Research ArticleAssessment of Knee Cartilage Stress Distribution andDeformation Using Motion Capture System and WearableSensors for Force Ratio Detection

N Mijailovic1 R Vulovic12 I Milankovic12 R Radakovic2 N Filipovic12 and A Peulic1

1Faculty of Engineering University of Kragujevac Sestre Janjic 6 34000 Kragujevac Serbia2Bioengineering Research and Development Center Kragujevac Prvoslava Stojanovica 6 34000 Kragujevac Serbia

Correspondence should be addressed to A Peulic aleksandarpeulickgacrs

Received 19 September 2014 Revised 19 December 2014 Accepted 16 January 2015

Academic Editor Eduardo Soudah

Copyright copy 2015 N Mijailovic 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

Knowledge about the knee cartilage deformation ratio as well as the knee cartilage stress distribution is of particular importancein clinical studies due to the fact that these represent some of the basic indicators of cartilage state and that they also provideinformation about joint cartilage wear so medical doctors can predict when it is necessary to perform surgery on a patient In thisresearch we apply various kinds of sensors such as a system of infrared cameras and reflective markers three-axis accelerometerand force plate The fluorescent marker and accelerometers are placed on the patientrsquos hip knee and ankle respectively Duringa normal walk we are recording the space position of markers acceleration and ground reaction force by force plate Measureddata are included in the biomechanical model of the knee joint Geometry for this model is defined from CT images This modelincludes the impact of ground reaction forces contact force between femur and tibia patient body weight ligaments and muscleforces The boundary conditions are created for the finite element method in order to noninvasively determine the cartilage stressdistribution

1 Introduction

Sports activities and daily routines such as standing walkingrunning jumping and other recreational activities imposerelatively large loads and movements on the human kneejoint These tasks could cause injuries and degenerationsin the joint ligaments menisci cartilage and bones Thusknowledge of in vivo joint motion and loading duringfunctional activities is needed to improve our understandingof possible knee joint degeneration and restoration Internalloadings of knee anatomical structures significantly dependon a lot of factors such as external loads body weightligaments strengths and muscles forces

In the paper [1] the knee implants were used to directlymeasure loads of participants during daily activities Invivo knee measurements are very invasive and practicallyimpossible for the case described in our studyThere aremanytechniques for measuring an external variable which can

be further used to create biomechanical and mathematicalmodels

Other studies [2] were based on the registration offluoroscopic images and computer model of the knee Themost recent method utilized force plate data CT or MRIskeletal structure data andmotion capture obtained from theinfrared position sensor [3 4] In another research paper [5]the accelerometer was used to estimate the angle of lowerextremities This is a pretty cheap technique but requiresadditional processing of collected data and the error of esti-mated angle is up to six percent The measure performancecan be improved using a combination of accelerometer andgyroscope sensor such as goniometer [6ndash8]

In the study [9] stress on the knee cartilage duringkneeling and standing using finite element models is com-pared They used magnetic resonance (MR) images of theflexed knee to build a geometrical model As a computationaltool they used commercial software MIMICS The results

Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2015 Article ID 963746 8 pageshttpdxdoiorg1011552015963746

2 Computational and Mathematical Methods in Medicine

of those studies showed some differences in high-stressregions between kneeling and standing The conclusion wasthat the peak von Mises stress and contact pressure onthe cartilage were higher in kneeling The study [10] usedcomputed tomography (CT) images of knee structures duringstatic loading to determine cartilage strains and meniscalmovement in a human knee at different time periods ofstanding and to compare them with the subject-specific3D finite element (FE) model The results of these experi-ments showed that 80 of the maximum strain in cartilagedeveloped immediately and after that cartilage continued todeform slowly In the study [11] magnetic resonance (MR)images of the right knee of a 27-year-old male subject wereused to determine the subsequent alteration in the fluidpressurization in the human knee using a three-dimensionalcomputer model The results of these studies indicated aredistribution of stresses within the tissue and a relocation ofthe loading between the tissue matrix and fluid pressure

The purpose of this study was to estimate stress distribu-tion in the knee cartilage For that purpose the appropriatesystem of cameras and force plate platform were used Thedeformation of cartilage wasmeasured usingmarker positiondata and the 3D model of the lower leg segment The modelswere established from computed tomography (CT) imagesSimultaneously the deformation is assessed only matchingsingle infrared camera images and CT image using softwarefor image registration technique In the experimental part theaccelerometer sensor was used which potentially can providemore information about the gait In the computer simulationthe FEM analysis was applied with an adaptive change ofmechanical parameters of tissue variation in order to matchthe measured force and deformation

2 Materials and Methods

21 Mechanical Model of the Knee Joint Knee joint motionrepresents a complex combination of rotations and trans-lations The major parts involved in the knee kinematicalbehavior include femur tibia and patella Forces that act ata knee joint are given in Figure 1

The dominant forces that act at a knee joint are bodyweight and ground reaction force which are opposite toeach other Muscle forces as well as contact forces betweenfemur and tibia are also included in the model Equilibriumequations of the knee joint are given below [5]

119865119903+ 119865119887+ 1198651199011

sdot 1198731+ 1198651199012

sdot 1198732+

7

sum

119894=1

119865119894= 0

119872119903+ 119865119903times 119875119903+ 119865119887times 119875119887+ 1198651199011

sdot 1198731times 1198751+ 1198651199012

sdot 1198732times 1198752

+

7

sum

119894=1

119865119894times 119881119894= 0

(1)

where 119865119903is the ground reaction force 119865

119887is the body weight

1198651199011

and 1198651199012

are the two contact point forces 1198731and 119873

2

are the two contact points normal 119865 (119894 = 1 sdot sdot sdot 7) are theligament and capsule forces 119872

119903is the knee joint driver

Body weightMuscleforce

Ground reaction force

Muscleforce

Ligament force

Contact force

Ligament force

Figure 1 Forces on a knee joint

moment along local 119911 axis and119875119903 119875119887 1198751 1198752and119881 (119894 = 1 sdot sdot sdot 7)

are the position vectors where the corresponding forces arebeing applied [13] We assumed that femur and tibia couldbe represented as rigid bodies and that their deformationswere very small in contrast to relatively large deformations ofcartilage and ligaments Note that synovial fluid significantlyreduces the friction between cartilage surfaces and menisci

A simplified spring-damper-mass model which was usedin this study is shown in Figure 2 It consists of four massesThe upper body was modeled using two masses one rep-resenting its rigid mass 119898

3 and the other representing its

wobbling masses 1198984 The thigh leg and foot of the sup-

porting leg weremodeled using twomasses one representingits rigid mass 119898

1 and the other representing its wobbling

masses1198982

The total bodymass was obtained from the participant Inthe following system of equations (Equation (2)) a dynamicssystem is described [12] and was later used to calculate theresultant force and moment of the knee cartilage during thestance phase of the gait cycle

11989811+ 1198961(1199091minus 1199093) + 1198962(1199091minus 1199092) + 1198881(1minus 3)

+ 1198882(1minus 2) = 119898

1119892 minus 119865119892

11989822minus 1198962(1199091minus 1199092) + 1198963(1199092minus 1199093)

+ 1198882(1minus 2) = 119898

2119892

11989833minus 1198961(1199091minus 1199093) minus 1198963(1199092minus 1199093)

+ (1198964+ 1198965) (1199093minus 1199094) minus 1198881(1minus 3)

+ 1198884(3minus 4) = 119898

3119892

(2)

In (2) 1198981was the lower body rigid mass and 119898

2was the

wobbling mass 1198983was the upper body rigid mass and 119898

4

was the wobbling mass 1198961was the compressive spring and

Computational and Mathematical Methods in Medicine 3

k5

k4

k3k1

k2

m1

m2

m4

m3

Ground reaction model

x3

x1

x2

x4 c4

c1

c2

Figure 2 A simplified spring-damper-mass model used in thecomputer simulation The components of the dynamics systempresented are lower body rigid mass (119898

1) and wobbling mass (119898

2)

upper body rigid mass (1198983) and wobbling mass (119898

4) compressive

spring (1198961) and damper (119888

1) that connect the upper and lower rigid

bodies spring (1198963) and springdamper unit (119896

2 1198882) connecting the

lower wobblingmass to the upper and lower rigid bodies and spring(1198965) and springdamper unit (119896

4 1198884) connecting the upper wobbling

mass to the upper rigid mass (adopted from [12])

1198881was the damper that connected the upper and lower rigid

bodies 1198963was the spring and 119896

2-1198882was the spring-damper

unit which connected the lower wobbling mass to the upperand lower rigid bodies and 119896

5was the spring and 119896

4-1198884was

the spring damper unit which connected the upper wobblingmass to the upper rigid mass [12] 119865

119892was the vertical contact

force which was defined as

119865119892=

119860119888sdot (119886119909119887

1+ 119888119909119889

1119890

1) 1199091gt 0

0 1199091le 0

(3)

119860119888is contact area and 119886 119887 119888 119889 and 119890 are the parameters of

the ground reaction model which defined the deformation ofthe shoes during standing Parameters for soft and hard shoesare shown in Table 1

Cartilage was considered as a porous deformable bodyfilled with fluid occupying the whole pore volume Thephysical quantities for this analysis were the displacement ofsolidu relative fluid velocity with respect to the solid (Darcyrsquosvelocity) q fluid pressure p and electrical potential 120601 Thegoverning equations for the coupled problem are described asfollows First we considered the solid equilibrium equation

(1 minus 119899) L119879120590119904+ (1 minus 119899) 120588

119904b + kminus1119899q minus (1 minus 119899) 120588

119904u = 0 (4)

Table 1 Parameter for ground reaction model

119886 119887 119888 119889 119890

Soft shoe 106 156 2 times 104 073 10Hard shoe 106 138 2 times 104 075 10

where 120590119904was the stress in the solid phase 119899 was porosity k

was the permeability matrix 120588119904was the density of the solid

b was body force per unit mass q was relative velocity ofthe fluid and u was acceleration of the solid material Theoperator L119879 was

L119879 =

[[[[[[[

[

120597

1205971199091

0 0120597

1205971199092

0120597

1205971199093

0120597

1205971199092

0120597

1205971199091

120597

1205971199093

0

0 0120597

1205971199093

0120597

1205971199092

120597

1205971199091

]]]]]]]

]

(5)

The equilibrium equation of the fluid phase (no electrokineticcoupling) was

119899nablap + 119899120588119891b minus kminus1119899q minus 119899120588

119891k119891= 0 (6)

where pwas pore fluid pressure 120588119891was fluid density and was

k fluid velocityThis equation is also known as the generalizedDarcyrsquos law Both equilibrium equations were written per unitvolume of the mixture Combining (3) and (5) we obtain

L119879120590 + 120588b minus 120588u minus 120588119891q = 0 (7)

where 120590 was the total stress which can be expressed in termsof 120590119904and p as

120590 = (1 minus 119899)120590119904minus 119899mp (8)

and 120588 = (1 minus 119899)120588119904+ 119899120588119891was the mixture density

Here m was a constant vector defined as m119879 =

1 1 1 0 0 0 to indicate that the pressure contributes tothe normal stresses only We also had to take into accountthe fact that the pressure has a positive sign in compressionTensional stresses and strains were considered positive aswell In the following analysis we employed the effectivestress 1205901015840 defined as

1205901015840

= 120590 +mp (9)

which was relevant for the constitutive relations of the solidUsing the definition of relative velocity q as the volume of thefluid passing in a unit time through a unit area of the mixture(Darcyrsquos velocity) we obtained

q = 119899 (k119891minus u) (10)

and transformed (6) into

minusnablap + 120588119891b minus kminus1q minus 120588

119891u minus

120588119891

119899q = 0 (11)

4 Computational and Mathematical Methods in Medicine

Thefinal continuity equation using the elastic constitutive lawand fluid incompressibility was given in the form

nabla119879q + (m119879 minus m119879C119864

3119870119904

) e

+ (1 minus 119899

119870119904

+119899

119870119891

minusm119879C119864m91198702119904

) p = 0

(12)

The resulting FE system of equations was solved incremen-tally [14] with a time step Δ119905 We imposed the condition thatthe balance equations are satisfied at the end of each time step(119905+Δ119905) Hence we derived the following system of equations

[[[[[

[

muu 0 0 0

0 0 0 0

mqu 0 0 0

0 0 0 0

]]]]]

]

119905+Δ119905u119905+Δ119905p119905+Δ119905q119905+Δ119905

+

[[[[[

[

0 0 cuq 0

cpu cpp 0 0

0 0 cqq 0

0 0 0 0

]]]]]

]

119905+Δ119905u119905+Δ119905p119905+Δ119905q119905+Δ119905

+

[[[[[

[

kuu kup 0 0

0 0 kpq 0

0 kqp kqq kq1206010 k120601p 0 k

120601120601

]]]]]

]

ΔuΔpΔqΔ120601

=

119905+Δ119905

119865u119905+Δ119905

119865p119905+Δ119905

119865q119905+Δ119905

119865120601

(13)

where 119865u 119865p 119865q and 119865120601were forces in the balance equa-

tions for displacement pressure fluid velocity and electricalpotential respectively andmuu andmqu were mass terms inmass matrix [14]

22 Experimental Parts In this study we used a commercialmotion capture system OptiTrack This system consists ofsix infrared cameras and four retroreflective markers Themarkers are 15 cm in diameter and are attached at the preciseanatomical locations of the participantrsquos leg for unilateralgain analysis These locations were great trochanter regionfemoral lateral epicondyle tuberosity of the tibia and thecenter of the anterior region of ankle joint (see Figure 3)

The computerized camera system with accompanyingsoftware captures the exact motion of retroreflective markersand thus records their trajectorywhile the volunteer performswalking over the force plate The cameras were connectedto a computer that collects gait kinematical data The resultof motion tracking is a series of 3D coordinates for eachnumbered marker To better understand kinematics andkinetics of gait we used a three-axial accelerometer

We used Sun SPOT accelerometers (Sun Small Pro-grammable Object Technology) to wirelessly detect the mid-dle of the gait stance phase that is the moment when theground reaction force reaches its maximum value The Sun

Great trochanter region

Femoral lateral epicondyle

Tuberosity of the tibia

Center of ankle joint

Figure 3 Reflective markers position on the examinee leg

SPOT has a sensor board which consists of 2G6G 3-axisaccelerometer temperature sensor and light sensor In theexperimental part the Sun SPOT LIS3L02AQ accelerometeris used to measure the orientation or motion in threedimensions119883 119884 and119885with the sample rate of 100Hz Eachof these components represents the sumof static accelerationsdefined by angle of inclination to the corresponding axis anddynamics component stemming from the movement duringthe walk The ground reaction force was sampled from themultiaxis AMTI force plate at the rate of 100Hz Beforethe experiment calibration was conducted to work out thespace coordinate system for the camera system field of viewThe calibration was performed fully in accordance with theproposed manufacturerrsquos procedure

