Efficient Electrical Impedance Tomography Software Based on the Dual Reciprocity Boundary Element Methods

这项小型企业创新第一阶段研究项目将开发高效的计算算法，利用电阻抗断层扫描（EIT）对医学和工业中的二维（2-D）和三维（3-D）应用进行精确成像。EIT试图通过在物体表面施加特定的电流，并测量在物体表面产生的电压，来确定物体内部电导率的分布。与其他成像方法相比，如果成功，EIT在经济，方便和安全方面具有显着优势，可用于各种临床和工业应用。虽然在实验EIT技术和EIT的数学建模方面取得了很大进展，但它仍然局限于实验室情况和二维成像对象。将EIT扩展到实际情况的主要障碍似乎是缺乏能够执行准确数据反演的有效算法。传统的EIT反演算法要么基于启发式技术，只适用于2-D环状几何，要么基于使用有限元的完整数值解。在本研究中，计算效率更高的边界元方法（BEM）将通过使用双互易技术的新算法扩展到EIT。这些算法将允许在复杂的2-D和3-D几何中进行有效的成像，并将显着减少问题的大小，避免繁琐的网格/网格生成，并提供数量级的加速。第一阶段的研究将开发利用双互易边界元反演EIT数据的数值算法和软件。开发的软件将在分析生成的正向问题数据上进行测试。第二阶段将开发算法，开发一个原型EIT系统，使用并进一步完善第一阶段的算法。第三阶段将使开发的系统和软件商业化。

This Small Business Innovation Phase I Research project will develop efficient computational algorithms that will enable accurate imaging using Electrical Impedance Tomography (EIT) for both two-dimensional (2-D) and three-dimensional (3-D) applications in medicine and industry. EIT attempts to determine the distribution of electrical conductivity inside objects by applying specified currents at their surface, and measuring the voltage induced there. In comparison to other imaging methods, if successful, EIT offers significant advantages in economy, convenience, and safety for a wide variety of clinical and industrial applications. While much progress in experimental EIT techniques and in the mathematical modeling of EIT have been made, it remains restricted to laboratory situations and imaging objects in 2-D. The chief stumbling block to extending EIT to practical situations appears to be the lack of efficient algorithms that can perform accurate inversion of data. Conventional inversion algorithms in EIT are based on either heuristic techniques that are only applicable to 2-D ring-like geometries, or on full numerical solution using Finite Elements. In the proposed research the much more computationally efficient Boundary Element Method (BEM) will be extended to EIT by using new algorithms that use dual reciprocity techniques. These algorithms will allow efficient imaging in complicated 2-D and 3-D geometries and will significantly reduce problem size, avoid cumbersome grid/mesh generation, and offer order of magnitude speed-up. Phase I research will develop the numerical algorithms and software for inverting EIT data using Dual Reciprocity BEM. The software developed will be tested on analytically generated forward problem data. Phase II will develop algorithms in the develop a prototype EIT system using and further refining the Phase I algorithm. Phase III will commercialize the developed system and software.