Impact of stalling events on microcirculatory hemodynamics in the aged brain.

OBJECTIVE: The role of cerebral microvasculature in cognitive dysfunction can be investigated by identifying the impact of blood flow on cortical tissue oxygenation. In this paper, the impact of capillary stalls on microcirculatory characteristics such as flow and hematocrit (Ht) in the cortical angioarchitecture is studied. METHODS: Using a deterministic mathematical model to simulate blood flow in a realistic mouse cortex, hemodynamics parameters, including pressure, flow, vessel diameter-adjustable hematocrit, and transit time are calculated as a function of stalling events. RESULTS: Using a non-linear plasma skimming model, it is observed that Ht increases in the penetrating arteries from the pial vessels as a function of cortical depth. The incidence of stalling on Ht distribution along the blood network vessels shows reduction of RBCs around the tissue near occlusion sites and decreased Ht concentration downstream from the blockage points. Moreover, upstream of the occlusion, there is a noticeable increase of the Ht, leading to larger flow resistance due to higher blood viscosity. We predicted marked changes in transit time behavior due to stalls which match trends observed in mice in vivo. CONCLUSIONS: These changes to blood cell quantity and quality may be implicated in the development of Alzheimer's disease and contribute to the course of the illness.

Constitutive relationship and governing physical properties for magnetophoresis.

Magnetophoresis is an important physical process with application to drug delivery, biomedical imaging, separation, and mixing. Other than empirically, little is known about how the magnetic field and magnetic properties of a solution affect the flux of magnetic particles. A comprehensive explanation of these effects on the transport of magnetic particles has not been developed yet. Here we formulate a consistent, constitutive equation for the magnetophoretic flux of magnetic nanoparticles suspended in a medium exposed to a stationary magnetic field. The constitutive relationship accounts for contributions from magnetic diffusion, magnetic convection, residual magnetization, and electromagnetic drift. We discovered that the key physical properties governing the magnetophoresis are magnetic diffusion coefficient, magnetic velocity, and activity coefficient, which depend on relative magnetic energy and the molar magnetic susceptibility of particles. The constitutive equation also reveals previously unknown ballistic and diffusive limits for magnetophoresis wherein the paramagnetic particles either aggregate near the magnet or diffusive away from the magnet, respectively. In the diffusive limit, the particle concentration is linearly proportional to the relative magnetic energy of the suspension of paramagnetic particles. The region of the localization of paramagnetic particles near the magnet decreases with increasing the strength of the magnet. The dynamic accumulation of nanoparticles, measured as the thickness of the nanoparticle aggregate, near the magnet compares well with the theoretical prediction. The effect of convective mixing on the rate of magnetophoresis is also discussed for the magnetic targeting applications.

Voxelized simulation of cerebral oxygen perfusion elucidates hypoxia in aged mouse cortex.

Departures of normal blood flow and metabolite distribution from the cerebral microvasculature into neuronal tissue have been implicated with age-related neurodegeneration. Mathematical models informed by spatially and temporally distributed neuroimage data are becoming instrumental for reconstructing a coherent picture of normal and pathological oxygen delivery throughout the brain. Unfortunately, current mathematical models of cerebral blood flow and oxygen exchange become excessively large in size. They further suffer from boundary effects due to incomplete or physiologically inaccurate computational domains, numerical instabilities due to enormous length scale differences, and convergence problems associated with condition number deterioration at fine mesh resolutions. Our proposed simple finite volume discretization scheme for blood and oxygen microperfusion simulations does not require expensive mesh generation leading to the critical benefit that it drastically reduces matrix size and bandwidth of the coupled oxygen transfer problem. The compact problem formulation yields rapid and stable convergence. Moreover, boundary effects can effectively be suppressed by generating very large replica of the cortical microcirculation in silico using an image-based cerebrovascular network synthesis algorithm, so that boundaries of the perfusion simulations are far removed from the regions of interest. Massive simulations over sizeable portions of the cortex with feature resolution down to the micron scale become tractable with even modest computer resources. The feasibility and accuracy of the novel method is demonstrated and validated with in vivo oxygen perfusion data in cohorts of young and aged mice. Our oxygen exchange simulations quantify steep gradients near penetrating blood vessels and point towards pathological changes that might cause neurodegeneration in aged brains. This research aims to explain mechanistic interactions between anatomical structures and how they might change in diseases or with age. Rigorous quantification of age-related changes is of significant interest because it might aide in the search for imaging biomarkers for dementia and Alzheimer's disease.

