Mathematical relationships between bone density and mechanical properties:​ a literature review

Helgason, Benedikt; Perilli, Egon; Schileo, Enrico; Taddei, Fulvia; Brynjólfsson, Sigurður; Viceconti, Marco

Year	Entry
2013	Shang-cheng W, Dong-mei W, Fang W, Qiu-gen W, Chun-hui W, Shan-guang C. Tensile and compressive mechanical property of human bone tissue [in Chinese]. Ch J Tissue Eng Res. 2013;17(7):1180-1184.
2022	Brynskog E, Iraeus J, Pipkorn B, Davidsson J. Population variance in pelvic response to lateral impacts: a global sensitivity analysis. In: Proceedings of the 2022 International IRCOBI Conference on the Biomechanics of Injury. September 14-16, 2022; Porto, Portugal.173-196.
2021	Martelli S, Giorgi M, Dall'Ara E, Perilli E. Damage tolerance and toughness of elderly human femora. Acta Biomater. March 15, 2021;123:167-177.
2019	Knowles NK, Ip K, Ferreira LM. The effect of material heterogeneity, element type, and down-sampling on trabecular stiffness in micro finite element models. Ann Biomed Eng. February 2019;47(2):615-623.
2019	Knowles NK, Kusins J, Faieghi M, Ryan M, Dall’Ara E, Ferreira LM. Material mapping of QCT-derived scapular models: a comparison with micro-CT loaded specimens using digital volume correlation. Ann Biomed Eng. November 2019;47(11):2188-2198.
2016	Morales-Orcajo E, Bayod J, Barbosa de Las Casas E. Computational foot modeling: scope and applications. Arch Comput Methods Eng. September 2016;23(3):389-416.
2020	Janc K, Tarasiuk J, Lipinski P, Bonnet A-S, Wronski S. Assessment of mechanical properties of bone trabeculae as an inverse problem of heterogeneous material modeling. Arch Mech. 2020;72(5):385-414.
2020	Schileo E, Pitocchi J, Falcinelli C, Taddei F. Cortical bone mapping improves finite element strain prediction accuracy at the proximal femur. Bone. July 2020;136:115348.
2021	Winsor C, Li X, Qasim M, Henak CR, Pickhardt PJ, Ploeg H, Viceconti M. Evaluation of patient tissue selection methods for deriving equivalent density calibration for femoral bone quantitative CT analyses. Bone. February 2021;143:115759.
2011	Tassani S, Particelli F, Perilli E, Traina F, Baruffaldi F, Viceconti M. Dependence of trabecular structure on bone quantity: a comparison between osteoarthritic and non-pathological bone. Clin Biomech (Bristol, Avon). July 2011;26:632-639.
2020	Huang Z, Nie Y, Li Y. Microstructural modeling and multiscale mechanical properties analysis of cancellous bone. CMC-Comput Mater Con. 2020;62(1):245-265.
2019	Kalajahi SMH, Nazemi SM, Johnston JD. Separate modeling of cortical and trabecular bone offers little improvement in FE predictions of local structural stiffness at the proximal tibia. Comput Methods Biomech Biomed Eng. 2019;22(16):1258-1268.
2020	Silva-Henao JD, Rueda Esteban RJ, Marañon-Leon A, Casas-Rodríguez JP. Post-yield mechanical properties of bovine trabecular bone: relationships with bone volume fraction and strain rate. Eng Fract Mech. June 15, 2020;232:107053.
2018	Levrero-Florencio F, Pankaj P. Using non-linear homogenization to improve the performance of macroscopic damage models of trabecular bone. Front Physiol. May 2018;9:545.
2008	Schileo E, Dall’Ara E, Taddei F, Malandrino A, Schotkamp T, Baleani M, Viceconti M. An accurate estimation of bone density improves the accuracy of subject-specific finite element models. J Biomech. August 7, 2008;41(11):2483-2491.
2008	Austman RL, Milner JS, Holdsworth DW, Dunning CE. The effect of the density–modulus relationship selected to apply material properties in a finite element model of long bone. J Biomech. November 14, 2008;41(15):3171-3176.
2010	Cristofolini L, Conti G, Juszczyk M, Cremonini S, Sint Jan SV, Viceconti M. Structural behaviour and strain distribution of the long bones of the human lower limbs. J Biomech. March 22, 2010;43(5):826-835.
