Exploring the potential of Physics-Informed Neural Networks to extract vascularization data from DCE-MRI in the presence of diffusion

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is widely used to assess tissue vascularization, particularly in oncological applications. However, the most widely used pharmacokinetic (PK) models do not account for contrast agent (CA) diffusion between neighboring voxels, which can limit the accuracy of the results, especially in cases of heterogeneous tumors. To address this issue, previous works have proposed algorithms that incorporate diffusion phenomena into the formulation. However, these algorithms often face convergence problems due to the ill-posed nature of the problem. In this work, we present a new approach to fitting DCE-MRI data that incorporates CA diffusion by using Physics-Informed Neural Networks (PINNs). PINNs can be trained to fit measured data obtained from DCE-MRI while ensuring the mass conservation equation from the PK model. We compare the performance of PINNs to previous algorithms on different 1D cases inspired by previous works from literature. Results show that PINNs retrieve vascularization parameters more accurately from diffusion-corrected tracer-kinetic models. Furthermore, we demonstrate the robustness of PINNs compared to other traditional algorithms when faced with noisy or incomplete data. Overall, our results suggest that PINNs can be a valuable tool for improving the accuracy of DCE-MRI data analysis, particularly in cases where CA diffusion plays a significant role.

A multiscale orchestrated computational framework to reveal emergent phenomena in neuroblastoma

Neuroblastoma is a complex and aggressive type of cancer that affects children. Current treatments involve a combination of surgery, chemotherapy, radiotherapy, and stem cell transplantation. However, treatment outcomes vary due to the heterogeneous nature of the disease. Computational models have been used to analyse data, simulate biological processes, and predict disease progression and treatment outcomes. While continuum cancer models capture the overall behaviour of tumours, and agent-based models represent the complex behaviour of individual cells, multiscale models represent interactions at different organisational levels, providing a more comprehensive understanding of the system. In 2018, the PRIMAGE consortium was formed to build a cloud-based decision support system for neuroblastoma, including a multi-scale model for patient-specific simulations of disease progression. In this work we have developed this multi-scale model that includes data such as patient's tumour geometry, cellularity, vascularization, genetics and type of chemotherapy treatment, and integrated it into an online platform that runs the simulations on a high-performance computation cluster using Onedata and Kubernetes technologies. This infrastructure will allow clinicians to optimise treatment regimens and reduce the number of costly and time-consuming clinical trials. This manuscript outlines the challenging framework's model architecture, data workflow, hypothesis, and resources employed in its development.

Characterization of mutant versions of the R-RAS2/TC21 GTPase found in tumors

The R-RAS2 GTP hydrolase (GTPase) (also known as TC21) has been traditionally considered quite similar to classical RAS proteins at the regulatory and signaling levels. Recently, a long-tail hotspot mutation targeting the R-RAS2/TC21 Gln⁷² residue (Q72L) was identified as a potent oncogenic driver. Additional point mutations were also found in other tumors at low frequencies. Despite this, little information is available regarding the transforming role of these mutant versions and their relevance for the tumorigenic properties of already-transformed cancer cells. Here, we report that many of the RRAS2 mutations found in human cancers are highly transforming when expressed in immortalized cell lines. Moreover, the expression of endogenous R-RAS2^Q72L is important for maintaining optimal levels of PI3K and ERK activities as well as for the adhesion, invasiveness, proliferation, and mitochondrial respiration of ovarian and breast cancer cell lines. Endogenous R-RAS2^Q72L also regulates gene expression programs linked to both cell adhesion and inflammatory/immune-related responses. Endogenous R-RAS2^Q72L is also quite relevant for the in vivo tumorigenic activity of these cells. This dependency is observed even though these cancer cell lines bear concurrent gain-of-function mutations in genes encoding RAS signaling elements. Finally, we show that endogenous R-RAS2, unlike the case of classical RAS proteins, specifically localizes in focal adhesions. Collectively, these results indicate that gain-of-function mutations of R-RAS2/TC21 play roles in tumor initiation and maintenance that are not fully redundant with those regulated by classical RAS oncoproteins.

Confined Cell Migration and Asymmetric Hydraulic Environments to Evaluate The Metastatic Potential of Cancer Cells

Metastasis, a hallmark of cancer development, is also the leading reason for most cancer-related deaths. Furthermore, cancer cells are highly adaptable to microenvironments and can migrate along pre-existing channel-like tracks of anatomical structures. However, more representative three-dimensional models are required to reproduce the heterogeneity of metastatic cell migration in vivo to further understand the metastasis mechanism and develop novel therapeutic strategies against it. Here, we designed and fabricated different microfluidic-based devices that recreate confined migration and diverse environments with asymmetric hydraulic resistances. Our results show different migratory potential between metastatic and nonmetastatic cancer cells in confined environments. Moreover, although nonmetastatic cells have not been tested against barotaxis due to their low migration capacity, metastatic cells present an enhanced preference to migrate through the lowest resistance path, being sensitive to barotaxis. This device, approaching the study of metastasis capability based on confined cell migration and barotactic cell decisions, may pave the way for the implementation of such technology to determine and screen the metastatic potential of certain cancer cells.

