice [81] and as high as 014 in rats [82]

Moreover the permeability (the ease with which the fluidcanmovewithin a porous system)which is related to porosityis also a very important measure for the poroelastic modelIn the current study viscosity was assumed 0001 Pa s (ieviscosity of water) Permeability depends on the numberorientation and size of the canaliculi as well as on theamount of filling by osteocytes and their processes Whileit is too hard to determine it directly there have been esti-mations of permeability of the osteocyte-lacunar-canalicularsystems ranging over 8 orders of magnitude [52] with theestimated values ranging from 5 times 10minus25 to 7172 times 10minus17 (m2)[19 42 55 72 78 83 84] The value of permeability wasdetermined or estimated by different methods for examplethe theoretical method [19 52 83] experimental method[47 78] and nanoindentation technology [85] Such variation


in the reportedestimated values may be a consequence ofmany factors including differences in theoretical assump-tionsboundary conditions experimental errors associatedwith the nested porosities in bone which are difficult toisolate the freshness of the tissue tested and the presenceof the soft tissues inside the lacunae and canaliculi [31]According to the analysis from a previous study [31] tobe able to produce fluid flow inside canaliculi and stimu-late osteocytes the permeability in the lacunar-canaliculardomain should be sim10minus20m2 or smaller In our study thepermeability values are 06 times 10minus19 4 times 10minus20 and 50 times10minus15m2 in the cell body and process in PCM and canaliculiand in the ECM respectively The permeability is not aconstant value and thus the strain-dependent permeabilitywas implemented in the present FE model Our result isconsistent with Darcyrsquos law that the fluid velocity and porepressure vary with the hydraulic permeability Our studyindicates that the poroelastic material property can affectthe biomechanical responses to the mechanical stimulus andthe permeability is important in controlling the fluid flowbehaviours in the poroelastic model

5 Conclusions

Although there have been some previous studies usingFE analysis models mostly under compressive loads toexamine biomechanical behaviours of the osteocyte-lacunar-canalicular system these studies had not taken the boneporoelastic properties into account The current study hasdeveloped a 3D poroelastic idealized FE model to investi-gate the biomechanical responses of the osteocyte-lacunar-canalicular system under different degrees of compressiveloading stimuli It was found that predicted maximum prin-cipal strains of osteocytes were sim633 4272 12820 and 21528the maximum pore pressures were sim898 7424 1759 and2857 kPa and the maximum fluid velocity values were sim269 1819 5665 and 9798 120583ms when the model was under150 microstrains (disuse) 1000 microstrains (physiological)3000 microstrains (overuse) and 5000 microstrains (patho-logical overload) respectively The values of the strain porepressure and fluid velocity which were found to be thehighest at the proximal region of cell processes increase withthe global loading This new model can potentially be usedto predict the mechanobiological behaviours of osteocytesunder physiological or pathological loadings which mayprovide an insight into understanding the mechanisms ofmechanosensation and mechanotransduction of the bone

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Liping Wang and Cory J Xian conceived and designed thesimulations and wrote the paper Liping Wang and JianghuiDong performed the simulations Liping Wang analysedthe data Liping Wang Jianghui Dong and Cory J Xiancontributed reagentsmaterialsanalysis tools

Acknowledgments

This work was supported by Natural Science Foundation ofChina project grant (81671928) Liping Wang is supported byAustralian National Health and Medical Research Council(NHMRC) Postgraduate Research Scholarship grant andCory J Xian is supported by the NHMRC Senior ResearchFellowship

References

[1] L You S Weinbaum S C Cowin and M B SchafflerldquoUltrastructure of the osteocyte process and its pericellularmatrixrdquo The Anatomical Record vol 278A no 2 pp 505ndash5132004

[2] A R Stern and D P Nicolella ldquoMeasurement and estimationof osteocyte mechanical strainrdquo Bone vol 54 no 2 pp 191ndash1952013

[3] E B Rego T Inubushi A Kawazoe et al ldquoEffect of PGE2induced by compressive and tensile stresses on cementoblastdifferentiation in vitrordquo Archives of Oral Biolog vol 56 no 11pp 1238ndash1246 2011

[4] A L Rath L F Bonewald J Ling J X Jiang M E VanDyke and D P Nicolella ldquoCorrelation of cell strain in singleosteocytes with intracellular calcium but not intracellular nitricoxide in response to fluid flowrdquo Journal of Biomechanics vol 43no 8 pp 1560ndash1564 2010

[5] L F Bonewald ldquoOsteocytes as dynamic multifunctional cellsrdquoAnnals of the New York Academy of Sciences vol 1116 pp 281ndash290 2007

[6] M Capulli R Paone and N Rucci ldquoOsteoblast and osteo-cyte games without frontiersrdquo Archives of Biochemistry andBiophysics vol 561 pp 3ndash12 2014

[7] A JMichalek and J C Iatridis ldquoA numerical study to determinepericellular matrix modulus and evaluate its effects on themicromechanical environment of chondrocytesrdquo Journal ofBiomechanics vol 40 no 6 pp 1405ndash1409 2007

[8] L F Bonewald ldquoThe amazing osteocyterdquo Journal of Bone andMineral Research vol 26 no 2 pp 229ndash238 2011

[9] C Fotia G M L Messina G Marletta N Baldini andG Ciapetti ldquoHyaluronan-based pericellular matrix substrateelectrostatic charges and early cell adhesion eventsrdquo EuropeanCells and Materials vol 26 pp 133ndash149 2013

[10] J Klein-Nulend A D Bakker R G Bacabac A Vatsa andS Weinbaum ldquoMechanosensation and transduction in osteo-cytesrdquo Bone vol 54 no 2 pp 182ndash190 2013

[11] E H Burger and J Klein-Nulend ldquoMechanotransduction inbonemdashrole of the lacuno-canalicular networkrdquo The FASEBJournal vol 13 no 8 pp S101ndashS112 1999

[12] M D Johnston C M Edwards W F Bodmer P K Mainiand S J Chapman ldquoExamples of mathematical modeling Talesfrom the cryptrdquo Cell Cycle vol 6 no 17 pp 2106ndash2112 2007

[13] R H Kufahl and S Saha ldquoA theoretical model for stress-generated fluid flow in the canaliculi-lacunae network in bonetissuerdquo Journal of Biomechanics vol 23 no 2 pp 171ndash180 1990

[14] S Weinbaum S C Cowin and Y Zeng ldquoA model for theexcitation of osteocytes by mechanical loading-induced bonefluid shear stressesrdquo Journal of Biomechanics vol 27 no 3 pp339ndash360 1994

