Statistical Analysis of Raman Spectroscopy Data in a Bone Healing Study

• Activity Number: 153
• Type: Invited
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Arash Amini*+ and Liza Levina and Kirby Shedden
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: Raman Spectroscopy ; Bone Mineralization ; Regression models ; Multivariate Analysis ; Sparse representations ; Functional data analysis

Abstract

We consider some statistical aspects of dealing with data obtained by Raman Spectroscopy, henceforth referred to as RS. We will investigate the data from a particular experiment, in which RS is used to study the bone healing process. The data is a collection of Raman spectra from roughly 30 rats, recorded across a time span of 8 weeks, during which surgically induced bone fractures in their legs were observed as they healed. In each data acquisition round, 50 spectra (per rat, per time point) were recorded at different spatial positions, in an attempt to capture the 3D nature of the process, akin to the principles used in tomography.

For the analysis, we first propose a sparse functional representation of the spectra which can be used for denoising, dimension reduction and identifying anomalies. We then consider the problem of prediction of bone mineral density, and some other quantities correlating with bone health, based on the Raman spectra. To form the prediction, we will use a suitably regularized regression model applied to the sparse representation obtained earlier. The generalization ability of the predictor is examined using cross-validation.