Mathematical synthesis of the cortical circulation for the whole mouse brain-part II: Microcirculatory closure.

Recent advancements in multiphoton imaging and vascular reconstruction algorithms have increased the amount of data on cerebrovascular circulation for statistical analysis and hemodynamic simulations. Experimental observations offer fundamental insights into capillary network topology but mainly within a narrow field of view typically spanning a small fraction of the cortical surface (less than 2%). In contrast, larger-resolution imaging modalities, such as computed tomography (CT) or magnetic resonance imaging (MRI), have whole-brain coverage but capture only larger blood vessels, overlooking the microscopic capillary bed. To integrate data acquired at multiple length scales with different neuroimaging modalities and to reconcile brain-wide macroscale information with microscale multiphoton data, we developed a method for synthesizing hemodynamically equivalent vascular networks for the entire cerebral circulation. This computational approach is intended to aid in the quantification of patterns of cerebral blood flow and metabolism for the entire brain. In part I, we described the mathematical framework for image-guided generation of synthetic vascular networks covering the large cerebral arteries from the circle of Willis through the pial surface network leading back to the venous sinuses. Here in part II, we introduce novel procedures for creating microcirculatory closure that mimics a realistic capillary bed. We demonstrate our capability to synthesize synthetic vascular networks whose morphometrics match empirical network graphs from three independent state-of-the-art imaging laboratories using different image acquisition and reconstruction protocols. We also successfully synthesized twelve vascular networks of a complete mouse brain hemisphere suitable for performing whole-brain blood flow simulations. Synthetic arterial and venous networks with microvascular closure allow whole-brain hemodynamic predictions. Simulations across all length scales will potentially illuminate organ-wide supply and metabolic functions that are inaccessible to models reconstructed from image data with limited spatial coverage.

Simulations of blood as a suspension predicts a depth dependent hematocrit in the circulation throughout the cerebral cortex.

Recent advances in modeling oxygen supply to cortical brain tissue have begun to elucidate the functional mechanisms of neurovascular coupling. While the principal mechanisms of blood flow regulation after neuronal firing are generally known, mechanistic hemodynamic simulations cannot yet pinpoint the exact spatial and temporal coordination between the network of arteries, arterioles, capillaries and veins for the entire brain. Because of the potential significance of blood flow and oxygen supply simulations for illuminating spatiotemporal regulation inside the cortical microanatomy, there is a need to create mathematical models of the entire cerebral circulation with realistic anatomical detail. Our hypothesis is that an anatomically accurate reconstruction of the cerebrocirculatory architecture will inform about possible regulatory mechanisms of the neurovascular interface. In this article, we introduce large-scale networks of the murine cerebral circulation spanning the Circle of Willis, main cerebral arteries connected to the pial network down to the microcirculation in the capillary bed. Several multiscale models were generated from state-of-the-art neuroimaging data. Using a vascular network construction algorithm, the entire circulation of the middle cerebral artery was synthesized. Blood flow simulations indicate a consistent trend of higher hematocrit in deeper cortical layers, while surface layers with shorter vascular path lengths seem to carry comparatively lower red blood cell (RBC) concentrations. Moreover, the variability of RBC flux decreases with cortical depth. These results support the notion that plasma skimming serves a self-regulating function for maintaining uniform oxygen perfusion to neurons irrespective of their location in the blood supply hierarchy. Our computations also demonstrate the practicality of simulating blood flow for large portions of the mouse brain with existing computer resources. The efficient simulation of blood flow throughout the entire middle cerebral artery (MCA) territory is a promising milestone towards the final aim of predicting blood flow patterns for the entire brain.