[15] Y Zeng S C Cowin and S Weinbaum ldquoA fiber matrix modelfor fluid flow and streaming potentials in the canaliculi of an


osteonrdquo Annals of Biomedical Engineering vol 22 no 3 pp280ndash292 1994

[16] YWang LMMcNamaraM B Schaffler and SWeinbaum ldquoAmodel for the role of integrins in flow induced mechanotrans-duction in osteocytesrdquo Proceedings of the National Acadamy ofSciences of the United States of America vol 104 no 40 pp15941ndash15946 2007

[17] LWang S C Cowin SWeinbaum and S P Fritton ldquoModelingtracer transport in an osteon under cyclic loadingrdquo Annals ofBiomedical Engineering vol 28 no 10 pp 1200ndash1209 2000

[18] Y Han S C Cowin M B Schaffler and S WeinbaumldquoMechanotransduction and strain amplification in osteocytecell processesrdquo Proceedings of the National Acadamy of Sciencesof the United States of America vol 101 no 47 pp 16689ndash166942004

[19] S Gururaja H J Kim C C Swan R A Brand and R S LakesldquoModeling deformation-induced fluid flow in cortical bonersquoscanalicular-lacunar systemrdquo Annals of Biomedical Engineeringvol 33 no 1 pp 7ndash25 2005

[20] S V N Jaecques H Van Oosterwyck L Muraru et alldquoIndividualised micro CT-based finite element modelling as atool for biomechanical analysis related to tissue engineering ofbonerdquo Biomaterials vol 25 no 9 pp 1683ndash1696 2004

[21] R Hambli ldquoConnecting mechanics and bone cell activitiesin the bone remodeling process an integrated finite elementmodelingrdquo Frontiers in Bioengineering and Biotechnology vol2 2014

[22] L Podshivalov A Fischer and P Z Bar-Yoseph ldquoOn the road topersonalized medicine multiscale computational modeling ofbone tissuerdquoArchives of Computational Methods in EngineeringState-of-the-Art Reviews vol 21 no 4 pp 399ndash479 2014

[23] B R McCreadie and S J Hollister ldquoStrain concentrationssurrounding an ellipsoid model of lacunae and osteocytesrdquoComputer Methods in Biomechanics and Biomedical Engineer-ing vol 1 no 1 pp 61ndash68 1997

[24] A R Bonivtch L F Bonewald and D P Nicolella ldquoTissuestrain amplification at the osteocyte lacuna a microstructuralfinite element analysisrdquo Journal of Biomechanics vol 40 no 10pp 2199ndash2206 2007

[25] J A Sanz-Herrera JM Garcıa-Aznar andMDoblare ldquoMicro-macro numerical modelling of bone regeneration in tissueengineeringrdquo Computer Methods Applied Mechanics and Engi-neering vol 197 no 33-40 pp 3092ndash3107 2008

[26] S W Verbruggen T J Vaughan and L M McNamaraldquoStrain amplification in bonemechanobiology a computationalinvestigation of the in vivo mechanics of osteocytesrdquo Journal ofthe Royal Society Interface vol 9 no 75 pp 2735ndash2744 2012

[27] B Hesse P Varga M Langer et al ldquoCanalicular networkmorphology is themajor determinant of the spatial distributionof mass density in human bone tissue Evidence by means ofsynchrotron radiation phase-contrast nano-CTrdquo Journal of Boneand Mineral Research vol 30 no 2 pp 346ndash356 2015

[28] L Wang J Dong and C J Xian ldquoStrain amplification analysisof an osteocyte under static and cyclic loading a finite elementstudyrdquo BioMed Research International vol 2015 Article ID376474 14 pages 2015

[29] J Qiu A D Baik X L Lu et al ldquoA noninvasive approach todetermine viscoelastic properties of an individual adherent cellunder fluid flowrdquo Journal of Biomechanics vol 47 no 6 pp1537ndash1541 2014

[30] P Varga B Hesse M Langer et al ldquoSynchrotron X-ray phasenano-tomography-based analysis of the lacunarndashcanalicular

network morphology and its relation to the strains experiencedby osteocytes in situ as predicted by case-specific finite elementanalysisrdquo Biomechanics and Modeling in Mechanobiology vol14 no 2 pp 267ndash282 2015

[31] L Cardoso S P FrittonGGailaniM Benalla and S C CowinldquoAdvances in assessment of bone porosity permeability andinterstitial fluid flowrdquo Journal of Biomechanics vol 46 no 2 pp253ndash265 2013

[32] G C Goulet N Hamilton D Cooper et al ldquoInfluence ofvascular porosity on fluid flow and nutrient transport in loadedcortical bonerdquo Journal of Biomechanics vol 41 no 10 pp 2169ndash2175 2008

[33] S P Fritton and S Weinbaum ldquoFluid and solute transport inbone flow-induced mechanotransductionrdquo Annual Review ofFluid Mechanics vol 41 pp 347ndash374 2009

[34] M Lovett K Lee A Edwards and D L Kaplan ldquoVasculariza-tion strategies for tissue engineeringrdquo Tissue Engineering Part BReviews vol 15 no 3 pp 353ndash370 2009

[35] K M Reich C V Gay and J A Frangos ldquoFluid shear stressas a mediator of osteoblast cyclic adenosine monophosphateproductionrdquo Journal of Cellular Physiology vol 143 no 1 pp100ndash104 1990

[36] K M Reich and J A Frangos ldquoEffect of flow on prostaglandinE2 and inositol trisphosphate levels in osteoblastsrdquo AmericanJournal of Physiology-Cell Physiology vol 261 no 3 pp C428ndashC432 1991

[37] M L Knothe Tate P Niederer and U Knothe ldquoIn vivo tracertransport through the lacunocanalicular system of rat bone inan environment devoid of mechanical loadingrdquo Bone vol 22no 2 pp 107ndash117 1998

[38] A F T Mak D T Huang J D Zhang and P TongldquoDeformation-induced hierarchical flows and drag forces inbone canaliculi and matrix microporosityrdquo Journal of Biome-chanics vol 30 no 1 pp 11ndash18 1997

[39] S C Cowin ldquoBone poroelasticityrdquo Journal of Biomechanics vol32 no 3 pp 217ndash238 1999

[40] G B Gailani and S C Cowin ldquoThe unconfined compression ofa poroelastic annular cylindrical diskrdquo Mechanics of Materialsvol 40 no 6 pp 507ndash523 2008

[41] S C Cowin and M M Mehrabadi ldquoCompressible and incom-pressible constituents in anisotropic poroelasticity the problemof unconfined compression of a diskrdquo Journal of the Mechanicsand Physics of Solids vol 55 no 1 pp 161ndash193 2007

[42] G C Goulet D Coombe R J Martinuzzi and R F ZernickeldquoPoroelastic evaluation of fluid movement through the lacuno-canalicular systemrdquo Annals of Biomedical Engineering vol 37no 7 pp 1390ndash1402 2009

