TECHNICAL PAPER Bone density growth and the biomechanics of healthy and prosthetic femur Joan O’Connor 1 • Lavinia A. Borges 1 • Fernando P. Duda 1,2 • Anto ˆnio G. B. da Cruz 3 Received: 5 March 2017 / Accepted: 25 July 2017 / Published online: 7 August 2017 Ó The Brazilian Society of Mechanical Sciences and Engineering 2017 Abstract The development of computational models to describe bone behavior when prosthetic devices are used has gained tremendous importance. In particular, compu- tational modeling for bone growth and resorption processes can be a useful tool to determine the implant success or failure. We present a model for investigating bone density growth for healthy and prosthetic femur with a total hip arthroplasty. The model, which is based on a continuum theory for density growth and remodeling in biological materials that accounts for the coupling between biological and mechanical effects, is implemented in COMSOL Multiphysics and two simulation examples are presented. In the first example, where mechanical loads due to daily physical activities are considered, it is shown that higher stress zones (in prosthetic femur mid-diaphysis of about 46 MPa) and lower stress zones (in prosthetic femur neck of about 28 MPa) are candidates for bone growth and resorption zones, respectively. In addition, it is shown that higher and lower stress levels in these zones may lead to possible periprosthetic fractures (bone mid-diaphysis overloaded in 7–10 MPa post-operatively) and eventually to implant aseptic loosening due to resorption (bone femoral neck unloaded in 13–17 MPa post-operatively). In the second example, where the mechanical load corre- sponds to the average of the loads considered previously, the obtained results for bone density are in good agreement with real bone density distribution in the proximal femur, which illustrates the model capability to locate bone den- sity growth zones (of about 1615 kg=m 3 in the mid-dia- physis) and bone density resorption zones (of about 1259 kg=m 3 in the neck) due to mechanical loads for the femur post-operative condition after a total hip arthroplasty sur- gical procedure. Keywords Bone  Continuum mechanics  Density growth  Finite elements 1 Introduction Total hip arthroplasty (THA) implantations associated with degenerative and traumatic hip conditions, such as osteoarthritis, post-traumatic arthritis, and hip fractures, reach about 500,000 procedures performed annually in the UK and USA, and are estimated in more than one million worldwide [26, 52, 60]. In addition, the elderly population is growing as life expectancy increases; consequently, the demand for THA is increasing and is expected to grow by 174% in about 572,000 THA by the year 2030, only in the Technical Editor: Estevam Barbosa Las Casas. & Joan O’Connor joan@mecsol.ufrj.br Lavinia A. Borges lavinia@ufrj.br Fernando P. Duda duda@mecanica.coppe.ufrj.br Anto ˆnio G. B. da Cruz aguicruz@ufpa.br 1 Department of Mechanical Engineering, PEM/COPPE, Federal University of Rio de Janeiro, UFRJ, PO Box 68503, Rio de Janeiro, RJ 21945-970, Brazil 2 Department of Nanotechnology Engineering Program, PENt/ COPPE, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ 21941-972, Brazil 3 Faculty of Mechanical Engineering, ITEC, Federal University of Para ´, PO Box 8619, Bele ´m, PA 66.075-900, Brazil 123 J Braz. Soc. Mech. Sci. Eng. (2017) 39:3743–3756 DOI 10.1007/s40430-017-0874-x