Mathematical Tools for Non-invasive Spectroscopic Monitoring of Blood Chemistry

研究者和他的同事们共同努力，从分析、几何和统计学的角度来分析高维光谱数据的问题。分析化学家面临的一个主要挑战是如何组织和处理大量的测量和计算数据。最近的研究表明，特殊的几何结构可以有效地转录和模拟光谱测量和物质组成之间的关系。研究人员开发工具来识别这些结构，并使分析和特征提取过程自动化。特别是，研究人员专注于血液的近红外光谱，目的是通过无创光谱测量来估计各种血液分析物的浓度。多学科团队采用连贯的方法，其中化学分析，血液病理学和传感器工程的各个方面与数学分析工具相互作用。他们适应和扩展计算软件的化学光谱的特定几何形状，其中的数据流形需要参数化的各种组成材料的浓度。为了实现这种参数化，他们利用数学工具对数据进行局部多尺度描述，并利用聚类技术对基因阵列的表达谱进行数据分析。将光照射在皮肤上，就可以获得皮肤下血液及其化学成分的光谱数据。因此，如果人们能够理解这些数据，无创血液分析是可能的。研究者和他的同事们运用了一系列数学和统计学的思想来构建能够理解这些数据的工具。由于血液化学在健康中所起的作用，有重要的医疗回报。此外，在科学和工程领域，寻找有效的方法来理解大量高维数据是一个潜在的数学问题，因此该项目的潜在影响甚至更广泛。该项目为学生和博士后提供跨学科的研究和培训机会。

The investigator and his colleagues undertake a coordinatedeffort to bring to bear ideas from analysis, geometry, andstatistics on the problem of analysing spectroscopic data in highdimensions. A major challenge confronting the analytical chemistinvolves the organization and manipulation of massive amounts ofdata, both measured and computed. Recent work indicates thatspecial geometric structures allow for efficient transcriptionand modeling of the relation between spectral measurements andmaterial composition. The investigators develop tools to identifysuch structures and to automate the process of analysis andfeature extraction. In particular, the investigators concentrateon near-infrared spectra of blood, with the goal being toestimate concentrations of various blood analytes fromnoninvasive spectrometric measurements. The multidisciplinaryteam undertakes a coherent approach in which various aspects ofchemical analysis, blood pathology, and sensor engineeringinteract with mathematical analytic tools. They adapt and extendcomputational software to the particular geometry of chemicalspectra, for which the data manifolds need to be parametrized bythe concentrations of various constituent materials. To achievesuch parametrizations, they exploit mathematical tools for localmultiscale descriptions of data together with clusteringtechniques that occur naturally in the context of data analysisfor expression profiles of gene arrays. Shining a light on the skin allows one to get spectral dataabout the blood beneath the skin and its chemical components.Hence noninvasive blood analysis is possible, if only one couldmake sense of the data. The investigator and his colleagues applya range of mathematical and statistical ideas to build tools thatcan make sense of such data. There are important medical payoffsbecause of the role blood chemistry plays in health. Moreover,the underlying mathematical problem, to find efficient ways tomake sense of enormous volumes of high-dimensional data, arisesacross science and engineering, so the potential impact of theproject is even wider. The project provides interdisciplinaryresearch and training opportunities for students and postdocs.