The volunteer performs walking along 25 meter distancepath away with his own ordinary velocity and attachedinfrared marker and accelerometers sensor on the left legResults for marker coordinates and corresponding accel-erations measured by the three-axial accelerometer arepresented in Figure 4

According to [15ndash17]measured values formarker positionare influenced by noise due to the wobbling of the partici-pantrsquos skin The value of this uncertainty is in range plusmn2mm

The force plate is positioned in the first half of the walkingpath During the experiment the participants were asked towalk along so the force plate records the value of the groundreaction force (Figure 5)

The force value is zero in the beginning of the walkand when the participant stands on the force plate startingwith the heel the force gradually increases and reaches themaximum and then drops to zero again when the foot isdetached by the force plate

Computational and Mathematical Methods in Medicine 5

0 05 1 15 2 25 3 35 4450

500

550

600

650

Time (s)

Posit

ion

(mm

)

0 05 1 15 2 25 3 35 4 45minus4

minus2

0

2

4

Time (s)

Femoral lateral epicondyleTuberosity of tibia

Y

Z

X

Acce

lera

tion

(m2s

)

Figure 4 Position of reflective marker during walking and corre-sponding three-axial acceleration

3 Results

One of the main tasks for preparing data for FEM simulationis matching the infrared reflective marker position obtainedby infrared camera and landmark position on the CT imageswhen cartilage is unreformed This procedure is knownas image registration and ANTs (Free software for imageregistration) is used [18]

Main goal of the registration process is obtained fromthe transformation parameter that maps the marker positionin deformed and undeformed knee cartilage In general thisprocess is finding the optimal transformation thatmaps everypixel of image with the presence of deformation and anotherstatic image when cartilage is undeformed As similaritymeasure of image the mutual information is used The stan-dard algorithm in registration process is elastic deformationprocedure The idea is to model the contours on one of thematching images as elastic object which deformed under theinfluence of some external forces [19] In each step of thedeformation the images are compared and value of externalforces is now proportional to the difference between thesecases on the basis of mutual information value The processis repeated until the difference between the images is greaterthan some error of convergence The result of registrationbetween CT and infrared images is shown in Figure 6The measured difference of the marker positions betweendeformed and undeformed cartilage is 178plusmn06mm Imagesshowing markers matching these cases are presented inFigures 6(a) and 6(c) respectivelyThemeasured uncertaintyof 006mm corresponds to the dimension of a single pixelThe error in estimation of the deformation is significantly

0 05 1 15 2 25 3 35 4Time (s)

minus1000

100200300400500600

Forc

e (N

)

Figure 5 Ground reaction forces during standing on the force plate

greater due to the influence of the distortion of the cameralens skin movements and insufficiently accurate registrationresult

Simultaneously we create a 3D model using CT slicesThe CT slices are segmented using a threshold value andcompared with gray value of the image pixel The segmentedimages are submitted by the edge detection operator forboundary extraction The merging of adjacent boundary isdone in each slice and final 3D model is created (Figure 2)This model includes femur tibia cartilage surroundingtissue and skin

The anatomical point (tuberosity of tibia and femorallateral epicondyle) can be easily detected in the modeland initial position of the marker can be obtained Usingthe measured position of infrared marker (Figure 4) andanatomical position of the marked point on the created 3Dmodel (Figure 7(c)) we can obtain a vertical deformation ofcartilage as difference of these valuesThe observedmeasuredvalue coincides with the point when the ground reactionforce is in the maximum According to Figure 5 this momentis 149 seconds after starting the recording of gait and thedeformation is 230 plusmn 001mmThe measured uncertainty of001mm emerges as a consequence of the limited resolutionof the motion capture camera system and resolution of theCT scanner This methodology for obtained deformation ismore precise than registration method but it requires moreprocessor time and memory

Using the same procedure for image segmentation a fullmodel of knee joint is created The model consists of femurtibia and cartilage

We used measured values for the displacement andground reaction force in order to calculate correspondingmatrix elements in the relation (13) Upon model creationwe applied boundary conditions (a) we clamped the distalend of tibia and (b) axially loaded the femur with themaximally measured ground reaction force 119865

119892 max = 511N(Figure 8(a))

Formodeling the cartilage andmeniscuswe implementeda finite element formulation where the nodal variables aredisplacements of solid u fluid pressure p Darcyrsquos velocityq and electrical potential 120601 with estimated matrix elementsA standard procedure of integration over the element volumewas performed and the Gaussrsquos theorem was employed Animplicit time integration scheme was implemented

The tetrahedralmeshmodel had 20537 elements and 4693nodes (Figure 8(b)) We used PAK solver [20] for the FEM

6 Computational and Mathematical Methods in Medicine

(a) (b) (c)

Figure 6 Registration infrared image and CT image (a) Infrared camera image (b) CT image (c) registered image

(a) (b) (c)

Femoral lateral epicondyle

Tuberosity of the tibia

Figure 7 3D model of knee (a) Raw CT slices (b) segmented CT images (c) 3D model with marker position

analysis Total execution time of the analysis was around 30minutes on the core I7 processorwith 12GBof RAMmemory

The initial mechanical characteristic Youngrsquos modulusand Poissonrsquos ratio for the femur and tibia were amountedto 119864 = 20GPa and ] = 03 for the isotropic cartilage119864 = 10MPa and ] = 045 and for the transversely isotropicmenisci 119864 = 20MPa and ] = 03 All these values were takenfrom the literature [21]

These values were adaptively changed for the purposeof correspondence between the measured deformation andground reaction force

The final value of the Youngrsquos modulus of the cartilage is562MPa with error of estimation of 001MPa The Youngrsquosmodulus for the femur and tibia is adapted to the 18GPawhilethe Poisonrsquos ratio is 045

Resultant stress distribution of the FEM analysis for theelements of the knee joint is given in Figure 8(c)

The von Mises stress on the cartilage is presented inFigure 9 As it can be seen the maximal value of stress hasMPa magnitude of order and is located on the boundaryof the cartilage This is in compliance with the fact that iscartilage is the weakest part of the knee joint with a tendencyto injury and fraying

The procedure described in this study can offer very use-ful information for physicians in order to better understandinjury formation and improve the process of rehabilitation

and in some perspective as a support in clinical decisionmaking

4 Conclusion

The main goal of this study was to introduce a newapproach towards a noninvasive effective stress calculationfor a specific participant Input data were provided from theexperimental measurements during the participantrsquos walkingtest whereupon finite element analysis was performed givingthe distribution of the effective stress in the major anatomicalelements of the knee joint femur tibia and cartilage Thisapproach demonstrates a great possibility for preoperativeand postoperative surgical planning and treatment of theknee injuries for specific patients

This study contains some limitations We neglected theskin movement artifact during the experiment and theinfluence of ligament presence However the current modelallows us to investigate the effect of different biomechanicalfactors and loads on the stress distribution at the knee joint Inthis study we used data obtained from infrared cameras andforce plate sensors Besides in our future work we will try toreplace a relatively expensive system of infrared cameras witha much cost effective system of accelerometers so that we willbe able to calculate positional data of anatomical points of thelower extremities solely by using their accelerationsThe verypromising are techniques of the image registration that can be

Computational and Mathematical Methods in Medicine 7

Fg max

(a) (b)

Max 2695e6times106

25

2

15

1

05

Min 1316341

(c)

Figure 8 FEM analysis model (a) Model filled with the tetrahedral mesh element (b) knee von Misses stress distribution in [Pa]

Max 1878e6times106

18

16

14

12

1

08

06

04

02

Min 110e4

Figure 9 Knee cartilage von Misses stress distribution [Pa]

8 Computational and Mathematical Methods in Medicine

used for assessment of gait parameter using a cheaper mobilecell camera This will be a consideration of the future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This paper is supported by theMinistry of Education Scienceand Technological Development of the Republic of Serbia(Projects numbers III41007 and ON 174028)

References

[1] I Kutzner B Heinlein F Graichen et al ldquoLoading of the kneejoint during activities of daily living measured in vivo in fivesubjectsrdquo Journal of Biomechanics vol 43 no 11 pp 2164ndash21732010

[2] G Li S K van deVelde and J T Bingham ldquoValidation of a non-invasive fluoroscopic imaging technique for the measurementof dynamic knee joint motionrdquo Journal of Biomechanics vol 41no 7 pp 1616ndash1622 2008

[3] C Reinschmidt A J van den Bogert A Lundberg et alldquoTibiofemoral and tibiocalcanealmotion duringwalking exter-nal vs Skeletal markersrdquo Gait and Posture vol 6 no 2 pp 98ndash109 1997

[4] N H Yang P K Canavan H Nayeb-Hashemi B Najafi and AVaziri ldquoProtocol for constructing subject-specific biomechani-cal models of knee jointrdquo Computer Methods in Biomechanicsand Biomedical Engineering vol 13 no 5 pp 589ndash603 2010

[5] M D Djuric-Jovicic N S Jovicic and D B Popovic ldquoKine-matics of gait new method for angle estimation based onaccelerometersrdquo Sensors vol 11 no 11 pp 10571ndash10585 2011

[6] H Dejnabadi B M Jolles and K Aminian ldquoA new approach toaccurate measurement of uniaxial joint angles based on a com-bination of accelerometers and gyroscopesrdquo IEEE Transactionson Biomedical Engineering vol 52 no 8 pp 1478ndash1484 2005

[7] K Tong and M H Granat ldquoA practical gait analysis systemusing gyroscopesrdquoMedical Engineering and Physics vol 21 no2 pp 87ndash94 1999

[8] W Tao T Liu R Zheng and H Feng ldquoGait analysis usingwearable sensorsrdquo Sensors vol 12 no 2 pp 2255ndash2283 2012

[9] Y Wang Y Fan and M Zhang ldquoComparison of stress onknee cartilage during kneeling and standing using finite elementmodelsrdquoMedical Engineering amp Physics vol 36 no 4 pp 439ndash447 2014

[10] K S Halonen M E Mononen J S Jurvelin J Toyras J Saloand R K Korhonen ldquoDeformation of articular cartilage duringstatic loading of a knee jointmdashexperimental and finite elementanalysisrdquo Journal of Biomechanics vol 47 no 10 pp 2467ndash24742014

[11] Y Dabiri and L P Li ldquoAltered knee joint mechanics in sim-ple compression associated with early cartilage degenerationrdquoComputational amp Mathematical Methods in Medicine vol 2013Article ID 862903 11 pages 2013

[12] N Filipovic R Vulovic A Peulic R Radakovic D Kosanicand B Ristic ldquoNoninvasive determination of knee cartilagedeformation during jumpingrdquo Journal of Sports Science andMedicine vol 8 no 4 pp 584ndash590 2009

[13] J Wismans F Veldpaus J Janssen A Huson and P StrubenldquoA three-dimensional mathematical model of the knee-jointrdquoJournal of Biomechanics vol 13 no 8 pp 677ndash685 1980

[14] M Kojic N Filipovic and S Mijailovic ldquoA large strain finiteelement analysis of cartilage deformation with electrokineticcouplingrdquo Computer Methods in Applied Mechanics and Engi-neering vol 190 no 18-19 pp 2447ndash2464 2001

[15] E H Garling B L Kaptein B Mertens et al ldquoSoft-tissueartefact assessment during step-up using fluoroscopy and skin-mountedmarkersrdquo Journal of Biomechanics vol 40 supplement1 pp S18ndashS24 2007

[16] C-C Chen Y-J Chen S-C Chen H-S Lin and T-W LuldquoEvaluation of soft-tissue artifacts when using anatomical andtechnical markers to measure mandibular motionrdquo Journal ofDental Sciences vol 6 no 2 pp 95ndash101 2011

[17] R Dumas V Camomilla T Bonci L Cheze and A CappozzoldquoGeneralized mathematical representation of the soft tissueartefactrdquo Journal of Biomechanics vol 47 no 2 pp 476ndash4812014

[18] B B Avants N Tustison and G Song ldquoAdvanced normal-ization tools (ANTS)rdquo The Insight Journal 2009 httphdlhandlenet103803113

[19] R Bajcsy and S Kovacic ldquoMultiresolution elastic matchingrdquoComputer Vision Graphics and Image Processing vol 46 no1 pp 1ndash21 1989

[20] N Filipovic M Kojic M Zivkovic R Slavkovic and NGrujovic PAK-FS Finite Element Program for Fluid-StructureInteraction Faculty of Mechanical Engineering University ofKragujevac Kragujevac Serbia 2010

[21] Z Ming and F Yubo Computational Biomechanics of theMusculoskeletal System CRC Press 2014

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Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

2 Computational and Mathematical Methods in Medicine

of those studies showed some differences in high-stressregions between kneeling and standing The conclusion wasthat the peak von Mises stress and contact pressure onthe cartilage were higher in kneeling The study [10] usedcomputed tomography (CT) images of knee structures duringstatic loading to determine cartilage strains and meniscalmovement in a human knee at different time periods ofstanding and to compare them with the subject-specific3D finite element (FE) model The results of these experi-ments showed that 80 of the maximum strain in cartilagedeveloped immediately and after that cartilage continued todeform slowly In the study [11] magnetic resonance (MR)images of the right knee of a 27-year-old male subject wereused to determine the subsequent alteration in the fluidpressurization in the human knee using a three-dimensionalcomputer model The results of these studies indicated aredistribution of stresses within the tissue and a relocation ofthe loading between the tissue matrix and fluid pressure

The purpose of this study was to estimate stress distribu-tion in the knee cartilage For that purpose the appropriatesystem of cameras and force plate platform were used Thedeformation of cartilage wasmeasured usingmarker positiondata and the 3D model of the lower leg segment The modelswere established from computed tomography (CT) imagesSimultaneously the deformation is assessed only matchingsingle infrared camera images and CT image using softwarefor image registration technique In the experimental part theaccelerometer sensor was used which potentially can providemore information about the gait In the computer simulationthe FEM analysis was applied with an adaptive change ofmechanical parameters of tissue variation in order to matchthe measured force and deformation

2 Materials and Methods

21 Mechanical Model of the Knee Joint Knee joint motionrepresents a complex combination of rotations and trans-lations The major parts involved in the knee kinematicalbehavior include femur tibia and patella Forces that act ata knee joint are given in Figure 1

The dominant forces that act at a knee joint are bodyweight and ground reaction force which are opposite toeach other Muscle forces as well as contact forces betweenfemur and tibia are also included in the model Equilibriumequations of the knee joint are given below [5]

