Danny Z. Chen

Optimal Surface Segmentation in Volumetric Images-A Graph-Theoretic Approach

Efficient segmentation of globally optimal surfaces representing object boundaries in volumetric data sets is important and challenging in many medical image analysis applications. We have developed an optimal surface detection method capable of simultaneously detecting multiple interacting surfaces, in which the optimality is controlled by the cost functions designed for individual surfaces and by several geometric constraints defining the surface smoothness and interrelations. The method solves the surface segmentation problem by transforming it into computing a minimum s{\hbox{-}} t cut in a derived arc-weighted directed graph. The proposed algorithm has a low-order polynomial time complexity and is computationally efficient. It has been extensively validated on more than 300 computer-synthetic volumetric images, 72 CT-scanned data sets of different-sized plexiglas tubes, and tens of medical images spanning various imaging modalities. In all cases, the approach yielded highly accurate results. Our approach can be readily extended to higher-dimensional image segmentation.

Task scheduling and voltage selection for energy minimization

In this paper, we present a two-phase framework that integrates task assignment, ordering and voltage selection (VS) together to minimize energy consumption of real-time dependent tasks executing on a given number of variable voltage processors. Task assignment and ordering in the first phase strive to maximize the opportunities that can be exploited for lowering voltage levels during the second phase, i.e., voltage selection. In the second phase, we formulate the VS problem as an Integer Programming (IP) problem and solve the IP efficiently. Experimental results demonstrate that our framework is very effective in executing tasks at lower voltage levels under different system configurations.

Arc-modulated radiation therapy (AMRT) : a single-arc form of intensity-modulated arc therapy

Arc-modulated radiation therapy (AMRT) is a novel rotational intensity-modulated radiation therapy (IMRT) technique developed for a clinical linear accelerator that aims to deliver highly conformal radiation treatment using just one arc of gantry rotation. Compared to fixed-gantry IMRT and the multiple-arc intensity-modulated arc therapy (IMAT) techniques, AMRT promises the same treatment quality with a single-arc delivery. In this paper, we present a treatment planning scheme for AMRT, which addresses the challenges in inverse planning, leaf sequencing and dose calculation. The feasibility and performance of this AMRT treatment planning scheme have been verified with multiple clinical cases of various sites on Varian linear accelerators.

Optimal Net Surface Problems with Applications

In this paper, we study an interesting geometric graph called multi-column graph in the d-D space (d ? 3), and formulate two combinatorial optimization problems called the optimal net surface problems on such graphs. Our formulations capture a number of important problems such as surface reconstruction with a given topology, medical image segmentation, and metric labeling. We prove that the optimal net surface problems on general d-D multicolumn graphs (d ? 3) are NP-hard. For two useful special cases of these d-D (d ? 3) optimal net surface problems (on the so-called proper ordered multi-column graphs) that often arise in applications, we present polynomial time algorithms. We further apply our algorithms to some surface reconstruction problems in 3-D and 4-D, and some medical image segmentation problems in 3-D and 4-D, obtaining polynomial time solutions for these problems. The previously best known algorithms for some of these applied problems, even for relatively simple cases, take at least exponential time. Our approaches for these applied problems can be extended to higher dimensions.

Planar Spanners and Approximate Shortest Path Queries among Obstacles in the Plane

We consider the problem of finding an obstacle-avoiding path between two points s and t in the plane, amidst a set of disjoint polygonal obstacles with a total of n vertices. The length of this path should be within a small constant factor c of the length of the shortest possible obstacle-avoiding s-t path measured in the L p -metric. Such an approximate shortest path is called a c-short path, or a short path with stretch factor c. The goal is to preprocess the obstacle-scattered plane by creating an efficient data structure that enables fast reporting of a c-short path (or its length). In this paper, we give a family of algorithms for the above problem that achieve an interesting trade-off between the stretch factor, the query time and the preprocessing bounds. Our main results are algorithms that achieve logarithmic length query time, after subquadratic time and space preprocessing.

A Multiscale Model of Venous Thrombus Formation with Surface-Mediated Control of Blood Coagulation Cascade

A combination of the extended multiscale model, new image processing algorithms, and biological experiments is used for studying the role of Factor VII (FVII) in venous thrombus formation. A detailed submodel of the tissue factor pathway of blood coagulation is introduced within the framework of the multiscale model to provide a detailed description of coagulation cascade. Surface reactions of the extrinsic coagulation pathway on membranes of platelets are studied under different flow conditions. It is shown that low levels of FVII in blood result in a significant delay in thrombin production, demonstrating that FVII plays an active role in promoting thrombus development at an early stage.

