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

Vascular synthesis based on hemodynamic efficiency principle recapitulates measured cerebral circulation properties in the human brain

Quantifying anatomical and hemodynamical properties of the brain vasculature in vivo is difficult due to limited spatiotemporal resolution neuroimaging, variability between subjects, and bias between acquisition techniques. This work introduces a metabolically inspired vascular synthesis algorithm for creating a digital representation of the cortical blood supply in humans. Spatial organization and segment resistances of a cortical vascular network were generated. Cortical folding and macroscale arterial and venous vessels were reconstructed from anatomical MRI and MR angiography. The remaining network, including ensembles representing the parenchymal capillary bed, were synthesized following a mechanistic principle based on hydrodynamic efficiency of the cortical blood supply. We evaluated the digital model by comparing its simulated values with in vivo healthy human brain measurements of macrovessel blood velocity from phase contrast MRI and capillary bed transit times and bolus arrival times from dynamic susceptibility contrast. We find that measured and simulated values reasonably agree and that relevant neuroimaging observables can be recapitulated in silico. This work provides a basis for describing and testing quantitative aspects of the cerebrovascular circulation that are not directly observable. Future applications of such digital brains include the investigation of the organ-wide effects of simulated vascular and metabolic pathologies.

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.

Cerebral perfusion simulation using realistically generated synthetic trees for healthy and stroke patients

BACKGROUND AND OBJECTIVE

Cerebral vascular diseases are among the most burdensome diseases faced by society. However, investigating the pathophysiology of diseases as well as developing future treatments still relies heavily on expensive in-vivo and in-vitro studies. The generation of realistic, patient-specific models of the cerebrovascular system capable of simulating hemodynamics and perfusion promises the ability to simulate diseased states, therefore accelerating development cycles using in silico studies and opening opportunities for the individual assessment of diseased states, treatment planning, and the prediction of outcomes. By providing a patient-specific, anatomically detailed and validated model of the human cerebral vascular system, we aim to provide the basis for future in silico investigations of the cerebral physiology and pathology.

METHODS

In this retrospective study, a processing pipeline for patient-specific quantification of cerebral perfusion was developed and applied to healthy individuals and a stroke patient. Major arteries are segmented from 3T MR angiography data. A synthetic tree generation algorithm titled tissue-growth based optimization (GBO)1 is used to extend vascular trees beyond the imaging resolution. To investigate the anatomical accuracy of the generated trees, morphological parameters are compared against those of 7 T MRI, 9.4 T MRI, and dissection data. Using the generated vessel model, hemodynamics and perfusion are simulated by solving one-dimensional blood flow equations combined with Darcy flow equations.

RESULTS

Morphological data of three healthy individuals (mean age 47 years ± 15.9 [SD], 2 female) was analyzed. Bifurcation and physiological characteristics of the synthetically generated vessels are comparable to those of dissection data. The inability of MRI based segmentation to resolve small branches and the small volume investigated cause a mismatch in the comparison to MRI data. Cerebral perfusion was estimated for healthy individuals and a stroke patient. The simulated perfusion is compared against Arterial-Spin-Labeling MRI perfusion data. Good qualitative agreement is found between simulated and measured cerebral blood flow (CBF)2. Ischemic regions are predicted well, however ischemia severity is overestimated.

CONCLUSIONS

GBO successfully generates detailed cerebral vascular models with realistic morphological parameters. Simulations based on the resulting networks predict perfusion territories and ischemic regions successfully.

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.

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.

