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.

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.

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.

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.

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.

Numerical modelling of the angiogenesis process in wound contraction.

Angiogenesis consists of the growth of new blood vessels from the pre-existing vasculature. This phenomenon takes place in several biological processes, including wound healing. In this work, we present a mathematical model of angiogenesis applied to skin wound healing. The developed model includes biological (capillaries and fibroblasts), chemical (oxygen and angiogenic growth factor concentrations) and mechanical factors (cell traction forces and extracellular matrix deformation) that influence the evolution of the healing process. A novelty from previous works, apart from the coupling of angiogenesis and wound contraction, is the more realistic modelling of skin as a hyperelastic material. Large deformations are addressed using an updated Lagrangian approach. The coupled non-linear model is solved with the finite element method, and the process is studied over two wound geometries (circular and elliptical) of the same area. The results indicate that the elliptical wound vascularizes two days earlier than the circular wound but that they experience a similar contraction level, reducing its size by 25 %.

Numerical estimation of 3D mechanical forces exerted by cells on non-linear materials.

The exchange of physical forces in both cell-cell and cell-matrix interactions play a significant role in a variety of physiological and pathological processes, such as cell migration, cancer metastasis, inflammation and wound healing. Therefore, great interest exists in accurately quantifying the forces that cells exert on their substrate during migration. Traction Force Microscopy (TFM) is the most widely used method for measuring cell traction forces. Several mathematical techniques have been developed to estimate forces from TFM experiments. However, certain simplifications are commonly assumed, such as linear elasticity of the materials and/or free geometries, which in some cases may lead to inaccurate results. Here, cellular forces are numerically estimated by solving a minimization problem that combines multiple non-linear FEM solutions. Our simulations, free from constraints on the geometrical and the mechanical conditions, show that forces are predicted with higher accuracy than when using the standard approaches.

A lattice-based approach to model distraction osteogenesis.

Distraction osteogenesis is a well-known technique in which new bone tissue is created when a distraction displacement is applied through an external frame. This orthopedic process is nowadays focus of intense research, both experimentally and numerically, as there are still many aspects not well understood. The aim of this study is to simulate bone distraction by means of a combined discrete-continuum approach based on a lattice formulation. Existing computational models simulate the main processes of distraction osteogenesis from a continuum perspective, considering as state variables the population of cells and tissue distributions. Results of the continuum and lattice-based approaches are similar with respect to the global evolution of the different cells but rather different in terms of the type of ossification process. Differences in the size of the soft interzone in the gap have also been found. In addition, the discrete-continuum formulation allows including a more realistic approach of the migration/proliferation process with a discrete random walk model instead of the Fick's law used in continuum approaches. Also, blood vessel growth can be simulated explicitly in this model with the inclusion of the endothelial cells. Further study is needed to provide additional insights to understand coupled phenomena at different scales in the cell-tissue interactions. However this work provides a first preliminary step for improving multiscale models.

Biomechanical response of a mandible in a patient affected with hemifacial microsomia before and after distraction osteogenesis.

Distraction osteogenesis (DO) has gained wide acceptance in the craniofacial surgery due to the huge possibilities it offers. However this orthopaedic field is under continuous development as it still presents uncertainties. In this context, numerical modelling/analysis may help us to design patient specific treatments once they have been experimentally verified. This paper presents a finite element analysis of the biomechanical behavior of a patient's mandible with hemifacial microsomia (HFM) before and after distraction. In order to check the effectiveness of the clinical protocol, the predicted biomechanical response will also be compared with that of a symmetrical healthy mandible. Strain and displacement fields, masticatory forces as well as reaction forces at the condyles are evaluated in each mandible analyzed. The results show that the present model is a useful tool to understand the normal function of the mandible and to predict changes due to alterations in the mandible geometry, such as those occurring in hemifacial microsomia.

A reaction-diffusion model for long bones growth.

Bone development is characterized by differentiation and growth of chondrocytes from the proliferation zone to the hypertrophying one. These two cellular processes are controlled by a complex signalling regulatory loop between different biochemical signals, whose production depends on the current cell density, constituting a coupled cell-chemical system. In this work, a mathematical model of the process of early bone growth is presented, extending and generalizing other earlier approaches on the same topic. A reaction-diffusion regulatory loop between two chemical factors: parathyroid hormone-related peptide (PTHrP) and Indian hedgehog (Ihh) is hypothesized, where PTHrP is activated by Ihh and inhibits Ihh production. Chondrocytes proliferation and hypertrophy are described by means of population equations being both regulated by the PTHrP and Ihh concentrations. In the initial stage of bone growth, these two cellular proceses are considered to be directionally dependent, modelling the well known column cell formation, characteristic of endochondral ossification. This coupled set of equations is solved within a finite element framework, getting an estimation of the chondrocytes spatial distribution, growth of the diaphysis and formation of the epiphysis of a long bone. The results obtained are qualitatively similar to the actual physiological ones and quantitatively close to some available experimental data. Finally, this extended approach allows finding important relations between the model parameters to get stability of the physiological process and getting additional insight on the spatial and directional distribution of cells and paracrine factors.

A mathematical model for bone tissue regeneration inside a specific type of scaffold.

Bone tissue regeneration using scaffolds is receiving an increasing interest in orthopedic surgery and tissue engineering applications. In this study, we present the geometrical characterization of a specific family of scaffolds based on a face cubic centered (FCC) arrangement of empty pores leading to analytical formulae of porosity and specific surface. The effective behavior of those scaffolds, in terms of mechanical properties and permeability, is evaluated through the asymptotic homogenization theory applied to a representative volume element identified with the unit cell FCC. Bone growth into the scaffold is estimated by means of a phenomenological model that considers a macroscopic effective stress as the mechanical stimulus that regulates bone formation. Cell migration within the scaffold is modeled as a diffusion process based on Fick's law which allows us to estimate the cell invasion into the scaffold microstructure. The proposed model considers that bone growth velocity is proportional to the concentration of cells and regulated by the mechanical stimulus. This model allows us to explore what happens within the scaffold, the surrounding bone and their interaction. The mathematical model has been numerically implemented and qualitatively compared with previous experimental results found in the literature for a scaffold implanted in the femoral condyle of a rabbit. Specifically, the model predicts around 19 and 23% of bone regeneration for non-grafted and grafted scaffolds, respectively, both with an initial porosity of 76%.

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

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

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

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

A comparative analysis of different treatments for distal femur fractures using the finite element method.

The main objective of this work is the evaluation, by means of the finite element method (FEM) of the mechanical stability and long-term microstructural modifications in bone induced to three different kinds of fractures of the distal femur by three types of implants: the Condyle Plate, the less invasive stabilization system plate (LISS) and the distal femur nail (DFN). The displacement and the stress distributions both in bone and implants and the internal bone remodelling process after fracture and fixation are obtained and analysed by computational simulation. The main conclusions of this work are that distal femoral fractures can be treated correctly with the Condyle Plate, the LISS plate and the DFN. The stresses both in LISS and DFN implant are high especially around the screws. When respect to remodelling, the LISS produces an important resorption in the fractured region, while the other two implants do not strongly modify bone tissue microstructure.