A framed-quadtree approach for determining Euclidean shortest paths in a 2-D environment

In this paper we investigate the problem of finding a Euclidean (L/sub 2/) shortest path between two distinct locations in a planar environment. We propose a novel cell decomposition approach which calculates an L/sub 2/ distance transform through the use of a circular path-planning wave. The proposed method is based on a new data structure, called the framed-quadtree, which combines together the accuracy of high resolution grid-based path planning techniques with the efficiency of quadtree-based techniques, hence having the advantages of both. The heart of this method is a linear time algorithm for computing certain special dynamic Voronoi diagrams. The proposed method does not place any unrealistic constraints on obstacles or on the environment and represents an improvement in accuracy and efficiency over traditional path planning approaches in this area.

Predicting Protein-Protein Interactions from Protein Domains Using a Set Cover Approach

One goal of contemporary proteome research is the elucidation of cellular protein interactions. Based on currently available protein-protein interaction and domain data, we introduce a novel method, maximum specificity set cover (MSSC), for the prediction of protein-protein interactions. In our approach, we map the relationship between interactions of proteins and their corresponding domain architectures to a generalized weighted set cover problem. The application of a greedy algorithm provides sets of domain interactions which explain the presence of protein interactions to the largest degree of specificity. Utilizing domain and protein interaction data of S. cerevisiae, MSSC enables prediction of previously unknown protein interactions, links that are well supported by a high tendency of coexpression and functional homogeneity of the corresponding proteins. Focusing on concrete examples, we show that MSSC reliably predicts protein interactions in well-studied molecular systems, such as the 26S proteasome and RNA polymerase II of S. cerevisiae. We also show that the quality of the predictions is comparable to the maximum likelihood estimation while MSSC is faster. This new algorithm and all data sets used are accessible through a Web portal at http://ppi-cse.nd.edu

Simultaneous segmentation of multiple closed surfaces using optimal graph searching

This paper presents a general graph-theoretic technique for simultaneously segmenting multiple closed surfaces in volumetric images, which employs a novel graph-construction scheme based on triangulated surface meshes obtained from a topological presegmentation. The method utilizes an efficient graph-cut algorithm that guarantees global optimality of the solution under given cost functions and geometric constraints. The methods applicability to difficult biomedical image analysis problems was demonstrated in a case study of co-segmenting the bone and cartilage surfaces in 3-D magnetic resonance (MR) images of human ankles. The results of our automated segmentation were validated against manual tracings in 55 randomly selected image slices. Highly accurate segmentation results were obtained, with signed surface positioning errors for the bone and cartilage surfaces being 0.02 +/- 0.11mm and 0.17 +/- 0.12mm, respectively.

Leaf-sequencing for intensity-modulated arc therapy using graph algorithms

Intensity-modulated arc therapy (IMAT) is a rotational IMRT technique. It uses a set of overlapping or nonoverlapping arcs to create a prescribed dose distribution. Despite its numerous advantages, IMAT has not gained widespread clinical applications. This is mainly due to the lack of an effective IMAT leaf-sequencing algorithm that can convert the optimized intensity patterns for all beam directions into IMAT treatment arcs. To address this problem, we have developed an IMAT leaf-sequencing algorithm and software using graph algorithms in computer science. The input to our leaf-sequencing software includes (1) a set of (continuous) intensity patterns optimized by a treatment planning system at a sequence of equally spaced beam angles (typically 10 degrees apart), (2) a maximum leaf motion constraint, and (3) the number of desired arcs, k. The output is a set of treatment arcs that best approximates the set of optimized intensity patterns at all beam angles with guaranteed smooth delivery without violating the maximum leaf motion constraint. The new algorithm consists of the following key steps. First, the optimized intensity patterns are segmented into intensity profiles that are aligned with individual MLC leaf pairs. Then each intensity profile is segmented into k MLC leaf openings using a k-link shortest path algorithm. The leaf openings for all beam angles are subsequently connected together to form 1D IMAT arcs under the maximum leaf motion constraint using a shortest path algorithm. Finally, the 1D IMAT arcs are combined to form IMAT treatment arcs of MLC apertures. The performance of the implemented leaf-sequencing software has been tested for four treatment sites (prostate, breast, head and neck, and lung). In all cases, our leaf-sequencing algorithm produces efficient and highly conformal IMAT plans that rival their counterpart, the tomotherapy plans, and significantly improve the IMRT plans. Algorithm execution times ranging from a few seconds to 2 min are observed on a laptop computer equipped with a 2.0 GHz Pentium M processor.