A Mathematical Modelling Study of Chemotactic Dynamics in Cell Cultures: The Impact of Spatio-temporal Heterogeneity.

As motivated by studies of cellular motility driven by spatiotemporal chemotactic gradients in microdevices, we develop a framework for constructing approximate analytical solutions for the location, speed and cellular densities for cell chemotaxis waves in heterogeneous fields of chemoattractant from the underlying partial differential equation models. In particular, such chemotactic waves are not in general translationally invariant travelling waves, but possess a spatial variation that evolves in time, and may even oscillate back and forth in time, according to the details of the chemotactic gradients. The analytical framework exploits the observation that unbiased cellular diffusive flux is typically small compared to chemotactic fluxes and is first developed and validated for a range of exemplar scenarios. The framework is subsequently applied to more complex models considering the chemoattractant dynamics under more general settings, potentially including those of relevance for representing pathophysiology scenarios in microdevice studies. In particular, even though solutions cannot be constructed in all cases, a wide variety of scenarios can be considered analytically, firstly providing global insight into the important mechanisms and features of cell motility in complex spatiotemporal fields of chemoattractant. Such analytical solutions also provide a means of rapid evaluation of model predictions, with the prospect of application in computationally demanding investigations relating theoretical models and experimental observation, such as Bayesian parameter estimation.

Computational modeling of multiple myeloma interactions with resident bone marrow cells.

The interaction of multiple myeloma with bone marrow resident cells plays a key role in tumor progression and the development of drug resistance. The tumor cell response involves contact-mediated and paracrine interactions. The heterogeneity of myeloma cells and bone marrow cells makes it difficult to reproduce this environment in in-vitro experiments. The use of in-silico established tools can help to understand these complex problems. In this article, we present a computational model based on the finite element method to define the interactions of multiple myeloma cells with resident bone marrow cells. This model includes cell migration, which is controlled by stress-strain equilibrium, and cell processes such as proliferation, differentiation, and apoptosis. A series of computational experiments were performed to validate the proposed model. Cell proliferation by the growth factor IGF-1 is studied for different concentrations ranging from 0-10 ng/mL. Cell motility is studied for different concentrations of VEGF and fibronectin in the range of 0-100 ng/mL. Finally, cells were simulated under a combination of IGF-1 and VEGF stimuli whose concentrations are considered to be dependent on the cancer-associated fibroblasts in the extracellular matrix. Results show a good agreement with previous in-vitro results. Multiple myeloma growth and migration are shown to correlate linearly to the IGF-1 stimuli. These stimuli are coupled with the mechanical environment, which also improves cell growth. Moreover, cell migration depends on the fiber and VEGF concentration in the extracellular matrix. Finally, our computational model shows myeloma cells trigger mesenchymal stem cells to differentiate into cancer-associated fibroblasts, in a dose-dependent manner.

Understanding glioblastoma invasion using physically-guided neural networks with internal variables.

Microfluidic capacities for both recreating and monitoring cell cultures have opened the door to the use of Data Science and Machine Learning tools for understanding and simulating tumor evolution under controlled conditions. In this work, we show how these techniques could be applied to study Glioblastoma, the deadliest and most frequent primary brain tumor. In particular, we study Glioblastoma invasion using the recent concept of Physically-Guided Neural Networks with Internal Variables (PGNNIV), able to combine data obtained from microfluidic devices and some physical knowledge governing the tumor evolution. The physics is introduced in the network structure by means of a nonlinear advection-diffusion-reaction partial differential equation that models the Glioblastoma evolution. On the other hand, multilayer perceptrons combined with a nodal deconvolution technique are used for learning the go or grow metabolic behavior which characterises the Glioblastoma invasion. The PGNNIV is here trained using synthetic data obtained from in silico tests created under different oxygenation conditions, using a previously validated model. The unravelling capacity of PGNNIV enables discovering complex metabolic processes in a non-parametric way, thus giving explanatory capacity to the networks, and, as a consequence, surpassing the predictive power of any parametric approach and for any kind of stimulus. Besides, the possibility of working, for a particular tumor, with different boundary and initial conditions, permits the use of PGNNIV for defining virtual therapies and for drug design, thus making the first steps towards in silico personalised medicine.

Predicting cell behaviour parameters from glioblastoma on a chip images. A deep learning approach.

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 ρ > 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.

Enhanced Piezoelectric Fibered Extracellular Matrix to Promote Cardiomyocyte Maturation and Tissue Formation: A 3D Computational Model.

Mechanical and electrical stimuli play a key role in tissue formation, guiding cell processes such as cell migration, differentiation, maturation, and apoptosis. Monitoring and controlling these stimuli on in vitro experiments is not straightforward due to the coupling of these different stimuli. In addition, active and reciprocal cell-cell and cell-extracellular matrix interactions are essential to be considered during formation of complex tissue such as myocardial tissue. In this sense, computational models can offer new perspectives and key information on the cell microenvironment. Thus, we present a new computational 3D model, based on the Finite Element Method, where a complex extracellular matrix with piezoelectric properties interacts with cardiac muscle cells during the first steps of tissue formation. This model includes collective behavior and cell processes such as cell migration, maturation, differentiation, proliferation, and apoptosis. The model has employed to study the initial stages of in vitro cardiac aggregate formation, considering cell-cell junctions, under different extracellular matrix configurations. Three different cases have been purposed to evaluate cell behavior in fibered, mechanically stimulated fibered, and mechanically stimulated piezoelectric fibered extra-cellular matrix. In this last case, the cells are guided by the coupling of mechanical and electrical stimuli. Accordingly, the obtained results show the formation of more elongated groups and enhancement in cell proliferation.

Mathematical formulation and parametric analysis of in vitro cell models in microfluidic devices: application to different stages of glioblastoma evolution.

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.

Design and experimental validation of a magnetic device for stem cell culture.

Cell culture of bone and tendon tissues requires mechanical stimulation of the cells in order to mimic their physiological state. In the present work, a device has been conceived and developed to generate a controlled magnetic field with a homogeneous gradient in the working space. The design requirement was to maximize the magnetic flux gradient, assuring a minimum magnetizing value in a 15 mm × 15 mm working area, which highly increases the normal operating range of this sort of devices. The objective is to use the machine for two types of biological tests: magnetic irradiation of biological samples and force generation on paramagnetic particles embedded in scaffolds for cell culture. The device has been manufactured and experimentally validated by evaluating the force exerted on magnetic particles in a viscous fluid. Apart from the magnetic validation, the device has been tested for irradiating biological samples. In this case, viability of human dental pulp stem cells has been studied in vitro after electromagnetic field exposition using the designed device. After three days of irradiation treatment, cellular microtissues showed a 59% increase in the viable cell number. Irradiated cells did not show morphological differences when compared with control cells.