Contact patterns in the ankle joint after lateral ligamentous injury during internal rotation: A computational study.

Lateral ankle instability, resulting from the inability of ankle ligaments to heal after injury, is believed to cause a change in the articular contact mechanics that may promote cartilage degeneration. Considering that lateral ligaments' insufficiency has been related to rotational instability of the talus, and that few studies have addressed the contact mechanics under this condition, the aim of this work was to evaluate if a purely rotational ankle instability could cause non-physiological changes in contact pressures in the ankle joint cartilages using the finite element method. A finite element model of a healthy ankle joint, including bones, cartilages and nine ligaments, was developed. Pure internal talus rotations of 3.67°, 9.6° and 13.43°, measured experimentally for three ligamentous configurations, were applied. The ligamentous configurations consisted in a healthy condition, an injured condition in which the anterior talofibular ligament was cut, and an injured condition in which the anterior talofibular and calcaneofibular ligaments were cut. For all simulations, the contact areas and maximum contact pressures were evaluated for each cartilage. The results showed not only an increase of the maximum contact pressures in the ankle cartilages, but also novel contact regions at the anteromedial and posterolateral sections of the talar cartilage with increasing internal rotation. The anteromedial and posterolateral contact regions observed due to pathological internal rotations of the talus are a computational evidence that supports the link between a pure rotational instability and the pattern of pathological cartilaginous load seen in patients with long-term lateral chronic ankle instability.

Comparison of 3 supraspinatus tendon repair techniques - a 3D computational finite element analysis.

Considering that optimal contact area and pressure at the tendon-bone interface are associated with better footprint repair and outcomes, the aim of this study was to compare the performance of standard double-row, transosseous equivalent (TOE), and partial articular supraspinatus tendon avulsion (PASTA) techniques for the treatment of full-thickness tears of the supraspinatus tendon using 3D finite element models. Loading consisted, alternately, in a preloading of 10 N and 20 N of the sutures. The footprint coverage of the standard double-row, TOE, and PASTA techniques was estimated to represent 19%, 30%, and 35%, respectively, of the repair area. The average contact pressures followed an opposite trend, i.e., the largest was estimated for the standard double-row technique, whereas the lowest was estimated for the PASTA technique. Despite the present study advancing the computational modelling of rotator cuff repair, and the results being consistent with the literature, its findings must be evaluated cautiously, bearing in mind its limitations.

Primary stability analysis of stemless shoulder implants.

Although the primary stability of joint implants is fundamental for successful osseointegration, little is know about this issue in the context of stemless shoulder implants. Considering 3D finite element models, the purpose of this study was to evaluate the primary stability of five stemless designs, based on the Sidus, SMR, Simpliciti, Eclipse, and Global Icon stemless systems. Three alternative bone quality conditions were considered for cancellous bone. For the Sidus, SMR, and Simpliciti designs, which do not possess a collar that sits on the cortical rim of the humeral resected surface, contact and no contact conditions were considered between the bone surface and the humeral head components. Micromotions at bone-implant interfaces promoting osseointegration were computed as a measure of primary stability for eight load cases consisting of peak in vivo joint loads measured during selected upper limb activities. Under good bone quality conditions, all stemless designs presented micromotions below 150 µm. The Eclipse-based and Global-Icon based designs were the least sensitive to bone quality. Stemless designs presenting a solid collar or contact between the humeral head component and bone provided more stability. Overall, the Eclipse-based and Global Icon-based designs presented the best performance from the primary stability point of view. However, if bone adaptation data available in the literature are considered along with the primary stability data computed here, the Global Icon-based design, as well as other designs, might be considered superior long-term options due to their better compromise between primary stability and impact on bone adaptation.

Factores de riesgo de fractura incidente en pacientes con cáncer de mama tratadas con inhibidores de la aromatasa: cohorte B-ABLE / Risk factors for incident fracture in patients with breast cancertreated with aromatase inhibitors: B-ABLE cohort

