Paulo R. Fernandes

Numerical modeling of bone tissue adaptation—A hierarchical approach for bone apparent density and trabecular structure

In this work, a three-dimensional model for bone remodeling is presented, taking into account the hierarchical structure of bone. The process of bone tissue adaptation is mathematically described with respect to functional demands, both mechanical and biological, to obtain the bone apparent density distribution (at the macroscale) and the trabecular structure (at the microscale). At global scale bone is assumed as a continuum material characterized by equivalent (homogenized) mechanical properties. At local scale a periodic cellular material model approaches bone trabecular anisotropy as well as bone surface area density. For each scale there is a material distribution problem governed by density-based design variables which at the global level can be identified with bone relative density. In order to show the potential of the model, a three-dimensional example of the proximal femur illustrates the distribution of bone apparent density as well as microstructural designs characterizing both anisotropy and bone surface area density. The bone apparent density numerical results show a good agreement with Dual-energy X-ray Absorptiometry (DXA) exams. The material symmetry distributions obtained are comparable to real bone microstructures depending on the local stress field. Furthermore, the compact bone porosity is modeled giving a transversal isotropic behavior close to the experimental data. Since, some computed microstructures have no permeability one concludes that bone tissue arrangement is not a simple stiffness maximization issue but biological factors also play an important role.

Permeability analysis of scaffolds for bone tissue engineering

Porous artificial bone substitutes, especially bone scaffolds coupled with osteobiologics, have been developed as an alternative to the traditional bone grafts. The bone scaffold should have a set of properties to provide mechanical support and simultaneously promote tissue regeneration. Among these properties, scaffold permeability is a determinant factor as it plays a major role in the ability for cells to penetrate the porous media and for nutrients to diffuse. Thus, the aim of this work is to characterize the permeability of the scaffold microstructure, using both computational and experimental methods. Computationally, permeability was estimated by homogenization methods applied to the problem of a fluid flow through a porous media. These homogenized permeability properties are compared with those obtained experimentally. For this purpose a simple experimental setup was used to test scaffolds built using Solid Free Form techniques. The obtained results show a linear correlation between the computational and the experimental permeability. Also, this study showed that permeability encompasses the influence of both porosity and pore size on mass transport, thus indicating its importance as a design parameter. This work indicates that the mathematical approach used to determine permeability may be useful as a scaffold design tool.

Fabrication of computationally designed scaffolds by low temperature 3D printing

The development of artificial bone substitutes that mimic the properties of bone and simultaneously promote the desired tissue regeneration is a current issue in bone tissue engineering research. An approach to create scaffolds with such characteristics is based on the combination of novel design and additive manufacturing processes. The objective of this work is to characterize the microstructural and the mechanical properties of scaffolds developed by coupling both topology optimization and a low temperature 3D printing process. The scaffold design was obtained using a topology optimization approach to maximize the permeability with constraints on the mechanical properties. This procedure was studied to be suitable for the fabrication of a cage prototype for tibial tuberosity advancement application, which is one of the most recent and promising techniques to treat cruciate ligament rupture in dogs. The microstructural and mechanical properties of the scaffolds manufactured by reacting α/β-tricalcium phosphate with diluted phosphoric acid were then assessed experimentally and the scaffolds strength reliability was determined. The results demonstrate that the low temperature 3D printing process is a reliable option to create synthetic scaffolds with tailored properties, and when coupled with topology optimization design it can be a powerful tool for the fabrication of patient-specific bone implants.

Multiscale modeling of bone tissue with surface and permeability control

Natural biological materials usually present a hierarchical arrangement with various structural levels. The biomechanical behavior of the complex hierarchical structure of bone is investigated with models that address the various levels corresponding to different scales. Models that simulate the bone remodeling process concurrently at different scales are in development. We present a multiscale model for bone tissue adaptation that considers the two top levels, whole bone and trabecular architecture. The bone density distribution is calculated at the macroscale (whole bone) level, and the trabecular structure at the microscale level takes into account its mechanical properties as well as surface density and permeability. The bone remodeling process is thus formulated as a material distribution problem at both scales. At the local level, the biologically driven information of surface density and permeability characterizes the trabecular structure. The model is tested by a three-dimensional simulation of bone tissue adaptation for the human femur. The density distribution of the model shows good agreement with the actual bone density distribution. Permeability at the microstructural level assures interconnectivity of pores, which mimics the interconnectivity of trabecular bone essential for vascularization and transport of nutrients. The importance of this multiscale model relays on the flexibility to control the morphometric parameters that characterize the trabecular structure. Therefore, the presented model can be a valuable tool to define bone quality, to assist with diagnosis of osteoporosis, and to support the development of bone substitutes.

On the optimal shape of hip implants

The success of a total hip arthroplasty is strongly related to the initial stability of the femoral component and to the stress shielding effect. In fact, for cementless stems, initial stability is essential to promote bone ingrowth into the stem coating. An inefficient primary stability is also a cause of thigh pain. In addition, the bone adaptation after the surgery can lead to an excessive bone loss and, consequently, can compromise the success of the implant. These factors depend on prosthesis design, namely on material, interface conditions and shape. Although, surgeons use stems with very different geometries, new computational tools using structural optimization methods have been used to achieve a better design in order to improve initial stability and therefore, the implant durability. In this work, a multi-criteria shape optimization process is developed to study the relationship between implants performance and geometry. The multi-criteria objective function takes into account the initial stability of the femoral stem and the effect of stress shielding on bone adaptation after the surgery. Then, the optimized stems are tested using a concurrent model for bone remodeling and osseointegration to evaluate long-term performance. Additionally, the sensitivity to misalignments is analyzed, since femoral stems are often placed in varus or valgus position. Results show that the different criteria are contradictory resulting in different characteristics for the hip stem. However, the multi-criteria formulation leads to compromise solutions, with a combination of the geometric characteristics obtained for each criterion separately.

