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.

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.

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.

Mechano-sensing and cell migration: a 3D model approach.

Cell migration is essential for tissue development in different physiological and pathological conditions. It is a complex process orchestrated by chemistry, biological factors, microstructure and surrounding mechanical properties. Focusing on the mechanical interactions, cells do not only exert forces on the matrix that surrounds them, but they also sense and react to mechanical cues in a process called mechano-sensing. Here, we hypothesize the involvement of mechano-sensing in the regulation of directional cell migration through a three-dimensional (3D) matrix. For this purpose, we develop a 3D numerical model of individual cell migration, which incorporates the mechano-sensing process of the cell as the main mechanism regulating its movement. Consistent with this hypothesis, we found that factors, such as substrate stiffness, boundary conditions and external forces, regulate specific and distinct cell movements.

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.

On the modelling of biological patterns with mechanochemical models: Insights from analysis and computation.

The diversity of biological form is generated by a relatively small number of underlying mechanisms. Consequently, mathematical and computational modelling can, and does, provide insight into how cellular level interactions ultimately give rise to higher level structure. Given cells respond to mechanical stimuli, it is therefore important to consider the effects of these responses within biological self-organisation models. Here, we consider the self-organisation properties of a mechanochemical model previously developed by three of the authors in Acta Biomater. 4, 613-621 (2008), which is capable of reproducing the behaviour of a population of cells cultured on an elastic substrate in response to a variety of stimuli. In particular, we examine the conditions under which stable spatial patterns can emerge with this model, focusing on the influence of mechanical stimuli and the interplay of non-local phenomena. To this end, we have performed a linear stability analysis and numerical simulations based on a mixed finite element formulation, which have allowed us to study the dynamical behaviour of the system in terms of the qualitative shape of the dispersion relation. We show that the consideration of mechanotaxis, namely changes in migration speeds and directions in response to mechanical stimuli alters the conditions for pattern formation in a singular manner. Furthermore without non-local effects, responses to mechanical stimuli are observed to result in dispersion relations with positive growth rates at arbitrarily large wavenumbers, in turn yielding heterogeneity at the cellular level in model predictions. This highlights the sensitivity and necessity of non-local effects in mechanically influenced biological pattern formation models and the ultimate failure of the continuum approximation in their absence.

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.

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.

Modelling actin polymerization: the effect on confined cell migration.

The aim of this work is to model cell motility under conditions of mechanical confinement. This cell migration mode may occur in extravasation of tumour and neutrophil-like cells. Cell migration is the result of the complex action of different forces exerted by the interplay between myosin contractility forces and actin processes. Here, we propose and implement a finite element model of the confined migration of a single cell. In this model, we consider the effects of actin and myosin in cell motility. Both filament and globular actin are modelled. We model the cell considering cytoplasm and nucleus with different mechanical properties. The migration speed in the simulation is around 0.1 µm/min, which is in agreement with existing literature. From our simulation, we observe that the nucleus size has an important role in cell migration inside the channel. In the simulation the cell moves further when the nucleus is smaller. However, this speed is less sensitive to nucleus stiffness. The results show that the cell displacement is lower when the nucleus is stiffer. The degree of adhesion between the channel walls and the cell is also very important in confined migration. We observe an increment of cell velocity when the friction coefficient is higher.

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.

Computational simulation of dental implant osseointegration through resonance frequency analysis.

The aim of this study is to predict the evolution of the resonance frequency of the bone-implant interface in a dental implant by means of finite element simulation. A phenomenological interface model able to simulate the mechanical effects of the osseointegration process at the bone-implant interface is applied and compared with some experimental results in rabbits. An early stage of slow bone ingrowth, followed by a faster osseointegration phase until final stability is predicted by the simulations. The evolution of the resonance frequency of the implant and surrounding tissues along the simulation period was also obtained, observing a 3-fold increase in the first principal frequency. These findings are in quantitative agreement with the experimental measurements and suggest that the model can be useful to evaluate the influence of mechanical factors such as implant geometry or implant loading on the indirect evaluation of the process of implant osseintegration.

A web-based application for automated quantification of chemical gradients induced in microfluidic devices.

Advances in microfabrication have allowed the development and popularization of microfluidic devices, which are powerful tools to recreate three-dimensional (3-D) biologically relevant in vitro models. These microenvironments are usually generated by using hydrogels and induced chemical gradients. Going further, computational models enable, after validation, the simulation of such conditions without the necessity of real experiments, thus saving costs and time. In this work we present a web-based application that allows, based on a previous numerical model, the assessment of different chemical gradients induced within a 3-D extracellular matrix. This application enables the estimation of the spatio-temporal chemical distribution inside microfluidic devices, by defining a first set of parameters characterizing the chip geometry, and a second set characterizing the diffusion properties of the hydrogel-based matrix. The simulated chemical concentration profiles generated within a synthetic hydrogel are calculated remotely on a server and returned to the website in less than 3 min, thus offering a quick automatic quantification to any user. To ensure the day-to-day applicability, user requirements were investigated prior to tool development, pre-selecting some of the most common geometries. The tool is freely available online, after user registration, on http://m2be.unizar.es/insilico_cell under the software tab. Four different microfluidic device geometries were defined to study the dependence of the geometrical parameters onto the gradient formation processes. The numerical predictions demonstrate that growth factor diffusion within 3-D matrices strongly depends not only on the physics of diffusion, but also on the geometrical parameters that characterizes these complex devices. Additionally, the effect of the combination of different hydrogels inside a microfluidic device was studied. The automatization of microfluidic device geometries generation provide a powerful tool which facilitates to any user the possibility to automatically create its own microfluidic device, greatly reducing the experimental validation processes and advancing in the understanding of in vitro 3-D cell responses without the necessity of using commercial software or performing real testing experiments.

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.

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

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-ß 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-ß 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-ß 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-ß activity.

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.

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.

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.