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

A fully synthetic three-dimensional human cerebrovascular model based on histological characteristics to investigate the hemodynamic fingerprint of the layer BOLD fMRI signal formation

Recent advances in functional magnetic resonance imaging (fMRI) at ultra-high field (≥7 tesla), novel hardware, and data analysis methods have enabled detailed research on neurovascular function, such as cortical layer-specific activity, in both human and nonhuman species. A widely used fMRI technique relies on the blood oxygen level-dependent (BOLD) signal. BOLD fMRI offers insights into brain function by measuring local changes in cerebral blood volume, cerebral blood flow, and oxygen metabolism induced by increased neuronal activity. Despite its potential, interpreting BOLD fMRI data is challenging as it is only an indirect measurement of neuronal activity. Computational modeling can help interpret BOLD data by simulating the BOLD signal formation. Current developments have focused on realistic 3D vascular models based on rodent data to understand the spatial and temporal BOLD characteristics. While such rodent-based vascular models highlight the impact of the angioarchitecture on the BOLD signal amplitude, anatomical differences between the rodent and human vasculature necessitate the development of human-specific models. Therefore, a computational framework integrating human cortical vasculature, hemodynamic changes, and biophysical properties is essential. Here, we present a novel computational approach: a three-dimensional VAscular MOdel based on Statistics (3D VAMOS), enabling the investigation of the hemodynamic fingerprint of the BOLD signal within a model encompassing a fully synthetic human 3D cortical vasculature and hemodynamics. Our algorithm generates microvascular and macrovascular architectures based on morphological and topological features from the literature on human cortical vasculature. By simulating specific oxygen saturation states and biophysical interactions, our framework characterizes the intravascular and extravascular signal contributions across cortical depth and voxel-wise levels for gradient-echo and spin-echo readouts. Thereby, the 3D VAMOS computational framework demonstrates that using human characteristics significantly affects the BOLD fingerprint, making it an essential step in understanding the fundamental underpinnings of layer-specific fMRI experiments.

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.

In Silico Design of Heterogeneous Microvascular Trees Using Generative Adversarial Networks and Constrained Constructive Optimization

OBJECTIVE

Designing physiologically adequate microvascular trees is of crucial relevance for bioengineering functional tissues and organs. Yet, currently available methods are poorly suited to replicate the morphological and topological heterogeneity of real microvascular trees because the parameters used to control tree generation are too simplistic to mimic results of the complex angiogenetic and structural adaptation processes in vivo.

METHODS

We propose a method to overcome this limitation by integrating a conditional deep convolutional generative adversarial network (cDCGAN) with a local fractal dimension-oriented constrained constructive optimization (LFDO-CCO) strategy. The cDCGAN learns the patterns of real microvascular bifurcations allowing for their artificial replication. The LFDO-CCO strategy connects the generated bifurcations hierarchically to form microvascular trees with a vessel density corresponding to that observed in healthy tissues.

RESULTS

The generated artificial microvascular trees are consistent with real microvascular trees regarding characteristics such as fractal dimension, vascular density, and coefficient of variation of diameter, length, and tortuosity.

CONCLUSIONS

These results support the adoption of the proposed strategy for the generation of artificial microvascular trees in tissue engineering as well as for computational modeling and simulations of microcirculatory physiology.

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.

A Deep Learning Approach for Improving Two-Photon Vascular Imaging Speeds

A potential method for tracking neurovascular disease progression over time in preclinical models is multiphoton fluorescence microscopy (MPM), which can image cerebral vasculature with capillary-level resolution. However, obtaining high-quality, three-dimensional images with traditional point scanning MPM is time-consuming and limits sample sizes for chronic studies. Here, we present a convolutional neural network-based (PSSR Res-U-Net architecture) algorithm for fast upscaling of low-resolution or sparsely sampled images and combine it with a segmentation-less vectorization process for 3D reconstruction and statistical analysis of vascular network structure. In doing so, we also demonstrate that the use of semi-synthetic training data can replace the expensive and arduous process of acquiring low- and high-resolution training pairs without compromising vectorization outcomes, and thus open the possibility of utilizing such approaches for other MPM tasks where collecting training data is challenging. We applied our approach to images with large fields of view from a mouse model and show that our method generalizes across imaging depths, disease states and other differences in neurovasculature. Our pretrained models and lightweight architecture can be used to reduce MPM imaging time by up to fourfold without any changes in underlying hardware, thereby enabling deployability across a range of settings.

