Brain Capillary Networks Across Species: A few Simple Organizational Requirements Are Sufficient to Reproduce Both Structure and Function

Isoflurane lowers the cerebral metabolic rate of oxygen and prevents hypoxia during cortical spreading depolarization in vitro: An integrative experimental and modeling study

Cortical spreading depolarization (SD) imposes a massive increase in energy demand and therefore evolves as a target for treatment following acute brain injuries. Anesthetics are empirically used to reduce energy metabolism in critical brain conditions, yet their effect on metabolism during SD remains largely unknown. We investigated oxidative metabolism during SD in brain slices from Wistar rats. Extracellular potassium ([K+]o), local field potential and partial tissue oxygen pressure (ptiO2) were measured simultaneously. The cerebral metabolic rate of oxygen (CMRO2) was calculated using a reaction-diffusion model. By that, we tested the effect of clinically relevant concentrations of isoflurane on CMRO2 during SD and modeled tissue oxygenation for different capillary pO2 values. During SD, CMRO2 increased 2.7-fold, resulting in transient hypoxia in the slice core. Isoflurane decreased CMRO2, reduced peak [K+]o, and prolonged [K+]o clearance, which indicates reduced synaptic transmission and sodium-potassium ATPase inhibition. Modeling tissue oxygenation during SD illustrates the need for increased capillary pO2 levels to prevent hypoxia. In the absence thereof, isoflurane could improve tissue oxygenation by lowering CMRO2. Therefore, isoflurane is a promising candidate for pre-clinical studies on neuronal survival in conditions involving SD.

Is CAA a perivascular brain clearance disease? A discussion of the evidence to date and outlook for future studies

The brain's network of perivascular channels for clearance of excess fluids and waste plays a critical role in the pathogenesis of several neurodegenerative diseases including cerebral amyloid angiopathy (CAA). CAA is the main cause of hemorrhagic stroke in the elderly, the most common vascular comorbidity in Alzheimer's disease and also implicated in adverse events related to anti-amyloid immunotherapy. Remarkably, the mechanisms governing perivascular clearance of soluble amyloid β-a key culprit in CAA-from the brain to draining lymphatics and systemic circulation remains poorly understood. This knowledge gap is critically important to bridge for understanding the pathophysiology of CAA and accelerate development of targeted therapeutics. The authors of this review recently converged their diverse expertise in the field of perivascular physiology to specifically address this problem within the framework of a Leducq Foundation Transatlantic Network of Excellence on Brain Clearance. This review discusses the overarching goal of the consortium and explores the evidence supporting or refuting the role of impaired perivascular clearance in the pathophysiology of CAA with a focus on translating observations from rodents to humans. We also discuss the anatomical features of perivascular channels as well as the biophysical characteristics of fluid and solute transport.

Modeling oxygen transport in the brain: An efficient coarse-grid approach to capture perivascular gradients in the parenchyma

Recent progresses in intravital imaging have enabled highly-resolved measurements of periarteriolar oxygen gradients (POGs) within the brain parenchyma. POGs are increasingly used as proxies to estimate the local baseline oxygen consumption, which is a hallmark of cell activity. However, the oxygen profile around a given arteriole arises from an interplay between oxygen consumption and delivery, not only by this arteriole but also by distant capillaries. Integrating such interactions across scales while accounting for the complex architecture of the microvascular network remains a challenge from a modelling perspective. This limits our ability to interpret the experimental oxygen maps and constitutes a key bottleneck toward the inverse determination of metabolic rates of oxygen. We revisit the problem of parenchymal oxygen transport and metabolism and introduce a simple, conservative, accurate and scalable direct numerical method going beyond canonical Krogh-type models and their associated geometrical simplifications. We focus on a two-dimensional formulation, and introduce the concepts needed to combine an operator-splitting and a Green's function approach. Oxygen concentration is decomposed into a slowly-varying contribution, discretized by Finite Volumes over a coarse cartesian grid, and a rapidly-varying contribution, approximated analytically in grid-cells surrounding each vessel. Starting with simple test cases, we thoroughly analyze the resulting errors by comparison with highly-resolved simulations of the original transport problem, showing considerable improvement of the computational-cost/accuracy balance compared to previous work. We then demonstrate the model ability to flexibly generate synthetic data reproducing the spatial dynamics of oxygen in the brain parenchyma, with sub-grid resolution. Based on these synthetic data, we show that capillaries distant from the arteriole cannot be overlooked when interpreting POGs, thus reconciling recent measurements of POGs across cortical layers with the fundamental idea that variations of vascular density within the depth of the cortex may reveal underlying differences in neuronal organization and metabolic load.

Modeling hypoxia-induced radiation resistance and the impact of radiation sources

Hypoxia contributes significantly to resistance in radiotherapy. Our research rigorously examines the influence of microvascular morphology on radiotherapy outcome, specifically focusing on how microvasculature shapes hypoxia within the microenvironment and affects resistance to a standard treatment regimen (30×2GyRBE). Our computational modeling extends to the effects of different radiation sources. For photons and protons, our analysis establishes a clear correlation between hypoxic volume distribution and treatment effectiveness, with vascular density and regularity playing a crucial role in treatment success. On the contrary, carbon ions exhibit distinct effectiveness, even in areas of intense hypoxia and poor vascularization. This finding points to the potential of carbon-based hadron therapy in overcoming hypoxia-induced resistance to RT. Considering that the spatial scale analyzed in this study is closely aligned with that of imaging data voxels, we also address the implications of these findings in a clinical context envisioning the possibility of detecting subvoxel hypoxia.

Reconstructing microvascular network skeletons from 3D images: What is the ground truth?

Structural changes to microvascular networks are increasingly highlighted as markers of pathogenesis in a wide range of disease, e.g. Alzheimer's disease, vascular dementia and tumour growth. This has motivated the development of dedicated 3D imaging techniques, alongside the creation of computational modelling frameworks capable of using 3D reconstructed networks to simulate functional behaviours such as blood flow or transport processes. Extraction of 3D networks from imaging data broadly consists of two image processing steps: segmentation followed by skeletonisation. Much research effort has been devoted to segmentation field, and there are standard and widely-applied methodologies for creating and assessing gold standards or ground truths produced by manual annotation or automated algorithms. The Skeletonisation field, however, lacks widely applied, simple to compute metrics for the validation or optimisation of the numerous algorithms that exist to extract skeletons from binary images. This is particularly problematic as 3D imaging datasets increase in size and visual inspection becomes an insufficient validation approach. In this work, we first demonstrate the extent of the problem by applying 4 widely-used skeletonisation algorithms to 3 different imaging datasets. In doing so we show significant variability between reconstructed skeletons of the same segmented imaging dataset. Moreover, we show that such a structural variability propagates to simulated metrics such as blood flow. To mitigate this variability we introduce a new, fast and easy to compute super metric that compares the volume, connectivity, medialness, bifurcation point identification and homology of the reconstructed skeletons to the original segmented data. We then show that such a metric can be used to select the best performing skeletonisation algorithm for a given dataset, as well as to optimise its parameters. Finally, we demonstrate that the super metric can also be used to quickly identify how a particular skeletonisation algorithm could be improved, becoming a powerful tool in understanding the complex implication of small structural changes in a network.