119865119903+ 119865119887+ 1198651199011

sdot 1198731+ 1198651199012

sdot 1198732+

7

sum

119894=1

119865119894= 0

119872119903+ 119865119903times 119875119903+ 119865119887times 119875119887+ 1198651199011

sdot 1198731times 1198751+ 1198651199012

sdot 1198732times 1198752

+

7

sum

119894=1

119865119894times 119881119894= 0

(1)

where 119865119903is the ground reaction force 119865

119887is the body weight

1198651199011

and 1198651199012

are the two contact point forces 1198731and 119873

2

are the two contact points normal 119865 (119894 = 1 sdot sdot sdot 7) are theligament and capsule forces 119872

119903is the knee joint driver

Body weightMuscleforce

Ground reaction force

Muscleforce

Ligament force

Contact force

Ligament force

Figure 1 Forces on a knee joint

moment along local 119911 axis and119875119903 119875119887 1198751 1198752and119881 (119894 = 1 sdot sdot sdot 7)

are the position vectors where the corresponding forces arebeing applied [13] We assumed that femur and tibia couldbe represented as rigid bodies and that their deformationswere very small in contrast to relatively large deformations ofcartilage and ligaments Note that synovial fluid significantlyreduces the friction between cartilage surfaces and menisci

A simplified spring-damper-mass model which was usedin this study is shown in Figure 2 It consists of four massesThe upper body was modeled using two masses one rep-resenting its rigid mass 119898

3 and the other representing its

wobbling masses 1198984 The thigh leg and foot of the sup-

porting leg weremodeled using twomasses one representingits rigid mass 119898

1 and the other representing its wobbling

masses1198982

The total bodymass was obtained from the participant Inthe following system of equations (Equation (2)) a dynamicssystem is described [12] and was later used to calculate theresultant force and moment of the knee cartilage during thestance phase of the gait cycle

11989811+ 1198961(1199091minus 1199093) + 1198962(1199091minus 1199092) + 1198881(1minus 3)

+ 1198882(1minus 2) = 119898

1119892 minus 119865119892

11989822minus 1198962(1199091minus 1199092) + 1198963(1199092minus 1199093)

+ 1198882(1minus 2) = 119898

2119892

11989833minus 1198961(1199091minus 1199093) minus 1198963(1199092minus 1199093)

+ (1198964+ 1198965) (1199093minus 1199094) minus 1198881(1minus 3)

+ 1198884(3minus 4) = 119898

3119892

(2)

In (2) 1198981was the lower body rigid mass and 119898

2was the

wobbling mass 1198983was the upper body rigid mass and 119898

4

was the wobbling mass 1198961was the compressive spring and

Computational and Mathematical Methods in Medicine 3

k5

k4

k3k1

k2

m1

m2

m4

m3

Ground reaction model

x3

x1

x2

x4 c4

c1

c2

Figure 2 A simplified spring-damper-mass model used in thecomputer simulation The components of the dynamics systempresented are lower body rigid mass (119898

1) and wobbling mass (119898

2)

upper body rigid mass (1198983) and wobbling mass (119898

4) compressive

spring (1198961) and damper (119888

1) that connect the upper and lower rigid

bodies spring (1198963) and springdamper unit (119896

2 1198882) connecting the

lower wobblingmass to the upper and lower rigid bodies and spring(1198965) and springdamper unit (119896

4 1198884) connecting the upper wobbling

mass to the upper rigid mass (adopted from [12])

1198881was the damper that connected the upper and lower rigid

bodies 1198963was the spring and 119896

2-1198882was the spring-damper

unit which connected the lower wobbling mass to the upperand lower rigid bodies and 119896

5was the spring and 119896

4-1198884was

the spring damper unit which connected the upper wobblingmass to the upper rigid mass [12] 119865

119892was the vertical contact

force which was defined as

119865119892=

119860119888sdot (119886119909119887

1+ 119888119909119889

1119890

1) 1199091gt 0

0 1199091le 0

(3)

119860119888is contact area and 119886 119887 119888 119889 and 119890 are the parameters of

the ground reaction model which defined the deformation ofthe shoes during standing Parameters for soft and hard shoesare shown in Table 1

Cartilage was considered as a porous deformable bodyfilled with fluid occupying the whole pore volume Thephysical quantities for this analysis were the displacement ofsolidu relative fluid velocity with respect to the solid (Darcyrsquosvelocity) q fluid pressure p and electrical potential 120601 Thegoverning equations for the coupled problem are described asfollows First we considered the solid equilibrium equation

(1 minus 119899) L119879120590119904+ (1 minus 119899) 120588

119904b + kminus1119899q minus (1 minus 119899) 120588

119904u = 0 (4)

Table 1 Parameter for ground reaction model

119886 119887 119888 119889 119890

Soft shoe 106 156 2 times 104 073 10Hard shoe 106 138 2 times 104 075 10

where 120590119904was the stress in the solid phase 119899 was porosity k

was the permeability matrix 120588119904was the density of the solid

b was body force per unit mass q was relative velocity ofthe fluid and u was acceleration of the solid material Theoperator L119879 was

L119879 =

[[[[[[[

[

120597

1205971199091

0 0120597

1205971199092

0120597

1205971199093

0120597

1205971199092

0120597

1205971199091

120597

1205971199093

0

0 0120597

1205971199093

0120597

1205971199092

120597

1205971199091

]]]]]]]

]

(5)

The equilibrium equation of the fluid phase (no electrokineticcoupling) was

119899nablap + 119899120588119891b minus kminus1119899q minus 119899120588

119891k119891= 0 (6)

where pwas pore fluid pressure 120588119891was fluid density and was

k fluid velocityThis equation is also known as the generalizedDarcyrsquos law Both equilibrium equations were written per unitvolume of the mixture Combining (3) and (5) we obtain

L119879120590 + 120588b minus 120588u minus 120588119891q = 0 (7)

where 120590 was the total stress which can be expressed in termsof 120590119904and p as

120590 = (1 minus 119899)120590119904minus 119899mp (8)

and 120588 = (1 minus 119899)120588119904+ 119899120588119891was the mixture density

Here m was a constant vector defined as m119879 =

1 1 1 0 0 0 to indicate that the pressure contributes tothe normal stresses only We also had to take into accountthe fact that the pressure has a positive sign in compressionTensional stresses and strains were considered positive aswell In the following analysis we employed the effectivestress 1205901015840 defined as

1205901015840

= 120590 +mp (9)

which was relevant for the constitutive relations of the solidUsing the definition of relative velocity q as the volume of thefluid passing in a unit time through a unit area of the mixture(Darcyrsquos velocity) we obtained

q = 119899 (k119891minus u) (10)

and transformed (6) into

minusnablap + 120588119891b minus kminus1q minus 120588

119891u minus

120588119891

119899q = 0 (11)

4 Computational and Mathematical Methods in Medicine

Thefinal continuity equation using the elastic constitutive lawand fluid incompressibility was given in the form

nabla119879q + (m119879 minus m119879C119864

3119870119904

) e

+ (1 minus 119899

119870119904

+119899

119870119891

minusm119879C119864m91198702119904

) p = 0

(12)

The resulting FE system of equations was solved incremen-tally [14] with a time step Δ119905 We imposed the condition thatthe balance equations are satisfied at the end of each time step(119905+Δ119905) Hence we derived the following system of equations

[[[[[

[

muu 0 0 0

0 0 0 0

mqu 0 0 0

0 0 0 0

]]]]]

]

119905+Δ119905u119905+Δ119905p119905+Δ119905q119905+Δ119905

+

[[[[[

[

0 0 cuq 0

cpu cpp 0 0

0 0 cqq 0

0 0 0 0

]]]]]

]

119905+Δ119905u119905+Δ119905p119905+Δ119905q119905+Δ119905

+

[[[[[

[

kuu kup 0 0

0 0 kpq 0

0 kqp kqq kq1206010 k120601p 0 k

120601120601

]]]]]

]

ΔuΔpΔqΔ120601

=

119905+Δ119905

119865u119905+Δ119905

119865p119905+Δ119905

119865q119905+Δ119905

119865120601

(13)

where 119865u 119865p 119865q and 119865120601were forces in the balance equa-

tions for displacement pressure fluid velocity and electricalpotential respectively andmuu andmqu were mass terms inmass matrix [14]

22 Experimental Parts In this study we used a commercialmotion capture system OptiTrack This system consists ofsix infrared cameras and four retroreflective markers Themarkers are 15 cm in diameter and are attached at the preciseanatomical locations of the participantrsquos leg for unilateralgain analysis These locations were great trochanter regionfemoral lateral epicondyle tuberosity of the tibia and thecenter of the anterior region of ankle joint (see Figure 3)

The computerized camera system with accompanyingsoftware captures the exact motion of retroreflective markersand thus records their trajectorywhile the volunteer performswalking over the force plate The cameras were connectedto a computer that collects gait kinematical data The resultof motion tracking is a series of 3D coordinates for eachnumbered marker To better understand kinematics andkinetics of gait we used a three-axial accelerometer

We used Sun SPOT accelerometers (Sun Small Pro-grammable Object Technology) to wirelessly detect the mid-dle of the gait stance phase that is the moment when theground reaction force reaches its maximum value The Sun

Great trochanter region

Femoral lateral epicondyle

Tuberosity of the tibia

Center of ankle joint

Figure 3 Reflective markers position on the examinee leg

SPOT has a sensor board which consists of 2G6G 3-axisaccelerometer temperature sensor and light sensor In theexperimental part the Sun SPOT LIS3L02AQ accelerometeris used to measure the orientation or motion in threedimensions119883 119884 and119885with the sample rate of 100Hz Eachof these components represents the sumof static accelerationsdefined by angle of inclination to the corresponding axis anddynamics component stemming from the movement duringthe walk The ground reaction force was sampled from themultiaxis AMTI force plate at the rate of 100Hz Beforethe experiment calibration was conducted to work out thespace coordinate system for the camera system field of viewThe calibration was performed fully in accordance with theproposed manufacturerrsquos procedure

The volunteer performs walking along 25 meter distancepath away with his own ordinary velocity and attachedinfrared marker and accelerometers sensor on the left legResults for marker coordinates and corresponding accel-erations measured by the three-axial accelerometer arepresented in Figure 4

According to [15ndash17]measured values formarker positionare influenced by noise due to the wobbling of the partici-pantrsquos skin The value of this uncertainty is in range plusmn2mm

The force plate is positioned in the first half of the walkingpath During the experiment the participants were asked towalk along so the force plate records the value of the groundreaction force (Figure 5)

The force value is zero in the beginning of the walkand when the participant stands on the force plate startingwith the heel the force gradually increases and reaches themaximum and then drops to zero again when the foot isdetached by the force plate

Computational and Mathematical Methods in Medicine 5

0 05 1 15 2 25 3 35 4450

500

550

600

650

Time (s)

Posit

ion

(mm

)

0 05 1 15 2 25 3 35 4 45minus4

minus2

0

2

4

Time (s)

Femoral lateral epicondyleTuberosity of tibia

Y

Z

X

Acce

lera

tion

(m2s

)

Figure 4 Position of reflective marker during walking and corre-sponding three-axial acceleration

3 Results

One of the main tasks for preparing data for FEM simulationis matching the infrared reflective marker position obtainedby infrared camera and landmark position on the CT imageswhen cartilage is unreformed This procedure is knownas image registration and ANTs (Free software for imageregistration) is used [18]

Main goal of the registration process is obtained fromthe transformation parameter that maps the marker positionin deformed and undeformed knee cartilage In general thisprocess is finding the optimal transformation thatmaps everypixel of image with the presence of deformation and anotherstatic image when cartilage is undeformed As similaritymeasure of image the mutual information is used The stan-dard algorithm in registration process is elastic deformationprocedure The idea is to model the contours on one of thematching images as elastic object which deformed under theinfluence of some external forces [19] In each step of thedeformation the images are compared and value of externalforces is now proportional to the difference between thesecases on the basis of mutual information value The processis repeated until the difference between the images is greaterthan some error of convergence The result of registrationbetween CT and infrared images is shown in Figure 6The measured difference of the marker positions betweendeformed and undeformed cartilage is 178plusmn06mm Imagesshowing markers matching these cases are presented inFigures 6(a) and 6(c) respectivelyThemeasured uncertaintyof 006mm corresponds to the dimension of a single pixelThe error in estimation of the deformation is significantly

0 05 1 15 2 25 3 35 4Time (s)

minus1000

100200300400500600

Forc

e (N

)

Figure 5 Ground reaction forces during standing on the force plate

greater due to the influence of the distortion of the cameralens skin movements and insufficiently accurate registrationresult

Simultaneously we create a 3D model using CT slicesThe CT slices are segmented using a threshold value andcompared with gray value of the image pixel The segmentedimages are submitted by the edge detection operator forboundary extraction The merging of adjacent boundary isdone in each slice and final 3D model is created (Figure 2)This model includes femur tibia cartilage surroundingtissue and skin

The anatomical point (tuberosity of tibia and femorallateral epicondyle) can be easily detected in the modeland initial position of the marker can be obtained Usingthe measured position of infrared marker (Figure 4) andanatomical position of the marked point on the created 3Dmodel (Figure 7(c)) we can obtain a vertical deformation ofcartilage as difference of these valuesThe observedmeasuredvalue coincides with the point when the ground reactionforce is in the maximum According to Figure 5 this momentis 149 seconds after starting the recording of gait and thedeformation is 230 plusmn 001mmThe measured uncertainty of001mm emerges as a consequence of the limited resolutionof the motion capture camera system and resolution of theCT scanner This methodology for obtained deformation ismore precise than registration method but it requires moreprocessor time and memory

Using the same procedure for image segmentation a fullmodel of knee joint is created The model consists of femurtibia and cartilage

We used measured values for the displacement andground reaction force in order to calculate correspondingmatrix elements in the relation (13) Upon model creationwe applied boundary conditions (a) we clamped the distalend of tibia and (b) axially loaded the femur with themaximally measured ground reaction force 119865

119892 max = 511N(Figure 8(a))

Formodeling the cartilage andmeniscuswe implementeda finite element formulation where the nodal variables aredisplacements of solid u fluid pressure p Darcyrsquos velocityq and electrical potential 120601 with estimated matrix elementsA standard procedure of integration over the element volumewas performed and the Gaussrsquos theorem was employed Animplicit time integration scheme was implemented

The tetrahedralmeshmodel had 20537 elements and 4693nodes (Figure 8(b)) We used PAK solver [20] for the FEM

6 Computational and Mathematical Methods in Medicine

(a) (b) (c)

Figure 6 Registration infrared image and CT image (a) Infrared camera image (b) CT image (c) registered image

(a) (b) (c)

Femoral lateral epicondyle

Tuberosity of the tibia

Figure 7 3D model of knee (a) Raw CT slices (b) segmented CT images (c) 3D model with marker position

analysis Total execution time of the analysis was around 30minutes on the core I7 processorwith 12GBof RAMmemory