[43] G Gailani and S Cowin ldquoRamp loading in Russian dollporoelasticityrdquo Journal of the Mechanics and Physics of Solidsvol 59 no 1 pp 103ndash120 2011

[44] P E Palacio-Mancheno A I Larriera S B Doty L Cardosoand S P Fritton ldquo3D assessment of cortical bone porosity andtissue mineral density using high-resolution 120583cT Effects ofresolution and threshold methodrdquo Journal of Bone and MineralResearch vol 29 no 1 pp 142ndash150 2014

[45] T D Nguyen A Oloyede and Y Gu ldquoA poroviscohyperelasticmodel for numerical analysis of mechanical behavior of singlechondrocyterdquo Computer Methods in Biomechanics and Biomed-ical Engineering vol 19 no 2 pp 126ndash136 2016

[46] T-H Lim and J H Hong ldquoPoroelastic properties of bovinevertebral trabecular bonerdquo Journal of Orthopaedic Research vol18 no 4 pp 671ndash677 2000


[47] T H Smit J M Huyghe and S C Cowin ldquoEstimationof the poroelastic parameters of cortical bonerdquo Journal ofBiomechanics vol 35 no 6 pp 829ndash835 2002

[48] U Andreaus I Giorgio and A Madeo ldquoModeling of theinteraction between bone tissue and resorbable biomaterial aslinear elastic materials with voidsrdquo Zeitschrift fur AngewandteMathematik und Physik vol 66 no 1 pp 209ndash237 2014

[49] I Giorgio U Andreaus D Scerrato and F dellrsquoIsola ldquoAvisco-poroelastic model of functional adaptation in bonesreconstructed with bio-resorbable materialsrdquo Biomechanics andModeling in Mechanobiology vol 15 no 5 pp 1325ndash1343 2016

[50] C C Swan R S Lakes R A Brand and K J StewartldquoMicromechanically based poroelastic modeling of fluid flow inHaversian bonerdquo Journal of Biomechanical Engineering vol 125no 1 pp 25ndash37 2003

[51] B R McCreadie S J Hollister M B Schaffler and S AGoldstein ldquoOsteocyte lacuna size and shape in womenwith andwithout osteoporotic fracturerdquo Journal of Biomechanics vol 37no 4 pp 563ndash572 2004

[52] L Wang S P Fritton S C Cowin and S Weinbaum ldquoFluidpressure relaxation depends upon osteonal microstructureModeling an oscillatory bending experimentrdquo Journal of Biome-chanics vol 32 no 7 pp 663ndash672 1999

[53] R L Duncan and C H Turner ldquoMechanotransduction andthe functional response of bone to mechanical strainrdquo CalcifiedTissue International vol 57 no 5 pp 344ndash358 1995

[54] N Basso and J N M Heersche ldquoCharacteristics of in vitroosteoblastic cell loading modelsrdquo Bone vol 30 no 2 pp 347ndash351 2002

[55] T Beno Y-J Yoon S C Cowin and S P Fritton ldquoEstimationof bone permeability using accurate microstructural measure-mentsrdquo Journal of Biomechanics vol 39 no 13 pp 2378ndash23872006

[56] L MMcNamara R J Majeska S Weinbaum V Friedrich andM B Schaffler ldquoAttachment of osteocyte cell processes to thebone matrixrdquo Anatomical Record vol 292 no 3 pp 355ndash3632009

[57] U E Pazzaglia and T Congiu ldquoThe cast imaging of the osteonlacunar-canalicular systemand the implicationswith functionalmodels of intracanalicular flowrdquo Journal of Anatomy vol 222no 2 pp 193ndash202 2013

[58] M L Knothe Tate R Steck and E J Anderson ldquoBone asan inspiration for a novel class of mechanoactive materialsrdquoBiomaterials vol 30 no 2 pp 133ndash140 2009

[59] E K Moo W Herzog S K Han N A Abu Osman BPingguan-Murphy and S Federico ldquoMechanical behaviour ofin-situ chondrocytes subjected to different loading rates Afinite element studyrdquo Biomechanics andModeling inMechanobi-ology vol 11 no 7 pp 983ndash993 2012

[60] E K Moo S K Han S Federico et al ldquoExtracellular matrixintegrity affects the mechanical behaviour of in-situ chondro-cytes under compressionrdquo Journal of Biomechanics vol 47 no5 pp 1004ndash1013 2014

[61] T D Nguyen and Y Gu ldquoDetermination of strain-rate-dependent mechanical behavior of living and fixed osteocytesand chondrocytes using atomic force microscopy and inversefinite element analysisrdquo Journal of Biomechanical Engineeringvol 136 no 10 Article ID 101004 2014

[62] D B Burr C Milgrom and D Fyhrie ldquoIn vivo measurement ofhuman tibial strains during vigorous activityrdquo Bone vol 18 no5 pp 405ndash410 1996

[63] D P Nicolella D E Moravits A M Gale L F Bonewald andJ Lankford ldquoOsteocyte lacunae tissue strain in cortical bonerdquoJournal of Biomechanics vol 39 no 9 pp 1735ndash1743 2006

[64] W M Lai V C Mow and V Roth ldquoEffects of nonlinearstrain-dependent permeability and rate of compression on thestress behavior of articular cartilagerdquo Journal of BiomechanicalEngineering vol 103 no 2 pp 61ndash66 1981

[65] M K Kwan W M Lai and V C Mow ldquoA finite deformationtheory for cartilage and other soft hydrated connective tissues-I Equilibrium resultsrdquo Journal of Biomechanics vol 23 no 2pp 145ndash155 1990

[66] M H Holmes ldquoFinite deformation of soft tissue Analysisof a mixture model in uni-axial compressionrdquo Journal ofBiomechanical Engineering vol 108 no 4 pp 372ndash381 1986

[67] M Argoubi and A Shirazi-Adl ldquoPoroelastic creep responseanalysis of a lumbar motion segment in compressionrdquo Journalof Biomechanics vol 29 no 10 pp 1331ndash1339 1996

[68] M H Holmes and V C Mow ldquoThe nonlinear characteristicsof soft gels and hydrated connective tissues in ultrafiltrationrdquoJournal of Biomechanics vol 23 no 11 pp 1145ndash1156 1990

[69] D P Nicolella and J Lankford ldquoMicrostructural strain nearosteocyte lacuna in cortical bone in vitrordquo Journal of Muscu-loskeletal and Neuronal Interactions vol 2 no 3 pp 261ndash2632002

[70] C Price X ZhouW Li and LWang ldquoReal-timemeasurementof solute transport within the lacunar-canalicular system ofmechanically loaded bone Direct evidence for load-inducedfluid flowrdquo Journal of Bone and Mineral Research vol 26 no2 pp 277ndash285 2011