Thermodynamic limitations on brain oxygen metabolism: physiological implications

Recent thermodynamic modelling indicates that maintaining the brain tissue ratio of O2 to CO2 (abbreviated tissue O2 /CO2 ) is critical for preserving the entropy increase available from oxidative metabolism of glucose, with a fall of that available entropy leading to a reduction of the phosphorylation potential and impairment of brain energy metabolism. This provides a novel perspective for understanding physiological responses under different conditions in terms of preserving tissue O2 /CO2 . To enable estimation of tissue O2 /CO2 in the human brain, a detailed mathematical model of O2 and CO2 transport was developed, and applied to reported physiological responses to different challenges, asking: how well is tissue O2 /CO2 preserved? Reported experimental results for increased neural activity, hypercapnia and hypoxia due to high altitude are consistent with preserving tissue O2 /CO2 . The results highlight two physiological mechanisms that control tissue O2 /CO2 : cerebral blood flow, which modulates tissue O2 ; and ventilation rate, which modulates tissue CO2 . The hypoxia modelling focused on humans at high altitude, including acclimatized lowlanders and Tibetan and Andean adapted populations, with a primary finding that decreasing CO2 by increasing ventilation rate is more effective for preserving tissue O2 /CO2 than increasing blood haemoglobin content to maintain O2 delivery to tissue. This work focused on the function served by particular physiological responses, and the underlying mechanisms require further investigation. The modelling provides a new framework and perspective for understanding how blood flow and other physiological factors support energy metabolism in the brain under a wide range of conditions. KEY POINTS: Thermodynamic modelling indicates that preserving the O2 /CO2 ratio in brain tissue is critical for preserving the entropy change available from oxidative metabolism of glucose and the phosphorylation potential underlying energy metabolism. A detailed model of O2 and CO2 transport was developed to allow estimation of the tissue O2 /CO2 ratio in the human brain in different physiological states. Reported experimental results during hypoxia, hypercapnia and increased oxygen metabolic rate in response to increased neural activity are consistent with maintaining brain tissue O2 /CO2 ratio. The hypoxia modelling of high-altitude acclimatization and adaptation in humans demonstrates the critical role of reducing CO2 with increased ventilation for preserving tissue O2 /CO2 . Preservation of tissue O2 /CO2 provides a novel perspective for understanding the function of observed physiological responses under different conditions in terms of preserving brain energy metabolism, although the mechanisms underlying these functions are not well understood.

Enhanced perfusion following exposure to radiotherapy: A theoretical investigation

Tumour angiogenesis leads to the formation of blood vessels that are structurally and spatially heterogeneous. Poor blood perfusion, in conjunction with increased hypoxia and oxygen heterogeneity, impairs a tumour's response to radiotherapy. The optimal strategy for enhancing tumour perfusion remains unclear, preventing its regular deployment in combination therapies. In this work, we first identify vascular architectural features that correlate with enhanced perfusion following radiotherapy, using in vivo imaging data from vascular tumours. Then, we present a novel computational model to determine the relationship between these architectural features and blood perfusion in silico. If perfusion is defined to be the proportion of vessels that support blood flow, we find that vascular networks with small mean diameters and large numbers of angiogenic sprouts show the largest increases in perfusion post-irradiation for both biological and synthetic tumours. We also identify cases where perfusion increases due to the pruning of hypoperfused vessels, rather than blood being rerouted. These results indicate the importance of considering network composition when determining the optimal irradiation strategy. In the future, we aim to use our findings to identify tumours that are good candidates for perfusion enhancement and to improve the efficacy of combination therapies.

A versatile micromodel technology to explore biofilm development in porous media flows

Bacterial biofilms that grow in porous media are critical to ecosystem processes and applications ranging from soil bioremediation to bioreactors for treating wastewater or producing value-added products. However, understanding and engineering the complex phenomena that drive the development of biofilms in such systems remains a challenge. Here we present a novel micromodel technology to explore bacterial biofilm development in porous media flows. The technology consists of a set of modules that can be combined as required for any given experiment and conveniently tuned for specific requirements. The core module is a 3D-printed micromodel where biofilm is grown into a perfusable porous substrate. High-precision additive manufacturing, in particular stereolithography, is used to fabricate porous scaffolds with precisely controlled architectures integrating flow channels with diameters down to several hundreds of micrometers. The system is instrumented with: ultraviolet-C light-emitting diodes; on-line measurements of oxygen consumption and pressure drop across the porous medium; camera and spectrophotometric cells for the detection of biofilm detachment events at the outlet. We demonstrate how this technology can be used to study the development of Pseudomonas aeruginosa biofilm for several days within a network of flow channels. We find complex dynamics whereby oxygen consumption reaches a steady-state but not the pressure drop, which instead features a permanent regime with large fluctuations. We further use X-ray computed microtomography to image the spatial distribution of biofilms and computational fluid dynamics to link biofilm development with local flow properties. By combining the advantages of additive manufacturing for the creation of reproducible 3D porous microarchitectures with the flow control and instrumentation accuracy of microfluidics, our system provides a platform to study the dynamics of biofilm development in 3D porous media and to rapidly test new concepts in process engineering.

Co-infecting Haemoproteus species (Haemosporida, Apicomplexa) show different host tissue tropism during exo-erythrocytic development in Fringilla coelebs (Fringillidae)

Avian haemosporidians of the genera Plasmodium, Haemoproteus, and Leucocytozoon are common blood parasites in wild birds all over the world. Despite their importance as pathogens potentially compromising host fitness and health, little is known about the exo-erythrocytic development of these parasites, particularly during co-infections which predominate in wildlife. This study aimed to address this issue using Haemoproteus parasites of Fringilla coelebs, a common bird species of the Western Palearctic and host to a variety of haemosporidian parasite lineages. Blood and tissue samples of 20 F. coelebs, positive for haemosporidians by blood film microscopy, were analysed by PCR and sequencing to determine cytochrome b lineages of the parasites. Tissue sections were examined for exo-erythrocytic stages by histology and in situ hybridization applying genus-, species-, and lineage-specific probes which target the 18S rRNA of the parasites. In addition, laser microdissection of tissue stages was performed to identify parasite lineages. Combined molecular results of PCR, laser microdissection, and in situ hybridization showed a high rate of co-infections, with Haemoproteus lineages dominating. Exo-erythrocytic meronts of five Haemoproteus spp. were described for the first known time, including Haemoproteus magnus hCCF6, Haemoproteus fringillae hCCF3, Haemoproteus majoris hCCF5, Haemoproteus sp. hROFI1, and Haemoproteus sp. hCCF2. Merogonic stages were observed in the vascular system, presenting a formerly unknown mode of exo-erythrocytic development in Haemoproteus parasites. Meronts and megalomeronts of these species were distinct regarding their morphology and organ distribution, indicating species-specific patterns of merogony and different host tissue tropism. New pathological aspects of haemoproteosis were reported. Furthermore, phylogenetic analysis of Haemoproteus spp. with regard to their exo-erythrocytic stages points towards separation of non-megalomeront-forming species from megalomeront-forming species, calling for further studies on exo-erythrocytic development of haemosporidian parasites to explore the phylogenetic character of this trait.

A mechanistic computational framework to investigate the hemodynamic fingerprint of the blood oxygenation level-dependent signal

Blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI) is one of the most used imaging techniques to map brain activity or to obtain clinical information about human cortical vasculature, in both healthy and disease conditions. Nevertheless, BOLD fMRI is an indirect measurement of brain functioning triggered by neurovascular coupling. The origin of the BOLD signal is quite complex, and the signal formation thus depends, among other factors, on the topology of the cortical vasculature and the associated hemodynamic changes. To understand the hemodynamic evolution of the BOLD signal response in humans, it is beneficial to have a computational framework available that virtually resembles the human cortical vasculature, and simulates hemodynamic changes and corresponding MRI signal changes via interactions of intrinsic biophysical and magnetic properties of the tissues. To this end, we have developed a mechanistic computational framework that simulates the hemodynamic fingerprint of the BOLD signal based on a statistically defined, three-dimensional, vascular model that approaches the human cortical vascular architecture. The microvasculature is approximated through a Voronoi tessellation method and the macrovasculature is adapted from two-photon microscopy mice data. Using this computational framework, we simulated hemodynamic changes-cerebral blood flow, cerebral blood volume, and blood oxygen saturation-induced by virtual arterial dilation. Then we computed local magnetic field disturbances generated by the vascular topology and the corresponding blood oxygen saturation changes. This mechanistic computational framework also considers the intrinsic biophysical and magnetic properties of nearby tissue, such as water diffusion and relaxation properties, resulting in a dynamic BOLD signal response. The proposed mechanistic computational framework provides an integrated biophysical model that can offer better insights regarding the spatial and temporal properties of the BOLD signal changes.

Sensitivity analysis of a multi-physics model for the vascular microenvironment

The vascular microenvironment is the scale at which microvascular transport, interstitial tissue properties and cell metabolism interact. The vascular microenvironment has been widely studied by means of quantitative approaches, including multi-physics mathematical models as it is a central system for the pathophysiology of many diseases, such as cancer. The microvascular architecture is a key factor for fluid balance and mass transfer in the vascular microenvironment, together with the physical parameters characterizing the vascular wall and the interstitial tissue. The scientific literature of this field has witnessed a long debate about which factor of this multifaceted system is the most relevant. The purpose of this work is to combine the interpretative power of an advanced multi-physics model of the vascular microenvironment with state of the art and robust sensitivity analysis methods, in order to determine the factors that most significantly impact quantities of interest, related in particular to cancer treatment. We are particularly interested in comparing the factors related to the microvascular architecture with the ones affecting the physics of microvascular transport. Ultimately, this work will provide further insight into how the vascular microenvironment affects cancer therapies, such as chemotherapy, radiotherapy or immunotherapy.

