A New Multiscale Representation for Shapes and Its Application to Blood Vessel Recovery

In this paper, we will first introduce a novel multiscale representation (MSR) for shapes. Based on the MSR, we will then design a surface inpainting algorithm to recover 3D geometry of blood vessels. Because of the nature of irregular morphology in vessels and organs, both phantom and real inpainting scenarios were tested using our new algorithm. Successful vessel recoveries are demonstrated with numerical estimation of the degree of arteriosclerosis and vessel occlusion.Comment: 12 pages, 3 figure

Mathematical modeling of local perfusion in large distensible microvascular networks

Microvessels -blood vessels with diameter less than 200 microns- form large, intricate networks organized into arterioles, capillaries and venules. In these networks, the distribution of flow and pressure drop is a highly interlaced function of single vessel resistances and mutual vessel interactions. In this paper we propose a mathematical and computational model to study the behavior of microcirculatory networks subjected to different conditions. The network geometry is composed of a graph of connected straight cylinders, each one representing a vessel. The blood flow and pressure drop across the single vessel, further split into smaller elements, are related through a generalized Ohm's law featuring a conductivity parameter, function of the vessel cross section area and geometry, which undergo deformations under pressure loads. The membrane theory is used to describe the deformation of vessel lumina, tailored to the structure of thick-walled arterioles and thin-walled venules. In addition, since venules can possibly experience negative transmural pressures, a buckling model is also included to represent vessel collapse. The complete model including arterioles, capillaries and venules represents a nonlinear system of PDEs, which is approached numerically by finite element discretization and linearization techniques. We use the model to simulate flow in the microcirculation of the human eye retina, a terminal system with a single inlet and outlet. After a phase of validation against experimental measurements, we simulate the network response to different interstitial pressure values. Such a study is carried out both for global and localized variations of the interstitial pressure. In both cases, significant redistributions of the blood flow in the network arise, highlighting the importance of considering the single vessel behavior along with its position and connectivity in the network

Multicellular Systems Biology of Development

Embryonic development depends on the precise coordination of cell fate specification, patterning and morphogenesis. Although great strides have been made in the molecular understanding of each of these processes, how their interplay governs the formation of complex tissues remains poorly understood. New techniques for experimental manipulation and image quantification enable the study of development in unprecedented detail, resulting in new hypotheses on the interactions between known components. By expressing these hypotheses in terms of rules and equations, computational modeling and simulation allows one to test their consistency against experimental data. However, new computational methods are required to represent and integrate the network of interactions between gene regulation, signaling and biomechanics that extend over the molecular, cellular and tissue scales. In this thesis, I present a framework that facilitates computational modeling of multiscale multicellular systems and apply it to investigate pancreatic development and the formation of vascular networks. This framework is based on the integration of discrete cell-based models with continuous models for intracellular regulation and intercellular signaling. Specifically, gene regulatory networks are represented by differential equations to analyze cell fate regulation; interactions and distributions of signaling molecules are modeled by reaction-diffusion systems to study pattern formation; and cell-cell interactions are represented in cell-based models to investigate morphogenetic processes. A cell-centered approach is adopted that facilitates the integration of processes across the scales and simultaneously constrains model complexity. The computational methods that are required for this modeling framework have been implemented in the software platform Morpheus. This modeling and simulation environment enables the development, execution and analysis of multi-scale models of multicellular systems. These models are represented in a new domain-specific markup language that separates the biological model from the computational methods and facilitates model storage and exchange. Together with a user-friendly graphical interface, Morpheus enables computational modeling of complex developmental processes without programming and thereby widens its accessibility for biologists. To demonstrate the applicability of the framework to problems in developmental biology, two case studies are presented that address different aspects of the interplay between cell fate specification, patterning and morphogenesis. In the first, I focus on the interplay between cell fate stability and intercellular signaling. Specifically, two studies are presented that investigate how mechanisms of cell-cell communication affect cell fate regulation and spatial patterning in the pancreatic epithelium. Using bifurcation analysis and simulations of spatially coupled differential equations, it is shown that intercellular communication results in a multistability of gene expression states that can explain the scattered spatial distribution and low cell type ratio of nascent islet cells. Moreover, model analysis shows that disruption of intercellular communication induces a transition between gene expression states that can explain observations of in vitro transdifferentiation from adult acinar cells into new islet cells. These results emphasize the role of the multicellular context in cell fate regulation during development and may be used to optimize protocols for cellular reprogramming. The second case study focuses on the feedback between patterning and morphogenesis in the context of the formation of vascular networks. Integrating a cell-based model of endothelial chemotaxis with a reaction-diffusion model representing signaling molecules and extracellular matrix, it is shown that vascular network patterns with realistic morphometry can arise when signaling factors are retained by cell-modified matrix molecules. Through the validation of this model using in vitro assays, quantitative estimates are obtained for kinetic parameters that, when used in quantitative model simulations, confirm the formation of vascular networks under measured biophysical conditions. These results demonstrate the key role of the extracellular matrix in providing spatial guidance cues, a fact that may be exploited to enhance vascularization of engineered tissues. Together, the modeling framework, software platform and case studies presented in this thesis demonstrate how cell-centered computational modeling of multi-scale and multicellular systems provide powerful tools to help disentangle the complex interplay between cell fate specification, patterning and morphogenesis during embryonic development

Aquatics reconstruction software: the design of a diagnostic tool based on computer vision algorithms