Mechanical competition triggered by innate immune signaling drives the collective extrusion of bacterially infected epithelial cells

Intracellular pathogens alter their host cells' mechanics to promote dissemination through tissues. Conversely, host cells may respond to the presence of pathogens by altering their mechanics to limit infection. Here, we monitored epithelial cell monolayers infected with intracellular bacterial pathogens, Listeria monocytogenes or Rickettsia parkeri, over days. Under conditions in which these pathogens trigger innate immune signaling through NF-κB and use actin-based motility to spread non-lytically intercellularly, we found that infected cell domains formed three-dimensional mounds. These mounds resulted from uninfected cells moving toward the infection site, collectively squeezing the softer and less contractile infected cells upward and ejecting them from the monolayer. Bacteria in mounds were less able to spread laterally in the monolayer, limiting the growth of the infection focus, while extruded infected cells underwent cell death. Thus, the coordinated forceful action of uninfected cells actively eliminates large domains of infected cells, consistent with this collective cell response representing an innate immunity-driven process.

PRIMAGE project: predictive in silico multiscale analytics to support childhood cancer personalised evaluation empowered by imaging biomarkers

PRIMAGE is one of the largest and more ambitious research projects dealing with medical imaging, artificial intelligence and cancer treatment in children. It is a 4-year European Commission-financed project that has 16 European partners in the consortium, including the European Society for Paediatric Oncology, two imaging biobanks, and three prominent European paediatric oncology units. The project is constructed as an observational in silico study involving high-quality anonymised datasets (imaging, clinical, molecular, and genetics) for the training and validation of machine learning and multiscale algorithms. The open cloud-based platform will offer precise clinical assistance for phenotyping (diagnosis), treatment allocation (prediction), and patient endpoints (prognosis), based on the use of imaging biomarkers, tumour growth simulation, advanced visualisation of confidence scores, and machine-learning approaches. The decision support prototype will be constructed and validated on two paediatric cancers: neuroblastoma and diffuse intrinsic pontine glioma. External validation will be performed on data recruited from independent collaborative centres. Final results will be available for the scientific community at the end of the project, and ready for translation to other malignant solid tumours.

An iterative finite element-based method for solving inverse problems in traction force microscopy

BACKGROUND AND OBJECTIVE

During the last years different model solutions were proposed for solving cell forces under different conditions. The solution relies on a deformation field that is obtained under cell relaxation with a chemical cocktail. Once the deformation field of the matrix is determined, cell forces can be computed by an inverse algorithm, given the mechanical properties of the matrix. Most of the Traction Force Microscopy (TFM) methods presented so far relied on a linear stress-strain response of the matrix. However, the mechanical response of some biopolymer networks, such as collagen gels is more complex. In this work, we present a numerical method for solving cell forces on non-linear materials.

METHODS

The proposed method relies on solving the inverse problem based on an iterative optimization. The objective function is defined by least-square minimization of the difference between the target and the current computed deformed configuration of the cell, and the iterative formulation is based on the solution of several direct mechanical problems. The model presents a well-posed discretized inverse elasticity problem in the absence of regularization. The algorithm can be easily implemented in any kind of Finite Element (FE) code as a sequence of different standard FE analysis.

RESULTS

To illustrate the proposed iterative formulation we apply the theoretical model to some illustrative examples by using real experimental data of Normal Human Dermal Fibroblast cells (NHDF) migrating inside a 2 mg/ml collagen-based gel. Different examples of application have been simulated to test the inverse numerical model proposed and to investigate the effect of introducing the correct cell properties onto the obtained cell forces. The algorithm converges after a small number of iterations, generating errors of around 5% for the tractions field in the cell contour domain. The resulting maximum traction values increased by 11% as a consequence of doubling the mechanical properties of the cell domain.

CONCLUSIONS

With the results generated from computations we demonstrate the application of the algorithm and explain how the mechanical properties of both, the cell and the gel, domains are important for arriving to the correct results when using inverse traction force reconstruction algorithms, however, have only a minor effect on the resulting traction values.

Breast Cancer Cells Adapt Contractile Forces to Overcome Steric Hindrance

Cell migration through the extracellular matrix is governed by the interplay between cell-generated propulsion forces, adhesion forces, and resisting forces arising from the steric hindrance of the matrix. Steric hindrance in turn depends on matrix porosity, matrix deformability, cell size, and cell deformability. In this study, we investigate how cells respond to changes in steric hindrance that arise from altered cell mechanical properties. Specifically, we measure traction forces, cell morphology, and invasiveness of MDA-MB 231 breast cancer cells in three-dimensional collagen gels. To modulate cell mechanical properties, we either decrease nuclear deformability by twofold overexpression of the nuclear protein lamin A or we introduce into the cells stiff polystyrene beads with a diameter larger than the average matrix pore size. Despite this increase of steric hindrance, we find that cell invasion is only marginally inhibited, as measured by the fraction of motile cells and the mean invasion depth. To compensate for increased steric hindrance, cells employ two alternative strategies. Cells with higher nuclear stiffness increase their force polarity, whereas cells with large beads increase their net contractility. Under both conditions, the collagen matrix surrounding the cells stiffens dramatically and carries increased strain energy, suggesting that increased force polarity and increased net contractility are functionally equivalent strategies for overcoming an increased steric hindrance.

From individual to collective 3D cancer dissemination: roles of collagen concentration and TGF-β

Cancer cells have the ability to migrate from the primary (original) site to other places in the body. The extracellular matrix affects cancer cell migratory capacity and has been correlated with tissue-specific spreading patterns. However, how the matrix orchestrates these behaviors remains unclear. Here, we investigated how both higher collagen concentrations and TGF-β regulate the formation of H1299 cell (a non-small cell lung cancer cell line) spheroids within 3D collagen-based matrices and promote cancer cell invasive capacity. We show that at low collagen concentrations, tumor cells move individually and have moderate invasive capacity, whereas when the collagen concentration is increased, the formation of cell clusters is promoted. In addition, when the concentration of TGF-β in the microenvironment is lower, most of the clusters are aggregates of cancer cells with a spheroid-like morphology and poor migratory capacity. In contrast, higher concentrations of TGF-β induced the formation of clusters with a notably higher invasive capacity, resulting in clear strand-like collective cell migration. Our results show that the concentration of the extracellular matrix is a key regulator of the formation of tumor clusters that affects their development and growth. In addition, chemical factors create a microenvironment that promotes the transformation of idle tumor clusters into very active, invasive tumor structures. These results collectively demonstrate the relevant regulatory role of the mechano-chemical microenvironment in leading the preferential metastasis of tumor cells to specific tissues with high collagen concentrations and TFG-β activity.

Degradation of extracellular matrix regulates osteoblast migration: A microfluidic-based study

Bone regeneration is strongly dependent on the capacity of cells to move in a 3D microenvironment, where a large cascade of signals is activated. To improve the understanding of this complex process and to advance in the knowledge of the role of each specific signal, it is fundamental to analyze the impact of each factor independently. Microfluidic-based cell culture is an appropriate technology to achieve this objective, because it allows recreating realistic 3D local microenvironments by taking into account the extracellular matrix, cells and chemical gradients in an independent or combined scenario. The main aim of this work is to analyze the impact of extracellular matrix properties and growth factor gradients on 3D osteoblast movement, as well as the role of cell matrix degradation. For that, we used collagen-based hydrogels, with and without crosslinkers, under different chemical gradients, and eventually inhibiting metalloproteinases to tweak matrix degradation. We found that osteoblast's 3D migratory patterns were affected by the hydrogel properties and the PDGF-BB gradient, although the strongest regulatory factor was determined by the ability of cells to remodel the matrix.

Quantifying 3D chemotaxis in microfluidic-based chips with step gradients of collagen hydrogel concentrations

Cell migration is an essential process involved in crucial stages of tissue formation, regeneration or immune function as well as in pathological processes including tumor development or metastasis. During the last few years, the effect of gradients of soluble molecules on cell migration has been widely studied, and complex systems have been used to analyze cell behavior under simultaneous mechano-chemical stimuli. Most of these chemotactic assays have, however, focused on specific substrates in 2D. The aim of the present work is to develop a novel microfluidic-based chip that allows the long-term chemoattractant effect of growth factors (GFs) on 3D cell migration to be studied, while also providing the possibility to analyze the influence of the interface generated between different adjacent hydrogels. Namely, 1.5, 2, 2.5 and 4 mg ml^-1 concentrations of collagen type I were alternatively combined with 5, 10 or 50 ng ml^-1 concentrations of PDGF and VEGF (as a negative control). To achieve this goal, we have designed a new microfluidic device including three adjacent chambers to introduce hydrogels that allow the generation of a collagen concentration step gradient. This versatile and simple platform was tested by using dermal human fibroblasts embedded in 3D collagen matrices. Images taken over a week were processed to quantify the number of cells in each zone. We found, in terms of cell distribution, that the presence of PDGF, especially in small concentrations, was a strong chemoattractant for dermal human fibroblasts across the gels regardless of their collagen concentration and step gradient direction, whereas the effects of VEGF or collagen step gradient concentrations alone were negligible.

A phenomenological cohesive model for the macroscopic simulation of cell-matrix adhesions

Cell adhesion is crucial for cells to not only physically interact with each other but also sense their microenvironment and respond accordingly. In fact, adherent cells can generate physical forces that are transmitted to the surrounding matrix, regulating the formation of cell-matrix adhesions. The main purpose of this work is to develop a computational model to simulate the dynamics of cell-matrix adhesions through a cohesive formulation within the framework of the finite element method and based on the principles of continuum damage mechanics. This model enables the simulation of the mechanical adhesion between cell and extracellular matrix (ECM) as regulated by local multidirectional forces and thus predicts the onset and growth of the adhesion. In addition, this numerical approach allows the simulation of the cell as a whole, as it models the complete mechanical interaction between cell and ECM. As a result, we can investigate and quantify how different mechanical conditions in the cell (e.g., contractile forces, actin cytoskeletal properties) or in the ECM (e.g., stiffness, external forces) can regulate the dynamics of cell-matrix adhesions.

