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 Merit The 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 Impacts This 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.
