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La combinación de modelos matemáticos y dispositivos microfluídicos permite recrear procesos biológicos complejos como la evolución del glioblastoma (GBM). En este trabajo, se utiliza un enfoque multidisciplinar para evaluar las diferencias en el comportamiento tumoral en distintos sustratos, con el objetivo de estudiar su influencia en la progresión del tumor.

En este trabajo se presenta el uso y las ventajas de los modelos basados en agentes (ABMs) como herramienta para validar hipótesis biológicas y entender procesos celulares fundamentales que permitan posteriormente simular sistemas más complejos. Mediante este tipo de modelos se estudiarán algunos procesos involucrados en la evolución del glioblastoma (GBM) tales como la formación de pseudoempalizadas y del núcleo necrótico. Los resultados obtenidos se han contrastado con datos experimentales y datos previos obtenidos con modelos continuos en este grupo.

La combinación de medidas en dispositivos microfluídicos con técnicas de inteligencia artificial permite estudiar fenómenos celulares complejos difíciles de encarar con los métodos tradicionales. En este trabajo se usan redes neuronales guiadas por la física para explicar los cambios metabólicos celulares y predecir el comportamiento de cultivos de glioblastoma ante estímulos variables, dando los primeros pasos hacia la medicina in silico personalizada.

Las numerosas posibilidades que ofrece la microfluídica a nivel de obtención y monitorización de grandes cantidades de datos abren la puerta a la aplicación de técnicas de aprendizaje profundo al análisis de la evolución cultivos celulares, un campo poco explorado hasta la fecha. En este trabajo, se desarrolla una red neuronal para identificar, a partir de imágenes de cultivos celulares de glioblastoma en dispositivos microfluidicos, los parámetros que gobiernan el comportamiento de este tumor cerebral.

The broad possibilities offered by microfluidic devices in relation to massive data monitoring and acquisition open the door to the use of deep learning technologies in a very promising field: cell culture monitoring. In this work, we develop a methodology for parameter identification in cell culture from fluorescence images using Convolutional Neural Networks (CNN). We apply this methodology to the in vitro study of glioblastoma (GBM), the most common, aggressive and lethal primary brain tumour. In particular, the aim is to predict the three parameters defining the go or grow GBM behaviour, which is determinant for the tumour prognosis and response to treatment. The data used to train the network are obtained from a mathematical model, previously validated with in vitro experimental results. The resulting CNN provides remarkably accurate predictions (Pearson''s ¿ > 0.99 for all the parameters). Besides, it proves to be sound, to filter noise and to generalise. After training and validation with synthetic data, we predict the parameters corresponding to a real image of a microfluidic experiment. The obtained results show good performance of the CNN. The proposed technique may set the first steps towards patient-specific tools, able to predict in real-time the tumour evolution for each particular patient, thanks to a combined in vitro-in silico approach. © 2021 The Author(s)

Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer many times from paucity of data, while they may involve a large number of variables and parameters that interact in complex and non-stationary ways, obeying certain physical laws. Moreover, a physically-based model is not only useful for making predictions, but to gain knowledge by the interpretation of its structure, parameters, and mathematical properties. The solution to these shortcomings seems to be the seamless blending of the tremendous predictive power of the data-driven approach with the scientific consistency and interpretability of physically-based models. We use here the concept of Physically-Guided Neural Networks (PGNN) to predict the input-output relation in a physical system, while, at the same time, fulfilling the physical constraints. With this goal, the internal hidden state variables of the system are associated with a set of internal neuron layers, whose values are constrained by known physical relations, as well as any additional knowledge on the system. Furthermore, when having enough data, it is possible to infer knowledge about the internal structure of the system and, if parameterized, to predict the state parameters for a particular input-output relation. We show that this approach, besides getting physically-based predictions, accelerates the training process, reduces the amount of data required to get similar accuracy, partly filters the intrinsic noise in the experimental data and improves its extrapolation capacity. (C) 2021 ElsevierB.V. All rights reserved.

Se presenta una metodología hibrida que combina el aprendizaje de las redes neuronales y la incorporación de la física sobre ciertas capas internas de la red. La herramienta tiene poder predictivo y explicativo, mejora a las redes clásicas en velocidad, necesidad de datos, capacidad de filtrado y poder de extrapolación.

La epigenética juega un papel crucial en el desarrollo tumoral, en particular en la adquisición de resistencia. Se presenta un enfoque novedoso en la comunidad científica, utilizando un modelo matemático con variables internas, inspirado en la teoría de la plasticidad para describir este fenómeno.

In silico models and computer simulation are invaluable tools to better understand complex biological processes such as cancer evolution. However, the complexity of the biological environment, with many cell mechanisms in response to changing physical and chemical external stimuli, makes the associated mathematical models highly non-linear and multiparametric. One of the main problems of these models is the determination of the parameters’ values, which are usually fitted for specific conditions, making the conclusions drawn difficult to generalise. We analyse here an important biological problem: the evolution of hypoxia-driven migratory structures in Glioblastoma Multiforme (GBM), the most aggressive and lethal primary brain tumour. We establish a mathematical model considering the interaction of the tumour cells with oxygen concentration in what is called the go or grow paradigm. We reproduce in this work three different experiments, showing the main GBM structures (pseudopalisade and necrotic core formation), only changing the initial and boundary conditions. We prove that it is possible to obtain versatile mathematical tools which, together with a sound parametric analysis, allow to explain complex biological phenomena. We show the utility of this hybrid “biomimetic in vitro-in silico” platform to help to elucidate the mechanisms involved in cancer processes, to better understand the role of the different phenomena, to test new scientific hypotheses and to design new data-driven experiments.

The data-driven methodology with application to continuum mechanics relies upon two main pillars: (i) experimental characterization of stress–strain pairs associated to different loading states, and (ii) numerical elaboration of the elasticity equations as an optimization (searching) algorithm using compatibility and equilibrium as constraints. The purpose of this work is to implement a multiscale data-driven approach using experimental data of cortical bone tissue at different scales. First, horse cortical bone samples are biaxially loaded and the strain fields are recorded over a region of interest using a digital image correlation technique. As a result, both microscopic strain fields and macroscopic strain states are obtained by a homogenization procedure, associated to macroscopic stress loading states which are considered uniform along the sample. This experimental outcome is here referred as a multiscale dataset. Second, the proposed multiscale data-driven methodology is implemented and analyzed in an example of application. Results are presented both in the macroscopic and microscopic scales, with the latter considered just as a post-process step in the formulation. The macroscopic results show non-smooth strain and stress patterns as a consequence of the tissue heterogeneity which suggest that a preassumed linear homogeneous orthotropic model may be inaccurate for bone tissue. Microscopic results show fluctuating strain fields – as a consequence of the interaction and evolution of the microconstituents – an order of magnitude higher than the averaged macroscopic solution, which evidences the need of a multiscale approach for the mechanical analysis of cortical bone, since the driving force of many biological bone processes is local at the microstructural level. Finally, the proposed multiscale data-driven technique may also be an adequate strategy for the solution of intractable large size multiscale FE computational approaches since the solution at the microscale is obtained as a postprocessing. As a main conclusion, the proposed multiscale data-driven methodology is a useful alternative to overcome limitations in the continuum mechanical study of the bone tissue. This methodology may also be considered as a useful strategy for the analysis of additional biological or technological hierarchical multiscale materials., The authors gratefully acknowledge the support of Ministerio de Economía y Competitividad del Gobierno España, Spain through the grants DPI2014-58233-P, DPI2017-82501-P, and PGC2018-097257-B-C31; as well as Consejería de Economía y Conocimiento de la Junta de Andalucía, Spain (US-1261691, FEDER, UE).

The data-driven approach was formally introduced in the field of computational mechanics just a few years ago, but it has gained increasing interest and application as disruptive technology in many other fields of physics and engineering. Although the fundamental bases of the method have been already settled, there are still many challenges to solve, which are often inherently linked to the problem at hand. In this paper, the data-driven methodology is applied to a particular problem in tissue biomechanics, a context where this approach is particularly suitable due to the difficulty in establishing accurate and general constitutive models, due to the intrinsic intra and inter-individual variability of the microstructure and associated mechanical properties of biological tissues. The problem addressed here corresponds to the characterization and mechanical simulation of a piece of cortical bone tissue. Cortical horse bone tissue was mechanically tested using a biaxial machine. The displacement field was obtained by means of digital image correlation and then transformed into strains by approximating the displacement derivatives in the bone virtual geometric image. These results, together with the approximated stress state, assumed as uniform in the small pieces tested, were used as input in the flowchart of the data-driven methodology to solve several numerical examples, which were compared with the corresponding classical model-based fitted solution. From these results, we conclude that the datadriven methodology is a useful tool to directly simulate problems of biomechanical interest without the imposition (model-free) of complex spatial and individually-varying constitutive laws. The presented data-driven approach recovers the natural spatial variation of the solution, resulting from the complex structure of bone tissue, i.e. heterogeneity, microstructural hierarchy and multifactorial architecture, making it possible to add the intrinsic stochasticity of biological tissues into the data set and into the numerical approach.

