Simulation of angiogenesis in three dimensions: Application to cerebral cortex

Abstract

The vasculature is a dynamic structure, growing and regressing in response to embryonic development, growth, changing physiological demands, wound healing, tumor growth and other stimuli. At the microvascular level, network geometry is not predetermined, but emerges as a result of biological responses of each vessel to the stimuli that it receives. These responses may be summarized as angiogenesis, remodeling and pruning. Previous theoretical simulations have shown how two-dimensional vascular patterns generated by these processes in the mesentery are consistent with experimental observations. During early development of the brain, a mesh-like network of vessels is formed on the surface of the cerebral cortex. This network then forms branches into the cortex, forming a three-dimensional network throughout its thickness. Here, a theoretical model is presented for this process, based on known or hypothesized vascular response mechanisms together with experimentally obtained information on the structure and hemodynamics of the mouse cerebral cortex. According to this model, essential components of the system include sensing of oxygen levels in the midrange of partial pressures and conducted responses in vessel walls that propagate information about metabolic needs of the tissue to upstream segments of the network. The model provides insights into the effects of deficits in vascular response mechanisms, and can be used to generate physiologically realistic microvascular network structures.

Competition for endothelial cell polarity drives vascular morphogenesis in the mouse retina

“…NOTCH, CXCR4,and BMP signaling have been linked to arteriogenesis and/or to modulate EC shear-stress responses ( Baeyens et al., 2015 ; Cartier and Hla, 2019 ; Mack et al., 2017 ; Tanaka et al., 2021 ) and thus are prime candidates to fine-tune the S>R transition at the single-cell level. Moreover, computational modeling of adaptation and maladaptation showed that well-organized vascular networks rely on tight feedback between vessel caliber control and hemodynamics ( Alberding and Secomb, 2021 ; Pries et al., 2009 ) and the transfer of information from distal to proximal vessels in arteries ( Pries et al., 2010 ). How these flows of information relate to EC polarity and the S>R transition remains to be explored.…”

Functional implications of microvascular heterogeneity for oxygen uptake and utilization

“…Since brain tissue is intolerant of hypoxia, the lack of acute vascular responses to hypoxia in brain is surprising (Leithner & Royl, 2014). Simulations suggest that a possible resolution to this apparent paradox may be that the long‐term processes of angiogenesis and structural adaptation are sensitive to oxygen levels (Alberding & Secomb, 2021), ensuring that tissue is well oxygenated under resting conditions.…”

A three-dimensional, discrete-continuum model of blood pressure in microvascular networks

“…Advances in biomedical imaging of vascular tissues [4][5][6][7] have paved the way for computational studies which integrate complete vascular architectures with biophysical models to probe the microenvironment in silico in a manner that is currently inaccessible in a traditional experimental setting 8 . Due to the computational challenges of simulating network-scale blood rheology and dynamics using mesh-based methods, many studies apply one-dimensional (1D) Poiseuille flow models (see Figure 1A) to these vascular network datasets to provide insight into a wide range of biological applications, for example, in cerebral blood flow [9][10][11][12] , angiogenesis 13,14 and cancer 4,[15][16][17] . Nonetheless, with the emergence of whole-organ vascular imaging 6 , the computational demands of fully-discrete 1D fluid and mass transport models are increasing due to the sheer number of blood vessels in imaged samples (> O(10 6 )).…”

“…In these models, the vascular network is represented as a graph (see Figure 1A). This approach provides insight into a wide range of biological applications such as cerebral blood flow [9][10][11][12] , angiogenesis 13,14 , and cancer 4,[15][16][17] . Nonetheless, with the emergence of whole-organ vascular imaging 6 , the computational demands of fully-discrete 1D fluid and mass transport models are increasing due to the sheer number of blood vessels in imaged samples (> O(10 9 )).…”