Mathematical modelling of the restenosis process after stent implantation

The stenting procedure has evolved to become a highly successful technique for the clinical treatment of advanced atherosclerotic lesions in arteries. However, the development of in-stent restenosis remains a key problem. In this work, a novel two-dimensional continuum mathematical model is proposed to describe the complex restenosis process following the insertion of a stent into a coronary artery. The biological species considered to play a key role in restenosis development are growth factors, matrix metalloproteinases, extracellular matrix, smooth muscle cells and endothelial cells. Diffusion–reaction equations are used for modelling the mass balance between species in the arterial wall. Experimental data from the literature have been used in order to estimate model parameters. Moreover, a sensitivity analysis has been performed to study the impact of varying the parameters of the model on the evolution of the biological species. The results demonstrate that this computational model qualitatively captures the key characteristics of the lesion growth and the healing process within an artery subjected to non-physiological mechanical forces. Our results suggest that the arterial wall response is driven by the damage area, smooth muscle cell proliferation and the collagen turnover among other factors

The application of agent-based modeling and fuzzy-logic controllers for the study of magnesium biomaterials

Agent-based modeling (ABM) is a powerful approach for studying complex systems and their underlying properties by explicitly modeling the actions and interactions of individual agents. Over the past decade, numerous software programs have been developed to address the needs of the ABM community. However, these solutions often suffer from limitations in design, a lack of comprehensive documentation, or poor performance. As the first objective of this thesis, we introduce CppyABM-a general-purpose software for ABM that provides simulation tools in both Python and C++. CppyABM also enables ABM development using a combination of C++ and Python, taking advantage of the computational performance of C++ and the data analysis and visualization tools of Python. We demonstrate the capabilities of CppyABM through its application to various problems in ecology, virology, and computational biology. As the second objective of this thesis, we use ABM and fuzzy logic controllers (FLCs) to numerically study the effects of magnesium (Mg2+) ions on osteogenesis. Mg-based materials have emerged as the next generation of biomaterials that degrade in the body after implantation and eliminate the need for secondary surgery. We develop two computer models using ABM and FLC and calibrate them based on cell culture experiments. The models were able to capture the regulatory effects of Mg2+ ions and other important factors such as inflammatory cytokines on mesenchymal stem cells (MSC) activities. The models were also able to shed light on the fundamental differences in the cells cultured in different experiments such as proliferation capacity and sensitivity to environmental factors

Modeling the extracellular matrix in cell migration and morphogenesis:a guide for the curious biologist

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies

Mathematical models for immunology:current state of the art and future research directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years

Numerical modelling of additive manufacturing process for stainless steel tension testing samples

Nowadays additive manufacturing (AM) technologies including 3D printing grow rapidly and they are expected to replace conventional subtractive manufacturing technologies to some extents. During a selective laser melting (SLM) process as one of popular AM technologies for metals, large amount of heats is required to melt metal powders, and this leads to distortions and/or shrinkages of additively manufactured parts. It is useful to predict the 3D printed parts to control unwanted distortions and shrinkages before their 3D printing. This study develops a two-phase numerical modelling and simulation process of AM process for 17-4PH stainless steel and it considers the importance of post-processing and the need for calibration to achieve a high-quality printing at the end. By using this proposed AM modelling and simulation process, optimal process parameters, material properties, and topology can be obtained to ensure a part 3D printed successfully

Cell Migration within 3D Microenvironments: an Integrative Perspective from the Membrane to the Nucleus

La migración celular es fundamental para la vida y el desarrollo. Desafortunadamente, la movilidad celular también está asociada con algunas de las principales causas de morbilidad y mortalidad, incluidos los trastornos inmunitarios, esqueléticos y cardiovasculares, así como la metástasis del cáncer. Las células dependen en su capacidad para percibir y responder a estímulos externos en muchos procesos fisiológicos y patológicos (p. ej., desarrollo embrionario, angiogénesis, reparación de tejidos y progresión tumoral). El objetivo global de esta tesis doctoral fue investigar la respuesta migratoria de células individuales a señales bioquímicas y biofísicas. En particular, el enfoque de esta investigación se centró en los mecanismos que permiten a las células percibir e internalizar señales bioquímicas y biofísicas y la influencia de estos estímulos en la respuesta migratoria de las células individuales.El primer estudio tuvo como objetivo establecer una metodología para facilitar la integración de estudios teóricos con datos experimentales. Al minimizar la intervención del usuario, el sistema propuesto basado en técnicas de optimización Bayesiana gestionó de manera eficiente la calibración de los modelos in silico, que de otro modo sería tediosa y propensa a errores. Posteriormente, se construyó un modelo in silico para investigar cómo los estímulos bioquímicos y biofísicos influyen en el movimiento celular en tres dimensiones. Este modelo computacional integró algunos de los principales actores que permiten a las células percibir y responder a señales externas, que pueden actuar a diferentes escalas e interactuar entre sí. Los resultados mostraron, por un lado, que las células cambian su comportamiento migratorio en función de la pendiente de los gradientes químicos y la concentración absoluta de factores químicos (por ejemplo, factores de crecimiento) a su alrededor. Por otro lado, estos resultados revelaron que la respuesta migratoria de las células a la rigidez y densidad de la matriz depende de su fenotipo. En general, la tesis destaca la dependencia de la migración celular tridimensional al fenotipo de las células (es decir, el tamaño de su núcleo, la deformabilidad del mismo) y las propiedades del microambiente circundante (por ejemplo, el perfil químico, la rigidez de la matriz, el confinamiento).Cell migration is fundamental for life and development. Unfortunately, cell motility is also associated with some of the leading causes of morbidity and mortality, including immune, skeletal, and cardiovascular disorders as well as cancer metastasis. Cells rely on their ability to perceive and respond to external stimuli in many physiological and pathological processes (e.g., embryonic development, angiogenesis, tissue repair, and tumor progression). The global objective of this doctoral thesis was to investigate the migratory response of individual cells to biochemical and biophysical cues. In particular, the focus of this research was on the mechanisms enabling cells to perceive and internalize biochemical and biophysical cues and the influence of these stimuli on the migratory response of individual cells. The first study aimed at establishing a methodology to facilitate the integration of theoretical studies with experimental data. By minimizing user intervention, the proposed framework based on Bayesian optimization techniques efficiently handled the otherwise tedious and error-prone calibration of in silico models. Afterward, an in silico model was built to investigate how biochemical and biophysical stimuli influence three-dimensional cell motion. This computational model integrated some of the main actors enabling cells to probe and respond to external cues, which may act at different scales and interact with each other. The results showed, on the one hand, that cells change their migratory behavior based on the slope of chemical gradients and the absolute concentration of chemical factors (e.g., growth factors) around them. On the other hand, these results revealed that cells’ migratory response to matrix stiffness and density depends on their phenotype. Overall, this thesis highlights the dependence of three-dimensional cell migration on both cells’ phenotype (i.e., nucleus size, deformability) and the properties of the surrounding microenvironment (e.g., chemical profile, matrix rigidity, confinement).<br /