[71] B Wang X Zhou C Price W Li J Pan and L WangldquoQuantifying load-induced solute transport and solute-matrixinteraction within the osteocyte lacunar-canalicular systemrdquoJournal of Bone and Mineral Research vol 28 no 5 pp 1075ndash1086 2013

[72] S C Cowin G Gailani and M Benalla ldquoHierarchical poroe-lasticity movement of interstitial fluid between porosity levelsin bonesrdquo Philosophical Transactions of the Royal Society AMathematical Physical amp Engineering Sciences vol 367 no1902 pp 3401ndash3444 2009

[73] M J Gomez-Benito L A Gonzalez-Torres E Reina-Romo JGrasa B Seral and et al ldquoInfluence of high-frequency cyclicalstimulation on the bone fracture-healing process mathematicaland experimental modelsrdquo Philosophical Transactions of theRoyal Society A Mathematical Physical amp Engineering Sciencesvol 369 no 1954 pp 4278ndash4294 2011

[74] L You S C Cowin M B Schaffler and S Weinbaum ldquoAmodel for strain amplification in the actin cytoskeleton ofosteocytes due to fluid drag on pericellular matrixrdquo Journal ofBiomechanics vol 34 no 11 pp 1375ndash1386 2001

[75] Y Wang L M McNamara M B Schaffler and S WeinbaumldquoStrain amplification and integrin based signaling in osteo-cytesrdquo Journal ofMusculoskeletal and Neuronal Interactions vol8 no 4 pp 332ndash334 2008

[76] S Wentzell R Sterling Nesbitt J Macione and S KothaldquoMeasuring strain using digital image correlation of secondharmonic generation imagesrdquo Journal of Biomechanics vol 46no 12 pp 2032ndash2038 2013

[77] K Piekarski and M Munro ldquoTransport mechanism operatingbetween blood supply and osteocytes in long bonesrdquo Naturevol 269 no 5623 pp 80ndash82 1977

[78] G Gailani M Benalla R Mahamud S C Cowin and L Car-doso ldquoExperimental determination of the permeability in the


lacunar-canalicular porosity of bonerdquo Journal of BiomechanicalEngineering vol 131 no 10 Article ID 101007-1 2009

[79] H M FROST ldquoMeasurement of osteocytes per unit volumeand volume components of osteocytes and canaliculae inmanrdquoHenry Ford Hospital Medical Bulletin vol 8 pp 208ndash211 1960

[80] M A Morris J A Lopez-Curto S P F Hughes K-N An J BBassingthwaighte and P J Kelly ldquoFluid spaces in canine boneandmarrowrdquoMicrovascular Research vol 23 no 2 pp 188ndash2001982

[81] P SchneiderMMeier RWepf and RMuller ldquoSerial FIBSEMimaging for quantitative 3D assessment of the osteocyte lacuno-canalicular networkrdquo Bone vol 49 no 2 pp 304ndash311 2011

[82] D Sharma C Ciani P A R Marin J D Levy S B Doty andS P Fritton ldquoAlterations in the osteocyte lacunar-canalicularmicroenvironment due to estrogen deficiencyrdquo Bone vol 51 no3 pp 488ndash497 2012

[83] D Zhang S Weinbaum and S C Cowin ldquoEstimates of thepeak pressures in bone pore waterrdquo Journal of BiomechanicalEngineering vol 120 no 6 pp 697ndash703 1998

[84] T Lemaire S Naıli and A Remond ldquoStudy of the influ-ence of fibrous pericellular matrix in the cortical interstitialfluid movement with hydroelectrochemical effectsrdquo Journal ofBiomechanical Engineering vol 130 no 1 p 011001 2008

[85] M LOyen ldquoPoroelastic nanoindentation responses of hydratedbonerdquo Journal ofMaterials Research vol 23 no 5 pp 1307ndash13142008

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process and heat transfer and evaluate bone strength [21 22]McCreadie and Hollister (1997) were the first researchers tostudy the mechanical behaviours of lacunae and osteocytesby using an idealized 3D linearly isotropic material FE model[23] Bonivtch et al (2007) analysed the microstructuralresponses of the osteocyte lacuna by using a parametriclinearly isotropic material FE model [24] Sanz-Herrera etal (2008) developed the FE and the Voxel-FE models atthe macroscopic and microscopic scales [25] More recentlywith the development of computer and FE analysis softwarethe FE analysis has been widely applied to investigate thebiomechanical behaviours of osteocytes [26ndash29] 3D linearlyisotropic material FE models of osteocytes have been devel-oped including an idealized model and biorealistic (confo-cal image-derived) model [26] A linearly isotropic mate-rial 3D biorealistic osteocyte FE model was created basedon synchrotron X-ray phase nanotomography [30] Strainamplification analysis was conducted on an osteocyte understatic and cyclic loading using an idealized linearly isotropicmaterial 3D FE model [28] Based on quasi-3-dimensional(quasi-3D) cell microscopy a fluidndashstructure interaction FEmethod was used to study viscoelastic property [29] Thusthe FE model analysis is an effective alternative method forthe in vitro biomechanical studies [22]

Since nutrients and exchanges of metabolic products orbiochemical signals of osteocytes depend on the movementof interstitial fluid [31] basically nutrients are transportedby both fluid flow and diffusion within the bone [32ndash34]Reich et al (1990) [35] and Reich and Frangos (1991) [36]were the first to conduct fluid flow studies on bone cells inculture and they found that osteoblasts and endothelial cellshad similar responses to fluid shear stress excitation Smallmolecules (eg amino acids) can be diffusively transportedalone to the osteocytes [37] The solute transport occurredthrough the lacunar-canalicular system under cyclic loadingwhen the concentrations were different in the lacunar flowbetween the inward and outward [33] Goulet et al [32]used a homogeneous model and a vascularized model todemonstrate the bulk fluid movement and fluid exchangebetween the canals and the lacunocanalicular porosity Theprocess of the diffusional mixing was very fast and thenumerous osteocyte lacunae are used as mixing chambers[17] Osteocytes were proposed to be stimulated by relativelysmall fluid shear stresses acting on the membranes of theosteocytes [14] In addition since the passage of interstitialpore fluid adjacent to dendritic cell structure occurs in theporosity of the bone hierarchical microstructure interactionof fluid and the osteocyte-lacunar-canalicular system hasbeen regarded to play an important role in bone tissuemechanosensing andmechanotransductionThus it has beenrecognized that understanding the actual physics of flows inbone is important for the analyses of bone remodelling andthe bone hierarchical microstructure [38]

