Multiscale investigation of the functional properties of the human femur

Abstract

The mechanical strength of human bones has often been investigated in the past. Bone failure is related to musculoskeletal loading, tissue properties, bone metabolism, etc. This is intrinsically a multiscale problem. However, organ-level performance in most cases is investigated as a separate problem, incorporating only part (if any) of the information available at a higher scale (body level) or at a lower one (tissue level, cell level). A multiscale approach is proposed, where models available at different levels are integrated. A middle-out strategy is taken: the main model to be investigated is at the organ level. The organ-level model incorporates as an input the outputs from the bodylevel (musculoskeletal loads), tissue-level (constitutive equations) and cell-level models (bone remodelling). In this paper, this approach is exemplified by a clinically relevant application: fractures of the proximal femur. We report how a finite-element model of the femur (organ level) becomes part of a multiscale model. A significant effort is related to model validation: a number of experiments were designed to quantify the model's sensitivity and accuracy. When possible, the clinical accuracy and the clinical impact of a model should be assessed. Whereas a large amount of information is available at all scales, only organ-level models are really mature in this perspective. More work is needed in the future to integrate all levels fully, while following a sound scientific method to assess the relevance and validity of such an integrated model.

Computer-aided design and finite-element modelling of biomaterial scaffolds for bone tissue engineering

“…Multiscale modelling has been developed in many disciplines (Stoneham & Harding 2003;Coveney & Fowler 2005;Cohen & Harel 2007;Southern et al 2008). Already multiscale analyses have been applied to the heart (Noble 2002), cancer (Bellomo et al 2008), the design of aortic valves (Weinberg & Kaazempur Mofrad 2009), trabecular bone failure (Müller & van Lenthe 2006), teeth (Miura et al 2009) and the human femur (Cristofolini et al 2008). It has recently been applied to tissue engineering for bone regeneration (Sanz-Herrera et al 2009).…”

Extracting accurate strain measurements in bone mechanics: A critical review of current methods

“…In the same years, the group of Cristofolini & Viceconti performed several studies aimed at experimentally measuring the strain response of intact bones using SGs [8], [13], [35]. The strain distribution in the proximal human femoral metaphysis was measured in different configurations resembling single leg stance, using non-destructive tests [36].…”

“…However, there is no consensus about the optimal constitutive model and bone strength criterion to be implemented in such FE models [4]- [7]. This is because bone is a complex composite material, with properties that among other things change with time-and length-scale [8], [9]. Treating bone fractures, e.g.…”

Multiscale Bone Remodelling with Spatial P Systems

“…The state of each cell j in C (i,2) at a time t (i,2) is defined by its mass fraction m j (i,2) (t (i,2) ), varying from 0 (bone marrow) to 1 (fully mineralized). The mechanical stimulus F ,2) ) the strain energy density of j at time t (i,2) -is calculated by the Meshless Cell Method [9] (MCM). Each cell j modifies its mass according to the error signal e j (i,2) (t (i,2) ) between the mechanical stimulus and the internal equilibrium state, determined by the condition e j (i,2) (t (i,2) ) = 0; when this condition does not hold, a local collision formula 5 modifies the mass fraction (m j (i,2) (t (i,2) + ∆t (i,2) )) to restore the equilibrium condition.…”

“…morphology and metabolic activity) [7,8,17]. On the contrary, the actual knowledge about bone remodelling shows several gaps at different resolution degrees at the same time [9]. For instance:…”