Stochastic PCA-Based Bone Models from Inverse Transform Sampling: Proof of Concept for Mandibles and Proximal Femurs

Principal components analysis is a powerful technique which can be used to reduce data dimensionality. With reference to three-dimensional bone shape models, it can be used to generate an unlimited number of models, defined by thousands of nodes, from a limited (less than twenty) number of scalars. The full procedure has been here described in detail and tested. Two databases were used as input data: the first database comprised 40 mandibles, while the second one comprised 98 proximal femurs. The “average shape” and principal components that were required to cover at least 90% of the whole variance were identified for both bones, as well as the statistical distributions of the respective principal components weights. Fifteen principal components sufficed to describe the mandibular shape, while nine components sufficed to describe the proximal femur morphology. A routine has been set up to generate any number of mandible or proximal femur geometries, according to the actual statistical shape distributions. The set-up procedure can be generalized to any bone shape given a sufficiently large database of the respective 3D shapes.

[1]  P J Prendergast,et al.  A method to reconstruct patient-specific proximal femur surface models from planar pre-operative radiographs. , 2010, Medical engineering & physics.

[2]  E. Zanetti,et al.  Numerical Simulation of an Intramedullary Elastic Nail: Expansion Phase and Load-Bearing Behavior , 2018, Front. Bioeng. Biotechnol..

[3]  Paul G M Knoops,et al.  Statistical shape modelling for the analysis of head shape variations. , 2021, Journal of cranio-maxillo-facial surgery : official publication of the European Association for Cranio-Maxillo-Facial Surgery.

[4]  Marco Viceconti,et al.  Evaluation of the generality and accuracy of a new mesh morphing procedure for the human femur. , 2011, Medical engineering & physics.

[5]  Algimantas Krisciukaitis,et al.  Evaluation of complexity of induced necrosis zone shape by means of principal component analysis , 2014 .

[6]  Ryan Willing,et al.  Accuracy assessment of 3D bone reconstructions using CT: an intro comparison. , 2015, Medical engineering & physics.

[7]  S. Porziani,et al.  Radial basis functions mesh morphing for the analysis of cracks propagation , 2018 .

[8]  Kim-Han Thung,et al.  Estimating Reference Shape Model for Personalized Surgical Reconstruction of Craniomaxillofacial Defects , 2020, IEEE Transactions on Biomedical Engineering.

[9]  A. Veneziano,et al.  Surface smoothing, decimation, and their effects on 3D biological specimens. , 2018, American journal of physical anthropology.

[10]  Cristina Bignardi,et al.  Osteoporotic hip fracture prediction: is T-score based criterion enough? A Hip Structural Analysis based model. , 2018, Journal of biomechanical engineering.

[11]  M. Viceconti,et al.  Finite element analysis informed variable selection for femoral fracture risk prediction. , 2021, Journal of the mechanical behavior of biomedical materials.

[12]  Heike Hufnagel A probabilistic framework for point-based shape modeling in medical image analysis , 2011 .

[13]  Jim Morrison,et al.  Statistics for Engineers: An Introduction , 2009 .

[14]  Michele Calì,et al.  Mandible Morphing Through Principal Components Analysis , 2019, DSMIE-2019.

[15]  Jean-François Ganghoffer,et al.  3D couple-stress moduli of porous polymeric biomaterials using µCT image stack and FE characterization , 2016 .

[16]  P. M. Calderale,et al.  Radiograph-based femur morphing method , 2005, Medical and Biological Engineering and Computing.

[17]  Umberto Morbiducci,et al.  Combining shape and intensity dxa-based statistical approaches for osteoporotic HIP fracture risk assessment , 2020, Comput. Biol. Medicine.

[18]  Rita Ambu,et al.  Design of a Customized Neck Orthosis for FDM Manufacturing with a New Sustainable Bio-composite , 2019, Lecture Notes in Mechanical Engineering.

[19]  Jean-François Ganghoffer,et al.  Homogenized strain gradient remodeling model for trabecular bone microstructures , 2019, Continuum Mechanics and Thermodynamics.

[20]  R. Eastell,et al.  Distribution of bone density and cortical thickness in the proximal femur and their association with hip fracture in postmenopausal women: a quantitative computed tomography study , 2013, Osteoporosis International.

[21]  Xiaozhong Chen,et al.  Parametric design of patient-specific fixation plates for distal femur fractures , 2018, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[22]  Alan Brunton,et al.  Review of statistical shape spaces for 3D data with comparative analysis for human faces , 2012, Comput. Vis. Image Underst..

[23]  J. Mayerson,et al.  Management of Metastatic Disease of the Upper Extremity. , 2020, The Journal of the American Academy of Orthopaedic Surgeons.

[24]  Maxime Sermesant,et al.  Statistical Shape Analysis of Surfaces in Medical Images Applied to the Tetralogy of Fallot Heart , 2013 .

[25]  H. Tullos,et al.  The anatomic basis of femoral component design. , 1988, Clinical orthopaedics and related research.

[26]  E. Zanetti,et al.  Mechanical Behavior of Elastic Self-Locking Nails for Intramedullary Fracture Fixation: A Numerical Analysis of Innovative Nail Designs , 2020, Frontiers in Bioengineering and Biotechnology.

[27]  J. Gower Generalized procrustes analysis , 1975 .

[28]  M. Viceconti,et al.  Patient-specific finite element estimated femur strength as a predictor of the risk of hip fracture: the effect of methodological determinants , 2016, Osteoporosis International.

[29]  Travis D. Eliason,et al.  Statistical shape modeling describes variation in tibia and femur surface geometry between Control and Incidence groups from the osteoarthritis initiative database. , 2010, Journal of biomechanics.

[30]  B Schmutz,et al.  Customization of a generic 3D model of the distal femur using diagnostic radiographs , 2008, Journal of medical engineering & technology.

[31]  P. Claes,et al.  Accurate reconstructions of pelvic defects and discontinuities using statistical shape models , 2020, Computer methods in biomechanics and biomedical engineering.

[32]  Joanna M Stephen,et al.  Comparative accuracy of lower limb bone geometry determined using MRI, CT, and direct bone 3D models , 2020, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[33]  Marco Evangelos Biancolini,et al.  Fast Radial Basis Functions for Engineering Applications , 2018 .