The initial mechanical characteristic Youngrsquos modulusand Poissonrsquos ratio for the femur and tibia were amountedto 119864 = 20GPa and ] = 03 for the isotropic cartilage119864 = 10MPa and ] = 045 and for the transversely isotropicmenisci 119864 = 20MPa and ] = 03 All these values were takenfrom the literature [21]

These values were adaptively changed for the purposeof correspondence between the measured deformation andground reaction force

The final value of the Youngrsquos modulus of the cartilage is562MPa with error of estimation of 001MPa The Youngrsquosmodulus for the femur and tibia is adapted to the 18GPawhilethe Poisonrsquos ratio is 045

Resultant stress distribution of the FEM analysis for theelements of the knee joint is given in Figure 8(c)

The von Mises stress on the cartilage is presented inFigure 9 As it can be seen the maximal value of stress hasMPa magnitude of order and is located on the boundaryof the cartilage This is in compliance with the fact that iscartilage is the weakest part of the knee joint with a tendencyto injury and fraying

The procedure described in this study can offer very use-ful information for physicians in order to better understandinjury formation and improve the process of rehabilitation

and in some perspective as a support in clinical decisionmaking

4 Conclusion

The main goal of this study was to introduce a newapproach towards a noninvasive effective stress calculationfor a specific participant Input data were provided from theexperimental measurements during the participantrsquos walkingtest whereupon finite element analysis was performed givingthe distribution of the effective stress in the major anatomicalelements of the knee joint femur tibia and cartilage Thisapproach demonstrates a great possibility for preoperativeand postoperative surgical planning and treatment of theknee injuries for specific patients

This study contains some limitations We neglected theskin movement artifact during the experiment and theinfluence of ligament presence However the current modelallows us to investigate the effect of different biomechanicalfactors and loads on the stress distribution at the knee joint Inthis study we used data obtained from infrared cameras andforce plate sensors Besides in our future work we will try toreplace a relatively expensive system of infrared cameras witha much cost effective system of accelerometers so that we willbe able to calculate positional data of anatomical points of thelower extremities solely by using their accelerationsThe verypromising are techniques of the image registration that can be

Computational and Mathematical Methods in Medicine 7

Fg max

(a) (b)

Max 2695e6times106

25

2

15

1

05

Min 1316341

(c)

Figure 8 FEM analysis model (a) Model filled with the tetrahedral mesh element (b) knee von Misses stress distribution in [Pa]

Max 1878e6times106

18

16

14

12

1

08

06

04

02

Min 110e4

Figure 9 Knee cartilage von Misses stress distribution [Pa]

8 Computational and Mathematical Methods in Medicine

used for assessment of gait parameter using a cheaper mobilecell camera This will be a consideration of the future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This paper is supported by theMinistry of Education Scienceand Technological Development of the Republic of Serbia(Projects numbers III41007 and ON 174028)

References

[1] I Kutzner B Heinlein F Graichen et al ldquoLoading of the kneejoint during activities of daily living measured in vivo in fivesubjectsrdquo Journal of Biomechanics vol 43 no 11 pp 2164ndash21732010

[2] G Li S K van deVelde and J T Bingham ldquoValidation of a non-invasive fluoroscopic imaging technique for the measurementof dynamic knee joint motionrdquo Journal of Biomechanics vol 41no 7 pp 1616ndash1622 2008

[3] C Reinschmidt A J van den Bogert A Lundberg et alldquoTibiofemoral and tibiocalcanealmotion duringwalking exter-nal vs Skeletal markersrdquo Gait and Posture vol 6 no 2 pp 98ndash109 1997

[4] N H Yang P K Canavan H Nayeb-Hashemi B Najafi and AVaziri ldquoProtocol for constructing subject-specific biomechani-cal models of knee jointrdquo Computer Methods in Biomechanicsand Biomedical Engineering vol 13 no 5 pp 589ndash603 2010

[5] M D Djuric-Jovicic N S Jovicic and D B Popovic ldquoKine-matics of gait new method for angle estimation based onaccelerometersrdquo Sensors vol 11 no 11 pp 10571ndash10585 2011

[6] H Dejnabadi B M Jolles and K Aminian ldquoA new approach toaccurate measurement of uniaxial joint angles based on a com-bination of accelerometers and gyroscopesrdquo IEEE Transactionson Biomedical Engineering vol 52 no 8 pp 1478ndash1484 2005

[7] K Tong and M H Granat ldquoA practical gait analysis systemusing gyroscopesrdquoMedical Engineering and Physics vol 21 no2 pp 87ndash94 1999

[8] W Tao T Liu R Zheng and H Feng ldquoGait analysis usingwearable sensorsrdquo Sensors vol 12 no 2 pp 2255ndash2283 2012

[9] Y Wang Y Fan and M Zhang ldquoComparison of stress onknee cartilage during kneeling and standing using finite elementmodelsrdquoMedical Engineering amp Physics vol 36 no 4 pp 439ndash447 2014

[10] K S Halonen M E Mononen J S Jurvelin J Toyras J Saloand R K Korhonen ldquoDeformation of articular cartilage duringstatic loading of a knee jointmdashexperimental and finite elementanalysisrdquo Journal of Biomechanics vol 47 no 10 pp 2467ndash24742014

[11] Y Dabiri and L P Li ldquoAltered knee joint mechanics in sim-ple compression associated with early cartilage degenerationrdquoComputational amp Mathematical Methods in Medicine vol 2013Article ID 862903 11 pages 2013

[12] N Filipovic R Vulovic A Peulic R Radakovic D Kosanicand B Ristic ldquoNoninvasive determination of knee cartilagedeformation during jumpingrdquo Journal of Sports Science andMedicine vol 8 no 4 pp 584ndash590 2009

[13] J Wismans F Veldpaus J Janssen A Huson and P StrubenldquoA three-dimensional mathematical model of the knee-jointrdquoJournal of Biomechanics vol 13 no 8 pp 677ndash685 1980

[14] M Kojic N Filipovic and S Mijailovic ldquoA large strain finiteelement analysis of cartilage deformation with electrokineticcouplingrdquo Computer Methods in Applied Mechanics and Engi-neering vol 190 no 18-19 pp 2447ndash2464 2001

[15] E H Garling B L Kaptein B Mertens et al ldquoSoft-tissueartefact assessment during step-up using fluoroscopy and skin-mountedmarkersrdquo Journal of Biomechanics vol 40 supplement1 pp S18ndashS24 2007

[16] C-C Chen Y-J Chen S-C Chen H-S Lin and T-W LuldquoEvaluation of soft-tissue artifacts when using anatomical andtechnical markers to measure mandibular motionrdquo Journal ofDental Sciences vol 6 no 2 pp 95ndash101 2011

[17] R Dumas V Camomilla T Bonci L Cheze and A CappozzoldquoGeneralized mathematical representation of the soft tissueartefactrdquo Journal of Biomechanics vol 47 no 2 pp 476ndash4812014

[18] B B Avants N Tustison and G Song ldquoAdvanced normal-ization tools (ANTS)rdquo The Insight Journal 2009 httphdlhandlenet103803113

[19] R Bajcsy and S Kovacic ldquoMultiresolution elastic matchingrdquoComputer Vision Graphics and Image Processing vol 46 no1 pp 1ndash21 1989

[20] N Filipovic M Kojic M Zivkovic R Slavkovic and NGrujovic PAK-FS Finite Element Program for Fluid-StructureInteraction Faculty of Mechanical Engineering University ofKragujevac Kragujevac Serbia 2010

[21] Z Ming and F Yubo Computational Biomechanics of theMusculoskeletal System CRC Press 2014

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Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

Computational and Mathematical Methods in Medicine 3

k5

k4

k3k1

k2

m1

m2

m4

m3

Ground reaction model

x3

x1

x2

x4 c4

c1

c2

Figure 2 A simplified spring-damper-mass model used in thecomputer simulation The components of the dynamics systempresented are lower body rigid mass (119898

1) and wobbling mass (119898

2)

upper body rigid mass (1198983) and wobbling mass (119898

4) compressive

spring (1198961) and damper (119888

1) that connect the upper and lower rigid

bodies spring (1198963) and springdamper unit (119896

2 1198882) connecting the

lower wobblingmass to the upper and lower rigid bodies and spring(1198965) and springdamper unit (119896

4 1198884) connecting the upper wobbling

mass to the upper rigid mass (adopted from [12])

1198881was the damper that connected the upper and lower rigid

bodies 1198963was the spring and 119896

2-1198882was the spring-damper

unit which connected the lower wobbling mass to the upperand lower rigid bodies and 119896

5was the spring and 119896

4-1198884was

the spring damper unit which connected the upper wobblingmass to the upper rigid mass [12] 119865

119892was the vertical contact

force which was defined as

119865119892=

119860119888sdot (119886119909119887

1+ 119888119909119889

1119890

1) 1199091gt 0

0 1199091le 0

(3)

119860119888is contact area and 119886 119887 119888 119889 and 119890 are the parameters of

the ground reaction model which defined the deformation ofthe shoes during standing Parameters for soft and hard shoesare shown in Table 1

Cartilage was considered as a porous deformable bodyfilled with fluid occupying the whole pore volume Thephysical quantities for this analysis were the displacement ofsolidu relative fluid velocity with respect to the solid (Darcyrsquosvelocity) q fluid pressure p and electrical potential 120601 Thegoverning equations for the coupled problem are described asfollows First we considered the solid equilibrium equation

(1 minus 119899) L119879120590119904+ (1 minus 119899) 120588

119904b + kminus1119899q minus (1 minus 119899) 120588

119904u = 0 (4)

Table 1 Parameter for ground reaction model

119886 119887 119888 119889 119890

Soft shoe 106 156 2 times 104 073 10Hard shoe 106 138 2 times 104 075 10

where 120590119904was the stress in the solid phase 119899 was porosity k

was the permeability matrix 120588119904was the density of the solid

b was body force per unit mass q was relative velocity ofthe fluid and u was acceleration of the solid material Theoperator L119879 was

L119879 =

[[[[[[[

[

120597

1205971199091

0 0120597

1205971199092

0120597

1205971199093

0120597

1205971199092

0120597

1205971199091

120597

1205971199093

0

0 0120597

1205971199093

0120597

1205971199092

120597

1205971199091

]]]]]]]

]

(5)

The equilibrium equation of the fluid phase (no electrokineticcoupling) was

119899nablap + 119899120588119891b minus kminus1119899q minus 119899120588

119891k119891= 0 (6)

where pwas pore fluid pressure 120588119891was fluid density and was

k fluid velocityThis equation is also known as the generalizedDarcyrsquos law Both equilibrium equations were written per unitvolume of the mixture Combining (3) and (5) we obtain

L119879120590 + 120588b minus 120588u minus 120588119891q = 0 (7)

where 120590 was the total stress which can be expressed in termsof 120590119904and p as

120590 = (1 minus 119899)120590119904minus 119899mp (8)

and 120588 = (1 minus 119899)120588119904+ 119899120588119891was the mixture density

Here m was a constant vector defined as m119879 =

1 1 1 0 0 0 to indicate that the pressure contributes tothe normal stresses only We also had to take into accountthe fact that the pressure has a positive sign in compressionTensional stresses and strains were considered positive aswell In the following analysis we employed the effectivestress 1205901015840 defined as

1205901015840

= 120590 +mp (9)

which was relevant for the constitutive relations of the solidUsing the definition of relative velocity q as the volume of thefluid passing in a unit time through a unit area of the mixture(Darcyrsquos velocity) we obtained

q = 119899 (k119891minus u) (10)

and transformed (6) into

minusnablap + 120588119891b minus kminus1q minus 120588

119891u minus

120588119891

119899q = 0 (11)

4 Computational and Mathematical Methods in Medicine

Thefinal continuity equation using the elastic constitutive lawand fluid incompressibility was given in the form

nabla119879q + (m119879 minus m119879C119864

3119870119904

) e

+ (1 minus 119899

119870119904

+119899

119870119891

minusm119879C119864m91198702119904

) p = 0

(12)

The resulting FE system of equations was solved incremen-tally [14] with a time step Δ119905 We imposed the condition thatthe balance equations are satisfied at the end of each time step(119905+Δ119905) Hence we derived the following system of equations

[[[[[

[

muu 0 0 0

0 0 0 0

mqu 0 0 0

0 0 0 0

]]]]]

]

119905+Δ119905u119905+Δ119905p119905+Δ119905q119905+Δ119905

+

[[[[[

[

0 0 cuq 0

cpu cpp 0 0

0 0 cqq 0

0 0 0 0

]]]]]

]

119905+Δ119905u119905+Δ119905p119905+Δ119905q119905+Δ119905

+

[[[[[

[

kuu kup 0 0

0 0 kpq 0

0 kqp kqq kq1206010 k120601p 0 k

120601120601

]]]]]

]

ΔuΔpΔqΔ120601

=

119905+Δ119905

119865u119905+Δ119905

119865p119905+Δ119905

119865q119905+Δ119905

119865120601

(13)

where 119865u 119865p 119865q and 119865120601were forces in the balance equa-

tions for displacement pressure fluid velocity and electricalpotential respectively andmuu andmqu were mass terms inmass matrix [14]

22 Experimental Parts In this study we used a commercialmotion capture system OptiTrack This system consists ofsix infrared cameras and four retroreflective markers Themarkers are 15 cm in diameter and are attached at the preciseanatomical locations of the participantrsquos leg for unilateralgain analysis These locations were great trochanter regionfemoral lateral epicondyle tuberosity of the tibia and thecenter of the anterior region of ankle joint (see Figure 3)

The computerized camera system with accompanyingsoftware captures the exact motion of retroreflective markersand thus records their trajectorywhile the volunteer performswalking over the force plate The cameras were connectedto a computer that collects gait kinematical data The resultof motion tracking is a series of 3D coordinates for eachnumbered marker To better understand kinematics andkinetics of gait we used a three-axial accelerometer

We used Sun SPOT accelerometers (Sun Small Pro-grammable Object Technology) to wirelessly detect the mid-dle of the gait stance phase that is the moment when theground reaction force reaches its maximum value The Sun

Great trochanter region

Femoral lateral epicondyle

Tuberosity of the tibia

Center of ankle joint

Figure 3 Reflective markers position on the examinee leg

SPOT has a sensor board which consists of 2G6G 3-axisaccelerometer temperature sensor and light sensor In theexperimental part the Sun SPOT LIS3L02AQ accelerometeris used to measure the orientation or motion in threedimensions119883 119884 and119885with the sample rate of 100Hz Eachof these components represents the sumof static accelerationsdefined by angle of inclination to the corresponding axis anddynamics component stemming from the movement duringthe walk The ground reaction force was sampled from themultiaxis AMTI force plate at the rate of 100Hz Beforethe experiment calibration was conducted to work out thespace coordinate system for the camera system field of viewThe calibration was performed fully in accordance with theproposed manufacturerrsquos procedure

