Physiologically based modeling of 3-D vascular networks and CT scan angiography

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.

In silico simulation of hepatic arteries: An open-source algorithm for efficient synthetic data generation

BACKGROUND

In silico testing of novel image reconstruction and quantitative algorithms designed for interventional imaging requires realistic high-resolution modeling of arterial trees with contrast dynamics. Furthermore, data synthesis for training of deep learning algorithms requires that an arterial tree generation algorithm be computationally efficient and sufficiently random.

PURPOSE

The purpose of this paper is to provide a method for anatomically and physiologically motivated, computationally efficient, random hepatic arterial tree generation.

METHODS

The vessel generation algorithm uses a constrained constructive optimization approach with a volume minimization-based cost function. The optimization is constrained by the Couinaud liver classification system to assure a main feeding artery to each Couinaud segment. An intersection check is included to guarantee non-intersecting vasculature and cubic polynomial fits are used to optimize bifurcation angles and to generate smoothly curved segments. Furthermore, an approach to simulate contrast dynamics and respiratory and cardiac motion is also presented.

RESULTS

The proposed algorithm can generate a synthetic hepatic arterial tree with 40 000 branches in 11 s. The high-resolution arterial trees have realistic morphological features such as branching angles (MAD with Murray's law= 1.2 ± 1 . 2 o $ = \;1.2 \pm {1.2^o}$ ), radii (median Murray deviation= 0.08 $ = \;0.08$ ), and smoothly curved, non-intersecting vessels. Furthermore, the algorithm assures a main feeding artery to each Couinaud segment and is random (variability = 0.98 ± 0.01).

CONCLUSIONS

This method facilitates the generation of large datasets of high-resolution, unique hepatic angiograms for the training of deep learning algorithms and initial testing of novel 3D reconstruction and quantitative algorithms designed for interventional imaging.

A hybrid approach to full-scale reconstruction of renal arterial network

The renal vasculature, acting as a resource distribution network, plays an important role in both the physiology and pathophysiology of the kidney. However, no imaging techniques allow an assessment of the structure and function of the renal vasculature due to limited spatial and temporal resolution. To develop realistic computer simulations of renal function, and to develop new image-based diagnostic methods based on artificial intelligence, it is necessary to have a realistic full-scale model of the renal vasculature. We propose a hybrid framework to build subject-specific models of the renal vascular network by using semi-automated segmentation of large arteries and estimation of cortex area from a micro-CT scan as a starting point, and by adopting the Global Constructive Optimization algorithm for generating smaller vessels. Our results show a close agreement between the reconstructed vasculature and existing anatomical data obtained from a rat kidney with respect to morphometric and hemodynamic parameters.

Rigorous mathematical optimization of synthetic hepatic vascular trees

In this paper, we introduce a new framework for generating synthetic vascular trees, based on rigorous model-based mathematical optimization. Our main contribution is the reformulation of finding the optimal global tree geometry into a nonlinear optimization problem (NLP). This rigorous mathematical formulation accommodates efficient solution algorithms such as the interior point method and allows us to easily change boundary conditions and constraints applied to the tree. Moreover, it creates trifurcations in addition to bifurcations. A second contribution is the addition of an optimization stage for the tree topology. Here, we combine constrained constructive optimization (CCO) with a heuristic approach to search among possible tree topologies. We combine the NLP formulation and the topology optimization into a single algorithmic approach. Finally, we attempt the validation of our new model-based optimization framework using a detailed corrosion cast of a human liver, which allows a quantitative comparison of the synthetic tree structure with the tree structure determined experimentally down to the fifth generation. The results show that our new framework is capable of generating asymmetric synthetic trees that match the available physiological corrosion cast data better than trees generated by the standard CCO approach.

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.