Parallel computing techniques applied to the simultaneous design of structure and material

In this work a computational procedure for two-scale topology optimization problem using parallel computing techniques is developed. The goal is to obtain simultaneously the best structure and material, minimizing structural compliance. An algorithmic strategy is presented in a suitable way for parallelization. In terms of parallel computing facilities, an IBM Cluster 1350 is used comprising 70 computing nodes each with two dual core processors, for a total of 280 cores. Scalability studies are performed with mechanical structures of low/moderate dimensions. Finally the applicability of the proposed methodology is demonstrated solving a grand challenge problem that is the simulation of trabecular bone adaptation.

Influence of femoral stem geometry, material and extent of porous coating on bone ingrowth and atrophy in cementless total hip arthroplasty: an iterative finite element model

This work presents a computational model for the concurrent study of bone remodelling and ingrowth around cementless femoral stems in total hip arthroplasty. It is assumed that biological fixation depends upon the magnitude of relative displacement at the bone–stem interface as well as an ongoing updating of interface conditions during the remodelling process. The remodelling model determines the distribution of bone density by producing the stiffest structure for a given set of biological conditions at the point of equilibrium in bone turnover. Changes in bone density and patterns of ingrowth are compared for different stem geometries, materials and lengths of surface coating. Patterns of bone ingrowth on the tapered stem were independent of extent of porous coating, while ingrowth varied with the length of coating on the cylindrical stem. This model integrates knowledge of under what mechanical conditions bone ingrowth occurs on prosthetic stem surfaces with remodelling behaviour over time.

The Influence of the Pelvic Bone on the Computational Results of the Acetabular Component of a Total Hip Prosthesis

The computational models developed to evaluate the hip joint performance usually neglect the presence of the pelvic bone. However, deformation depends on the stiffness of the underlying bone, and thus, the inclusion of the pelvic bone in the model influences the computed contact pressure and wear. This work discusses the influence of the pelvic bone, and how it depends on the acetabular component stiffness. It was modeled as two different polyethylene acetabular cups, considering or not a metal-backing for both 28 mm and 32 mm diametric cups. Two finite element models are developed, considering either the acetabular component rigidly fixed or attached to the deformable bone. Results present 28% and 42% difference on the contact pressure for a polyethylene cup without metal-backing when the support conditions are changed, for the 28 mm and 32 mm cups, respectively. Linear wear results present 21% and 31% difference for the same type of cups of 28 mm and 32 mm, correspondingly. The numerical results obtained in the present work show that to model the pelvic bone of the patient with a metal-backed cup did not greatly affect contact pressures and linear wear. However, when a total hip replacement is performed with an all-polyethylene acetabular cup, the presence of the pelvic bone in the model has a major influence.

A quantitative comparison of a bone remodeling model with dual-energy X-ray absorptiometry and analysis of the inter-individual biological variability of femoral neck T-score

The development of consistent procedures with the inclusion of patient-specific data is essential in the computational modeling of biological processes, in order to achieve clinical relevant data. In this work, these issues are addressed with the development of a methodology that combines the gold standard technique for bone mineral density measurement and osteoporosis diagnosis, Dual energy X-ray absorptiometry (DXA), with a computational model for bone remodeling simulation. The DXA results were divided in three samples constituted from proximal femur DXA exams of patients in different stages of bone mineral density (normal, osteopenia and osteoporosis). These results were quantitatively compared with computational model results. A correlation study was performed between femoral neck T-score and a parameter from the model to ascertain the hypothesis of adjusting the model accordingly to biological variables. The results evidenced the predictive ability of the computational model in the estimation of femoral neck bone mineral content (BMC), with a maximum relative error of 3.92%. On the other hand, a strong correlation (R=-0.862) was found between the variables in study and a mathematical relationship was obtained to estimate the range of values for a model parameter that leads to biological relevant results. The methodology developed and the results obtained represent a solid and reliable basis to further studies on bone quality, ensuring the validity of the computational model in the simulation of bone remodeling process.

Bone remodelling analysis of the humerus after a shoulder arthroplasty

The shoulder arthroplasty has become an efficient treatment for some pathologies. However there are complications that can compromise its success. Among them, the stress shielding effect on the humerus has been reported as a possible cause of failure. The objective of this work was to investigate the bone remodelling in the humerus after a shoulder arthroplasty. For this purpose, computational models were developed to analyse the stress shielding contribution to the humeral component failure of shoulder arthroplasties, with a cemented and an uncemented prosthesis. A computational remodelling model was used to characterize the bone apparent density at each site of the humerus. The density distribution was obtained by the solution of a problem that takes into account both structural stiffness and the metabolic cost of bone maintenance. Bone was subjected to 6 load cases that include the glenohumeral reaction force and the action of 10 muscles. In the implanted models, different interface conditions were tested for the bone-implant and the cement-implant interfaces. Moreover, a pathological case defined by a poorer quality of bone was considered. In the healthy situation, the models that better model in vivo conditions showed no significant changes in bone mass. However, the results for the pathological case showed some bone resorption which supports the importance given to the quality of bone in the success of the joint replacement. Bearing in mind the conditions addressed, the results lead to conclude that the stress shielding is not a key factor for the humeral component failure of shoulder arthroplasties in a healthy situation though several issues, including muscle function and bone quality, may heighten its effect.