OBJETIVO: Los inhibidores de la aromatasa (IA) se han asociado con una pérdida de masa ósea acelerada y un mayor riesgo de fracturas osteoporóticas. Con este trabajo se pretendió evaluar los factores de riesgo de fractura incidente en pacientes con cáncer de mama que reciben IA. MATERIAL Y MÉTODOS: Estudio prospectivo-observacional de cohorte de mujeres con cáncer de mama que inician tratamiento con IA (cohorte B-ABLE). Las pacientes realizaron tratamiento durante 5 años o bien 2 ó 3 años si habían recibido previamente tamoxifeno. Se les evaluó la salud ósea desde el inicio del tratamiento hasta un año después de finalizar dicho tratamiento mediante densitometría ósea, marcadores de remodelado óseo, niveles de vitamina D y una radiografía antero-posterior y otra lateral de columna. Se realizó el cálculo de riesgo de fractura mediante la herramienta FRAX® antes de iniciar IA. Se utilizaron modelos de Cox para calcular los ratios de riesgo (HR [IC 95%]) de fractura. RESULTADOS: Un total de 943 pacientes fueron incluidas en el estudio. El 5,4% sufrieron una fractura incidente, la mayoría durante el tratamiento con IA, aunque un 21,5% ocurrieron durante el primer año después de finalizar la terapia. La mayoría de las fracturas incidentes fueron vertebrales clínicas (29,4%) y de Colles (31,4%). El 86,3% de las pacientes tenían un diagnóstico de osteopenia u osteoporosis en el momento de la fractura y el 33% tenían los niveles de β-CTX (isómero β del telopéptido carboxiterminal del colágeno tipo I) por encima de la normalidad. Las pacientes diagnosticadas de osteoporosis o con riesgo de fractura al inicio del estudio fueron tratadas con antirresortivos óseos. No se encontraron diferencias significativas en el riesgo de fractura entre pacientes con y sin tratamiento antirresortivo: HR=1,75 [IC 95%: 0,88 a 3,46]. Tampoco se encontraron diferencias entre las pacientes que habían hecho tratamiento previo con tamoxifeno respecto a las que no (HR=1,00 [IC 95%: 0,39 a 2,56]). La herramienta FRAX® dio valores de media dentro del rango de riesgo intermedio, con 13 pacientes con valores de alto riesgo de fractura principal. CONCLUSIONES: El principal factor de riesgo detectado para fractura incidente en pacientes tratadas con IA es el diagnóstico de osteopenia u osteoporosis. El cálculo de la herramienta FRAX® y la determinación de los niveles de β-CTX son herramientas útiles para identificar a pacientes de alto riesgo

OBJETIVO:Aromatase inhibitors (AI) have been associated with an accelerated loss of bone mass and an increased risk ofosteoporosis fractures. This study assesses the risk factors for incident fracture in breast cancer patients receiving AI. MATERIAL AND METHODS:Prospective‐observational cohort study of women with breast cancer who begin treatment withAI (B‐ABLE cohort). Patients were treated for 5 years or 2 or 3 years if they had previously received tamoxifen. Bone healthwas assessed from the beginning of the treatment until one year post treatment by bone densitometry, bone remodelingmarkers, vitamin D levels and an anteroposterior and lateral spine radiography. The fracture risk calculation was performedusing the FRAX® tool before starting AI. Cox models were used to calculate the risk ratios (HR [95% CI]) of fracture. RESULTS: A total of 943 patients were included in the study.5.4% suffered an incident fracture, most during AI treatment,although 21.5% occurred during the first year after the end of therapy. Most of the incident fractures were clinical vertebral (29.4%) and Colles (31.4%).86.3% of the patients had a diagnosis of osteopenia or osteoporosis at the time of the fractureand 33% had the levels of β‐CTX (β isomer of the carboxyterminal telopeptide of type I collagen) above normal. Patients diagnosed with osteoporosis or at risk of fracture at the start of the study were treated with bone antiresorptives. No significant differences in fracture risk were found between patients with and without antiresorptive therapy: HR=1.75[95% CI: 0.88 to 3.46]. Nor were differences found among patients who had previously treated with tamoxifen comparedto those who did not (HR=1.00 [95% CI 0.39 to 2.56]). The FRAX®tool gave average values within the intermediate riskrange, with 13 patients with high risk of major fracture values. CONCLUSIONS:The main risk factor detected for incident fracture in patients treated with AI is the diagnosis of osteopeniaor osteoporosis. The calculation of the FRAX® tool and the determination of β‐CTX levels are useful tools to identifyhigh‐risk patients

Bone remodelling of the humerus after a resurfacing and a stemless shoulder arthroplasty.