Phenomenological modelling and simulation of cell clusters in 3D cultures

Cell clustering and aggregation are fundamental processes in the development of several tissues and the progression of many diseases. The formation of these aggregates also has a direct impact on the oxygen concentration in their surroundings due to cellular respiration and poor oxygen diffusion through clusters. In this work, we propose a mathematical model that is capable of simulating cell cluster formation in 3D cultures through combining a particle-based and a finite element approach to recreate complex experimental conditions. Cells are modelled considering cell proliferation, cell death and cell-cell mechanical interactions. Additionally, the oxygen concentration profile is calculated through finite element analysis using a reaction-diffusion model that considers cell oxygen consumption and diffusion through the extracellular matrix and the cell clusters. In our model, the local oxygen concentration in the medium determines both cell proliferation and cell death. Numerical predictions are also compared with experimental data from the literature. The simulation results indicate that our model can predict cell clustering, cluster growth and oxygen distribution in 3D cultures. We conclude that the initial cell distribution, cell death and cell proliferation dynamics determine the size and density of clusters. Moreover, these phenomena are directly affected by the oxygen transport in the 3D culture.

Subject-specific musculoskeletal loading of the tibia: Computational load estimation

The systematic development of subject-specific computer models for the analysis of personalized treatments is currently a reality. In fact, many advances have recently been developed for creating virtual finite element-based models. These models accurately recreate subject-specific geometries and material properties from recent techniques based on quantitative image analysis. However, to determine the subject-specific forces, we need a full gait analysis, typically in combination with an inverse dynamics simulation study. In this work, we aim to determine the subject-specific forces from the computer tomography images used to evaluate bone density. In fact, we propose a methodology that combines these images with bone remodelling simulations and artificial neural networks. To test the capability of this novel technique, we quantify the personalized forces for five subject-specific tibias using our technique and a gait analysis. We compare both results, finding that similar vertical loads are estimated by both methods and that the dominant part of the load can be reliably computed. Therefore, we can conclude that the numerical-based technique proposed in this work has great potential for estimating the main forces that define the mechanical behaviour of subject-specific bone.

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.

Biomechanical assessment and clinical analysis of different intramedullary nailing systems for oblique fractures

The aim of this study is to evaluate the fracture union or non-union for a specific patient that presented oblique fractures in tibia and fibula, using a mechanistic-based bone healing model. Normally, this kind of fractures can be treated through an intramedullary nail using two possible configurations that depends on the mechanical stabilisation: static and dynamic. Both cases are simulated under different fracture geometries in order to understand the effect of the mechanical stabilisation on the fracture healing outcome. The results of both simulations are in good agreement with previous clinical experience. From the results, it is demonstrated that the dynamization of the fracture improves healing in comparison with a static or rigid fixation of the fracture. This work shows the versatility and potential of a mechanistic-based bone healing model to predict the final outcome (union, non-union, delayed union) of realistic 3D fractures where even more than one bone is involved.

Modeling the formation of cell-matrix adhesions on a single 3D matrix fiber

Cell-matrix adhesions are crucial in different biological processes like tissue morphogenesis, cell motility, and extracellular matrix remodeling. These interactions that link cell cytoskeleton and matrix fibers are built through protein clutches, generally known as adhesion complexes. The adhesion formation process has been deeply studied in two-dimensional (2D) cases; however, the knowledge is limited for three-dimensional (3D) cases. In this work, we simulate different local extracellular matrix properties in order to unravel the fundamental mechanisms that regulate the formation of cell-matrix adhesions in 3D. We aim to study the mechanical interaction of these biological structures through a three dimensional discrete approach, reproducing the transmission pattern force between the cytoskeleton and a single extracellular matrix fiber. This numerical model provides a discrete analysis of the proteins involved including spatial distribution, interaction between them, and study of the different phenomena, such as protein clutches unbinding or protein unfolding.

Fibroblast Migration in 3D is Controlled by Haptotaxis in a Non-muscle Myosin II-Dependent Manner

Cell migration in 3D is a key process in many physiological and pathological processes. Although valuable knowledge has been accumulated through analysis of various 2D models, some of these insights are not directly applicable to migration in 3D. In this study, we have confined biomimetic hydrogels within microfluidic platforms in the presence of a chemoattractant (platelet-derived growth factor-BB). We have characterized the migratory responses of human fibroblasts within them, particularly focusing on the role of non-muscle myosin II. Our results indicate a prominent role for myosin II in the integration of chemotactic and haptotactic migratory responses of fibroblasts in 3D confined environments.

Inducing chemotactic and haptotactic cues in microfluidic devices for three-dimensional in vitro assays

Microfluidic devices allow for the production of physiologically relevant cellular microenvironments by including biomimetic hydrogels and generating controlled chemical gradients. During transport, the biomolecules interact in distinct ways with the fibrillar networks: as purely diffusive factors in the soluble fluid or bound to the matrix proteins. These two main mechanisms may regulate distinct cell responses in order to guide their directional migration: caused by the substrate-bound chemoattractant gradient (haptotaxis) or by the gradient established within the soluble fluid (chemotaxis). In this work 3D diffusion experiments, in combination with ELISA assays, are performed using microfluidic platforms in order to quantify the distribution of PDGF-BB and TGF-β1 across collagen and fibrin gels. Furthermore, to gain a deeper understanding of the fundamental processes, the experiments are reproduced by computer simulations based on a reaction-diffusion transport model. This model yields an accurate prediction of the experimental results, confirming that diffusion and binding phenomena are established within the microdevice.