Poroelasticity is a well-developed theory for investigatingthe interaction of fluid and solid phases in a fluid-saturatedporousmedium [39ndash41] which has been an importantmeansapplied in research into bone and the osteocyte-lacunar-canalicular system [31 42ndash45] Based on the theory of poroe-lasticity the poroelastic properties include drained shear

modulus drained and undrained Poissonrsquos and Skemptonrsquoscoefficient and permeability coefficient [39 46 47] Thisporoelastic theorywas the firstmodel used to study the small-scale fluid mechanics within the lacunar-canalicular porosityusing Brinkmanrsquos equation (Darcyrsquos law and Stokes equation)Theporoelastic properties should be taken into account in thestudy of the osteocyte-lacunar-canalicular system [48 49] Acomputational model was developed to explore load-inducedfluid flow in bone as a mechanotransduction mechanismunder physiologically realistic loadingwith different frequen-cies [50] Subsequently a 2D anisotropic poroelastic modelwas used to study the local fluid flow characteristics in thevicinity of a single lacuna [19] More recently Nguyen et alstudied the mechanical behaviours of one single chondrocyteby using poroviscohyperelastic model [45]

However the material properties of the models in someof the previous studies [23 24 26 51] were assumedsolid in which the fluid or the interaction between fluidand solid matrix was ignored Although the poroelasticproperties were considered in some studies these modelswere theoretical models [42 47 52] or 2D FE models[19] In addition while foregoing FE models had focusedon the physiological compressive loading there has beenlittle attempt reported investigatingcomparing the effectsof disuse (150 microstrains) physiological (1000 micros-trains) overuse (3000 microstrains) and pathological over-load (5000 microstrains) compressive loads [53 54] onthe osteocyte-lacunar-canalicular system using FE modelanalyses In the current study an idealized 3D poroelasticFE model was developed to investigate the biomechanicalresponses of the osteocyte-lacunar-canalicular system whensubjected to four different compressive loads Since it hasbeen stated that in general the disuse load was under 200120583120576the physiological load was between 200 and 2500 120583120576 and theoveruse loading range was 2500ndash5000 120583120576 [53] consistentlythe osteocyte-lacunar-canalicular system FE model in thecurrent study was selected to be under the global compressiveloads of 150microstrains (disuse) 1000microstrains (physio-logical) 3000 microstrains (overuse) and 5000 microstrains(pathological overload) respectively Under these loads thefollowing three analyses were made (1) the distributionsof the maximum principal strains (2) the distributions ofthe maximum pore pressures and (3) the maximum fluidvelocities of the FE model

2 Materials and Methods

21 Geometry and a 3D Model of the Idealized Osteocyte-Lacunar-Canalicular System The osteocyte-lacunar-canalic-ular system was idealized as a 3D structure (Figure 1) Theosteocyte lacuna was described as a triaxial ellipsoid whichcan be expressed as follows [55]

(119909119897 )2 + ( 119910119898)

2 + (119911119899)2 = 1 (1)

where 119897 119898 and 119899 are the semiaxes of the osteocyte lacunain 119909 119910 and 119911 directions respectively 119909 119910 and 119911 are theminor major and intermediate axes of the osteocyte lacuna


y

x

z

O

(a) (b)

(c) (d) (e)











PCM

ECM

Osteocyte

Canaliculus

Processes

X Z

Y


(a)

0 02 04 06 08 1

05

1

Normalized time

Am

plitu

de

(b)






120590119879 = 120590119864 minus 119901119868 (2)

nabla119906 + nabla997888rarr119902 = 0 (3)



997888rarr119902 = minus119896nabla119901 (4)


997888rarr119902 = 997888rarrV times 119899119891 (5)




1198901 + 119890 (6)


1198991198911 minus 119899119891 (7)

119896 = 1198960 [119890 (1 + 1198900)1198900 (1 + 119890) ]2

exp [119872( 1 + 1198901 + 1198900 minus 1)] (8)






amplificationfactor




3 Results




+4727+2727+2063+1400+1134+887+318minus279

(a)

+4727+2727+2063+1400+1134+887+318minus279

(b)


POR

t = Tt = 08Tt = 06Tt = 04T

t = 002T t = 01T t = 012T t = 02T


minus1925e minus 02

(a)

POR


minus1925e minus 02

(b)

POR


minus1925e minus 02

(c)







t = T

t = 01T t = 012Tt = 002T

t = 02T

(a)



(b)



(c)







A B C D

E

(a)


Stra

in (u

m)


Point DPoint E

minus50

0

50

100

150

200

250

300

350

400

450

Stra

in (u

m)

Point APoint D

0

5

10

15

20

25

30

35

40


150 150

(b)

Stra

in (u

m)

Point APoint D

0

20

40

60

80

100

120

140

160


Stra

in (u

m)


Point DPoint E

0

500

1000

1500

2000

2500

3000

3500


1000 1000

(c)

Figure 7 Continued


Stra

in (u

m)

Point APoint D


0

100

200

300

400

500

600

700

Stra

in (u

m)


Point DPoint E

minus2000

0

2000

4000

6000

8000

10000

12000


3000 3000

(d)

Stra

in (u

m)

Point APoint D

0

200

400

600

800

1000

1200


Stra

in (u

m)


Point DPoint E


minus2000

0

2000

4000

6000

8000

10000

12000

14000

160005000 5000

(e)






4 Discussion



0

1

2

3

4

5

6

7

8


Point DPoint E

minus1

Pore

pre

ssur

e (kP

a)


150

(a)Po

re p

ress

ure (

kPa)


Point DPoint E


minus10

0

10

20

30

40

50

60

70

1000

(b)

Pore

pre

ssur

e (kP

a)


Point DPoint E


minus20

0

20

40

60

80

100

120

140

160

3000

(c)

Pore

pre

ssur

e (kP

a)


Point DPoint E

minus50

0

50

100

150

200

250


5000

(d)





Flui

d ve

loci

ty (u

ms

)


0

0005

001

0015

002

0025

003

Point APoint B

Point CPoint D

Point E

150

(a)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035


Point APoint B

Point CPoint D

Point E

1000

(b)

Flui

d ve

loci

ty (u

ms

)


0

01

02

03

04

05

06

07

08

09

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025


Point CPoint D


Point CPoint D

Point E

3000 3000

(c)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035

Point CPoint D

Point E


Flui

d ve

loci

ty (u

ms

)

Point APoint B

Point CPoint D

Point E


002040608

112141618

25000 5000

(d)













5 Conclusions






Acknowledgments


References
































































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of




















y

x

z

O

(a) (b)

(c) (d) (e)











PCM

ECM

Osteocyte

Canaliculus

Processes

X Z

Y


(a)

0 02 04 06 08 1

05

1

Normalized time

Am

plitu

de

(b)






120590119879 = 120590119864 minus 119901119868 (2)

nabla119906 + nabla997888rarr119902 = 0 (3)



997888rarr119902 = minus119896nabla119901 (4)


997888rarr119902 = 997888rarrV times 119899119891 (5)




