Damien Lacroix

A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading.

Bone has a capability to repair itself when it is fractured. Repair involves the generation of intermediate tissues, such as fibrous connective tissue, cartilage and woven bone, before final bone healing can occur. The intermediate tissues serve to stabilise the mechanical environment and provide a scaffold for differentiation of new tissues. The repair process is fundamentally affected by mechanical loading and by the geometric configuration of the fracture fragments. Biomechanical analyses of fracture healing have previously computed the stress distribution within the callus and identified the components of the stress tensor favouring or inhibiting differentiation of particular tissue phenotypes. In this paper, a biphasic poroelastic finite element model of a fracture callus is used to simulate the time-course of tissue differentiation during fracture healing. The simulation begins with granulation tissue (post-inflammation phase) and finishes with bone resorption. The biomechanical regulatory model assumes that tissue differentiation is controlled by a combination of shear strain and fluid flow acting within the tissue. High shear strain and fluid flows are assumed to deform the precursor cells stimulating formation of fibrous connective tissue, lower levels stimulate formation of cartilage, and lower again allows ossification. This mechano-regulatory scheme was tested by simulating healing in fractures with different gap sizes and loading magnitudes. The appearance and disappearance of the various tissues found in a callus was similar to histological observation. The effect of gap size and loading magnitude on the rate of reduction of the interfragmentary strain was sufficiently close to confirm the hypothesis that tissue differentiation phenomena could be governed by the proposed mechano-regulation model.

Biomechanical model to simulate tissue differentiation and bone regeneration: application to fracture healing

Bone regeneration is a common biological process occurring, for example, during fracture healing or osseo-integration of prostheses. Computer simulation of bone regeneration is difficult to carry out because it is a complex sequence of cell-mediated processes regulated by mechanobiological stimuli. An algorithm to predict the time-course of intramembranous and endochondral ossification has been developed. The algorithm assumes that there are precursor cells in the undifferentiated tissue and that these cells differentiate into either fibroblasts (to form fibrous connective tissue), chondrocytes (to form cartilaginous tissue) or osteoblasts (to form bone), based on a combination of biophysical stimuli derived from strain in the collagenous matrix and flow of the interstitial fluid. Both these stimuli are known to deform the precursor cells, and the authors hypothesise that this causes activation of cell differentiation pathways. The observation that precursor cells take time to spread throughout the fracture callus has been included in the algorithm. The algorithm was tested in an investigation of the fracture healing of a long bone using an axisymmetric finite element model. The spatio-temporal sequence of tissue phenotypes that appear in the course of fracture healing was successfully simulated. Furthermore, the origin of the precursor cells (either surrounding muscle, bone marrow or periosteum) was predicted to have a fundamental effect on the healing pattern and on the rate of reduction of the interfragmentary strain (IFS). The initial IFS=0.15 drops to 0.01 within seven iterations if cells originated from the surrounding soft tissue, but took more than 50% longer if cells originated in the inner cambium layer of the periosteum, and four times longer if precursor cells originated from the bone marrow only.

A finite element study of mechanical stimuli in scaffolds for bone tissue engineering

Mechanical stimuli are one of the factors that affect cell proliferation and differentiation in the process of bone tissue regeneration. Knowledge on the specific deformation sensed by cells at a microscopic level when mechanical loads are applied is still missing in the development of biomaterials for bone tissue engineering. The objective of this study was to analyze the behavior of the mechanical stimuli within some calcium phosphate-based scaffolds in terms of stress and strain distributions in the solid material phase and fluid velocity, fluid pressure and fluid shear stress distributions in the pores filled of fluid, by means of micro computed tomographed (CT)-based finite element (FE) models. Two samples of porous materials, one of calcium phosphate-based cement and another of biodegradable glass, were used. Compressive loads equivalent to 0.5% of compression applied to the solid material phase and interstitial fluid flows with inlet velocities of 1, 10 and 100 microm/s applied to the interconnected pores were simulated, changing also the inlet side and the viscosity of the medium. Similar strain distributions for both materials were found, with compressive and tensile strain maximal values of 1.6% and 0.6%, respectively. Mean values were consistent with the applied deformation. When 10 microm/s of inlet fluid velocity and 1.45 Pas viscosity, maximal values of fluid velocity were 12.76 mm/s for CaP cement and 14.87 mm/s for glass. Mean values were consistent with the inlet ones applied, and mean values of shear stress were around 5 x 10(-5)Pa. Variations on inlet fluid velocity and fluid viscosity produce proportional and independent changes in fluid velocity, fluid shear stress and fluid pressure. This study has shown how mechanical loads and fluid flow applied on the scaffolds cause different levels of mechanical stimuli within the samples according to the morphology of the materials.