Automatic recognition of subject-specific cerebrovascular trees.

PURPOSE: An image filter designed for reconstructing cerebrovascular trees from MR images is described. Current imaging techniques capture major cerebral vessels reliably, but often fail to detect small vessels, whose contrast is suppressed due to limited resolution, slow blood flow rate, and distortions around bifurcations or nonvascular structures. An incomplete view of angioarchitecture limits the information available to physicians. METHODS: A novel Hessian-based filter for contrast-enhancement in MR angiography and venography for blood vessel reconstruction without introducing dangling segments is presented. We quantify filter performance with receiver-operating-characteristic and dice-similarity-coefficient analysis. Total extracted vascular length, number-of-segments, volume, surface-to-distance, and positional error are calculated for validation. RESULTS: Reconstruction of cerebrovascular trees from MR images of six volunteers show that the new filter renders more complete representations of subject-specific cerebrovascular networks. Validation with phantom models shows the filter correctly detects blood vessels across all length scales without failing at bifurcations or distorting diameters. CONCLUSION: The novel filter can potentially improve the diagnosis of cerebrovascular diseases by delivering metrics and anatomy of the vasculature. It also facilitates the automated analysis of large datasets by computing biometrics free of operator subjectivity. The high quality reconstruction enables computational mesh generation for subject-specific hemodynamic simulations. Magn Reson Med 77:398-410, 2017. © 2016 Wiley Periodicals, Inc.

Image-guidance technology and the surgical resection of spinal column tumors.

Precision imaging is paramount to achieving success in surgical resection of many spinal tumors, whether the goal involves guiding a surgical cure for primary tumors or improving neurological decompression for metastatic lesions. Pre-operatively, image visualization is intimately involved with defining a clear target and surgical planning. Intra-operatively, image-guidance technology allows for surgeons to maximize the probability for gross total resection of spinal cord tumors and minimize damage to adjacent structures. Through this review, it is evident that spinal surgery has undergone significant advancements with the continued technological progression of different modalities of imaging guided technologies. Sophisticated imaging techniques compliment the surgeon's knowledge by providing an intraoperative reference to spinal column anatomy. This review discusses research efforts focusing on immersive imaging guided interactions with subject specific medical images that could enhance a surgeon's ability to plan and perform complex spinal oncology procedures with safety and efficiency.

Computational and In Vitro Experimental Investigation of Intrathecal Drug Distribution: Parametric Study of the Effect of Injection Volume, Cerebrospinal Fluid Pulsatility, and Drug Uptake.

BACKGROUND: Intrathecal drug delivery is an attractive option to circumvent the blood-brain barrier for pain management through its increased efficacy of pain relief, reduction in adverse side effects, and cost-effectiveness. Unfortunately, there are limited guidelines for physicians to choose infusion or drug pump settings to administer therapeutic doses to specific regions of the spine or the brain. Although empiric trialing of intrathecal drugs is critical to determine the sustained side effects, currently there is no inexpensive in vitro method to guide the selection of spinal drug delivery parameters. The goal of this study is to demonstrate current computational capabilities to predict drug biodistribution while varying 3 parameters: (1) infusion settings, (2) drug chemistry, and (3) subject-specific anatomy and cerebrospinal fluid dynamics. We will discuss strategies to systematically optimize these 3 parameters to administer drug molecules to targeted tissue locations in the central nervous system. METHODS: We acquired anatomical data from magnetic resonance imaging (MRI) and velocity measurements in the spinal cerebrospinal fluid with CINE-MRI for 2 subjects. A bench-top surrogate of the subject-specific central nervous system was constructed to match measured anatomical dimensions and volumes. We generated a computational mesh for the bench-top model. Idealized simulations of tracer distribution were compared with bench-top measurements for validation. Using reconstructions from MRI data, we also introduced a subject-specific computer model for predicting drug spread for the human volunteer. RESULTS: MRI velocity measurements at 3 spinal regions of interest reasonably matched the simulated flow fields in a subject-specific computer mesh. Comparison between the idealized spine computations and bench-top tracer distribution experiments demonstrate agreement of our drug transport predictions to this physical model. Simulated multibolus drug infusion theoretically localizes drug to the cervical and thoracic region. Continuous drug pump and single bolus injection were successful to target the lumbar spine in the simulations. The parenchyma might be targeted suitably by multiple boluses followed by a flush infusion. We present potential guidelines that take into account drug specific kinetics for tissue uptake, which influence the speed of drug dispersion in the model and potentially influence tissue targeting. CONCLUSIONS: We present potential guidelines considering drug-specific kinetics of tissue uptake, which determine the speed of drug dispersion and influence tissue targeting. However, there are limitations to this analysis in that the parameters were obtained from an idealized healthy patient in a supine position. The proposed methodology could assist physicians to select clinical infusion parameters for their patients and provide guidance to optimize treatment algorithms. In silico optimization of intrathecal drug delivery therapies presents the first steps toward a possible care paradigm in the future that is specific to personalized patient anatomy and diseases.