Imaging of the pial arterial vasculature of the human brain in vivo using high-resolution 7T time-of-flight angiography

The pial arterial vasculature of the human brain is the only blood supply to the neocortex, but quantitative data on the morphology and topology of these mesoscopic arteries (diameter 50–300 µm) remains scarce. Because it is commonly assumed that blood flow velocities in these vessels are prohibitively slow, non-invasive time-of-flight magnetic resonance angiography (TOF-MRA)—which is well suited to high 3D imaging resolutions—has not been applied to imaging the pial arteries. Here, we provide a theoretical framework that outlines how TOF-MRA can visualize small pial arteries in vivo, by employing extremely small voxels at the size of individual vessels. We then provide evidence for this theory by imaging the pial arteries at 140 µm isotropic resolution using a 7 Tesla (T) magnetic resonance imaging (MRI) scanner and prospective motion correction, and show that pial arteries one voxel width in diameter can be detected. We conclude that imaging pial arteries is not limited by slow blood flow, but instead by achievable image resolution. This study represents the first targeted, comprehensive account of imaging pial arteries in vivo in the human brain. This ultra-high-resolution angiography will enable the characterization of pial vascular anatomy across the brain to investigate patterns of blood supply and relationships between vascular and functional architecture.

Personalized 0D-1D multiscale hemodynamic modeling and wave dynamics analysis of cerebral circulation for an elderly patient with dementia

Senile dementia is associated with pronounced alterations in cerebral circulation. A fundamental understanding of intracranial hemodynamics and wave dynamics is essential for assessing dementia risk. Recent findings suggest that higher carotid artery wave intensity (WI) can predict future cognitive impairments in the elderly. However, wave power (WP) is more advantageous for assessing the risk of cognitive impairment and dementia because of its conservative form, which allows quantification of detailed WP distribution among the entire cerebrovascular network. Unfortunately, intracranial hemodynamics and wave dynamics in elderly patients with dementia remain poorly understood due to ethical issues and technical challenges. In this paper, we proposed a novel and easily achievable personalized methodology for the 0D-1D model of cerebral circulation using widely available clinical data on transcranial Doppler ultrasonography velocity, cerebral artery anatomy from magnetic resonance imaging, and brachial artery pressure. Using the proposed model, we simulated the cerebral blood flows and compared the wave dynamics between a healthy elderly subject and one living with dementia. Moreover, we performed a variance-based global sensitivity analysis to quantify the model-predicted WI and WP sensitivity to the uncertainties of model inputs. This provided more precise information for model personalization and further insights into the wave dynamics of cerebral circulation. In conclusion, the proposed personalized model framework provides a practical approach for patient-specific modeling and WI/WP analysis of cerebral circulation through noninvasive clinical data. The wave dynamics features of higher WI and lower WP in cerebral arteries may be an invaluable biomarker for assessing dementia risk.

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.

Distinct association between cerebral arterial pulsatility and subtypes of cerebral small vessel disease

Background

Increased arterial resistance is a potential pathological mechanism of cerebral small vessel disease (cSVD).

Aim

In this study, we aimed to investigate the association between pulsatility index (PI) representing cerebral arterial resistance and subtypes of cSVD in patients with lacunar stroke.

Methods

We included consecutive lacunar stroke patients between 2010 and 2013. White matter hyperintensity (WMH) volume was rated using semi-automated quantitative methods. Additionally, the presence of old lacunar infarct (OLI), cerebral microbleed (CMB), or enlarged perivascular space (EPVS) was also evaluated. The relationship between PI, measured in each middle cerebral artery, and the subtype/burden of cSVD was analyzed in the relevant hemisphere.

Results

A total of 206 lacunar patients were included and 412 hemispheres were analyzed (mean age: 64 years, male: 68.4%). In multivariable analysis, PI was positively associated with the WMH volume [beta = 1.372, 95% confidence interval (CI) = 0.624 to 2.120, P < 0.001] after adjusting for confounders. PI was also related to the presence of OLI (adjusted odds ratio = 11.37, 95% CI = 2.55–48.56, P = 0.001); however, this relationship was not significant in CMB or EPVS. Regarding the cSVD burden, PI increased according to the WMH tertiles (P for trend < 0.001), the burden of OLI (P for trend < 0.001), and EPVS tertiles (P for trend < 0.001), showing a quantitative relationship.

Conclusions

Ipsilateral PI is closely associated with cSVD in patients with lacunar stroke. Furthermore, this association is different between subtypes of cSVD, which is suggestive of underlying pathophysiological differences.