3D Printable Vascular Networks Generated by Accelerated Constrained Constructive Optimization for Tissue Engineering

One of the greatest challenges in fabricating artificial tissues and organs is the incorporation of vascular networks to support the biological requirements of the embedded cells, encouraging tissue formation and maturation. With the advent of 3D printing technology, significant progress has been made with respect to generating vascularized artificial tissues. Current algorithms to generate arterial/venous trees are computationally expensive and offer limited freedom to optimize the resulting structures. Furthermore, there is no method for algorithmic generation of vascular networks that can recapitulate the complexity of the native vasculature for more than two trees, and export directly to a 3D printing format. Here, we report such a method, using an accelerated constructive constrained optimization approach, by decomposing the process into construction, optimization, and collision resolution stages. The new approach reduces computation time to minutes at problem sizes where previous implementations have reported days. With the optimality criterion of maximizing the volume of useful tissue which could be grown around such a network, an approach of alternating stages of construction and batch optimization of all node positions is introduced and shown to yield consistently more optimal networks. The approach does not place a limit on the number of interpenetrating networks that can be constructed in a given space; indeed we demonstrate a biomimetic, liver-like tissue model. Methods to account for the limitations of 3D printing are provided, notably the minimum feature size and infill at sharp angles, through padding and angle reduction, respectively.

Development of a Customizable Hepatic Arterial Tree and Particle Transport Model for Use in Treatment Planning

Optimal treatment planning for radioembolization of hepatic cancers produces sufficient dose to tumors for control and dose to normal liver parenchyma that is below the threshold for toxicity. The non-uniform distribution of particles in liver microanatomy complicates the planning process as different functional regions receive different doses. Having realistic and patient-specific models of the arterial tree and microsphere trapping would be useful for developing more optimal treatment plans. We propose a macrocell-based growth method to generate models of the hepatic arterial tree from the proper hepatic artery to the terminal arterioles supplying the capillaries in the parenchyma. We show how these trees can be adapted to match patient values of pressure, flow, and vessel diameters while still conforming to laws controlling vessel bifurcation, changes in pressure, and blood flow. We also introduce a method to model particle transport within the tree that accounts for vessel and particle diameter distributions and show the non-uniform microsphere deposition pattern that results. Potential applications include investigating dose heterogeneity and microsphere deposition patterns.

Algorithmically generated rodent hepatic vascular trees in arbitrary detail

Physiologically realistic geometric models of the vasculature in the liver are indispensable for modelling hepatic blood flow, the main connection between the liver and the organism. Current in vivo imaging techniques do not provide sufficiently detailed vascular trees for many simulation applications, so it is necessary to use algorithmic refinement methods. The method of Constrained Constructive Optimization (CCO) (Schreiner et al., 2006) is well suited for this purpose. Its results after calibration have been previously compared to experimentally acquired human vascular trees (Schwen and Preusser, 2012). The goal of this paper is to extend this calibration to the case of rodents (mice and rats), the most commonly used animal models in liver research. Based on in vivo and ex vivo micro-CT scans of rodent livers and their vasculature, we performed an analysis of various geometric features of the vascular trees. Starting from pruned versions of the original vascular trees, we applied the CCO procedure and compared these algorithmic results to the original vascular trees using a suitable similarity measure. The calibration of the postprocessing improved the algorithmic results compared to those obtained using standard CCO. In terms of angular features, the average similarity increased from 0.27 to 0.61, improving the total similarity from 0.28 to 0.40. Finally, we applied the calibrated algorithm to refine measured vascular trees to the (higher) level of detail desired for specific applications. Having successfully adapted the CCO algorithm to the rodent model organism, the resulting individual-specific refined hepatic vascular trees can now be used for advanced modeling involving, e.g., detailed blood flow simulations.

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.

