J. Folgado

A contact model with ingrowth control for bone remodelling around cementless stems.

This work presents a computational model for bone remodelling around cementless stems. The problem is formulated as a material optimisation problem considering the bone and stem surfaces to be in contact. To emphasise the behaviour of the bone/stem interface, the computer model detects the existence of bone ingrowth during the remodelling; consequently, the contact conditions are changed for a better interface simulation. The trabecular bone is modelled as a strictly orthotropic material with equivalent properties computed by homogenisation. The distribution of bone relative density is obtained by the minimisation of a function that considers both the bone structural stiffness and the biological cost associated with metabolic maintenance of bone tissue. The situation of multiple load conditions is considered. The remodelling law, obtained from the necessary conditions for an optimum, is derived analytically from the optimisation problem and solved numerically using a suitable finite element mesh. The formulation is applied to an implanted femur. Results of bone density and ingrowth distribution are obtained for different coating conditions. Bone ingrowth does not occur over the entire coated surfaces. Indeed, we observed regions where separation or high relative displacement occurs that preclude bone ingrowth attachment. This prediction of the model is consistent with clinical observations of bone ingrowth. Thus, this model, which detect bone ingrowth and allow modification of the interface conditions, are useful for analysis of existing stems as well as design optimisation of coating extent and location on such stems.

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.

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.

Shape Optimization of a Cementless Hip Stem for a Minimum of Interface Stress and Displacement

The primary stem stability is an essential factor for success of cementless hip stems. A correct choice of the stem geometry can improve the stem stability and, consequently, increase the life time of a hip implant. In this work, it is proposed a computational model for shape optimization of cementless hip stems. The optimization problem is formulated by the minimization of relative displacement and stress on bone/stem interface using a multi-criteria objective function. Also multiple loads are considered to incorporate several daily life activities. Design variables are parameters that characterize the geometry of selected cross sections, which are subject to geometric constraints to ensure a clinically admissible shape. The stem/bone set is considered a structure in equilibrium with contact conditions on interface. The contact formulation allows us to analyze different lengths of porous coating. The optimization problem is solved numerically by a steepest descent method. The interface stress and relative displacement are obtained solving the contact problem by the finite element method. Numerical examples are presented for a two-dimensional model of a hip stem, however, the formulation is general and can be applied to the three-dimensional case. The model gives indications about the relation between shape, porous coating and prosthesis stability.

In silico Mechano-Chemical Model of Bone Healing for the Regeneration of Critical Defects: The Effect of BMP-2

The healing of bone defects is a challenge for both tissue engineering and modern orthopaedics. This problem has been addressed through the study of scaffold constructs combined with mechanoregulatory theories, disregarding the influence of chemical factors and their respective delivery devices. Of the chemical factors involved in the bone healing process, bone morphogenetic protein-2 (BMP-2) has been identified as one of the most powerful osteoinductive proteins. The aim of this work is to develop and validate a mechano-chemical regulatory model to study the effect of BMP-2 on the healing of large bone defects in silico. We first collected a range of quantitative experimental data from the literature concerning the effects of BMP-2 on cellular activity, specifically proliferation, migration, differentiation, maturation and extracellular matrix production. These data were then used to define a model governed by mechano-chemical stimuli to simulate the healing of large bone defects under the following conditions: natural healing, an empty hydrogel implanted in the defect and a hydrogel soaked with BMP-2 implanted in the defect. For the latter condition, successful defect healing was predicted, in agreement with previous in vivo experiments. Further in vivo comparisons showed the potential of the model, which accurately predicted bone tissue formation during healing, bone tissue distribution across the defect and the quantity of bone inside the defect. The proposed mechano-chemical model also estimated the effect of BMP-2 on cells and the evolution of healing in large bone defects. This novel in silico tool provides valuable insight for bone tissue regeneration strategies.

Critical analysis of musculoskeletal modelling complexity in multibody biomechanical models of the upper limb

The inverse dynamics technique applied to musculoskeletal models, and supported by optimisation techniques, is used extensively to estimate muscle and joint reaction forces. However, the solutions of the redundant muscle force sharing problem are sensitive to the detail and modelling assumptions of the models used. This study presents four alternative biomechanical models of the upper limb with different levels of discretisation of muscles by bundles and muscle paths, and their consequences on the estimation of the muscle and joint reaction forces. The muscle force sharing problem is solved for the motions of abduction and anterior flexion, acquired using video imaging, through the minimisation of an objective function describing muscle metabolic energy consumption. While looking for the optimal solution, not only the equations of motion are satisfied but also the stability of the glenohumeral and scapulothoracic joints is preserved. The results show that a lower level of muscle discretisation provides worse estimations regarding the muscle forces. Moreover, the poor discretisation of muscles relevant to the joint in analysis limits the applicability of the biomechanical model. In this study, the biomechanical model of the upper limb describing the infraspinatus by a single bundle could not solve the complete motion of anterior flexion. Despite the small differences in the magnitude of the forces predicted by the biomechanical models with more complex muscular systems, in general, there are no significant variations in the muscular activity of equivalent muscles.