1198901 + 119890 (6)


1198991198911 minus 119899119891 (7)

119896 = 1198960 [119890 (1 + 1198900)1198900 (1 + 119890) ]2

exp [119872( 1 + 1198901 + 1198900 minus 1)] (8)






amplificationfactor




3 Results




+4727+2727+2063+1400+1134+887+318minus279

(a)

+4727+2727+2063+1400+1134+887+318minus279

(b)


POR

t = Tt = 08Tt = 06Tt = 04T

t = 002T t = 01T t = 012T t = 02T


minus1925e minus 02

(a)

POR


minus1925e minus 02

(b)

POR


minus1925e minus 02

(c)







t = T

t = 01T t = 012Tt = 002T

t = 02T

(a)



(b)



(c)







A B C D

E

(a)


Stra

in (u

m)


Point DPoint E

minus50

0

50

100

150

200

250

300

350

400

450

Stra

in (u

m)

Point APoint D

0

5

10

15

20

25

30

35

40


150 150

(b)

Stra

in (u

m)

Point APoint D

0

20

40

60

80

100

120

140

160


Stra

in (u

m)


Point DPoint E

0

500

1000

1500

2000

2500

3000

3500


1000 1000

(c)

Figure 7 Continued


Stra

in (u

m)

Point APoint D


0

100

200

300

400

500

600

700

Stra

in (u

m)


Point DPoint E

minus2000

0

2000

4000

6000

8000

10000

12000


3000 3000

(d)

Stra

in (u

m)

Point APoint D

0

200

400

600

800

1000

1200


Stra

in (u

m)


Point DPoint E


minus2000

0

2000

4000

6000

8000

10000

12000

14000

160005000 5000

(e)






4 Discussion



0

1

2

3

4

5

6

7

8


Point DPoint E

minus1

Pore

pre

ssur

e (kP

a)


150

(a)Po

re p

ress

ure (

kPa)


Point DPoint E


minus10

0

10

20

30

40

50

60

70

1000

(b)

Pore

pre

ssur

e (kP

a)


Point DPoint E


minus20

0

20

40

60

80

100

120

140

160

3000

(c)

Pore

pre

ssur

e (kP

a)


Point DPoint E

minus50

0

50

100

150

200

250


5000

(d)





Flui

d ve

loci

ty (u

ms

)


0

0005

001

0015

002

0025

003

Point APoint B

Point CPoint D

Point E

150

(a)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035


Point APoint B

Point CPoint D

Point E

1000

(b)

Flui

d ve

loci

ty (u

ms

)


0

01

02

03

04

05

06

07

08

09

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025


Point CPoint D


Point CPoint D

Point E

3000 3000

(c)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035

Point CPoint D

Point E


Flui

d ve

loci

ty (u

ms

)

Point APoint B

Point CPoint D

Point E


002040608

112141618

25000 5000

(d)













5 Conclusions






Acknowledgments


References
































































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of




















PCM

ECM

Osteocyte

Canaliculus

Processes

X Z

Y


(a)

0 02 04 06 08 1

05

1

Normalized time

Am

plitu

de

(b)






120590119879 = 120590119864 minus 119901119868 (2)

nabla119906 + nabla997888rarr119902 = 0 (3)



997888rarr119902 = minus119896nabla119901 (4)


997888rarr119902 = 997888rarrV times 119899119891 (5)




1198901 + 119890 (6)


1198991198911 minus 119899119891 (7)

119896 = 1198960 [119890 (1 + 1198900)1198900 (1 + 119890) ]2

exp [119872( 1 + 1198901 + 1198900 minus 1)] (8)






amplificationfactor




3 Results




+4727+2727+2063+1400+1134+887+318minus279

(a)

+4727+2727+2063+1400+1134+887+318minus279

(b)


POR

t = Tt = 08Tt = 06Tt = 04T

t = 002T t = 01T t = 012T t = 02T


minus1925e minus 02

(a)

POR


minus1925e minus 02

(b)

POR


minus1925e minus 02

(c)







t = T

t = 01T t = 012Tt = 002T

t = 02T

(a)



(b)



(c)







A B C D

E

(a)


Stra

in (u

m)


Point DPoint E

minus50

0

50

100

150

200

250

300

350

400

450

Stra

in (u

m)

Point APoint D

0

5

10

15

20

25

30

35

40


150 150

(b)

Stra

in (u

m)

Point APoint D

0

20

40

60

80

100

120

140

160


Stra

in (u

m)


Point DPoint E

0

500

1000

1500

2000

2500

3000

3500


1000 1000

(c)

Figure 7 Continued


Stra

in (u

m)

Point APoint D


0

100

200

300

400

500

600

700

Stra

in (u

m)


Point DPoint E

minus2000

0

2000

4000

6000

8000

10000

12000


3000 3000

(d)

Stra

in (u

m)

Point APoint D

0

200

400

600

800

1000

1200


Stra

in (u

m)


Point DPoint E


minus2000

0

2000

4000

6000

8000

10000

12000

14000

160005000 5000

(e)






4 Discussion



0

1

2

3

4

5

6

7

8


Point DPoint E

minus1

Pore

pre

ssur

e (kP

a)


150

(a)Po

re p

ress

ure (

kPa)


Point DPoint E


minus10

0

10

20

30

40

50

60

70

1000

(b)

Pore

pre

ssur

e (kP

a)


Point DPoint E


minus20

0

20

40

60

80

100

120

140

160

3000

(c)

Pore

pre

ssur

e (kP

a)


Point DPoint E

minus50

0

50

100

150

200

250


5000

(d)





Flui

d ve

loci

ty (u

ms

)


0

0005

001

0015

002

0025

003

Point APoint B

Point CPoint D

Point E

150

(a)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035


Point APoint B

Point CPoint D

Point E

1000

(b)

Flui

d ve

loci

ty (u

ms

)


0

01

02

03

04

05

06

07

08

09

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025


Point CPoint D


Point CPoint D

Point E

3000 3000

(c)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035

Point CPoint D

Point E


Flui

d ve

loci

ty (u

ms

)

Point APoint B

Point CPoint D

Point E


002040608

112141618

25000 5000

(d)













5 Conclusions






Acknowledgments


References
































































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of





















120590119879 = 120590119864 minus 119901119868 (2)

nabla119906 + nabla997888rarr119902 = 0 (3)



997888rarr119902 = minus119896nabla119901 (4)


997888rarr119902 = 997888rarrV times 119899119891 (5)




1198901 + 119890 (6)


1198991198911 minus 119899119891 (7)

119896 = 1198960 [119890 (1 + 1198900)1198900 (1 + 119890) ]2

exp [119872( 1 + 1198901 + 1198900 minus 1)] (8)






amplificationfactor




3 Results




+4727+2727+2063+1400+1134+887+318minus279

(a)