The volunteer performs walking along 25 meter distancepath away with his own ordinary velocity and attachedinfrared marker and accelerometers sensor on the left legResults for marker coordinates and corresponding accel-erations measured by the three-axial accelerometer arepresented in Figure 4

According to [15ndash17]measured values formarker positionare influenced by noise due to the wobbling of the partici-pantrsquos skin The value of this uncertainty is in range plusmn2mm

The force plate is positioned in the first half of the walkingpath During the experiment the participants were asked towalk along so the force plate records the value of the groundreaction force (Figure 5)

The force value is zero in the beginning of the walkand when the participant stands on the force plate startingwith the heel the force gradually increases and reaches themaximum and then drops to zero again when the foot isdetached by the force plate

Computational and Mathematical Methods in Medicine 5

0 05 1 15 2 25 3 35 4450

500

550

600

650

Time (s)

Posit

ion

(mm

)

0 05 1 15 2 25 3 35 4 45minus4

minus2

0

2

4

Time (s)

Femoral lateral epicondyleTuberosity of tibia

Y

Z

X

Acce

lera

tion

(m2s

)

Figure 4 Position of reflective marker during walking and corre-sponding three-axial acceleration

3 Results

One of the main tasks for preparing data for FEM simulationis matching the infrared reflective marker position obtainedby infrared camera and landmark position on the CT imageswhen cartilage is unreformed This procedure is knownas image registration and ANTs (Free software for imageregistration) is used [18]

Main goal of the registration process is obtained fromthe transformation parameter that maps the marker positionin deformed and undeformed knee cartilage In general thisprocess is finding the optimal transformation thatmaps everypixel of image with the presence of deformation and anotherstatic image when cartilage is undeformed As similaritymeasure of image the mutual information is used The stan-dard algorithm in registration process is elastic deformationprocedure The idea is to model the contours on one of thematching images as elastic object which deformed under theinfluence of some external forces [19] In each step of thedeformation the images are compared and value of externalforces is now proportional to the difference between thesecases on the basis of mutual information value The processis repeated until the difference between the images is greaterthan some error of convergence The result of registrationbetween CT and infrared images is shown in Figure 6The measured difference of the marker positions betweendeformed and undeformed cartilage is 178plusmn06mm Imagesshowing markers matching these cases are presented inFigures 6(a) and 6(c) respectivelyThemeasured uncertaintyof 006mm corresponds to the dimension of a single pixelThe error in estimation of the deformation is significantly

0 05 1 15 2 25 3 35 4Time (s)

minus1000

100200300400500600

Forc

e (N

)

Figure 5 Ground reaction forces during standing on the force plate

greater due to the influence of the distortion of the cameralens skin movements and insufficiently accurate registrationresult

Simultaneously we create a 3D model using CT slicesThe CT slices are segmented using a threshold value andcompared with gray value of the image pixel The segmentedimages are submitted by the edge detection operator forboundary extraction The merging of adjacent boundary isdone in each slice and final 3D model is created (Figure 2)This model includes femur tibia cartilage surroundingtissue and skin

The anatomical point (tuberosity of tibia and femorallateral epicondyle) can be easily detected in the modeland initial position of the marker can be obtained Usingthe measured position of infrared marker (Figure 4) andanatomical position of the marked point on the created 3Dmodel (Figure 7(c)) we can obtain a vertical deformation ofcartilage as difference of these valuesThe observedmeasuredvalue coincides with the point when the ground reactionforce is in the maximum According to Figure 5 this momentis 149 seconds after starting the recording of gait and thedeformation is 230 plusmn 001mmThe measured uncertainty of001mm emerges as a consequence of the limited resolutionof the motion capture camera system and resolution of theCT scanner This methodology for obtained deformation ismore precise than registration method but it requires moreprocessor time and memory

Using the same procedure for image segmentation a fullmodel of knee joint is created The model consists of femurtibia and cartilage

We used measured values for the displacement andground reaction force in order to calculate correspondingmatrix elements in the relation (13) Upon model creationwe applied boundary conditions (a) we clamped the distalend of tibia and (b) axially loaded the femur with themaximally measured ground reaction force 119865

119892 max = 511N(Figure 8(a))

Formodeling the cartilage andmeniscuswe implementeda finite element formulation where the nodal variables aredisplacements of solid u fluid pressure p Darcyrsquos velocityq and electrical potential 120601 with estimated matrix elementsA standard procedure of integration over the element volumewas performed and the Gaussrsquos theorem was employed Animplicit time integration scheme was implemented

The tetrahedralmeshmodel had 20537 elements and 4693nodes (Figure 8(b)) We used PAK solver [20] for the FEM

6 Computational and Mathematical Methods in Medicine

(a) (b) (c)

Figure 6 Registration infrared image and CT image (a) Infrared camera image (b) CT image (c) registered image

(a) (b) (c)

Femoral lateral epicondyle

Tuberosity of the tibia

Figure 7 3D model of knee (a) Raw CT slices (b) segmented CT images (c) 3D model with marker position

analysis Total execution time of the analysis was around 30minutes on the core I7 processorwith 12GBof RAMmemory

The initial mechanical characteristic Youngrsquos modulusand Poissonrsquos ratio for the femur and tibia were amountedto 119864 = 20GPa and ] = 03 for the isotropic cartilage119864 = 10MPa and ] = 045 and for the transversely isotropicmenisci 119864 = 20MPa and ] = 03 All these values were takenfrom the literature [21]

These values were adaptively changed for the purposeof correspondence between the measured deformation andground reaction force

The final value of the Youngrsquos modulus of the cartilage is562MPa with error of estimation of 001MPa The Youngrsquosmodulus for the femur and tibia is adapted to the 18GPawhilethe Poisonrsquos ratio is 045

Resultant stress distribution of the FEM analysis for theelements of the knee joint is given in Figure 8(c)

The von Mises stress on the cartilage is presented inFigure 9 As it can be seen the maximal value of stress hasMPa magnitude of order and is located on the boundaryof the cartilage This is in compliance with the fact that iscartilage is the weakest part of the knee joint with a tendencyto injury and fraying

The procedure described in this study can offer very use-ful information for physicians in order to better understandinjury formation and improve the process of rehabilitation

and in some perspective as a support in clinical decisionmaking

4 Conclusion

The main goal of this study was to introduce a newapproach towards a noninvasive effective stress calculationfor a specific participant Input data were provided from theexperimental measurements during the participantrsquos walkingtest whereupon finite element analysis was performed givingthe distribution of the effective stress in the major anatomicalelements of the knee joint femur tibia and cartilage Thisapproach demonstrates a great possibility for preoperativeand postoperative surgical planning and treatment of theknee injuries for specific patients

This study contains some limitations We neglected theskin movement artifact during the experiment and theinfluence of ligament presence However the current modelallows us to investigate the effect of different biomechanicalfactors and loads on the stress distribution at the knee joint Inthis study we used data obtained from infrared cameras andforce plate sensors Besides in our future work we will try toreplace a relatively expensive system of infrared cameras witha much cost effective system of accelerometers so that we willbe able to calculate positional data of anatomical points of thelower extremities solely by using their accelerationsThe verypromising are techniques of the image registration that can be

Computational and Mathematical Methods in Medicine 7

Fg max

(a) (b)

Max 2695e6times106

25

2

15

1

05

Min 1316341

(c)

Figure 8 FEM analysis model (a) Model filled with the tetrahedral mesh element (b) knee von Misses stress distribution in [Pa]

Max 1878e6times106

18

16

14

12

1

08

06

04

02

Min 110e4

Figure 9 Knee cartilage von Misses stress distribution [Pa]

8 Computational and Mathematical Methods in Medicine

used for assessment of gait parameter using a cheaper mobilecell camera This will be a consideration of the future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This paper is supported by theMinistry of Education Scienceand Technological Development of the Republic of Serbia(Projects numbers III41007 and ON 174028)

References

[1] I Kutzner B Heinlein F Graichen et al ldquoLoading of the kneejoint during activities of daily living measured in vivo in fivesubjectsrdquo Journal of Biomechanics vol 43 no 11 pp 2164ndash21732010

[2] G Li S K van deVelde and J T Bingham ldquoValidation of a non-invasive fluoroscopic imaging technique for the measurementof dynamic knee joint motionrdquo Journal of Biomechanics vol 41no 7 pp 1616ndash1622 2008

[3] C Reinschmidt A J van den Bogert A Lundberg et alldquoTibiofemoral and tibiocalcanealmotion duringwalking exter-nal vs Skeletal markersrdquo Gait and Posture vol 6 no 2 pp 98ndash109 1997

[4] N H Yang P K Canavan H Nayeb-Hashemi B Najafi and AVaziri ldquoProtocol for constructing subject-specific biomechani-cal models of knee jointrdquo Computer Methods in Biomechanicsand Biomedical Engineering vol 13 no 5 pp 589ndash603 2010

[5] M D Djuric-Jovicic N S Jovicic and D B Popovic ldquoKine-matics of gait new method for angle estimation based onaccelerometersrdquo Sensors vol 11 no 11 pp 10571ndash10585 2011

[6] H Dejnabadi B M Jolles and K Aminian ldquoA new approach toaccurate measurement of uniaxial joint angles based on a com-bination of accelerometers and gyroscopesrdquo IEEE Transactionson Biomedical Engineering vol 52 no 8 pp 1478ndash1484 2005

[7] K Tong and M H Granat ldquoA practical gait analysis systemusing gyroscopesrdquoMedical Engineering and Physics vol 21 no2 pp 87ndash94 1999

[8] W Tao T Liu R Zheng and H Feng ldquoGait analysis usingwearable sensorsrdquo Sensors vol 12 no 2 pp 2255ndash2283 2012

[9] Y Wang Y Fan and M Zhang ldquoComparison of stress onknee cartilage during kneeling and standing using finite elementmodelsrdquoMedical Engineering amp Physics vol 36 no 4 pp 439ndash447 2014

[10] K S Halonen M E Mononen J S Jurvelin J Toyras J Saloand R K Korhonen ldquoDeformation of articular cartilage duringstatic loading of a knee jointmdashexperimental and finite elementanalysisrdquo Journal of Biomechanics vol 47 no 10 pp 2467ndash24742014

[11] Y Dabiri and L P Li ldquoAltered knee joint mechanics in sim-ple compression associated with early cartilage degenerationrdquoComputational amp Mathematical Methods in Medicine vol 2013Article ID 862903 11 pages 2013

[12] N Filipovic R Vulovic A Peulic R Radakovic D Kosanicand B Ristic ldquoNoninvasive determination of knee cartilagedeformation during jumpingrdquo Journal of Sports Science andMedicine vol 8 no 4 pp 584ndash590 2009

[13] J Wismans F Veldpaus J Janssen A Huson and P StrubenldquoA three-dimensional mathematical model of the knee-jointrdquoJournal of Biomechanics vol 13 no 8 pp 677ndash685 1980

[14] M Kojic N Filipovic and S Mijailovic ldquoA large strain finiteelement analysis of cartilage deformation with electrokineticcouplingrdquo Computer Methods in Applied Mechanics and Engi-neering vol 190 no 18-19 pp 2447ndash2464 2001

[15] E H Garling B L Kaptein B Mertens et al ldquoSoft-tissueartefact assessment during step-up using fluoroscopy and skin-mountedmarkersrdquo Journal of Biomechanics vol 40 supplement1 pp S18ndashS24 2007

[16] C-C Chen Y-J Chen S-C Chen H-S Lin and T-W LuldquoEvaluation of soft-tissue artifacts when using anatomical andtechnical markers to measure mandibular motionrdquo Journal ofDental Sciences vol 6 no 2 pp 95ndash101 2011

[17] R Dumas V Camomilla T Bonci L Cheze and A CappozzoldquoGeneralized mathematical representation of the soft tissueartefactrdquo Journal of Biomechanics vol 47 no 2 pp 476ndash4812014

[18] B B Avants N Tustison and G Song ldquoAdvanced normal-ization tools (ANTS)rdquo The Insight Journal 2009 httphdlhandlenet103803113

[19] R Bajcsy and S Kovacic ldquoMultiresolution elastic matchingrdquoComputer Vision Graphics and Image Processing vol 46 no1 pp 1ndash21 1989

[20] N Filipovic M Kojic M Zivkovic R Slavkovic and NGrujovic PAK-FS Finite Element Program for Fluid-StructureInteraction Faculty of Mechanical Engineering University ofKragujevac Kragujevac Serbia 2010

[21] Z Ming and F Yubo Computational Biomechanics of theMusculoskeletal System CRC Press 2014

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

4 Computational and Mathematical Methods in Medicine

Thefinal continuity equation using the elastic constitutive lawand fluid incompressibility was given in the form

nabla119879q + (m119879 minus m119879C119864

3119870119904

) e

+ (1 minus 119899

119870119904

+119899

119870119891

minusm119879C119864m91198702119904

) p = 0

(12)

The resulting FE system of equations was solved incremen-tally [14] with a time step Δ119905 We imposed the condition thatthe balance equations are satisfied at the end of each time step(119905+Δ119905) Hence we derived the following system of equations

[[[[[

[

muu 0 0 0

0 0 0 0

mqu 0 0 0

0 0 0 0

]]]]]

]

119905+Δ119905u119905+Δ119905p119905+Δ119905q119905+Δ119905

+

[[[[[

[

0 0 cuq 0

cpu cpp 0 0

0 0 cqq 0

0 0 0 0

]]]]]

]

119905+Δ119905u119905+Δ119905p119905+Δ119905q119905+Δ119905

+

[[[[[

[

kuu kup 0 0

0 0 kpq 0

0 kqp kqq kq1206010 k120601p 0 k

120601120601

]]]]]

]

ΔuΔpΔqΔ120601

=

119905+Δ119905

119865u119905+Δ119905

119865p119905+Δ119905

119865q119905+Δ119905

119865120601

(13)

where 119865u 119865p 119865q and 119865120601were forces in the balance equa-

tions for displacement pressure fluid velocity and electricalpotential respectively andmuu andmqu were mass terms inmass matrix [14]

22 Experimental Parts In this study we used a commercialmotion capture system OptiTrack This system consists ofsix infrared cameras and four retroreflective markers Themarkers are 15 cm in diameter and are attached at the preciseanatomical locations of the participantrsquos leg for unilateralgain analysis These locations were great trochanter regionfemoral lateral epicondyle tuberosity of the tibia and thecenter of the anterior region of ankle joint (see Figure 3)

