A numerical framework for the simulation of molecular diffusion in the micro-vascular system

Although direct simulations of the whole cerebral microcirculation are computationally cumbersome, we will show that they can be carried out on a smaller scale (about 50 to 10000 vessels). For that purpose, we introduce a numerical framework able to solve the fully coupled problem: tissue-diffusion and vessels- advection/diffusion

Structural and hemodynamic comparison of anatomical and synthetic cerebral capillary networks

A computational method is presented for generating synthetic, random 3D capillary networks which match the topological, geometrical and functional properties of the cerebral microcirculation. These networks, which can be generated in volumes larger than can currently be extracted by high-resolution imaging, can then be coupled to lower-resolution data sets of whole-brain vasculature to model blood flow and mass transport, and to validate equivalent continuum/hybrid models. Another motivation is to reveal the dominant structural features of cerebral capillary networks, which can then be tuned to model different brain regions or pathological states such as Alzheimer’s disease. Previous works [1, 2] lacked physiological basis, and although resulting networks conformed to expected global morphometric properties, were not subjected to thorough topological or functional analysis. In contrast, our approach is based on the physiological assumption that the maximum separation of tissue cells from the nearest capillary is limited by the diffusion distance of oxygen [3]. Previously, synthetic, space-filling 2D networks were constructed by placing one point randomly in each cell of an n × n grid; from this set of points, Voronoi diagrams were extracted with the edges producing a 2D network with mainly three capillaries per vertex, a characteristic feature of cerebral capillary networks. Here, we extend this approach to 3D. In 3D, Voronoi diagrams produce polyhedrons with many capillaries per vertex. To derive a network with only bifurcations, clusters of vertices were systematically merged and capillaries then removed randomly. Geometrical metrics such as the mean/S.D. of lengths and edge/length/vertex densities were compared to those of capillary regions extracted from mouse cerebral anatomical data sets [5, 6]. Capillary loops were studied to measure the interconnected network topology, while the distribution of extravascular distances allowed comparison of the spatial arrangement of capillaries. Finally, hemodynamic properties were captured through the network permeability. Overall, synthetic networks showed excellent agreement with the anatomical data. This work was supported by ERC BrainMicroFlow GA615102. We acknowledge D. Kleinfeld, P. Tsai and P. Blinder for kindly sharing their anatomical data with us

Structural and hemodynamic comparison of synthetic and anatomical cerebral capillary networks

A computational method is presented for generating 3D synthetic, random capillary networks which match the topological, geometrical and functional properties of the cerebral microcirculation. This enables production of larger capillary networks than can currently be extracted using high-resolution imaging modalities. These networks can then be coupled to lower-resolution data sets of whole-brain vasculature (capillaries unresolved) to model blood flow and mass transport, and to validate equivalent continuum/hybrid models. Another motivation is to reveal the dominant structural features of cerebral capillary networks, enabling us to tune these features to model different brain regions or pathological states such as Alzheimer's disease. Previous works (Linninger et al, Ann Biomed Eng, 2013; Su et al, Microcirc, 2012) lacked physiological basis, and although resulting networks conformed to expected global morphometric properties, they were not subjected to thorough topological or functional analysis. In contrast, our approach is based on the physiological assumption that the maximum separation of tissue cells from the nearest capillary is limited by the diffusion distance of oxygen (Lorthois & Cassot, J Theor Biol, 2010). Previously, synthetic, space-filling 2D networks were constructed by placing one point randomly in each cell of an n × n grid; from this set of points, Voronoi diagrams were extracted with the edges producing a 2D capillary network with mainly three capillaries per vertex, a characteristic feature of cerebral capillary networks. Here, we present a 3D extension of this approach and compare the resulting structural and hemodynamic properties to those of anatomical cerebral capillary networks. In 3D, Voronoi diagrams produce polyhedrons with many capillaries at each vertex. To derive a network with only bifurcations, clusters of vertices were systematically merged and capillaries were then randomly removed. The resulting network structures were compared to capillary regions extracted from human and mouse anatomical data sets (Cassot et al, Microcirc, 2006; Tsai et al, J NeuroSci, 2009; Blinder et al, Nat Neurosci, 2013), showing excellent agreement. Geometrical metrics included the mean/S.D. of capillary lengths and edge/length/vertex densities. To measure the interconnected network topology, capillary loops were identified and the mean number of edges per loop, loop length, and number of loops per edge were compared. The spatial arrangement of capillaries was compared by studying the distribution of extravascular distances. Finally, the permeability was computed as a hemodynamic measure of blood flow conductivity

