Liangjia Zhu

Graph Curvature for Differentiating Cancer Networks

Cellular interactions can be modeled as complex dynamical systems represented by weighted graphs. The functionality of such networks, including measures of robustness, reliability, performance, and efficiency, are intrinsically tied to the topology and geometry of the underlying graph. Utilizing recently proposed geometric notions of curvature on weighted graphs, we investigate the features of gene co-expression networks derived from large-scale genomic studies of cancer. We find that the curvature of these networks reliably distinguishes between cancer and normal samples, with cancer networks exhibiting higher curvature than their normal counterparts. We establish a quantitative relationship between our findings and prior investigations of network entropy. Furthermore, we demonstrate how our approach yields additional, non-trivial pair-wise (i.e. gene-gene) interactions which may be disrupted in cancer samples. The mathematical formulation of our approach yields an exact solution to calculating pair-wise changes in curvature which was computationally infeasible using prior methods. As such, our findings lay the foundation for an analytical approach to studying complex biological networks.

Automatic Delineation of the Myocardial Wall From CT Images Via Shape Segmentation and Variational Region Growing

Prognosis and diagnosis of cardiac diseases frequently require quantitative evaluation of the ventricle volume, mass, and ejection fraction. The delineation of the myocardial wall is involved in all of these evaluations, which is a challenging task due to large variations in myocardial shapes and image quality. In this paper, we present an automatic method for extracting the myocardial wall of the left and right ventricles from cardiac CT images. In the method, the left and right ventricles are located sequentially, in which each ventricle is detected by first identifying the endocardium and then segmenting the epicardium. To this end, the endocardium is localized by utilizing its geometric features obtained on-line from a CT image. After that, a variational region-growing model is employed to extract the epicardium of the ventricles. In particular, the location of the endocardium of the left ventricle is determined via using an active contour model on the blood-pool surface. To localize the right ventricle, the active contour model is applied on a heart surface extracted based on the left ventricle segmentation result. The robustness and accuracy of the proposed approach is demonstrated by experimental results from 33 human and 12 pig CT images.

Automatic Segmentation of the Left Atrium From MR Images via Variational Region Growing With a Moments-Based Shape Prior

The planning and evaluation of left atrial ablation procedures are commonly based on the segmentation of the left atrium, which is a challenging task due to large anatomical variations. In this paper, we propose an automatic approach for segmenting the left atrium from magnetic resonance imagery. The segmentation problem is formulated as a problem in variational region growing. In particular, the method starts locally by searching for a seed region of the left atrium from an MR slice. A global constraint is imposed by applying a shape prior to the left atrium represented by Zernike moments. The overall growing process is guided by the robust statistics of intensities from the seed region along with the shape prior to capture the entire atrial region. The robustness and accuracy of our approach are demonstrated by experimental results from 64 human MR images.

Automated Dispersion and Orientation Analysis for Carbon Nanotube Reinforced Polymer Composites

The properties of carbon nanotube (CNT)/polymer composites are strongly dependent on the dispersion and orientation of CNTs in the host matrix. Quantification of the dispersion and orientation of CNTs by means of microstructure observation and image analysis has been demonstrated as a useful way to understand the structure-property relationship of CNT/polymer composites. However, due to the various morphologies and large amount of CNTs in one image, automatic and accurate identification of CNTs has become the bottleneck for dispersion/orientation analysis. To solve this problem, shape identification is performed for each pixel in the filler identification step, so that individual CNTs can be extracted from images automatically. The improved filler identification enables more accurate analysis of CNT dispersion and orientation. The dispersion index and orientation index obtained for both synthetic and real images from model compounds correspond well with the observations. Moreover, these indices help to explain the electrical properties of CNT/silicone composite, which is used as a model compound. This method can also be extended to other polymer composites with high-aspect-ratio fillers.

Optimal-mass-transfer-based estimation of glymphatic transport in living brain

It was recently shown that the brain-wide cerebrospinal fluid (CSF) and interstitial fluid exchange system designated the ‘glymphatic pathway’ plays a key role in removing waste products from the brain, similarly to the lymphatic system in other body organs . It is therefore important to study the flow patterns of glymphatic transport through the live brain in order to better understand its functionality in normal and pathological states. Unlike blood, the CSF does not flow rapidly through a network of dedicated vessels, but rather through para-vascular channels and brain parenchyma in a slower time-domain, and thus conventional fMRI or other blood-flow sensitive MRI sequences do not provide much useful information about the desired flow patterns. We have accordingly analyzed a series of MRI images, taken at different times, of the brain of a live rat, which was injected with a paramagnetic tracer into the CSF via the lumbar intrathecal space of the spine. Our goal is twofold: (a) find glymphatic (tracer) flow directions in the live rodent brain; and (b) provide a model of a (healthy) brain that will allow the prediction of tracer concentrations given initial conditions. We model the liquid flow through the brain by the diffusion equation. We then use the Optimal Mass Transfer (OMT) approach to derive the glymphatic flow vector field, and estimate the diffusion tensors by analyzing the (changes in the) flow. Simulations show that the resulting model successfully reproduces the dominant features of the experimental data. Keywords: inverse problem, optimal mass transport, diffusion equation, cerebrospinal fluid flow in brain, optical flow, liquid flow modeling, Monge Kantorovich problem, diffusion tensor estimation