The computerized camera system with accompanyingsoftware captures the exact motion of retroreflective markersand thus records their trajectorywhile the volunteer performswalking over the force plate The cameras were connectedto a computer that collects gait kinematical data The resultof motion tracking is a series of 3D coordinates for eachnumbered marker To better understand kinematics andkinetics of gait we used a three-axial accelerometer

We used Sun SPOT accelerometers (Sun Small Pro-grammable Object Technology) to wirelessly detect the mid-dle of the gait stance phase that is the moment when theground reaction force reaches its maximum value The Sun

Great trochanter region

Femoral lateral epicondyle

Tuberosity of the tibia

Center of ankle joint

Figure 3 Reflective markers position on the examinee leg

SPOT has a sensor board which consists of 2G6G 3-axisaccelerometer temperature sensor and light sensor In theexperimental part the Sun SPOT LIS3L02AQ accelerometeris used to measure the orientation or motion in threedimensions119883 119884 and119885with the sample rate of 100Hz Eachof these components represents the sumof static accelerationsdefined by angle of inclination to the corresponding axis anddynamics component stemming from the movement duringthe walk The ground reaction force was sampled from themultiaxis AMTI force plate at the rate of 100Hz Beforethe experiment calibration was conducted to work out thespace coordinate system for the camera system field of viewThe calibration was performed fully in accordance with theproposed manufacturerrsquos procedure

The volunteer performs walking along 25 meter distancepath away with his own ordinary velocity and attachedinfrared marker and accelerometers sensor on the left legResults for marker coordinates and corresponding accel-erations measured by the three-axial accelerometer arepresented in Figure 4

According to [15ndash17]measured values formarker positionare influenced by noise due to the wobbling of the partici-pantrsquos skin The value of this uncertainty is in range plusmn2mm

The force plate is positioned in the first half of the walkingpath During the experiment the participants were asked towalk along so the force plate records the value of the groundreaction force (Figure 5)

The force value is zero in the beginning of the walkand when the participant stands on the force plate startingwith the heel the force gradually increases and reaches themaximum and then drops to zero again when the foot isdetached by the force plate

Computational and Mathematical Methods in Medicine 5

0 05 1 15 2 25 3 35 4450

500

550

600

650

Time (s)

Posit

ion

(mm

)

0 05 1 15 2 25 3 35 4 45minus4

minus2

0

2

4

Time (s)

Femoral lateral epicondyleTuberosity of tibia

Y

Z

X

Acce

lera

tion

(m2s

)

Figure 4 Position of reflective marker during walking and corre-sponding three-axial acceleration

3 Results

One of the main tasks for preparing data for FEM simulationis matching the infrared reflective marker position obtainedby infrared camera and landmark position on the CT imageswhen cartilage is unreformed This procedure is knownas image registration and ANTs (Free software for imageregistration) is used [18]

Main goal of the registration process is obtained fromthe transformation parameter that maps the marker positionin deformed and undeformed knee cartilage In general thisprocess is finding the optimal transformation thatmaps everypixel of image with the presence of deformation and anotherstatic image when cartilage is undeformed As similaritymeasure of image the mutual information is used The stan-dard algorithm in registration process is elastic deformationprocedure The idea is to model the contours on one of thematching images as elastic object which deformed under theinfluence of some external forces [19] In each step of thedeformation the images are compared and value of externalforces is now proportional to the difference between thesecases on the basis of mutual information value The processis repeated until the difference between the images is greaterthan some error of convergence The result of registrationbetween CT and infrared images is shown in Figure 6The measured difference of the marker positions betweendeformed and undeformed cartilage is 178plusmn06mm Imagesshowing markers matching these cases are presented inFigures 6(a) and 6(c) respectivelyThemeasured uncertaintyof 006mm corresponds to the dimension of a single pixelThe error in estimation of the deformation is significantly

0 05 1 15 2 25 3 35 4Time (s)

minus1000

100200300400500600

Forc

e (N

)

Figure 5 Ground reaction forces during standing on the force plate

greater due to the influence of the distortion of the cameralens skin movements and insufficiently accurate registrationresult

Simultaneously we create a 3D model using CT slicesThe CT slices are segmented using a threshold value andcompared with gray value of the image pixel The segmentedimages are submitted by the edge detection operator forboundary extraction The merging of adjacent boundary isdone in each slice and final 3D model is created (Figure 2)This model includes femur tibia cartilage surroundingtissue and skin

The anatomical point (tuberosity of tibia and femorallateral epicondyle) can be easily detected in the modeland initial position of the marker can be obtained Usingthe measured position of infrared marker (Figure 4) andanatomical position of the marked point on the created 3Dmodel (Figure 7(c)) we can obtain a vertical deformation ofcartilage as difference of these valuesThe observedmeasuredvalue coincides with the point when the ground reactionforce is in the maximum According to Figure 5 this momentis 149 seconds after starting the recording of gait and thedeformation is 230 plusmn 001mmThe measured uncertainty of001mm emerges as a consequence of the limited resolutionof the motion capture camera system and resolution of theCT scanner This methodology for obtained deformation ismore precise than registration method but it requires moreprocessor time and memory

Using the same procedure for image segmentation a fullmodel of knee joint is created The model consists of femurtibia and cartilage

We used measured values for the displacement andground reaction force in order to calculate correspondingmatrix elements in the relation (13) Upon model creationwe applied boundary conditions (a) we clamped the distalend of tibia and (b) axially loaded the femur with themaximally measured ground reaction force 119865

119892 max = 511N(Figure 8(a))

Formodeling the cartilage andmeniscuswe implementeda finite element formulation where the nodal variables aredisplacements of solid u fluid pressure p Darcyrsquos velocityq and electrical potential 120601 with estimated matrix elementsA standard procedure of integration over the element volumewas performed and the Gaussrsquos theorem was employed Animplicit time integration scheme was implemented

The tetrahedralmeshmodel had 20537 elements and 4693nodes (Figure 8(b)) We used PAK solver [20] for the FEM

6 Computational and Mathematical Methods in Medicine

(a) (b) (c)

Figure 6 Registration infrared image and CT image (a) Infrared camera image (b) CT image (c) registered image

(a) (b) (c)

Femoral lateral epicondyle

Tuberosity of the tibia

Figure 7 3D model of knee (a) Raw CT slices (b) segmented CT images (c) 3D model with marker position

analysis Total execution time of the analysis was around 30minutes on the core I7 processorwith 12GBof RAMmemory

The initial mechanical characteristic Youngrsquos modulusand Poissonrsquos ratio for the femur and tibia were amountedto 119864 = 20GPa and ] = 03 for the isotropic cartilage119864 = 10MPa and ] = 045 and for the transversely isotropicmenisci 119864 = 20MPa and ] = 03 All these values were takenfrom the literature [21]

These values were adaptively changed for the purposeof correspondence between the measured deformation andground reaction force

The final value of the Youngrsquos modulus of the cartilage is562MPa with error of estimation of 001MPa The Youngrsquosmodulus for the femur and tibia is adapted to the 18GPawhilethe Poisonrsquos ratio is 045

Resultant stress distribution of the FEM analysis for theelements of the knee joint is given in Figure 8(c)

The von Mises stress on the cartilage is presented inFigure 9 As it can be seen the maximal value of stress hasMPa magnitude of order and is located on the boundaryof the cartilage This is in compliance with the fact that iscartilage is the weakest part of the knee joint with a tendencyto injury and fraying

The procedure described in this study can offer very use-ful information for physicians in order to better understandinjury formation and improve the process of rehabilitation

and in some perspective as a support in clinical decisionmaking

4 Conclusion

The main goal of this study was to introduce a newapproach towards a noninvasive effective stress calculationfor a specific participant Input data were provided from theexperimental measurements during the participantrsquos walkingtest whereupon finite element analysis was performed givingthe distribution of the effective stress in the major anatomicalelements of the knee joint femur tibia and cartilage Thisapproach demonstrates a great possibility for preoperativeand postoperative surgical planning and treatment of theknee injuries for specific patients

This study contains some limitations We neglected theskin movement artifact during the experiment and theinfluence of ligament presence However the current modelallows us to investigate the effect of different biomechanicalfactors and loads on the stress distribution at the knee joint Inthis study we used data obtained from infrared cameras andforce plate sensors Besides in our future work we will try toreplace a relatively expensive system of infrared cameras witha much cost effective system of accelerometers so that we willbe able to calculate positional data of anatomical points of thelower extremities solely by using their accelerationsThe verypromising are techniques of the image registration that can be

Computational and Mathematical Methods in Medicine 7

Fg max

(a) (b)

Max 2695e6times106

25

2

15

1

05

Min 1316341

(c)

Figure 8 FEM analysis model (a) Model filled with the tetrahedral mesh element (b) knee von Misses stress distribution in [Pa]

Max 1878e6times106

18

16

14

12

1

08

06

04

02

Min 110e4

Figure 9 Knee cartilage von Misses stress distribution [Pa]

8 Computational and Mathematical Methods in Medicine

used for assessment of gait parameter using a cheaper mobilecell camera This will be a consideration of the future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This paper is supported by theMinistry of Education Scienceand Technological Development of the Republic of Serbia(Projects numbers III41007 and ON 174028)

References

[1] I Kutzner B Heinlein F Graichen et al ldquoLoading of the kneejoint during activities of daily living measured in vivo in fivesubjectsrdquo Journal of Biomechanics vol 43 no 11 pp 2164ndash21732010

[2] G Li S K van deVelde and J T Bingham ldquoValidation of a non-invasive fluoroscopic imaging technique for the measurementof dynamic knee joint motionrdquo Journal of Biomechanics vol 41no 7 pp 1616ndash1622 2008

[3] C Reinschmidt A J van den Bogert A Lundberg et alldquoTibiofemoral and tibiocalcanealmotion duringwalking exter-nal vs Skeletal markersrdquo Gait and Posture vol 6 no 2 pp 98ndash109 1997

[4] N H Yang P K Canavan H Nayeb-Hashemi B Najafi and AVaziri ldquoProtocol for constructing subject-specific biomechani-cal models of knee jointrdquo Computer Methods in Biomechanicsand Biomedical Engineering vol 13 no 5 pp 589ndash603 2010

[5] M D Djuric-Jovicic N S Jovicic and D B Popovic ldquoKine-matics of gait new method for angle estimation based onaccelerometersrdquo Sensors vol 11 no 11 pp 10571ndash10585 2011

[6] H Dejnabadi B M Jolles and K Aminian ldquoA new approach toaccurate measurement of uniaxial joint angles based on a com-bination of accelerometers and gyroscopesrdquo IEEE Transactionson Biomedical Engineering vol 52 no 8 pp 1478ndash1484 2005

[7] K Tong and M H Granat ldquoA practical gait analysis systemusing gyroscopesrdquoMedical Engineering and Physics vol 21 no2 pp 87ndash94 1999

[8] W Tao T Liu R Zheng and H Feng ldquoGait analysis usingwearable sensorsrdquo Sensors vol 12 no 2 pp 2255ndash2283 2012

[9] Y Wang Y Fan and M Zhang ldquoComparison of stress onknee cartilage during kneeling and standing using finite elementmodelsrdquoMedical Engineering amp Physics vol 36 no 4 pp 439ndash447 2014

[10] K S Halonen M E Mononen J S Jurvelin J Toyras J Saloand R K Korhonen ldquoDeformation of articular cartilage duringstatic loading of a knee jointmdashexperimental and finite elementanalysisrdquo Journal of Biomechanics vol 47 no 10 pp 2467ndash24742014

[11] Y Dabiri and L P Li ldquoAltered knee joint mechanics in sim-ple compression associated with early cartilage degenerationrdquoComputational amp Mathematical Methods in Medicine vol 2013Article ID 862903 11 pages 2013

[12] N Filipovic R Vulovic A Peulic R Radakovic D Kosanicand B Ristic ldquoNoninvasive determination of knee cartilagedeformation during jumpingrdquo Journal of Sports Science andMedicine vol 8 no 4 pp 584ndash590 2009

[13] J Wismans F Veldpaus J Janssen A Huson and P StrubenldquoA three-dimensional mathematical model of the knee-jointrdquoJournal of Biomechanics vol 13 no 8 pp 677ndash685 1980

[14] M Kojic N Filipovic and S Mijailovic ldquoA large strain finiteelement analysis of cartilage deformation with electrokineticcouplingrdquo Computer Methods in Applied Mechanics and Engi-neering vol 190 no 18-19 pp 2447ndash2464 2001

[15] E H Garling B L Kaptein B Mertens et al ldquoSoft-tissueartefact assessment during step-up using fluoroscopy and skin-mountedmarkersrdquo Journal of Biomechanics vol 40 supplement1 pp S18ndashS24 2007

[16] C-C Chen Y-J Chen S-C Chen H-S Lin and T-W LuldquoEvaluation of soft-tissue artifacts when using anatomical andtechnical markers to measure mandibular motionrdquo Journal ofDental Sciences vol 6 no 2 pp 95ndash101 2011

[17] R Dumas V Camomilla T Bonci L Cheze and A CappozzoldquoGeneralized mathematical representation of the soft tissueartefactrdquo Journal of Biomechanics vol 47 no 2 pp 476ndash4812014

[18] B B Avants N Tustison and G Song ldquoAdvanced normal-ization tools (ANTS)rdquo The Insight Journal 2009 httphdlhandlenet103803113

[19] R Bajcsy and S Kovacic ldquoMultiresolution elastic matchingrdquoComputer Vision Graphics and Image Processing vol 46 no1 pp 1ndash21 1989

[20] N Filipovic M Kojic M Zivkovic R Slavkovic and NGrujovic PAK-FS Finite Element Program for Fluid-StructureInteraction Faculty of Mechanical Engineering University ofKragujevac Kragujevac Serbia 2010

[21] Z Ming and F Yubo Computational Biomechanics of theMusculoskeletal System CRC Press 2014

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

Computational and Mathematical Methods in Medicine 5

0 05 1 15 2 25 3 35 4450

500

550

600

650

Time (s)

Posit

ion

(mm

)

0 05 1 15 2 25 3 35 4 45minus4

minus2

0

2

4

Time (s)

Femoral lateral epicondyleTuberosity of tibia

Y

Z

X

Acce

lera

tion

(m2s

)

Figure 4 Position of reflective marker during walking and corre-sponding three-axial acceleration

3 Results

One of the main tasks for preparing data for FEM simulationis matching the infrared reflective marker position obtainedby infrared camera and landmark position on the CT imageswhen cartilage is unreformed This procedure is knownas image registration and ANTs (Free software for imageregistration) is used [18]

