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[Background]Recent advances in microscopy enable the acquisition of large numbers of tomographic images from living tissues. Three-dimensional microscope images are often displayed with volume rendering by adjusting the transfer functions. However, because the emissions from fluorescent materials and the optical properties based on point spread functions affect the imaging results, the intensity value can differ locally, even in the same structure. Further, images obtained from brain tissues contain a variety of neural structures such as dendrites and axons with complex crossings and overlapping linear structures. In these cases, the transfer functions previously used fail to optimize image generation, making it difficult to explore the connectivity of these tissues. [Results]This paper proposes an interactive visual exploration method by which the transfer functions are modified locally and interactively based on multidimensional features in the images. A direct editing interface is also provided to specify both the target region and structures with characteristic features, where all manual operations can be performed on the rendered image. This method is demonstrated using two-photon microscope images acquired from living mice, and is shown to be an effective method for interactive visual exploration of overlapping similar structures. [Conclusions]An interactive visualization method was introduced for local improvement of visualization by volume rendering in two-photon microscope images containing regions in which linear nerve structures crisscross in a complex manner. The proposed method is characterized by the localized multidimensional transfer function and interface where the parameters can be determined by the user to suit their particular visualization requirements.

This paper introduces a new design and application for direct volume manipulation for visualizing the intraoperative liver resection process. So far, interactive volume deformation and resection have been independently handled due to the difficulty of representing elastic behavior of volumetric objects. Our framework models global shape editing and discontinuous local deformation by merging proxy geometry encoding and displacement mapping. A local-frame-based elastic model is presented to allow stable editing of the liver shape including bending and twisting while preserving the volume. Several tests using clinical CT data have confirmed the developed software and interface can represent the intraoperative state of liver and produce local views of reference vascular structures, which provides a "road map of vessels" that are key features when approaching occluded tumors during surgery.

[Background]Dendrites of cortical neurons are widely spread across several layers of the cortex. Recently developed two-photon microscopy systems are capable of visualizing the morphology of neurons within deeper layers of the brain and generate large amounts of volumetric imaging data from living tissue. [Method]For visual exploration of the three-dimensional (3D) structure of dendrites and the connectivity among neurons in the brain, we propose a visualization software and interface for 3D images based on a new transfer function design using volume rendered feature spaces. This software enables the visualization of multidimensional descriptors of shape and texture extracted from imaging data to characterize tissue. It also allows the efficient analysis and visualization of large data sets. [Results]We apply and demonstrate the software to two-photon microscopy images of a living mouse brain. By applying the developed visualization software and algorithms to two-photon microscope images of the mouse brain, we identified a set of feature values that distinguish characteristic structures such as soma, dendrites and apical dendrites in mouse brain. Also, the visualization interface was compared to conventional 1D/2D transfer function system. [Conclusions]We have developed a visualization tool and interface that can represent 3D feature values as textures and shapes. This visualization system allows the analysis and characterization of the higher-dimensional feature values of living tissues at the micron level and will contribute to new discoveries in basic biology and clinical medicine.

This paper proposes a 3-D cardiovascular modeling system based on neonatal echocardiographic images. With the system, medical doctors can interactively construct patient-specific cardiovascular models, and share the complex topology and the shape information. For the construction of cardiovascular models with a variety of congenital heart diseases, we propose a set of algorithms and interface that enable editing of the topology and shape of the 3-D models. In order to facilitate interactivity, the centerline and radius of the vessels are used to edit the surface of the heart vessels. This forms a skeleton where the centerlines of blood vessel serve as the nodes and edges, while the radius of the blood vessel is given as an attribute value to each node. Moreover, parent-child relationships are given to each skeleton. They are expressed as the directed acyclic graph, where the skeletons are viewed as graph nodes and the connecting points are graph edges. The cardiovascular models generated from some patient data confirmed that the developed technique is capable of constructing cardiovascular disease models in a tolerable timeframe. It is successful in representing the important structures of the patient-specific heart vessels for better understanding in preoperative planning and electric medical recording of the congenital heart disease.

Individuals, cities, and nations compete for limited resources in many areas of the world. The social costs generated by competition include the over-exploitation of renewable resources and the depletion of non-renewable resources. This dissertation examines the problem of competition for limited resources in a game-theoretic framework. The goal is to gain insight regarding how economic agents choose strategies and programs regarding resources, so that we may design public policies that will motivate individuals, firms, and nations to generate greater values with limited resources. This dissertation demonstrates how to estimate those gains using game theory models involving Nash bargaining solutions and Markov perfect equilibria. Empirical versions of the models are solved using dynamic programming and numerical methods. In Manuscript One, a Nash bargaining model is applied to the problem of competition for limited water resources along the Rio Grande in southwestern Texas. Two cities, El Paso, Texas and Ciudad Juarez in Chihuahua, Mexico, withdraw water for municipal and industrial uses from the Hueco Bolson aquifer that lies beneath the international border. This empirical application of a bargaining model provides insight regarding the potential gains from cooperation regarding water resource management in the region. Finding solutions to dynamic, economic problems can require sophisticated mathematical tools, particularly when working with stochastic systems and when seeking solutions with desirable properties, such as subgame perfection. Two methods that can be used to solve non-cooperative dynamic game theory models are described in Manuscript Two: Ricatti equation methods and collocation. Either approach can be used to obtain Markov perfect equilibrium solutions to dynamic problems. Each has advantages and disadvantages. In Manuscript Three, numerical methods are used to solve non-cooperative dynamic game theory models involving the depletion of a non-renewab