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.

Multibody System of the Upper Limb Including a Reverse Shoulder Prosthesis

The reverse shoulder replacement, recommended for the treatment of several shoulder pathologies such as cuff tear arthropathy and fractures in elderly people, changes the biomechanics of the shoulder when compared to the normal anatomy. Although several musculoskeletal models of the upper limb have been presented to study the shoulder joint, only a few of them focus on the biomechanics of the reverse shoulder. This work presents a biomechanical model of the upper limb, including a reverse shoulder prosthesis, to evaluate the impact of the variation of the joint geometry and position on the biomechanical function of the shoulder. The biomechanical model of the reverse shoulder is based on a musculoskeletal model of the upper limb, which is modified to account for the properties of the DELTA® reverse prosthesis. Considering two biomechanical models, which simulate the anatomical and reverse shoulder joints, the changes in muscle lengths, muscle moment arms, and muscle and joint reaction forces are evaluated. The muscle force sharing problem is solved for motions of unloaded abduction in the coronal plane and unloaded anterior flexion in the sagittal plane, acquired using video-imaging, through the minimization of an objective function related to muscle metabolic energy consumption. After the replacement of the shoulder joint, significant changes in the length of the pectoralis major, latissimus dorsi, deltoid, teres major, teres minor, coracobrachialis, and biceps brachii muscles are observed for a reference position considered for the upper limb. The shortening of the teres major and teres minor is the most critical since they become unable to produce active force in this position. Substantial changes of muscle moment arms are also observed, which are consistent with the literature. As expected, there is a significant increase of the deltoid moment arms and more fibers are able to elevate the arm. The solutions to the muscle force sharing problem support the biomechanical advantages attributed to the reverse shoulder design and show an increase in activity from the deltoid, teres minor, and coracobrachialis muscles. The glenohumeral joint reaction forces estimated for the reverse shoulder are up to 15% lower than those in the normal shoulder anatomy. The data presented here complements previous publications, which, all together, allow researchers to build a biomechanical model of the upper limb including a reverse shoulder prosthesis.

Computational analysis of bone remodeling during an anterior cervical fusion

The anterior cervical fusion is an established surgical procedure for spine stabilization after the removal of an intervertebral disc. However, it is not yet clear which bone graft represents the best choice and whether surgical devices can be efficient and beneficial for fusion. The aim of this work is to study the influence of the spine instrumentation on bone remodeling after a cervical spine surgery and, consequently, on the fusion process. A finite element model of the cervical spine was developed, having computed tomography images as input. Bone was modeled as a porous material characterized by the relative density at each point and the bone remodeling law was derived assuming that bone self-adapts in order to achieve the stiffest structure for the supported loads, with the total bone mass regulated by the metabolic cost of maintaining bone tissue. Apart from the analysis of healthy cervical spine, different surgical scenarios were tested: bone graft with or without a cage and the use of a stabilization plate system. Results showed that the anterior and posterior regions of the disc space are more important to stress transmission and that spinal devices reduce bone growth within bone grafts, being plate systems the most interfering elements. The material of the interbody cages plays a major role in fusion and, therefore, it should be carefully chosen.

Computational model of mesenchymal migration in 3D under chemotaxis

Abstract Cell chemotaxis is an important characteristic of cellular migration, which takes part in crucial aspects of life and development. In this work, we propose a novel in silico model of mesenchymal 3D migration with competing protrusions under a chemotactic gradient. Based on recent experimental observations, we identify three main stages that can regulate mesenchymal chemotaxis: chemosensing, dendritic protrusion dynamics and cell–matrix interactions. Therefore, each of these features is considered as a different module of the main regulatory computational algorithm. The numerical model was particularized for the case of fibroblast chemotaxis under a PDGF-bb gradient. Fibroblasts migration was simulated embedded in two different 3D matrices – collagen and fibrin – and under several PDGF-bb concentrations. Validation of the model results was provided through qualitative and quantitative comparison with in vitro studies. Our numerical predictions of cell trajectories and speeds were within the measured in vitro ranges in both collagen and fibrin matrices. Although in fibrin, the migration speed of fibroblasts is very low, because fibrin is a stiffer and more entangling matrix. Testing PDGF-bb concentrations, we noticed that an increment of this factor produces a speed increment. At 1 ng mL−1 a speed peak is reached after which the migration speed diminishes again. Moreover, we observed that fibrin exerts a dampening behavior on migration, significantly affecting the migration efficiency.