Starling forces drive intracranial water exchange during normal and pathological states.

AIM: To quantify the exchange of water between cerebral compartments, specifically blood, tissue, perivascular pathways, and cerebrospinal fluid-filled spaces, on the basis of experimental data and to propose a dynamic global model of water flux through the entire brain to elucidate functionally relevant fluid exchange phenomena. METHODS: The mechanistic computer model to predict brain water shifts is discretized by cerebral compartments into nodes. Water and species flux is calculated between these nodes across a network of arcs driven by Hagen-Poiseuille flow (blood), Darcy flow (interstitial fluid transport), and Starling's Law (transmembrane fluid exchange). Compartment compliance is accounted for using a pressure-volume relationship to enforce the Monro-Kellie doctrine. This nonlinear system of differential equations is solved implicitly using MATLAB software. RESULTS: The model predictions of intraventricular osmotic injection caused a pressure rise from 10 to 22 mmHg, followed by a taper to 14 mmHg over 100 minutes. The computational results are compared to experimental data with R2=0.929. Moreover, simulated osmotic therapy of systemic (blood) injection reduced intracranial pressure from 25 to 10 mmHg. The modeled volume and intracranial pressure changes following cerebral edema agree with experimental trends observed in animal models with R2=0.997. CONCLUSION: The model successfully predicted time course and the efficacy of osmotic therapy for clearing cerebral edema. Furthermore, the mathematical model implicated the perivascular pathways as a possible conduit for water and solute exchange. This was a first step to quantify fluid exchange throughout the brain.

Hydrocephalus: the role of cerebral aquaporin-4 channels and computational modeling considerations of cerebrospinal fluid.

Aquaporin-4 (AQP4) channels play an important role in brain water homeostasis. Water transport across plasma membranes has a critical role in brain water exchange of the normal and the diseased brain. AQP4 channels are implicated in the pathophysiology of hydrocephalus, a disease of water imbalance that leads to CSF accumulation in the ventricular system. Many molecular aspects of fluid exchange during hydrocephalus have yet to be firmly elucidated, but review of the literature suggests that modulation of AQP4 channel activity is a potentially attractive future pharmaceutical therapy. Drug therapy targeting AQP channels may enable control over water exchange to remove excess CSF through a molecular intervention instead of by mechanical shunting. This article is a review of a vast body of literature on the current understanding of AQP4 channels in relation to hydrocephalus, details regarding molecular aspects of AQP4 channels, possible drug development strategies, and limitations. Advances in medical imaging and computational modeling of CSF dynamics in the setting of hydrocephalus are summarized. Algorithmic developments in computational modeling continue to deepen the understanding of the hydrocephalus disease process and display promising potential benefit as a tool for physicians to evaluate patients with hydrocephalus.

Hematocrit distribution and tissue oxygenation in large microcirculatory networks.