Computer vision methods can be applied to a variety of medical and surgical applications, and many techniques and algorithms are available that can be used to recover 3D shapes and information from images range and volume data. Complex practical applications, however, are rarely approachable with a single technique, and require detailed analysis on how they can be subdivided in subtasks that are computationally treatable and that, at the same time, allow for the appropriate level of user-interaction. In this paper we show an example of a complex application where, following criteria of efficiency, reliability and user friendliness, several computer vision techniques have been selected and customized to build a system able to support diagnosis and endovascular treatment of Abdominal Aortic Aneurysms. The system reconstructs the geometrical representation of four different structures related to the aorta (vessel lumen, thrombus, calcifications and skeleton) from CT angiography data. In this way it supports the three dimensional measurements required for a careful geometrical evaluation of the vessel, that is fundamental to decide if the treatment is necessary and to perform, in this case, its planning. The system has been realized within the European trial AQUATICS (IST-1999-20226 EUTIST-M WP 12), and it has been widely tested on clinical data

Generalizable automated pixel-level structural segmentation of medical and biological data

Over the years, the rapid expansion in imaging techniques and equipments has driven the demand for more automation in handling large medical and biological data sets. A wealth of approaches have been suggested as optimal solutions for their respective imaging types. These solutions span various image resolutions, modalities and contrast (staining) mechanisms. Few approaches generalise well across multiple image types, contrasts or resolution. This thesis proposes an automated pixel-level framework that addresses 2D, 2D+t and 3D structural segmentation in a more generalizable manner, yet has enough adaptability to address a number of specific image modalities, spanning retinal funduscopy, sequential fluorescein angiography and two-photon microscopy. The pixel-level segmentation scheme involves: i ) constructing a phase-invariant orientation field of the local spatial neighbourhood; ii ) combining local feature maps with intensity-based measures in a structural patch context; iii ) using a complex supervised learning process to interpret the combination of all the elements in the patch in order to reach a classification decision. This has the advantage of transferability from retinal blood vessels in 2D to neural structures in 3D. To process the temporal components in non-standard 2D+t retinal angiography sequences, we first introduce a co-registration procedure: at the pairwise level, we combine projective RANSAC with a quadratic homography transformation to map the coordinate systems between any two frames. At the joint level, we construct a hierarchical approach in order for each individual frame to be registered to the global reference intra- and inter- sequence(s). We then take a non-training approach that searches in both the spatial neighbourhood of each pixel and the filter output across varying scales to locate and link microvascular centrelines to (sub-) pixel accuracy. In essence, this \link while extract" piece-wise segmentation approach combines the local phase-invariant orientation field information with additional local phase estimates to obtain a soft classification of the centreline (sub-) pixel locations. Unlike retinal segmentation problems where vasculature is the main focus, 3D neural segmentation requires additional exibility, allowing a variety of structures of anatomical importance yet with different geometric properties to be differentiated both from the background and against other structures. Notably, cellular structures, such as Purkinje cells, neural dendrites and interneurons, all display certain elongation along their medial axes, yet each class has a characteristic shape captured by an orientation field that distinguishes it from other structures. To take this into consideration, we introduce a 5D orientation mapping to capture these orientation properties. This mapping is incorporated into the local feature map description prior to a learning machine. Extensive performance evaluations and validation of each of the techniques presented in this thesis is carried out. For retinal fundus images, we compute Receiver Operating Characteristic (ROC) curves on existing public databases (DRIVE & STARE) to assess and compare our algorithms with other benchmark methods. For 2D+t retinal angiography sequences, we compute the error metrics ("Centreline Error") of our scheme with other benchmark methods. For microscopic cortical data stacks, we present segmentation results on both surrogate data with known ground-truth and experimental rat cerebellar cortex two-photon microscopic tissue stacks.Open Acces

Three-dimensional model-based analysis of vascular and cardiac images

This thesis is concerned with the geometrical modeling of organs to perform medical image analysis tasks. The thesis is divided in two main parts devoted to model linear vessel segments and the left ventricle of the heart, respectively. Chapters 2 to 4 present different aspects of a model-based technique for semi-automated quantification of linear vessel segments from 3-D Magnetic Resonance Angiography (MRA). Chapter 2 is concerned with a multiscale filter for the enhancement of vessels in 2-D and 3-D angiograms. Chapter 3 applies the filter developed in Chapter 2 to determine the central vessel axis in 3-D MRA images. This procedure is initialized using an efficient user interaction technique that naturally incorporates the knowledge of the operator about the vessel of interest. Also in this chapter, a linear vessel model is used to recover the position of the vessel wall in order to carry out an accurate quantitative analysis of vascular morphology. Prior knowledge is provided in two main forms: a cylindrical model introduces a shape prior while prior knowledge on the image acquisition (type of MRA technique) is used to define an appropriate vessel boundary criterion. In Chapter 4 an extensive in vitro and in vivo evaluation of the algorithm introduced in Chapter 3 is described. Chapters 5 to 7 change the focus to 3D cardiac image analysis from Magnetic Resonance Imaging. Chapter 5 presents an extensive survey, a categorization and a critical review of the field of cardiac modeling. Chapter 6 and Chapter 7 present successive refinements of a method for building statistical models of shape variability with particular emphasis on cardiac modeling. The method is based on an elastic registration method using hierarchical free-form deformations. A 3D shape model of the left and right ventricles of the heart was constructed. This model contains both the average shape of these organs as well as their shape variability. The methodology presented in the last two chapters could also be applied to other anatomical structures. This has been illustrated in Chapter 6 with examples of geometrical models of the nucleus caudate and the radius

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus