Mathematical Sciences: Mathematical and Experimental Studiesof Pulsatile Flow in Free Moving Elastic Tubes

数学科学：自由运动弹性管中脉动流的数学和实验研究

• 批准号: 9209129
• 负责人: Dalin Tang
• 金额: $ 6万
• 依托单位: Worcester Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-09-15 至 1995-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9209129&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Experimental; Studiesof; Pulsatile

The investigators develop a two-dimensional (axisymmetric) nonlinear mathematical model of viscous flow in tapered free moving elastic tubes, a numerical method to solve the model, and an ultrasonic method to measure the movement of vessel walls in an experimental model. The model is intended to represent blood flow in large arteries with stenoses and atherosclerosis. Detailed localized numerical solution for the flow in free moving elastic tubes with local hardening, thickening and occlusions is obtained. Corresponding experiments are made in the lab using elastic tubes. The numerical and experimental results are compared and the mathematical model may be further refined. Those results are also compared with published results of in vivo measurements to verify the validity of the models and techniques. The numerical results obtained and experimental techniques developed in this project will lead to better understanding of blood flow in large arteries and may be of clinical value in the future. As is well-known, cardiovascular diseases are the leading causes of morbidity and mortality in the United States. Specific diseases are typically atherosclerosis, stenoses, and aneurysms that often remain undetected due to inadequate diagnostic techniques. This research aims to provide a valid improved mathematical model for blood flow in large arteries, an efficient numerical method for mathematical simulations, and an accurate noninvasive ultrasound measurement technique. These could be very useful for the early diagnosis of blood vessel diseases and therefore have the potential to save many lives in the future. The numerical method developed in this project is also applicable to many other free moving boundary problems and is itself of significance to applied mathematics.

研究人员开发了一个二维（轴对称） 渐缩自由管粘性流的非线性数学模型 移动弹性管，数值方法来解决模型，和 一种超声波方法来测量血管壁的运动， 实验模型。 该模型旨在代表血液 大动脉狭窄和动脉粥样硬化的血流。 自由运动中流动的详细局部化数值解 局部硬化、增厚和闭塞的弹性管， 得到了 在实验室进行了相应的实验， 弹性管 数值计算和实验结果表明， 比较，并且可以进一步改进数学模型。 这些结果也与发表的结果进行了比较，在体内 测量，以验证模型和技术的有效性。 所获得的数值结果和实验技术 在这个项目中开发将导致更好地了解 大动脉中的血流，并可能在 未来 众所周知，心血管疾病是 美国发病率和死亡率的原因。 具体 典型的疾病是动脉粥样硬化、狭窄和动脉瘤 由于诊断不充分， 技术. 本研究旨在提供一种有效的改进的 大动脉血流的数学模型，一个有效的 数学模拟的数值方法，以及一个精确的 非侵入性超声测量技术。 这些可能是 对血管疾病的早期诊断非常有用， 因此有可能在未来拯救许多生命。 本计画所发展之数值方法亦适用 许多其他自由移动边界问题，本身就是 对应用数学的意义。