OBJECTIVE: Oxygen tension in the brain is controlled by the microcirculatory supply of RBC, but the effect of non-Newtonian blood flow rheology on tissue oxygenation is not well characterized. This study assesses different biphasic blood flow models for predicting tissue oxygen tension as a function of microcirculatory hemodynamics. METHODS: Two existing plasma-skimming laws are compared against measured RBC distributions in rat and hamster microcirculatory networks. A novel biphasic blood flow model is introduced. The computational models predict tissue oxygenation in the mesentery, cremaster muscle, and the human secondary cortex. RESULTS: This investigation shows deficiencies in prior models, including inconsistent plasma-skimming trends and insufficient oxygen perfusion due to the high prevalence (33%) of RBC-free microvessels. Our novel method yields physiologically sound RBC distributions and tissue oxygen tensions within one standard deviation of experimental measurements. CONCLUSIONS: A simple, novel biphasic blood flow model is introduced with equal or better predictive power when applied to historic raw data sets. It can overcome limitations of prior models pertaining to trifurcations, anastomoses, and loops. This new plasma-skimming law eases the computations of bulk blood flow and hematocrit fields in large microcirculatory networks and converges faster than prior procedures.

Current status of intratumoral therapy for glioblastoma.

With emerging drug delivery technologies becoming accessible, more options are expected to become available to patients with glioblastoma (GBM) in the near future. It is important for clinicians to be familiar with the underlying mechanisms and limitations of intratumoral drug delivery, and direction of recent research efforts. Tumor-adjacent brain is an extremely complex living matrix that creates challenges with normal tissue intertwining with tumor cells. For convection-enhanced delivery (CED), the role of tissue anisotropy for better predicting the biodistribution of the infusate has recently been studied. Computational predictive methods are now available to better plan CED therapy. Catheter design and placement­in addition to the agent being used­are critical components of any protocol. This paper overviews intratumoral therapies for GBM, highlighting key anatomic and physiologic perspectives, selected agents (especially immunotoxins), and some new developments such as the description of the glymphatic system.

Intramedullary spinal cord tumors: a review of current and future treatment strategies.

Intramedullary spinal cord tumors have low incidence rates but are associated with difficult treatment options. The majority of patients with these tumors can be initially treated with an attempted resection. Unfortunately, those patients who cannot undergo gross-total resection or have subtotal resection are left with few treatment options, such as radiotherapy and chemotherapy. These adjuvant treatments, however, are associated with the potential for significant adverse side effects and still leave patients with a poor prognosis. To successfully manage these patients and improve both their quality of life and prognosis, novel treatment options must be developed to supplement subtotal resection. New research is underway investigating alternative therapeutic approaches for these patients, including directed, localized drug delivery and nanomedicine techniques. These and other future investigations will hopefully lead to promising new therapies for these devastating diseases.

Dynamic regulation of aquaporin-4 water channels in neurological disorders.

Aquaporin-4 water channels play a central role in brain water regulation in neurological disorders. Aquaporin-4 is abundantly expressed at the astroglial endfeet facing the cerebral vasculature and the pial membrane, and both its expression level and subcellular localization significantly influence brain water transport. However, measurements of aquaporin-4 levels in animal models of brain injury often report opposite trends of change at the injury core and the penumbra. Furthermore, aquaporin-4 channels play a beneficial role in brain water clearance in vasogenic edema, but a detrimental role in cytotoxic edema and exacerbate cell swelling. In light of current evidence, we still do not have a complete understanding of the role of aquaporin-4 in brain water transport. In this review, we propose that the regulatory mechanisms of aquaporin-4 at the transcriptional, translational, and post-translational levels jointly regulate water permeability in the short and long time scale after injury. Furthermore, in order to understand why aquaporin-4 channels play opposing roles in cytotoxic and vasogenic edema, we discuss experimental evidence on the dynamically changing osmotic gradients between blood, extracellular space, and the cytosol during the formation of cytotoxic and vasogenic edema. We conclude with an emerging picture of the distinct osmotic environments in cytotoxic and vasogenic edema, and propose that the directions of aquaporin-4-mediated water clearance in these two types of edema are distinct. The difference in water clearance pathways may provide an explanation for the conflicting observations of the roles of aquaporin-4 in edema resolution.

A computational model of cerebrospinal fluid production and reabsorption driven by Starling forces.

