Jean Marie Crolet

Human cortical bone: the SiNuPrOs model

Many models that have been developed for cortical bone oversimplify much of the architectural and physical complexity. With SiNuPrOs model, a more complete approach is investigated: it is multiscale because it contains five structural levels and multi physic because it takes into account simultaneously structure (with various properties: elasticity, piezoelectricity, porous medium), fluid and mineralization process modelization. The multiscale aspect is modeled by using 18 structural parameters in a specific application of the mathematical theory of homogenization and 10 other physical parameters are necessary for the multi physic aspect. The modelization of collagen as a piezoelectric medium has needed the development of a new behaviour law allowing a better simulation of the effect of a medium considered as evolving during a mineralization process. Then the main interest of SiNuPrOs deals with the possibility to study, at each level of the cortical architecture, either the elastic properties or the fluid motion or the piezoelectric effects or both of them. All these possibilities constitute a very large work and all this mass of information (fluid aspects, even at the nanoscopic scale, piezoelectric phenomena and simulations) will be presented in several papers. This first one is only devoted to the presentation of this model with an application to the computation of elastic properties at the macroscopic scale. The computational methods have been packed into software also called SiNuPrOs and allowing a large number of predictive simulations corresponding to various different configurations.

A new numerical concept for modeling hydroxyapatite in human cortical bone.

This research presents a new modelling procedure which allows the computation of the physical properties of the human cortical bone, considered as a strongly heterogeneous medium consisting of bony architecture and the physical properties of the two basic components: the collagen and the hydroxyapatite (Hap). The numerical simulations are based on the homogenisation theory, however, since the size of the Hap crystals are small compared to the size of a collagen stick, a new entity (the elementary volume of mineral content (EVMC)) is defined at the nanoscopic scale. This model permits the testing of all the possible structural configurations that may be present and suggests that the anisotropy of the bone is not only induced by the haversian structure but by the properties of the Hap crystals and their special organisation.

Human cortical bone: the SiNuPrOs model. Part II--a multi-scale study of permeability.

Cortical bone is more and more considered as a porous medium and this induces the necessity of the determination of the physical properties associated with such a concept: the porosity and the permeability. If porosity does not present a major problem, at least for the order of magnitude, there is a difficulty for the permeability. According to experimental sources, values vary between 10− 13 and 10− 23 m2: it seems obvious that the same entities have not been measured. This article proposes a new vision of the permeability based on a concept of multi-scale medium corresponding to the scales already introduced in the SiNuPrOs model which has been developed for cortical bone. According to this model, several architectural levels are proposed and a mathematical development based on the homogenisation theory, which can be applied to each of these levels, allows a numerical computation of the permeability tensor coefficients. A comparative analysis of our simulations and some experimental results (already published) shows a good accordance with the literature.

Mechanotransduction in cortical bone and the role of piezoelectricity: a numerical approach

This paper is a contribution to a plausible explanation of the mechanotransduction phenomenon in cortical bone during its remodelling. Our contribution deals only with the mechanical processes and the biological aspects have not been taken into account. It is well known that osteoblasts are able to generate bone in a suitable bony substitute only under fluid action. But the bone created in this manner is not organised to resist specific mechanical stress. Our aim was to suggest the nature of the physical information that can be transmitted – directly or via a biological or biochemical process – to the cell to initiate a cellular activity inducing the reconstruction of the osteon that is best adapted to local mechanical stresses. For this, the cell must have, from our point of view, a good knowledge of its structural environment. But this knowledge exists at the cellular scale while the bone is loaded at the macroscopic scale. This study is based on the SiNuPrOs model that allows exchange of information between the different structural scales of cortical bone. It shows that more than the fluid, the collagen – via its piezoelectric properties – plays an essential role in the transmission of information between the macroscopic and nanoscopic scales. Moreover, this process allows us to explain various dysfunctions and even some diseases.

Collagen fibres effect on the mechanical properties of cortical bone. A numerical approach

Many models of cortical bone oversimplify architecture and its physical complexity. A more complete approach is investigated with the SiNuPrOs model (Racila and Crolet 2007, 2008). This model is multi scale because it contains five structural levels and multi physic because it takes into account structure (with various properties: elasticity, piezoelectricity, porous media), fluid and mineralisation process modelisation. The multi scale aspect is modelled by using 18 structural parameters in a specific application of the mathematical theory of homogenisation and 10 other physical parameters are used for the multi physic aspect. The modelisation of Hap crystallisation around collagen needs a new behaviour law allowing a better simulation of the mineralisation process. The computational methods have been packed into software also called SiNuPrOs that allows a large number of predictive simulations corresponding to various configurations. We used this software to study the role of the collagen fibre orientation in the mechanical behaviour of cortical bone.

Decreasing of mechanotransduction process with age

Bone remodelling is a very complex process involving several inter-related phenomena. It is known that mechanotransduction is one of them and there are various attempts to explain this process. Recently, it was shown (Crolet et al. 2010) using the SiNuPrOs model (PredoiRacila and Crolet 2008), which is both a mathematical model and a numerical simulation of the mechanical behaviour of human cortical bone, that after adhesion on a bone surface, cells could determine the mechanical properties of the surrounding tissue and, in particular, its degree of mineralisation. For a consistent explanation, one must assume that the cell responds to this information either by continuing the process of mineralisation or by inhibiting the order to destroy the structure. If our interpretation of this process is correct, it should help us to explain a few pathologies. The case proposed here is the ageing of bone tissue. The question is to know what happens to the mechanical stimuli that the structure induces when a patient ages.