BACKGROUND: New implant designs, such as resurfacing and stemless implants, have been developed to improve the long-term outcomes of the shoulder arthroplasty. However, it is not yet fully understood if their influence on the bone load distribution can compromise the long-term stability of the implant due to bone mass changes. Using three-dimensional finite element models, the aim of the present study was to analyse the bone remodelling process of the humerus after the introduction of resurfacing and stemless implants based on the Global C.A.P. and Sidus Stem-Free designs, respectively. METHODS: The 3D geometric model of the humerus was generated from the CT data of the Visible Human Project and the resurfacing and stemless implants were modelled in Solidworks. Considering a native humerus model, a humerus model with the resurfacing implant, and a humerus model with the stemless implant, three finite element models were developed in Abaqus. Bone remodelling simulations were performed considering healthy and poor bone quality conditions. The loading condition considered comprised 6 load cases of standard shoulder movements, including muscle and joint reaction forces estimated by a multibody model of the upper limb. FINDINGS: The results showed similar levels of bone resorption for the resurfacing and stemless implants for common humeral regions. The regions underneath the head of the resurfacing implant, unique to this design, showed the largest bone loss. For both implants, bone resorption was more pronounced for the poor bone quality condition than for the healthy bone quality condition. INTERPRETATION: The stemless implant lost less density at the fixation site, which might suggest that these implants may be better supported in the long-term than the resurfacing implants. However, further investigation is necessary to allow definite recommendations.

Computational model of mesenchymal migration in 3D under chemotaxis.

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.

Full-thickness tears of the supraspinatus tendon: A three-dimensional finite element analysis.

Knowledge regarding the likelihood of propagation of supraspinatus tears is important to allow an early identification of patients for whom a conservative treatment is more likely to fail, and consequently, to improve their clinical outcome. The aim of this study was to investigate the potential for propagation of posterior, central, and anterior full-thickness tears of different sizes using the finite element method. A three-dimensional finite element model of the supraspinatus tendon was generated from the Visible Human Project data. The mechanical behaviour of the tendon was fitted from experimental data using a transversely isotropic hyperelastic constitutive model. The full-thickness tears were simulated at the supraspinatus tendon insertion by decreasing the interface area. Tear sizes from 10% to 90%, in 10% increments, of the anteroposterior length of the supraspinatus footprint were considered in the posterior, central, and anterior regions of the tendon. For each tear, three finite element analyses were performed for a supraspinatus force of 100N, 200N, and 400N. Considering a correlation between tendon strain and the risk of tear propagation, the simulated tears were compared qualitatively and quantitatively by evaluating the volume of tendon for which a maximum strain criterion was not satisfied. The finite element analyses showed a significant impact of tear size and location not only on the magnitude, but also on the patterns of the maximum principal strains. The mechanical outcome of the anterior full-thickness tears was consistently, and significantly, more severe than that of the central or posterior full-thickness tears, which suggests that the anterior tears are at greater risk of propagating than the central or posterior tears.

A new shoulder model with a biologically inspired glenohumeral joint.

Kinematically unconstrained biomechanical models of the glenohumeral (GH) joint are needed to study the GH joint function, especially the mechanisms of joint stability. The purpose of this study is to develop a large-scale multibody model of the upper limb that simulates the 6 degrees of freedom (DOF) of the GH joint and to propose a novel inverse dynamics procedure that allows the evaluation of not only the muscle and joint reaction forces of the upper limb but also the GH joint translations. The biomechanical model developed is composed of 7 rigid bodies, constrained by 6 anatomical joints, and acted upon by 21 muscles. The GH joint is described as a spherical joint with clearance. Assuming that the GH joint translates according to the muscle load distribution, the redundant muscle load sharing problem is formulated considering as design variables the 3 translational coordinates associated with the GH joint translations, the joint reaction forces associated with the remaining kinematic constraints, and the muscle activations. For the abduction motion in the frontal plane analysed, the muscle and joint reaction forces estimated by the new biomechanical model proposed are similar to those estimated by a model in which the GH joint is modeled as an ideal spherical joint. Even though this result supports the assumption of an ideal GH joint to study the muscle load sharing problem, only a 6 DOF model of the GH joint, as the one proposed here, provides information regarding the joint translations. In this study, the biomechanical model developed predicts an initial upward and posterior migration of the humeral head, followed by an inferior and anterior movement, which is in good agreement with the literature.

Computational reverse shoulder prosthesis model: Experimental data and verification.

The reverse shoulder prosthesis aims to restore the stability and function of pathological shoulders, but the biomechanical aspects of the geometrical changes induced by the implant are yet to be fully understood. Considering a large-scale musculoskeletal model of the upper limb, the aim of this study is to evaluate how the Delta reverse shoulder prosthesis influences the biomechanical behavior of the shoulder joint. In this study, the kinematic data of an unloaded abduction in the frontal plane and an unloaded forward flexion in the sagittal plane were experimentally acquired through video-imaging for a control group, composed of 10 healthy shoulders, and a reverse shoulder group, composed of 3 reverse shoulders. Synchronously, the EMG data of 7 superficial muscles were also collected. The muscle force sharing problem was solved through the minimization of the metabolic energy consumption. The evaluation of the shoulder kinematics shows an increase in the lateral rotation of the scapula in the reverse shoulder group, and an increase in the contribution of the scapulothoracic joint to the shoulder joint. Regarding the muscle force sharing problem, the musculoskeletal model estimates an increased activity of the deltoid, teres minor, clavicular fibers of the pectoralis major, and coracobrachialis muscles in the reverse shoulder group. The comparison between the muscle forces predicted and the EMG data acquired revealed a good correlation, which provides further confidence in the model. Overall, the shoulder joint reaction force was lower in the reverse shoulder group than in the control group.

Computational analysis of polyethylene wear in anatomical and reverse shoulder prostheses.

The wear of ultra-high molecular weight polyethylene, UHMWPE, components has been associated with the failure of joint prostheses in the hip, knee, and shoulder. Considering that in vitro experiments are generally too expensive and time-consuming, computational models are an attractive alternative to study the wear behavior of UHMWPE components. The objective of the present study was to develop a computational wear model to evaluate the wear resistance of anatomical and reverse shoulder prostheses. The effects of the wear law and the updating of the UHMWPE surface on the prediction of wear were also considered. Apart from Archard's law, a new wear law, so-called second generation law, which includes the concept of cross-shear and a pressure-independent wear factor, was considered. The wear analyses were performed considering three shoulder joint motions. The muscle and joint reaction forces applied were estimated by an inverse biomechanical model of the upper limb. The results show that abrasive wear is as important for the reverse components as it is for the anatomical. Nevertheless, the volumetric wears estimated over 1 year are within the range considered clinically desirable to reduce the risk of osteolysis. For the anatomical components, the predictions from Archard's law compare better, than those of the second generation law, to the experimental and clinical data available in the literature. Yet, the opposite result is obtained for the reverse components. From the numerical point of view, an updating procedure for the UHMWPE surface is mandatory to improve the numerical predictions.

Bone remodelling of the scapula after a total shoulder arthroplasty.

According to Wolff's law, the changes in stress after a prosthesis implantation may modify the shape and internal structure of bone, thus compromising the long-term prosthesis fixation and, consequently, be a significant factor for glenoid loosening. The aim of the present study is to evaluate the changes in the bone adaptation process of the scapula after an anatomical and reverse total shoulder arthroplasty. Five finite element models of the implanted scapula are developed considering the implantation of three anatomical, cemented, all-polyethylene components; an anatomical, cementless, metal-backed component; and a reverse, all-metal component. The methodology followed to simulate the bone adaptation of the scapula was previously validated for the intact model, prior to the prosthesis implantation. Additionally, the influence of the bone quality on the adaptation process is also investigated by considering an osteoporotic condition. The results show that the stress shielding phenomenon is more concerning in cementless, metal-based components than in cemented, all-polyethylene components, regardless of the bone quality. Consequently, as far as the bone adaptation process of the bone is concerned, cemented, all-polyethylene components are better suited for the treatment of the shoulder joint.

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.

Biomechanical analysis of the anterior cervical fusion.

This paper presents a biomechanical analysis of the cervical C5-C6 functional spine unit before and after the anterior cervical discectomy and fusion. The aim of this work is to study the influence of the medical procedure and its instrumentation on range of motion and stress distribution. First, a three-dimensional finite element model of the lower cervical spine is obtained from computed tomography images using a pipeline of image processing, geometric modelling and mesh generation software. Then, a finite element study of parameters' influence on motion and a stress analysis at physiological and different post-operative scenarios were made for the basic movements of the cervical spine. It was confirmed that the results were very sensitive to intervertebral disc properties. The insertion of an anterior cervical plate influenced the stress distribution at the vertebral level as well as in the bone graft. Additionally, stress values in the graft decreased when it is used together with a cage.

Wear analysis in anatomical and reversed shoulder prostheses.

This paper describes the development of a computational model to calculate wear rates in total shoulder prostheses, for a 5-150 degrees arm abduction. Anatomical keeled and pegged prosthesis as well as reversed prosthesis were the studied implants. The bone models were built based on computed tomography (CT) images and using a computer aided design-based modelling pipeline. The finite element method was used to solve the contact problem between the surface of the polyethylene (PE) components and the corresponding articular component. The aim of this work was to determine linear and volumetric PE wear, for several radial mismatches, in conditions of pathological (rheumatoid arthritis) and non-pathological bone. Results showed that contact pressures and linear wear developed in anatomical prosthesis were higher than those visualised in reversed prosthesis. However, anatomical prosthesis exhibited a better volumetric wear performance. Moreover, our findings indicated higher values of volumetric wear in higher congruent models and on pathological bone conditions.

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.

Bone remodelling analysis of a bovine femur for a veterinary implant design.

The response of bovine bone to the presence of an implant is analysed with the aim of simulating bone remodelling in a developing model of a polymeric intramedullary interlocking nail for veterinary use. A 3-D finite element model of the femur diaphysis is built based on computed tomography images and using a CAD-based modelling pipeline. The bone remodelling process after the surgery is analysed and compared with the healthy bone. The remodelling law assumes that bone adapts to the mechanical environment. For the analyses a consistent set of loads is determined for the bovine walk cycle. The remodelling results reproduce the morphologic features of bone and provide evidence of the difference on the bone behaviour when comparing metallic and polymeric nails. Our findings indicate that an intramedullary polymeric nail has the advantage over the metallic one of improving long-term bone healing and possibly avoiding the need of the implant removal.

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.

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.

Synthesis, Crystal Structure, and Magnetic Properties of Oxalato-Copper(II) Complexes with 3,3-Bis(2-imidazolyl)propionic Acid, an Imidazole-Carboxylate Polyfunctional Ligand: From Mononuclear Entities to Ladder-Like Chains.

The synthesis of five new Cu(II) compounds of formula [Cu(HBIP)(C(2)O(4))].H(2)O (1), [Cu(HBIP)(C(2)O(4))(OH(2))].2H(2)O (2), [{Cu(HBIP)Cl}(2)(&mgr;-C(2)O(4))].2H(2)O (3), [{Cu(BIP)}(2)(&mgr;-C(2)O(4))].2H(2)O (4) and [{Cu(BIP)}(2)(&mgr;-C(2)O(4))].6H(2)O (5), together with their spectral and magnetic characterization, is reported. Crystal structures of compounds 2, 3 and 5 have been solved. All these compounds crystallize in the triclinic system, space group P&onemacr;, with a = 7.3322(3) Å, b = 10.014(1) Å, c = 11.541(1) Å, alpha = 113.22(1) degrees, beta = 91.37(1) degrees, gamma = 94.51(1) degrees, Z = 2 for compound 2; a = 7.444(2) Å, b = 8.518(2) Å, c = 11.231(2) Å, alpha = 97.45(2) degrees, beta = 98.99(2) degrees, gamma = 97.95(2) degrees, Z = 1 for compound 3; and a = 7.977(1) Å, b = 8.656(1) Å, c = 11.807(1) Å, alpha = 69.06(1) degrees, beta = 86.07(1) degrees, gamma = 67.36(1) degrees, Z = 1 for compound 5. In compound 2 the asymmetric unit consists of one isolated neutral [Cu(HBIP)(C(2)O(4))(OH(2))] molecule and two noncoordinated water molecules. The Cu(II) ion is five-coordinated (4+1 coordination mode) with HBIP and oxalato entities acting as bidentate ligands and the water molecule as the fifth ligand. The structure of compound 3 is made up of centrosymmetric binuclear [{Cu(HBIP)(Cl)}(2)(&mgr;-C(2)O(4))] units and noncoordinated water molecules. The two copper atoms are linked through a bis-bidentate oxalato group leading to a metal-metal separation of 5.28(3) Å. The coordination stereochemistry of the CuN(2)O(2)Cl chromophore is approximately SP. Compound 5 exhibits a structure built of ladder-like chains. In these chains the rungs are constituted by the neutral dinuclear centrosymmetric [(BIP)Cu(C(2)O(4))Cu(BIP)] entities. The oxalato group bridges two copper atoms in a bis-bidentate fashion, whereas the BIP acts as a tridentate ligand, connecting through their carboxylate groups these dimeric units along the a axis. The copper atom is involved in a five-coordinated CuN(2)O(2)O' chromophore, with a coordination geometry intermediate between SP and TBP. The magnetic properties of all complexes have been investigated. Compound 1 and 2 follow a Curie-Weiss law with very low values of theta. The other three compounds exhibit an antiferromagnetic coupling, with 2J = -265 cm(-)(1) for 3, 2J = -108 cm(-)(1) for 4, and 2J = -5.7 cm(-)(1) for 5. The strength of the exchange interaction is discussed on the basis of the structural features and correlated with published magneto-structural data on similar oxalato-bridged copper(II) compounds.