Numerical simulation of bone remodelling around dental implants

Crestal bone loss can result in the failure of dental implants and can be caused, by among other factors, the development of non-physiological mechanical conditions. Bone remodelling (BR) is the physiological process through which bone adapts itself to the mechanical environment. A previously published mathematical model of BR is used in this work to study the homogenized structural evolution of peri-implant bone. This model is used to study the influence of the diameter and length of a dental implant of pure titanium on its long-term stability. The temporal evolution of porosity and microstructural damage of the peri-implant bone are the variables analysed in this study. The results show that damage and porosity increase as the implant length decreases and, more pronouncedly, as its diameter decreases. The increase in damage and porosity levels is localized, as many other studies confirm, at the implant neck due to the stress concentration that is created in that area. The main conclusion of this study is that in implants with a diameter equal to or greater than 3 mm the damage is under control and there is no mechanical failure of the peri-implant bone in the long term.

Piezoelectricity could predict sites of formation/resorption in bone remodelling and modelling

We have developed a mathematical approach for modelling the piezoelectric behaviour of bone tissue in order to evaluate the electrical surface charges in bone under different mechanical conditions. This model is able to explain how bones change their curvature, where osteoblasts or osteoclasts could detect in the periosteal/endosteal surfaces the different electrical charges promoting bone formation or resorption. This mechanism also allows to understand the BMU progression in function of the electro-mechanical bone behaviour.

An interspecies computational study on limb lengthening

Distraction osteogenesis is a surgical technique that produces large volumes of new bone by gradually separating two osteotomized bone segments. A previously proposed mechanical-based model that includes the effect of pre-traction stresses (stress level in the gap tissue before each distraction step) during limb lengthening is used here. In the present work, the spatial and temporal patterns of tissue distribution during distraction osteogenesis in different species (sheep, rabbit) and in the human are compared numerically to predict experimental results. Interspecies differential characteristics such as size, distraction protocol, and rate of distraction, among others, are chosen according to experiments. Tissue distributions and reaction forces are then analysed as indicators of the healing pattern. The results obtained are in agreement with experimental findings regarding both tissue distribution and reaction forces. The ability of the model to qualitatively predict the two animal models and the human healing pattern in distraction osteogenesis indicates its potential in understanding the influence of mechanics in this complex process.

Scaffold microarchitecture determines internal bone directional growth structure: a numerical study

A number of successful results have been reported in bone tissue engineering, although the routine clinical practice has not been reached so far. One of the reasons is the poor understanding of the role of each scaffold design parameter in its functional performance, which yields an uncertain outcome of each clinical application. Specifically, the role of internal scaffold microarchitectural shape on the regeneration rate and distribution of newly formed bone is still unknown. This work is focused on the in-silico determination of the role of scaffold microstructural anisotropy in bone tissue regeneration. A multiscale approach of the problem is established distinguishing between macroscopic region domain (bone organ and scaffold) and microscopic domain (scaffold microstructure). Results show that, once the scaffold microstructure is properly interconnected and the porosity is sufficiently high, similar rates of bone regeneration are found. However, the main conclusion of the work is that initial scaffold microstructural anisotropy has important consequences since it determines the spatial distribution of the newly formed tissue.

Comparative analysis of bone remodelling models with respect to computerised tomography-based finite element models of bone

Subject-specific finite element models are an extensively used tool for the numerical analysis of the biomechanical behaviour of human bones. However, bone modelling is not an easy task due to the complex behaviour of bone tissue, involving non-homogeneous and anisotropic mechanical properties. Moreover, bone is a living tissue and therefore its microstructure and mechanical properties evolve with time in a known process called bone remodelling. This phenomenon has been widely studied, many being the numerical models that have been formulated to predict density distribution and its evolution in several bones. The aim of the present study is to assess the capability of a bone remodelling model to predict the bone density distribution of different types of human bone (femur, tibia and mandible) comparing the obtained results with the bone density estimated by means of computerised tomography. Good accuracy was observed for the bone remodelling predictions including the thickness of the cortical layer.

On the effect of substrate curvature on cell mechanics

Cell movement on a substrate or within the extracellular matrix is the phenomenological response to a biochemical signals' cascade transcripted into biophysical processes and viceversa. The process is complex in nature, including different length scales from the whole cell to organelle and protein levels, where substrate/ECM curvature has been shown to play an important role on cell's behavior. From a macroscopic perspective, the cytoskeleton may be modeled as a continuum body unbalanced by internal protein motors. In this work, we propose a cell constitutive model to simulate cell attachment on curved substrates, activated by contractile forces. We first analyze a single fiber bundle composed by microtubules, actin filaments and myosin machinery. Then, the model is macroscopically extended to the cytoskeletal level using homogenization. Substrate curvature has two implications in our model: (i) it forces fibers to work in a curved (bent) position and (ii) it eventually creates a pre-deformation state in the cytoskeleton. Interestingly, the model shows higher contractile force inhibition as curvature increases when implemented over different substrate morphologies, being this consistent with experimental results. The presented model may result useful in many new regenerative medicine techniques, miniaturized experimental tests, or to analyze cell behavior on manufactured nanoscaffolds for tissue engineering.