Data-driven methods are an innovative model-free approach for engineering and sciences, still in process of maturation. The idea behind is the combination of data analytics techniques, to handle the huge amount of data derived from continuous monitoring or experimental measurements, and of the constraints imposed by universal physical laws, particular to the field in hands. A well-known problem in the former corresponds to the quality and completeness of the available data that, sometimes, are so poor that make the predictions useless. In data-driven simulation-based engineering and sciences (DDSBES), the intrinsic physical constraints may help in completing the missing data in a more precise manner, by forcing them to remain in the manifold defined by the physical laws. In this work, a suitable imputation method to complete incomplete data that preserves the data context-dependent structure is presented. This is accomplished by enforcing the data to fulfill the set of physical constraints, specific to the problem. For this purpose, a generalization of the weighted mean concept is proposed, where the distance to the admissible points (in a physical sense) is used as a weighting function to get the optimal candidate. The method is evaluated in a classical regression problem, where it is compared with other standard methods, showing better results. Then, its application is illustrated in two data-driven problems, where no filling data procedure has been yet proposed, showing good predictive capability, provided that the data are close enough to the actual system state.

Microfluidic systems have emerged as a technique with the potential to recreate biomimetic microenvironments that permit in vitro modeling of several important organ functions (organ-on-chip) as well as to analyze cellular processes. This allows designing experiments for validating scientific hypotheses and better understand complex biological processes, and determine biological parameters in an unprecedented way. The crosstalk between this new experimental capacity and mathematical models within a general framework is extensively discussed in this chapter, reviewing the formulation of cell processes, together with their interaction with the surrounding environment. Also, its particularization to a particular problem of interest such as the analysis of tumor evolution, which can be modeled in organ-on-chip devices. One of the important cases of the solid tumors is glioblastoma (GBM), the most lethal primary brain tumor. One of the characteristics in such types of tumors is the appearance of hypercellularized regions, named as pseudopalisades. These structures have been hypothesized to be produced by oxygen and nutrient depletion caused by tumor-induced blood vessel occlusion. However, despite the important instrumental role of these pseudopalisades in GBM's spread and invasion, the recreation of these in vitro has remained challenging. To analyze this problem, we designed a microdevice that comprises a central microchamber flanked by two lateral microchannels, separated by a series of projections. GBM cells were then embedded within a collagen hydrogel in the central microchamber thereby mimicking the three-dimensional structure and distribution. The lateral microchannels were used to perfuse different media or drugs, so normoxic, hypoxic, and necrotic regions may be naturally generated. In this chapter, we detail the model itself and the fitting of the model parameters. We compare the experimental and numerical results and we discuss the experimental trends and the underlying hypotheses.

Los microentornos celulares multi fenotípicos que se reproducen en dispositivos microfluídicos Organ-On-Chip son sistemas biológicos extremadamente complejos de modelar. Para diferentes poblaciones celulares, se deben considerar las interacciones químicas con nutrientes u otras señales, la disposición espacial, la rigidez y características del sustrato, la advección y difusión de fluidos y procesos celulares como la proliferación, la migración, la diferenciación y la muerte. Todos estos fenómenos están altamente acoplados, lo que da lugar en un problema no lineal muy complejo de resolver. En este trabajo se plantea un modelo matemático basado en las ecuaciones del continuo, capaz de reproducir diferentes configuraciones de experimentos llevados a cabo en el laboratorio y que, por lo tanto, serviría para predecir la evolución de poblaciones tumorales, así como la respuesta a terapias diseñadas para combatir el cáncer.

Data Science has burst into simulation-based engineering sciences with an impressive impulse. However, data are never uncertainty-free and a suitable approach is needed to face data measurement errors and their intrinsic randomness in problems with well-established physical constraints. As in previous works, this problem is here faced by hybridizing a standard mathematical modeling approach with a new data-driven solver accounting for the phenomenological part of the problem, with the aim of finding a solution point, satisfying some constraints, that minimizes a distance to a given data-set. However, unlike such works that are established in a deterministic framework, we use the Mahalanobis distance in order to incorporate statistical second order uncertainty of data in computations, i.e. variance and correlation. We develop the underlying stochastic theoretical framework and establish the fundamental mathematical and statistical properties. The performance of the resulting reliability-based data-driven procedure is evaluated in a simple but illustrative unidimensional problem as well as in a more realistic solution of a 3D structural problem with a material with intrinsically random constitutive behavior as concrete. The results show, in comparison with other data-driven solvers, better convergence, higher accuracy, clearer interpretation, and major flexibility besides the relevance of allowing uncertainty management with low computational demand.