- Mathematical Models of the Cerebral Microcirculation in Health and Pathophysiology -- A computational model of the tumor microenvironment applied to fractionated radiotherapy -- Microvascular modeling for medical imaging and toxicity assessment -- Finite element software and performance for network models with multipliers -- A Fast-Fourier Preconditioned Schur Complement Method for the Simulation of Cerebrocortical Oxygen Supply -- Robust Preconditioning of Mixed-Dimensional PDEs on 3𝒅-1𝒅 domains coupled with Lagrange Multipliers -- Numerical approaches for multiphase microfluids -- Application of the Zenger correction to an elliptic PDE with Dirac source term.

Microcirculation is a key area of interest within the realms of biology and medicine. As a vital discipline, microcirculatory biology forms a significant part of established medical fields like cardiovascular medicine and oncology, and is increasingly relevant in emerging fields such as neuroscience. With its multifaceted nature, the study of microcirculation has evolved from basic observations and experiments to embrace cutting-edge imaging technologies, quantitative methods, and the power of data science. This volume brings together a series of insightful chapters that highlight the latest trends in modeling microcirculation. It casts a spotlight on the vital role of microcirculation in brain function modeling and the innovative applications of microvascular models in oncology. Readers will be introduced to state-of-the-art methodologies of microcirculation modeling. A key focus is on mixed-dimensional models, mathematical methods adept at describing complex interactions within lower dimensional manifolds. Each chapter thoughtfully navigates the mathematical, computational, and practical challenges of these approaches, underscoring their effectiveness in capturing the essence of microcirculation. This book offers a window into the latest advancements and methodologies that are shaping the future of this vital field.