Development of optimized vascular fractal tree models using level set distance function

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.

Fractals in Neuroimaging

Several natural phenomena can be described by studying their statistical scaling patterns, hence leading to simple geometrical interpretation. In this regard, fractal geometry is a powerful tool to describe the irregular or fragmented shape of natural features, using spatial or time-domain statistical scaling laws (power-law behavior) to characterize real-world physical systems. This chapter presents some works on the usefulness of fractal features, mainly the fractal dimension and the related Hurst exponent, in the characterization and identification of pathologies and radiological features in neuroimaging, mainly, magnetic resonance imaging.

Approaches to vascular network, blood flow, and metabolite distribution modeling in brain tissue

The cardiovascular system plays a key role in the transport of nutrients, ensuring a continuous supply of all cells of the body with the metabolites necessary for life. The blood supply to the brain is carried out by the large arteries located on its surface, which branch into smaller arterioles that penetrate the cerebral cortex and feed the capillary bed, thereby forming an extensive branching network. The formation of blood vessels is carried out via vasculogenesis and angiogenesis, which play an important role in both embryo and adult life. The review presents approaches to modeling various aspects of both the formation of vascular networks and the construction of the formed arterial tree. In addition, a brief description of models that allows one to study the blood flow in various parts of the circulatory system and the spatiotemporal metabolite distribution in brain tissues is given. Experimental study of these issues is not always possible due to both the complexity of the cardiovascular system and the mechanisms through which the perfusion of all body cells is carried out. In this regard, mathematical models are a good tool for studying hemodynamics and can be used in clinical practice to diagnose vascular diseases and assess the need for treatment.

Stability and Thrombogenicity Analysis of Collagen/Carbon Nanotube Nanocomposite Coatings Using a Reversible Microfluidic Device

Currently, the development of stable and antithrombogenic coatings for cardiovascular implants is socially important. This is especially important for coatings exposed to high shear stress from flowing blood, such as those on ventricular assist devices. A method of layer-by-layer formation of nanocomposite coatings based on multi-walled carbon nanotubes (MWCNT) in a collagen matrix is proposed. A reversible microfluidic device with a wide range of flow shear stresses has been developed for hemodynamic experiments. The dependence of the resistance on the presence of a cross-linking agent for collagen chains in the composition of the coating was demonstrated. Optical profilometry determined that collagen/c-MWCNT and collagen/c-MWCNT/glutaraldehyde coatings obtained sufficiently high resistance to high shear stress flow. However, the collagen/c-MWCNT/glutaraldehyde coating was almost twice as resistant to a phosphate-buffered solution flow. A reversible microfluidic device made it possible to assess the level of thrombogenicity of the coatings by the level of blood albumin protein adhesion to the coatings. Raman spectroscopy demonstrated that the adhesion of albumin to collagen/c-MWCNT and collagen/c-MWCNT/glutaraldehyde coatings is 1.7 and 1.4 times lower than the adhesion of protein to a titanium surface, widely used for ventricular assist devices. Scanning electron microscopy and energy dispersive spectroscopy determined that blood protein was least detected on the collagen/c-MWCNT coating, which contained no cross-linking agent, including in comparison with the titanium surface. Thus, a reversible microfluidic device is suitable for preliminary testing of the resistance and thrombogenicity of various coatings and membranes, and nanocomposite coatings based on collagen and c-MWCNT are suitable candidates for the development of cardiovascular devices.

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.

Fractal analysis of perfusion imaging in synovitis: a novel imaging biomarker for grading inflammatory activity based on assessing angiogenesis

Objectives

The mutual and intertwined dependence of inflammation and angiogenesis in synovitis is widely acknowledged. However, no clinically established tool for objective and quantitative assessment of angiogenesis is routinely available. This study establishes fractal analysis as a novel method to quantitatively assess inflammatory activity based on angiogenesis in synovitis.

Methods

First, we established a pathophysiological framework for synovitis including fractal analysis of software perfusion phantoms, which allowed to derive explainability with a known and controllable reference standard for vascular structure. Second, we acquired MRI datasets of patients with suspected rheumatoid arthritis of the hand, and three imaging experts independently assessed synovitis analogue to Rheumatoid Arthritis MRI Scoring (RAMRIS) criteria. Finally, we performed fractal analysis of dynamic first-pass perfusion MRI in vivo to evaluate angiogenesis in relation to inflammatory activity with RAMRIS as reference standard.

Results

Fractal dimension (FD) achieved highly significant discriminability for different degrees of inflammatory activity (p<0.01) in software phantoms with known ground-truth of angiogenic structure. FD indicated increasingly chaotic perfusion patterns with increasing grades of inflammatory activity (Spearman’s ρ=0.94, p<0.001). In 36 clinical patients, fractal analysis quantitatively and objectively discriminated individual RAMRIS scores (p≤0.05). Area under the receiver-operating curve was 0.84 (95% CI 0.7 to 0.89) for fractal analysis when considering RAMRIS as ground-truth. Fractal analysis additionally identified angiogenesis in cases where RAMRIS underestimated inflammatory activity.