Using the LeiCNS-PK3.0 Physiologically-Based Pharmacokinetic Model to Predict Brain Extracellular Fluid Pharmacokinetics in Mice

INTRODUCTION

The unbound brain extracelullar fluid (brainECF) to plasma steady state partition coefficient, Kp,uu,BBB, values provide steady-state information on the extent of blood-brain barrier (BBB) transport equilibration, but not on pharmacokinetic (PK) profiles seen by the brain targets. Mouse models are frequently used to study brain PK, but this information cannot directly be used to inform on human brain PK, given the different CNS physiology of mouse and human. Physiologically based PK (PBPK) models are useful to translate PK information across species.

AIM

Use the LeiCNS-PK3.0 PBPK model, to predict brain extracellular fluid PK in mice.

METHODS

Information on mouse brain physiology was collected from literature. All available connected data on unbound plasma, brainECF PK of 10 drugs (cyclophosphamide, quinidine, erlotonib, phenobarbital, colchicine, ribociclib, topotecan, cefradroxil, prexasertib, and methotrexate) from different mouse strains were used. Dosing regimen dependent plasma PK was modelled, and Kpuu,BBB values were estimated, and provided as input into the LeiCNS-PK3.0 model to result in prediction of PK profiles in brainECF.

RESULTS

Overall, the model gave an adequate prediction of the brainECF PK profile for 7 out of the 10 drugs. For 7 drugs, the predicted versus observed brainECF data was within two-fold error limit and the other 2 drugs were within five-fold error limit.

CONCLUSION

The current version of the mouse LeiCNS-PK3.0 model seems to reasonably predict available information on brainECF from healthy mice for most drugs. This brings the translation between mouse and human brain PK one step further.

MRI-based parameter inference for cerebral perfusion modelling in health and ischaemic stroke

Cerebral perfusion modelling is a promising tool to predict the impact of acute ischaemic stroke treatments on the spatial distribution of cerebral blood flow (CBF) in the human brain. To estimate treatment efficacy based on CBF, perfusion simulations need to become suitable for group-level investigations and thus account for physiological variability between individuals. However, computational perfusion modelling to date has been restricted to a few patient-specific cases. This study set out to establish automated parameter inference for perfusion modelling based on neuroimaging data and thus enable CBF simulations of groups. Magnetic resonance imaging (MRI) data from 75 healthy senior adults were utilised. Brain geometries were computed from healthy reference subjects' T1-weighted MRI. Haemodynamic model parameters were determined from spatial CBF maps measured by arterial spin labelling (ASL) perfusion MRI. Thereafter, perfusion simulations were conducted in 75 healthy cases followed by 150 acute ischaemic stroke cases representing an occlusion and CBF cessation in the left and right middle cerebral arteries. The anatomical fitness of the brain geometries was evaluated by comparing the simulated grey (GM) and white matter (WM) volumes to measurements in healthy reference subjects. Strong positive correlations were found in both tissue types (GM: Pearson's r 0.74, P<0.001; WM: Pearson's r 0.84, P<0.001). Haemodynamic parameter tuning was verified by comparing the total volumetric blood flow rate to the brain in healthy reference subjects and simulations (Pearson's r 0.89, P<0.001). In acute ischaemic stroke cases, the simulated infarct volume using a perfusion-based estimate was 197±25 ml. Computational predictions were in agreement with anatomical and haemodynamic values from the literature concerning T1-weighted, T2-weighted, and phase-contrast MRI measurements in healthy scenarios and acute ischaemic stroke cases. The acute stroke simulations did not capture small infarcts (left tail of the distribution), which could be explained by neglected compensatory mechanisms, e.g. collaterals. The proposed parameter inference method provides a foundation for group-level CBF simulations and for in silico clinical stroke trials which could assist in medical device and drug development.

The role of leptomeningeal collaterals in redistributing blood flow during stroke

Leptomeningeal collaterals (LMCs) connect the main cerebral arteries and provide alternative pathways for blood flow during ischaemic stroke. This is beneficial for reducing infarct size and reperfusion success after treatment. However, a better understanding of how LMCs affect blood flow distribution is indispensable to improve therapeutic strategies. Here, we present a novel in silico approach that incorporates case-specific in vivo data into a computational model to simulate blood flow in large semi-realistic microvascular networks from two different mouse strains, characterised by having many and almost no LMCs between middle and anterior cerebral artery (MCA, ACA) territories. This framework is unique because our simulations are directly aligned with in vivo data. Moreover, it allows us to analyse perfusion characteristics quantitatively across all vessel types and for networks with no, few and many LMCs. We show that the occlusion of the MCA directly caused a redistribution of blood that was characterised by increased flow in LMCs. Interestingly, the improved perfusion of MCA-sided microvessels after dilating LMCs came at the cost of a reduced blood supply in other brain areas. This effect was enhanced in regions close to the watershed line and when the number of LMCs was increased. Additional dilations of surface and penetrating arteries after stroke improved perfusion across the entire vasculature and partially recovered flow in the obstructed region, especially in networks with many LMCs, which further underlines the role of LMCs during stroke.

A spatially distributed model of brain metabolism highlights the role of diffusion in brain energy metabolism

The different active roles of neurons and astrocytes during neuronal activation are associated with the metabolic processes necessary to supply the energy needed for their respective tasks at rest and during neuronal activation. Metabolism, in turn, relies on the delivery of metabolites and removal of toxic byproducts through diffusion processes and the cerebral blood flow. A comprehensive mathematical model of brain metabolism should account not only for the biochemical processes and the interaction of neurons and astrocytes, but also the diffusion of metabolites. In the present article, we present a computational methodology based on a multidomain model of the brain tissue and a homogenization argument for the diffusion processes. In our spatially distributed compartment model, communication between compartments occur both through local transport fluxes, as is the case within local astrocyte-neuron complexes, and through diffusion of some substances in some of the compartments. The model assumes that diffusion takes place in the extracellular space (ECS) and in the astrocyte compartment. In the astrocyte compartment, the diffusion across the syncytium network is implemented as a function of gap junction strength. The diffusion process is implemented numerically by means of a finite element method (FEM) based spatial discretization, and robust stiff solvers are used to time integrate the resulting large system. Computed experiments show the effects of ECS tortuosity, gap junction strength and spatial anisotropy in the astrocyte network on the brain energy metabolism.

Diameter-dependent assessment of microvascular leakage following ultrasound-mediated blood-brain barrier opening

Blood brain barrier disruption (BBBD) using focused ultrasound (FUS) and microbubbles (MB) is an effective tool for therapeutic delivery to the brain. BBBD depends to a great extent on MB oscillations. Because the brain vasculature is heterogenic in diameter, reduced MB oscillations in smaller blood vessels, together with a lower number of MBs in capillaries, can lead to variations in BBBD. Therefore, evaluating the impact of microvasculature diameter on BBBD is of great importance. We present a method to characterize molecules extravasation following FUS-mediated BBBD, at a single blood vessel resolution. Evans blue (EB) leakage was used as marker for BBBD, whereas blood vessels localization was done using FITC labeled Dextran. Automated image processing pipeline was developed to quantify the extent of extravasation as function of microvasculature diameter, including a wide range of vascular morphological parameters. Variations in MB vibrational response were observed in blood vessel mimicking fibers with varied diameters. Higher peak negative pressures (PNP) were required to initiate stable cavitation in fibers with smaller diameters. In vivo in the treated brains, EB extravasation increased as a function of blood vessel diameter. The percentage of strong BBBD blood vessels increased from 9.75% for 2-3 μm blood vessels to 91.67% for 9-10 μm. Using this method, it is possible to conduct a diameter-dependent analysis that measures vascular leakage resulting from FUS-mediated BBBD at a single blood vessel resolution.

