title: Relationship between the shape and density distribution of the femur and its natural frequencies of vibration.
abstract: It has been recently suggested that mechanical loads applied at frequencies close to the natural frequencies of bone could enhance bone apposition due to the resonance phenomenon. Other applications of bone modal analysis are also suggested. For the above-mentioned applications, it is important to understand how patient-specific bone shape and density distribution influence the natural frequencies of bones. We used finite element models to study the effects of bone shape and density distribution on the natural frequencies of the femur in free boundary conditions. A statistical shape and appearance model that describes shape and density distribution independently was created, based on a training set of 27 femora. The natural frequencies were then calculated for different shape modes varied around the mean shape while keeping the mean density distribution, for different appearance modes around the mean density distribution while keeping the mean bone shape, and for the 27 training femora. Single shape or appearance modes could cause up to 15% variations in the natural frequencies with certain modes having the greatest impact. For the actual femora, shape and density distribution changed the natural frequencies by up to 38%. First appearance mode that describes the general cortical bone thickness and trabecular bone density had one of the strongest impacts. The first appearance mode could therefore provide a sensitive measure of general bone health and disease progression. Since shape and density could cause large variations in the calculated natural frequencies, patient-specific FE models are needed for accurate estimation of bone natural frequencies.
authors.affiliation: Department of Biomechanical Engineering, Faculty of Mechanical, Maritime, and Materials Engineering, Delft University of Technology (TU Delft), Mekelweg 2, Delft 2628 CD, The Netherlands.
authors.forename: G
authors.initials: G
authors.lastname: Campoli
authors.affiliation: Biomechanics and Imaging Group, Department of Orthopaedics, Leiden University Medical Center, P.O. Box 9600, 2300 RC Leiden, The Netherlands.
authors.forename: N
authors.initials: N
authors.lastname: Baka
authors.affiliation: Biomechanics and Imaging Group, Department of Orthopaedics, Leiden University Medical Center, P.O. Box 9600, 2300 RC Leiden, The Netherlands.
authors.forename: B L
authors.initials: BL
authors.lastname: Kaptein
authors.affiliation: Department of Biomechanical Engineering, Faculty of Mechanical, Maritime, and Materials Engineering, Delft University of Technology (TU Delft), Mekelweg 2, Delft 2628 CD, The Netherlands; Biomechanics and Imaging Group, Department of Orthopaedics, Leiden University Medical Center, P.O. Box 9600, 2300 RC Leiden, The Netherlands.
authors.forename: E R
authors.initials: ER
authors.lastname: Valstar
authors.affiliation: Visualization & Data Analysis Medical Planning & Computational Medicine Groups, Zuse Institute Berlin (ZIB), Berlin, Germany.
authors.forename: S
authors.initials: S
authors.lastname: Zachow
authors.affiliation: Department of Biomechanical Engineering, Faculty of Mechanical, Maritime, and Materials Engineering, Delft University of Technology (TU Delft), Mekelweg 2, Delft 2628 CD, The Netherlands; Departments of Orthopedics and Rheumatology, Utrecht University Medical Center, Utrecht, The Netherlands.
authors.forename: H
authors.initials: H
authors.lastname: Weinans
authors.affiliation: Department of Biomechanical Engineering, Faculty of Mechanical, Maritime, and Materials Engineering, Delft University of Technology (TU Delft), Mekelweg 2, Delft 2628 CD, The Netherlands. Electronic address: a.a.zadpoor@tudelft.nl.
authors.forename: A A
authors.initials: AA
authors.lastname: Zadpoor
mesh_terms: D015519:Bone Density; D005260:Female; D005269:Femur / Q000033:anatomy & histology* / Q000000981:diagnostic imaging / Q000502:physiology*; D020342:Finite Element Analysis; D006801:Humans; D008297:Male; D066230:Patient-Specific Modeling; D014057:Tomography, X-Ray Computed; D014732:Vibration
keywords: Bone appearance; Bone shape; Femur; Finite element method; Modal analysis