Physico-chemical characterization of the tumour microenvironment of pancreatic ductal adenocarcinoma

Pancreatic ductal adenocarcinoma (PDAC) is a highly aggressive lethal malignancy that accounts for more than 90% of pancreatic cancer diagnoses. Our research is focused on the physico-chemical properties of the tumour microenvironment (TME), including its tumoural extracellular matrix (tECM), as they may have an important impact on the success of cancer therapies. PDAC xenografts and their decellularized tECM offer a great material source for research in terms of biomimicry with the original human tumour. Our aim was to evaluate and quantify the physico-chemical properties of the PDAC TME. Both cellularized (native TME) and decellularized (tECM) patient-derived PDAC xenografts were analyzed. A factorial design of experiments identified an optimal combination of factors for effective xenograft decellularization. Our results provide a complete advance in our understanding of the PDAC TME and its corresponding stroma, showing that it presents an interconnected porous architecture with very low permeability and small pores due to the contractility of the cellular components. This fact provides a potential therapeutic strategy based on the therapeutic agent size.

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.

Effects of tumour heterogeneous properties on modelling the transport of radiative particles

Dose calculation plays a critical role in radiotherapy (RT) treatment planning, and there is a growing need to develop accurate dose deposition models that incorporate heterogeneous tumour properties. Deterministic models have demonstrated their capability in this regard, making them the focus of recent treatment planning studies as they serve as a basis for simplified models in RT treatment planning. In this study, we present a simplified deterministic model for photon transport based on the Boltzmann transport equation (BTE) as a proof-of-concept to illustrate the impact of heterogeneous tumour properties on RT treatment planning. We employ the finite element method (FEM) to simulate the photon flux and dose deposition in real cases of diffuse intrinsic pontine glioma (DIPG) and neuroblastoma (NB) tumours. Importantly, in light of the availability of pipelines capable of extracting tumour properties from magnetic resonance imaging (MRI) data, we highlight the significance of such data. Specifically, we utilise cellularity data extracted from DIPG and NB MRI images to demonstrate the importance of heterogeneity in dose calculation. Our model simplifies the process of simulating a RT treatment system and can serve as a useful starting point for further research. To simulate a full RT treatment system, one would need a comprehensive model that couples the transport of electrons and photons.

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.

Fluid flow to mimic organ function in 3D in vitro models

Many different strategies can be found in the literature to model organ physiology, tissue functionality, and disease in vitro; however, most of these models lack the physiological fluid dynamics present in vivo. Here, we highlight the importance of fluid flow for tissue homeostasis, specifically in vessels, other lumen structures, and interstitium, to point out the need of perfusion in current 3D in vitro models. Importantly, the advantages and limitations of the different current experimental fluid-flow setups are discussed. Finally, we shed light on current challenges and future focus of fluid flow models applied to the newest bioengineering state-of-the-art platforms, such as organoids and organ-on-a-chip, as the most sophisticated and physiological preclinical platforms.

Hydrocolloids of Egg White and Gelatin as a Platform for Hydrogel-Based Tissue Engineering

Innovative materials are needed to produce scaffolds for various tissue engineering and regenerative medicine (TERM) applications, including tissue models. Materials derived from natural sources that offer low production costs, easy availability, and high bioactivity are highly preferred. Chicken egg white (EW) is an overlooked protein-based material. Whilst its combination with the biopolymer gelatin has been investigated in the food technology industry, mixed hydrocolloids of EW and gelatin have not been reported in TERM. This paper investigates these hydrocolloids as a suitable platform for hydrogel-based tissue engineering, including 2D coating films, miniaturized 3D hydrogels in microfluidic devices, and 3D hydrogel scaffolds. Rheological assessment of the hydrocolloid solutions suggested that temperature and EW concentration can be used to fine-tune the viscosity of the ensuing gels. Fabricated thin 2D hydrocolloid films presented globular nano-topography and in vitro cell work showed that the mixed hydrocolloids had increased cell growth compared with EW films. Results showed that hydrocolloids of EW and gelatin can be used for creating a 3D hydrogel environment for cell studies inside microfluidic devices. Finally, 3D hydrogel scaffolds were fabricated by sequential temperature-dependent gelation followed by chemical cross-linking of the polymeric network of the hydrogel for added mechanical strength and stability. These 3D hydrogel scaffolds displayed pores, lamellae, globular nano-topography, tunable mechanical properties, high affinity for water, and cell proliferation and penetration properties. In conclusion, the large range of properties and characteristics of these materials provide a strong potential for a large variety of TERM applications, including cancer models, organoid growth, compatibility with bioprinting, or implantable devices.