Finite element study of scaffold architecture design and culture conditions for tissue engineering

Tissue engineering scaffolds provide temporary mechanical support for tissue regeneration and transfer global mechanical load to mechanical stimuli to cells through its architecture. In this study the interactions between scaffold pore morphology, mechanical stimuli developed at the cell microscopic level, and culture conditions applied at the macroscopic scale are studied on two regular scaffold structures. Gyroid and hexagonal scaffolds of 55% and 70% porosity were modeled in a finite element analysis and were submitted to an inlet fluid flow or compressive strain. A mechanoregulation theory based on scaffold shear strain and fluid shear stress was applied for determining the influence of each structures on the mechanical stimuli on initial conditions. Results indicate that the distribution of shear stress induced by fluid perfusion is very dependent on pore distribution within the scaffold. Gyroid architectures provide a better accessibility of the fluid than hexagonal structures. Based on the mechanoregulation theory, the differentiation process in these structures was more sensitive to inlet fluid flow than axial strain of the scaffold. This study provides a computational approach to determine the mechanical stimuli at the cellular level when cells are cultured in a bioreactor and to relate mechanical stimuli with cell differentiation.

The influence of the scaffold design on the distribution of adhering cells after perfusion cell seeding

In natural tissues, the extracellular matrix composition, cell density and physiological properties are often non-homogeneous. Here we describe a model system, in which the distribution of cells throughout tissue engineering scaffolds after perfusion seeding can be influenced by the pore architecture of the scaffold. Two scaffold types, both with gyroid pore architectures, were designed and built by stereolithography: one with isotropic pore size (412 ± 13 μm) and porosity (62 ± 1%), and another with a gradient in pore size (250-500 μm) and porosity (35%-85%). Computational fluid flow modelling showed a uniform distribution of flow velocities and wall shear rates (15-24 s(-1)) for the isotropic architecture, and a gradient in the distribution of flow velocities and wall shear rates (12-38 s(-1)) for the other architecture. The distribution of cells throughout perfusion-seeded scaffolds was visualised by confocal microscopy. The highest densities of cells correlated with regions of the scaffolds where the pores were larger, and the fluid velocities and wall shear rates were the highest. Under the applied perfusion conditions, cell deposition is mainly determined by local wall shear stress, which, in turn, is strongly influenced by the architecture of the pore network of the scaffold.

Commentary: Deciphering the link between architecture and biological response of a bone graft substitute.

Hundreds of studies have been devoted to the search for the ideal architecture for bone scaffold. Despite these efforts, results are often contradictory, and rules derived from these studies are accordingly vague. In fact, there is enough evidence to postulate that ideal scaffold architecture does not exist. The aim of this document is to explain this statement and review new approaches to decipher the existing but complex link between scaffold architecture and in vivo response.

Computational modelling of the mechanical environment of osteogenesis within a polylactic acid–calcium phosphate glass scaffold

A computational model based on finite element method (FEM) and computational fluid dynamics (CFD) is developed to analyse the mechanical stimuli in a composite scaffold made of polylactic acid (PLA) matrix with calcium phosphate glass (Glass) particles. Different bioreactor loading conditions were simulated within the scaffold. In vitro perfusion conditions were reproduced in the model. Dynamic compression was also reproduced in an uncoupled fluid-structure scheme: deformation level was studied analyzing the mechanical response of scaffold alone under static compression while strain rate was studied considering the fluid flow induced by compression through fixed scaffold. Results of the model show that during perfusion test an inlet velocity of 25 microm/s generates on scaffold surface a fluid flow shear stress which may stimulate osteogenesis. Dynamic compression of 5% applied on the PLA-Glass scaffold with a strain rate of 0.005 s(-1) has the benefit to generate mechanical stimuli based on both solid shear strain and fluid flow shear stress on large scaffold surface area. Values of perfusion inlet velocity or compression strain rate one order of magnitude lower may promote cell proliferation while values one order of magnitude higher may be detrimental for cells. FEM-CFD scaffold models may help to determine loading conditions promoting bone formation and to interpret experimental results from a mechanical point of view.