2010	Tassani S, Öhman C, Baleani M, Baruffaldi F, Viceconti M. Anisotropy and inhomogeneity of the trabecular structure can describe the mechanical strength of osteoarthritic cancellous bone. J Biomech. April 19, 2010;43(6):1160-1166.
2010	Santos L, Romeu JC, Canhão H, Fonseca JE, Fernandes PR. A quantitative comparison of a bone remodeling model with dual-energy X-ray absorptiometry and analysis of the inter-individual biological variability of femoral neck T-score. J Biomech. December 1, 2010;43(16):3150-3155.
2011	Varghese B, Short D, Penmetsa R, Goswami T, Hangartner T. Computed-tomography-based finite-element models of long bones can accurately capture strain response to bending and torsion. J Biomech. April 29, 2011;(7):1374-1379.
2011	Grimal Q, Rus G, Parnell WJ, Laugier P. A two-parameter model of the effective elastic tensor for cortical bone. J Biomech. May 17, 2011;44(8):1621-1625.
2011	Trabelsi N, Yosibash Z, Wutte C, Augat P, Eberle S. Patient-specific finite element analysis of the human femur: a double-blinded biomechanical validation. J Biomech. June 3, 2011;44(9):1666-1672.
2011	Juszczyk MM, Cristofolini L, Viceconti M. The human proximal femur behaves linearly elastic up to failure under physiological loading conditions. J Biomech. August 11, 2011;44(12):2259-2266.
2012	Wille H, Rank E, Yosibash Z. Prediction of the mechanical response of the femur with uncertain elastic properties. J Biomech. April 30, 2012;45(7):1140-1148.
2013	Nishiyama KK, Gilchrist S, Guy P, Cripton P, Boyd SK. Proximal femur bone strength estimated by a computationally fast finite element analysis in a sideways fall configuration. J Biomech. April 26, 2013;46(7):1231-1236.
2013	Hazrati Marangalou J, Ito K, Cataldi M, Taddei F, van Rietbergen B. A novel approach to estimate trabecular bone anisotropy using a database approach. J Biomech. September 27, 2013;46(14):2356-2362.
2014	Ali AA, Cristofolini L, Schileo E, Hu H, Taddei F, Kim RH, Rullkoetter PJ, Laz PJ. Specimen-specific modeling of hip fracture pattern and repair. J Biomech. January 22, 2014;47(2):536-543.
2018	Enns-Bray WS, Ferguson SJ, Helgason B. Strain rate dependency of bovine trabecular bone under impact loading at sideways fall velocity. J Biomech. June 2018;75:46-52.
2023	Soukup JW, Jeffery J, Drizin SR, Hetzel SJ, Stone DS, Eriten M, Ploeg H-L, Henak CR. Correlation of mineral density and elastic modulus of dog dentin using μ-CT and nanoindentation. J Biomech. January 2023;147:111434.
2010	Charlebois M, Pretterklieber M, Zysset PK. The role of fabric in the large strain compressive behavior of human trabecular bone. J Biomech Eng. 2010;132(12):121006.
2015	Oftadeh R, Perez-Viloria M, Villa-Camacho JC, Vaziri A, Nazarian A. Biomechanics and mechanobiology of trabecular bone: a review. J Biomech Eng. January 2015;137(1):010802.
2013	Christen D, Melton LJ III, Zwahlen A, Amin S, Khosla S, Müller R. Improved fracture risk assessment based on nonlinear micro-finite element simulations from HRpQCT images at the distal radius. J Bone Miner Res. December 2013;28(12):2601-2608.
2010	Lievers WB, Waldman SD, Pilkey AK. Minimizing specimen length in elastic testing of end-constrained cancellous bone. J Mech Behav Biomed Mater. January 2010;3(1):22-30.
2015	Grassi L, Isaksson H. Extracting accurate strain measurements in bone mechanics: a critical review of current methods. J Mech Behav Biomed Mater. October 2015;50:43-54.
2019	Knowles NK, Langohr GDG, Faieghi M, Nelson A, Ferreira LM. Development of a validated glenoid trabecular density-modulus relationship. J Mech Behav Biomed Mater. February 2019;90:140-145.