Collagen-Laponite Nanoclay Hydrogels for Tumor Spheroid Growth

The extracellular matrix (ECM) plays an important regulatory role in the development and progression of tumoral tissue. Its functions and properties are crucial in determining tumor cell behavior such as invasion, migration, and malignancy development. Our study explores the role of collagen type I in cancer development and spread using engineered tumor models like multicellular spheroids grown in collagen-based hydrogels to simulate early tumor formation. We employ microfluidic techniques to test the hypothesis that (i) adding Laponite nanoclay to collagen hydrogels modifies mechanical and rheological properties and (ii) changing the stiffness of the collagen microenvironment affects tumor spheroid growth. Our findings support our theories and suggest the use of ECM components and engineered tumor models in cancer research, offering a biocompatible and biomimetic method to tailor the mechanical properties of conventional collagen hydrogels.

Computational modelling of the mechanical behaviour of protein-based hydrogels

Protein-based hydrogels have been extensively studied in the field of biomaterials given their ability to mimic living tissues and their special resemblance to the extracellular matrix. Despite this, the methods used for the control of mechanical properties of hydrogels are very limited, focusing mainly on their elasticity, with an often unrealistic characterization of mechanical properties such as extensibility, stiffness and viscoelasticity. Being able to control these properties is essential for the development of new biomaterials, since it has been demonstrated that mechanical properties affect cell behaviour and biological processes. To better understand the mechanical behaviour of these biopolymers, a computational model is here developed to characterize the mechanical behaviour of two different protein-based hydrogels. Strain-stress tests and stress-relaxation tests are evaluated computationally and compared to the results obtained experimentally in a previous work. To achieve this goal the Finite Element Method is used, combining hyperelastic and viscoelastic models. Different hyperelastic constitutive models (Mooney-Rivlin, Neo-Hookean, first and third order Ogden, and Yeoh) are proposed to estimate the mechanical properties of the protein-based hydrogels by least-square fitting of the in-vitro uniaxial test results. Among these models, the first order Ogden model with a viscoelastic model defined in Prony parameters better reproduces the strain-stress response and the change of stiffness with strain observed in the in-vitro tests.

Hybrid computational models of multicellular tumour growth considering glucose metabolism

Cancer cells metabolize glucose through metabolic pathways that differ from those used by healthy and differentiated cells. In particular, tumours have been shown to consume more glucose than their healthy counterparts and to use anaerobic metabolic pathways, even under aerobic conditions. Nevertheless, scientists have still not been able to explain why cancer cells evolved to present an altered metabolism and what evolutionary advantage this might provide them. Experimental and computational models have been increasingly used in recent years to understand some of these biological questions. Multicellular tumour spheroids are effective experimental models as they replicate the initial stages of avascular solid tumour growth. Furthermore, these experiments generate data which can be used to calibrate and validate computational studies that aim to simulate tumour growth. Hybrid models are of particular relevance in this field of research because they model cells as individual agents while also incorporating continuum representations of the substances present in the surrounding microenvironment that may participate in intracellular metabolic networks as concentration or density distributions. Henceforth, in this review, we explore the potential of computational modelling to reveal the role of metabolic reprogramming in tumour growth.

