Mathematical theory and numerical analysis of bioluminescence tomography
نویسندگان
چکیده
Molecular imaging is widely recognized as the main stream in the next generation of biomedical imaging. Bioluminescence tomography (BLT) is a rapidly developing new area of molecular imaging. The goal of BLT is to provide quantitative three-dimensional reconstruction of a bioluminescent source distribution within a small animal from optical signals on the surface of the animal body. In this paper, a mathematical framework is established for BLT. Solution existence and uniqueness are established. Continuous dependence of the solution is demonstrated with respect to data. Stable BLT schemes are studied, leading to error estimates and convergence of the methods. A numerical example is presented to illustrate the algorithmic performance. (Some figures in this article are in colour only in the electronic version)
منابع مشابه
Bioluminescence Tomography: Biomedical Background, Mathematical Theory, and Numerical Approximation.
Over the last couple of years molecular imaging has been rapidly developed to study physiological and pathological processes in vivo at the cellular and molecular levels. Among molecular imaging modalities, optical imaging stands out for its unique advantages, especially performance and cost-effectiveness. Bioluminescence tomography (BLT) is an emerging optical imaging mode with promising biome...
متن کاملStudies of a Mathematical Model for Temperature-modulated Bioluminescence Tomography
We introduce and study a mathematical model for temperature-modulated bioluminescence tomography (TBT). The model is capable of self-adjusting values of experimental parameters that are used in the formulation. Major theoretical results of the paper include: solution existence of the model, convergence of numerical solutions, an iterative scheme based on linearization, studies of the solution l...
متن کاملMathematical Study and Numerical Simulation of Multispectral Bioluminescence Tomography
Multispectral bioluminescence tomography (BLT) attracts increasingly more attention in the area of optical molecular imaging. In this paper, we analyze the properties of the solutions to the regularized and discretized multispectral BLT problems. First, we show the solution existence, uniqueness, and its continuous dependence on the data. Then, we introduce stable numerical schemes and derive e...
متن کاملTheoretical and numerical analysis on multispectral bioluminescence tomography
Recently, molecular imaging has been rapidly developed to study physiological and pathological processes in vivo at the cellular and molecular levels. Among molecular imaging modalities, optical imaging has attracted a major attention for its unique advantages. In this paper, we establish a mathematical framework for multispectral bioluminescence tomography (BLT) that allows simultaneous studie...
متن کاملA new general mathematical framework for bioluminescence tomography
Bioluminescence tomography (BLT) is a recently developed area in biomedical imaging. The goal of BLT is to quantitatively reconstruct a bioluminescent source distribution within a small animal from optical signals on the surface of the animal body. While there have been theoretical investigations of the BLT problem in the literature, in this paper, we propose a more general mathematical framewo...
متن کامل