A new numerical approach to mechanically analyse biological structures

References

• Andrade AFD, Paiva WS, Amorim RLOD, Figueiredo EG, Rusafa Neto E, Teixeira MJ. 2009. Mecanismos de lesão cerebral no traumatismo cranioencefálico. Rev Assoc Med Bras. 55(1):75–81. doi:10.1590/S0104-42302009000100020.
   PubMedGoogle Scholar
• Atluri SN, Zhu T. 1998. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput Mech. 22(2):117–127. doi:10.1007/s004660050346.
   Web of Science ®Google Scholar
• Belinha J. 2014. Meshless methods in biomechanics: bone tissue remodelling analysis. In: Tavares JMRS, Natal Jorge, RM, editors. Lecture notes in computational vision and biomechanics. Vol. 16. Dordrecht (Netherlands): Springer. doi:10.1007/978-3-319-06400-0.
   Google Scholar
• Belinha J, Dinis LMJS, Natal Jorge RM. 2013a. Composite laminated plate analysis using the natural radial element method. Compos Struct. 103:50–67. doi:10.1016/j.compstruct.2013.03.018.
   Web of Science ®Google Scholar
• Belinha J, Dinis LMJS, Natal Jorge RM. 2013b. The natural radial element method. Int J Numer Meth Eng. 93(12):1286–1313. doi:10.1002/nme.4427.
   Web of Science ®Google Scholar
• Belinha J, Dinis LMJS, Natal Jorge RM. 2013c. Analysis of thick plates by the natural radial element method. Int J Mech Sci. 76(12):33–48. doi:10.1016/j.ijmecsci.2013.08.011.
   Google Scholar
• Belinha J, Dinis LMJS, Natal Jorge RM. 2015. The meshless methods in the bone tissue remodelling analysis. Procedia Eng. 110:51–58. doi:10.1016/j.proeng.2015.07.009.
   Google Scholar
• Belinha J, Dinis LMJS, Natal Jorge RM. 2016. The analysis of the bone remodelling around femoral stems: a meshless approach. Math Comput Simulat. 121:64–94. doi:10.1016/j.matcom.2015.09.002.
   Web of Science ®Google Scholar
• Belinha J, Natal Jorge RM, Dinis LMJS. 2012. Bone tissue remodelling analysis considering a radial point interpolator meshless method. Eng Anal Bound Elem. 36(11):1660–1670. doi:10.1016/j.enganabound.2012.05.009.
   Web of Science ®Google Scholar
• Belytschko T, Lu YY, Gu L. 1994. Element-free Galerkin methods. Int J Numer Meth Eng. 37(2):229–256. doi:10.1002/nme.1620370205.
   Web of Science ®Google Scholar
• Cueto E, Sukumar N, Calvo B, Martínez M. A, Cegoñino J, Doblaré M. 2003. Overview and recent advances in natural neighbour Galerkin methods. ARCO. 10(4):307–384. doi:10.1007/BF02736253.
   Google Scholar
• Delaunay B. 1934. Sur la sphére vide. A la memoire de Georges Voronoï. Bulletin de L’Academie Des Sciences de l’URSS. Classe Des Sciences Mathematiques et Na. 7:793–800.
   Google Scholar
• Dinis LMJS, Natal Jorge RM, Belinha J. 2007. Analysis of 3D solids using the natural neighbour radial point interpolation method. Comput Methods Appl Mech Eng. 196(13–16):2009–2028. doi:10.1016/j.cma.2006.11.002.
   Web of Science ®Google Scholar
• Dinis LMJS, Natal Jorge RM, Belinha J. 2008. Analysis of plates and laminates using the natural neighbour radial point interpolation method. Eng Anal Bound Elem. 32(3):267–279. doi:10.1016/j.enganabound.2007.08.006.
   Web of Science ®Google Scholar
• Duarte HMS, Rafael Andrade J, Dinis LMJS, Natal Jorge RM, Belinha J. 2016. Numerical analysis of dental implants using a new advanced discretization technique. Mech Adv Mater Struct. 23(4):467–479. doi:10.1080/15376494.2014.987410.
   Web of Science ®Google Scholar
• Giordano C, Cloots RJH, van Dommelen JAW, Kleiven S. 2014. The influence of anisotropy on brain injury prediction. J Biomech. 47(5):1052–1059. doi:10.1016/j.jbiomech.2013.12.036.
   PubMed Web of Science ®Google Scholar
• Hardy RL. 1990. Theory and applications of the multiquadric-biharmonic method 20 years of discovery 1968–1988. Comput Math Appl. 19(8–9):163–208. doi:10.1016/0898-1221(90)90272-L.
   Web of Science ®Google Scholar
• Khoury S, Benavides R. 2018. Pain with traumatic brain injury and psychological disorders. Prog Neuropsychopharmacol Biol Psychiatry. 87:224–233. doi:10.1016/j.pnpbp.2017.06.007.
   PubMed Web of Science ®Google Scholar
• Lalys F, Haegelen C, Ferre J-C, El-Ganaoui O, Jannin P. 2010. Construction and assessment of a 3-T MRI brain template. Neuroimage. 49(1):345–354. doi:10.1016/J.NEUROIMAGE.2009.08.007.
   PubMed Web of Science ®Google Scholar
• Liang Z, Luo Y. 2015. A QCT-based nonsegmentation finite element head model for studying traumatic brain injury. Appl Bionics Biomech. 2015:1–8. doi:10.1155/2015/837585.