PhysiCOOL: A generalized framework for model Calibration and Optimization Of modeLing projects

In silico models of biological systems are usually very complex and rely on a large number of parameters describing physical and biological properties that require validation. As such, parameter space exploration is an essential component of computational model development to fully characterize and validate simulation results. Experimental data may also be used to constrain parameter space (or enable model calibration) to enhance the biological relevance of model parameters. One widely used computational platform in the mathematical biology community is PhysiCell, which provides a standardized approach to agent-based models of biological phenomena at different time and spatial scales. Nonetheless, one limitation of PhysiCell is the lack of a generalized approach for parameter space exploration and calibration that can be run without high-performance computing access. Here, we present PhysiCOOL, an open-source Python library tailored to create standardized calibration and optimization routines for PhysiCell models.

A microfluidic-based analysis of 3D macrophage migration after stimulation by Mycobacterium, Salmonella and Escherichia

Macrophages play an essential role in the process of recognition and containment of microbial infections. These immune cells are recruited to infectious sites to reach and phagocytose pathogens. Specifically, in this article, bacteria from the genus Mycobacterium, Salmonella and Escherichia, were selected to study the directional macrophage movement towards different bacterial fractions. We recreated a three-dimensional environment in a microfluidic device, using a collagen-based hydrogel that simulates the mechanical microarchitecture associated to the Extra Cellular Matrix (ECM). First, we showed that macrophage migration is affected by the collagen concentration of their environment, migrating greater distances at higher velocities with decreasing collagen concentrations. To recreate the infectious microenvironment, macrophages were exposed to lateral gradients of bacterial fractions obtained from the intracellular pathogens M. tuberculosis and S. typhimurium. Our results showed that macrophages migrated directionally, and in a concentration-dependent manner, towards the sites where bacterial fractions are located, suggesting the presence of attractants molecules in all the samples. We confirmed that purified M. tuberculosis antigens, as ESAT-6 and CFP-10, stimulated macrophage recruitment in our device. Finally, we also observed that macrophages migrate towards fractions from non-pathogenic bacteria, such as M. smegmatis and Escherichia coli. In conclusion, our microfluidic device is a useful tool which opens new perspectives to study the recognition of specific antigens by innate immune cells.

A 3D multi-agent-based model for lumen morphogenesis: the role of the biophysical properties of the extracellular matrix

The correct function of many organs depends on proper lumen morphogenesis, which requires the orchestration of both biological and mechanical aspects. However, how these factors coordinate is not yet fully understood. Here, we focus on the development of a mechanistic model for computationally simulating lumen morphogenesis. In particular, we consider the hydrostatic pressure generated by the cells' fluid secretion as the driving force and the density of the extracellular matrix as regulators of the process. For this purpose, we develop a 3D agent-based-model for lumen morphogenesis that includes cells' fluid secretion and the density of the extracellular matrix. Moreover, this computer-based model considers the variation in the biological behavior of cells in response to the mechanical forces that they sense. Then, we study the formation of the lumen under different-mechanical scenarios and conclude that an increase in the matrix density reduces the lumen volume and hinders lumen morphogenesis. Finally, we show that the model successfully predicts normal lumen morphogenesis when the matrix density is physiological and aberrant multilumen formation when the matrix density is excessive.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00366-022-01654-1.

Decellularization of tumours: A new frontier in tissue engineering

Cancer is one of the leading causes of death worldwide. The tumour extracellular matrix (ECM) has unique features in terms of composition and mechanical properties, resulting in a structurally and chemically different ECM to that of native, healthy tissues. This paper reviews to date the efforts into decellularization of tumours, which in the authors’ view represents a new frontier in the ever evolving field of tumour tissue engineering. An overview of the ECM and its importance in cancer is given, ending with examples of research using decellularized tumours, which has already indicated potential therapeutic targets, unravelled malignancy mechanisms or response to chemotherapy agents. The review highlights that more research is needed in this area, which can answer important questions related to tumour formation and progression to ultimately identify new and effective therapeutic targets. Within the near-future of personalized medicine, this research can create patient-specific tumour models and therapeutic regimes.

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.

Multiscale modeling of bone tissue mechanobiology

Mechanical environment has a crucial role in our organism at the different levels, ranging from cells to tissues and our own organs. This regulatory role is especially relevant for bones, given their importance as load-transmitting elements that allow the movement of our body as well as the protection of vital organs from load impacts. Therefore bone, as living tissue, is continuously adapting its properties, shape and repairing itself, being the mechanical loads one of the main regulatory stimuli that modulate this adaptive behavior. Here we review some key results of bone mechanobiology from computational models, describing the effect that changes associated to the mechanical environment induce in bone response, implant design and scaffold-driven bone regeneration.

