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.

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.

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.

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.

Traction Force Microscopy in 3-Dimensional Extracellular Matrix Networks.

Cell migration through a three-dimensional (3-D) matrix depends strongly on the ability of cells to generate traction forces. To overcome the steric hindrance of the matrix, cells need to generate sufficiently high traction forces but also need to distribute these forces spatially in a migration-promoting way. This unit describes a protocol to measure spatial maps of cell traction forces in 3-D biopolymer networks such as collagen, fibrin, or Matrigel. Traction forces are computed from the relationship between measured force-induced matrix deformations surrounding the cell and the known mechanical properties of the matrix. The method does not rely on knowledge of the cell surface coordinates and takes nonlinear mechanical properties of the matrix into account. © 2017 by John Wiley & Sons, Inc.

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.

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.

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.

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.

Finite element simulation for the mechanical characterization of soft biological materials by atomic force microscopy.

The characterization of the mechanical properties of soft materials has been traditionally performed through uniaxial tensile tests. Nevertheless, this method cannot be applied to certain extremely soft materials, such as biological tissues or cells that cannot be properly subjected to these tests. Alternative non-destructive tests have been designed in recent years to determine the mechanical properties of soft biological tissues. One of these techniques is based on the use of atomic force microscopy (AFM) to perform nanoindentation tests. In this work, we investigated the mechanical response of soft biological materials to nanoindentation with spherical indenters using finite element simulations. We studied the responses of three different material constitutive laws (elastic, isotropic hyperelastic and anisotropic hyperelastic) under the same process and analyzed the differences thereof. Whereas linear elastic and isotropic hyperelastic materials can be studied using an axisymmetric simplification, anisotropic hyperelastic materials require three-dimensional analyses. Moreover, we established the limiting sample size required to determine the mechanical properties of soft materials while avoiding boundary effects. Finally, we compared the results obtained by simulation with an estimate obtained from Hertz theory. Hertz theory does not distinguish between the different material constitutive laws, and thus, we proposed corrections to improve the quantitative measurement of specific material properties by nanoindentation experiments.

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.

Challenges in the Modeling of Wound Healing Mechanisms in Soft Biological Tissues.

Numerical models have become one of the most powerful tools in biomechanics and mechanobiology allowing highly detailed simulations. One of the fields in which they have broadly evolved during the last years is in soft tissue modeling. Particularly, wound healing in the skin is one of the processes that has been approached by computational models due to the difficulty of performing experimental investigations. During the last decades wound healing simulations have evolved from numerical models which considered only a few number of variables and simple geometries to more complex approximations that take into account a higher number of factors and reproduce more realistic geometries. Moreover, thanks to improved experimental observations, a larger number of processes, such as cellular stress generation or vascular growth, that take place during wound healing have been identified and modeled. This work presents a review of the most relevant wound healing approximations, together with an identification of the most relevant criteria that can be used to classify them. In addition, and looking towards the actual state of the art in the field, some future directions, challenges and improvements are analyzed for future developments.

Nonlinear finite element simulations of injuries with free boundaries: application to surgical wounds.

Wound healing is a process driven by biochemical and mechanical variables in which a new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work, we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Because of the regularity of this morphology, we approximate the evolution of the wound through its cross section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem; while allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction, we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the nonlinear problem, we use the finite element method (FEM) and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds.