Bone regeneration during distraction osteogenesis: Mechano-regulation … · 2006-11-20 · Bone regeneration during distraction osteogenesis: Mechano-regulation by shear strain and

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Bone regeneration during distraction osteogenesis: Mechano-regulationby shear strain and fluid velocity

Hanna Isakssona,b, Olivier Comasb, Corrinus C. van Donkelaarb, Jesus Mediavillab,Wouter Wilsonb, Rik Huiskesb,c, Keita Itoa,b,�

aAO Research Institute, Clavadelerstrasse 8, 7270 Davos Platz, SwitzerlandbDepartment of Biomedical Engineering, Eindhoven University of Technology, The Netherlands

cDepartment of Orthopaedics, University of Maastricht, The Netherlands

Accepted 18 September 2006

Abstract

Corroboration of mechano-regulation algorithms is difficult, partly because repeatable experimental outcomes under a controlled

mechanical environment are necessary, but rarely available. In distraction osteogenesis (DO), a controlled displacement is used to

regenerate large volumes of new bone, with predictable and reproducible outcomes, allowing to computationally study the potential

mechanisms that stimulate bone formation. We hypothesized that mechano-regulation by octahedral shear strain and fluid velocity can

predict the spatial and temporal tissue distributions seen during experimental DO. Variations in predicted tissue distributions due to

alterations in distraction rate and frequency could then also be studied. An in vivo ovine tibia experiment evaluating bone-segment

transport (distraction, 1mm/day) over an intramedullary nail was used for comparison. A 2D axisymmetric finite element model, with a

geometry originating from the experimental data, was created and included into a previously developed model of tissue differentiation.

Cells migrated and proliferated into the callus, differentiating into fibroblasts, chondrocytes or osteoblasts, dependent on the biophysical

stimuli. Matrix production was modelled with an osmotic swelling model to allow tissues to grow at individual rates. The temporal and

spatial tissue distributions predicted by the computational model agreed well with those seen experimentally. In addition, it was observed

that decreased distraction rate (0.5mm/d vs. 0.25mm/d) increased the overall time needed for complete bone regeneration, whereas

increased distraction frequency (0.5mm/12 h vs. 0.25mm/6 h) stimulated faster bone regeneration, as found in experimental findings by

others. Thus, the algorithm regulated by octahedral shear strain and fluid velocity was able to predict the bone regeneration patterns

dependent on distraction rate and frequency during DO.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Tissue differentiation; Mechanobiology; Finite-element analysis; Tissue growth; Bone-segment transport

1. Introduction

Osteogenesis has frequently been studied experimentallyand computationally. In osteogenesis, associated differen-tiation of precursor cells is sensitive to the local mechanicalenvironment. There have been several propositions of howthis is mechano-regulated. However, corroboration ofthese algorithms are difficult (Isaksson et al., 2006a),

e front matter r 2006 Elsevier Ltd. All rights reserved.

iomech.2006.09.028

ing author. AO Research Institute, Clavadelerstrasse 8,

tz, Switzerland. Tel.: +41 81 414 24 50;

22 95.

ess: [email protected] (K. Ito).

s article as: Isaksson et al., Bone regeneration during distract

omechanics (2006), doi:10.1016/j.jbiomech.2006.09.028

mostly because repeatable experimental outcomes undercontrolled mechanical environments are required, butrarely available in experimental or clinical studies.Distraction osteogenesis (DO) is a procedure by which

controlled displacement of a bone fragment is used togenerate large volumes of new bone that have been lost dueto trauma, infection or tumour resection (Ilizarov, 1989a;Richards et al., 1998). It can also be used to correct avariety of orthopaedic deformities and malformations. Theoutcome is predictable and reproducible. Therefore, it is asuitable model for studying the potential mechanisms thatstimulate bone formation and for examining the role ofmechanical forces. DO is usually separated into three

ion osteogenesis: Mechano-regulation by shear strain and fluid velocity.

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Fig. 1. Experimental and computational model. (a) The experimental

model from Brunner et al. (1994) including initial defect and corticotomy,

followed by a distraction phase (bone segment transport) and final

consolidation period. (b) The initial two-dimensional axisymmetric finite

element model was created from the experimental measurements. The

initial gap size was 1mm. The nail diameter was 7mm, the cortical bone’s

inner diameter 14mm, and outer diameter 20mm.

H. Isaksson et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]2

phases. The first is the latency phase, immediatelyfollowing osteotomy before distraction. The second is thedistraction phase in which there is active distraction of thebony segments for a certain time at specific rates (totaldistance/day) and frequencies (number of distractions/day). During this period, tissue differentiation is initiated,with some sparse bone formation. The third is theconsolidation phase, during which there is no distraction,which finally leads to bony union. The rate of boneformation during DO is directly related to the distractionrate (Ilizarov, 1989b; Li et al., 1999, 2000), frequency(Aarnes et al., 2002; Ilizarov, 1989b; Mizuta et al., 2003)and the strain/stress generated in the distraction gap (Liet al., 1997, 1999). Meyer et al. (2001a) showed that themagnitude of distraction-generated mechanical tensiondirectly influenced the phenotypic differentiation of thecells within the distraction gap.

Although DO provides an attractive setting for the studyof mechanical effects on bone regeneration, very littlecomputational evaluation has been performed. Morganet al. (2006) investigated the local physical environmentwithin an osteotomy gap during long bone DO andcorrelated tissue dilatation (volumetric strain) with differ-entiation of mesenchymal tissue. They evaluated distrac-tion and tissue relaxation during one single day of thedistraction period. Loboa et al. (2005) used finite-element(FE) analysis to correlate bone formation with magnitudesof tensile strain and hydrostatic pressure (Carter et al.,1998) during mandibular DO at four time points. So far nostudies have described the process of tissue differentiationduring DO both spatially and temporally during thecomplete distraction process. This type of computationalevaluation of DO will provide useful information about thelocal stress and strain magnitudes that lead to the highestamount of bone regeneration, and enable optimization oftreatments.