Microfluidic model of monocyte extravasation reveals the role of hemodynamics and subendothelial matrix mechanics in regulating endothelial integrity

Extravasation of circulating cells is an essential process that governs tissue inflammation and the body's response to pathogenic infection. To initiate anti-inflammatory and phagocytic functions within tissues, immune cells must cross the vascular endothelial barrier from the vessel lumen to the subluminal extracellular matrix. In this work, we present a microfluidic approach that enables the recreation of a three-dimensional, perfused endothelial vessel formed by human endothelial cells embedded within a collagen-rich matrix. Monocytes are introduced into the vessel perfusate, and we investigate the role of luminal flow and collagen concentration on extravasation. In vessels conditioned with the flow, increased monocyte adhesion to the vascular wall was observed, though fewer monocytes extravasated to the collagen hydrogel. Our results suggest that the lower rates of extravasation are due to the increased vessel integrity and reduced permeability of the endothelial monolayer. We further demonstrate that vascular permeability is a function of collagen hydrogel mass concentration, with increased collagen concentrations leading to elevated vascular permeability and increased extravasation. Collectively, our results demonstrate that extravasation of monocytes is highly regulated by the structural integrity of the endothelial monolayer. The microfluidic approach developed here allows for the dissection of the relative contributions of these cues to further understand the key governing processes that regulate circulating cell extravasation and inflammation.

Mechano-driven regeneration predicts response variations in large animal model based on scaffold implantation site and individual mechano-sensitivity

It is well founded that the mechanical environment may regulate bone regeneration in orthopedic applications. The purpose of this study is to investigate the mechanical contributions of the scaffold and the host to bone regeneration, in terms of subject specificity, implantation site and sensitivity to the mechanical environment. Using a computational approach to model mechano-driven regeneration, bone ingrowth in porous titanium scaffolds was simulated in the distal femur and proximal tibia of three goats and compared to experimental results. The results showed that bone ingrowth shifted from a homogeneous distribution pattern, when scaffolds were in contact with trabecular bone (max local ingrowth 12.47%), to a localized bone ingrowth when scaffolds were implanted in a diaphyseal location (max local ingrowth 20.64%). The bone formation dynamics revealed an apposition rate of 0.37±0.28%/day in the first three weeks after implantation, followed by limited increase in bone ingrowth until the end of the experiment (12 weeks). According to in vivo data, we identified one animal whose sensitivity to mechanical stimulation was higher than the other two. Moreover, we found that the stimulus initiating bone formation was consistently higher in the femur than in the tibia for all the individuals. Overall, the dependence of the osteogenic response on the host biomechanics means that, from a mechanical perspective, the regenerative potential depends on both the scaffold and the host environment. Therefore, this work provides insights on how the mechanical conditions of both the recipient and the scaffold contribute to meet patient and location-specific characteristics.

A novel algorithm to resolve lack of convergence and checkerboard instability in bone adaptation simulations using non-local averaging

Checkerboard is a typical instability in finite element (FE) simulations of bone adaptation and topology optimization in general. It consists in a patchwork pattern with elements of alternating stiffness, producing lack of convergence and instabilities in the predicted bone density. Averaging techniques have been proposed to solve this problem. One of the most acknowledged techniques (node based formulation) has severe drawbacks such as: high sensitivity to mesh density and type of element integration (full vs reduced) and, more importantly, oscillatory solutions also leading to lack of convergence. We propose a new solution consisting in a non-local smoothing technique. It defines, as the mechanical stimulus governing bone adaptation in a certain integration point of the mesh, the average of the stimuli obtained in the neighbour integration points. That average is weighted with a decay function of the distance to the centre of the neighbourhood. The new technique has been shown to overcome all the referred problems and perform in a robust way. It was tested on a hollow cylinder, resembling the diaphysis of a long bone, subjected to bending or torsion. Checkerboard instability was eliminated and local convergence of bone adaptation was achieved rapidly, in contrast to the other averaging technique and to the model without control of checkerboard instability. The new algorithm was also tested with good results on the same geometry but in a model containing a void, which produces a stress concentration that usually leads to checkerboard instability, like in other applications such as simulations of bone-implant interfaces.