Main goal of the registration process is obtained fromthe transformation parameter that maps the marker positionin deformed and undeformed knee cartilage In general thisprocess is finding the optimal transformation thatmaps everypixel of image with the presence of deformation and anotherstatic image when cartilage is undeformed As similaritymeasure of image the mutual information is used The stan-dard algorithm in registration process is elastic deformationprocedure The idea is to model the contours on one of thematching images as elastic object which deformed under theinfluence of some external forces [19] In each step of thedeformation the images are compared and value of externalforces is now proportional to the difference between thesecases on the basis of mutual information value The processis repeated until the difference between the images is greaterthan some error of convergence The result of registrationbetween CT and infrared images is shown in Figure 6The measured difference of the marker positions betweendeformed and undeformed cartilage is 178plusmn06mm Imagesshowing markers matching these cases are presented inFigures 6(a) and 6(c) respectivelyThemeasured uncertaintyof 006mm corresponds to the dimension of a single pixelThe error in estimation of the deformation is significantly

0 05 1 15 2 25 3 35 4Time (s)

minus1000

100200300400500600

Forc

e (N

)

Figure 5 Ground reaction forces during standing on the force plate

greater due to the influence of the distortion of the cameralens skin movements and insufficiently accurate registrationresult

Simultaneously we create a 3D model using CT slicesThe CT slices are segmented using a threshold value andcompared with gray value of the image pixel The segmentedimages are submitted by the edge detection operator forboundary extraction The merging of adjacent boundary isdone in each slice and final 3D model is created (Figure 2)This model includes femur tibia cartilage surroundingtissue and skin

The anatomical point (tuberosity of tibia and femorallateral epicondyle) can be easily detected in the modeland initial position of the marker can be obtained Usingthe measured position of infrared marker (Figure 4) andanatomical position of the marked point on the created 3Dmodel (Figure 7(c)) we can obtain a vertical deformation ofcartilage as difference of these valuesThe observedmeasuredvalue coincides with the point when the ground reactionforce is in the maximum According to Figure 5 this momentis 149 seconds after starting the recording of gait and thedeformation is 230 plusmn 001mmThe measured uncertainty of001mm emerges as a consequence of the limited resolutionof the motion capture camera system and resolution of theCT scanner This methodology for obtained deformation ismore precise than registration method but it requires moreprocessor time and memory

Using the same procedure for image segmentation a fullmodel of knee joint is created The model consists of femurtibia and cartilage

We used measured values for the displacement andground reaction force in order to calculate correspondingmatrix elements in the relation (13) Upon model creationwe applied boundary conditions (a) we clamped the distalend of tibia and (b) axially loaded the femur with themaximally measured ground reaction force 119865

119892 max = 511N(Figure 8(a))

Formodeling the cartilage andmeniscuswe implementeda finite element formulation where the nodal variables aredisplacements of solid u fluid pressure p Darcyrsquos velocityq and electrical potential 120601 with estimated matrix elementsA standard procedure of integration over the element volumewas performed and the Gaussrsquos theorem was employed Animplicit time integration scheme was implemented

The tetrahedralmeshmodel had 20537 elements and 4693nodes (Figure 8(b)) We used PAK solver [20] for the FEM

6 Computational and Mathematical Methods in Medicine

(a) (b) (c)

Figure 6 Registration infrared image and CT image (a) Infrared camera image (b) CT image (c) registered image

(a) (b) (c)

Femoral lateral epicondyle

Tuberosity of the tibia

Figure 7 3D model of knee (a) Raw CT slices (b) segmented CT images (c) 3D model with marker position

analysis Total execution time of the analysis was around 30minutes on the core I7 processorwith 12GBof RAMmemory

The initial mechanical characteristic Youngrsquos modulusand Poissonrsquos ratio for the femur and tibia were amountedto 119864 = 20GPa and ] = 03 for the isotropic cartilage119864 = 10MPa and ] = 045 and for the transversely isotropicmenisci 119864 = 20MPa and ] = 03 All these values were takenfrom the literature [21]

These values were adaptively changed for the purposeof correspondence between the measured deformation andground reaction force

The final value of the Youngrsquos modulus of the cartilage is562MPa with error of estimation of 001MPa The Youngrsquosmodulus for the femur and tibia is adapted to the 18GPawhilethe Poisonrsquos ratio is 045

Resultant stress distribution of the FEM analysis for theelements of the knee joint is given in Figure 8(c)

The von Mises stress on the cartilage is presented inFigure 9 As it can be seen the maximal value of stress hasMPa magnitude of order and is located on the boundaryof the cartilage This is in compliance with the fact that iscartilage is the weakest part of the knee joint with a tendencyto injury and fraying

The procedure described in this study can offer very use-ful information for physicians in order to better understandinjury formation and improve the process of rehabilitation

and in some perspective as a support in clinical decisionmaking

4 Conclusion

The main goal of this study was to introduce a newapproach towards a noninvasive effective stress calculationfor a specific participant Input data were provided from theexperimental measurements during the participantrsquos walkingtest whereupon finite element analysis was performed givingthe distribution of the effective stress in the major anatomicalelements of the knee joint femur tibia and cartilage Thisapproach demonstrates a great possibility for preoperativeand postoperative surgical planning and treatment of theknee injuries for specific patients

This study contains some limitations We neglected theskin movement artifact during the experiment and theinfluence of ligament presence However the current modelallows us to investigate the effect of different biomechanicalfactors and loads on the stress distribution at the knee joint Inthis study we used data obtained from infrared cameras andforce plate sensors Besides in our future work we will try toreplace a relatively expensive system of infrared cameras witha much cost effective system of accelerometers so that we willbe able to calculate positional data of anatomical points of thelower extremities solely by using their accelerationsThe verypromising are techniques of the image registration that can be

Computational and Mathematical Methods in Medicine 7

Fg max

(a) (b)

Max 2695e6times106

25

2

15

1

05

Min 1316341

(c)

Figure 8 FEM analysis model (a) Model filled with the tetrahedral mesh element (b) knee von Misses stress distribution in [Pa]

Max 1878e6times106

18

16

14

12

1

08

06

04

02

Min 110e4

Figure 9 Knee cartilage von Misses stress distribution [Pa]

8 Computational and Mathematical Methods in Medicine

used for assessment of gait parameter using a cheaper mobilecell camera This will be a consideration of the future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This paper is supported by theMinistry of Education Scienceand Technological Development of the Republic of Serbia(Projects numbers III41007 and ON 174028)

References

[1] I Kutzner B Heinlein F Graichen et al ldquoLoading of the kneejoint during activities of daily living measured in vivo in fivesubjectsrdquo Journal of Biomechanics vol 43 no 11 pp 2164ndash21732010

[2] G Li S K van deVelde and J T Bingham ldquoValidation of a non-invasive fluoroscopic imaging technique for the measurementof dynamic knee joint motionrdquo Journal of Biomechanics vol 41no 7 pp 1616ndash1622 2008

[3] C Reinschmidt A J van den Bogert A Lundberg et alldquoTibiofemoral and tibiocalcanealmotion duringwalking exter-nal vs Skeletal markersrdquo Gait and Posture vol 6 no 2 pp 98ndash109 1997

[4] N H Yang P K Canavan H Nayeb-Hashemi B Najafi and AVaziri ldquoProtocol for constructing subject-specific biomechani-cal models of knee jointrdquo Computer Methods in Biomechanicsand Biomedical Engineering vol 13 no 5 pp 589ndash603 2010

[5] M D Djuric-Jovicic N S Jovicic and D B Popovic ldquoKine-matics of gait new method for angle estimation based onaccelerometersrdquo Sensors vol 11 no 11 pp 10571ndash10585 2011

[6] H Dejnabadi B M Jolles and K Aminian ldquoA new approach toaccurate measurement of uniaxial joint angles based on a com-bination of accelerometers and gyroscopesrdquo IEEE Transactionson Biomedical Engineering vol 52 no 8 pp 1478ndash1484 2005

[7] K Tong and M H Granat ldquoA practical gait analysis systemusing gyroscopesrdquoMedical Engineering and Physics vol 21 no2 pp 87ndash94 1999

[8] W Tao T Liu R Zheng and H Feng ldquoGait analysis usingwearable sensorsrdquo Sensors vol 12 no 2 pp 2255ndash2283 2012

[9] Y Wang Y Fan and M Zhang ldquoComparison of stress onknee cartilage during kneeling and standing using finite elementmodelsrdquoMedical Engineering amp Physics vol 36 no 4 pp 439ndash447 2014

[10] K S Halonen M E Mononen J S Jurvelin J Toyras J Saloand R K Korhonen ldquoDeformation of articular cartilage duringstatic loading of a knee jointmdashexperimental and finite elementanalysisrdquo Journal of Biomechanics vol 47 no 10 pp 2467ndash24742014

[11] Y Dabiri and L P Li ldquoAltered knee joint mechanics in sim-ple compression associated with early cartilage degenerationrdquoComputational amp Mathematical Methods in Medicine vol 2013Article ID 862903 11 pages 2013

[12] N Filipovic R Vulovic A Peulic R Radakovic D Kosanicand B Ristic ldquoNoninvasive determination of knee cartilagedeformation during jumpingrdquo Journal of Sports Science andMedicine vol 8 no 4 pp 584ndash590 2009

[13] J Wismans F Veldpaus J Janssen A Huson and P StrubenldquoA three-dimensional mathematical model of the knee-jointrdquoJournal of Biomechanics vol 13 no 8 pp 677ndash685 1980

[14] M Kojic N Filipovic and S Mijailovic ldquoA large strain finiteelement analysis of cartilage deformation with electrokineticcouplingrdquo Computer Methods in Applied Mechanics and Engi-neering vol 190 no 18-19 pp 2447ndash2464 2001

[15] E H Garling B L Kaptein B Mertens et al ldquoSoft-tissueartefact assessment during step-up using fluoroscopy and skin-mountedmarkersrdquo Journal of Biomechanics vol 40 supplement1 pp S18ndashS24 2007

[16] C-C Chen Y-J Chen S-C Chen H-S Lin and T-W LuldquoEvaluation of soft-tissue artifacts when using anatomical andtechnical markers to measure mandibular motionrdquo Journal ofDental Sciences vol 6 no 2 pp 95ndash101 2011

[17] R Dumas V Camomilla T Bonci L Cheze and A CappozzoldquoGeneralized mathematical representation of the soft tissueartefactrdquo Journal of Biomechanics vol 47 no 2 pp 476ndash4812014

[18] B B Avants N Tustison and G Song ldquoAdvanced normal-ization tools (ANTS)rdquo The Insight Journal 2009 httphdlhandlenet103803113

[19] R Bajcsy and S Kovacic ldquoMultiresolution elastic matchingrdquoComputer Vision Graphics and Image Processing vol 46 no1 pp 1ndash21 1989

[20] N Filipovic M Kojic M Zivkovic R Slavkovic and NGrujovic PAK-FS Finite Element Program for Fluid-StructureInteraction Faculty of Mechanical Engineering University ofKragujevac Kragujevac Serbia 2010

[21] Z Ming and F Yubo Computational Biomechanics of theMusculoskeletal System CRC Press 2014

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

6 Computational and Mathematical Methods in Medicine

(a) (b) (c)

Figure 6 Registration infrared image and CT image (a) Infrared camera image (b) CT image (c) registered image

(a) (b) (c)

Femoral lateral epicondyle

Tuberosity of the tibia

Figure 7 3D model of knee (a) Raw CT slices (b) segmented CT images (c) 3D model with marker position

analysis Total execution time of the analysis was around 30minutes on the core I7 processorwith 12GBof RAMmemory

The initial mechanical characteristic Youngrsquos modulusand Poissonrsquos ratio for the femur and tibia were amountedto 119864 = 20GPa and ] = 03 for the isotropic cartilage119864 = 10MPa and ] = 045 and for the transversely isotropicmenisci 119864 = 20MPa and ] = 03 All these values were takenfrom the literature [21]

These values were adaptively changed for the purposeof correspondence between the measured deformation andground reaction force

The final value of the Youngrsquos modulus of the cartilage is562MPa with error of estimation of 001MPa The Youngrsquosmodulus for the femur and tibia is adapted to the 18GPawhilethe Poisonrsquos ratio is 045

Resultant stress distribution of the FEM analysis for theelements of the knee joint is given in Figure 8(c)

The von Mises stress on the cartilage is presented inFigure 9 As it can be seen the maximal value of stress hasMPa magnitude of order and is located on the boundaryof the cartilage This is in compliance with the fact that iscartilage is the weakest part of the knee joint with a tendencyto injury and fraying

The procedure described in this study can offer very use-ful information for physicians in order to better understandinjury formation and improve the process of rehabilitation

and in some perspective as a support in clinical decisionmaking

4 Conclusion

The main goal of this study was to introduce a newapproach towards a noninvasive effective stress calculationfor a specific participant Input data were provided from theexperimental measurements during the participantrsquos walkingtest whereupon finite element analysis was performed givingthe distribution of the effective stress in the major anatomicalelements of the knee joint femur tibia and cartilage Thisapproach demonstrates a great possibility for preoperativeand postoperative surgical planning and treatment of theknee injuries for specific patients

This study contains some limitations We neglected theskin movement artifact during the experiment and theinfluence of ligament presence However the current modelallows us to investigate the effect of different biomechanicalfactors and loads on the stress distribution at the knee joint Inthis study we used data obtained from infrared cameras andforce plate sensors Besides in our future work we will try toreplace a relatively expensive system of infrared cameras witha much cost effective system of accelerometers so that we willbe able to calculate positional data of anatomical points of thelower extremities solely by using their accelerationsThe verypromising are techniques of the image registration that can be

Computational and Mathematical Methods in Medicine 7

Fg max

(a) (b)

Max 2695e6times106

25

2

15

1

05

Min 1316341

(c)

Figure 8 FEM analysis model (a) Model filled with the tetrahedral mesh element (b) knee von Misses stress distribution in [Pa]

Max 1878e6times106

18

16

14

12

1

08

06

04

02

Min 110e4

Figure 9 Knee cartilage von Misses stress distribution [Pa]

8 Computational and Mathematical Methods in Medicine

used for assessment of gait parameter using a cheaper mobilecell camera This will be a consideration of the future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This paper is supported by theMinistry of Education Scienceand Technological Development of the Republic of Serbia(Projects numbers III41007 and ON 174028)

References

[1] I Kutzner B Heinlein F Graichen et al ldquoLoading of the kneejoint during activities of daily living measured in vivo in fivesubjectsrdquo Journal of Biomechanics vol 43 no 11 pp 2164ndash21732010

[2] G Li S K van deVelde and J T Bingham ldquoValidation of a non-invasive fluoroscopic imaging technique for the measurementof dynamic knee joint motionrdquo Journal of Biomechanics vol 41no 7 pp 1616ndash1622 2008