Computational modelling of bone cement polymerization: temperature and residual stresses

The two major concerns associated with the use of bone cement are the generation of residual stresses and possible thermal necrosis of surrounding bone. An accurate modelling of these two factors could be a helpful tool to improve cemented hip designs. Therefore, a computational methodology based on previous published works is presented in this paper combining a kinetic and an energy balance equation. New assumptions are that both the elasticity modulus and the thermal expansion coefficient depend on the bone cement polymerization fraction. This model allows to estimate the thermal distribution in the cement which is later used to predict the stress-locking effect, and to also estimate the cement residual stresses. In order to validate the model, computational results are compared with experiments performed on an idealized cemented femoral implant. It will be shown that the use of the standard finite element approach cannot predict the exact temporal evolution of the temperature nor the residual stresses, underestimating and overestimating their value, respectively. However, this standard approach can estimate the peak and long-term values of temperature and residual stresses within acceptable limits of measured values. Therefore, this approach is adequate to evaluate residual stresses for the mechanical design of cemented implants. In conclusion, new numerical techniques should be proposed in order to achieve accurate simulations of the problem involved in cemented hip replacements.

A mathematical approach to bone tissue engineering

Tissue engineering is becoming consolidated in the biomedical field as one of the most promising strategies in tissue repair and regenerative medicine. Within this discipline, bone tissue engineering involves the use of cell-loaded porous biomaterials, i.e. bioscaffolds, to promote bone tissue regeneration in bone defects or diseases such as osteoporosis, although it has not yet been incorporated into daily clinical practice. The overall success of a particular bone tissue engineering application depends strongly on scaffold design parameters, which do away with long and expensive clinical protocols. Computer simulation is a useful tool that may reduce animal experiments and help to identify optimal patient-specific designs after concise model validation. In this paper, we present a novel mathematical approach to bone regeneration within scaffolds, based on a multiscale framework. Results are presented over an actual scaffold microstructure, showing the potential of computer simulation, and how it can aid in the task of making bone tissue engineering a reality in clinical practice.

On scaffold designing for bone regeneration: A computational multiscale approach

Scaffold design for bone tissue engineering applications involves many parameters that directly influence the rate of bone tissue regeneration onto its microstructural surface. To improve scaffold functionality, increasing interest is being focused on in vitro and in vivo research in order to obtain the optimal scaffold design for a specific application. However, the evaluation of the effect of each specific scaffold parameter on tissue regeneration using these techniques requires costly protocols and long-term experiments. In this paper, we elucidate the effect of some scaffold parameters on bone tissue regeneration by means of a mathematically based approach. By virtue of in silico experiments, factors such as scaffold stiffness, porosity, resorption kinetics, pore size and pre-seeding are analyzed in a specific bone tissue application found in the literature. The model predicts the in vivo rate of bone formation within the scaffold, the scaffold degradation and the interaction between the implanted scaffold and the surrounding bone. Results show an increasing rate of bone regeneration with increasing scaffold stiffness, scaffold mean pore size and pre-seeding, whereas the collapse of the scaffold occurs for a faster biomaterial resorption kinetics. Requiring further experimental validation, the model can be useful for the assessment of scaffold design and for the analysis of scaffold parameters in tissue regeneration.

Permeability evaluation of 45S5 Bioglass-based scaffolds for bone tissue engineering

Permeability is a key parameter for microstructural design of scaffolds, since it is related to their capability for waste removal and nutrients/oxygen supply. In this framework, Darcy's experiments were carried out in order to determine the relationship between the pressure drop gradient and the fluid flow velocity in Bioglass-based scaffolds to obtain the scaffold's permeability. Using deionised water as working fluid, the measured average permeability value on scaffolds of 90-95% porosity was 1.96 x 10(-9) m(2). This value lies in the published range of permeability values for trabecular bone.

Does increased bone-cement interface strength have negative consequences for bulk cement integrity? A finite element study

Implant loosening is one of the most important modes of failure of cemented total hip replacement. It may be related to the cement strength, cement-prosthesis interface, cement-bone interface, surgical technique, or stem design. The main purpose of this study is to investigate the effect of bone-cement interface mechanical properties on cement degradation. The computational methodology proposed herein combines a previously developed bone-cement interface damage model and an accumulative damage model for bulk cement. This has been applied to a finite element model of an Exeter cemented hip implant. A higher strength of the bone-cement interface due to a higher amount of interdigitated bone results in faster cement deterioration. Over time, damage both at the bone-cement interface and in the cement mantle worsens. Also, a larger debonded area was predicted proximally, as observed in clinical practice. We conclude that the computational model proposed herein allows a realistic simulation of the bone-cement interface debonding and cement degradation, being a useful tool in the design of this kind of medical devices.