+4727+2727+2063+1400+1134+887+318minus279

(b)


POR

t = Tt = 08Tt = 06Tt = 04T

t = 002T t = 01T t = 012T t = 02T


minus1925e minus 02

(a)

POR


minus1925e minus 02

(b)

POR


minus1925e minus 02

(c)







t = T

t = 01T t = 012Tt = 002T

t = 02T

(a)



(b)



(c)







A B C D

E

(a)


Stra

in (u

m)


Point DPoint E

minus50

0

50

100

150

200

250

300

350

400

450

Stra

in (u

m)

Point APoint D

0

5

10

15

20

25

30

35

40


150 150

(b)

Stra

in (u

m)

Point APoint D

0

20

40

60

80

100

120

140

160


Stra

in (u

m)


Point DPoint E

0

500

1000

1500

2000

2500

3000

3500


1000 1000

(c)

Figure 7 Continued


Stra

in (u

m)

Point APoint D


0

100

200

300

400

500

600

700

Stra

in (u

m)


Point DPoint E

minus2000

0

2000

4000

6000

8000

10000

12000


3000 3000

(d)

Stra

in (u

m)

Point APoint D

0

200

400

600

800

1000

1200


Stra

in (u

m)


Point DPoint E


minus2000

0

2000

4000

6000

8000

10000

12000

14000

160005000 5000

(e)






4 Discussion



0

1

2

3

4

5

6

7

8


Point DPoint E

minus1

Pore

pre

ssur

e (kP

a)


150

(a)Po

re p

ress

ure (

kPa)


Point DPoint E


minus10

0

10

20

30

40

50

60

70

1000

(b)

Pore

pre

ssur

e (kP

a)


Point DPoint E


minus20

0

20

40

60

80

100

120

140

160

3000

(c)

Pore

pre

ssur

e (kP

a)


Point DPoint E

minus50

0

50

100

150

200

250


5000

(d)





Flui

d ve

loci

ty (u

ms

)


0

0005

001

0015

002

0025

003

Point APoint B

Point CPoint D

Point E

150

(a)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035


Point APoint B

Point CPoint D

Point E

1000

(b)

Flui

d ve

loci

ty (u

ms

)


0

01

02

03

04

05

06

07

08

09

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025


Point CPoint D


Point CPoint D

Point E

3000 3000

(c)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035

Point CPoint D

Point E


Flui

d ve

loci

ty (u

ms

)

Point APoint B

Point CPoint D

Point E


002040608

112141618

25000 5000

(d)













5 Conclusions






Acknowledgments


References
































































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of




















+4727+2727+2063+1400+1134+887+318minus279

(a)

+4727+2727+2063+1400+1134+887+318minus279

(b)


POR

t = Tt = 08Tt = 06Tt = 04T

t = 002T t = 01T t = 012T t = 02T


minus1925e minus 02

(a)

POR


minus1925e minus 02

(b)

POR


minus1925e minus 02

(c)







t = T

t = 01T t = 012Tt = 002T

t = 02T

(a)



(b)



(c)







A B C D

E

(a)


Stra

in (u

m)


Point DPoint E

minus50

0

50

100

150

200

250

300

350

400

450

Stra

in (u

m)

Point APoint D

0

5

10

15

20

25

30

35

40


150 150

(b)

Stra

in (u

m)

Point APoint D

0

20

40

60

80

100

120

140

160


Stra

in (u

m)


Point DPoint E

0

500

1000

1500

2000

2500

3000

3500


1000 1000

(c)

Figure 7 Continued


Stra

in (u

m)

Point APoint D


0

100

200

300

400

500

600

700

Stra

in (u

m)


Point DPoint E

minus2000

0

2000

4000

6000

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3000 3000

(d)

Stra

in (u

m)

Point APoint D

0

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1200


Stra

in (u

m)


Point DPoint E


minus2000

0

2000

4000

6000

8000

10000

12000

14000

160005000 5000

(e)






4 Discussion



0

1

2

3

4

5

6

7

8


Point DPoint E

minus1

Pore

pre

ssur

e (kP

a)


150

(a)Po

re p

ress

ure (

kPa)


Point DPoint E


minus10

0

10

20

30

40

50

60

70

1000

(b)

Pore

pre

ssur

e (kP

a)


Point DPoint E


minus20

0

20

40

60

80

100

120

140

160

3000

(c)

Pore

pre

ssur

e (kP

a)


Point DPoint E

minus50

0

50

100

150

200

250


5000

(d)





Flui

d ve

loci

ty (u

ms

)


0

0005

001

0015

002

0025

003

Point APoint B

Point CPoint D

Point E

150

(a)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035


Point APoint B

Point CPoint D

Point E

1000

(b)

Flui

d ve

loci

ty (u

ms

)


0

01

02

03

04

05

06

07

08

09

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025


Point CPoint D


Point CPoint D

Point E

3000 3000

(c)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035

Point CPoint D

Point E


Flui

d ve

loci

ty (u

ms

)

Point APoint B

Point CPoint D

Point E


002040608

112141618

25000 5000

(d)













5 Conclusions






Acknowledgments


References
































































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of





















t = T

t = 01T t = 012Tt = 002T

t = 02T

(a)



(b)



(c)







A B C D

E

(a)


Stra

in (u

m)


Point DPoint E

minus50

0

50

100

150

200

250

300

350

400

450

Stra

in (u

m)

Point APoint D

0

5

10

15

20

25

30

35

40


150 150

(b)

Stra

in (u

m)

Point APoint D

0

20

40

60

80

100

120

140

160


Stra

in (u

m)


Point DPoint E

0

500

1000

1500

2000

2500

3000

3500


1000 1000

(c)

Figure 7 Continued


Stra

in (u

m)

Point APoint D


0

100

200

300

400

500

600

700

Stra

in (u

m)


Point DPoint E

minus2000

0

2000

4000

6000

8000

10000

12000


3000 3000

(d)

Stra

in (u

m)

Point APoint D

0

200

400

600

800

1000

1200


Stra

in (u

m)


Point DPoint E


minus2000

0

2000

4000

6000

8000

10000

12000

14000

160005000 5000

(e)






4 Discussion



0

1

2

3

4

5

6

7

8


Point DPoint E

minus1

Pore

pre

ssur

e (kP

a)


150

(a)Po

re p

ress

ure (

kPa)


Point DPoint E


minus10

0

10

20

30

40

50

60

70

1000

(b)

Pore

pre

ssur

e (kP

a)


Point DPoint E


minus20

0

20

40

60

80

100

120

140

160

3000

(c)

Pore

pre

ssur

e (kP

a)


Point DPoint E

minus50

0

50

100

150

200

250


5000

(d)





Flui

d ve

loci

ty (u

ms

)