Upscaling mass transfer in brain capillary networks

Brain perfusion imaging techniques rely on the measurement of spatio-temporal concentration fields of various endogenous or exogenous tracers in the brain tissue. Their resolution is typically between 1 mm3 Magnetic Resonance Imaging) and (10 mm)3 Positron Emission Tomography). This is much coarser than the diameters of most arterioles and venules, which are typically below 100 μm, and, of course, of capillaries, whose diameters are tenfold smaller. This implies that methods to deduce the regional blood flow rate out of these large-scale concentration fields should rely on upscaled models, i.e. models describing the macro-scale behavior of the vascular system with effective properties taking into account its microstructure. To derive such models, the Volume Averaging Technique, which has been previously developed for upscaling mass transfer in heterogeneous porous media, can be applied to the advection-diffusion equations. Capillary networks indeed exhibit a space filling mesh-like structure, for which a Representative Elementary Volume (REV), can be extracted: a 3D network of capillaries with diameters ranging from 1 to 10 μm embedded in tissue, with volume about (150 to 300 μm)3. In this technique, closure equations must be solved in REVs to deduce effective coefficients, representing its macro-scale behavior. Being able to solve closure equations on any 3D network geometry taking into account individual vessels is a computational challenge. Here, we developed a numerical framework to solve partial differential equations on anatomically accurate capillary networks using the finite element library Feel++. This framework is used to 1) solve the closure equations on a REV and deduce its effective coefficients and 2) perform direct simulations of mass transfers problems as references to validate the upscaling procedure

An energy approach describes spine equilibrium in adolescent idiopathic scoliosis

The adolescent idiopathic scoliosis (AIS) is a 3D deformity of the spine whose origin is unknown and clinical evolution unpredictable. In this work, a mixed theoretical and numerical approach based on energetic considerations is proposed to study the global spine deformations. The introduced mechanical model aims at overcoming the limitations of computational cost and high variability in physical parameters. The model is constituted of rigid vertebral bodies associated with 3D effective stiffness tensors. The spine equilibrium is found using minimization methods of the mechanical total energy which circumvents forces and loading calculation. The values of the model parameters exhibited in the stiffness tensor are retrieved using a combination of clinical images post-processing and inverse algorithms implementation. Energy distribution patterns can then be evaluated at the global spine scale to investigate given time patient-specific features. To verify the reliability of the numerical methods, a simplified model of spine was implemented. The methodology was then applied to a clinical case of AIS (13-year-old girl, Lenke 1A). Comparisons of the numerical spine geometry with clinical data equilibria showed numerical calculations were performed with great accuracy. The patient follow-up allowed us to highlight the energetic role of the apical and junctional zones of the deformed spine, the repercussion of sagittal bending in sacro-illiac junctions and the significant role of torsion with scoliosis aggravation. Tangible comparisons of output measures with clinical pathology knowledge provided a reliable basis for further use of those numerical developments in AIS classification, scoliosis evolution prediction and potentially surgical planning

Brain capillary networks across species : a few simple organizational requirements are sufficient to reproduce both structure and function

Despite the key role of the capillaries in neurovascular function, a thorough characterization of cerebral capillary network properties is currently lacking. Here, we define a range of metrics (geometrical, topological, flow, mass transfer, and robustness) for quantification of structural differences between brain areas, organs, species, or patient populations and, in parallel, digitally generate synthetic networks that replicate the key organizational features of anatomical networks (isotropy, connectedness, space-filling nature, convexity of tissue domains, characteristic size). To reach these objectives, we first construct a database of the defined metrics for healthy capillary networks obtained from imaging of mouse and human brains. Results show that anatomical networks are topologically equivalent between the two species and that geometrical metrics only differ in scaling. Based on these results, we then devise a method which employs constrained Voronoi diagrams to generate 3D model synthetic cerebral capillary networks that are locally randomized but homogeneous at the network-scale. With appropriate choice of scaling, these networks have equivalent properties to the anatomical data, demonstrated by comparison of the defined metrics. The ability to synthetically replicate cerebral capillary networks opens a broad range of applications, ranging from systematic computational studies of structure-function relationships in healthy capillary networks to detailed analysis of pathological structural degeneration, or even to the development of templates for fabrication of 3D biomimetic vascular networks embedded in tissue-engineered constructs

