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.

中文翻译：

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具有最小重网格的复杂神经细胞形态空间分辨能量代谢模型的割有限元方法

彻底了解脑代谢对于解决神经退行性疾病至关重要。星形胶质细胞是神经胶质细胞，通过向神经元提供能量来发挥重要的代谢作用。此外，星形胶质细胞为邻近的神经元提供支架和体内平衡功能，并促进血脑屏障。最近的研究表明，星形胶质细胞的复杂形态会影响其功能，特别是影响这些细胞代谢养分并为神经元提供能量的效率，但对系统的了解仍然难以捉摸。建模和仿真代表了解决这一挑战并加深我们对脑能量代谢的理解的有效框架。这需要在复杂域上求解一组代谢偏微分方程，仍然是一个挑战。在本文中，我们提出，测试和验证一种简单的数值方法来解决星形胶质细胞代谢途径的简化模型。该方法可以处理任意复杂的细胞形态，并且使用户能够快速而简单地修改模型方程式，而无需对所涉及的数值方法有深入的了解。用新方法（CutFEM）获得的结果与有限元方法（FEM）一样准确，而CutFEM则使细胞形态从离散化中解开，使我们能够处理二维和三维中任意复杂的形态。该方法可以处理任意复杂的细胞形态，并且使用户能够快速而简单地修改模型方程式，而无需对所涉及的数值方法有深入的了解。用新方法（CutFEM）获得的结果与有限元方法（FEM）一样准确，而CutFEM则使细胞形态从离散化中解开，使我们能够处理二维和三维中任意复杂的形态。该方法可以处理任意复杂的细胞形态，并且使用户能够快速而简单地修改模型方程式，而无需对所涉及的数值方法有深入的了解。用新方法（CutFEM）获得的结果与有限元方法（FEM）一样准确，而CutFEM则使细胞形态从离散化中解开，使我们能够处理二维和三维中任意复杂的形态。