Nonlocal Models in Biology and Life Sciences: Sources, Developments, and Applications

Nonlocality is important in realistic mathematical models of physical and biological systems at small-length scales. It characterizes the properties of two individuals located in different locations. This review illustrates different nonlocal mathematical models applied to biology and life sciences. The major focus has been given to sources, developments, and applications of such models. Among other things, a systematic discussion has been provided for the conditions of pattern formations in biological systems of population dynamics. Special attention has also been given to nonlocal interactions on networks, network coupling and integration, including models for brain dynamics that provide us with an important tool to better understand neurodegenerative diseases. In addition, we have discussed nonlocal modelling approaches for cancer stem cells and tumor cells that are widely applied in the cell migration processes, growth, and avascular tumors in any organ. Furthermore, the discussed nonlocal continuum models can go sufficiently smaller scales applied to nanotechnology to build biosensors to sense biomaterial and its concentration. Piezoelectric and other smart materials are among them, and these devices are becoming increasingly important in the digital and physical world that is intrinsically interconnected with biological systems. Additionally, we have reviewed a nonlocal theory of peridynamics, which deals with continuous and discrete media and applies to model the relationship between fracture and healing in cortical bone, tissue growth and shrinkage, and other areas increasingly important in biomedical and bioengineering applications. Finally, we provided a comprehensive summary of emerging trends and highlighted future directions in this rapidly expanding field.Comment: 71 page

Modeling The Spatiotemporal Dynamics Of Cells In The Lung

Multiple research problems related to the lung involve a need to take into account the spatiotemporal dynamics of the underlying component cells. Two such problems involve better understanding the nature of the allergic inflammatory response to explore what might cause chronic inflammatory diseases such as asthma, and determining the rules underlying stem cells used to engraft decellularized lung scaffolds in the hopes of growing new lungs for transplantation. For both problems, we model the systems computationally using agent-based modeling, a tool that enables us to capture these spatiotemporal dynamics by modeling any biological system as a collection of agents (cells) interacting with each other and within their environment. This allows to test the most important pieces of biological systems together rather than in isolation, and thus rapidly derive biological insights from resulting complex behavior that could not have been predicted beforehand, which we can then use to guide wet lab experimentation. For the allergic response, we hypothesized that stimulation of the allergic response with antigen results in a response with formal similarity to a muscle twitch or an action potential, with an inflammatory phase followed by a resolution phase that returns the system to baseline. We prepared an agent-based model (ABM) of the allergic inflammatory response and determined that antigen stimulation indeed results in a twitch-like response. To determine what might cause chronic inflammatory diseases where the twitch presumably cannot resolve back to baseline, we then tested multiple potential defects to the model. We observed that while most of these potential changes lessen the magnitude of the response but do not affect its overall behavior, extending the lifespan of activated pro-inflammatory cells such as neutrophils and eosinophil results in a prolonged inflammatory response that does not resolve to baseline. Finally, we performed a series of experiments involving continual antigen stimulation in mice, determining that there is evidence in the cytokine, cellular and physiologic (mechanical) response consistent with our hypothesis of a finite twitch and an associated refractory period. For stem cells, we made a 3-D ABM of a decellularized scaffold section seeded with a generic stem cell type. We then programmed in different sets of rules that could conceivably underlie the cell\u27s behavior, and observed the change in engraftment patterns in the scaffold over selected timepoints. We compared the change in those patterns against the change in experimental scaffold images seeded with C10 epithelial cells and mesenchymal stem cells, two cell types whose behaviors are not well understood, in order to determine which rulesets more closely match each cell type. Our model indicates that C10s are more likely to survive on regions of higher substrate while MSCs are more likely to proliferate on regions of higher substrate