[3] C Reinschmidt A J van den Bogert A Lundberg et alldquoTibiofemoral and tibiocalcanealmotion duringwalking exter-nal vs Skeletal markersrdquo Gait and Posture vol 6 no 2 pp 98ndash109 1997

[4] N H Yang P K Canavan H Nayeb-Hashemi B Najafi and AVaziri ldquoProtocol for constructing subject-specific biomechani-cal models of knee jointrdquo Computer Methods in Biomechanicsand Biomedical Engineering vol 13 no 5 pp 589ndash603 2010

[5] M D Djuric-Jovicic N S Jovicic and D B Popovic ldquoKine-matics of gait new method for angle estimation based onaccelerometersrdquo Sensors vol 11 no 11 pp 10571ndash10585 2011

[6] H Dejnabadi B M Jolles and K Aminian ldquoA new approach toaccurate measurement of uniaxial joint angles based on a com-bination of accelerometers and gyroscopesrdquo IEEE Transactionson Biomedical Engineering vol 52 no 8 pp 1478ndash1484 2005

[7] K Tong and M H Granat ldquoA practical gait analysis systemusing gyroscopesrdquoMedical Engineering and Physics vol 21 no2 pp 87ndash94 1999

[8] W Tao T Liu R Zheng and H Feng ldquoGait analysis usingwearable sensorsrdquo Sensors vol 12 no 2 pp 2255ndash2283 2012

[9] Y Wang Y Fan and M Zhang ldquoComparison of stress onknee cartilage during kneeling and standing using finite elementmodelsrdquoMedical Engineering amp Physics vol 36 no 4 pp 439ndash447 2014

[10] K S Halonen M E Mononen J S Jurvelin J Toyras J Saloand R K Korhonen ldquoDeformation of articular cartilage duringstatic loading of a knee jointmdashexperimental and finite elementanalysisrdquo Journal of Biomechanics vol 47 no 10 pp 2467ndash24742014

[11] Y Dabiri and L P Li ldquoAltered knee joint mechanics in sim-ple compression associated with early cartilage degenerationrdquoComputational amp Mathematical Methods in Medicine vol 2013Article ID 862903 11 pages 2013

[12] N Filipovic R Vulovic A Peulic R Radakovic D Kosanicand B Ristic ldquoNoninvasive determination of knee cartilagedeformation during jumpingrdquo Journal of Sports Science andMedicine vol 8 no 4 pp 584ndash590 2009

[13] J Wismans F Veldpaus J Janssen A Huson and P StrubenldquoA three-dimensional mathematical model of the knee-jointrdquoJournal of Biomechanics vol 13 no 8 pp 677ndash685 1980

[14] M Kojic N Filipovic and S Mijailovic ldquoA large strain finiteelement analysis of cartilage deformation with electrokineticcouplingrdquo Computer Methods in Applied Mechanics and Engi-neering vol 190 no 18-19 pp 2447ndash2464 2001

[15] E H Garling B L Kaptein B Mertens et al ldquoSoft-tissueartefact assessment during step-up using fluoroscopy and skin-mountedmarkersrdquo Journal of Biomechanics vol 40 supplement1 pp S18ndashS24 2007

[16] C-C Chen Y-J Chen S-C Chen H-S Lin and T-W LuldquoEvaluation of soft-tissue artifacts when using anatomical andtechnical markers to measure mandibular motionrdquo Journal ofDental Sciences vol 6 no 2 pp 95ndash101 2011

[17] R Dumas V Camomilla T Bonci L Cheze and A CappozzoldquoGeneralized mathematical representation of the soft tissueartefactrdquo Journal of Biomechanics vol 47 no 2 pp 476ndash4812014

[18] B B Avants N Tustison and G Song ldquoAdvanced normal-ization tools (ANTS)rdquo The Insight Journal 2009 httphdlhandlenet103803113

[19] R Bajcsy and S Kovacic ldquoMultiresolution elastic matchingrdquoComputer Vision Graphics and Image Processing vol 46 no1 pp 1ndash21 1989

[20] N Filipovic M Kojic M Zivkovic R Slavkovic and NGrujovic PAK-FS Finite Element Program for Fluid-StructureInteraction Faculty of Mechanical Engineering University ofKragujevac Kragujevac Serbia 2010

[21] Z Ming and F Yubo Computational Biomechanics of theMusculoskeletal System CRC Press 2014

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

Computational and Mathematical Methods in Medicine 7

Fg max

(a) (b)

Max 2695e6times106

25

2

15

1

05

Min 1316341

(c)

Figure 8 FEM analysis model (a) Model filled with the tetrahedral mesh element (b) knee von Misses stress distribution in [Pa]

Max 1878e6times106

18

16

14

12

1

08

06

04

02

Min 110e4

Figure 9 Knee cartilage von Misses stress distribution [Pa]

8 Computational and Mathematical Methods in Medicine

used for assessment of gait parameter using a cheaper mobilecell camera This will be a consideration of the future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This paper is supported by theMinistry of Education Scienceand Technological Development of the Republic of Serbia(Projects numbers III41007 and ON 174028)

References

[1] I Kutzner B Heinlein F Graichen et al ldquoLoading of the kneejoint during activities of daily living measured in vivo in fivesubjectsrdquo Journal of Biomechanics vol 43 no 11 pp 2164ndash21732010

[2] G Li S K van deVelde and J T Bingham ldquoValidation of a non-invasive fluoroscopic imaging technique for the measurementof dynamic knee joint motionrdquo Journal of Biomechanics vol 41no 7 pp 1616ndash1622 2008

[3] C Reinschmidt A J van den Bogert A Lundberg et alldquoTibiofemoral and tibiocalcanealmotion duringwalking exter-nal vs Skeletal markersrdquo Gait and Posture vol 6 no 2 pp 98ndash109 1997

[4] N H Yang P K Canavan H Nayeb-Hashemi B Najafi and AVaziri ldquoProtocol for constructing subject-specific biomechani-cal models of knee jointrdquo Computer Methods in Biomechanicsand Biomedical Engineering vol 13 no 5 pp 589ndash603 2010

[5] M D Djuric-Jovicic N S Jovicic and D B Popovic ldquoKine-matics of gait new method for angle estimation based onaccelerometersrdquo Sensors vol 11 no 11 pp 10571ndash10585 2011

[6] H Dejnabadi B M Jolles and K Aminian ldquoA new approach toaccurate measurement of uniaxial joint angles based on a com-bination of accelerometers and gyroscopesrdquo IEEE Transactionson Biomedical Engineering vol 52 no 8 pp 1478ndash1484 2005

[7] K Tong and M H Granat ldquoA practical gait analysis systemusing gyroscopesrdquoMedical Engineering and Physics vol 21 no2 pp 87ndash94 1999

[8] W Tao T Liu R Zheng and H Feng ldquoGait analysis usingwearable sensorsrdquo Sensors vol 12 no 2 pp 2255ndash2283 2012

[9] Y Wang Y Fan and M Zhang ldquoComparison of stress onknee cartilage during kneeling and standing using finite elementmodelsrdquoMedical Engineering amp Physics vol 36 no 4 pp 439ndash447 2014

[10] K S Halonen M E Mononen J S Jurvelin J Toyras J Saloand R K Korhonen ldquoDeformation of articular cartilage duringstatic loading of a knee jointmdashexperimental and finite elementanalysisrdquo Journal of Biomechanics vol 47 no 10 pp 2467ndash24742014

[11] Y Dabiri and L P Li ldquoAltered knee joint mechanics in sim-ple compression associated with early cartilage degenerationrdquoComputational amp Mathematical Methods in Medicine vol 2013Article ID 862903 11 pages 2013

[12] N Filipovic R Vulovic A Peulic R Radakovic D Kosanicand B Ristic ldquoNoninvasive determination of knee cartilagedeformation during jumpingrdquo Journal of Sports Science andMedicine vol 8 no 4 pp 584ndash590 2009

[13] J Wismans F Veldpaus J Janssen A Huson and P StrubenldquoA three-dimensional mathematical model of the knee-jointrdquoJournal of Biomechanics vol 13 no 8 pp 677ndash685 1980

[14] M Kojic N Filipovic and S Mijailovic ldquoA large strain finiteelement analysis of cartilage deformation with electrokineticcouplingrdquo Computer Methods in Applied Mechanics and Engi-neering vol 190 no 18-19 pp 2447ndash2464 2001

[15] E H Garling B L Kaptein B Mertens et al ldquoSoft-tissueartefact assessment during step-up using fluoroscopy and skin-mountedmarkersrdquo Journal of Biomechanics vol 40 supplement1 pp S18ndashS24 2007

[16] C-C Chen Y-J Chen S-C Chen H-S Lin and T-W LuldquoEvaluation of soft-tissue artifacts when using anatomical andtechnical markers to measure mandibular motionrdquo Journal ofDental Sciences vol 6 no 2 pp 95ndash101 2011

[17] R Dumas V Camomilla T Bonci L Cheze and A CappozzoldquoGeneralized mathematical representation of the soft tissueartefactrdquo Journal of Biomechanics vol 47 no 2 pp 476ndash4812014

[18] B B Avants N Tustison and G Song ldquoAdvanced normal-ization tools (ANTS)rdquo The Insight Journal 2009 httphdlhandlenet103803113

[19] R Bajcsy and S Kovacic ldquoMultiresolution elastic matchingrdquoComputer Vision Graphics and Image Processing vol 46 no1 pp 1ndash21 1989

[20] N Filipovic M Kojic M Zivkovic R Slavkovic and NGrujovic PAK-FS Finite Element Program for Fluid-StructureInteraction Faculty of Mechanical Engineering University ofKragujevac Kragujevac Serbia 2010

[21] Z Ming and F Yubo Computational Biomechanics of theMusculoskeletal System CRC Press 2014

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

8 Computational and Mathematical Methods in Medicine

used for assessment of gait parameter using a cheaper mobilecell camera This will be a consideration of the future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This paper is supported by theMinistry of Education Scienceand Technological Development of the Republic of Serbia(Projects numbers III41007 and ON 174028)

References

[1] I Kutzner B Heinlein F Graichen et al ldquoLoading of the kneejoint during activities of daily living measured in vivo in fivesubjectsrdquo Journal of Biomechanics vol 43 no 11 pp 2164ndash21732010

[2] G Li S K van deVelde and J T Bingham ldquoValidation of a non-invasive fluoroscopic imaging technique for the measurementof dynamic knee joint motionrdquo Journal of Biomechanics vol 41no 7 pp 1616ndash1622 2008

[3] C Reinschmidt A J van den Bogert A Lundberg et alldquoTibiofemoral and tibiocalcanealmotion duringwalking exter-nal vs Skeletal markersrdquo Gait and Posture vol 6 no 2 pp 98ndash109 1997

[4] N H Yang P K Canavan H Nayeb-Hashemi B Najafi and AVaziri ldquoProtocol for constructing subject-specific biomechani-cal models of knee jointrdquo Computer Methods in Biomechanicsand Biomedical Engineering vol 13 no 5 pp 589ndash603 2010

[5] M D Djuric-Jovicic N S Jovicic and D B Popovic ldquoKine-matics of gait new method for angle estimation based onaccelerometersrdquo Sensors vol 11 no 11 pp 10571ndash10585 2011

[6] H Dejnabadi B M Jolles and K Aminian ldquoA new approach toaccurate measurement of uniaxial joint angles based on a com-bination of accelerometers and gyroscopesrdquo IEEE Transactionson Biomedical Engineering vol 52 no 8 pp 1478ndash1484 2005

[7] K Tong and M H Granat ldquoA practical gait analysis systemusing gyroscopesrdquoMedical Engineering and Physics vol 21 no2 pp 87ndash94 1999

[8] W Tao T Liu R Zheng and H Feng ldquoGait analysis usingwearable sensorsrdquo Sensors vol 12 no 2 pp 2255ndash2283 2012

[9] Y Wang Y Fan and M Zhang ldquoComparison of stress onknee cartilage during kneeling and standing using finite elementmodelsrdquoMedical Engineering amp Physics vol 36 no 4 pp 439ndash447 2014

[10] K S Halonen M E Mononen J S Jurvelin J Toyras J Saloand R K Korhonen ldquoDeformation of articular cartilage duringstatic loading of a knee jointmdashexperimental and finite elementanalysisrdquo Journal of Biomechanics vol 47 no 10 pp 2467ndash24742014

[11] Y Dabiri and L P Li ldquoAltered knee joint mechanics in sim-ple compression associated with early cartilage degenerationrdquoComputational amp Mathematical Methods in Medicine vol 2013Article ID 862903 11 pages 2013

[12] N Filipovic R Vulovic A Peulic R Radakovic D Kosanicand B Ristic ldquoNoninvasive determination of knee cartilagedeformation during jumpingrdquo Journal of Sports Science andMedicine vol 8 no 4 pp 584ndash590 2009

[13] J Wismans F Veldpaus J Janssen A Huson and P StrubenldquoA three-dimensional mathematical model of the knee-jointrdquoJournal of Biomechanics vol 13 no 8 pp 677ndash685 1980

[14] M Kojic N Filipovic and S Mijailovic ldquoA large strain finiteelement analysis of cartilage deformation with electrokineticcouplingrdquo Computer Methods in Applied Mechanics and Engi-neering vol 190 no 18-19 pp 2447ndash2464 2001

[15] E H Garling B L Kaptein B Mertens et al ldquoSoft-tissueartefact assessment during step-up using fluoroscopy and skin-mountedmarkersrdquo Journal of Biomechanics vol 40 supplement1 pp S18ndashS24 2007

[16] C-C Chen Y-J Chen S-C Chen H-S Lin and T-W LuldquoEvaluation of soft-tissue artifacts when using anatomical andtechnical markers to measure mandibular motionrdquo Journal ofDental Sciences vol 6 no 2 pp 95ndash101 2011

[17] R Dumas V Camomilla T Bonci L Cheze and A CappozzoldquoGeneralized mathematical representation of the soft tissueartefactrdquo Journal of Biomechanics vol 47 no 2 pp 476ndash4812014

[18] B B Avants N Tustison and G Song ldquoAdvanced normal-ization tools (ANTS)rdquo The Insight Journal 2009 httphdlhandlenet103803113

[19] R Bajcsy and S Kovacic ldquoMultiresolution elastic matchingrdquoComputer Vision Graphics and Image Processing vol 46 no1 pp 1ndash21 1989

[20] N Filipovic M Kojic M Zivkovic R Slavkovic and NGrujovic PAK-FS Finite Element Program for Fluid-StructureInteraction Faculty of Mechanical Engineering University ofKragujevac Kragujevac Serbia 2010

[21] Z Ming and F Yubo Computational Biomechanics of theMusculoskeletal System CRC Press 2014

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom