Gianni Campoli

Mechanical behavior of regular open-cell porous biomaterials made of diamond lattice unit cells.

Cellular structures with highly controlled micro-architectures are promising materials for orthopedic applications that require bone-substituting biomaterials or implants. The availability of additive manufacturing techniques has enabled manufacturing of biomaterials made of one or multiple types of unit cells. The diamond lattice unit cell is one of the relatively new types of unit cells that are used in manufacturing of regular porous biomaterials. As opposed to many other types of unit cells, there is currently no analytical solution that could be used for prediction of the mechanical properties of cellular structures made of the diamond lattice unit cells. In this paper, we present new analytical solutions and closed-form relationships for predicting the elastic modulus, Poisson׳s ratio, critical buckling load, and yield (plateau) stress of cellular structures made of the diamond lattice unit cell. The mechanical properties predicted using the analytical solutions are compared with those obtained using finite element models. A number of solid and porous titanium (Ti6Al4V) specimens were manufactured using selective laser melting. A series of experiments were then performed to determine the mechanical properties of the matrix material and cellular structures. The experimentally measured mechanical properties were compared with those obtained using analytical solutions and finite element (FE) models. It has been shown that, for small apparent density values, the mechanical properties obtained using analytical and numerical solutions are in agreement with each other and with experimental observations. The properties estimated using an analytical solution based on the Euler-Bernoulli theory markedly deviated from experimental results for large apparent density values. The mechanical properties estimated using FE models and another analytical solution based on the Timoshenko beam theory better matched the experimental observations.

Computational load estimation of the femur.

The density distribution and, thus, mechanical properties of long bones such as the femur are dependent on their loading. Many bone tissue adaptation theories are proposed to describe the density distribution that results from a given set of loading parameters. It is relatively easy to measure the density distribution of long bones, for example, using Computed Tomography (CT). However, there is no easy non-invasive method for in-vivo measurement of musculoskeletal loads. It is therefore interesting to investigate whether or not it is possible to predict the musculoskeletal loads that have resulted in a certain measured density distribution using bone tissue adaptation models. An inverse problem has to be solved for that purpose. In this paper, we use Artificial Neural Networks (ANNs) to solve the associated inverse problem and estimate the loading parameters that have resulted in the CT-measured three-dimensional density distribution of a proximal femur. An ANN is trained using a dataset generated by solving the forward tissue adaptation model for a large number of loading parameters. Before training the ANN with the generated training dataset, a Gaussian noise component is added to the density distribution. This improves the robustness of the trained ANN against deviations of the measured density distribution from the predictions of the forward bone tissue adaptation model. It is shown that the proposed technique is capable of predicting loading parameters that result in a density distribution close to the measured density distribution.

Mechanical factors explain development of cam-type deformity.

OBJECTIVE A cam-type deformity drastically increases the risk of hip osteoarthritis (OA). Since this type of skeletal anomaly is more prevalent among young active adults, it is hypothesized that the loading conditions experienced during certain types of vigorous physical activities stimulates formation of cam-type deformity. We further hypothesize that the growth plate shape modulates the influence of mechanical factors on the development of cam-type deformity. DESIGN We used finite element (FE) models of the proximal femur with an open growth plate to study whether mechanical factors could explain the development of cam-type deformity in adolescents. Four different loading conditions (representing different types of physical activities) and three different levels of growth plate extension towards the femoral neck were considered. Mechanical stimuli at the tissue level were calculated by means of the osteogenic index (OI) for all loading conditions and growth plate shape variations. RESULTS Loading conditions and growth plate shape influence the distribution of OI in hips with an open growth plate, thereby driving the development of cam-type deformity. In particular, specific types of loads experienced during physical activities and a larger growth plate extension towards the femoral neck increase the chance of cam-type deformity. CONCLUSIONS Specific loading patterns seem to stimulate the development of cam-type deformity by modifying the distribution of the mechanical stimulus. This is in line with recent clinical studies and reveals mechanobiological mechanisms that trigger the development of cam-type deformity. Avoiding these loading patterns during skeletal growth might be a potential preventative strategy for future hip OA.

Subject-specific modeling of the scapula bone tissue adaptation

Adaptation of the scapula bone tissue to mechanical loading is simulated in the current study using a subject-specific three-dimensional finite element model of an intact cadaveric scapula. The loads experienced by the scapula during different types of movements are determined using a subject-specific large-scale musculoskeletal model of the shoulder joint. The obtained density distributions are compared with the CT-measured density distribution of the same scapula. Furthermore, it is assumed that the CT-measured density distribution can be estimated as a weighted linear combination of the density distributions calculated for different loads experienced during daily life. An optimization algorithm is used to determine the weighting factors of fourteen different loads such that the difference between the weighted linear combination of the calculated density distributions and the CT-measured density is minimal. It is shown that the weighted linear combination of the calculated densities matches the CT-measured density distribution better than every one of the density distributions calculated for individual movements. The weighting factors of nine out of fourteen loads were estimated to be zero or very close to zero. The five loads that had larger weighting factors were associated with either one of the following categories: (1) small-load small-angle abduction or flexion movements that occur frequently during our daily lives or (2) large-load large-angle abduction or flexion movements that occur infrequently during our daily lives.

Effects of densitometry, material mapping and load estimation uncertainties on the accuracy of patient-specific finite-element models of the scapula

Patient-specific biomechanical models including patient-specific finite-element (FE) models are considered potentially important tools for providing personalized healthcare to patients with musculoskeletal diseases. A multi-step procedure is often needed to generate a patient-specific FE model. As all involved steps are associated with certain levels of uncertainty, it is important to study how the uncertainties of individual components propagate to final simulation results. In this study, we considered a specific case of this problem where the uncertainties of the involved steps were known and the aim was to determine the uncertainty of the predicted strain distribution. The effects of uncertainties of three important components of patient-specific models, including bone density, musculoskeletal loads and the parameters of the material mapping relationship on the predicted strain distributions, were studied. It was found that the number of uncertain components and the level of their uncertainty determine the uncertainty of simulation results. The ‘average’ uncertainty values were found to be relatively small even for high levels of uncertainty in the components of the model. The ‘maximum’ uncertainty values were, however, quite high and occurred in the areas of the scapula that are of the greatest clinical relevance. In addition, the uncertainty of the simulation result was found to be dependent on the type of movement analysed, with abduction movements presenting consistently lower uncertainty values than flexion movements.

Characterization of the Crack Tip Behaviour in Fibre Metal Laminates by Means of Digital Image Correlation

This paper presents the study on the crack tip beha viour in Fibre Metal Laminates under static loading. The effect on the strain field due to the variation of layup and fibre/prepreg has been analyzed. The strain field has been measur ed using digital image correlation and evaluated by comparing it with the strain field pre dicted with FE analysis, which provided information about the interlaminar shear mechanisms. In addition, the paper demonstrates the power of the digital image correlation techniqu e for in situ strain measurements, offering new insight into the damage mechanisms that prevail in FMLs under static loading.

Determination of the mechanical and physical properties of cartilage by coupling poroelastic-based finite element models of indentation with artificial neural networks

One of the most widely used techniques to determine the mechanical properties of cartilage is based on indentation tests and interpretation of the obtained force-time or displacement-time data. In the current computational approaches, one needs to simulate the indentation test with finite element models and use an optimization algorithm to estimate the mechanical properties of cartilage. The modeling procedure is cumbersome, and the simulations need to be repeated for every new experiment. For the first time, we propose a method for fast and accurate estimation of the mechanical and physical properties of cartilage as a poroelastic material with the aid of artificial neural networks. In our study, we used finite element models to simulate the indentation for poroelastic materials with wide combinations of mechanical and physical properties. The obtained force-time curves are then divided into three parts: the first two parts of the data is used for training and validation of an artificial neural network, while the third part is used for testing the trained network. The trained neural network receives the force-time curves as the input and provides the properties of cartilage as the output. We observed that the trained network could accurately predict the properties of cartilage within the range of properties for which it was trained. The mechanical and physical properties of cartilage could therefore be estimated very fast, since no additional finite element modeling is required once the neural network is trained. The robustness of the trained artificial neural network in determining the properties of cartilage based on noisy force-time data was assessed by introducing noise to the simulated force-time data. We found that the training procedure could be optimized so as to maximize the robustness of the neural network against noisy force-time data.

Relationship between the shape and density distribution of the femur and its natural frequencies of vibration

It has been recently suggested that mechanical loads applied at frequencies close to the natural frequencies of bone could enhance bone apposition due to the resonance phenomenon. Other applications of bone modal analysis are also suggested. For the above-mentioned applications, it is important to understand how patient-specific bone shape and density distribution influence the natural frequencies of bones. We used finite element models to study the effects of bone shape and density distribution on the natural frequencies of the femur in free boundary conditions. A statistical shape and appearance model that describes shape and density distribution independently was created, based on a training set of 27 femora. The natural frequencies were then calculated for different shape modes varied around the mean shape while keeping the mean density distribution, for different appearance modes around the mean density distribution while keeping the mean bone shape, and for the 27 training femora. Single shape or appearance modes could cause up to 15% variations in the natural frequencies with certain modes having the greatest impact. For the actual femora, shape and density distribution changed the natural frequencies by up to 38%. First appearance mode that describes the general cortical bone thickness and trabecular bone density had one of the strongest impacts. The first appearance mode could therefore provide a sensitive measure of general bone health and disease progression. Since shape and density could cause large variations in the calculated natural frequencies, patient-specific FE models are needed for accurate estimation of bone natural frequencies.

SUBJECT-SPECIFIC MODELING OF THE ADAPTATION OF THE SCAPULA BONE TISSUE

The morphology and microstructure of bone tissue is, at least partially, determined by the mechanical loads it experiences. Joint replacement surgeries on the shoulder joint are general practice in orthopaedic surgery. The fixation of these implants depends strongly on the bone stock of the shoulder blade (the scapula), which is often diminished. More knowledge with respect to the relationship between scapula muscle loading and the consequences for its bone stock could therefore be helpful. A few numerical models of bone adaptation of the shoulder blade have recently become available. Detailed loading estimates of the shoulder are currently available through a largescale musculoskeletal model of the shoulder and elbow, namely Delft Shoulder and Elbow Model (DSEM) [van der Helm, 1994]. The aim of the present study is to determine the bone density distribution in the scapula from a bone adaptation model that uses the loads estimated by DSEM. Subsequently, this predicted bone density will be related to the density distribution measured using computed tomography (CT), thereby corroborating the applied model.

PREDICTION OF THE FEMURAL LOAD USING BONE ADAPTATION MODELS AND ARTIFICIAL NEURAL NETWORKS

Bone adaptation models in combination with finite element modelling can be used to determine the density distribution that results from a given set of loads. Conversely, one may be interested in the loads that have resulted in a given density distribution. The possibility of determining the loads that have resulted in a given density distribution provides us with a non-invasive tool for estimation of musculoskeletal loading over a certain period of time. Unlike the forward problem, the solution of the inverse problem is not straightforward, because the governing nonlinear differential equations of the inverse problem are not known. This study presents a novel technique for estimation of the loads from the bone density distribution. Artificial Neural Networks (ANNs) are proposed as a tool for construction of a nonlinear mapping from the space of density distribution to the space of loading parameters.