2019	Alexander SL, Gunnarsson CA, Weerasooriya T. Influence of the mesostructure on the compressive mechanical response of adolescent porcine cranial bone. J Mech Behav Biomed Mater. August 2019;96:96-107.
2019	Lee Y, Ogihara N, Lee T. Assessment of finite element models for prediction of osteoporotic fracture. J Mech Behav Biomed Mater. September 2019;97:312-320.
2020	Bahia MT, Hecke MB, Mercuri EGF, Pinheiro MM. A bone remodeling model governed by cellular micromechanics and physiologically based pharmacokinetics. J Mech Behav Biomed Mater. April 2020;104:103657.
2020	Colabella L, Cisilino A, Fachinotti V, Capiel C, Kowalczyk P. Multiscale design of artificial bones with biomimetic elastic microstructures. J Mech Behav Biomed Mater. August 2020;108:103748.
2020	Fleps I, Bahaloo H, Zysset PK, Ferguson SJ, Pálsson H, Helgason B. Empirical relationships between bone density and ultimate strength: a literature review. J Mech Behav Biomed Mater. October 2020;110:103866.
2021	Sas A, Helgason B, Ferguson SJ, van Lenthe GH. Mechanical and morphological characterization of PMMA/bone composites in human femoral heads. J Mech Behav Biomed Mater. March 2021;115:104247.
2020	Knowles NK, Kusins J, Columbus MP, Athwal GS, Ferreira LM. Morphological and apparent‐level stiffness variations between normal and osteoarthritic bone in the humeral head. J Orthop Res. March 2020;38(3):503-509.
2022	Baines AJ, Babazadeh-Naseri A, Dunbar NJ, Lewis VO, Fregly BJ. Bilateral asymmetry of bone density adjacent to pelvic sarcomas: a retrospective study using computed tomography. J Orthop Res. March 2022;40(3):644-653.
2022	Soltanmohammadi P, Tavakoli A, Langohr GDG, Athwal GS, Willing R. Structural analysis of hollow versus solid-stemmed shoulder implants of proximal humeri with different bone qualities. J Orthop Res. March 2022;40(3):674-684.
2022	Youssefian S, Bressner JA, Osanov M, Guest JK, Zbijewski WB, Levin AS. Sensitivity of the stress field of the proximal femur predicted by CT-based FE analysis to modeling uncertainties. J Orthop Res. May 2022;40(5):1163-1173.
2023	Mirzaei M, Jafari R, Allaveisi F, Jafari H, Alavi F. Fracture analysis of healthy and osteoporotic femora using clinical CT images, phantomless densitometry, and linear FE method. J Orthop Res. March 2023;41(3):629-640.
2019	Yassine RA, Hamade RF. Transversely isotropic and isotropic material considerations in determining the mechanical response of geometrically accurate bovine tibia bone. Med Biol Eng Comput. October 2019;57(10):2159-2178.
2010	Aiyangar AK, Au AG, Crenshaw TD, Ploeg H-L. Recovery of bone strength in young pigs from an induced short-term dietary calcium deficit followed by a calcium replete diet. Med Eng Phys. December 2010;32(10):1116-1123.
2011	Cong A, Buijs JOD, Dragomir-Daescu D. In situ parameter identification of optimal density–elastic modulus relationships in subject-specific finite element models of the proximal femur. Med Eng Phys. March 2011;33(2):164-173.
2019	Yue Y, Yang H, Li Y, Zhong H, Tang Q, Wang J, Wang R, He H, Chen W, Chen D. Combining ultrasonic and computed tomography scanning to characterize mechanical properties of cancellous bone in necrotic human femoral heads. Med Eng Phys. April 2019;66:12-17.
2019	Väänänen SP, Grassi L, Venäläinen MS, Matikka H, Zheng Y, Jurvelin JS, Isaksson H. Automated segmentation of cortical and trabecular bone to generate finite element models for femoral bone mechanics. Med Eng Phys. September 2019;70:19-28.
2012	Dall’Ara E, Pahr D, Varga P, Kainberger F, Zysset P. QCT-based finite element models predict human vertebral strength in vitro significantly better than simulated DEXA. Osteoporos Int. February 2012;23(2):563-572.
