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REVIEW

Pharmaceutical Applications of Separation of Absorption andScattering in Near-Infrared Spectroscopy (NIRS)

ZHENQI SHI, CARL A. ANDERSON

Graduate School of Pharmaceutical Sciences, Duquesne University, Pittsburgh, Pennsylvania 15282

Received 14 December 2009; accepted 20 April 2010

Published online 2 June 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jps.22228

ABSTRACT: The number of near-infrared (NIR) spectroscopic applications in the pharmaceu-tical sciences has grown significantly in the last decade. Despite its widespread application, the

fundamental interaction between NIR radiation and pharmaceutical materials is often not

mechanistically well understood. Separation of absorption and scattering in near-infrared

spectroscopy (NIRS) is intended to extract absorption and scattering spectra (i.e., absorption

and reduced scattering coefficients) from reflectance/transmittance NIR measurements. Thepurpose of the separation is twofold: (1) to enhance the understanding of the individual roles

played by absorption and scattering in NIRS and (2) to apply the separated absorption and

scattering spectra for practical spectroscopic analyses. This review paper surveys the multiple

techniques reported to date on the separation of NIR absorption and scattering within phar-

maceutical applications, focusing on the instrumentations, mathematical approaches used to

separate absorption and scattering and related pharmaceutical applications. This literature

review is expected to enhance the understanding and thereby the utility of NIRS in pharma-

ceutical science. Further, the measurement and subsequent understanding of the separation of

absorption and scattering is expected to increase not only the number of NIRS applications, but

also their robustness. 2010 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci

99:47664783, 2010

Keywords: near-infrared spectroscopy; absorption spectroscopy; light-scattering; Monte

Carlo; radiative transport equation

INTRODUCTION

The number of near-infrared spectroscopic applica-

tions in pharmaceutical science has grown signifi-

cantly in the last decade. These applications have

rapidly permeated the research and development

activities in the pharmaceutical industry, including

raw material characterization, powder blending

monitoring, granulation process control, tablet

manufacture and finished products characteriza-

tion.1,2 Much of the appeal of this technique is due to

the fact that a wealth of chemical and physical

information can be obtained noninvasively within

seconds, often without the need for any sample

preparation.

As NIR spectra contain information pertaining

to both the chemical and physical properties of

the sample matrix, multivariate modeling is often

required to correlate spectral information with the

chemical or physical properties of the analyte of

interest. In spite of the extensive application of NIRS,

the underlying optical behavior of NIR radiation in

pharmaceutical materials is often not mechanisti-

cally well understood.

It is well known that two primary events occur

when NIR light impinges on a turbid medium (e.g.,

biological tissues or pharmaceutical solids): absorp-

tion and scattering.2Absorption reduces the intensity

of photons of specific energy due to an alteration of

the molecular dipole of a bond; therefore, chemical

attributes such as concentration are expected to affect

absorption events. Scattering, on the other hand, is

caused by mismatched refractive indices at particle

air/particleparticle interstitial spaces within the

sample; therefore, physical parameters such as

sample density and porosity are dominant factors

in determining scattering events. Considerable suc-

cess has been achieved in the field of biomedical optics

when separated absorption and scattering properties

Correspondence to: Carl A. Anderson (Telephone: 412-396-1102;Fax: 412-396-4660; E-mail: [email protected])

Journal of Pharmaceutical Sciences, Vol. 99, 47664783 (2010)

2010 Wiley-Liss, Inc. and the American Pharmacists Association

4766 JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 12, DECEMBER 2010


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were used to describe underlying optical behaviors in

tissue samples.3,4 The separated absorption and

scattering properties are often used to understand

the optical behaviors in tissues, correlating them

directly with the chemical and physical features of the

tissue medium. The major goal in tissue optics is to

utilize the separated absorbing and scattering proper-

ties of tissue samples for diagnostic and therapeuticapplications.

Due to the common features shared by tissue

samples and pharmaceutical solids (as both are

turbid media), more and more attention has been

paid to the separation of NIR absorption and

scattering in pharmaceutical applications. The two

main purposes of the separation are to improve the

understanding of individual roles played by absorp-

tion and scattering in NIRS, and to utilize the

separated absorption and scattering spectra for

qualitative and quantitative applications. To date,

five techniques to separate NIR absorption and

scattering of pharmaceutical related materials have

been reported: spatially resolved spectroscopy,58

frequency-resolved spectroscopy,921 time-resolved

spectroscopy,2227 the integrating sphere based

reflectance and transmittance measurements,2831

and measurements of remission, absorption and

transmission fractions through layers of material

of different thicknesses.32,33 A review of how these

techniques are applied specifically to pharmaceutical

application has yet to be reported.

