Abstract:We present a two phase model for microcirculation that describes the interaction of plasma with red blood cells. The model takes into account of typical effects characterizing the microcirculation, such as the Fahraeus-Lindqvist effect and plasma skimming. Besides these features, the model describes the interaction of capillaries with the surrounding tissue. More precisely, the model accounts for the interaction of capillary transmural flow with the surrounding interstitial pressure. Furthermore, the capillari… Show more
“…The model described the flow within the gel by means of Darcy's equation, and the flow in the MVNs with the Poiseuille equation for laminar, fully developed flow, taking into account network junctions, and filtration through the capillary membrane, which was described by Equation . The model was solved by means of the finite element method using the GetFem++ software, as previously shown . The MVNs (1/4 of the length of the device, repeated spatially) were reconstructed from confocal images using the FIJI “skeletonize” function to compute the skeleton of the network.…”
In vitro prediction of physiologically relevant transport of therapeutic molecules across the microcirculation represents an intriguing opportunity to predict efficacy in human populations. On‐chip microvascular networks (MVNs) show physiologically relevant values of molecular permeability, yet like most systems, they lack an important contribution to transport: the ever‐present fluid convection through the endothelium. Quantification of transport through the MVNs by current methods also requires confocal imaging and advanced analytical techniques, which can be a bottleneck in industry and academic laboratories. Here, it is shown that by recapitulating physiological transmural flow across the MVNs, the concentration of small and large molecule therapeutics can be directly sampled in the interstitial fluid and analyzed using standard analytical techniques. The magnitudes of transport measured in MVNs reveal trends with molecular size and type (protein versus nonprotein) that are expected in vivo, supporting the use of the MVNs platform as an in vitro tool to predict distribution of therapeutics in vivo.
“…The model described the flow within the gel by means of Darcy's equation, and the flow in the MVNs with the Poiseuille equation for laminar, fully developed flow, taking into account network junctions, and filtration through the capillary membrane, which was described by Equation . The model was solved by means of the finite element method using the GetFem++ software, as previously shown . The MVNs (1/4 of the length of the device, repeated spatially) were reconstructed from confocal images using the FIJI “skeletonize” function to compute the skeleton of the network.…”
In vitro prediction of physiologically relevant transport of therapeutic molecules across the microcirculation represents an intriguing opportunity to predict efficacy in human populations. On‐chip microvascular networks (MVNs) show physiologically relevant values of molecular permeability, yet like most systems, they lack an important contribution to transport: the ever‐present fluid convection through the endothelium. Quantification of transport through the MVNs by current methods also requires confocal imaging and advanced analytical techniques, which can be a bottleneck in industry and academic laboratories. Here, it is shown that by recapitulating physiological transmural flow across the MVNs, the concentration of small and large molecule therapeutics can be directly sampled in the interstitial fluid and analyzed using standard analytical techniques. The magnitudes of transport measured in MVNs reveal trends with molecular size and type (protein versus nonprotein) that are expected in vivo, supporting the use of the MVNs platform as an in vitro tool to predict distribution of therapeutics in vivo.
“…Despite this fact, in many publications that are concerned with modelling of blood flow in microvascular networks, blood is considered as an incompressible fluid. 8,25,32,40,41 (A3) The non-Newtonian flow behaviour is accounted for by an algebraic relationship.…”
Section: Basic Modelling Assumptionsmentioning
confidence: 99%
“…In order to model flow within the tissue, we do not use pore network models 43 that attempt to resolve each pore and pore throat, but we apply homogenised or REV-based flow models such as Darcy's law. 8,44,45 In this context, it is assumed that the parameters characterising the porous structure like porosity and permeability are constant. Since we do not have any information on the tissue surrounding the given network, we assume that the porosity is constant and that the permeability tensor is diagonal and isotropic with constant values.…”
Section: Basic Modelling Assumptionsmentioning
confidence: 99%
“…Numerical simulation techniques have become an important part in testing hypotheses when experimental investigations are not possible or are limited by accessibility, size and resolution. [3][4][5][6][7][8][9] To be able to perform conclusive blood flow simulations, it is crucial to have a precise description of the network. This means that accurate data on the radii, lengths and connectivity of the vessels as well as the location of the vessels are required.…”
In this work, we introduce an algorithmic approach to generate microvascular networks starting from larger vessels that can be reconstructed without noticeable segmentation errors. Contrary to larger vessels, the reconstruction of fine-scale components of microvascular networks shows significant segmentation errors, and an accurate mapping is time and cost intense. Thus there is a need for fast and reliable reconstruction algorithms yielding surrogate networks having similar stochastic properties as the original ones. The microvascular networks are constructed in a marching way by adding vessels to the outlets of the vascular tree from the previous step. To optimise the structure of the vascular trees, we use Murray's law to determine the radii of the vessels and bifurcation angles. In each step, we compute the local gradient of the partial pressure of oxygen and adapt the orientation of the new vessels to this gradient. At the same time, we use the partial pressure of oxygen to check whether the considered tissue block is supplied sufficiently with oxygen. Computing the partial pressure of oxygen, we use a 3D-1D coupled model for blood flow and oxygen transport. To decrease the complexity of a fully coupled 3D model, we reduce the blood vessel network to a 1D graph structure and use a bi-directional coupling with the tissue which is described by a 3D homogeneous porous medium. The resulting surrogate networks are analysed with respect to morphological and physiological aspects. K E Y W O R D S 3D-1D coupled flow models, blood flow simulations, dimensionally reduced models, flows in porous media, oxygen transport, vascular growth
“…A recent study describes contrast agent perfusion based on diffusive transport with a mixed‐dimension model. The herein presented fluid‐mechanical model is similar to the drug proliferation model described in Cattaneo and Zunino and introduced in Possenti et al It is derived here for the specific application of contrast agent perfusion in brain tissue. The mathematical background of such models is analyzed in several works …”
We propose a new mathematical model to learn capillary leakage coefficients from dynamic susceptibility contrast MRI data. To this end, we derive an embedded mixed‐dimension flow and transport model for brain tissue perfusion on a subvoxel scale. This model is used to obtain the contrast agent concentration distribution in a single MRI voxel during a perfusion MRI sequence. We further present a magnetic resonance signal model for the considered sequence including a model for local susceptibility effects. This allows modeling MR signal‐time curves that can be compared with clinical MRI data. The proposed model can be used as a forward model in the inverse modeling problem of inferring model parameters such as the diffusive capillary wall conductivity. Acute multiple sclerosis lesions are associated with a breach in the integrity of the blood‐brain barrier. Applying the model to perfusion MR data of a patient with acute multiple sclerosis lesions, we conclude that diffusive capillary wall conductivity is a good indicator for characterizing activity of lesions, even if other patient‐specific model parameters are not well‐known.
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