2020	Luo Y. Age-related periosteal expansion at femoral neck among elderly women may maintain bending stiffness, but not femoral strength. Osteoporos Int. February 2020;31(2):371-377.
2010	Cristofolini L, Schileo E, Juszczyk M, Taddei F, Martelli S, Viceconti M. Mechanical testing of bones: the positive synergy of finite–element models and in vitro experiments. Philos Trans R Soc A-Math Phys Eng Sci. June 13, 2010;368(1920):2725-2763.
2013	Cesar R, Boffa RS, Fachine LT, Leivas TP, Silva AMH, Pereira CAM, Reiff RBM, Rollo JMDA. Evaluation of trabecular microarchitecture of normal osteoporotic and osteopenic human vertebrae. Procedia Eng. 2013;59:6-15.
2020	Frank EG. A Fluid Structure Interaction Model of Trabecular Bone [PhD thesis]. University of Bath; September 2020.
2020	Aggleton J. First-Hand Experience: A Methodology for Exploring Bone Architecture [PhD thesis]. Bristol, UK: University of Bristol; January 2020.
2016	Haider IT. An Investigation on the Influence of Stumbling Loads on Femoral Fracture Risk, Using a Novel Gradient Enhanced Quasibrittle Finite Element Model [PhD thesis]. Carleton University; 2016.
2011	Genc KO. The Effects of Altered Gravity Environments on the Mechanobiology of Bone: From Bedrest to Spaceflight [PhD thesis]. Cleveland, OH: Case Western Reserve University; August 2011.
2024	Szabo E. Insights Into the Mechanical Behavior of Maturing Cortical Bone: A Porcine Model [PhD thesis]. Cleveland, OH: Case Western Reserve University; May 2024.
2010	Shetye S. Development of a Novel Endoprosthesis for Canine Limb-Sparing Using a Finite Element Approach [PhD thesis]. Colorado State University; 2010.
2013	Ali A. Development of a Computational Approach to Assess Hip Fracture and Repair: Considerations of Intersubject and Surgical Alignment Variability [Master's thesis]. University of Denver; November 2013.
2016	Navacchia A. Multiscale Musculoskeletal Modeling of the Lower Limb to Perform Personalized Simulations of Movement [PhD thesis]. University of Denver; November 2016.
2016	Florencio FL. Multiscale Modelling of Trabecular Bone: From Micro to Macroscale [PhD thesis]. Edinburgh, Scotland: University of Edinburgh; 2016.
2018	Xie S. Characterisation of Time-Dependent Mechanical Behaviour of Trabecular Bone and Its Constituents [PhD thesis]. Edinburgh, Scotland: University of Edinburgh; 2018.
2019	Bin Rosli AH. Characterisation of Trabecular Bone Behaviour Under Impact [PhD thesis]. Edinburgh, Scotland: University of Edinburgh; 2019.
2012	Christen DB. Nonlinear Failure Prediction in Human Bone: A Clinical Approach Based on High Resolution Imaging [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2012.
2018	Enns-Bray WS. Identifying Individuals Predisposed to Hip Fracture [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2018.
2019	Fleps I. Assessing the Risk of Hip Fracture: Subject-Specific Dynamic Models for the Simulation of Sideways Fall Impact [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2019.
2020	Lewandowski K. Numerical Investigation of Bone Adaptation to Exercise and Fracture in Thoroughbred Racehorses [PhD thesis]. Glasgow, UK: University of Glasgow; February 2020.
2016	Currier EJ. Predicting Peak Load of the Femoral Neck Using Structural Parameters [Master's thesis]. University of Illinois at Urbana-Champaign; 2016.
2014	Holub O. Biomechanics of Spinal Metastases [PhD thesis]. University of Leeds; April 2014.
2021	Schwarzenberg PM. Development and Validation of Virtual Mechanical Testing of Bone Fracture Healing [PhD thesis]. Lehigh University; August 2021.
2022	Grumbles D. Response Surface Optimization to Determine Validity Range for Density Modulus Relationship on Intact Ovine Tibiae [Master's thesis]. Lehigh University; August 2022.
2022	Inglis BJ. Biomechanical Duality of Fracture Healing Captured Using Virtual Mechanical Testing and Validated in Ovine Bones [Master's thesis]. Lehigh University; August 2022.