0

0005

001

0015

002

0025

003

Point APoint B

Point CPoint D

Point E

150

(a)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035


Point APoint B

Point CPoint D

Point E

1000

(b)

Flui

d ve

loci

ty (u

ms

)


0

01

02

03

04

05

06

07

08

09

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025


Point CPoint D


Point CPoint D

Point E

3000 3000

(c)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035

Point CPoint D

Point E


Flui

d ve

loci

ty (u

ms

)

Point APoint B

Point CPoint D

Point E


002040608

112141618

25000 5000

(d)













5 Conclusions






Acknowledgments


References
































































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of




















A B C D

E

(a)


Stra

in (u

m)


Point DPoint E

minus50

0

50

100

150

200

250

300

350

400

450

Stra

in (u

m)

Point APoint D

0

5

10

15

20

25

30

35

40


150 150

(b)

Stra

in (u

m)

Point APoint D

0

20

40

60

80

100

120

140

160


Stra

in (u

m)


Point DPoint E

0

500

1000

1500

2000

2500

3000

3500


1000 1000

(c)

Figure 7 Continued


Stra

in (u

m)

Point APoint D


0

100

200

300

400

500

600

700

Stra

in (u

m)


Point DPoint E

minus2000

0

2000

4000

6000

8000

10000

12000


3000 3000

(d)

Stra

in (u

m)

Point APoint D

0

200

400

600

800

1000

1200


Stra

in (u

m)


Point DPoint E


minus2000

0

2000

4000

6000

8000

10000

12000

14000

160005000 5000

(e)






4 Discussion



0

1

2

3

4

5

6

7

8


Point DPoint E

minus1

Pore

pre

ssur

e (kP

a)


150

(a)Po

re p

ress

ure (

kPa)


Point DPoint E


minus10

0

10

20

30

40

50

60

70

1000

(b)

Pore

pre

ssur

e (kP

a)


Point DPoint E


minus20

0

20

40

60

80

100

120

140

160

3000

(c)

Pore

pre

ssur

e (kP

a)


Point DPoint E

minus50

0

50

100

150

200

250


5000

(d)





Flui

d ve

loci

ty (u

ms

)


0

0005

001

0015

002

0025

003

Point APoint B

Point CPoint D

Point E

150

(a)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035


Point APoint B

Point CPoint D

Point E

1000

(b)

Flui

d ve

loci

ty (u

ms

)


0

01

02

03

04

05

06

07

08

09

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025


Point CPoint D


Point CPoint D

Point E

3000 3000

(c)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035

Point CPoint D

Point E


Flui

d ve

loci

ty (u

ms

)

Point APoint B

Point CPoint D

Point E


002040608

112141618

25000 5000

(d)













5 Conclusions






Acknowledgments


References
































































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of




















Stra

in (u

m)

Point APoint D


0

100

200

300

400

500

600

700

Stra

in (u

m)


Point DPoint E

minus2000

0

2000

4000

6000

8000

10000

12000


3000 3000

(d)

Stra

in (u

m)

Point APoint D

0

200

400

600

800

1000

1200


Stra

in (u

m)


Point DPoint E


minus2000

0

2000

4000

6000

8000

10000

12000

14000

160005000 5000

(e)






4 Discussion



0

1

2

3

4

5

6

7

8


Point DPoint E

minus1

Pore

pre

ssur

e (kP

a)


150

(a)Po

re p

ress

ure (

kPa)


Point DPoint E


minus10

0

10

20

30

40

50

60

70

1000

(b)

Pore

pre

ssur

e (kP

a)


Point DPoint E


minus20

0

20

40

60

80

100

120

140

160

3000

(c)

Pore

pre

ssur

e (kP

a)


Point DPoint E

minus50

0

50

100

150

200

250


5000

(d)





Flui

d ve

loci

ty (u

ms

)


0

0005

001

0015

002

0025

003

Point APoint B

Point CPoint D

Point E

150

(a)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035


Point APoint B

Point CPoint D

Point E

1000

(b)

Flui

d ve

loci

ty (u

ms

)


0

01

02

03

04

05

06

07

08

09

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025


Point CPoint D


Point CPoint D

Point E

3000 3000

(c)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035

Point CPoint D

Point E


Flui

d ve

loci

ty (u

ms

)

Point APoint B

Point CPoint D

Point E


002040608

112141618

25000 5000

(d)













5 Conclusions






Acknowledgments


References
































































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of




















0

1

2

3

4

5

6

7

8


Point DPoint E

minus1

Pore

pre

ssur

e (kP

a)


150

(a)Po

re p

ress

ure (

kPa)


Point DPoint E


minus10

0

10

20

30

40

50

60

70

1000

(b)

Pore

pre

ssur

e (kP

a)


Point DPoint E


minus20

0

20

40

60

80

100

120

140

160

3000

(c)

Pore

pre

ssur

e (kP

a)


Point DPoint E

minus50

0

50

100

150

200

250


5000

(d)





Flui

d ve

loci

ty (u

ms

)


0

0005

001

0015

002

0025

003

Point APoint B

Point CPoint D

Point E

150

(a)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035


Point APoint B

Point CPoint D

Point E

1000

(b)

Flui

d ve

loci

ty (u

ms

)


0

01

02

03

04

05

06

07

08

09

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025


Point CPoint D


Point CPoint D

Point E

3000 3000

(c)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035

Point CPoint D

Point E


Flui

d ve

loci

ty (u

ms

)

Point APoint B

Point CPoint D

Point E


002040608

112141618

25000 5000

(d)













5 Conclusions






Acknowledgments


References
































































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of




















Flui

d ve

loci

ty (u

ms

)


0

0005

001

0015

002

0025

003

Point APoint B

Point CPoint D

Point E

150

(a)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035


Point APoint B

Point CPoint D

Point E

1000

(b)

Flui

d ve

loci

ty (u

ms

)


0

01

02

03

04

05

06

07

08

09

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025


Point CPoint D


Point CPoint D

Point E

3000 3000

(c)

Flui

d ve

loci

ty (u

ms

)

0

005

01

015

02

025

03

035

Point CPoint D

Point E


Flui

d ve

loci

ty (u

ms

)

Point APoint B

Point CPoint D

Point E


002040608

112141618

25000 5000

(d)













5 Conclusions






Acknowledgments


References
































































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of






























5 Conclusions






Acknowledgments


References
































































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of





















5 Conclusions






Acknowledgments


References
































































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of



































































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of

































































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of
































of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of























of




Disease Markers



OncologyJournal of





PPAR Research



Volume 2018


Journal of

ObesityJournal of



















Documents

Computational Investigation on the Biomechanical Responses ... · 29/08/2017 · (soliddisplacement)and (porepressure)inABAQUS( ). =− ∇ +∇→ =0, where istheunittensor,∇representsgradient,and→