Research Article Effects of Frequency and Acceleration Amplitude on Osteoblast Mechanical Vibration Responses: A Finite Element Study Liping Wang, 1,2 Hung-Yao Hsu, 3 Xu Li, 1 and Cory J. Xian 1,2 1 Te Tird Afliated Hospital of Southern Medical University, Orthopaedic Hospital of Guangdong Province, Guangzhou 510630, China 2 Sansom Institute for Health Research, School of Pharmacy and Medical Sciences, University of South Australia, Adelaide, SA 5001, Australia 3 School of Engineering, University of South Australia, Adelaide, SA 5095, Australia Correspondence should be addressed to Xu Li; xuli nanfang@sina.com and Cory J. Xian; cory.xian@unisa.edu.au Received 22 June 2016; Revised 29 September 2016; Accepted 20 October 2016 Academic Editor: Ashraf S. Gorgey Copyright © 2016 Liping Wang et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Bone cells are deformed according to mechanical stimulation they receive and their mechanical characteristics. However, how osteoblasts are afected by mechanical vibration frequency and acceleration amplitude remains unclear. By developing 3D osteoblast fnite element (FE) models, this study investigated the efect of cell shapes on vibration characteristics and efect of acceleration (vibration intensity) on vibrational responses of cultured osteoblasts. Firstly, the developed FE models predicted natural frequencies of osteoblasts within 6.85–48.69 Hz. Ten, three diferent levels of acceleration of base excitation were selected (0.5, 1, and 2 g) to simulate vibrational responses, and acceleration of base excitation was found to have no infuence on natural frequencies of osteoblasts. However, vibration response values of displacement, stress, and strain increased with the increase of acceleration. Finally, stress and stress distributions of osteoblast models under 0.5 g acceleration in Z-direction were investigated further. It was revealed that resonance frequencies can be a monotonic function of cell height or bottom area when cell volumes and material properties were assumed as constants. Tese fndings will be useful in understanding how forces are transferred and infuence osteoblast mechanical responses during vibrations and in providing guidance for cell culture and external vibration loading in experimental and clinical osteogenesis studies. 1. Introduction It is widely accepted that bone is a dynamic tissue, because bone remodelling cells (including bone formation cells (osteoblasts) and bone degrading cells (osteoclasts)) can be activated under mechanical stimuli [1]. To analyse the exterior mechanical stimulation received by bone cells and their cellular responses, various mechanical stimuli have been used in in vitro studies since 1970 [2], for example, strain [3], fuid shear stress [4], and vibration [5]. An in vivo investigation of mice subjected to high-frequency mechanical signals suggested that some diseases or metabolic condi- tions can be inhibited or attenuated by vibrational stimuli, for example, adiposity [6]. Similarly, bone formation at the implantation sites and thus the osseointegration of bone- anchored implants can be enhanced by the vibrational stimuli [7, 8]. One in vitro sine-shaped vibration experiment with a displacement amplitude of 25 m and frequencies of 20– 60 Hz applied to the cultured osteoblasts revealed that the vibration with an acceleration amplitude of 0.05 g and fre- quency of 20 Hz was optimal for cell proliferation and that the vibration with 0.13 g and 60 Hz was optimal for metabolic activity [9]. In a later study, a sinusoidal inertia force (at an acceleration amplitude of 0, 0.125 g, 0.25 g, or 0.5 g and frequency of 50 Hz) applied to cultured osteoblasts caused levels of gene expression of alkaline phosphatase (ALP) (a marker of osteogenic diferentiation) to increase with the acceleration amplitude [10]. Furthermore, when MLO-Y4 osteocytes were exposed to low-magnitude, high-frequency vibration (0.3 g, 30, 60, and 90 Hz, 1 hour), their promoting efect on the osteoclast formation was inhibited [11]. Tese biomechanical experimental studies clearly illustrate that Hindawi Publishing Corporation BioMed Research International Volume 2016, Article ID 2735091, 16 pages http://dx.doi.org/10.1155/2016/2735091