Raman Spectroscopy of Blood and Urine Specimens - Emerging Raman Applications and Techniques in Biomedical and Pharmaceutical Fields - page 386

the application of pressure; the “whitening” of a pressed fingertip is an exam-
ple. Differences in fingertip spectra before and after the application of gentle
pressure have been shown to exhibit blood-like spectral features [6].
Finally, one can abandon the goal of extracting a “pure blood” spectrum
from that of the surrounding tissue, and instead search for correlations be-
tween a bulk-tissue Raman spectrum and the one or more blood analytes
whose concentrations are ultimately desired to be known. For example, as
depicted in Fig. 16.4c, a study could obtain Raman spectra from volunteers'
arms and simultaneously obtain blood samples whose chemical levels are an-
alyzed on a traditional chemical analyzer. Correlation analysis is then per-
formed in an attempt to predict a chemical's concentration based upon the
corresponding Raman data. In principle, if the calibration proves to be ac-
curate and robust, it does not matter whether the spectral signature of the
chemical actually arises from the blood, as opposed to the surrounding tissue
(e.g., interstitial fluid) or some weighted combination of the two. It could even
be possible that the target chemical contributes no Raman signal at all but
is correlated in concentration with another chemical that does. Details of the
calibration process are sketched in the following section.

16.4.3 Extracting Chemical Concentrations

This chapter focuses on extracting quantitative chemical concentrations. Pre-
sumably, those values are ultimately used to make a binary decision (clas-
sification), such as whether to take clinical action. In principle and often in
practice, one can go straight from Raman spectra to classification, bypassing
the step of interpreting chemical contributions. Here, however, we will confine
ourselves to converting the Raman signal into concentration predictions of one
or more chemicals present in the sample.

Assumption of Linearity

To convert an optical signal into a concentration prediction, a linear relation-
ship between the raw signal and the concentration is not necessary. Beer's
law for absorption spectroscopy, for instance, models transmitted light as a
decaying exponential function of concentration. In the case of Raman spec-
troscopy of biofluids, however, the measured signal often obeys two convenient
linearity conditions without any need for preprocessing. The first condition is
that any measured spectrum S of a sample from a certain population (say,
of blood samples from a hospital) is a linear superposition of a finite number
of pure basis spectra P i that characterize that population. One of these basis
spectra is presumably the pure spectrum P A of the chemical of interest, A .
The second linearity assumption is that the amount of P A present in the net
spectrum S is linearly proportional to the concentration c A of that chemical.
In formulaic terms, the assumptions take the mathematical form
S = c A P A +
i

c i P i

(16.1)