The mechano-regulation algorithm based on octahedralshear strain and fluid velocity was proposed by Prendergastet al. (1997) as a general tissue differentiation scheme. Thethreshold values for this algorithm were initially determinedto predict bone formation around implants (Huiskes et al.,1997). Thereafter it has been shown to predict tissuedifferentiation during secondary fracture healing (Lacroixand Prendergast, 2002; Lacroix et al., 2002; Isaksson et al.,2006b), in bone chambers (Geris et al., 2003, 2004) and duringosteochondral defect repair (Kelly and Prendergast, 2005).Recently, we demonstrated that it was more consistent withbone healing under both shear and compressive deformations(Isaksson et al., 2006a) than other algorithms (Carter et al.,1998; Claes and Heigele, 1999; Isaksson et al., 2006b).

During DO the tissue is subjected to tension, amechanical mode for which this algorithm has never beentested. For this study, we hypothesized that mechano-regulation by octahedral shear strain and fluid velocity canalso predict spatial and temporal tissue distributions seenexperimentally during DO, including variations due toalteration in distraction rate and frequency.

Please cite this article as: Isaksson et al., Bone regeneration during distract

Journal of Biomechanics (2006), doi:10.1016/j.jbiomech.2006.09.028

2. Methods

2.1. Experimental model

Data from an ovine in vivo experiment for evaluation of bone segment

transport over an intramedullary nail, previously conducted in our

institution, was used for comparison (Brunner et al., 1993, 1994). A distal

diaphyseal defect, either 20 or 45mm, was created in the left tibia. The

tibia was then stabilized with an unreamed static interlocking nail. After

corticotomy, bone segments were transported (distracted) using subcuta-

neous traction wires over the nail (Fig. 1(a)). Distraction started on post-

operative day 1 with a rate of 1mm/d until the defect was closed, followed

by consolidation. Animals were sacrificed after 12 weeks for the short

defects and 16 weeks for the long defects. Daily distraction forces were

measured before (resting force), during (peak force) and 5min after

distraction. The resting force represented the tension between the

distracted segment and the fixator before distraction. The peak force

was the sum of all forces between fixator and distracted segment after

1mm distraction. The relaxation behaviour was calculated as the

difference between resting force and peak force, divided by the peak

force, and was used as a measure of the viscoelasticity of the tissue.

Weekly standardized radiographs and undecalcified histology at the time

of completed transport were available for comparison.

2.2. FE model

A 2D axisymmetric FE mesh was created based on the geometry of the

tibia, the nail and the callus from the experimental data (Brunner et al.,

1994) (Fig. 1(b)). The initial corticotomy gap was set to 1mm. Boundary

conditions were applied according to the experimental model. The ends of

bone and marrow and the external callus boundary were assumed

impermeable. Distraction (1mm/d for 20 or 45 d) was applied to the top of

the cortical bone and started on post-operative day 1. Distraction was

followed by consolidation, where no active mechanical stimulation was

applied, according to the experimental protocol. Each iteration simulated

1 d, where distraction was performed over 1 s followed by 24 h of

relaxation, during which reaction forces were monitored. All tissues were

assumed to follow linear poroelasticity theory with properties taken from

literature (Table 1). The intramedullary nail was assumed to be rigid

compared to the biological tissues and the interfaces between the nail and

the tissues were modelled using finite sliding and zero friction (ABAQUS,

v 6.5, ABAQUS Inc. Pawtucket, RI, USA).



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Table 1

Material properties used to describe the tissues in this study

Cortical bone Marrow Granulation tissue Fibrous tissue Cartilage Immature bone Mature bone

Young’s modulus (MPa) 15750a 2 1 2b 10c 1000 6000d

Permeability (m4/Ns) 1E-17e 1E-14 1E-14 1E-14b 5E-15f 1E-13 3.7E-13g

Poisson’s ratio 0.325h 0.167 0.167 0.167 0.167i 0.325 0.325

Solid bulk modulus (MPa) 17 660a 2300j 2300j 2300j 3400k 17 660a 17 660a

Fluid bulk modulus (MPa) 2300 2300 2300 2300 2300 2300 2300

Porosity 0.04l 0.8 0.8 0.8 0.8m 0.8 0.8

a(Smit et al., 2002).b(Hori and Lewis, 1982).c(Lacroix and Prendergast, 2002).d(Claes and Heigele, 1999).e(Johnson et al., 1982).f(Armstrong and Mow, 1982).g(Ochoa and Hillberry, 1992).h(Cowin, 1999).i(Jurvelin et al., 1997).j(Anderson, 1967).k(Tepic et al., 1983).l(Schaffler and Burr, 1988).m(Mow et al., 1980).

Fig. 2. Bone regeneration as simulated in a mechano-regulated adaptive

model in MATLAB. The iterative procedure starts with a masstransport

analysis to determine cell concentrations followed by a stress analysis

where the biophysical stimuli, i.e. octahedral shear strain and fluid velocity

are calculated. The tissue phenotype is determined for each element

followed by matrix production simulated with a biphasic swelling model.

The callus geometry are re-meshed and the properties re-mapped, before

the tissue properties and cell concentrations are updated and next iteration

begins.

H. Isaksson et al. / Journal of Biomechanics ] (]]]]) ]]]–]]] 3

2.3. Adaptive tissue differentiation model

The adaptive tissue differentiation process was accomplished through

custom-written subroutines (MATLAB, The Mathworks Inc. v 7.1)

(Fig. 2) and based on an earlier adaptive model (Isaksson et al., 2006b).

