MedicalEngineering&Physics26(2004)493–501 www.elsevier.com/locate/medengphy Theroleofosteogenicindex,octahedralshearstress anddilatationalstressintheossificationofafracturecallus Trevor Noel Gardner a,b, ,SanjayMishra a ,LaurenceMarks c a Oxford Orthopaedic Engineering Centre, University of Oxford, Nuffield Orthopaedic Centre, Windmill Road, Headington, Oxford, OX3 7LD, UK b School of Sport and Exercise Sciences, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK c Integrated Analysis Solutions, Malvern House, 10 Bridge Street, Witney, OX28 1HY, UK Received4March2003;receivedinrevisedform4March2004;accepted19March2004 Abstract Theexactmechanismbywhichmechanicalstimulusregulatesthehealingprocessofabonefractureisnotunderstood.Thishas led to the development of several hypotheses that predict the pattern of differentiation of tissue during healing that may arise from characteristic fields of stress or strain at the fracture. These have so far remained unproved because data on stress fields in actual fracture tissue have been unavailable until recently. Thus the present study examines the predictive performance of the hypothesis proposed in J Orthop Res 6 (1988) 736, against measured and calculated data reported in J Biomech 33 (2000) 415, using a 2D FEM of a clinical fracture. The hypothesis was used to predict the influence of stress fields present in the Gardner et al. tissues at four temporal stages during healing. These predictions were then correlated with callus-size, rate of endochondral ossification and ossification pattern subsequently observed by Gardner et al. in the clinical fracture. Results corroborate the hypothesis that high octahedral shear stresses may increase the size of the callus during the initial phase of healing, and they also suggest that this may be true during the later stages of the fracture fixation period. However, compressive dilatational stresses were not found to inhibit endochondral ossification, as suggested by the hypothesis. Although high shear stresses were found in regions indicative of fibrous tissue as postulated by the hypothesis, this was not found to be the case for high tensile dilatational stresses. Also, contour diagrams of Osteogenic index (I) indicated only limited correlation with callus maturation and the pattern ofhealing.Therefore,thehypothesiswasnotwhollysuccessfulinpredictinghealingpattern. # 2004IPEM.PublishedbyElsevierLtd.Allrightreserved. Keywords: Fracturehealing;Callus;Osteogenicindex;Finiteelementmodel 1. Introduction Mechanical stimulus of callus tissue influences the rateandpatternofhealinginlongbonefractures [1–4]. Carter et al. [5] proposed a fracture healing hypothesis that characterised the mechanical stress environment beneficial to the revascularisation and ossification of a callus. The hypothesis was developed by investigating contours of stress in a reparative callus simulated by a 2Dfiniteelementmodel(FEM) [5,6].Patternsofosteo- genic index, octahedral shear and dilatational stress (hydrostatic stress) were calculated for a fracture geometry idealised as axisymmetric, with assumed material properties and simplified loading conditions. To establish the hypothesis, the type, magnitude and distribution of stresses produced by the model were correlated with typically observed patterns of tissue dif- ferentiation and callus formation reported in the litera- ture. The hypothesis maintains that in the early callus, intermittent shear stress will cause tissue proliferation and the formation of callus. Higher stresses will induce greater tissue proliferation and increase the size of the final callus. High shear stress and /or tensile dilata- tional stresses will stimulate the formation of fibrous tissue, and high compressive dilatational stresses will stimulate chondrogenesis. If cartilaginous tissue forms,  Corresponding author. Tel.: +44-1865-227451; fax: +44-1865- 742348. E-mail address: t.gardner@bham.ac.uk (T.N. Gardner). 1350-4533/$-seefrontmatter # 2004IPEM.PublishedbyElsevierLtd.Allrightreserved. doi:10.1016/j.medengphy.2004.03.009