Neutrophil adhesion in brain capillaries reduces cortical blood flow and impairs memory function in Alzheimer’s disease mouse models.

Cerebral blood flow (CBF) reductions in Alzheimer’s disease patients and related mouse models have been recognized for decades, but the underlying mechanisms and resulting consequences for Alzheimer’s disease pathogenesis remain poorly understood. In APP/PS1 and 5xFAD mice we found that an increased number of cortical capillaries had stalled blood flow as compared to in wild-type animals, largely due to neutrophils that had adhered in capillary segments and blocked blood flow. Administration of antibodies against the neutrophil marker Ly6G reduced the number of stalled capillaries, leading to both an immediate increase in CBF and rapidly improved performance in spatial and working memory tasks. This study identified a previously uncharacterized cellular mechanism that explains the majority of the CBF reduction seen in two mouse models of Alzheimer’s disease and demonstrated that improving CBF rapidly enhanced short-term memory function. Restoring cerebral perfusion by preventing neutrophil adhesion may provide a strategy for improving cognition in Alzheimer’s disease patients

Modeling and simulation of multi-fluid systems. Applications to blood flows

Dans ce travail, nous développons un cadre de calcul dédié à la simulation d'écoulements à plusieurs fluides. Nous présentons des validations et vérifications de ces méthodes sur des problèmes de capture d'interfaces et de simulations de bulles visqueuses.Nous montrons ensuite que ce cadre de calcul est adapté à la simulation d'objet rigides en écoulement.Puis, nous étendons ces méthodes à la simulation d'objets déformables simulant le comportement des globules rouges : les vésicules. Nous validons aussi ces simulations.Enfin nous appliquons les précédents modèles à des problèmes ouverts de microfluidique tels que la séparation d'une suspension dans une bifurcation microfluidique et la rhéologie en milieu confiné.In this work, we develop a framework dedicated to the simulation of multi-fluid systems. We present validations and verifications of these methods on interface capture problems and viscous bubbles simulations.We then show that this framework is well fitted for the simulation of the rigid bodies flow.Next, we extend these methods to the simulation of deformable objects reproducing the behavior of red blood cells: the vesicles. We also validate these simulations.Finally, we apply the previous models to open micro-fluidic problems such as the splitting of a suspension at a bifurcation and the rheology in a confined environment

Modelisation et simulation de systemes multi-fluides. Application aux ecoulements sanguins.

In this work, we develop a framework dedicated to the simulation of multi-fluid systems. We present validations and verifications of these methods on interface capture problems and viscous bubbles simulations.\\ We then show that this framework is well fitted for the simulation of the rigid bodies flow. Next, we extend these methods to the simulation of deformable objects reproducing the behavior of red blood cells: the vesicles. We also validate these simulations. Finally, we apply the previous models to open micro-fluidic problems such as the splitting of a suspension at a bifurcation and the rheology in a confined environment.Dans ce travail, nous développons un cadre de calcul dédié à la simulation d'écoulements à plusieurs fluides. Nous présentons des validations et vérifications de ces méthodes sur des problèmes de capture d'interfaces et de simulations de bulles visqueuses. Nous montrons ensuite que ce cadre de calcul est adapté à la simulation d'objet rigides en écoulement. Puis, nous étendons ces méthodes à la simulation d'objets déformables simulant le comportement des globules rouges : les vésicules. Nous validons aussi ces simulations. Enfin nous appliquons les précédents modèles à des problèmes ouverts de microfluidique tels que la séparation d'une suspension dans une bifurcation microfluidique et la rhéologie en milieu confiné