Computational modeling of bone density profiles in response to gait: a subject-specific approach
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The goal of this study is to explore the potential of computational growth models to predict bone density profiles in the proximal tibia in response to gait-induced loading. From a modeling point of view, we design a finite element-based computational algorithm using the theory of open system thermodynamics. In this algorithm, the biological problem, the balance of mass, is solved locally on the integration point level, while the mechanical problem, the balance of linear momentum, is solved globally on the node point level. Specifically, the local bone mineral density is treated as an internal variable, which is allowed to change in response to mechanical loading. From an experimental point of view, we perform a subject-specific gait analysis to identify the relevant forces during walking using an inverse dynamics approach. These forces are directly applied as loads in the finite element simulation. To validate the model, we take a Dual-Energy X-ray Absorptiometry scan of the subject’s right knee from which we create a geometric model of the proximal tibia. For qualitative validation, we compare the computationally predicted density profiles to the bone mineral density extracted from this scan. For quantitative validation, we adopt the region of interest method and determine the density values at fourteen discrete locations using standard and custom-designed image analysis tools. Qualitatively, our two- and three-dimensional density predictions are in excellent agreement with the experimental measurements. Quantitatively, errors are less than 3% for the two-dimensional analysis and less than 10% for the three-dimensional analysis. The proposed approach has the potential to ultimately improve the long-term success of possible treatment options for chronic diseases such as osteoarthritis on a patient-specific basis by accurately addressing the complex interactions between ambulatory loads and tissue changes.
KeywordsGrowth Open system thermodynamics Density Bone Finite elements Gait analysis
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- Andriacchi TP (1994) Dynamics of knee malalignment. Orthop Clin North Am 25: 395–403Google Scholar
- Andriacchi TP, Natarajan RN, Hurwitz DE (1997) Musculoskeletal dynamics, locomotion, and clinical applications. In: Mow VC, Hayes WC (eds) Basic orthopaedic biomechanics. 4th edn. Lippincott-Raven, Philadelphia, pp 37–67Google Scholar
- Carter DR, Hayes WC (1977) Compressive behavior of bone as a 2-phase porous structure. J Bone Joint Surg 59: 954–962Google Scholar
- Gandolini G, Salvioni PM (2004) Is BMD measurement an adequate surrogate for anti-fracture and efficacy?. Aging Clin Exp Res 16: 29–32Google Scholar
- Kaptoge S, Benevolenskaya LI, Bhalla AK, Cannata JB, Boonen S, Falch JA, Felsenberg D, Finn JD, Nuti R, Hoszowski K, Lorenc R, Miazgowski T, Jajic I, Lyritis G, Masaryk P, Naves-Diaz M, Poor G, Reid DM, Scheidt-Nave C, Stepan JJ, Todd CJ, Weber K, Woolf AD, Roy DK, Lunt M, Pye SR, O’Neill TW, Silman AJ, Reeve J (2005) Low BMD is less predictive than reported falls for future limb fractures in women across Europe: results from the European prospective osteoporosis study. Bone 36: 387–398CrossRefGoogle Scholar
- Radin EL, Rose RM (1986) Role of subchondral bone in the initiation and progression of cartilage damage. Clin Orthop Relat Res 213: 34–40Google Scholar