U.S.-France Cooperative Research: Modelling and Interrogation of Cancellous Bone

该提案要求资助一个美法合作研究项目，建立松质骨模型，然后根据超声数据对这些模型进行测试。美国团队由特拉华大学的罗伯特·吉尔伯特领导，由擅长建模、微分方程和反问题的应用数学家组成。法国研究小组的参与者来自国家卫生与医学研究所（INSERM）和弹性研究中心：问题与逆向研究中心（OEPDI），他们是实验家，将对美国研究小组生成的模型进行测试。运用的数学方法将是同质化理论、反问题和反同质化理论。美国研究团队计划解决生物学中两大数学挑战的问题，即涉及小梁非线性建模率的生物组织进化方程的均质化问题，以及小梁微观结构与复合骨基质超声响应分析的相关性问题。更广泛的影响该奖项是利用美国参与者在数学建模方面的专业知识，法国INSERM参与者在超声诊断和治疗应用方面的专业知识，以及法国OEPDI参与者在渐近，数值和实验方法方面的专业知识的合作。这项工作的结果将有助于理解、治疗和预防骨质疏松症，这是一个日益严重的问题在美国。这项合作将进一步促进研究和研究生的全球培训。

This proposal requests funding for a US-France cooperative research project modeling cancellous bone and then testing these models against ultrasound data. The US team, led by Robert Gilbert of the University of Delaware, is comprised of applied mathematicians with expertise in modeling, differential equations, and inverse problems. The French team, with participants at Institute de la Sante et de la Recherche Medicale (INSERM) and Ondes Elastiques: Problemes Directs et Inverses (OEPDI) are experimentalists and will test the models that are generated by the American team. Intellectual MeritThe mathematical methodology utilized will be the theory of homogenization, inverse problems, and inverse homogenization. The American research team is planning to address the problems representing two major mathematical challenges in biology, namely homogenization of evolution equations of biological tissue involving nonlinear modeling rates of the trabeculae, and the correlation of trabeculae microstructure with the analysis of the ultrasound response of the composite bone matrix. Broader ImpactsThis award is a collaboration leveraging the expertise in mathematical modeling of the US participants, the expertise in diagnostic and therapeutic applications of ultrasound of the French INSERM participants, and the expertise in asymptotic, numerical, and experimental methods of the French OEPDI participants. Outcome of this work will be useful for understanding, treating, and preventing osteoporosis, a growing problem in the US. The collaboration will further the research and global training of a graduate student.