The meshing of the callus was performed by an automatic meshing

algorithm into triangular elements, which were transformed into quad-

rilateral elements with a maximum area of 0.1mm2 for the FE analysis

(Brokken, 1999). The initial corticotomy consisted of granulation tissue,



without any precursor cells. The precursor cells could then migrate into

the callus from the boundaries between callus, marrow and periosteum, at

an unlimited supply. This was simulated as a diffusive process to

incorporate migration and proliferation of cells (Lacroix et al., 2002;

Isaksson et al., 2006b). The distraction was applied and the biophysical

stimuli were calculated in the FE analysis at maximal distraction. The new

tissue phenotypes were predicted according to the local magnitudes of

octahedral shear strain and fluid velocity (Prendergast et al., 1997). The

cells within an element of callus tissue were able to differentiate into

fibroblasts, chondrocytes or osteoblasts and to produce their respective

matrices. Cell differentiation and the type of matrix produced by the

present cells were only restricted by the mechanical environment. The

differentiation of the cells between one phenotype and another was not

explicitly modelled, but by having the type of matrix modulated by the

mechanical environment, tissue transformation over time and space was

modelled. There was one additional requisite that bone was only allowed

to form on already calcified surfaces (Claes and Heigele, 1999).

Matrix production of different tissue types was modelled to occur

separately, at individual rates, depending on cell type and cell density.

Matrix production and growth were simulated by applying a swelling

pressure to the growing element and considering the subsequent volume

expansion as being an increase in matrix. The biphasic swelling model of

Wilson et al. (2005) was adopted for this growth simulation. In this model

swelling pressure is given by

Dp ¼ RTð

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffic2F þ 4c2ext

qÞ � 2RTcext, (1)

where R is the gas constant, T the absolute temperature, cext the external

salt concentration and cF the fixed charged density which can be expressed

as a function of the tissue deformation as

cF ¼ cF;0nf ;0

nf ;0 � 1þ J

� �, (2)

where nf,0 is the initial fluid fraction of the tissue, cF,0 the initial amount of

negative charges in the tissue and J the determinant of the deformation

tensor. Before a simulation, all negative charges were set to zero and the

displaced geometry after the previous distraction served as input. Identical

geometrical boundary conditions were applied. Growth was induced by

introducing a non-zero amount of fixed charges in the growing element,

dependent on the cell type stimulated in the element (Table 2). The fixed-

charge density changes were chosen such that they resulted in growth/

volume changes within the range of those found experimentally for each



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Table 2

Material properties and constants used in the osmotic swelling model to predict tissue growth

Model parameters Resulting growth

nf,0 cF,0 (meq/mm3) Volume growth Bone growth rate

Fibrous tissue 0.8 7� 10�2 �15–20%

Cartilage 0.8 3.5� 10�2 �5–7%

Appositional bone growth 0.8 3.5� 10�2 �5mm/da

Endochondral bone growth 0.8 5.25� 10�2 �25mm/db

R ¼ 8.3145Nmm/mmolK

T ¼ 298K

cext ¼ 1.5� 10�4mmol/mm3

The assumed fluid fraction nf,0 and the fixed charged density cF,0 are inputs and the volume growth and bone growth rate are the calculated growth of the

various tissue types.a(Eriksen et al., 1984; Vedi et al., 2005).b(Wilsman et al., 1996a, b).


tissue type (Table 2). For bone, the amount of added fixed charges was

also dependent on whether bone formation was through intramembranous

or endochondral bone formation, i.e. which tissue type was previously

located in that element. The tissue was allowed to swell for 24 h until

equilibrium. The final tissue shape was then assumed stress free and used

as input for the next increment. Hence, all stresses induced by growth were

assumed to fully relax within 1 d. The new tissue material properties were

then calculated as the result of matrix production and degradation over

the past 5 iterations, using a rule of mixtures:

E�nþ1 ¼

Pni¼n�4Ei vgiPn

i¼n�4vgi

, (3)

where Ei was the elastic modulus at iteration i and vgi was the volume

growth fraction, calculated as the elemental volume after swelling divided

by the elemental volume before swelling pressure was induced. E�nþ1 was

the temporary new elastic modulus before considering cell distribution.

The cell concentrations were adjusted to the new tissue volumes (Eq. (4)),

such that the total cells remained the same after matrix production. The

final new modulus was calculated assuming a linear relation between the

modulus of the tissue and the number of cells with the corresponding

phenotype (Lacroix et al., 2002; Isaksson et al., 2006a, b) (Eq. (5)):

½cells�nþ1 ¼½cells�nvgn

, (4)

Enþ1 ¼½cells�nþ1½cells�max

� �E�nþ1 þ

½cells�max � ½cells�nþ1½cells�max

� �EGran, (5)

where [cells]n and [cells]n+1 were the cell densities in the elements before

and after considering growth, respectively, [cells]max was the maximal cell

density (assumed to be 100%), En+1 the final new elastic modulus and

Egran the elastic modulus for granulation tissue.

2.4. Model implementation

Marrow and cortical bone were not allowed to change material

properties or to produce matrix. Furthermore, the nail–callus interface did

not influence cell processes or matrix production. To avoid highly

deformed elements the callus was remeshed prior to every new increment

(Brokken, 1999). After remeshing all tissue properties were mapped from

the integration points of the previous mesh onto the integration points of

the new mesh, using interpolation (Peric et al., 1996; Brokken, 1999;

Mediavilla, 2005). The reaction forces of the transported bone segment

were measured with the computational model at the top of the cortical

bone during distraction and were monitored during the 24 h of matrix

production to calculate relaxation behaviour.