On the role of bone damage in calcium homeostasis

Bone serves as the reservoir of some minerals including calcium. If calcium is needed anywhere in the body, it can be removed from the bone matrix by resorption and put back into the blood flow. During bone remodelling the resorbed tissue is replaced by osteoid which gets mineralized very slowly. Then, calcium homeostasis is controlled by bone remodelling, among other processes: the more intense is the remodelling activity, the lower is the mineral content of bone matrix. Bone remodelling is initiated by the presence of microstructural damage. Some experimental evidences show that the fatigue properties of bone are degraded and more microdamage is accumulated due to the external load as the mineral content increases. That damage initiates bone remodelling and the mineral content is so reduced. Therefore, this process prevents the mineral content of bone matrix to reach very high (non-physiological) values. A bone remodelling model has been used to simulate this regulatory process. In this model, damage is an initiation factor for bone remodelling and is estimated through a fatigue algorithm, depending on the macroscopic strain level. Mineral content depends on bone remodelling and mineralization rate. Finally, the bone fatigue properties are defined as dependent on the mineral content, closing the interconnection between damage and mineral content. The remodelling model was applied to a simplified example consisting of a bar under tension with an initially heterogeneous mineral distribution. Considering the fatigue properties as dependent on the mineral content, the mineral distribution tends to be homogeneous with an ash fraction within the physiological range. If such dependance is not considered and fatigue properties are assumed constant, the homogenization is not always achieved and the mineral content may rise up to high non-physiological values. Thus, the interconnection between mineral content and fatigue properties is essential for the maintenance of bone's structural integrity as well as for the calcium homeostasis.

A damage model for the growth plate: Application to the prediction of slipped capital epiphysis

Despite slipped capital femoral epiphysis (SCFE) being one of the most common disorders of the adolescent hip, its early diagnosis is quite difficult. The main objective of this work is to apply an interface damage model to predict the failure of the bone-growth plate-bone interface. This model allows to evaluate the risk of development of SCFE and to investigate the range of mechanical properties of the physis that may cause slippage of the plate. This paper also studies the influence of different geometrical parameters and body weight of the patient on the development of SCFE. We have demonstrated, thanks to the proposed model, that higher physeal sloping and posterior sloping angles are associated to a higher probability of development of SCFE. In a similar way, increasing body weight results in a more probable slippage.

Computational simulation of fracture healing: Influence of interfragmentary movement on the callus growth

Bone fractures heal through a complex process involving several cellular events. This healing process can serve to study factors that control tissue growth and differentiation from mesenchymal stem cells. The mechanical environment at the fracture site is one of the factors influencing the healing process and controls size and differentiation patterns in the newly formed tissue. Mathematical models can be useful to unravel the complex relation between mechanical environment and tissue formation. In this study, we present a mathematical model that predicts tissue growth and differentiation patterns from local mechanical signals. Our aim was to investigate whether mechanical stimuli, through their influence on stem cell proliferation and chondrocyte hypertrophy, predict characteristic features of callus size and geometry. We found that the model predicted several geometric features of fracture calluses. For instance, callus size was predicted to increase with increasing movement. Also, increases in size were predicted to occur through increase in callus diameter but not callus length. These features agree with experimental observations. In addition, spatial and temporal tissue differentiation patterns were in qualitative agreement with well-known experimental results. We therefore conclude that local mechanical signals can probably explain the shape and size of fracture calluses.

Numerical estimation of bone density and elastic constants distribution in a human mandible

In this paper, we try to predict the distribution of bone density and elastic constants in a human mandible, based on the stress level produced by mastication loads using a mathematical model of bone remodelling. These magnitudes are needed to build finite element models for the simulation of the mandible mechanical behavior. Such a model is intended for use in future studies of the stability of implant-supported dental prostheses. Various models of internal bone remodelling, both phenomenological and more recently mechanobiological, have been developed to determine the relation between bone density and the stress level that bone supports. Among the phenomenological models, there are only a few that are also able to reproduce the level of anisotropy. These latter have been successfully applied to long bones, primarily the femur. One of these models is here applied to the human mandible, whose corpus behaves as a long bone. The results of bone density distribution and level of anisotropy in different parts of the mandible have been compared with various clinical studies, with a reasonable level of agreement.

A 3D computational simulation of fracture callus formation: influence of the stiffness of the external fixator

The stiffness of the external fixation highly influences the fracture healing pattern. In this work we study this aspect by means of a finite element model of a simple transverse mid-diaphyseal fracture of an ovine metatarsus fixed with a bilateral external fixator. In order to simulate the regenerative process, a previously developed mechanobiological model of bone fracture healing was implemented in three dimensions. This model is able to simulate tissue differentiation, bone regeneration, and callus growth. A physiological load of 500 N was applied and three different stiffnesses of the external fixator were simulated (2300, 1725, and 1150 N/mm). The interfragmentary strain and load sharing mechanism between bone and the external fixator were compared to those recorded in previous experimental works. The effects of the stiffness on the callus shape and tissue distributions in the fracture site were also analyzed. We predicted that a lower stiffness of the fixator delays fracture healing and causes a larger callus, in correspondence to well-documented clinical observations.