Conclusions

Based on angiogenesis and perfusion pathophysiology, fractal analysis non-invasively enables comprehensive, objective and quantitative characterisation of inflammatory angiogenesis with subjective and qualitative RAMRIS as reference standard. Further studies are required to establish the clinical value of fractal analysis for diagnosis, prognostication and therapy monitoring in inflammatory arthritis.

Adaptive constrained constructive optimisation for complex vascularisation processes

Mimicking angiogenetic processes in vascular territories acquires importance in the analysis of the multi-scale circulatory cascade and the coupling between blood flow and cell function. The present work extends, in several aspects, the Constrained Constructive Optimisation (CCO) algorithm to tackle complex automatic vascularisation tasks. The main extensions are based on the integration of adaptive optimisation criteria and multi-staged space-filling strategies which enhance the modelling capabilities of CCO for specific vascular architectures. Moreover, this vascular outgrowth can be performed either from scratch or from an existing network of vessels. Hence, the vascular territory is defined as a partition of vascular, avascular and carriage domains (the last one contains vessels but not terminals) allowing one to model complex vascular domains. In turn, the multi-staged space-filling approach allows one to delineate a sequence of biologically-inspired stages during the vascularisation process by exploiting different constraints, optimisation strategies and domain partitions stage by stage, improving the consistency with the architectural hierarchy observed in anatomical structures. With these features, the aDaptive CCO (DCCO) algorithm proposed here aims at improving the modelled network anatomy. The capabilities of the DCCO algorithm are assessed with a number of anatomically realistic scenarios.

Multiscale modeling of human cerebrovasculature: A hybrid approach using image-based geometry and a mathematical algorithm

The cerebral vasculature has a complex and hierarchical network, ranging from vessels of a few millimeters to superficial cortical vessels with diameters of a few hundred micrometers, and to the microvasculature (arteriole/venule) and capillary beds in the cortex. In standard imaging techniques, it is difficult to segment all vessels in the network, especially in the case of the human brain. This study proposes a hybrid modeling approach that determines these networks by explicitly segmenting the large vessels from medical images and employing a novel vascular generation algorithm. The framework enables vasculatures to be generated at coarse and fine scales for individual arteries and veins with vascular subregions, following the personalized anatomy of the brain and macroscale vasculatures. In this study, the vascular structures of superficial cortical (pial) vessels before they penetrate the cortex are modeled as a mesoscale vasculature. The validity of the present approach is demonstrated through comparisons with partially observed data from existing measurements of the vessel distributions on the brain surface, pathway fractal features, and vascular territories of the major cerebral arteries. Additionally, this validation provides some biological insights: (i) vascular pathways may form to ensure a reasonable supply of blood to the local surface area; (ii) fractal features of vascular pathways are not sensitive to overall and local brain geometries; and (iii) whole pathways connecting the upstream and downstream entire-scale cerebral circulation are highly dependent on the local curvature of the cerebral sulci.

Cerebral autoregulation in the complex vascular networks of the brain is an amazing achievement. We believe that numerical analysis of the cerebral blood circulation using an anatomically precise vascular model provides a powerful tool for evaluating the direct relationships between local- and global-scale blood flows. However, there is a lack of information about the overall vascular pathways in the human brain, preventing a monolithic model of the human cerebrovasculature from being established. This paper presents a multiscale model of human cerebrovasculature based on a hybrid approach that uses image-based geometries and a newly developed mathematical algorithm. One important argument of this paper is the validity of the cerebrovasculature represented in the model, which reflects anatomical features of major cerebral vasculatures and brain shape, and has strong similarities with available data for human superficial cortical vessels. Investigations of the reconstructed model allow us to derive some biological insights and associated hypotheses for the cerebral vasculature. The authors believe the present cerebrovascular model can be applied to numerical simulations of the entire-scale cerebral blood flow.

Fundamental constraints of vessels network architecture properties revealed by reconstruction of a rat brain vasculature

The studies of mammalian vasculature are an essential part of biomedical research, enabling the development of physiological understanding and forming the background of medical techniques and therapy. Despite the fact that the basic principles of vessel network description were established in the first quarter of the twentieth century, a digital model describing the vasculature in full accordance with experimental data has not yet been created. In the present study, we combine the determined structure design of basic arterial vessels with the stochastic creation of small vessel networks. By the example of rat brain arterial network model it was shown that the arterial blood volume and the magnitude of the blood flow impose a limitation on the network architecture. In particular, the bifurcation exponent (γ) should not be less than 2.7, and the optimal value of this parameter lies in the range of 2.9-3.0. Although the networks with a low γ appear as branched and complex, they do not fill out the phantom properly. Thus, the architecture of the vasculature is fundamentally determined by topological geometrical parameters.

Multiparametric topological analysis of reconstructed rat brain arterial system

All metabolic processes in living tissues are provided by the vascular system, whose functionality largely depends on its structure and topology. The paper proposes an algorithm for constructing the circulatory system based on a combination of stochastic and deterministic approaches. Analyses of the topological characteristics of arterial tree models with different values of the bifurcation exponent ([Formula: see text]) and length coefficient ([Formula: see text]) show that the maximum agreement with experimental data can be achieved only with the optimal values of both parameters (3.0 and 0.90, respectively). Application of the multiparametric optimization in conjunction with topological analysis makes it possible to quantify the biological division of the distributing and delivering vessels of a tree with a high degree of branching. The proposed approach allows both the correct spatial localization of the main arteries and the complex topology of the complete arterial system down to the capillaries to be reproduced.

