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See detailModelling astrocytic metabolism in actual cell morphologies
Farina, Sofia UL

Doctoral thesis (2022)

The human brain is the most structurally and biochemically complex organ, and its broad spectrum of diverse functions is accompanied by high energy demand. In order to address this high energy demand ... [more ▼]

The human brain is the most structurally and biochemically complex organ, and its broad spectrum of diverse functions is accompanied by high energy demand. In order to address this high energy demand, brain cells of the central nervous system are organised in a complex and balanced ecosystem, and perturbation of brain energy metabolism is known to be associated with neurodegenerative diseases such as Alzheimer's (AD) and Parkinson's disease. Among all cells composing this ecosystem, astrocytes contribute metabolically to produce the primary energy substrate of life, $\ATP$, and lactate, which can be exported to neurons to support their metabolism. Astrocytes have a star-shaped morphology, allowing them to connect on the one side with blood vessels to uptake glucose and on the other side with neurons to provide lactate. Astrocytes may also exhibit metabolic dysfunctions and modify their morphology in response to diseases. A mechanistic understanding of the morphology-dysfunction relation is still elusive. This thesis developed and applied a mechanistic multiscale modelling approach to investigate astrocytic metabolism in physiological morphologies in healthy and diseased human subjects. The complexity of cellular systems is a significant obstacle in investigating cellular behaviour. Systems biology tackles biological unknowns by combining computational and biological investigations. In order to address the elusive connection between metabolism and morphology in astrocytes, we developed a computational model of central energy metabolism in realistic morphologies. The underlying processes are described by a reaction-diffusion system that can represent cells more realistically by considering the actual three-dimensional shape than classical ordinary differential equation models where the cells are assumed to be spatially punctual, i.e. have no spatial dimension. Thus, the computational model we developed integrates high-resolution microscopy images of astrocytes from human post-mortem brain samples and simulates glucose metabolism in different physiological astrocytic human morphologies associated with AD and healthy conditions. The first part of the thesis is dedicated to presenting a numerical approach that includes complex morphologies. We investigate the classical finite element method (FEM) and cut finite element method (\cutfem{}) for simplified metabolic models in complex geometries. Establishing our image-driven numerical method leads to the second part of this thesis, where we investigate the crucial role played by the locations of reaction sites. We demonstrate that spatial organisation and chemical diffusivity play a pivotal role in the system output. Based on these new findings, we subsequently use microscopy images of healthy and Alzheimer's diseased human astrocytes to build simulations and investigate cell metabolism. In the last part of the thesis, we consider another critical process for astrocytic functionality: calcium signalling. The energy produced in metabolism is also partially used for calcium exchange between cell compartments and mainly can drive mitochondrial activity as a main ATP generating entity. Thus, the active cross-talk between glucose metabolism and calcium signalling can significantly impact the metabolic functionality of cells and requires deeper investigation. For this purpose, we extend our established metabolic model by a calcium signalling module and investigate the coupled system in two-dimensional geometries. Overall, the investigations showed the importance of spatially organised metabolic modelling and paved the way for a new direction of image-driven-meshless modelling of metabolism. Moreover, we show that complex morphologies play a crucial role in metabolic robustness and how astrocytes' morphological changes to AD conditions lead to impaired energy metabolism. [less ▲]

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See detailA Mechanistic Multiscale Metabolic Model in Human Astrocytes
Farina, Sofia UL

Presentation (2022, June 10)

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See detailA CutFEM Method for a Mechanistic Modelling of Astrocytic Metabolism in 3D Physiological Morphologies
Farina, Sofia UL; Voorsluijs, Valerie UL; Claus, Susanne et al

Scientific Conference (2022, June 07)

Investigating neurodegenerative diseases can be done complementary through biological and computational experiments. A good computational approach describing a simplification of the reality and focusing ... [more ▼]