Cell biophysical stimuli in lobopodium formation: a computer based approach

Different cell migration modes have been identified in 3D environments, e.g., modes incorporating lamellopodia or blebs. Recently, a new type of cellular migration has been investigated: lobopodia-based migration, which appears only in three-dimensional matrices under certain conditions. The cell creates a protrusion through which the nucleus slips, dividing the cell into two parts (front and rear) with different hydrostatic pressures. In this work, we elucidate the mechanical conditions that favour this type of migration.One of the hypotheses about this type of migration is that it depends on the mechanical properties of the extracellular matrix. That is, lobopodia-based migration is dependent on whether the extracellular matrix is linearly elastic or non-linearly elastic.To determine whether the mechanical properties of the extracellular matrix are crucial in the choice of cell migration mode and which mechanotransduction mechanism the cell might use, we develop a finite element model. From our simulations, we identify two different possible mechanotransduction mechanisms that could regulate the cell to switch from a lobopodial to a lamellipodial migration mode. The first relies on a differential pressure increase inside the cytoplasm while the cell contracts, and the second relies on a change in the fluid flow direction in non-linearly elastic extracellular matrices but not in linearly elastic matrices. The biphasic nature of the cell has been determined to mediate this mechanism and the different behaviours of cells in linearly elastic and non-linearly elastic matrices.

Primary Human Osteoblasts Cultured in a 3D Microenvironment Create a Unique Representative Model of Their Differentiation Into Osteocytes

Microengineered systems provide an in vitro strategy to explore the variability of individual patient response to tissue engineering products, since they prefer the use of primary cell sources representing the phenotype variability. Traditional in vitro systems already showed that primary human osteoblasts embedded in a 3D fibrous collagen matrix differentiate into osteocytes under specific conditions. Here, we hypothesized that translating this environment to the organ-on-a-chip scale creates a minimal functional unit to recapitulate osteoblast maturation toward osteocytes and matrix mineralization. Primary human osteoblasts were seeded in a type I collagen hydrogel, to establish the role of lower (2.5 × 10⁵ cells/ml) and higher (1 × 10⁶ cells/ml) cell density on their differentiation into osteocytes. A custom semi-automatic image analysis software was used to extract quantitative data on cellular morphology from brightfield images. The results are showing that cells cultured at a high density increase dendrite length over time, stop proliferating, exhibit dendritic morphology, upregulate alkaline phosphatase (ALP) activity, and express the osteocyte marker dental matrix protein 1 (DMP1). On the contrary, cells cultured at lower density proliferate over time, do not upregulate ALP and express the osteoblast marker bone sialoprotein 2 (BSP2) at all timepoints. Our work reveals that microengineered systems create unique conditions to capture the major aspects of osteoblast differentiation into osteocytes with a limited number of cells. We propose that the microengineered approach is a functional strategy to create a patient-specific bone tissue model and investigate the individual osteogenic potential of the patient bone cells.

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.

Image-based Characterization of 3D Collagen Networks and the Effect of Embedded Cells

Collagen microstructure is closely related to the mechanical properties of tissues and affects cell migration through the extracellular matrix. To study these structures, three-dimensional (3D) in vitro collagen-based gels are often used, attempting to mimic the natural environment of cells. Some key parameters of the microstructure of these gels are fiber orientation, fiber length, or pore size, which define the mechanical properties of the network and therefore condition cell behavior. In the present study, an automated tool to reconstruct 3D collagen networks is used to extract the aforementioned parameters of gels of different collagen concentration and determine how their microstructure is affected by the presence of cells. Two different experiments are presented to test the functionality of the method: first, collagen gels are embedded within a microfluidic device and collagen fibers are imaged by using confocal fluorescence microscopy; second, collagen gels are directly polymerized in a cell culture dish and collagen fibers are imaged by confocal reflection microscopy. Finally, we investigate and compare the collagen microstructure far from and in the vicinities of MDA-MB 23 cells, finding that cell activity during migration was able to strongly modify the orientation of the collagen fibers and the porosity-related values.