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.

Impedance boundary conditions for general transient hemodynamics

We discuss the implementation and calibration of a new generalized structured tree boundary condition for hemodynamics. The main idea is to approximate the impedance corresponding to the vessels downstream from a specific outlet. Unlike previous impedance conditions, the one considered here is applicable to general transient flows as opposed to periodic ones only. The physiological character of the approach significantly simplifies calibration. We also describe a novel way to incorporate autoregulation mechanisms in structured arterial trees at minimal computational cost. The strength of the approach is illustrated and validated on several examples through comparison with clinical data.

In silico modeling of magnetic resonance flow imaging in complex vascular networks

The paper presents a computational model of magnetic resonance (MR) flow imaging. The model consists of three components. The first component is used to generate complex vascular structures, while the second one provides blood flow characteristics in the generated vascular structures by the lattice Boltzmann method. The third component makes use of the generated vascular structures and flow characteristics to simulate MR flow imaging. To meet computational demands, parallel algorithms are applied in all the components. The proposed approach is verified in three stages. In the first stage, experimental validation is performed by an in vitro phantom. Then, the simulation possibilities of the model are shown. Flow and MR flow imaging in complex vascular structures are presented and evaluated. Finally, the computational performance is tested. Results show that the model is able to reproduce flow behavior in large vascular networks in a relatively short time. Moreover, simulated MR flow images are in accordance with the theoretical considerations and experimental images. The proposed approach is the first such an integrative solution in literature. Moreover, compared to previous works on flow and MR flow imaging, this approach distinguishes itself by its computational efficiency. Such a connection of anatomy, physiology and image formation in a single computer tool could provide an in silico solution to improving our understanding of the processes involved, either considered together or separately.

Morphometric, geographic, and territorial characterization of brain arterial trees

Morphometric information of the brain vascularization is valuable for a variety of clinical and scientific applications. In particular, this information is important when creating arterial tree models for imposing boundary conditions in numerical simulations of the brain hemodynamics. The purpose of this work is to provide quantitative descriptions of arterial branches, bifurcation patterns, shape, and geographical distribution of the arborization of the main cerebral arteries as well as estimations of the corresponding vascular territories. For this purpose, subject-specific digital reconstructions of the brain vascular network created from 3T magnetic resonance angiography images of healthy volunteers are used to derive population-averaged morphometric characteristics of the cerebral arterial trees. Copyri

Digital reconstruction and morphometric analysis of human brain arterial vasculature from magnetic resonance angiography

Characterization of the complex branching architecture of cerebral arteries across a representative sample of the human population is important for diagnosing, analyzing, and predicting pathological states. Brain arterial vasculature can be visualized by magnetic resonance angiography (MRA). However, most MRA studies are limited to qualitative assessments, partial morphometric analyses, individual (or small numbers of) subjects, proprietary datasets, or combinations of the above limitations. Neuroinformatics tools, developed for neuronal arbor analysis, were used to quantify vascular morphology from 3T time-of-flight MRA high-resolution (620 μm isotropic) images collected in 61 healthy volunteers (36/25 F/M, average age=31.2 ± 10.7, range=19-64 years). We present in-depth morphometric analyses of the global and local anatomical features of these arbors. The overall structure and size of the vasculature did not significantly differ across genders, ages, or hemispheres. The total length of the three major arterial trees stemming from the circle of Willis (from smallest to largest: the posterior, anterior, and middle cerebral arteries; or PCAs, ACAs, and MCAs, respectively) followed an approximate 1:2:4 proportion. Arterial size co-varied across individuals: subjects with one artery longer than average tended to have all other arteries also longer than average. There was no net right-left difference across the population in any of the individual arteries, but ACAs were more lateralized than MCAs. MCAs, ACAs, and PCAs had similar branch-level properties such as bifurcation angles. Throughout the arterial vasculature, there were considerable differences between branch types: bifurcating branches were significantly shorter and straighter than terminating branches. Furthermore, the length and meandering of bifurcating branches increased with age and with path distance from the circle of Willis. All reconstructions are freely distributed through a public database to enable additional analyses and modeling (cng.gmu.edu/brava).

Physiologically based construction of optimized 3-D arterial tree models

We present an approach to generate 3-D arterial tree models based on physiological principles while at the same time certain morphological properties are enforced at construction time in order to build individual vascular models down to the capillary level. The driving force of our approach is an angiogenesis model incorporating case-specific information about the metabolic activity in the considered domain. Additionally, we enforce morphometrically confirmed bifurcation statistics of vascular networks. The proposed method is able to generate artificial, yet physiologically plausible, arterial tree models that match the metabolic demand of the embedding tissue and fulfill the enforced morphological properties at the same time. We demonstrate the plausibility of our method on synthetic data for different metabolic configurations and analyze physiological and morphological properties of the generated tree models.