← Back to Search
Three-dimensional Micro-level Computational Study Of Wolff's Law Via Trabecular Bone Remodeling In The Human Proximal Femur Using Design Space Topology Optimization.
C. Boyle, I. Kim
Published 2011 · Medicine, Engineering
Download PDFAnalyze on Scholarcy
The law of bone remodeling, commonly referred to as Wolff's Law, asserts that the internal trabecular bone adapts to external loadings, reorienting with the principal stress trajectories to maximize mechanical efficiency creating a naturally optimum structure. The goal of the current study was to utilize an advanced structural optimization algorithm, called design space optimization (DSO), to perform a micro-level three-dimensional finite element bone remodeling simulation on the human proximal femur and analyse the results to determine the validity of Wolff's hypothesis. DSO optimizes the layout of material by iteratively distributing it into the areas of highest loading, while simultaneously changing the design domain to increase computational efficiency. The result is a "fully stressed" structure with minimized compliance and increased stiffness. The large-scale computational simulation utilized a 175 μm mesh resolution and the routine daily loading activities of walking and stair climbing. The resulting anisotropic trabecular architecture was compared to both Wolff's trajectory hypothesis and natural femur samples from literature using a variety of visualization techniques, including radiography and computed tomography (CT). The results qualitatively revealed several anisotropic trabecular regions, that were comparable to the natural human femurs. Quantitatively, the various regional bone volume fractions from the computational results were consistent with quantitative CT analyses. The global strain energy proceeded to become more uniform during optimization; implying increased mechanical efficiency was achieved. The realistic simulated trabecular geometry suggests that the DSO method can accurately predict bone adaptation due to mechanical loading and that the proximal femur is an optimum structure as the Wolff hypothesized.
This paper references
An Innovative CCD-Based High-Resolution CT System for Analysis of Trabecular Bone Tissue
F. Baruffaldi (2006)
Computational study of Wolff's law with trabecular architecture in the human proximal femur using topology optimization.
In Gwun Jang (2008)
Mechanical loading history and skeletal biology.
D. Carter (1987)
Proximal femur specimens: automated 3D trabecular bone mineral density analysis at multidetector CT--correlation with biomechanical strength measurement.
M. Huber (2008)
Time Domain Boundary Element Analysis of Wake Fields in Long Accelerator Structures
K. Fujita (2008)
The compressive behavior of bone as a two-phase porous structure.
D. Carter (1977)
Trabecular bone density and loading history: regulation of connective tissue biology by mechanical energy.
D. Carter (1987)
Trabecular Bone Tissue Strains in the Healthy and Osteoporotic Human Femur
B. van Rietbergen (2003)
Analogy of strain energy density based bone-remodeling algorithm and structural topology optimization.
In Gwun Jang (2009)
Mechanical loading histories and cortical bone remodeling
D. Carter (2006)
Scanning electron microscope studies of trabecular bone in the proximal end of the human femur.
W. Whitehouse (1974)
Simulation of Trabecular Surface Remodeling based on Local Stress Nonuniformity.
Taiji Adachi (1997)
Relationships between loading history and femoral cancellous bone architecture.
D. Carter (1989)
Mathematical analysis of trabecular 'trajectories' in apparent trajectorial structures: the unfortunate historical emphasis on the human proximal femur.
J. Skedros (2007)
Determination of muscle loading at the hip joint for use in pre-clinical testing.
M. Heller (2005)
Computer simulation of trabecular remodeling in human proximal femur using large-scale voxel FE models: Approach to understanding Wolff's law.
K. Tsubota (2009)
Automated 3D trabecular bone structure analysis of the proximal femur—prediction of biomechanical strength by CT and DXA
T. Baum (2009)
Structural properties of a new design of composite replicate femurs and tibias.
A. Heiner (2001)
On the Design of Compliant Mechanisms Using Topology Optimization
O. Sigmund (1997)
The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques.
C. Turner (1999)
Adaptive bone-remodeling theory applied to prosthetic-design analysis.
R. Huiskes (1987)
The Law of Bone Remodeling
J. Wolff (1986)
Hip joint loading during walking and running, measured in two patients.
G. Bergmann (1993)
Comparison of micro-level and continuum-level voxel models for strength predictions of the proximal femur
E. Verhulp (2005)
Functional adaptation of cancellous bone in human proximal femur predicted by trabecular surface remodeling simulation toward uniform stress state.
K. Tsubota (2002)
Cancellous bone architecture: advantages of nonorthogonal trabecular alignment under multidirectional joint loading.
R. Pidaparti (1997)
Optimal shape design as a material distribution problem
M. Bendsøe (1989)
Numerical modeling of bone tissue adaptation--a hierarchical approach for bone apparent density and trabecular structure.
P. Coelho (2009)
Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima
O. Sigmund (1998)
Topology optimization of three-dimensional linear elastic structures with a constraint on “perimeter”
P. Fernandes (1999)
The internal architecture of the femur and its clinical significance; the upper end.
W. J. Tobin (1955)
A model of bone adaptation as an optimization process.
M. Bagge (2000)
Direct Three‐Dimensional Morphometric Analysis of Human Cancellous Bone: Microstructural Data from Spine, Femur, Iliac Crest, and Calcaneus
T. Hildebrand (1999)
Das Gesetz der Transformation der Knochen
J. Wolff (1893)
Birth and death of bone cells: basic regulatory mechanisms and implications for the pathogenesis and treatment of osteoporosis.