Computational modeling of MR flow imaging by the lattice Boltzmann method and Bloch equation

In this work, a computational model of magnetic resonance (MR) flow imaging is proposed. The first model component provides fluid dynamics maps by applying the lattice Boltzmann method. The second one uses the flow maps and couples MR imaging (MRI) modeling with a new magnetization transport algorithm based on the Eulerian coordinate approach. MRI modeling is based on the discrete time solution of the Bloch equation by analytical local magnetization transformations (exponential scaling and rotations). Model is validated by comparison of experimental and simulated MR images in two three-dimensional geometries (straight and U-bend tubes) with steady flow under comparable conditions. Two-dimensional geometries, presented in literature, were also tested. In both cases, a good agreement is observed. Quantitative analysis shows in detail the model accuracy. Computational time is noticeably lower to prior works. These results demonstrate that the discrete time solution of Bloch equation coupled with the new magnetization transport algorithm naturally incorporates flow influence in MRI modeling. As a result, in the proposed model, no additional mechanism (unlike in prior works) is needed to consider flow artifacts, which implies its easy extensibility. In combination with its low computational complexity and efficient implementation, the model could have a potential application in study of flow disturbances (in MRI) in various conditions and in different geometries.

Analysis and algorithmic generation of hepatic vascular systems

A proper geometric model of the vascular systems in the liver is crucial for modeling blood flow, the connection between the organ and the rest of the organism. In vivo imaging does not provide sufficient details, so an algorithmic concept for extending measured vascular tree data is needed such that geometrically realistic structures can be generated. We develop a quantification of similarity in terms of different geometric features. This involves topological Strahler ordering of the vascular trees, statistical testing, and averaging. Invariant features are identified in human clinical in vivo CT scans. Results of the existing "Constrained Constructive Optimization" algorithm are compared to real vascular tree data. To improve bifurcation angles in the algorithmic results, we implement a postprocessing step calibrated to the measured features. This framework is finally applied to generate realistic additional details in a patient-specific hepatic vascular tree data set.

Vascular system modeling in parallel environment - distributed and shared memory approaches

This paper presents two approaches in parallel modeling of vascular system development in internal organs. In the first approach, new parts of tissue are distributed among processors and each processor is responsible for perfusing its assigned parts of tissue to all vascular trees. Communication between processors is accomplished by passing messages, and therefore, this algorithm is perfectly suited for distributed memory architectures. The second approach is designed for shared memory machines. It parallelizes the perfusion process during which individual processing units perform calculations concerning different vascular trees. The experimental results, performed on a computing cluster and multicore machines, show that both algorithms provide a significant speedup.

Multiscale model of liver DCE-MRI towards a better understanding of tumor complexity

The use of quantitative imaging for the characterization of hepatic tumors in magnetic resonance imaging (MRI) can improve the diagnosis and therefore the treatment of these life-threatening tumors. However, image parameters remain difficult to interpret because they result from a mixture of complex processes related to pathophysiology and to acquisition. These processes occur at variable spatial and temporal scales. We propose a multiscale model of liver dynamic contrast-enhanced (DCE) MRI in order to better understand the tumor complexity in images. Our design couples a model of the organ (tissue and vasculature) with a model of the image acquisition. At the macroscopic scale, vascular trees take a prominent place. Regarding the formation of MRI images, we propose a distributed model of parenchymal biodistribution of extracellular contrast agents. Model parameters can be adapted to simulate the tumor development. The sensitivity of the multiscale model of liver DCE-MRI was studied through observations of the influence of two physiological parameters involved in carcinogenesis (arterial flow and capillary permeability) on its outputs (MRI images at arterial and portal phases). Finally, images were simulated for a set of parameters corresponding to the five stages of hepatocarcinogenesis (from regenerative nodules to poorly differentiated HepatoCellular Carcinoma).

Physiological modeling of tumor-affected renal circulation

One way of gaining insight into what can be observed in medical images is through physiological modeling. For instance, anatomical and functional modifications occur in the organ during the appearance and the growth of a tumor. Some of these changes concern the vascularization. We propose a computational model of tumor-affected renal circulation that represents the local heterogeneity of different parts of the kidney (cortex, medulla). We present a simulation of vascular modifications related to vessel structure, geometry, density, and blood flow in case of renal cell carcinoma. We also use our model to simulate computed tomography scans of a kidney affected by the renal cell carcinoma, at two acquisition times after injection of a contrast product. This framework, based on a physiological model of the organ and physical model of medical image acquisition, offers an opportunity to help radiologists in their diagnostic tasks. This includes the possibility of linking image descriptors with physiological perturbations and markers of pathological processes.