Experimental evidence has cast doubt on the classical model of river-like cerebrospinal fluid (CSF) flow from the choroid plexus to the arachnoid granulations. We propose a novel model of water transport through the parenchyma from the microcirculation as driven by Starling forces. This model investigates the effect of osmotic pressure on water transport between the cerebral vasculature, the extracellular space (ECS), the perivascular space (PVS), and the CSF. A rigorous literature search was conducted focusing on experiments which alter the osmolarity of blood or ventricles and measure the rate of CSF production. Investigations into the effect of osmotic pressure on the volume of ventricles and the flux of ions in the blood, choroid plexus epithelium, and CSF are reviewed. Increasing the osmolarity of the serum via a bolus injection completely inhibits nascent fluid flow production in the ventricles. A continuous injection of a hyperosmolar solution into the ventricles can increase the volume of the ventricle by up to 125%. CSF production is altered by 0.231 µL per mOsm in the ventricle and by 0.835 µL per mOsm in the serum. Water flux from the ECS to the CSF is identified as a key feature of intracranial dynamics. A complete mathematical model with all equations and scenarios is fully described, as well as a guide to constructing a computational model of intracranial water balance dynamics. The model proposed in this article predicts the effects the osmolarity of ECS, blood, and CSF on water flux in the brain, establishing a link between osmotic imbalances and pathological conditions such as hydrocephalus and edema.

Phase contrast reflectance confocal brain imaging at 1650 nm.

Significance: The imaging depth of microscopy techniques is limited by the ability of light to penetrate biological tissue. Recent research has addressed this limitation by combining a reflectance confocal microscope with the NIR-II (or shortwave infrared) spectrum. This approach offers significant imaging depth, is straightforward in design, and remains cost-effective. However, the imaging system, which relies on intrinsic signals, could benefit from adjustments in its optical design and post-processing methods to differentiate cortical cells, such as neurons and small blood vessels. Aim: We implemented a phase contrast detection scheme to a reflectance confocal microscope using NIR-II spectral range as illumination. Approach: We analyzed the features retrieved in the images while testing the imaging depth. Moreover, we introduce an acquisition method for distinguishing dynamic signals from the background, allowing the creation of vascular maps similar to those produced by optical coherence tomography. Results: The phase contrast implementation is successful to retrieve deep images in the cortex up to 800 µm using a cranial window. Vascular maps were retrieved at similar cortical depth and the possibility of combining multiple images can provide a vessel network. Conclusions: Phase contrast reflectance confocal microscopy can improve the outlining of cortical cell bodies. With the presented framework, angiograms can be retrieved from the dynamic signal in the biological tissue. Our work presents an optical implementation and analysis techniques from a former microscope design.

Evaluation of cerebral microcirculation in a mouse model of systemic inflammation.

Significance: Perturbations in the microcirculatory system have been observed in neurological conditions, such as Alzheimer's disease or systemic inflammation. However, changes occurring at the level of the capillary are difficult to translate to biomarkers that could be measured macroscopically. Aim: We aim to evaluate whether transit time changes reflect capillary stalling and to what degree. Approach: We employ a combined spectral optical coherence tomography (OCT) and fluorescence optical imaging (FOI) system to investigate the relation between capillary stalling and transit time in a mouse model of systemic inflammation induced by intraperitoneal injection of lipopolysaccharide. Angiograms are obtained using OCT, and fluorescence signal images are acquired by the FOI system upon intravenous injection of fluorescein isothiocyanate via a catheter inserted into the tail vein. Results: Our findings reveal that lipopolysaccharide (LPS) administration significantly increases both the percentage and duration of capillary stalling compared to mice receiving a 0.9% saline injection. Moreover, LPS-induced mice exhibit significantly prolonged arteriovenous transit time compared to control mice. Conclusions: These observations suggest that capillary stalling, induced by inflammation, modulates cerebral mean transit time, a measure that has translational potential.

Functional Assessment of Cerebral Capillaries using Single Capillary Reporters in Ultrasound Localization Microscopy.