Modeling the response of homogeneous and heterogeneous cerebral capillary networks to local changes in vessel diameters

While microvascular cerebral capillary networks are known to be highly heterogeneous, previous computational models have predicted that heterogeneous cerebral capillary flow patterns result in lower brain tissue partial oxygen pressures. Moreover, as blood flow increases, the flux among capillaries homogenizes. This homogenization of flow is expected to improve the efficiency of oxygenation extraction from the blood. In this work, we use mathematical modeling to explore a possible functional role for the high degree of heterogeneity observed in cerebral capillary networks. Our results suggest that heterogeneity allows for a greater response of tissue oxygen levels to local changes in vessel diameters due to neuronal activation. This result is confirmed for a full 3-dimensional model of capillary networks that includes oxygen diffusion within the tissue region and a reduced model that accounts for changes in capillary blood flow.

Computational models for generating microvascular structures: Investigations beyond medical imaging resolution

Angiogenesis, arteriogenesis, and pruning are revascularization processes essential to our natural vascular development and adaptation, as well as central players in the onset and development of pathologies such as tumoral growth and stroke recovery. Computational modeling allows for repeatable experimentation and exploration of these complex biological processes. In this review, we provide an introduction to the biological understanding of the vascular adaptation processes of sprouting angiogenesis, intussusceptive angiogenesis, anastomosis, pruning, and arteriogenesis, discussing some of the more significant contributions made to the computational modeling of these processes. Each computational model represents a theoretical framework for how biology functions, and with rises in computing power and study of the problem these frameworks become more accurate and complete. We highlight physiological, pathological, and technological applications that can be benefit from the advances performed by these models, and we also identify which elements of the biology are underexplored in the current state-of-the-art computational models. This article is categorized under: Cancer > Computational Models Cardiovascular Diseases > Computational Models.

Red blood cell dynamics in extravascular biological tissues modelled as canonical disordered porous media

The dynamics of blood flow in the smallest vessels and passages of the human body, where the cellular character of blood becomes prominent, plays a dominant role in the transport and exchange of solutes. Recent studies have revealed that the microhaemodynamics of a vascular network is underpinned by its interconnected structure, and certain structural alterations such as capillary dilation and blockage can substantially change blood flow patterns. However, for extravascular media with disordered microstructure (e.g. the porous intervillous space in the placenta), it remains unclear how the medium’s structure affects the haemodynamics. Here, we simulate cellular blood flow in simple models of canonical porous media representative of extravascular biological tissue, with corroborative microfluidic experiments performed for validation purposes. For the media considered here, we observe three main effects: first, the relative apparent viscosity of blood increases with the structural disorder of the medium; second, the presence of red blood cells (RBCs) dynamically alters the flow distribution in the medium; third, symmetry breaking introduced by moderate structural disorder can promote more homogeneous distribution of RBCs. Our findings contribute to a better understanding of the cell-scale haemodynamics that mediates the relationship linking the function of certain biological tissues to their microstructure.

Multifunctional nanomedicine strategies to manage brain diseases

Brain diseases represent a substantial social and economic burden, currently affecting one in six individuals worldwide. Brain research has been focus of great attention in order to unravel the pathogenesis and complexity of brain diseases at the cellular, molecular, and microenvironmental levels. Due to the intrinsic nature of the brain, the presence of the highly restrictive blood-brain barrier (BBB), and the pathophysiology of most diseases, therapies can hardly be considered successful purely by the administration of one drug to a patient. Apart from improving pharmacokinetic parameters, tailoring biodistribution, and reducing the number of side effects, nanomedicines are able to actively co-target the therapeutics to the brain parenchyma and brain lesions, as well as to achieve the delivery of multiple cargos with therapeutic, diagnostic, and theranostic properties. Among other multivalent effects that can be personalized according to the disease needs, this represents a promising class of novel nanosystems, termed multifunctional nanomedicines. Herein, we review the principal mechanisms of therapeutic resistance of the most prevalent brain diseases, how to overcome this therapeutic resistance through the use of multifunctional nanomedicines that tackle multiple fronts of the disease microenvironment, and the promising therapeutic responses achieved by some of the most cutting-edge multifunctional nanomedicines reported in literature.

The potential role of ischaemia-reperfusion injury in chronic, relapsing diseases such as rheumatoid arthritis, Long COVID, and ME/CFS: evidence, mechanisms, and therapeutic implications

Ischaemia–reperfusion (I–R) injury, initiated via bursts of reactive oxygen species produced during the reoxygenation phase following hypoxia, is well known in a variety of acute circumstances. We argue here that I–R injury also underpins elements of the pathology of a variety of chronic, inflammatory diseases, including rheumatoid arthritis, ME/CFS and, our chief focus and most proximally, Long COVID. Ischaemia may be initiated via fibrin amyloid microclot blockage of capillaries, for instance as exercise is started; reperfusion is a necessary corollary when it finishes. We rehearse the mechanistic evidence for these occurrences here, in terms of their manifestation as oxidative stress, hyperinflammation, mast cell activation, the production of marker metabolites and related activities. Such microclot-based phenomena can explain both the breathlessness/fatigue and the post-exertional malaise that may be observed in these conditions, as well as many other observables. The recognition of these processes implies, mechanistically, that therapeutic benefit is potentially to be had from antioxidants, from anti-inflammatories, from iron chelators, and via suitable, safe fibrinolytics, and/or anti-clotting agents. We review the considerable existing evidence that is consistent with this, and with the biochemical mechanisms involved.

Quantification of hypoxic regions distant from occlusions in cerebral penetrating arteriole trees

The microvasculature plays a key role in oxygen transport in the mammalian brain. Despite the close coupling between cerebral vascular geometry and local oxygen demand, recent experiments have reported that microvascular occlusions can lead to unexpected distant tissue hypoxia and infarction. To better understand the spatial correlation between the hypoxic regions and the occlusion sites, we used both in vivo experiments and in silico simulations to investigate the effects of occlusions in cerebral penetrating arteriole trees on tissue hypoxia. In a rat model of microembolisation, 25 μm microspheres were injected through the carotid artery to occlude penetrating arterioles. In representative models of human cortical columns, the penetrating arterioles were occluded by simulating the transport of microspheres of the same size and the oxygen transport was simulated using a Green’s function method. The locations of microspheres and hypoxic regions were segmented, and two novel distance analyses were implemented to study their spatial correlation. The distant hypoxic regions were found to be present in both experiments and simulations, and mainly due to the hypoperfusion in the region downstream of the occlusion site. Furthermore, a reasonable agreement for the spatial correlation between hypoxic regions and occlusion sites is shown between experiments and simulations, which indicates the good applicability of in silico models in understanding the response of cerebral blood flow and oxygen transport to microemboli.

The brain function depends on the continuous oxygen supply through the bloodstream inside the microvasculature. Occlusions in the microvascular network will disturb the oxygen delivery in the brain and result in hypoxic tissues that can lead to infarction and cognitive dysfunction. To aid in understanding the formation of hypoxic tissues caused by micro-occlusions in the penetrating arteriole trees, we use rodent experiments and simulations of human vascular networks to study the spatial correlations between the hypoxic regions and the occlusion locations. Our results suggest that hypoxic regions can form distally from the occlusion site, which agrees with the previous observations in the rat brain. These distant hypoxic regions are primarily due to the lack of blood flow in the brain tissues downstream of the occlusion. Moreover, a reasonable agreement of the spatial relationship is found between the experiments and the simulations, which indicates the applicability of in silico models to study the effects of microemboli on the brain tissue.

Spectral fiber photometry derives hemoglobin concentration changes for accurate measurement of fluorescent sensor activity

Fiber photometry is an emerging technique for recording fluorescent sensor activity in the brain. However, significant hemoglobin absorption artifacts in fiber photometry data may be misinterpreted as sensor activity changes. Because hemoglobin exists widely in the brain, and its concentration varies temporally, such artifacts could impede the accuracy of photometry recordings. Here we present use of spectral photometry and computational methods to quantify photon absorption effects by using activity-independent fluorescence signals, which can be used to derive oxy- and deoxy-hemoglobin concentration changes. Although these changes are often temporally delayed compared with the fast-responding fluorescence spikes, we found that erroneous interpretation may occur when examining pharmacology-induced sustained changes and that sometimes hemoglobin absorption could flip the GCaMP signal polarity. We provide hemoglobin-based correction methods to restore fluorescence signals and compare our results with other commonly used approaches. We also demonstrated the utility of spectral fiber photometry for delineating regional differences in hemodynamic response functions.