Temporal and spatial tissue distributions, reaction forces and force

relaxation data were evaluated and compared to experimental results.



Additionally, to explore the models’ potential to explain biological

phenomena during DO, simulations with altered distraction rate (0.5 and

0.25mm/d) and frequency (0.5mm/12 h, and 0.25mm/6 h) were con-

ducted. When the distraction frequency was altered, the matrix produc-

tion/increment was adapted accordingly to ensure equal production rates.

Thus, each iteration simulated 12 or 6 h when the frequencies were 2 or 4

distractions/d, respectively.

3. Results

The experimental results, published in detail elsewhere,showed good reproducibility (Brunner et al., 1993, 1994).Post-operatively there was a narrow corticotomy gap.During the first week of distraction ‘graining’ appeared, i.e.small slightly radio-opaque areas appeared throughout thedistraction gap without any organized pattern. From thesecond week of distraction, strips of increased radioopacity were running from the two cortical bone endsand growing towards each other. A small overlappingcallus on the periosteal side was observed. Furthermore theobserved bone growth was more substantial on theperiosteal side compared to the endosteal side and the nailinterface. During distraction of the segment, bone forma-tion was clearly observed in the longitudinal direction ofdistraction, particularly with the larger defect size, withincreasing density over time, and with highest densitycloser to the cortical ends, where the initial bone formationwas seen. Throughout continued distraction of the bonefragment an area of soft tissue was located in the middle ofthe regenerate. During consolidation, reorganization andmaturation of regenerated bone occurred. Over time, thesoft tissue gap diminished and bony bridging occurred. Ingeneral the same patterns were observed in the short andlong regenerates, but in the long ones, the different stagesof healing were more clearly distinguished.Overall, the predicted tissue distributions agreed well

with those seen experimentally (Fig. 3). During the firstweek, the mesenchymal stem cells that migrated andproliferated into the callus mainly differentiated intofibroblasts. Thus, the predicted tissue distributions wereprimarily fibrous tissue. After 7 d, differentiation into



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Fig. 3. Tissue differentiation during distraction of the long defects followed by consolidation. Distraction rate and frequency are identical to the

experimental study, i.e. 1mm/d distracted once. (a) Predicted bone regeneration pattern. The tissue type was based on the average element moduli as

determined by the mixture theory (Eqs. (3)–(5)). (b) Stimulated cell types.


osteoblasts was first observed along the periosteum and inthe gap area (Fig. 3(b), iteration (it) 10). After 15 d bonetissue could be distinguished close to the periosteum.During distraction of the segment, bone continued todevelop. Slow creeping substitution of bone was seen in thelongitudinal direction of distraction, with a higher densityat the periosteal side (Fig. 3(a), it 35). Throughoutdistraction of the bone segment, there was a gap of softtissue in-between the bony ends, which reached a steadysize between day 30 and 40. The predicted areas of bonemainly remained immature until distraction was finalized.During consolidation, maturation of the bone occurredfollowed by final bony bridging. Similar distributions andstages of tissue differentiation were seen for both defectsizes (both in simulations and experiments), but thecontinued bone growth during distraction was mainly seenin the longer defects.

Reaction forces and relaxation behaviour were alsocompared. Reaction forces increased almost linearly duringthe first weeks of distraction in the experiment with atemporary drop in the rate of increase during the thirdweek in four out of five sheep (Fig. 4(a)) (Brunner et al.,1994). Computationally, the peak force was initially higherthan experimentally found and over time it decreasedslightly due to the increased soft tissue regenerate(Fig. 4(a)). Predicted relaxation forces compared well withthe experiments (Fig. 4(b)). The stress relaxation curves ofthe tissues during transport were initially between 60% and



70% in the experiment, compared to 65% computation-ally. During distraction the relaxation increased to about80% for both experimental results and the computationalprediction (Fig. 4(b)).When the distraction rate was decreased to 0.5mm/d or

0.25mm/d the total time for bone regeneration increased,even though the amount of bone formation at the samemagnitude of total distraction increased with decreasingrate (Fig. 5). When the distraction frequency increased to0.5mm distraction two times/day, or 0.25mm distractionfour times/day, the overall rate of bone formationincreased (Fig. 6). During the first week of distraction thetissue distributions were similar and mainly fibrous for allthree frequencies, but as distraction proceeded into thesecond and third week the amount of bone formationincreased with the frequency. Also the consolidation periodnecessary to achieve complete bridging became shorterwith increased distraction frequency.

4. Discussion

A mechano-regulation algorithm based on octahedralshear strain and fluid flow was able to predict the boneformation pattern observed experimentally during DOfrom initial corticotomy to final consolidation. Thecomparison of spatial and temporal patterns of boneregeneration was successful. The first bone formation wasseen in the cortical gap at the end of week two of



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Fig. 5. Bone regeneration patterns with various distraction rates. The

distraction rates simulated were (a) 1, (b) 0.5 and (c) 0.25mm/d, all with a

frequency of 1. The tissue type was based on the average element moduli

as determined by the mixture theory (Eqs. (3)–(5)).

Fig. 4. (a) Peak reaction forces after 1mm distraction and (b) relaxation

behaviour calculated by the computational model and measured

experimentally (Brunner et al., 1994).

Fig. 6. Bone regeneration patterns with various distraction frequencies.