The brain's microvascular cerebral capillary network plays a vital role in maintaining neuronal health, yet capillary dynamics are still not well understood due to limitations in existing imaging techniques. Here, we present Single Capillary Reporters (SCaRe) for transcranial Ultrasound Localization Microscopy (ULM), a novel approach enabling non-invasive, whole-brain mapping of single capillaries and estimates of their transit-time as a neurovascular biomarker. We accomplish this first through computational Monte Carlo and ultrasound simulations of microbubbles flowing through a fully-connected capillary network. We unveil distinct capillary flow behaviors which informs methodological changes to ULM acquisitions to better capture capillaries in vivo. Subsequently, applying SCaRe-ULM in vivo, we achieve unprecedented visualization of single capillary tracks across brain regions, analysis of layer-specific capillary heterogeneous transit times (CHT), and characterization of whole microbubble trajectories from arterioles to venules. Lastly, we evaluate capillary biomarkers using injected lipopolysaccharide to induce systemic neuroinflammation and track the increase in SCaRe-ULM CHT, demonstrating the capability to detect subtle capillary functional changes. SCaRe-ULM represents a significant advance in studying microvascular dynamics, offering novel avenues for investigating capillary patterns in neurological disorders and potential diagnostic applications.

MESH-FREE HIGH-RESOLUTION SIMULATION OF CEREBROCORTICAL OXYGEN SUPPLY WITH FAST FOURIER PRECONDITIONING.

Oxygen transfer from blood vessels to cortical brain tissue is representative of a class of problems with mixed-domain character. Large-scale efficient computation of tissue oxygen concentration is dependent on the manner in which the tubular network of blood vessels is coupled to the tissue mesh. Models which explicitly resolve the interface between the tissue and vasculature with a contiguous mesh are prohibitively expensive for very dense cerebral microvasculature. We propose a mixed-domain mesh-free technique whereby a vascular anatomical network (VAN) represented as a thin directed graph serves for convection of blood oxygen, and the surrounding extravascular tissue is represented as a Cartesian grid of 3D voxels throughout which oxygen is transported by diffusion. We split the network and tissue meshes by the Schur complement method of domain decomposition to obtain a reduced set of system equations for the tissue oxygen concentration. The use of a Cartesian grid allows the corresponding matrix equation to be solved approximately with a fast Fourier transform based Poisson solver, which serves as an effective preconditioner for Krylov subspace iteration. The performance of this method enables the steady state simulation of cortical oxygen perfusion for anatomically accurate vascular networks down to single micron resolution without the need for supercomputers. Practitioner Points: We present a novel mixed-domain framework for efficiently modeling O 2 extraction kinetics in the brain. Model equations are generated by graph-theoretic methods for mixed domains.Dual mesh domain decomposition with FFT preconditioning yields very fast simulation times for extremely high spatial resolution.

Mesh-free high-resolution simulation of cerebrocortical oxygen supply with fast Fourier preconditioning.

Oxygen transfer from blood vessels to cortical brain tissue is representative of a class of problems with mixed-domain character. Large-scale efficient computation of tissue oxygen concentration is dependent on the manner in which the tubular network of blood vessels is coupled to the tissue mesh. Models which explicitly resolve the interface between the tissue and vasculature with a contiguous mesh are prohibitively expensive for very dense cerebral microvasculature. We propose a mixed-domain mesh-free technique whereby a vascular anatomical network (VAN) represented as a thin directed graph serves for convection of blood oxygen, and the surrounding extravascular tissue is represented as a Cartesian grid of 3D voxels throughout which oxygen is transported by diffusion. We split the network and tissue meshes by the Schur complement method of domain decomposition to obtain a reduced set of system equations for the tissue oxygen concentration at steady state. The use of a Cartesian grid allows the corresponding matrix equation to be solved approximately with a fast Fourier transform-based Poisson solver, which serves as an effective preconditioner for Krylov subspace iteration. The performance of this method enables the steady-state simulation of cortical oxygen perfusion for anatomically accurate vascular networks down to single micron resolution without the need for supercomputers.