Fluid transport in the brain

The brain harbors a unique ability to, figuratively speaking, shift its gears. During wakefulness, the brain is geared fully toward processing information and behaving, while homeostatic functions predominate during sleep. The blood-brain barrier establishes a stable environment that is optimal for neuronal function, yet the barrier imposes a physiological problem; transcapillary filtration that forms extracellular fluid in other organs is reduced to a minimum in brain. Consequently, the brain depends on a special fluid [the cerebrospinal fluid (CSF)] that is flushed into brain along the unique perivascular spaces created by astrocytic vascular endfeet. We describe this pathway, coined the term glymphatic system, based on its dependency on astrocytic vascular endfeet and their adluminal expression of aquaporin-4 water channels facing toward CSF-filled perivascular spaces. Glymphatic clearance of potentially harmful metabolic or protein waste products, such as amyloid-β, is primarily active during sleep, when its physiological drivers, the cardiac cycle, respiration, and slow vasomotion, together efficiently propel CSF inflow along periarterial spaces. The brain's extracellular space contains an abundance of proteoglycans and hyaluronan, which provide a low-resistance hydraulic conduit that rapidly can expand and shrink during the sleep-wake cycle. We describe this unique fluid system of the brain, which meets the brain's requisites to maintain homeostasis similar to peripheral organs, considering the blood-brain-barrier and the paths for formation and egress of the CSF.

From a Demand-Based to a Supply-Limited Framework of Brain Metabolism

What defines the rate of energy use by the brain, as well as per neurons of different sizes in different structures and animals, is one fundamental aspect of neuroscience for which much has been theorized, but very little data are available. The prevalent theories and models consider that energy supply from the vascular system to different brain regions is adjusted both dynamically and in the course of development and evolution to meet the demands of neuronal activity. In this perspective, we offer an alternative view: that regional rates of energy use might be mostly constrained by supply, given the properties of the brain capillary network, the highly stable rate of oxygen delivery to the whole brain under physiological conditions, and homeostatic constraints. We present evidence that these constraints, based on capillary density and tissue oxygen homeostasis, are similar between brain regions and mammalian species, suggesting they derive from fundamental biophysical limitations. The same constraints also determine the relationship between regional rates of brain oxygen supply and usage over the full physiological range of brain activity, from deep sleep to intense sensory stimulation, during which the apparent uncoupling of blood flow and oxygen use is still a predicted consequence of supply limitation. By carefully separating "energy cost" into energy supply and energy use, and doing away with the problematic concept of energetic "demands," our new framework should help shine a new light on the neurovascular bases of metabolic support of brain function and brain functional imaging. We speculate that the trade-offs between functional systems and even the limitation to a single attentional spot at a time might be consequences of a strongly supply-limited brain economy. We propose that a deeper understanding of brain energy supply constraints will provide a new evolutionary understanding of constraints on brain function due to energetics; offer new diagnostic insight to disturbances of brain metabolism; lead to clear, testable predictions on the scaling of brain metabolic cost and the evolution of brains of different sizes; and open new lines of investigation into the microvascular bases of progressive cognitive loss in normal aging as well as metabolic diseases.

Quantitative Analysis of DCE and DSC-MRI: From Kinetic Modeling to Deep Learning

BACKGROUND

 Perfusion MRI is a well-established imaging modality with a multitude of applications in oncological and cardiovascular imaging. Clinically used processing methods, while stable and robust, have remained largely unchanged in recent years. Despite promising results from novel methods, their relatively minimal improvement compared to established methods did not generally warrant significant changes to clinical perfusion processing.

RESULTS AND CONCLUSION

 Machine learning in general and deep learning in particular, which are currently revolutionizing computer-aided diagnosis, may carry the potential to change this situation and truly capture the potential of perfusion imaging. Recent advances in the training of recurrent neural networks make it possible to predict and classify time series data with high accuracy. Combining physics-based tissue models and deep learning, using either physics-informed neural networks or universal differential equations, simplifies the training process and increases the interpretability of the resulting models. Due to their versatility, these methods will potentially be useful in bridging the gap between microvascular architecture and perfusion parameters, akin to MR fingerprinting in structural MR imaging. Still, further research is urgently needed before these methods may be used in clinical practice.

KEY POINTS

· Machine learning offers promising methods for processing of perfusion data.. · Recurrent neural networks can classify time series with high accuracy.. · Data augmentation is essentially especially when using small datasets..

CITATION FORMAT

· Rotkopf LT, Zhang KS, Tavakoli AA et al. Quantitative Analysis of DCE and DSC-MRI: From Kinetic Modeling to Deep Learning. Fortschr Röntgenstr 2022; DOI: 10.1055/a-1762-5854.

A few upstream bifurcations drive the spatial distribution of red blood cells in model microfluidic networks

The physics of blood flow in small vessel networks is dominated by the interactions between Red Blood Cells (RBCs), plasma and blood vessel walls. The resulting couplings between the microvessel network architecture and the heterogeneous distribution of RBCs at network-scale are still poorly understood. The main goal of this paper is to elucidate how a local effect, such as RBC partitioning at individual bifurcations, interacts with the global structure of the flow field to induce specific preferential locations of RBCs in model microfluidic networks. First, using experimental results, we demonstrate that persistent perturbations to the established hematocrit profile after diverging bifurcations may bias RBC partitioning at the next bifurcations. By performing a sensitivity analysis based upon network models of RBC flow, we show that these perturbations may propagate from bifurcation to bifurcation, leading to an outsized impact of a few crucial upstream bifurcations on the distribution of RBCs at network-scale. Based on measured hematocrit profiles, we further construct a modified RBC partitioning model that accounts for the incomplete relaxation of RBCs at these bifurcations. This model allows us to explain how the flow field results in a single pattern of RBC preferential location in some networks, while it leads to the emergence of two different patterns of RBC preferential location in others. Our findings have important implications in understanding and modeling blood flow in physiological and pathological conditions.

Novel, Emerging Chip Models of the Blood-Brain Barrier and Future Directions

The use of microfluidic chips is now allowing for more advanced modelling of the blood-brain barrier (BBB) in vitro, recapitulating heterotypic interactions, 3D architecture, and physiological flow. This chapter will give an introduction to these new technologies and how they are being applied to model the BBB and neurovascular unit (NVU). A foundational understanding of the fluid dynamics germane to the effective use of these chips will be set and an overview of how physical phenomena at the microscale can be exploited to enable new possibilities to control the cell culture environment. The four main approaches to construct microfluidic blood vessel mimetics will be discussed with examples of how these techniques are being applied to model the BBB and more recently to study specific neurovascular disease processes. Finally, practical guidance will be given for researchers wishing to adopt these new techniques along with a summary of the challenges, limitations faced, and new opportunities opened up by these advanced cell culture systems.

Network-driven anomalous transport is a fundamental component of brain microvascular dysfunction

Blood microcirculation supplies neurons with oxygen and nutrients, and contributes to clearing their neurotoxic waste, through a dense capillary network connected to larger tree-like vessels. This complex microvascular architecture results in highly heterogeneous blood flow and travel time distributions, whose origin and consequences on brain pathophysiology are poorly understood. Here, we analyze highly-resolved intracortical blood flow and transport simulations to establish the physical laws governing the macroscopic transport properties in the brain micro-circulation. We show that network-driven anomalous transport leads to the emergence of critical regions, whether hypoxic or with high concentrations of amyloid-β, a waste product centrally involved in Alzheimer's Disease. We develop a Continuous-Time Random Walk theory capturing these dynamics and predicting that such critical regions appear much earlier than anticipated by current empirical models under mild hypoperfusion. These findings provide a framework for understanding and modelling the impact of microvascular dysfunction in brain diseases, including Alzheimer's Disease.