A comparative FEA of the debonding process in different concepts of cemented hip implants

Debonding of the stem-cement interface and damage accumulation in the cement mantle are basic events that contribute to the long-term failure of cemented hip reconstructions. In this work, a numerical study with these two processes coupled is presented. On the one hand, debonding of the stem-cement interface was simulated by means of a cohesive surface theory that was implemented into an interface finite element. This interface model includes a tensile-shear behavior law, the fatigue failure of the interface, and the friction evolution between both surfaces. On the other hand, damage accumulation in the cement was formulated through the theory of continuum damage mechanics, considering cement damage due to tension, creep under compression, crack closure effects, non-linear damage accumulation and cement residual stresses appearing during polymerisation. This methodology was applied to simulate and compare the degradation process of the cement and stem-cement interface in four different concepts of design: Exeter, Charnley, Elite Plus and ABG II stems. As the actual mechanical properties of the surface of each specific prosthesis are not known, we assumed the same for all of them, distinguishing between polished and matt surfaces. With this assumption, the predicted results showed that the debonding process is very different for each implant depending on the stem geometry. Lower cement deterioration was obtained for the Exeter and ABG II stems, while the lowest stem-cement interface debonding was produced in the Exeter and the Elite Plus stems.

Probabilistic analysis of the influence of the bonding degree of the stem–cement interface in the performance of cemented hip prostheses

The long-term behavior of the stem-cement interface is one of the most frequent topics of discussion in the design of cemented total hip replacements, especially with regards to the process of damage accumulation in the cement layer. This effect is analyzed here comparing two different situations of the interface: completely bonded and debonded with friction. This comparative analysis is performed using a probabilistic computational approach that considers the variability and uncertainty of determinant factors that directly compromise the damage accumulation in the cement mantle. This stochastic technique is based on the combination of probabilistic finite elements (PFEM) and a cumulative damage approach known as B-model. Three random variables were considered: muscle and joint contact forces at the hip (both for walking and stair climbing), cement damage and fatigue properties of the cement. The results predicted that the regions with higher failure probability in the bulk cement are completely different depending on the stem-cement interface characteristics. In a bonded interface, critical sites appeared at the distal and medial parts of the cement, while for debonded interfaces, the critical regions were found distally and proximally. In bonded interfaces, the failure probability was higher than in debonded ones. The same conclusion may be established for stair climbing in comparison with walking activity.

Influence of fracture gap size on the pattern of long bone healing: a computational study

Following fractures, bones restore their original structural integrity through a complex process in which several cellular events are involved. Among other factors, this process is highly influenced by the mechanical environment of the fracture site. In this study, we present a mathematical model to simulate the effect of mechanical stimuli on most of the cellular processes that occur during fracture healing, namely proliferation, migration and differentiation. On the basis of these three processes, the model then simulates the evolution of geometry, distributions of cell types and elastic properties inside a healing fracture. The three processes were implemented in a Finite Element code as a combination of three coupled analysis stages: a biphasic, a diffusion and a thermoelastic step. We tested the mechano-biological regulatory model thus created by simulating the healing patterns of fractures with different gap sizes and different mechanical stimuli. The callus geometry, tissue differentiation patterns and fracture stiffness predicted by the model were similar to experimental observations for every analysed situation.

A bone remodelling model coupling microdamage growth and repair by 3D BMU-activity

Bone as most of living tissues is able, during its entire lifetime, to adapt its internal microstructure and subsequently its associated mechanical properties to its specific mechanical and physiological environment in a process commonly known as bone remodelling. Bone is therefore continuously renewed and micro-damage, accumulated by fatigue or creep, is removed minimizing the risk of fracture. Nevertheless, bone is not always able to repair itself completely. Actually, if bone repairing function is slower than micro-damage accumulation, a type of bone fracture, usually known as "stress fracture", can finally evolve. In this paper, we propose a bone remodelling continuous model able to simulate micro-damage growth and repair in a coupled way and able therefore to predict the occurrence of "stress fractures". The biological bone remodelling process is modelled in terms of equations that describe the activity of basic multicellular units. The predicted results show a good correspondence with experimental and clinical data. For example, in disuse, bone porosity increases until an equilibrium situation is achieved. In overloading, bone porosity decreases unless the damage rate is so high that causes resorption or "stress fracture".

Finite Element Prediction of Proximal Femoral Fracture Patterns Under Different Loads

The main purpose of this work is to discuss the ability of finite element analyses, together with an appropriate anisotropic fracture criterion, to predict the ultimate load and type of fracture in bones and more specifically in the proximal femur. We show here that the use of a three-dimensional anisotropic criterion provides better results than other well-known isotropic criteria. The criterion parameters and the anisotropic elastic properties were defined in terms of the bone tissue microstructure, quantified by the apparent density and the so-called “fabric tensor”, whose spatial distributions were obtained by means of an anisotropic remodeling model able to capture the main features of the internal structure of long bones. In order to check the validity of the results obtained, they have been compared with those of an experimental work that analyzes different types of fractures induced in the proximal femur by a static overload.