Nonlinear elasticity of the lung extracellular microenvironment is regulated by macroscale tissue strain

The extracellular matrix (ECM) of the lung provides physical support and key mechanical signals to pulmonary cells. Although lung ECM is continuously subjected to different stretch levels, detailed mechanics of the ECM at the scale of the cell is poorly understood. Here, we developed a new polydimethylsiloxane (PDMS) chip to probe nonlinear mechanics of tissue samples with atomic force microscopy (AFM). Using this chip, we performed AFM measurements in decellularized rat lung slices at controlled stretch levels. The AFM revealed highly nonlinear ECM elasticity with the microscale stiffness increasing with tissue strain. To correlate micro- and macroscale ECM mechanics, we also assessed macromechanics of decellularized rat lung strips under uniaxial tensile testing. The lung strips exhibited exponential macromechanical behavior but with stiffness values one order of magnitude lower than at the microscale. To interpret the relationship between micro- and macromechanical properties, we carried out a finite element (FE) analysis which revealed that the stiffness of the alveolar cell microenvironment is regulated by the global strain of the lung scaffold. The FE modeling also indicates that the scale dependence of stiffness is mainly due to the porous architecture of the lung parenchyma. We conclude that changes in tissue strain during breathing result in marked changes in the ECM stiffness sensed by alveolar cells providing tissue-specific mechanical signals to the cells. STATEMENT OF SIGNIFICANCE: The micromechanical properties of the extracellular matrix (ECM) are a major determinant of cell behavior. The ECM is exposed to mechanical stretching in the lung and other organs during physiological function. Therefore, a thorough knowledge of the nonlinear micromechanical properties of the ECM at the length scale that cells probe is required to advance our understanding of cell-matrix interplay. We designed a novel PDMS chip to perform atomic force microscopy measurements of ECM micromechanics on decellularized rat lung slices at different macroscopic strain levels. For the first time, our results reveal that the microscale stiffness of lung ECM markedly increases with macroscopic tissue strain. Therefore, changes in tissue strain during breathing result in variations in ECM stiffness providing tissue-specific mechanical signals to lung cells.

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.

Matrix architecture plays a pivotal role in 3D osteoblast migration: The effect of interstitial fluid flow

Osteoblast migration is a crucial process in bone regeneration, which is strongly regulated by interstitial fluid flow. However, the exact role that such flow exerts on osteoblast migration is still unclear. To deepen the understanding of this phenomenon, we cultured human osteoblasts on 3D microfluidic devices under different fluid flow regimes. Our results show that a slow fluid flow rate by itself is not able to alter the 3D migratory patterns of osteoblasts in collagen-based gels but that at higher fluid flow rates (increased flow velocity) may indirectly influence cell movement by altering the collagen microstructure. In fact, we observed that high fluid flow rates (1 µl/min) are able to alter the collagen matrix architecture and to indirectly modulate the migration pattern. However, when these collagen scaffolds were crosslinked with a chemical crosslinker, specifically, transglutaminase II, we did not find significant alterations in the scaffold architecture or in osteoblast movement. Therefore, our data suggest that high interstitial fluid flow rates can regulate osteoblast migration by means of modifying the orientation of collagen fibers. Together, these results highlight the crucial role of the matrix architecture in 3D osteoblast migration. In addition, we show that interstitial fluid flow in conjunction with the matrix architecture regulates the osteoblast morphology in 3D.

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.

