Restricted access
Research articles
Research articlesWhat makes an accurate and reliable subject-specific finite element model? A case study of an elephant femur
Published:13 July 2011https://doi.org/10.1098/rsif.2011.0323
Abstract
Finite element modelling is well entrenched in comparative vertebrate biomechanics as a tool to assess the mechanical design of skeletal structures and to better comprehend the complex interaction of their form–function relationships. But what makes a reliable subject-specific finite element model? To approach this question, we here present a set of convergence and sensitivity analyses and a validation study as an example, for finite element analysis (FEA) in general, of ways to ensure a reliable model. We detail how choices of element size, type and material properties in FEA influence the results of simulations. We also present an empirical model for estimating heterogeneous material properties throughout an elephant femur (but of broad applicability to FEA). We then use an ex vivo experimental validation test of a cadaveric femur to check our FEA results and find that the heterogeneous model matches the experimental results extremely well, and far better than the homogeneous model. We emphasize how considering heterogeneous material properties in FEA may be critical, so this should become standard practice in comparative FEA studies along with convergence analyses, consideration of element size, type and experimental validation. These steps may be required to obtain accurate models and derive reliable conclusions from them.
References
- 1
Hutchinson J. R. . 2011On the inference of function from structure using biomechanical modelling and simulation of extinct organisms. Biol. Lett. 7.doi:10.1098/rsbl.2011.0399 (doi:10.1098/rsbl.2011.0399). Link, ISI, Google Scholar - 2
Chang C. L.& Yang S. H. . 1998Finite element simulation of wheel impact test. J. Achievements Mater. Manuf. Eng. 28, 167–170.doi:10.1016/j.engfailanal.2008.12.010 (doi:10.1016/j.engfailanal.2008.12.010). Crossref, ISI, Google Scholar - 3
Cho Y. H., McCullough B. F.& Weissmann J. . 1996Considerations on finite-element method application in pavement structural analysis. Transport. Res. Rec. 1539, 96–101.doi:10.3141/1539-13 (doi:10.3141/1539-13). Crossref, Google Scholar - 4
Bessho M., Ohnishi I., Matsuyama J., Matsumoto T., Imai K.& Nakamura K. . 2007Prediction of strength and strain of the proximal femur by a CT-based finite element method. J. Biomech 40, 1745–1753.doi:10.1016/j.jbiomech.2006.08.003 (doi:10.1016/j.jbiomech.2006.08.003). Crossref, PubMed, ISI, Google Scholar - 5
Ellis B. J., Debski R. E., Moore S. M., McMahon P. J.& Weiss J. A. . 2007Methodology and sensitivity studies for finite element modeling of the inferior glenohumeral ligament complex. J. Biomech. 40, 603–612.doi:10.1016/j.jbiomech.2006.01.024 (doi:10.1016/j.jbiomech.2006.01.024). Crossref, PubMed, ISI, Google Scholar - 6
Helgason B., Taddei F., Palsson H., Schileo E., Cristofolini L., Viceconti M.& Brynjolfsson S. . 2008A modified method for assigning material properties to FE models of bones. Med. Eng. Phys. 30, 444–453.doi:10.1016/j.medengphy.2007.05.006 (doi:10.1016/j.medengphy.2007.05.006). Crossref, PubMed, ISI, Google Scholar - 7
Keyak J. H., Kaneko T. S., Rossi S. A., Pejcic M. R., Tehranzadeh J.& Skinner H. B. . 2005Predicting the strength of femoral shafts with and without metastatic lesions. Clin. Orthop. Relat. Res. 439, 161–170.doi:10.1097/01.blo.0000174736.50964.3b (doi:10.1097/01.blo.0000174736.50964.3b). Crossref, PubMed, ISI, Google Scholar - 8
Keyak J. H., Kaneko T. S., Tehranzadeh J.& Skinner H. B. . 2005Predicting proximal femoral strength using structural engineering models. Clin. Orthop. Relat. Res. 437, 219–228.doi:10.1097/01.blo.0000164400.37905.22 (doi:10.1097/01.blo.0000164400.37905.22). Crossref, ISI, Google Scholar - 9
Oden Z. M., Selvitelli D. M.& Bouxsein M. L. . 1999Effects of local density changes on the failure load of the proximal femur. J. Orthop. Res. 17, 661–667.doi:10.1002/jor.1100170507 (doi:10.1002/jor.1100170507). Crossref, PubMed, ISI, Google Scholar - 10
Alexander R. M., Goldspink G., Jayes A. S., Maloiy G. M. O.& Wathuta E. M. . 1979Allometry of the limb bones of mammals from shrew (Sorex) to elephant (Loxodonta). J. Zool. Lond. 189, 305–314.doi:10.1111/j.1469-7998.1979.tb03964.x (doi:10.1111/j.1469-7998.1979.tb03964.x). Crossref, ISI, Google Scholar - 11