Numerical simulation of fluid flow in the cortical part of a human femur

The homogenisation method developed in SiNuPrOs (Racila and Crolet 2007; Predoi-Racila and Crolet 2008) which is a mathematical model for human cortical bone, in order to determine macroscopic elastic properties from an architecture and the physical characteristics of the basic components, is now applied to the porous aspect of this medium. One preserves the hierarchical organisation of the architecture; therefore it is possible to compute different permeabilities for the various scales. Moreover, the coupling between these results and the elastic properties leads to poro-elastic simulations of a healthy femur. One pursues a macroscopic comparative analysis of the pressure and velocity fields depending on the localisation and the fluid viscosity in bone.

SINUPROS: human cortical bone multiscale model with a fluide–structure interaction

Cells live in a fluid environment located in a biological tissue and the knowledge of the behaviour of this fluid needs the knowledge of the tissue itself. In the present study, the biological tissue is the cortical bone which has a very complex architecture.

Dissecan osteochondritis of the elbow: a possible explanation with a numerical study

The osteochondritis is a developmental pathology that involves failure of normal development of the subchondral bone and articular cartilage of a joint. The term ‘dissecans’ refers to the case in which the lesion becomes completely detached from the rest of the bone, forming a loose body within the joint space. Such disorder only occurs in elbows of young athletes (children and adolescents) practicing competitive sports that involve repetitive movements of compression and hyperextension. The clinical model is the young baseball player (Figure 1). We are interested in the mechanism leading to such anomalies. It seems that bone remodelling must be considered for the understanding of this phenomenon. Several simulations have been developed to investigate the process of bone remodelling; in our study, we used the SiNuPrOs model (Predoi-Racila and Crolet 2008). The first analysis induced a paradoxal comment: the patient is young without health problems, and one can presume that all his physiological functions are efficient. The results obtained with SiNuPrOs show that an increase in physical activity leads to an increased process of bone remodelling.With such conditions, we should have a very good bone remodelling, but clinical observation proves that it is not. We can then conclude that bone remodelling is faulted: either young bone is immediately destroyed in response to high loading forces or the remodelling process induces itself the destruction of bone. The first assumption needs to accept that a large area of bone is under remodelling during the same period. Why is such a wide area found in one place and not elsewhere?We studied the second possibility because the SiNuPrOs model does not take into account a change in the bone remodelling law in the case of great external loads applied to bone. Several studies have already shown that the collagen plays a key role in bone remodelling: it can initiate the mineralisation process acting as a site of nucleation (Ferreira et al. 2009) and stimulate both bone resorption and formation (Fernandez et al. 2012). So, we decided to investigate the mechanical response of a collagen fibre in earlier steps of mineralisation.

Simulation of bone ingrowth in non-resorbable substitutes

It is now recognised that the cells responsible for bone remodelling could respond to two stimuli: a fluid flow around them or a potential difference existing on the free surface of collagen fibres where they adhere. Responses to these stimuli have different consequences: destruction of bone and building of new tissue with the same architecture or with a different architecture. If cells can create bone or fibrous tissue just when bathed in a fluid, how can they deduce the optimal architecture they must build? However, the electrical potential generated, thanks to the piezoelectric properties of collagen fibres, can provide this functional information because it is directly linked to the mechanical information inside the bony structure. The SiNuPros model (Predoi-Racila and Crolet 2008) shows that collagen is the perfect agent to transduce both the nature and the orientation of mechanical stresses to which bone is subjected. We are interested by the evaluation of fluid effect on bone remodelling, and for this we study the behaviour of porous non-resorbable bone graft substitutes because, in this case, the electric potential stimulus due to collagen does not exist. The first part of this study aimed at reviewing the influence of macropore diameter and macroporosity percentage on bone ingrowth in such substitutes. In our review based on 28 experimental and clinical studies, macroporosity percentage, macropore diameter and interconnectivity have been shown to affect bone ingrowth within a porous substitute. Microporosity most likely contributes to a faster development of the vascular network and to nutrient transfer (Hing et al. 2005), so it plays a minor role for bone ingrowth in non-resorbable substitutes. The presence of well-interconnected pores, rather than porosity percentage, is suitable to bone ingrowth; but since it is most difficult to evaluate interconnection size and most of the time the interconnection size is not quantified in commercial bone substitute, we decided to consider porosity (the sum of pore space and interconnection space). To summarise, the minimum requirement for macropore size in porous bone substitute is 100mm (Karageorgiou and Kaplan 2005); smaller pores usually allow fibrous or osteoid unmineralised tissue ingrowth. However, the optimal range of macropore size is still controversial: porous Nitinol bone substitutes show the highest bone ingrowth, even when the pore size is at the limit of the commonly accepted range (Zhu et al. 2008), and no significant differences have been found in bone ingrowth among the different porosity sizes. In synthetic porous hydroxyapatite and porous titanium bone substitutes, the volume of bone ingrowth is directly related to both percentage and size of macroporosity; however, in a porous titanium bone substitute with macropore size ranging from 50 to 125mm, good bone ingrowth can be observed (Xiangmei et al. 2011). Regarding porosity, it ranges from 39% to 80% in porous titanium bone substitute; from 42% to 66% in the porous Nitinol bone substitutes and from 30% to 80% in the synthetic hydroxyapatite bone substitutes. High porosity is favourable for bone ingrowth, but it results in a loss of mechanical properties.