   Web of Science ®Google Scholar
• Liu GR, Gu YT. 2001. A point interpolation method for two-dimensional solids. Int J Numer Meth Eng. 50(4):937–951. doi:10.1002/1097-0207(20010210)50:4 < 937::AID-NME62 > 3.0.CO;2-X.
   Web of Science ®Google Scholar
• Liu WK, Jun S, Zhang YF. 1995. Reproducing Kernel particle methods. Int J Numer Meth Fluids. 20(8–9):1081–1106. doi:10.1002/fld.1650200824.
   Web of Science ®Google Scholar
• Mao H, Zhang L, Jiang B, Genthikatti VV, Jin X, Zhu F, Makwana R, Gill A, Jandir G, Singh A, et al. 2013. Development of a finite element human head model partially validated with thirty five experimental cases. J Biomech Eng. 135(11):111002. doi:10.1115/1.4025101.
   PubMed Web of Science ®Google Scholar
• Marques M, Belinha J, Oliveira AF, Manzanares Céspedes MC, Natal Jorge RM. 2018. A multiscale homogenization procedure combining the fabric tensor with a natural neighbour meshless method. Eng Anal Bound Elem. doi:10.1016/j.enganabound.2018.05.007.
   Web of Science ®Google Scholar
• Meaney DF, Morrison B, Dale Bass C. 2014. The mechanics of traumatic brain injury: a review of what we know and what we need to know for reducing its societal burden. J Biomech Eng. 136(2):021008. doi:10.1115/1.4026364.
   PubMed Web of Science ®Google Scholar
• Meaney DF, Smith DH. 2011. Biomechanics of concussion. Clin Sports Med. 30(1):19–31. doi:10.1016/j.csm.2010.08.009.
   PubMed Web of Science ®Google Scholar
• Mimics® Medical Image Segmentation for Engineering on Anatomy™. Leuven (Belgium): Materialise NV. http://biomedical.materialise.com/mimics.
   Google Scholar
• Moreira SF, Belinha J, Dinis LMJS, Natal Jorge RM. 2014. A global numerical analysis of the ‘central incisor/local maxillary bone’ system using a meshless method. Mol Cel Biomech. 11(3):151–184. doi:10.3970/mcb.2014.011.151.
   PubMed Web of Science ®Google Scholar
• Mujalli RO, López G, Garach L. 2016. Bayes classifiers for imbalanced traffic accidents datasets. Accid Anal Prev. 88:37–51. doi:10.1016/j.aap.2015.12.003.
   PubMed Web of Science ®Google Scholar
• Nayroles B, Touzot G, Villon P. 1992. Generalizing the finite element method: diffuse approximation and diffuse elements. Comput Mech. 10(5):307–318. doi:10.1007/BF00364252.
   Google Scholar
• Peyroteo MMA, Belinha J, Vinga S, Dinis LMJS, Natal Jorge RM. 2018. Mechanical bone remodelling: comparative study of distinct numerical approaches. Eng Anal Bound Elem. February. doi:10.1016/j.enganabound.2018.01.011.
   Web of Science ®Google Scholar
• Roozenbeek B, Maas AIR, Menon DK. 2013. Changing patterns in the epidemiology of traumatic brain injury. Nat Rev Neurol. 9(4):231–236. doi:10.1038/nrneurol.2013.22.
   PubMed Web of Science ®Google Scholar
• Santos CF, Belinha J, Gentil F, Parente M, Jorge RN. 2018. The free vibrations analysis of the cupula in the inner ear using a natural neighbor meshless method. Eng Anal Bound Elem. 92:50–63. doi:10.1016/j.enganabound.2018.01.002.
   Web of Science ®Google Scholar
• Sibson R. 1981. A brief description of natural neighbor interpolation. In: Barnett V, editor. Interpolating multivariate data. Chichester (UK): Wiley; p. 21–36.
   Google Scholar
• Summers CR, Ivins B, Schwab KA. 2009. Traumatic brain injury in the United States: an epidemiologic overview. Mt Sinai J Med. 76(2):105–110. doi:10.1002/msj.20100.
   PubMedGoogle Scholar
• Tavares CSS, Belinha J, Dinis LMJS, Natal Jorge RM. 2015. The elasto-plastic response of the bone tissue due to the insertion of dental implants. Procedia Eng. 110:37–44. doi:10.1016/j.proeng.2015.07.007.
   Google Scholar
• Taylor JM, Montgomery MH, Gregory EJ, Berman NEJ. 2015. Exercise preconditioning improves traumatic brain injury outcomes. Brain Res. 1622:414–429. doi:10.1016/j.brainres.2015.07.009.
   PubMed Web of Science ®Google Scholar
• Voronoi G. 1908. Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire. Recherches sur les parallélloèdres primitifs. J Reine Angew Math. 1908(134):198–287. doi:10.1515/crll.1908.134.198.
   Google Scholar
• Wang JG, Liu GR. 2002. A point interpolation meshless method based on radial basis functions. Int J Numer Meth Eng. 54(11):1623–1648. doi:10.1002/nme.489.
   Web of Science ®Google Scholar
• Yang B, Tse K-M, Chen N, Tan L-B, Zheng Q-Q, Yang H-M, Hu M, Pan G, Lee H-P. 2014. Development of a finite element head model for the study of impact head injury. Biomed Res Int. 2014:1. doi:10.1155/2014/408278.
   Google Scholar
• Yue X, Wang L, Wang R. 2013. Tissue modeling and analyzing with finite element method: a review for cranium brain imaging. Int J Biomed Imag. 2013:1–12. doi:10.1155/2013/781603.
   Google Scholar