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.

Microvascular Specificity of Spin Echo BOLD fMRI: Impact of EPI Echo Train Length

A spatially specific fMRI acquisition requires specificity to the microvasculature that serves active neuronal sites. Macrovascular contributions will reduce the microvascular specificity but can be reduced by using spin echo (SE) sequences that use a π pulse to refocus static field inhomogeneities near large veins. The microvascular specificity of a SE-echo planar imaging (SE-EPI) scan depends on the echo train length (ETL)-duration, but the dependence is not well-characterized in humans at 7T. To determine how microvascular-specific SE-EPI BOLD is in humans at 7T, we developed a Monte Carlo voxel model that computes the signal of a proton ensemble residing in a vasculature subjected to a SE-EPI pulse sequence. We characterized the ETL-duration dependence of the microvascular specificity by simulating the BOLD signal as a function of ETL, the range adhering to experimentally realistic readouts. We performed a validation experiment for our simulation observations, in which we acquired a set of SE-EPI BOLD time series with varying ETL during a hyperoxic gas challenge. Both our simulations and measurements show an increase in macrovascular contamination as a function of ETL, with an increase of 30% according to our simulation and 60% according to our validation experiment between the shortest and longest ETL durations (23.1 - 49.7 ms). We conclude that the microvascular specificity decreases heavily with increasing ETL-durations. We recommend reducing the ETL-duration as much as possible to minimize macrovascular contamination in SE-EPI BOLD experiments. We additionally recommend scanning at high resolutions to minimize partial volume effects with CSF. CSF voxels show a large BOLD response, which can be attributed to both the presence of large veins (high blood volume) and molecular oxygen-induced T1-shortening (significant in a hyperoxia experiment). The magnified BOLD signal in a GM-CSF partial volume voxel reduces the desired microvascular specificity and, therefore, will hinder the interpretation of functional MRI activation patterns.

Challenges and opportunities of integrating imaging and mathematical modelling to interrogate biological processes

Advances in biological imaging have accelerated our understanding of human physiology in both health and disease. As these advances have developed, the opportunities gained by integrating with cutting-edge mathematical models have become apparent yet remain challenging. Combined imaging-modelling approaches provide unprecedented opportunity to correlate data on tissue architecture and function, across length and time scales, to better understand the mechanisms that underpin fundamental biology and also to inform clinical decisions. Here we discuss the opportunities and challenges of such approaches, providing literature examples across a range of organ systems. Given the breadth of the field we focus on the intersection of continuum modelling and in vivo imaging applied to the vasculature and blood flow, though our rationale and conclusions extend widely. We propose three key research pillars (image acquisition, image processing, mathematical modelling) and present their respective advances as well as future opportunity via better integration. Multidisciplinary efforts that develop imaging and modelling tools concurrently, and share them open-source with the research community, provide exciting opportunity for advancing these fields.

Cerebrospinal fluid dynamics coupled to the global circulation in holistic setting: Mathematical models, numerical methods and applications

This paper presents a mathematical model of the global, arterio-venous circulation in the entire human body, coupled to a refined description of the cerebrospinal fluid (CSF) dynamics in the craniospinal cavity. The present model represents a substantially revised version of the original Müller-Toro mathematical model. It includes one-dimensional (1D), non-linear systems of partial differential equations for 323 major blood vessels and 85 zero-dimensional, differential-algebraic systems for the remaining components. Highlights include the myogenic mechanism of cerebral blood regulation; refined vasculature for the inner ear, the brainstem and the cerebellum; and viscoelastic, rather than purely elastic, models for all blood vessels, arterial and venous. The derived 1D parabolic systems of partial differential equations for all major vessels are approximated by hyperbolic systems with stiff source terms following a relaxation approach. A major novelty of this paper is the coupling of the circulation, as described, to a refined description of the CSF dynamics in the craniospinal cavity, following Linninger et al. The numerical solution methodology employed to approximate the hyperbolic non-linear systems of partial differential equations with stiff source terms is based on the Arbitrary DERivative Riemann problem finite volume framework, supplemented with a well-balanced formulation, and a local time stepping procedure. The full model is validated through comparison of computational results against published data and bespoke MRI measurements. Then we present two medical applications: (i) transverse sinus stenoses and their relation to Idiopathic Intracranial Hypertension; and (ii) extra-cranial venous strictures and their impact in the inner ear circulation, and its implications for Ménière's disease.