The total distraction rate was 1mm/d divided into (a) 1 (1mm/24 h), 2

(0.5mm/12 h), or 4 (0.25mm/6 h) distractions/day. The tissue type was

based on the average element moduli as determined by the mixture theory

(Eqs. (3)–(5)).


distraction in both experiments and predictions. Theseevents were followed by progressive bone growth in thedirection of distraction, with increased bone density at theperiosteal side. Areas of soft tissue remaining in the gapthroughout distraction of the segment, and bone matura-tion seen during consolidation, were similar in bothexperiment and computational predictions. The mechano-regulation algorithm has previously been shown suitable topredict fracture healing, as well as other bone regenerativeprocesses. Now it has been taken one step further,by successfully predicting the bone formation patternsduring DO.

During DO the tissue is subjected to tension, in contrastto fracture healing where compression is predominant.With tensile loads, for example, the fluid velocity isdirectionally reversed, when compared to compressiveloading. The mechano-regulation algorithm only considersthe magnitude of the fluid velocity, and not the direction.Hence, in terms of the mechano-regulation algorithm, theloading conditions are not very different. The magnitudesof the two stimuli after distraction are displayed in Fig. 7.Furthermore, the relaxation behaviour over 24 h is shown.This confirms that the peak values of the stimuli indeedoccur around the time of maximal distraction. The

Please cite this article as: Isaksson et al., Bone regeneration during distraction osteogenesis: Mechano-regulation by shear strain and fluid velocity.



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Fig. 7. Spatial distributions and relaxation behaviour of fluid velocity and deviatoric strain at day 5. (a) Model geometry at the beginning of day 5. Two

elements are highlighted and further relaxation behaviour of these elements are displayed in (d) and (e). Spatial distributions of (b) fluid velocity and (c)

deviatoric strain after 1mm distraction at day 5. (d), (e) The relaxation behaviour over 1 d of the fluid velocity and the deviatoric strain are displayed in

two elements in the callus. Note that the time scale (x-axis) is logarithmic.


magnitudes of fluid velocity decreased rapidly as soon asdistraction was completed (Fig. 7(c)), while the deviatoricstrain remained high during the beginning of the relaxationperiod (Fig. 7(d)). Depending on the location in the callus,the strain values even slightly increased initially duringrelaxation. In those cases, the increases were minimal anddid not affect the predicted phenotype.

The relaxation behaviour of the tissue corresponded wellwith what was measured experimentally. This occursbecause relaxation is dominated by the modulus/perme-ability ratio of the callus tissue, which did not change muchduring the distraction period. In contrast, the reactionforces from the model did not agree with the experiment.This is probably not due to the mechano-regulationalgorithm itself and the predicted pattern of tissuedifferentiation, but to additional factors in the experi-mental model that were not included in the computationalmodel. In limb lengthening, or simple DO, there areprogressively higher and higher tensions on adjacent fascia,tendons and muscles (Simpson et al., 1995; Williams et al.,1999). This is because muscles are often attached across thedistraction gap. It can increase reaction forces substantially(Aronson and Harp, 1994) and also cause considerablepain for patients undergoing DO. However, in the currentexperimental model of bone segment transport (Brunner etal., 1994), these effects were reduced because the totallength of the tibia was kept constant, and most muscles areonly attached to the proximal and distal main fragments.



Still, most likely there were some contributions from theadjacent soft tissue (including muscles) on the measuredforces. Hence, that is one source of discrepancy. Anotherprobable cause for the disagreement in forces is that unlikesimple DO, the segment transport model required thecreation of a large gap distal to the transported segment,which would have been filled with soft tissues. Withdistraction of the segment, these tissues would have beencompressed, eventually completely, and the compressionwould result in an additional force component. Finally,throughout the distraction period, with the longitudinalalignment of collagen fibers under contract traction (Meyeret al., 2001b), the modulus of the soft tissue in the gapwould have increased, similar to other collagen-orientedsoft tissues, e.g. fascia, vessels, etc. (Hudetz et al., 1981;Birk and Silver, 1984; Billiar and Sacks, 2000a, b). None ofthese effects were included in the computational modeland, in combination, may be the source of discrepancy inreaction forces when compared to experimentally measuredmagnitudes.Even though DO is mechanically well defined, some

assumptions were necessary. The peak magnitudes of themechanical parameters immediately after distraction wereconsidered for the mechano-regulation, and the subsequentrelaxation was assumed to have minimal mechano-biolo-gical effects. Loading during consolidation was neglected,because the performance of the algorithm during distrac-tion (tensile displacements) was the main focus of this



ARTICLE IN PRESSH. Isaksson et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]8

study. Thus, the resorption criteria initially suggested forthe mechano-regulation algorithm had to be excluded inthis study. The nail was modelled with finite sliding andwas assumed to have no influence on cell processes. Thisassumption was chosen since experimentally no boneformation on the nail was seen during transport. Addi-tionally, to overcome computational difficulties with highrelative strains, the initial experimental corticotomy(�0.5mm) was modelled as a gap of 1mm, and thedistraction rate was initially chosen 0.5mm/d, increasing to1mm/d at day 3. This did not influence the tissuedifferentiation process since even with the lower distractionmagnitudes, fibroblasts were stimulated during this periodand matrix production of fibrous tissue occurred.