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

Scaffold biomaterials for tissue engineering can be produced in many different ways depending on the applications and the materials used. Most research into new biomaterials is based on an experimental trial-and-error approach that limits the possibility of making many variations to a single material and studying its interaction with its surroundings. Instead, computer simulation applied to tissue engineering can offer a more exhaustive approach to test and screen out biomaterials. In this paper, a review of the current approach in biomaterials designed through computer-aided design (CAD) and through finite-element modelling is given. First we review the approach used in tissue engineering in the development of scaffolds and the interactions existing between biomaterials, cells and mechanical stimuli. Then, scaffold fabrication through CAD is presented and characterization of existing scaffolds through computed images is reviewed. Several case studies of finite-element studies in tissue engineering show the usefulness of computer simulations in determining the mechanical environment of cells when seeded into a scaffold and the proper design of the geometry and stiffness of the scaffold. This creates a need for more advanced studies that include aspects of mechanobiology in tissue engineering in order to be able to predict over time the growth and differentiation of tissues within scaffolds. Finally, current perspectives indicate that more efforts need to be put into the development of such advanced studies, with the removal of technical limitations such as computer power and the inclusion of more accurate biological and genetic processes into the developed algorithms.

Simulation of angiogenesis and cell differentiation in a CaP scaffold subjected to compressive strains using a lattice modeling approach.

Mechanical stimuli are one of the factors that influence tissue differentiation. In the development of biomaterials for bone tissue engineering, mechanical stimuli and formation of a vascular network that transport oxygen to cells within the pores of the scaffolds are essential. Angiogenesis and cell differentiation have been simulated in scaffolds of regular porosity; however, the dynamics of differentiation can be different when the porosity is not uniform. The objective of this study was to investigate the effect of the mechanical stimuli and the capillary network formation on cell differentiation within a scaffold of irregular morphology. A porous scaffold of calcium phosphate based glass was used. The pores and the solid phase were discretized using micro computed tomography images. Cell activity was simulated within the interconnected pore domain of the scaffold using a lattice modeling approach. Compressive strains of 0.5 and 1% of total deformation were applied and two cases of mesenchymal stem cells initialization (in vitro seeding and in vivo) were simulated. Similar capillary networks were formed independently of the cell initialization mode and the magnitude of the mechanical strain applied. Most of vessels grew in the pores at the periphery of the scaffolds and were blocked by the walls of the scaffold. When 0.5% of strain was applied, 70% of the pore volume was affected by mechano-regulatory stimuli corresponding to bone formation; however, because of the lack of oxygen, only 40% of the volume was filled with osteoblasts. 40% of volume was filled with chondrocytes and 3% with fibroblasts. When the mechanical strain was increased to 1%, 11% of the pore volume was filled with osteoblasts, 59% with chondrocytes, and 8% with fibroblasts. This study has shown the dynamics of the correlation between mechanical load, angiogenesis and tissue differentiation within a scaffold with irregular morphology.

Finite element study of a novel intervertebral disc substitute.

Study Design. A new type of composite device with a similar structure to a natural lumbar intervertebral disc was modeled, and its mechanical interaction with a L3–L5 lumbar spine segment was studied by a finite element analysis. Objective. To identify the influence of the prosthesis on the biomechanical changes induced in a L3–L4 lumbar spine segment model after having substituted the physiologic L4–L5 intervertebral disc by the implant. Summary of Background Data. In our societies, the large number of back pain cases highly motivates the investigation of intervertebral disc prostheses. Postoperative complications induced by spinal fusion showed that the mechanical properties of the novel components and its interactivity with the rest of the spine are a critical point. Methods. The prosthesis replaced the L4–L5 intervertebral disc within a previously developed L3–L5 lumbar spine segment physiologic model. The effect of loads in compression, flexion, extension, and axial rotation was simulated, and two types of vertebrae-implant contact were compared to the physiologic model. Results. Models with disc substitute are much stiffer than the physiologic model. In case of perfect contact with the adjacent vertebrae, the implant behaves like a physiologic intervertebral disc and respects the surrounding motion segment biomechanics. Although no traumatic loads were calculated within the adjacent vertebrae, bone remodeling would be expected in the trabecular bone. Conclusion. By using numerical methods, this study allows prediction of the static mechanical behavior of a new device within a lumbar spine structure, which appears very useful for preclinical study.