Kokshenev V. B.& Christiansen P. . 2010Salient features in the locomotion of proboscideans revealed via the differential scaling of limb long bones. Biol. J. Linnean Soc. 100, 16–29.doi:10.1111/j.1095-8312.2010.01415 (doi:10.1111/j.1095-8312.2010.01415). Crossref, ISI, Google Scholar - 12
Zioupos P., Cook R. B.& Hutchinson J. R. . 2008Some basic relationships between density values in cancellous and cortical bone. J. Biomech. 41, 1961–1968.doi:10.1016/j.jbiomech.2008.03.025 (doi:10.1016/j.jbiomech.2008.03.025). Crossref, PubMed, ISI, Google Scholar - 13
Doube M., Kłosowski M. M., Arganda-Carreras I., Cordelières F., Dougherty R. P., Jackson J., Schmid B., Hutchinson J. R.& Shefelbine S. J. . 2010BoneJ: free and extensible bone image analysis in ImageJ. Bone 47, 1076–1079.doi:10.1016/j.bone.2010.08.023 (doi:10.1016/j.bone.2010.08.023). Crossref, PubMed, ISI, Google Scholar - 14
Panagiotopoulou O. . 2009Finite element analysis (FEA): applying an engineering method to functional morphology in anthropology and human biology. Ann. Hum. Biol. 36, 609–623.doi:10.1080/03014460903019879 (doi:10.1080/03014460903019879). Crossref, PubMed, ISI, Google Scholar - 15
Rayfield E. . 2007Finite element analysis and understanding the biomechanics and evolution of living and fossil organisms. Annu. Rev. Earth Planet Sci. 35, 541–576.doi:10.1146/annurev.earth.35.031306.140104 (doi:10.1146/annurev.earth.35.031306.140104). Crossref, ISI, Google Scholar - 16
Richmond B. G., Wright B. W., Grosse I., Dechow P. C., Ross C. F., Spencer M. A.& Strait D. S. . 2005Finite element analysis in functional morphology. Anat. Rec. A. 283A, 259–274.doi:10.1002/ar.a.20169 (doi:10.1002/ar.a.20169). Crossref, Google Scholar - 17
Kessler O., Lacatsu E., Sommers M. B., Mayr E.& Bottlang M. . 2006Malrotation in total knee arthroplasty: effect on tibial cortex strain captured by laser-based strain acquisition. Clin. Biomech. 21, 603–609.doi:10.1016/j.clinbiomech.2006.01.011 (doi:10.1016/j.clinbiomech.2006.01.011). Crossref, PubMed, ISI, Google Scholar - 18
Panagiotopoulou O., Curtis N., O'Higgins P.& Cobb S. N. . 2010Modelling subcortical bone in finite element analyses: a validation and sensitivity study in the macaque mandible. J. Biomech. 43, 1603–1611.doi:10.1016/j.jbiomech.2009.12.027 (doi:10.1016/j.jbiomech.2009.12.027). Crossref, PubMed, ISI, Google Scholar - 19
Panagiotopoulou O., Kupczik K.& Cobb S. N. . 2011The mechanical function of the periodontal ligament in the macaque mandible: a validation and sensitivity study using finite element analysis. J. Anat. 218, 75–86.doi:10.1111/j.1469-7580.2010.01257 (doi:10.1111/j.1469-7580.2010.01257). Crossref, PubMed, ISI, Google Scholar - 20
Tyrer J. R., Heras-Palou C.& Slater T. . 1995Three-dimensional human femoral strain analysis using ESPI. Opt. Lasers Eng. 23, 291–303.doi:10.1016/0143-8166(95)00035-M (doi:10.1016/0143-8166(95)00035-M). Crossref, ISI, Google Scholar - 21
Yang L., Zhang P., Liu S., Samala P. R., Su M.& Yokota H. . 2007Measurement of strain distributions in mouse femora with 3D-digital speckle pattern interferometry. Opt. Lasers Eng. 45, 843–851.doi:10.1016/j.optlaseng.2007.02.004 (doi:10.1016/j.optlaseng.2007.02.004). Crossref, PubMed, ISI, Google Scholar - 22
Currey J. D., Brear K.& Zioupos P. . 1997The effects of ageing and changes in mineral content in degrading the toughness of human femora. J. Biomech. 12, 459–469.doi:10.1016/0021-9290(95)00048-8 (doi:10.1016/0021-9290(95)00048-8). Crossref, ISI, Google Scholar - 23
Benzley S. E., Perry E., Merkley K., Clark B.& Sjaardema G. . 1995A comparison of all-hexahedral and all-tetrahedral finite element meshes for elastic and elasto–plastic analysis.Proc. 4th Int. Meshing Roundtable , pp. 179–191. Livermore, CA: Sandia National Laboratories. Google Scholar - 24
Cifuentes A. O.& Kalbag A. . 1992A performance study of tetrahedral and hexahedral elements in 3-D finite element structural analysis. Finite Element Anal. Des. 12, 313–318.doi:10.1016/0168-874X(92)90040-J (doi:10.1016/0168-874X(92)90040-J). Crossref, Google Scholar - 25
Strait D. S., Wang Q., Dechow P. C., Ross C. F., Richmond B. G., Spencer M. A.& Patel B. A. . 2005Modelling elastic properties in finite element analysis: how much precision is needed to produce an accurate model?Anat. Rec. A. 283, 275–287.doi:10.1002/ar.a.20172 (doi:10.1002/ar.a.20172). Crossref, Google Scholar
