Is Callus Formation Optimised for Fracture Stability? A Computational Study

Is Callus Formation Optimised for Fracture Stability?

A Computational Study Cameron Wilson1, Graeme Pettet2, Gongfa Chen2, Sanjay Mishra1, Roland Steck1, Martin Wullschleger1, Michael Schtz1,3Schools of 1 Engineering Systems & 2 Mathematical Sciences,Institute of Health & Biomedical Innovation, Queensland University of Technology;3 Department of Orthopaedics, Princess Alexandra Hospital1As part of computer modelling, hypothesis: callus grows to size for required stiffness.Ambitious aim, but primarily pilot study - test modelling / validation methods.Models of Fracture HealingWhat local mechanical conditions required for optimal healing?Static models: match mechanics to histology(Carter et al., 1988; Claes & Heigele, 1999) Iterative models: map mechanically-regulated healing processes (Ament & Hofer, 2000; Lacroix et al., 2002; Bailn-Plaza & van der Meulen, 2003; Gmez-Benito et al., 2005; Isaksson et al., 2006)Limitations:Initial geometry: pre-defined callusMaterial propertiesQualitative validationNeed validated initial conditions.2Computer models - many years.Local mechanical conditions governing healing.Independent of geometry apply to any case.Static models empirical rules.Iterative models: test rules & map healing.Good progress, but models sensitive to initial conditions.Starting callus geom. imposes limits on mech. response; material properties vary widely.Validation: histology. Quantitative mechanical would be useful.Models mechanical confirm mechanics of starting point correct.

(Fixation devices not often modelled explicitly, but opportunity to use models to compare effects of difft devices, giving further model validation & clinical relevance.)Aims: Bending Stiffness forQuantitative validationMechanical starting point

3Mechanically accurate starting point for iterative model?Bending stiffness validating against quantitative experimental data.Method to evaluate healing progress clinically.Test idea that callus size defined by bending stiffness stability.Experimental data: sheep studies by Schuetz & colleagues radiographs, histology and post-mortem mechanical tests. Used actual callus sizes & EI results for individual samples.Methods3D model simulating experimental 4-point bendingExperiment: mechanical tests 6 weeks after injuryLinear elastic materials; cylindrical cross-sectionAssume spherical callusTest range of callus sizes and elastic moduliSelect elastic modulus to match equivalent stiffness & callus size from experimentUse optimal & larger/smaller calluses as starting point in iterative 2D healing model43D FE model of 4-point bending test - fractured sheep tibia, 6 weeks.Linear elastic, cylindrical bone, spherical, uniform callus: not realistic, but reasonable to test method.EI vs callus size & elastic modulus.Optimum = actual callus size, & E to give experimental EI.This & larger/smaller calluses iterative healing model.Results: 4-Point Bending Simulation

54-point bending simulation; symmetry - save time - of shape.Results: 4-Point Bending Simulation

6EI vs E - 3 callus sizes. @ week 6, EI ~60% of predicted intact; curve levels off > experimental.EI vs volume: similar (shallower) trend. EI tapers off > actual size.E: strong influence on EI some maturation required before appreciable stiffness recovery.

(could be argued that stiffness much more strongly dependent on E than V, so size not determined by EI)

Week 6:EI = 69 Nm2 (experiment)Week 12:EI = 88 Nm2 (experiment)Intact:EI = 120 Nm2 (model)

Model: Healing Simulation7Progression of healing - iterative 2d axisymmetric in ABAQUS framework for experiments & alternative algorithms.Sheep tibial fracture with nail. Bone red; blue no bone; spectrum between shows degrees of mineralisation. Callus forms & matures - strain energy derived from Ament & Hofer (2000).Symmetry - cross-section.Application: Healing Simulation

8Implementing optimal, sub-optimal ( volume) & supra-optimal (4x volume): optimal & larger completion of healing process; as expect, smaller lacks stiffness & cannot unite. However, optimal size did heal, higher mineralisation before bridging. Expected: rapid resorption of supra-optimal.All that healed similar time.Two issues:Week 6 & uniform callus here healing virtually inevitable.Bending more demanding than axial including lateral instability/bending more differences & favour larger.

(Dont worry about commenting on unrealistic tissue distribution: can address this if questioned. Its actually not all that dissimilar to what I see with criteria derived from Shefelbine paper.)Conclusions & Future WorkBending stiffness: method of model validation.Starting point for mechanical models e.g. to investigate fixation methods:Preliminary study suggests little bending stiffness benefit in larger callus optimal?Need sufficiently early test data ( histology for initial conditions; useful investigating later stages? eg effects of fixation methods.Prelim. study: callus > experimental little benefit in EI, but more detailed modelling before claim optimisation criterion.For methods to be practical:Test data before large proportion of EI restored. Uniform callus inaccurate. Histology & mechanical test data together: more confident in initial conditions & in rules to determine outcomes.If understand & include underlying biology, may not need.

Additional comments:Of course, cells that form callus dont sense EI, so we dont suggest that stiffness restoration in itself determines callus size, but considering this helps us define local environment to which cells DO respond.Essential to understand fixator-bone mechanics (load-sharing & deformation)Lill et al. (2003) showed stiffness pretty well fully restored in 4 or 5 weeks (sheep tibia).

Recent progress:3D will allow comparison of difft fixns Lacroix & Prendergast (2002), Simon et al. (ESB 2004), Vijayakumar et al. (in press)Incorporation of biological elements has potential to decrease sensitivity to init. conditions, but still in early stages Bailn-Plaza & van der Meulen (2001), Gmez-Benito et al (2005), Lacroix et al. (2002), Simon et al (ORS 2003), Shefelbine et al (2005)

Groups current activities:Iterative model to 3D > GC has prelim model workingContinuum model for biological aspects > expect this to help with initial stage modelling > want simulation to be sensitive to initial conditions of injury, not initial conditions of the model.Might be interesting to compare predicted callus size to reach a defined level of stiffness using axial vs bending vs torsional vs shear criteria.AcknowledgementsSeed funding:Synthes, Inc.Institute of Health & Biomedical Innovation, QUT

Thank-you10Supplementary Material

11Same model but no pre-defined callus doesnt heal.Supplementary MaterialIntermediate callus sizes (X & 2X) in iterative models

12Similar to previous series, but with X & 2X callus volumes (instead of X & 4X).