Force loading explains spatial sensing of ligands by cells

Cells can sense the density and distribution of extracellular matrix (ECM) molecules by means of individual integrin proteins and larger, integrin-containing adhesion complexes within the cell membrane. This spatial sensing drives cellular activity in a variety of normal and pathological contexts. Previous studies of cells on rigid glass surfaces have shown that spatial sensing of ECM ligands takes place at the nanometre scale, with integrin clustering and subsequent formation of focal adhesions impaired when single integrin-ligand bonds are separated by more than a few tens of nanometres. It has thus been suggested that a crosslinking 'adaptor' protein of this size might connect integrins to the actin cytoskeleton, acting as a molecular ruler that senses ligand spacing directly. Here, we develop gels whose rigidity and nanometre-scale distribution of ECM ligands can be controlled and altered. We find that increasing the spacing between ligands promotes the growth of focal adhesions on low-rigidity substrates, but leads to adhesion collapse on more-rigid substrates. Furthermore, disordering the ligand distribution drastically increases adhesion growth, but reduces the rigidity threshold for adhesion collapse. The growth and collapse of focal adhesions are mirrored by, respectively, the nuclear or cytosolic localization of the transcriptional regulator protein YAP. We explain these findings not through direct sensing of ligand spacing, but by using an expanded computational molecular-clutch model, in which individual integrin-ECM bonds-the molecular clutches-respond to force loading by recruiting extra integrins, up to a maximum value. This generates more clutches, redistributing the overall force among them, and reducing the force loading per clutch. At high rigidity and high ligand spacing, maximum recruitment is reached, preventing further force redistribution and leading to adhesion collapse. Measurements of cellular traction forces and actin flow speeds support our model. Our results provide a general framework for how cells sense spatial and physical information at the nanoscale, precisely tuning the range of conditions at which they form adhesions and activate transcriptional regulation.

A hybrid computational model to explore the topological characteristics of epithelial tissues

Epithelial tissues show a particular topology where cells resemble a polygon-like shape, but some biological processes can alter this tissue topology. During cell proliferation, mitotic cell dilation deforms the tissue and modifies the tissue topology. Additionally, cells are reorganized in the epithelial layer and these rearrangements also alter the polygon distribution. We present here a computer-based hybrid framework focused on the simulation of epithelial layer dynamics that combines discrete and continuum numerical models. In this framework, we consider topological and mechanical aspects of the epithelial tissue. Individual cells in the tissue are simulated by an off-lattice agent-based model, which keeps the information of each cell. In addition, we model the cell-cell interaction forces and the cell cycle. Otherwise, we simulate the passive mechanical behaviour of the cell monolayer using a material that approximates the mechanical properties of the cell. This continuum approach is solved by the finite element method, which uses a dynamic mesh generated by the triangulation of cell polygons. Forces generated by cell-cell interaction in the agent-based model are also applied on the finite element mesh. Cell movement in the agent-based model is driven by the displacements obtained from the deformed finite element mesh of the continuum mechanical approach. We successfully compare the results of our simulations with some experiments about the topology of proliferating epithelial tissues in Drosophila. Our framework is able to model the emergent behaviour of the cell monolayer that is due to local cell-cell interactions, which have a direct influence on the dynamics of the epithelial tissue.

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.

Image analysis for the quantitative comparison of stress fibers and focal adhesions

Actin stress fibers (SFs) detect and transmit forces to the extracellular matrix through focal adhesions (FAs), and molecules in this pathway determine cellular behavior. Here, we designed two different computational tools to quantify actin SFs and the distribution of actin cytoskeletal proteins within a normalized cellular morphology. Moreover, a systematic cell response comparison between the control cells and those with impaired actin cytoskeleton polymerization was performed to demonstrate the reliability of the tools. Indeed, a variety of proteins that were present within the string beginning at the focal adhesions (vinculin) up to the actin SFs contraction (non-muscle myosin II (NMMII)) were analyzed. Finally, the software used allows for the quantification of the SFs based on the relative positions of FAs. Therefore, it provides a better insight into the cell mechanics and broadens the knowledge of the nature of SFs.