2023	Inacio JHV. Application of Virtual Mechanical Testing on Clinical Bone Fractures [PhD thesis]. Lehigh University; January 2023.
2016	Grassi L. Femoral Strength Prediction Using Finite Element Models: Validation of Models Based on CT and Reconstructed DXA Images Against Full-Field Strain Measurements [PhD thesis]. Lund, Sweden: Lund University; 2016.
2014	Jameson JR. Characterization of Bone Material Properties and Microstructure in Osteogenesis Imperfecta/brittle Bone Disease [PhD thesis]. Marquette University; December 2014.
2020	El-Monajjed K. Implementation of a Virtual Reality Module for Gaining Surgical Access Via Planned Oblique Lateral Lumbar Interbody Fusion [PhD thesis]. McGill University; December 2020.
2022	El Bojairami I. Assessment of Static Spinal Stability and Muscle Activation Strategies: A Comprehensive Approach Via a Novel Validated Finite Elements Spine Model Inclusive of Thoracolumbar Fascia, Intramuscular Pressure, and Intra-Abdominal Pressure [PhD thesis]. McGill University; April 2022.
2013	Vijayakumar V. Quantifying the Regional Variations in the Mechanical Properties of Cancellous Bone of the Tibia Using Indentation Testing and CT Imaging [Master's thesis]. Hamilton, ON: McMaster University; September 2013.
2015	Oftadeh R. Hierarchical Analysis and Multiscale Modelling of Cellular Structures: From Meta Materials to Bone Structure [PhD thesis]. Northeastern University; December 2015.
2015	Gargac J. Evaluation of Bone Healing, Damage, and Adaptation Using Computational Modeling and Image Processing Techniques [PhD thesis]. University of Notre Dame; July 2015.
2010	Garo A. Modélisation du corps vertébral en chargement dynamique: Intégration de l'effet de l'âge [Vertebral Body Modeling in Dynamic Loading: Integration of Age Effects] [PhD thesis]. École polytechnique de Montréal; December 2010.
2015	Bianco R. Biomécanique de l'ancrage de vis pédiculaires pour l'instrumentation du rachis [PhD thesis]. École polytechnique de Montréal; December 2015.
2018	Zimmermann Y. Développement d'une modélisation par éléments finis pour caractérisation non destructive de la biomécanique osseuse à partir d'images MICRO-CT [Master's thesis]. École polytechnique de Montréal; December 2018.
2019	Mustafy T. The Short and Long Term Effects of in Vivo Cyclic Axial Compression Applied During Puberty on Bone Growth, Morphometry and Biomechanics [PhD thesis]. École polytechnique de Montréal; July 2019.
2012	Tozzi G. In Vitro Studies of Bone-Cement Interface and Related Work on Cemented Acetabular Replacement [PhD thesis]. Portsmouth, England: University of Portsmouth; May 29, 2012.
2009	Lievers WB. Effects of Geometric and Material Property Changes on the Apparent Elastic Properties of Cancellous Bone [PhD thesis]. Queen's University; April 2009.
2024	Cameron E. Knee Joint Loading and Fracture Risk Analyses of Patients With Benign Bone Tumours: A Finite Element Analysis [Master's thesis]. Queen's University; August 15, 2024.
2023	Branni MG. Constitutive Models of Bone: The Human Femur [PhD thesis]. Queensland University of Technology; 2023.
2018	Groenen KHJ. Spinal (in)stability in Metastatic Bone Disease: Experimental, Computational, and Clinical Perspectives [PhD thesis]. Radboud University; 2018.
2012	Emerson NJ. Development of Patient-Specific CT-FE Modelling of Bone Through Validation Using Porcine Femora [PhD thesis]. University of Sheffield; September 2012.
2014	Gilchrist SM. Comparison of Proximal Femur Deformations, Failures and Fractures in Quasi-Static and Inertially-Driven Simulations of a Sideways Fall from Standing: An Experimental Study Utilizing Novel Fall Simulation, Digital Image Correlation, and Development of Digital Volume Correlation Techniques [PhD thesis]. Vancouver, BC: University of British Columbia; January 2014.
2016	Gustafson HM. Quantifying the Response of Vertebral Bodies to Compressive Loading Using Digital Image Correlation [PhD thesis]. Vancouver, BC: University of British Columbia; October 2016.
