Biomedical Engineering Reference
In-Depth Information
characterized system properties (e.g., a Raman scatterer whose presence in
the system was not known) that would doom an explicit calibration.
For the past two decades, the workhorse of implicit linear modeling has
been partial least squares (PLS) (see Haaland and Thomas [10] and Chap. 8).
PLS uses only training spectra and a target analyte's concentration to per-
form its calibration. If the Raman spectrum of the target is also available, this
can be folded into the calibration process. Various methods of utilizing this
information have been explored, including making a better model of the inter-
ference spectra [11] and requiring the regression vector to share the target's
main spectral features [12]. These methods usually provide only incremen-
tal advantages over standard PLS in most circumstances, but they are an
important part of the calibrator's toolbox when the information is available.
Three metrics characterizing chemometric concentration predictions are
commonly reported: the number of basis spectra in the optimal model (or
the “rank”), the root-mean-squared error of prediction (RMSEP), and the
correlation between the predicted and reference values (usually given as an
r
2
value). For a training set of
N
samples, a model of rank less than
N/
2or
N/
3
is generally regarded as unreliable, as mentioned above. When
N
is not large
enough to build independent training and validation sets of su
cient size,
often a cross-validation is performed, where one or more samples are rotated
out of the training set in sequence, until each sample's concentration has been
predicted. In this case, one should report a root-mean-squared error of cross-
validation (RMSECV), which is likely to be slightly lower than an RMSEP
value. The distinction is often not crucial, particularly in exploratory work;
the general term “error” will be used in the discussions below to apply to both
RMSEP and RMSECV unless noted otherwise.
For applications in which bulk optical properties vary from sample to sam-
ple, the linearity assumptions mentioned above can be strongly violated. This
is an issue, for example, in in vivo tissue measurements on a cohort of human
subjects. In this case, it is important to decouple the Raman spectral signature
from the modifications imparted by the turbidity. A recent pair of publica-
tions has reported a way of extracting the so-called “intrinsic Raman signal”
from turbid media [13, 14]. The general method requires an independent mea-
surement of the mean free scattering pathlength in the turbid medium; the
authors advertise, however, a future publication concering limiting cases that
can bypass this constraint.
16.5 Published Results
16.5.1 Best-Case Limits of Detection
Raman spectra of biological fluids always include a broad background com-
ponent, and usually this background is much stronger than the signal of the
analyte of interest. Although pure biofluids do not tend to autofluoresce as
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