A physiologically based pharmacokinetic model of vascular-extravascular exchanges during liver carcinogenesis: application to MRI contrast agents

The extraction of physiological parameters by non-invasive imaging techniques such as dynamic magnetic resonance imaging (MRI) or positron emission tomography requires a knowledge of molecular distribution and exchange between microvascularization and extravascular tissues. These phenomena not only depend on the physicochemical characteristics of the injected molecules but also the pathophysiological state of the targeted organ. We developed a five-compartment physiologically based pharmacokinetic model focused on hepatic carcinogenesis and MRI contrast agents. This model includes physical characteristics of the contrast agent, dual specific liver supply, microvessel wall properties and transport parameters that are compatible with hepatocarcinoma development. The evolution of concentrations in the five compartments showed significant differences in the distribution of three molecules (differentiated by their diameters and diffusion coefficients ranging, respectively, from 0.9 to 62 nm and from 68.10(-9) to 47.10(-7) cm(2) s(-1)) in simulated regeneration nodules and dysplastic nodules, as well as in medium- and poorly differentiated hepatocarcinoma. These results are in agreement with known vascular modifications such as arterialization that occur during hepatocarcinogenesis. This model can be used to study the pharmacokinetics of contrast agents and consequently to extract parameters that are characteristic of the tumor development (like permeability), after fitting simulated to in vivo data.

Simulation of biphasic CT findings in hepatic cellular carcinoma by a two-level physiological model

In this paper, we present a two-level physiological model that is able to reflect morphology and function of vascular networks, in clinical images. Our approach results from the combination of a macroscopic model, providing simulation of the growth and pathological modifications of vascular network, and a microvascular model, based on compartmental approach, which simulates blood and contrast medium transfer through capillary walls. The two-level model is applied to generate biphasic computed tomography of hepatocellular carcinoma. A contrast-enhanced sequence of simulated images is acquired, and enhancement curves extracted from normal and tumoral regions are compared to curves obtained from in vivo images. The model offers the potential of finding early indicators of disease in clinical vascular images.

System for the analysis and visualization of large 3D anatomical trees

Modern micro-CT and multi-detector helical CT scanners can produce high-resolution 3D digital images of various anatomical trees. The large size and complexity of these trees make it essentially impossible to define them interactively. Automatic approaches have been proposed for a few specific problems, but none of these approaches guarantee extracting geometrically accurate multi-generational tree structures. This paper proposes an interactive system for defining and visualizing large anatomical trees and for subsequent quantitative data mining. The system consists of a large number of tools for automatic image analysis, semi-automatic and interactive tree editing, and an assortment of visualization tools. Results are presented for a variety of 3D high-resolution images.

Coupling texture analysis and physiological modeling for liver dynamic MRI interpretation

We coupled our physiological model of the liver, to a MRI simulator (SIMRI) in order to find image markers of the tumor growth. Some pathological modifications related to the development of Hepatocellular carcinoma are simulated (flows, permeability, vascular density). Corresponding images simulated at typical acquisition phases (arterial, portal) are compared to real images. The evolution of some textural features with arterial flow is also presented.

Investigations into the relationship between hemodynamics and vascular alterations in an established arteriovenous fistula

Arteriovenous fistula are specific vessels created by a vascular operation in order to provide sufficient blood access for extracorporeal circulation in hemodialysis. They are subject to numerous pathologies that may be caused by hemodynamic effects. To better understand these effects, a specific patient's arteriovenous fistula was reconstructed from computed tomography angiography. Computational fluid dynamics software made it possible to solve fluid mechanics equations under physiological conditions. An accurate map of unsteady velocity profiles and wall shear stress was drawn up. The computed velocity profiles were successfully confronted with Echo Doppler investigation. Selected regions with or without calcification, the end stage of wall alteration, were examined in terms of the mechanical constraints generated by blood flow. In contrast with other authors, we did not observe any association between calcification and areas of oscillating shear stress. Nevertheless, a statistical analysis of the whole vessel envelop and specific sites of calcification suggested a potential association between calcification and high temporal wall shear stress gradients.