Parallel generation of extensive vascular networks with application to an archetypal human kidney model

Given the relevance of the inextricable coupling between microcirculation and physiology, and the relation to organ function and disease progression, the construction of synthetic vascular networks for mathematical modelling and computer simulation is becoming an increasingly broad field of research. Building vascular networks that mimic in vivo morphometry is feasible through algorithms such as constrained constructive optimization (CCO) and variations. Nevertheless, these methods are limited by the maximum number of vessels to be generated due to the whole network update required at each vessel addition. In this work, we propose a CCO-based approach endowed with a domain decomposition strategy to concurrently create vascular networks. The performance of this approach is evaluated by analysing the agreement with the sequentially generated networks and studying the scalability when building vascular networks up to 200 000 vascular segments. Finally, we apply our method to vascularize a highly complex geometry corresponding to the cortex of a prototypical human kidney. The technique presented in this work enables the automatic generation of extensive vascular networks, removing the limitation from previous works. Thus, we can extend vascular networks (e.g. obtained from medical images) to pre-arteriolar level, yielding patient-specific whole-organ vascular models with an unprecedented level of detail.

Arterial blood stealing as a mechanism of negative BOLD response: From the steady-flow with nonlinear phase separation to a windkessel-based model

Blood Oxygen Level Dependent (BOLD) signal indirectly characterizes neuronal activity by measuring hemodynamic and metabolic changes in the nearby microvasculature. A deeper understanding of how localized changes in electrical, metabolic and hemodynamic factors translate into a BOLD signal is crucial for the interpretation of functional brain imaging techniques. While positive BOLD responses (PBR) are widely considered to be linked with neuronal activation, the origins of negative BOLD responses (NBR) have remained largely unknown. As NBRs are sometimes observed in close proximity of regions with PBR, a blood "stealing" effect, i.e., redirection of blood from a passive periphery to the area with high neuronal activity, has been postulated. In this study, we used the Hagen-Poiseuille equation to model hemodynamics in an idealized microvascular network that account for the particulate nature of blood and nonlinearities arising from the red blood cell (RBC) distribution (i.e., the Fåhraeus, Fåhraeus-Lindqvist and the phase separation effects). Using this detailed model, we evaluate determinants driving this "stealing" effect in a microvascular network with geometric parameters within physiological ranges. Model simulations predict that during localized cerebral blood flow (CBF) increases due to neuronal activation-hyperemic response, blood from surrounding vessels is reallocated towards the activated region. This stealing effect depended on the resistance of the microvasculature and the uneven distribution of RBCs at vessel bifurcations. A parsimonious model consisting of two-connected windkessel regions sharing a supplying artery was proposed to simulate the stealing effect with a minimum number of parameters. Comparison with the detailed model showed that the parsimonious model can reproduce the observed response for hematocrit values within the physiological range for different species. Our novel parsimonious model promise to be of use for statistical inference (top-down analysis) from direct blood flow measurements (e.g., arterial spin labeling and laser Doppler/Speckle flowmetry), and when combined with theoretical models for oxygen extraction/diffusion will help account for some types of NBRs.

Segmentation-Less, Automated, Vascular Vectorization

Recent advances in two-photon fluorescence microscopy (2PM) have allowed large scale imaging and analysis of blood vessel networks in living mice. However, extracting network graphs and vector representations for the dense capillary bed remains a bottleneck in many applications. Vascular vectorization is algorithmically difficult because blood vessels have many shapes and sizes, the samples are often unevenly illuminated, and large image volumes are required to achieve good statistical power. State-of-the-art, three-dimensional, vascular vectorization approaches often require a segmented (binary) image, relying on manual or supervised-machine annotation. Therefore, voxel-by-voxel image segmentation is biased by the human annotator or trainer. Furthermore, segmented images oftentimes require remedial morphological filtering before skeletonization or vectorization. To address these limitations, we present a vectorization method to extract vascular objects directly from unsegmented images without the need for machine learning or training. The Segmentation-Less, Automated, Vascular Vectorization (SLAVV) source code in MATLAB is openly available on GitHub. This novel method uses simple models of vascular anatomy, efficient linear filtering, and vector extraction algorithms to remove the image segmentation requirement, replacing it with manual or automated vector classification. Semi-automated SLAVV is demonstrated on three in vivo 2PM image volumes of microvascular networks (capillaries, arterioles and venules) in the mouse cortex. Vectorization performance is proven robust to the choice of plasma- or endothelial-labeled contrast, and processing costs are shown to scale with input image volume. Fully-automated SLAVV performance is evaluated on simulated 2PM images of varying quality all based on the large (1.4×0.9×0.6 mm3 and 1.6×108 voxel) input image. Vascular statistics of interest (e.g. volume fraction, surface area density) calculated from automatically vectorized images show greater robustness to image quality than those calculated from intensity-thresholded images.

Metabolic Signaling in a Theoretical Model of the Human Retinal Microcirculation

Impaired blood flow and oxygenation contribute to many ocular pathologies, including glaucoma. Here, a mathematical model is presented that combines an image-based heterogeneous representation of retinal arterioles with a compartmental description of capillaries and venules. The arteriolar model of the human retina is extrapolated from a previous mouse model based on confocal microscopy images. Every terminal arteriole is connected in series to compartments for capillaries and venules, yielding a hybrid model for predicting blood flow and oxygenation throughout the retinal microcirculation. A metabolic wall signal is calculated in each vessel according to blood and tissue oxygen levels. As expected, a higher average metabolic signal is generated in pathways with a lower average oxygen level. The model also predicts a wide range of metabolic signals dependent on oxygen levels and specific network location. For example, for high oxygen demand, a threefold range in metabolic signal is predicted despite nearly identical PO2 levels. This whole-network approach, including a spatially nonuniform structure, is needed to describe the metabolic status of the retina. This model provides the geometric and hemodynamic framework necessary to predict ocular blood flow regulation and will ultimately facilitate early detection and treatment of ischemic and metabolic disorders of the eye.

Imaging faster neural dynamics with fast fMRI: A need for updated models of the hemodynamic response

Fast fMRI enables the detection of neural dynamics over timescales of hundreds of milliseconds, suggesting it may provide a new avenue for studying subsecond neural processes in the human brain. The magnitudes of these fast fMRI dynamics are far greater than predicted by canonical models of the hemodynamic response. Several studies have established nonlinear properties of the hemodynamic response that have significant implications for fast fMRI. We first review nonlinear properties of the hemodynamic response function that may underlie fast fMRI signals. We then illustrate the breakdown of canonical hemodynamic response models in the context of fast neural dynamics. We will then argue that the canonical hemodynamic response function is not likely to reflect the BOLD response to neuronal activity driven by sparse or naturalistic stimuli or perhaps to spontaneous neuronal fluctuations in the resting state. These properties suggest that fast fMRI is capable of tracking surprisingly fast neuronal dynamics, and we discuss the neuroscientific questions that could be addressed using this approach.

The Ageing Brain: Investigating the Role of Age in Changes to the Human Cerebral Microvasculature With an in silico Model

Ageing causes extensive structural changes to the human cerebral microvasculature, which have a significant effect on capillary bed perfusion and oxygen transport. Current models of brain capillary networks in the literature focus on healthy adult brains and do not capture the effects of ageing, which is critical when studying neurodegenerative diseases. This study builds upon a statistically accurate model of the human cerebral microvasculature based on ex-vivo morphological data. This model is adapted for “healthy” ageing using in-vivo measurements from mice at three distinct age groups—young, middle-aged, and old. From this new model, blood and molecular exchange parameters are calculated such as permeability and surface-area-to-volume ratio, and compared across the three age groups. The ability to alter the model vessel-by-vessel is used to create a continuous gradient of ageing. It was found that surface-area-to-volume ratio reduced in old age by 6% and permeability by 24% from middle-age to old age, and variability within the networks also increased with age. The ageing gradient indicated a threshold in the ageing process around 75 years old, after which small changes have an amplified effect on blood flow properties. This gradient enables comparison of studies measuring cerebral properties at discrete points in time. The response of middle aged and old aged capillary beds to micro-emboli showed a lower robustness of the old age capillary bed to vessel occlusion. As the brain ages, there is thus increased vulnerability of the microvasculature—with a “tipping point” beyond which further remodeling of the microvasculature has exaggerated effects on the brain. When developing in-silico models of the brain, age is a very important consideration to accurately assess risk factors for cognitive decline and isolate early biomarkers of microvascular health.

Simulation of angiogenesis in three dimensions: Application to cerebral cortex

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.