A cell-regulatory mechanism involving feedback between contraction and tissue formation guides wound healing progression

Wound healing is a process driven by cells. The ability of cells to sense mechanical stimuli from the extracellular matrix that surrounds them is used to regulate the forces that cells exert on the tissue. Stresses exerted by cells play a central role in wound contraction and have been broadly modelled. Traditionally, these stresses are assumed to be dependent on variables such as the extracellular matrix and cell or collagen densities. However, we postulate that cells are able to regulate the healing process through a mechanosensing mechanism regulated by the contraction that they exert. We propose that cells adjust the contraction level to determine the tissue functions regulating all main activities, such as proliferation, differentiation and matrix production. Hence, a closed-regulatory feedback loop is proposed between contraction and tissue formation. The model consists of a system of partial differential equations that simulates the evolution of fibroblasts, myofibroblasts, collagen and a generic growth factor, as well as the deformation of the extracellular matrix. This model is able to predict the wound healing outcome without requiring the addition of phenomenological laws to describe the time-dependent contraction evolution. We have reproduced two in vivo experiments to evaluate the predictive capacity of the model, and we conclude that there is feedback between the level of cell contraction and the tissue regenerated in the wound.

A time-dependent phenomenological model for cell mechano-sensing

Adherent cells normally apply forces as a generic means of sensing and responding to the mechanical nature of their surrounding environment. How these forces vary as a function of the extracellular rigidity is critical to understanding the regulatory functions that drive important phenomena such as wound healing or muscle contraction. In recognition of this fact, experiments have been conducted to understand cell rigidity-sensing properties under known conditions of the extracellular environment, opening new possibilities for modeling this active behavior. In this work, we provide a physics-based constitutive model taking into account the main structural components of the cell to reproduce its most significant contractile properties such as the traction forces exerted as a function of time and the extracellular stiffness. This model shows how the interplay between the time-dependent response of the acto-myosin contractile system and the elastic response of the cell components determines the mechano-sensing behavior of single cells.

Dynamic mechanisms of cell rigidity sensing: insights from a computational model of actomyosin networks

Cells modulate themselves in response to the surrounding environment like substrate elasticity, exhibiting structural reorganization driven by the contractility of cytoskeleton. The cytoskeleton is the scaffolding structure of eukaryotic cells, playing a central role in many mechanical and biological functions. It is composed of a network of actins, actin cross-linking proteins (ACPs), and molecular motors. The motors generate contractile forces by sliding couples of actin filaments in a polar fashion, and the contractile response of the cytoskeleton network is known to be modulated also by external stimuli, such as substrate stiffness. This implies an important role of actomyosin contractility in the cell mechano-sensing. However, how cells sense matrix stiffness via the contractility remains an open question. Here, we present a 3-D Brownian dynamics computational model of a cross-linked actin network including the dynamics of molecular motors and ACPs. The mechano-sensing properties of this active network are investigated by evaluating contraction and stress in response to different substrate stiffness. Results demonstrate two mechanisms that act to limit internal stress: (i) In stiff substrates, motors walk until they exert their maximum force, leading to a plateau stress that is independent of substrate stiffness, whereas (ii) in soft substrates, motors walk until they become blocked by other motors or ACPs, leading to submaximal stress levels. Therefore, this study provides new insights into the role of molecular motors in the contraction and rigidity sensing of cells.

A mathematical model for cell differentiation, as an evolutionary and regulated process

We introduce an approach which allows one to introduce the concept of cell plasticity into models for tissue regeneration. In contrast to most of the recent models for tissue regeneration, cell differentiation is considered a gradual process, which evolves in time and which is regulated by an arbitrary number of parameters. In the current approach, cell differentiation is modelled by means of a differentiation state variable. Cells are assumed to differentiate into an arbitrary number of cell types. The differentiation path is considered as reversible, unless differentiation has fully completed. Cell differentiation is incorporated into the partial differential equations (PDEs), which model the tissue regeneration process, by means of an advection term in the differentiation state space. This allows one to consider the differentiation path of cells, which is not possible if a reaction-like term is used for differentiation. The boundary conditions, which should be specified for the general PDEs, are derived from the flux of the fully non-differentiated cells and from the irreversibility of the fully completed differentiation process. An application of the proposed model for peri-implant osseointegration is considered. Numerical results are compared with experimental data. Potential lines of further development of the present approach are proposed.

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.