2013	Enns-Bray WS. Mapping Anisotropy of the Proximal Femur for Improved Image-Based Finite Element Analysis [Master's thesis]. Calgary, AB: University of Calgary; August 2013.
2017	Fung A. Experimental Validation of Finite Element Predicted Bone Strain in the Human Metatarsal [Master's thesis]. Calgary, AB: University of Calgary; April 2017.
2008	Goetz JE. Critical Aspects of Modeling Femoral Head Osteonecrosis in the Emu [PhD thesis]. University of Iowa; May 2008.
2012	Mengoni M. On the Development of an Integrated Bone Remodeling Law for Orthodontic Tooth Movements Models Using the Finite Element Method [PhD thesis]. Liège, Belgique: Université de Liège; June 2012.
2020	Amromanoh OA. An Experimental Study of the Effect of Bone Inorganic-Organic Composition on the Mechanical Properties [Master's thesis]. Winnipeg, MB: University of Manitoba; April 2020.
2019	Martig S. Compressive Fatigue Life and Micromorphology of Equine Metacarpal Subchondral Bone [PhD thesis]. University of Melbourne; June 2019.
2011	Wolfram U. Mechanical Multiscale Characterisation of Vertebral Trabecular Bone for the Prediction of Vertebral Fracture Risk [PhD thesis]. University of Ulm; 2011.
2020	Belda González R. Mechanical and Morphometric Characterization of Cancellous Bone [PhD thesis]. Universität Politècnica de València; March 2020.
2013	Amini M. Stiffness of the Proximal Tibial Bone in Normal and Osteoarthritic Conditions: A Parametric Finite Element Simulation Study [Master's thesis]. University of Saskatchewan; January 2013.
2018	Burnett WD. Relationships Between Image-Based and Mechanical Bone Properties With Pain in Knee Osteoarthritis [PhD thesis]. University of Saskatchewan; July 2018.
2018	Hosseini Kalajahi SM. Addressing Partial Volume Artifacts With Quantitative Computed Tomography-Based Finite Element Modeling of the Human Proximal Tibia [Master's thesis]. University of Saskatchewan; April 2018.
2020	Zaluski D. Validation of Subject Specific Computed Tomography-Based Finite Element Models of the Human Proximal Tibia Using Full-Field Experimental Displacement Measurements from Digital Volume Correlation [Master's thesis]. University of Saskatchewan; December 2020.
2014	Pakdel Sefidgar AR. The Craniomaxillofacial Skeleton: New Approaches in Computational Biomechanics and Fracture Stabilization [PhD thesis]. University of Toronto; 2014.
2018	Burke MV. Quantification of Changes in Vertebral Bone Quality in the Presence of Metastases [PhD thesis]. University of Toronto; 2018.
2019	Knowles NK. Improving Material Mapping in Glenohumeral Finite Element Models: A Multi-Level Evaluation [PhD thesis]. University of Western Ontario; 2019.
2021	Kusins J. A Multi-Level Mechanical Assessment of the Shoulder Coupled With Evaluation of Upper Extremity Predictive Finite Element Models [PhD thesis]. University of Western Ontario; 2021.
2009	García-Rodríguez S. Mechanical Behavior of Trabecular Bone [PhD thesis]. University of Wisconsin – Madison; 2009.
2016	Collins CJ. A Comprehensive Evaluation of Methods to Determine Mechanical Properties of Long Bone [PhD thesis]. University of Wisconsin – Madison; 2016.
2016	Meyer LA. Testing and Modeling Mechanical Properties of Ex Vivo Trabecular Bone [PhD thesis]. University of Wisconsin – Madison; 2016.
2022	Soukup JW. Structure-Function Relationships and Quantitative Morphology of the Canine Tooth in Domesticated Dogs [PhD thesis]. University of Wisconsin – Madison; 2022.
2022	Winsor C. Femoral Bone Quantitative CT Analyses With Internal Tissue-Based Phantomless Densitometric CT Calibration [PhD thesis]. University of Wisconsin – Madison; 2022.
2020	Mancuso ME. Defining the Multiscale Relationship Between Subject-Specific Bone Strain and Structural Adaptation in the Distal Radius of Women [PhD thesis]. Worcester, MA: Worcester Polytechnic Institute; July 2020.

Year	Entry
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