Mathematical modeling of cerebral capillary blood flow heterogeneity and its effect on brain tissue oxygen levels

Maintaining cerebral blood flow is critical for adequate neuronal function. Previous computational models of brain capillary networks have predicted that heterogeneous cerebral capillary flow patterns result in lower brain tissue partial oxygen pressures PO2). However, these previous models have often considered simple capillary networks in terms of their geometric properties. In this current work, we developed and analyzed computational models of brain capillary networks to determine how perturbations of network properties impact tissue oxygen levels. The models include variabilities in both their geometric (segment lengths and diameters) and three-dimensional, topological structure. Two classes of capillary network models are considered. The first consists of equations for the oxygen partial pressure, PO₂, in both a capillary network and the surrounding tissue. In order to gain insight into the behavior of this detailed model, we also consider a reduced model for changes in PO₂ in just the capillary network. The main result is that for a general class of networks, random perturbations of either segment diameters or conductances will always, on average, decrease the average tissue oxygen levels. This result is supported through both simulations of the models and mathematical analysis. Our results promise to expand our understanding of cerebral capillary blood flow and its impact on the brain function in health and disease.

The severity of microstrokes depends on local vascular topology and baseline perfusion

Cortical microinfarcts are linked to pathologies like cerebral amyloid angiopathy and dementia. Despite their relevance for disease progression, microinfarcts often remain undetected and the smallest scale of blood flow disturbance has not yet been identified. We employed blood flow simulations in realistic microvascular networks from the mouse cortex to quantify the impact of single-capillary occlusions. Our simulations reveal that the severity of a microstroke is strongly affected by the local vascular topology and the baseline flow rate in the occluded capillary. The largest changes in perfusion are observed in capillaries with two inflows and two outflows. This specific topological configuration only occurs with a frequency of 8%. The majority of capillaries have one inflow and one outflow and is likely designed to efficiently supply oxygen and nutrients. Taken together, microstrokes bear potential to induce a cascade of local disturbances in the surrounding tissue, which might accumulate and impair energy supply locally.

3D Imaging and Quantitative Characterization of Mouse Capillary Coronary Network Architecture

Simple Summary

The cardiovascular system is composed of two physically and functionally linked parts, the heart and the vascular network, composed of the arteries, capillaries, and veins. In this system, the heart maintains the blood flow, including its own through the coronary vascular network, bringing oxygen and nutrients required for its activity. Microvascularization constitutes the distal part of this network and is composed of small vessels, i.e., arterioles and capillaries. Coronary microvascular diseases are associated with the development of cardiac dysfunction. Identification of the coronary microvascular network structure is hence of critical importance for the understanding of heart diseases. The aim of our study was to establish an accessible methodology for 3D imaging and 3D processing to quantitatively characterize the capillary coronary network architecture in mice, a species largely used as an animal model of cardiac failure. This study proposes a standardized methodology for 3D image processing that allows the quantification of the 3D capillary architecture. Based on an open source software, the whole process is easily accessible for biologists. It is hence useful for the study of cardiovascular diseases and the development of future therapies.

Abstract

Characterization of the cardiac capillary network structure is of critical importance to understand the normal coronary functional properties and coronary microvascular diseases. The aim of our study was to establish an accessible methodology for 3D imaging and 3D processing to quantitatively characterize the capillary coronary network architecture in mice. Experiments were done on C57BL/6J mice. 3D imaging was performed by light sheet microscopy and confocal microscopy on iDISCO+ optical cleared hearts after labelling of the capillary endothelium by lectin injection. 3D images were processed with the open source software ImageJ. Non-visual image segmentation was based of the frequency distribution of the voxel greyscale values, followed by skeletonization and distance mapping. Capillary networks in left and right ventricles and septum were characterized by the volume network density, the fractal dimension, the number of segments and nodes and their ratio, the total network length, and the average length, diameter, and tortuosity of the segments. Scale-dependent parameter values can be impacted by the resolution limit of the 3D imaging technique. The proposed standardized methodology for 3D image processing is easily accessible for a biologist in terms of investment and difficulty level, and allows the quantification of the 3D capillary architecture and its statistical comparison in different conditions.

The capillary fascicle in skeletal muscle: Structural and functional physiology of RBC distribution in capillary networks

KEY POINTS

The capillary module, consisting of parallel capillaries from arteriole to venule, is classically considered as the building block of complex capillary networks. In skeletal muscle, this structure fails to address how blood flow is regulated along the entire length of the synchronously contracting muscle fibres. Using intravital video microscopy of resting extensor digitorum longus muscle in rats, we demonstrated the capillary fascicle as a series of interconnected modules forming continuous columns that align naturally with the dimensions of the muscle fascicle. We observed structural heterogeneity for module topology, and functional heterogeneity in space and time for capillary-red blood cell (RBC) haemodynamics within a module and between modules. We found that module RBC haemodynamics were independent of module resistance, providing direct evidence for microvascular flow regulation at the level of the capillary module. The capillary fascicle is an updated paradigm for characterizing blood flow and RBC distribution in skeletal muscle capillary networks.

ABSTRACT

Capillary networks are the fundamental site of oxygen exchange in the microcirculation. The capillary module (CM), consisting of parallel capillaries from terminal arteriole (TA) to post-capillary venule (PCV), is classically considered as the building block of complex capillary networks. In skeletal muscle, this structure fails to address how blood flow is regulated along the entire length of the synchronously contracting muscle fibres, requiring co-ordination from numerous modules. It has previously been recognized that TAs and PCVs interact with multiple CMs, creating interconnected networks. Using label-free intravital video microscopy of resting extensor digitorum longus muscle in rats, we found that these networks form continuous columns of linked CMs spanning thousands of microns, herein denoted as the capillary fascicle (CF); this structure aligns naturally with the dimensions of the muscle fascicle. We measured capillary-red blood cell (RBC) haemodynamics and module topology (n = 9 networks, 327 modules, 1491 capillary segments). The average module had length 481 μm, width 157 μm and 9.51 parallel capillaries. We observed structural heterogeneity for CM topology, and functional heterogeneity in space and time for capillary-RBC haemodynamics within a module and between modules. There was no correlation between capillary RBC velocity and lineal density. A passive inverse relationship between module length and haemodynamics was remarkably absent, providing direct evidence for microvascular flow regulation at the level of the CM. In summary, the CF is an updated paradigm for characterizing RBC distribution in skeletal muscle, and strengthens the theory of capillary networks as major contributors to the signal that regulates capillary perfusion.

A porous circulation model of the human brain for in silico clinical trials in ischaemic stroke

The advancement of ischaemic stroke treatment relies on resource-intensive experiments and clinical trials. In order to improve ischaemic stroke treatments, such as thrombolysis and thrombectomy, we target the development of computational tools for in silico trials which can partially replace these animal and human experiments with fast simulations. This study proposes a model that will serve as part of a predictive unit within an in silico clinical trial estimating patient outcome as a function of treatment. In particular, the present work aims at the development and evaluation of an organ-scale microcirculation model of the human brain for perfusion prediction. The model relies on a three-compartment porous continuum approach. Firstly, a fast and robust method is established to compute the anisotropic permeability tensors representing arterioles and venules. Secondly, vessel encoded arterial spin labelling magnetic resonance imaging and clustering are employed to create an anatomically accurate mapping between the microcirculation and large arteries by identifying superficial perfusion territories. Thirdly, the parameter space of the problem is reduced by analysing the governing equations and experimental data. Fourthly, a parameter optimization is conducted. Finally, simulations are performed with the tuned model to obtain perfusion maps corresponding to an open and an occluded (ischaemic stroke) scenario. The perfusion map in the occluded vessel scenario shows promising qualitative agreement with computed tomography images of a patient with ischaemic stroke caused by large vessel occlusion. The results highlight that in the case of vessel occlusion (i) identifying perfusion territories is essential to capture the location and extent of underperfused regions and (ii) anisotropic permeability tensors are required to give quantitatively realistic estimation of perfusion change. In the future, the model will be thoroughly validated against experiments.

