In situ parameter identification of optimal density–elastic modulus relationships in subject-specific finite element models of the proximal femur

• Published in: Medical engineering & physics Vol. 33; no. 2; pp. 164 - 173
• Main Authors: Cong, Alexander, Buijs, Jorn Op Den, Dragomir-Daescu, Dan
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.03.2011; Elsevier
• Subjects: Absorptiometry, Photon - methods; Aged; Aged, 80 and over; Biological and medical sciences; Bone density; Bone Density - physiology; Bone FEA; Bone mechanical properties; Compressive Strength; Computed tomography; Computer Simulation; Data processing; Elastic Modulus; Elasticity; Female; Femur; Femur - diagnostic imaging; Finite Element Analysis; Fractures; Fractures, Bone - diagnostic imaging; Fundamental and applied biological sciences. Psychology; Humans; Loading; Male; Mathematical models; Mechanical properties; Middle Aged; Models, Biological; Optimization; Power law; Radiology; Skeleton and joints; Stress, Mechanical; Tomography, X-Ray Computed - methods; Vertebrates: osteoarticular system, musculoskeletal system; Weight-Bearing; Bone FEA; Power law; Optimization; Bone mechanical properties; Human; Elastic modulus; Femur; In situ; Mechanical properties; Identification; Modeling; Osteoarticular system; Finite element method; Medical imagery; Bone mineral density; Computerized axial tomography; Biomedical engineering
• DOI: 10.1016/j.medengphy.2010.09.018
• ISSN: 1350-4533; 1873-4030

Quantitative computed tomography based finite element analysis of the femur is currently being investigated as a method for non-invasive stiffness and strength predictions of the proximal femur. The specific objective of this study was to determine better conversion relationships from QCT-derived bone density to elastic modulus, in order to achieve accurate predictions of the overall femoral stiffness in a fall-on-the-hip loading configuration. Twenty-two femurs were scanned, segmented and meshed for finite element analysis. The elastic moduli of the elements were assigned according to the average density in the element. The femurs were then tested to fracture and force–displacement data were collected to calculate femoral stiffness. Using a training set of nine femurs, finite element analyses were performed and the parameters of the density–elastic modulus relationship were iteratively adjusted to obtain optimal stiffness predictions in a least-squares sense. The results were then validated on the remaining 13 femurs. Our novel procedure resulted in parameter identification of both power and sigmoid functions for density–elastic modulus conversion for this specific loading scenario. Our in situ estimated power law achieved improved predictions compared to published power laws, and the sigmoid function yielded even smaller prediction errors. In the future, these results will be used to further improve the femoral strength predictions of our finite element models.