Tissue growth and matrix production were modelledusing a new approach. The effect of local matrixproduction on tissue morphology was simulated byinducing local tissue swelling in response to osmoticpressure. The parameters were chosen such that fibroustissue would grow faster than cartilage and bone. Morespecifically, volume increases up to 20% occurred in theregions where fibroblasts saturated the tissue producingfibrous matrix, while the growth rate of cartilage was lower(5–10%). These relative growth rates are compatible withexperimental findings. The growth during bone formationcorresponded to a bone apposition rate of 5–10 mm/d (Vediet al., 2005) and when calcification of cartilage occurred thevolume growth was higher due to hypertrophy prior tomineralization (Wilsman et al., 1996a, b) and the corre-sponding bone formation rate was about 20 mm/d (Wils-man et al., 1996a, b). Fig. 8 displays an example of thismodel, where the stimulated cell types after distraction arecompared with the resulting matrix production and tissuegrowth generated with the biphasic swelling model after10 d of distraction. The osmotic swelling model, originallydeveloped to describe cartilaginous tissues, was applied to

Fig. 8. The osmotic swelling model used simulates matrix production in

an element specific manner. (a) The stimulated cell phenotypes and (b) the

resulting volume growth after 10 iterations with distraction rate of 1mm/d

and frequency of 1 distraction/day.



compute matrix production. Hence, the concentrations offixed charges included during matrix production are onlyused to achieve a new geometrical shape of the callus. Thefixed charge densities and their effects on solid/fluidcontent in the tissue have no physical meaning and arenot used in subsequent iterations. The assumption about astress free geometrical shape after swelling/growth wasmade to avoid incremental stress increases in the tissue andto allow us to use the same set of parameters to achieve thesame amount of volume increase throughout the simula-tion. Furthermore, the relaxation times for the tissues areon the order of hours (Weiss et al., 2002; Bonifasi-Listaet al., 2005; Park and Ateshian, 2006; Huang et al., 2003).Hence, by modelling 24 h relaxation and matrix produc-tion, we believe we are well on the side where theassumption can be used. The matrix constitution in eachiteration is based only on the differentiation algorithm andthe rule of mixtures (Eq. (4)).Experimental findings by others have shown that the rate

of bone formation is directly related to the local strain/stress generated in the distraction gap (Li et al., 1997,1999), and that the amount of mechanical tension directlyinfluenced the phenotypic differentiation of the cells withinthe distraction gap (Meyer et al., 2001a). Our simulationswith altered distraction rates agreed with those findings.When the tension in the gap was lowered by a reduction indistraction rate, the bone formation/day increased. Still,the most favourable distraction rate was 1mm/d, becausethe total time needed to regenerate the bone in the defectwas shorter than for lower rates. This also agrees with thefindings of Ilizarov which showed 1mm/d to be the mostfavourable rate. Additionally, experimental studies haveshown that further increases in distraction rate can bedetrimental to healing (Ilizarov, 1989b; Choi et al., 2004)and lead to a distraction gap filled with mostly fibroustissue (Choi et al., 2004). In the current study, distractionrates above 1mm/d were not examined. Hence, we cannotcompare those experimental observations with our com-putational model. Ilizarov’s studies further showed that thegreater the distraction frequency, the better the outcome(Ilizarov, 1989b). Our predictions demonstrated the samepattern, where the rate of bone regeneration increased withdistraction frequency (Fig. 6). In our model, the bestpossible bone regeneration was achieved with a totaldistraction of 1mm/d divided into 4 sub-distractions of0.25mm/6 h. Experimental studies have also suggested thatthe division in endochondral and intramembranous boneformation during DO is related to the distraction rate (Liet al., 1999; Mizuta et al., 2003; Kessler et al., 2005). Withthis model the stimulated cell phenotypes and tissue typesproduced were altered similarly. With a lower distractionrate the proportion of the cells that differentiated intoosteoblasts without first going through a cartilage inter-mediate was increased.Tissue differentiation during DO, by a mechano-regula-

tion algorithm based on octahedral shear strain and fluidvelocity, was successfully simulated from distraction to



ARTICLE IN PRESSH. Isaksson et al. / Journal of Biomechanics ] (]]]]) ]]]–]]] 9

consolidation and was confirmed by experimental observa-tions in a model of bone segment transport. The rate ofbone formation depended on distraction rate and fre-quency, similar to experimental observations. Theserelationships can now be further investigated with thisalgorithm, which could potentially help adapt and optimizeDO treatment protocols.

Acknowledgements

The authors would like to thank Prof Ulrich Brunner forproviding experimental results and the AO Foundation,Switzerland, for financial support.

References

Aarnes, G.T., Steen, H., Ludvigsen, P., Kristiansen, L.P., Reikeras, O.,

2002. High frequency distraction improves tissue adaptation during leg

lengthening in humans. Journal of Orthopaedic Research 20, 789–792.

Anderson, C.B., 1967. Mechanics of fluids. In: Baumeister, T. (Ed.),

Marks’ Saturated Handbook of Mechanical Engineers. MacGraw-

Hill, New York, pp. 3.48–3.76.

Armstrong, C.G., Mow, V.C., 1982. Variations in the intrinsic mechanical

properties of human articular cartilage with age, degeneration, and

water content. Journal of Bone Joint Surgery 64A, 88–94.

Aronson, J., Harp, J.H., 1994. Mechanical forces as predictors of healing

during tibial lengthening by distraction osteogenesis. Clinical Ortho-

paedic and Related Research 301, 73–79.

Billiar, K.L., Sacks, M.S., 2000a. Biaxial mechanical properties of the

natural and glutaraldehyde treated aortic valve cusp—Part I: experi-

mental results. Journal of Biomechanical Engineering 122, 23–30.

Billiar, K.L., Sacks, M.S., 2000b. Biaxial mechanical properties of the

native and glutaraldehyde-treated aortic valve cusp: Part II—a

structural constitutive model. Journal of Biomechanical Engineering

122, 327–335.

Birk, D.E., Silver, F.H., 1984. Collagen fibrillogenesis in vitro: comparison

of types I, II, and III. Archives of Biochemistry and Biophysics 235,

178–185.

Bonifasi-Lista, C., Lake, S.P., Small, M.S., Weiss, J.A., 2005. Viscoelastic

properties of the human medial collateral ligament under longitudinal,

transverse and shear loading. Journal of Orthopaedic Research 23,

67–76.

Brokken, D., 1999. Numerical modelling of ductile fractures in blanking.

Ph.D. Thesis, Eindhoven University of Technology.

Brunner, U.H., Cordey, J., Kessler, S., Rahn, B.A., Schweiberer, L.,

Perren, S.M., 1993. Bone segment transport in combination with an

intramedullary nail. Injury 24, S29–S44.

Brunner, U.H., Cordey, J., Schweiberer, L., Perren, S.M., 1994. Force

required for bone segment transport in the treatment of large bone

defects using medullary nail fixation. Clinical Orthopaedic and Related

Research 301, 147–155.

Carter, D.R., Beaupre, G.S., Giori, N.J., Helms, J.A., 1998. Mechan-

obiology of skeletal regeneration. Clinical Orthopaedic and Related

Research 355S, S41–S55.

Choi, P., Ogilvie, C., Thompson, T., Miclau, T., Helms, J.H., 2004.

Cellular and molecular characterization of a murine non-union model.

Journal of Orthopaedic Research 22, 1100–1107.

Claes, L.E., Heigele, C.A., 1999. Magnitudes of local stress and strain

along bony surfaces predict the course and type of fracture healing.

Journal of Biomechanics 32, 255–266.

Cowin, S.C., 1999. Bone poroelasticity. Journal of Biomechanics 32,

217–238.

Eriksen, E.F., Gundersen, H.J.G., Melsen, F., Mosekilde, L., 1984.

Reconstruction of the formative site in iliac trabecular bone in 20



normal individuals employing a kinetic model for matrix and mineral

apposition. Metabolic Bone Disease and Related Research 5, 243–252.

Geris, L., Van Oosterwyck, H., Vander, S.J., Duyck, J., Naert, I., 2003.

Assessment of mechanobiological models for the numerical simulation

of tissue differentiation around immediately loaded implants. Com-

puter Methods in Biomechanics and Biomedical Enginering 6,

277–288.

Geris, L., Andreykiv, A., Oosterwyck, H.V., Sloten, J.V., Keulen Fv, F.F.,

Duyck, J., Naert, I., 2004. Numerical simulation of tissue differentia-

tion around loaded titanium implants in a bone chamber. Journal of

Biomechanics 37, 763–769.

Hori, R.Y., Lewis, J.L., 1982. Mechanical properties of the fibrous tissue

found at the bone–cement interface following total joint replacement.

Journal of Biomedical Materials Research 16, 911–927.

Huang, C.Y., Soltz, M.A., Kopacz, M., Mow, V.C., Ateshian, G.A., 2003.

Experimental verification of the roles of intrinsic matrix viscoelasticity

and tension–compression nonlinearity in the biphasic response of

cartilage. Journal of Biomechanical Engineering 125, 84–93.

Hudetz, A.G., Mark, G., Kovach, A.G., Kerenyi, T., Fody, L., Monos,

E., 1981. Biomechanical properties of normal and fibrosclerotic human

cerebral arteries. Atherosclerosis 39, 353–365.

Huiskes, R., van Driel, W.D., Prendergast, P.J., Soballe, K., 1997. A

biomechanical regulatory model for periprosthetic fibrous-tissue

differentiation. Materials in Medicine 8, 785–788.

Ilizarov, G.A., 1989a. The tension–stress effect on the genesis and growth

of tissues. Part I. The influence of stability of fixation and soft-tissue

preservation. Clinical Orthopaedic and Related Research, 249–281.

Ilizarov, G.A., 1989b. The tension–stress effect on the genesis and growth

of tissues. Part II. The influence of the rate and frequency of

distraction. Clinical Orthopaedic and Related Research, 263–285.

Isaksson, H., Donkelaar, C.C., Huiskes, R., Ito, K., 2006a. Corroboration

of mechanoregulatory algorithms for tissue differentiation during

fracture healing: comparison with in vivo results. Journal of

Orthopaedic Research 24, 898–907.

Isaksson, H., Wilson, W., van Donkelaar, C.C., Huiskes, R., Ito, K.,

2006b. Comparison of biophysical stimuli for mechano-regulation of

tissue differentiation during fracture healing. Journal of Biomechanics

39, 1507–1516.

Johnson, M.W., Chakkalakal, D.A., Harper, R.A., Katz, J.L., Rouhana,

S.W., 1982. Fluid flow in bone in vitro. Journal of Biomechanics 15,

881–885.

Jurvelin, J.S., Buschmann, M.D., Hunziker, E.B., 1997. Optical and

mechanical determination of Poisson’s ratio of adult bovine humeral

articular cartilage. Journal of Biomechanics 30, 235–241.

Kelly, D.J., Prendergast, P.J., 2005. Mechano-regulation of stem cell

differentiation and tissue regeneration in osteochondral defects.

Journal of Biomechanics 38, 1413–1422.

Kessler, P., Neukam, F.W., Wiltfang, J., 2005. Effects of distraction forces

and frequency of distraction on bony regeneration. British Journal of

Oral and Maxillofacial Surgery 43, 392–398.

Lacroix, D., Prendergast, P.J., 2002. A mechano-regulation model for

tissue differentiation during fracture healing: analysis of gap size and

loading. Journal of Biomechanics 35, 1163–1171.

Lacroix, D., Prendergast, P.J., Li, G., Marsh, D., 2002. Biomechanical

model to simulate tissue differentiation and bone regeneration:

application to fracture healing. Medical and Biological Engineering

and Computing 40, 14–21.

Li, G., Simpson, A.H., Kenwright, J., Triffitt, J.T., 1997. Assessment of

cell proliferation in regenerating bone during distraction osteogenesis

at different distraction rates. Journal of Orthopaedic Research 15,

765–772.