Quantification of Capillary Perfusion in an Animal Model of Acute Intracranial Hypertension

Intracranial hypertension (IH) is a common feature of many pathologies, including brain edema. In the brain, the extended network of capillaries ensures blood flow to meet local metabolic demands. Capillary circulation may be severely affected by IH, but no studies have quantified the effect of intracranial pressure (ICP) and cerebral perfusion pressure (CPP) on capillary perfusion during the development of brain edema. We used optical coherence tomography angiography to quantify relative changes of fractional perfused volume (FPV) in cortical capillaries and simultaneously monitored ICP and blood pressure (BP) in anesthetized male C57Bl/6NTac mice during development of brain edema induced by water intoxication (WI) within 30 min. WI induced severe IH and brain herniation. ICP and CPP reached 90.2 mm Hg and 38.4 mm Hg, respectively. FPV was significantly affected already at normal ICP (ICP <15 mm Hg, slope ≈ -1.46, p < 0.001) and, at the onset of IH (ICP = 20-22 mm Hg), FPV was 17.9 ± 13.3% lower than baseline. A decreasing trend was observed until the ICP peak (Δ%FPV = -43.6 ± 19.2%). In the ICP range of 7-42 mm Hg, relative changes in FPV were significantly correlated with ICP, BP, and CPP (p < 0.001), with ICP and CPP being the best predictors. In conclusion, elevated ICP induces a gradual collapse of the cerebral microvasculature, which is initiated before the clinical threshold of IH. In summary, the estimate of capillary perfusion might be essential in patients with IH to assess the state of the brain microcirculation and to improve the availability of oxygen and nutrients to the brain.

Angiogenic biomaterials to promote therapeutic regeneration and investigate disease progression

The vasculature is a key component of the tissue microenvironment. Traditionally known for its role in providing nutrients and oxygen to surrounding cells, the vasculature is now also acknowledged to provide signaling cues that influence biological outcomes in regeneration and disease. These cues come from the cells that comprise vasculature, as well as the dynamic biophysical and biochemical properties of the surrounding extracellular matrix that accompany vascular development and remodeling. In this review, we illustrate the larger role of the vasculature in the context of regenerative biology and cancer progression. We describe cellular, biophysical, biochemical, and metabolic components of vascularized microenvironments. Moreover, we provide an overview of multidimensional angiogenic biomaterials that have been developed to promote therapeutic vascularization and regeneration, as well as to mimic elements of vascularized microenvironments as a means to uncover mechanisms by which vasculature influences cancer progression and therapy.

The mass transfer coefficient for oxygen transport from blood to tissue in cerebral cortex

The functioning of cerebral cortex depends on adequate tissue oxygenation. MRI-based techniques allow estimation of blood oxygen levels, tissue perfusion, and oxygen consumption rate (CMRO₂), but do not directly measure partial pressure of oxygen (PO₂) in tissue. To address the estimation of tissue PO₂, the oxygen mass transfer coefficient (KTO₂) is here defined as the CMRO₂ divided by the difference in spatially averaged PO₂ between blood and tissue, and is estimated by analyzing Krogh-cylinder type models. Resistance to radial diffusion of oxygen from microvessels to tissue is distributed within vessels and in the extravascular tissue. The value of KTO₂ is shown to depend strongly on vascular length density and also on microvessel tube hematocrits and diameters, but to be insensitive to blood flow rate and to transient changes in flow or oxygen consumption. Estimated values of KTO₂ are higher than implied by previous studies, implying smaller declines in PO₂ from blood to tissue. Average tissue PO₂ can be estimated from MRI-based measurements as average blood PO₂ minus the product of KTO₂ and CMRO₂. For oxygen consumption rates and vascular densities typical of mouse cortex, the predicted difference between average blood and tissue PO₂ is about 10 mmHg.

Interactive visualization and analysis of morphological skeletons of brain vasculature networks with VessMorphoVis

MOTIVATION

Accurate morphological models of brain vasculature are key to modeling and simulating cerebral blood flow in realistic vascular networks. This in silico approach is fundamental to revealing the principles of neurovascular coupling. Validating those vascular morphologies entails performing certain visual analysis tasks that cannot be accomplished with generic visualization frameworks. This limitation has a substantial impact on the accuracy of the vascular models employed in the simulation.

RESULTS

We present VessMorphoVis, an integrated suite of toolboxes for interactive visualization and analysis of vast brain vascular networks represented by morphological graphs segmented originally from imaging or microscopy stacks. Our workflow leverages the outstanding potentials of Blender, aiming to establish an integrated, extensible and domain-specific framework capable of interactive visualization, analysis, repair, high-fidelity meshing and high-quality rendering of vascular morphologies. Based on the initial feedback of the users, we anticipate that our framework will be an essential component in vascular modeling and simulation in the future, filling a gap that is at present largely unfulfilled.

AVAILABILITY AND IMPLEMENTATION

VessMorphoVis is freely available under the GNU public license on Github at https://github.com/BlueBrain/VessMorphoVis. The morphology analysis, visualization, meshing and rendering modules are implemented as an add-on for Blender 2.8 based on its Python API (application programming interface). The add-on functionality is made available to users through an intuitive graphical user interface, as well as through exhaustive configuration files calling the API via a feature-rich command line interface running Blender in background mode.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

High fat diet worsens Alzheimer's disease-related behavioral abnormalities and neuropathology in APP/PS1 mice, but not by synergistically decreasing cerebral blood flow

Obesity is linked to increased risk for and severity of Alzheimer's disease (AD). Cerebral blood flow (CBF) reductions are an early feature of AD and are also linked to obesity. We recently showed that non-flowing capillaries, caused by adhered neutrophils, contribute to CBF reduction in mouse models of AD. Because obesity could exacerbate the vascular inflammation likely underlying this neutrophil adhesion, we tested links between obesity and AD by feeding APP/PS1 mice a high fat diet (Hfd) and evaluating behavioral, physiological, and pathological changes. We found trends toward poorer memory performance in APP/PS1 mice fed a Hfd, impaired social interactions with either APP/PS1 genotype or a Hfd, and synergistic impairment of sensory-motor function in APP/PS1 mice fed a Hfd. The Hfd led to increases in amyloid-beta monomers and plaques in APP/PS1 mice, as well as increased brain inflammation. These results agree with previous reports showing obesity exacerbates AD-related pathology and symptoms in mice. We used a crowd-sourced, citizen science approach to analyze imaging data to determine the impact of the APP/PS1 genotype and a Hfd on capillary stalling and CBF. Surprisingly, we did not see an increase in the number of non-flowing capillaries or a worsening of the CBF deficit in APP/PS1 mice fed a Hfd as compared to controls, suggesting that capillary stalling is not a mechanistic link between a Hfd and increased severity of AD in mice. Reducing capillary stalling by blocking neutrophil adhesion improved CBF and short-term memory function in APP/PS1 mice, even when fed a Hfd.

A topological encoding convolutional neural network for segmentation of 3D multiphoton images of brain vasculature using persistent homology

The clinical evidence suggests that cognitive disorders are associated with vasculature dysfunction and decreased blood flow in the brain. Hence, a functional understanding of the linkage between brain functionality and the vascular network is essential. However, methods to systematically and quantitatively describe and compare structures as complex as brain blood vessels are lacking. 3D imaging modalities such as multiphoton microscopy enables researchers to capture the network of brain vasculature with high spatial resolutions. Nonetheless, image processing and inference are some of the bottlenecks for biomedical research involving imaging, and any advancement in this area impacts many research groups. Here, we propose a topological encoding convolutional neural network based on persistent homology to segment 3D multiphoton images of brain vasculature. We demonstrate that our model out-performs state-of-the-art models in terms of the Dice coefficient and it is comparable in terms of other metrics such as sensitivity. Additionally, the topological characteristics of our model's segmentation results mimic manual ground truth. Our code and model are open source at https://github.com/mhaft/DeepVess.

The cerebral angiome: High resolution MicroCT imaging of the whole brain cerebrovasculature in female and male mice

The cerebrovascular system provides crucial functions that maintain metabolic and homeostatic states of the brain. Despite its integral role of supporting cerebral viability, the topological organization of these networks remains largely uncharacterized. This void in our knowledge surmises entirely from current technological limitations that prevent the capturing of data through the entire depth of the brain. We report high-resolution reconstruction and analysis of the complete vascular network of the entire brain at the capillary level in adult female and male mice using a vascular corrosion cast procedure. Vascular network analysis of the whole brain revealed sex-related differences of vessel hierarchy. In addition, region-specific network analysis demonstrated different patterns of angioarchitecture between brain subregions and sex. Furthermore, our group is the first to provide a three-dimensional analysis of the angioarchitecture and network organization in a single reconstructed tomographic data set that encompasses all hierarchy of vessels in the brain of the adult mouse.