S. Manolagas (2000)
From Wolff's law to the Utah paradigm: Insights about bone physiology and its clinical applications
H. Frost (2001)
Design space optimization using a numerical design continuation method
I. Kim (2002)
Design space optimization using design space adjustment and refinement
I. G. Jang (2007)
Topology Optimization: "Theory, Methods, And Applications"
M. Bendsøe (2011)
The Maka femur and its bearing on the antiquity of human walking: applying contemporary concepts of morphogenesis to the human fossil record.
C. Lovejoy (2002)
A new approach to variable-topology shape design using a constraint on perimeter
R. Haber (1996)
Composition of trabecular and cortical bone
J. K. Gong (1964)
Application of design space optimization to bone remodeling simulation of trabecular architecture in human proximal femur for higher computational efficiency
I. G. Jang (2010)
Hip contact forces and gait patterns from routine activities.
G. Bergmann (2001)
Bone remodeling in response to in vivo fatigue microdamage.
D. Burr (1985)
Computational simulation of simultaneous cortical and trabecular bone change in human proximal femur during bone remodeling.
I. G. Jang (2010)
An approach for time‐dependent bone modeling and remodeling—theoretical development
G. Beaupré (1990)
This paper is referenced by
Biomechanical analysis of femoral neck strength with respect to femoral head core decompression
P. Brown (2011)
Reconstruction of the biomechanical transfer path of femoral head necrosis: A subject-specific finite element investigation
Guang-Quan Zhou (2014)
Measurement of trabecular bone parameters with different bone thickness and voxel size in mice using micro CT
Nurin Nadzlah Abu Bakar (2019)
The Comparative Analysis of a Novel Acetabular Component against Hemispherical Component in Case of Extensive Acetabular Bone Defects — A Study of Finite Element Analysis
Wenhui Ma (2013)
Développement d'une tige fémorale biomimétique intégrant une structure cellulaire poreuse
Bruno Jetté (2018)
Numerical simulation of load-induced bone structural remodelling using stress-limit criterion
Ali Marzban (2015)
Three-dimensional characterization of trabecular bone mineral density of the proximal ulna using quantitative computed tomography.
J. Gil (2020)
Cancellous bone and theropod dinosaur locomotion. Part I—an examination of cancellous bone architecture in the hindlimb bones of theropods
P. Bishop (2018)
Biomechanical analysis of fibular graft techniques for nontraumatic osteonecrosis of the femoral head: a finite element analysis
J. Xu (2020)
Modeling trabecular microstructure evolution via genetic algorithm
Samuel W. L. Shames (2013)
Trabecular orientation in the human femur and tibia and the relationship with lower-limb alignment for patients with osteoarthritis of the knee.
S. A. Sampath (2015)
Novel “load adaptive algorithm based” procedure for 3D printing of cancellous bone-inspired structures
F. Naddeo (2017)
Scaling relations between trabecular bone volume fraction and microstructure at different skeletal sites.
C. Räth (2013)
Multiscale network characterization of the strength and robustness of trabecular bone
Chantal Nguyen (2019)
Acute Deformity Correction Using an Osteotomy
Vrisha Madhuri (2016)
Trabecular Pattern of the Proximal Ulna: A Morphological Study
George Zafiropoulos (2013)
A general method for the determination of the local orthotropic directions of heterogeneous materials : application to bone structures using μCT images
Christophe Cluzel (2018)
Should thorough Debridement be used in Fibular Allograft with impaction bone grafting to treat Femoral Head Necrosis: a biomechanical evaluation
G. Zhou (2015)
Computational model for the patella onset
Kalenia Márquez-Flórez (2018)
A new intramedullary sustained dynamic compression nail for the treatment of long bone fractures: a biomechanical study.
A. Karakaşlı (2015)
Adiponectin regulates bone mass in AIS osteopenia via RANKL/OPG and IL6 pathway
Hongqi Zhang (2019)
Three-Dimensional Characterization of Trabecular Bone Mineral Density of the Distal Radius Utilizing Quantitative Computed Tomography
Tyler S Pidgeon (2018)
A new efficient convergence criterion for reducing computational expense in topology optimization: reducible design variable method
S. Kim (2012)
The heterogeneity in femoral neck structure and strength
M. Kersh (2013)
Trabecular bone adaptation in a finite element frame model using load dependent fabric tensors
Éva Lakatos (2012)
Deterioration of Stress Distribution Due to Tunnel Creation in Single-Bundle and Double-Bundle Anterior Cruciate Ligament Reconstructions
Jie Yao (2012)
Effect of magnetic field on poroelastic bone model for internal remodeling
A. M. Abd-Alla (2013)
A Multi-Scale Approach to Implications of the Preferred Vertebral Trabecular Orientation on Spine Biomechanics
A. Gudde (2018)
Femoral bone mesoscale structural architecture prediction using musculoskeletal and finite element modelling
A. Phillips (2015)
Osteogenesis effect of biomaterials analyzed using topology optimization
Wang Lan (2015)
Human skeletal system virtualization by using solid voxels models
J. Alonso (2013)
A multiobjective topology optimization approach for cost and time minimization in additive manufacturing
L. Ryan (2019)See more