Investigating neurodegenerative diseases can be done complementary through biological and computational experiments. A good computational approach describing a simplification of the reality and focusing only on some features of the problem can help getting insights on the field. The question addressed in our work is the role of astrocytes in neurodegeneration. These cells have two interesting characteristics that we want to investigate in our model: first, their role as metabolic mediator between neurons and blood vessels and second, their peculiar morphology. In fact, metabolic dysfunctions and morphological changes have been noticed in astrocyte affected by neuropathology. Computationally the main difficulty arising from solving a metabolic model into cellular shape comes from the complexity of the domain. The shape of astrocytes are very ramified, with thin branches and sharp edges. As shown in our previous work \cite{Farina}, a \cutfem{} \cite{Burman} approach is a suitable tool to deal with this issue. In our latest work we use real human three-dimensional astrocyte morphologies obtained via microscopy \cite{Salamanca} as domain to solve our system. The performed simulations highlight the effect of morphological changes on the system output. Suggesting that our model can be crucial in understanding the morphological-dependency in neuropathologies and that the spatial component cannot be neglected. [less ▲]

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See detailA cut finite element method for spatially resolved energy metabolism models in complex neuro-cell morphologies with minimal remeshing
Farina, Sofia UL; Claus, Susanne; Hale, Jack UL et al

in Advanced Modeling and Simulation in Engineering Sciences (2021), 8

A thorough understanding of brain metabolism is essential to tackle neurodegenerative diseases. Astrocytes are glial cells which play an important metabolic role by supplying neurons with energy. In ... [more ▼]

A thorough understanding of brain metabolism is essential to tackle neurodegenerative diseases. Astrocytes are glial cells which play an important metabolic role by supplying neurons with energy. In addition, astrocytes provide scaffolding and homeostatic functions to neighboring neurons and contribute to the blood–brain barrier. Recent investigations indicate that the complex morphology of astrocytes impacts upon their function and in particular the efficiency with which these cells metabolize nutrients and provide neurons with energy, but a systematic understanding is still elusive. Modelling and simulation represent an effective framework to address this challenge and to deepen our understanding of brain energy metabolism. This requires solving a set of metabolic partial differential equations on complex domains and remains a challenge. In this paper, we propose, test and verify a simple numerical method to solve a simplified model of metabolic pathways in astrocytes. The method can deal with arbitrarily complex cell morphologies and enables the rapid and simple modification of the model equations by users also without a deep knowledge in the numerical methods involved. The results obtained with the new method (CutFEM) are as accurate as the finite element method (FEM) whilst CutFEM disentangles the cell morphology from its discretisation, enabling us to deal with arbitrarily complex morphologies in two and three dimensions. [less ▲]

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See detailA CutFEM Method for a spatial resolved energy metabolism model in complex cellular geometries
Farina, Sofia UL

Scientific Conference (2021, January)

Computational techniques have been widely used to tackle problems in the biological sciences. A com- promise between high quality simulations and simple but accurate models can help to understand un ... [more ▼]

Computational techniques have been widely used to tackle problems in the biological sciences. A com- promise between high quality simulations and simple but accurate models can help to understand un- known aspects of this field. In this work, we will show how the Cut Finite Element Method (CutFEM) [1] can be a powerful tool to solve a reaction diffusion PDE system that models the energy metabolism of a cell. The main difficulty to approach this problem is dealing with the morphology of the cell that can have sharp edges and evolves over time. While classical FEM requires the mesh conform to the domain boundary, CutFEM allows a non-conforming discretisation of the domain, and thus is especially suited for modeling complex and evolving cellular geometries. First, we introduce our simplified model for metabolic pathways taking place in a region small enough to consider the material property as homogeneous. The results obtained with FEM (FENICS Project [2][3]) and CutFEM suggest that the two methods are equivalent. This allows us to use CutFEM to increase the complexity of the domain, from a spherical shaped cell to an irregular astrocyte. We conclude that CutFEM is a robust method for tackling biological problems with complex geometries, opening the possibility to extend the complexity of our mathematical model including more features and to consider real cellular shapes that evolve in time in future work. [less ▲]

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See detailProject Advanced Discretisaztion Methods
Farina, Sofia UL

Presentation (2019, February 01)

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