A Complete System for Automatic Extraction of Left Ventricular Myocardium From CT Images Using Shape Segmentation and Contour Evolution

The left ventricular myocardium plays a key role in the entire circulation system and an automatic delineation of the myocardium is a prerequisite for most of the subsequent functional analysis. In this paper, we present a complete system for an automatic segmentation of the left ventricular myocardium from cardiac computed tomography (CT) images using the shape information from images to be segmented. The system follows a coarse-to-fine strategy by first localizing the left ventricle and then deforming the myocardial surfaces of the left ventricle to refine the segmentation. In particular, the blood pool of a CT image is extracted and represented as a triangulated surface. Then, the left ventricle is localized as a salient component on this surface using geometric and anatomical characteristics. After that, the myocardial surfaces are initialized from the localization result and evolved by applying forces from the image intensities with a constraint based on the initial myocardial surface locations. The proposed framework has been validated on 34-human and 12-pig CT images, and the robustness and accuracy are demonstrated.

Automatic segmentation of the left atrium from MRI images using salient feature and contour evolution

We propose an automatic approach for segmenting the left atrium from MRI images. In particular, the thoracic aorta is detected and used as a salient feature to find a seed region that lies inside the left atrium. A hybrid energy that combines robust statistics and localized region intensity information is employed to evolve active contours from the seed region to capture the whole left atrium. The experimental results demonstrate the accuracy and robustness of our approach.

Hierarchical nucleus segmentation in digital pathology images

Extracting nuclei is one of the most actively studied topic in the digital pathology researches. Most of the studies directly search the nuclei (or seeds for the nuclei) from the finest resolution available. While the richest information has been utilized by such approaches, it is sometimes difficult to address the heterogeneity of nuclei in different tissues. In this work, we propose a hierarchical approach which starts from the lower resolution level and adaptively adjusts the parameters while progressing into finer and finer resolution. The algorithm is tested on brain and lung cancers images from The Cancer Genome Atlas data set.

A Kalman Filtering Perspective for Multiatlas Segmentation

In multiatlas segmentation, one typically registers several atlases to the novel image, and their respective segmented label images are transformed and fused to form the final segmentation. In this work, we provide a new dynamical system perspective for multiatlas segmentation, inspired by the following fact: The transformation that aligns the current atlas to the novel image can be not only computed by direct registration but also inferred from the transformation that aligns the previous atlas to the image together with the transformation between the two atlases. This process is similar to the global positioning system on a vehicle, which gets position by inquiring from the satellite and by employing the previous location and velocity-neither answer in isolation being perfect. To solve this problem, a dynamical system scheme is crucial to combine the two pieces of information; for example, a Kalman filtering scheme is used. Accordingly, in this work, a Kalman multiatlas segmentation is proposed to stabilize the global/affine registration step. The contributions of this work are twofold. First, it provides a new dynamical systematic perspective for standard independent multiatlas registrations, and it is solved by Kalman filtering. Second, with very little extra computation, it can be combined with most existing multiatlas segmentation schemes for better registration/segmentation accuracy.

Estimation of Myocardial Volume at Risk from CT Angiography.

The determination of myocardial volume at risk distal to coronary stenosis provides important information for prognosis and treatment of coronary artery disease. In this paper, we present a novel computational framework for estimating the myocardial volume at risk in computed tomography angiography (CTA) imagery. Initially, epicardial and endocardial surfaces, and coronary arteries are extracted using an active contour method. Then, the extracted coronary arteries are projected onto the epicardial surface, and each point on this surface is associated with its closest coronary artery using the geodesic distance measurement. The likely myocardial region at risk on the epicardial surface caused by a stenosis is approximated by the region in which all its inner points are associated with the sub-branches distal to the stenosis on the coronary artery tree. Finally, the likely myocardial volume at risk is approximated by the volume in between the region at risk on the epicardial surface and its projection on the endocardial surface, which is expected to yield computational savings over risk volume estimation using the entire image volume. Furthermore, we expect increased accuracy since, as compared to prior work using the Euclidean distance, we employ the geodesic distance in this work. The experimental results demonstrate the effectiveness of the proposed approach on pig heart CTA datasets.