Copyright © 2014 American Scientific Publishers All rights reserved Printed in the United States of America RESEARCH ARTICLE Journal of Medical Imaging and Health Informatics Vol. 4, 1–5, 2014 Application of a Multi-Scale Mechanobiological Model for Bone Remodeling Emílio G. F. Mercuri ∗ , André L. Daniel, Roberto D. Machado, and Mildred B. Hecke Bioengineering Group, Federal University of Parana, Centro Politécnico—Jardim das Américas—C.P. 19011, CEP 81531-980, Curitiba, Paraná, Brazil Bone tissue is a dynamic system capable of changing its own density in response to biomechanical stimuli. The biological system studied herein consists of three cellular types, responsive osteoblasts, active osteoblasts and osteoclasts, and four types of signaling molecules, PTH, TGF-, RANKL and OPG. This article examines the biological response to a specific mechanical stimulus in a cellular model for bone remodeling. A two-dimensional example is proposed with spatial discretization performed through the finite element method. The temporal evolution of the biological variables and bone density is obtained using the Runge-Kutta method. Deformation energy served as mechanical stimulus to trigger cellular activity demonstrating the temporal evolution of density distribution in a model of a standard femur. This distribution is in agreement with other models in the literature. The main contribution of this paper is the coupling of mechanical and biological models. Another important fact is that the results can represent the local behavior of the proposed biological variables. The given example is a first step in the development of more advanced models to represent the imbalance of bone homeostasis. Keywords: Bone Remodeling, Finite Element Method, Multi-Scale Biomodeling, Mechanotransduction. 1. INTRODUCTION Osteoporosis is among the greatest public health problems. 1 The Brazilian Osteoporosis Study 2 (BRAZOS) indicated that approx- imately 6% of the adult Brazilian population suffers from osteo- porosis. The same study indicated that 12.8% of men and 15.1% of women above 50 years old have suffered low-impact fractures, also indicative of osteoporosis. Various pathological states can lead to abnormal bone modeling and remodeling activity. Dis- eases such as cancer, rheumatoid arthritis and Paget’s disease can affect the behavior of bone remodeling, leading to increased bone resorption and weakening. 3 4 In 1969, Frost described how cellular groups could unite to remodel tissue in a principle known as the mechanostat. 5 This principle states that an increase in the mechanical stress on a bone increases its resistance, and the mechanical disuse of a body part leads to an increase in tissue removal and, therefore, a loss of mineral density. In both cases, the change in mechanical resis- tance is caused by a phenomenon known as bone remodeling. 6 Computational studies can be used to test modeling and remodeling hypotheses ranging from the analysis of the effects of hormones, such as parathyroid (PTH), on cellular com- munication up to the phenomenon of stress shielding caused by prosthetics. 7 8 In this context, numerical and computational modeling aid in predicting the organization of such non-linear ∗ Author to whom correspondence should be addressed. biological systems. 9 The mathematical study of biological activ- ities in bone remodeling influenced by mechanical stimuli can therefore assist in making decisions regarding new directions for research and pharmacological interventions. Several models present the coupling of ordinary differential equations to simulate cell signaling between osteoblasts and osteoclasts; 7 10 11 however, none have dealt with a macroscopic bone geometry. This study aims to use a cellular interaction model (coupling of osteoclasts and osteoblasts) within a mechanical model of the bone tissue. The application is conducted considering the two- dimensional geometry of a femur. A mechanical stimulus is used to check and compare the response of the cellular model in updat- ing the physical properties of the bone. 2. MATERIAL AND METHODS The numerical calculation consists of a two-dimensional tran- sient analysis of the variation in constitutive bone properties and the geometry of the proximal region of the femur, which was obtained through a standardized femur solid model provided by the Biomechanics European Laboratory (BEL) Repository. 12 The adaptation required for the two-dimensional analysis was per- formed in the frontal plane in the central region of the femur. The finite element mesh, constructed and tested in MATLAB ®13 by the authors, contains 598 quadrilateral elements and 1979 nodes, and the dimensions of the model are provided in Figure 1. J. Med. Imaging Health Inf. Vol. 4, No. 1, 2014 2156-7018/2014/4/001/005 doi:10.1166/jmihi.2014.1229 1