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.

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.

Quantification of blood flow patterns in the cerebral arterial circulation of individual (human) subjects.

There is a growing research interest in quantifying blood flow distribution for the entire cerebral circulation to sharpen diagnosis and improve treatment options for cerebrovascular disease of individual patients. We present a methodology to reconstruct subject-specific cerebral blood flow patterns in accordance with physiological and fluid mechanical principles and optimally informed by in vivo neuroimage data of cerebrovascular anatomy and arterial blood flow rates. We propose an inverse problem to infer blood flow distribution across the visible portion of the arterial network that best matches subject-specific anatomy and a given set of volumetric flow measurements. The optimization technique also mitigates the effect of uncertainties by reconciling incomplete flow data and by dissipating unavoidable acquisition errors associated with medical imaging data.

Mathematical synthesis of the cortical circulation for the whole mouse brain-part I. theory and image integration.

Microcirculation plays a significant role in cerebral metabolism and blood flow control, yet explaining and predicting functional mechanisms remains elusive because it is difficult to make physiologically accurate mathematical models of the vascular network. As a precursor to the human brain, this paper presents a computational framework for synthesizing anatomically accurate network models for the cortical blood supply in mouse. It addresses two critical deficiencies in cerebrovascular modeling. At the microscopic length scale of individual capillaries, we present a novel synthesis method for building anatomically consistent capillary networks with loops and anastomoses (=microcirculatory closure). This overcomes shortcomings in existing algorithms which are unable to create closed circulatory networks. A second critical innovation allows the incorporation of detailed anatomical features from image data into vascular growth. Specifically, computed tomography and two photon laser scanning microscopy data are input into the novel synthesis algorithm to build the cortical circulation for the entire mouse brain in silico. Computer predictions of blood flow and oxygen exchange executed on synthetic large-scale network models are expected to elucidate poorly understood functional mechanisms of the cerebral circulation.

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.

Modeling the diffusion of D-2-hydroxyglutarate from IDH1 mutant gliomas in the central nervous system.

Background: Among diffusely infiltrative gliomas in adults, 20%-30% contain a point mutation in isocitrate dehydrogenase 1 (IDH1mut), which increases production of D-2-hydroxyglutarate (D2HG). This is so efficient that D2HG often reaches 30 mM within IDH1mut gliomas. Yet, while up to 100 µM D2HG can be detected in the circulating cerebrospinal fluid of IDH1mut glioma patients, the exposure of nonneoplastic cells within and surrounding an IDH1mut glioma to D2HG is unknown and difficult to measure directly. Methods: Conditioned medium from patient-derived wild type IDH1 (IDH1wt) and IDH1mut glioma cells was analyzed for D2HG by liquid chromatography-mass spectrometry (LC-MS). Mathematical models of D2HG release and diffusion around an IDH1mut glioma were independently generated based on fluid dynamics within the brain and on previously reported intratumoral and cerebrospinal D2HG concentrations. Results: LC-MS analysis indicates that patient-derived IDH1mut glioma cells release 3.7-97.0 pg D2HG per cell per week. Extrapolating this to an average-sized tumor (30 mL glioma volume and 1 × 108 cells/mL tumor), the rate of D2HG release by an IDH1mut glioma (SA) is estimated at 3.2-83.0 × 10-12 mol/mL/sec. Mathematical models estimate an SA of 2.9-12.9 × 10-12 mol/mL/sec, within the range of the in vitro LC-MS data. In even the most conservative of these models, the extracellular concentration of D2HG exceeds 3 mM within a 2 cm radius from the center of an IDH1mut glioma. Conclusions: The microenvironment of an IDH1mut glioma is likely being exposed to high concentrations of D2HG, in the low millimolar range. This has implications for understanding how D2HG affects nonneoplastic cells in an IDH1mut glioma.

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.

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.