Li, G., Simpson, A.H., Kenwright, J., Triffitt, J.T., 1999. Effect of

lengthening rate on angiogenesis during distraction osteogenesis.


Li, G., Virdi, A.S., Ashhurst, D.E., Simpson, A.H.R.W., Triffitt, J.T.,

2000. Tissues formed during distraction osteogenesis in the rabbit are

determined by the distraction rate: localization of the cells that expres



ARTICLE IN PRESSH. Isaksson et al. / Journal of Biomechanics ] (]]]]) ]]]–]]]10

the mRNAs and the distribution of types I and II collagens. Cell

Biology International 24, 25–33.

Loboa, E.G., Fang, T.D., Parker, D.W., Warren, S.M., Fong, K.D.,

Longaker, M.T., Carter, D.R., 2005. Mechanobiology of mandibular

distraction osteogenesis: finite element analyses with a rat model.


Mediavilla, J., 2005. Continous and discontinuous modelling of ductile

fractures. Ph.D. Thesis, Eindhoven University of Technology.

Meyer, U., Meyer, T., Wiesmann, H.P., Kruse-Losler, B., Vollmer, D.,

Stratmann, U., Joos, U., 2001a. Mechanical tension in distraction

osteogenesis regulates chondrocytic differentiation. International

Journal of Oral and Maxillofacial Surgery 30, 522–530.

Meyer, U., Wiesmann, H.P., Meyer, T., Schulze-Osthoff, D., Jasche, J.,

Kruse-Losler, B., Joos, U., 2001b. Microstructural investigation of

strain-related collagen mineralization. British Journal of Oral and

Maxillofacial Surgery 39, 381–389.

Mizuta, H., Nakamura, E., Mizumoto, Y., Kudo, S., Takagi, K., 2003. Effect

of distraction frequency on bone formation during bone lengthening: a

study in chickens. Acta Orthopaedica Scandinavica 74, 709–713.

Morgan, E.F., Longaker, M.T., Carter, D.R., 2006. Relationships

between tissue dilatation and differentiation in distraction osteogen-

esis. Matrix Biology 25, 94–103.

Mow, V.C., Kuei, S.C., Lai, W.M., Armstrong, C.G., 1980. Biphasic creep

and stress relaxation of articular cartilage in compression? Theory and

experiments. Journal of Biomechanical Engineering 102, 73–84.

Ochoa, J.A., Hillberry, B.M., 1992. Permeability of bovine cancellous

bone. In: Transactions of the 38th ORS, Washington DC.

Park, S., Ateshian, G.A., 2006. Dynamic response of immature bovine

articular cartilage in tension and compression, and nonlinear

viscoelastic modeling of the tensile response. Journal of Biomechanical

Engineering 128, 623–630.

Peric, D., Hochard, Ch., Dutko, M., Owen, D.R.J., 1996. Transfer

operators for evolving meshes in small strain elasto-placticity.

Computer Methods in Applied Mechanics and Engineering 137,

129–141.

Prendergast, P.J., Huiskes, R., Soballe, K., 1997. ESB Research Award

1996. Biophysical stimuli on cells during tissue differentiation at

implant interfaces. Journal of Biomechanics 30, 539–548.



Richards, M., Goulet, J.A., Weiss, J.A., Waanders, N.A., Schaffler, M.B.,

Goldstein, S.A., 1998. Bone regeneration and fracture healing.

Experience with distraction osteogenesis model. Clinical Orthopaedic

and Related Research 355S, S191–S204.

Schaffler, M.B., Burr, D.B., 1988. Stiffness of compact bone: effects of

porosity and density. Journal of Biomechanics 21, 13–16.

Simpson, A.H., Williams, P.E., Kyberd, P., Goldspink, G., Kenwright, J.,

1995. The response of muscle to leg lengthening. Journal of Bone and

Joint Surgery 77Br, 630–636.

Smit, T.H., Huyghe, J.M., Cowin, S.C., 2002. Estimation of the

poroelastic parameters of cortical bone. Journal of Biomechanics 35,

829–835.

Tepic, S., Macirowski, T., Mann, R.W., 1983. Mechanical properties of

articular cartilage elucidated by osmotic loading and ultrasound.

Proceedings of the National Academy of Science USA 80, 3331–3333.

Vedi, S., Elkin, S.L., Compston, J.E., 2005. A histomorphometric study of

cortical bone of the iliac crest in patients treated with glucocorticoids.

Calcified Tissue International 77, 79–83.

Weiss, J.A., Gardiner, J.C., Bonifasi-Lista, C., 2002. Ligament material

behavior is nonlinear, viscoelastic and rate-independent under shear

loading. Journal of Biomechanics 35, 943–950.

Williams, P., Simpson, H., Kyberd, P., Kenwright, J., Goldspink, G.,

1999. Effect of rate of distraction on loss of range of joint movement,

muscle stiffness, and intramuscular connective tissue content during

surgical limb-lengthening: a study in the rabbit. The Anatomical

Record 255, 78–83.

Wilsman, N.J., Farnum, C.E., Green, E.M., Lieferman, E.M., Clayton,

M.K., 1996a. Cell cycle analysis of proliferative zone chondrocytes in

growth plates elongating at different rates. Journal of Orthopaedic

Research 14, 562–572.

Wilsman, N.J., Farnum, C.E., Leiferman, E.M., Fry, M., Barreto, C.,

1996b. Differential growth by growth plates as a function of multiple

parameters of chondrocytic kinetics. Journal of Orthopaedic Research

14, 927–936.

Wilson, W., van Donkelaar, C.C., Huyghe, J.M., 2005. A comparison

between mechano-electrochemical and biphasic swelling theories for

soft hydrated tissues. Journal of Biomechanical Engineering 127,

158–165.



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