A two-field computational model couples cellular brain development with cortical folding - Zarzor, Mohammad Saeed; Käßmair, Stefan; Steinmann, Paul; Blümcke, Ingmar; Budday, Silvia (Brain Multiphysics, 2021)
The convoluted macroscopic shape of the mammalian brain plays an important role for brain function. To date, the link between the cellular processes during brain development and normal or abnormal cortical folding on the macroscopic scale remains insufficiently understood. Disruption of cellular division, migration, or connectivity may lead to malformations of cortical development associated with neurological disorders like schizophrenia, autism, or epilepsy. Here, we use a computational model, which couples an advection-diffusion model with finite growth, to assess the link between cellular division and migration on the cell scale and growth and cortical folding on the tissue or organ scale. It introduces the cell density as independent field controlling volumetric growth. This allows us to numerically study the influence of cell migration velocity, cell diffusivity, and the temporally changing local stiffness of brain tissue on the cortical folding process during normal brain development. We show that the model is capable of capturing the local distribution of cells through the comparison with histologically stained sections of the developing human brain. Our results further demonstrate that it is important to take temporal changes in tissue stiffness into account, which naturally occur during brain development. The present study constitutes an important step towards a computational model that could help to better understand, diagnose, and, eventually, treat neurological disorders arising from abnormal cellular development and cortical malformations.<br
Keywords: Brain development; Cortical folding; Neurogenesis; Finite growth; Multifield modeling; Mechanical instability

Exploring the interplay between cellular development and mechanics in the developing human brain - Zarzor, Mohammad Saeed; Käßmair, Stefan; Steinmann, Paul; Blümcke, Ingmar; Budday, Silvia (Proceedings in Applied Mathematics and Mechanics, 2021)
The human brain has a complex structure on both cellular and organ scales. This structure is closely related to the brain's abilities and functions. Disruption of one of the biological processes occurring during brain development on the cellular scale may affect the cortical folding pattern of the brain on the organ scale. However, the link between disruptions in cellular brain development and associated cortical malformation remains largely unknown. From a mechanical perspective, the forces generated during development lead to mechanical instability and, eventually, the mergence of cortical folds. To fully understand mechanism underlying malformations of cortical development, it is key to consider both the events that occur on the cellular scale and the mechanical forces generated on the organ scale. Here we present a computational model describing cellular division and migration on the cellular scale, as well as growth and cortical folding on the tissue or organ scale, in a continuous way by a coupled finite growth and advection-diffusion model. We introduce the cell density as an independent field controlling the volumetric growth. Furthermore, we formulate a positive relation between cell density and cortical layer stiffness. This allows us to study the influence of the migration velocity, the cell diffusivity, the local stiffness, and the local connectivity of cells on the cortical folding process and mechanical properties during normal and abnormal brain development numerically. We show how an increase in the density of the neurons increases the layer's mechanical stiffness. Moreover, weWe validate our simulation results through the comparison with histological sections of the fetal human brain. The current model aims to be a first step towards providing a reliable platform to systematically evaluate the role of different cellular events on the cortical folding process and vice vers

Exploring the role of different cell types on cortical folding in the developing human brain through computational modeling - Zarzor, Mohammad Saeed; Ma, Qiang; Almurey, Median; Kainz, Bernhard; Budday, Silvia (Scientific Reports, 2024)
The human brain’s distinctive folding pattern has attracted the attention of researchers from different fields. Neuroscientists have provided insights into the role of four fundamental cell types crucial during embryonic development: radial glial cells, intermediate progenitor cells, outer radial glial cells, and neurons. Understanding the mechanisms by which these cell types influence the number of cortical neurons and the emerging cortical folding pattern necessitates accounting for the mechanical forces that drive the cortical folding process. Our research aims to explore the correlation between biological processes and mechanical forces through computational modeling. We introduce cell-density fields, characterized by a system of advection-diffusion equations, designed to replicate the characteristic behaviors of various cell types in the developing brain. Concurrently, we adopt the theory of finite growth to describe cortex expansion driven by increasing cell density. Our model serves as an adjustable tool for understanding how the behavior of individual cell types reflects normal and abnormal folding patterns. Through comparison with magnetic resonance images of the fetal brain, we explore the correlation between morphological changes and underlying cellular mechanisms. Moreover, our model sheds light on the spatiotemporal relationships among different cell types in the human brain and enables cellular deconvolution of histological sections.
CRIS-Team Scopus Importer:2024-11-15
Keywords: Cortical folding; Coupled problems; Human brain development; Multi-field modeling; Outer radial glial cells

Exploring the role of the outer subventricular zone during cortical folding through a physics-based model - Zarzor, Mohammad Saeed; Blümcke, Ingmar; Budday, Silvia (eLife, 2023)
The human brain has a highly complex structure both on the microscopic and on the macroscopic scales. Increasing evidence has suggested the role of mechanical forces for cortical folding - a classical hallmark of the human brain. However, the link between cellular processes at the microscale and mechanical forces at the macroscale remains insufficiently understood. Recent findings suggest that an additional proliferating zone, the outer subventricular zone (OSVZ), is decisive for the particular size and complexity of the human cortex. To better understand how the OSVZ affects cortical folding, we establish a multifield computational model that couples cell proliferation in different zones and migration at the cell scale with growth and cortical folding at the organ scale by combining an advection-diffusion model with the theory of finite growth. We validate our model based on data from histologically stained sections of the human fetal brain and predict 3D pattern formation. Finally, we address open questions regarding the role of the OSVZ for the formation of cortical folds. The presented framework not only improves our understanding of human brain development, but could eventually help diagnose and treat neuronal disorders arising from disruptions in cellular development and associated malformations of cortical development.
CRIS-Team Scopus Importer:2023-04-28
Keywords: finite element simulations; human; human brain development; multifield modeling; neuroscience; outer radial glial cells; outer subventricular zone; physics of living systems

Multifield computational model for human brain development: Explicit numerical stabilization - Zarzor, Mohammad Saeed; Steinmann, Paul; Budday, Silvia (Proceedings in Applied Mathematics and Mechanics, 2023)
The morphological surface of the human brain is still puzzling to scientists. During the last few decades, studies have addressed different aspects of this phenomenon. The underlying cellular processes occurring at the microscopic scale are certainly important for the folding process. However, there is also an essential contribution from mechanical forces generated at the macroscopic scale during these processes. Many previous studies confirmed this fact, but still, most of them have not considered the link between cellular processes and mechanical forces. Recently, we have explained how the proliferation in different zones of the brain, cell migration, and neuronal connectivity affect the folding through a multifield computational model coupling an advection-diffusion model with the theory of finite growth. We mathematically describe the cellular behavior of cells to control mechanical growth in both radial and circumferential directions. To deal with issues regarding numerical stability of the advection-diffusion equation, which lead to temporal and spatial numerical oscillations, reduced efficiency of the numerical solver, and inaccurate results, we introduce an artificial diffusivity, which we apply only when the actual cell density does not satisfy the balance equation. The proposed method stabilizes the numerical solution and significantly improves the simulation results without additional numerical cost. It allows us to study brain development in 2D and 3D.<br