A clear understanding of these optical phenomena

is expected to facilitate the application of NIRS to

pharmaceutical science, particularly as efforts toengage process analytical technology (PAT)-based

manufacturing strategies intensify. Therefore, a

literature review detailing the separation of absorp-

tion and scattering in pharmaceutical materials is

expected to aid in the implementation of NIRS

through a fundamental understanding of the under-

lying optical phenomena. This fundamental under-

standing will greatly increase the potential success

and longevity of NIRS methods in the pharmaceutical

industry.

The goal of this paper is to review the approaches

that have been applied in pharmaceutical analyses,

focusing on the following perspectives: (1) instru-

mentation, (2) mathematical approaches to separate

absorption and scattering, and (3) related pharma-

ceutical applications for the individual techniques

as mentioned above. The review begins with a

theoretical background of light propagation in

turbid media, followed by a literature survey and a

comparison among these techniques from both

theoretical and application standpoints, and con-

cludes with a discussion of the authors perspective

on future trends of these techniques in the pharma-

ceutical applications.

THEORYLIGHT PROPAGATION IN TURBIDMEDIA

Turbid Medium

In physics and chemistry, light propagation is often

described by its wave-like and particle-like proper-

ties. Wave-like properties indicate light to be an

oscillating electromagnetic (EM) field with a con-tinuous range of energies. This is also referred to as

the classical theory of light propagation. Particle-like

properties indicate that light waves consist of

packets of energy called photons, which are described

by the quantum model. Quantum theory introduces

the idea that light and matter exchange energy as

photons.

It is well known that light propagation in dilute,

nonscattering solution systems is described by the

LambertBeers law. Since a diluted sample does

not scatter light, a fixed path-length is typically

used in LambertBeers law. If the sample multiplyscatters light, then a distribution of path-lengths

will be observed. Multiply scattering, also called

multiple scattering, is the photon behavior in

which individual photons are scattered a large

number of times before eventually escaping from or

being absorbed by the medium. Thus, the descrip-

tion of light propagation in strongly scattering

media becomes more complicated than is expressed

by the LambertBeers law. Examples for multiply

scattering media are concentrated solutions, col-

loids, semi-solids, and solids, etc. This is also the

reason that models for light propagation in strongly

scattering media have been used so widely in

medicine (i.e., tissue optics), agriculture, the paper

industry, and pharmaceuticals. The most common

examples of strongly scattering media in the

pharmaceutical field are solid materials, either in

free powder or consolidated compact forms. A

sampling medium exhibiting the multiply scatter-

ing property is normally referred to as a turbid

medium.

Radiative Transport Equation

Considerable success has been achieved in describ-ing the light propagation in turbid media by the

application of radiative transfer theory (radiative

transport equation, RTE).3,4 Radiative transfer

theory is not specific to light and has other

important applications in areas such as neutron

transport and thermodynamics. In the RTE formal-

ism, light propagation is considered equivalent to

the flow of discrete photons, which are either

absorbed or scattered by the medium. RTE only

accounts for the transport of light energy in the

medium. It ignores the wave amplitude and

phases and does not itself include effects such as

DOI 10.1002/jps JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 12, DECEMBER 2010

SEPARATION OF ABSORPTION AND SCATTERING IN NIRS 4767


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diffraction, interference, or polarization. Further,

no correlation between the radiation fields is

considered in RTE (i.e., photons are independent

of each other).

In radiative transfer theory, a small packet of light

energy (I) is considered by defining its position (r)directed in a cone of solid angle (dV) and oriented in

the direction of propagation ^s in a sample medium.As it propagates in the medium, the packet loses a

fraction of its energy due to absorption and scattering

out of^s (the first term on the right side of Eq. 1), butalso gains energy from light scattered into the ^sdirection from other ^s0 directions (the second term onthe right side of Eq. 1). These processes are quantified

by the integral-differential equation known as the

RTE:3

^s ~rIr; ^s ma msIr; ^s ma ms

4p Zp^s ^s0Ir; ^sdV 1

where p^s ^s0 is the scattering phase function (SPF)between the ^s and ^s0 directions. ma and ms are theabsorption and scattering coefficients of the sample

medium, respectively. In RTE, the ms and ma are

defined as follows.

A medium containing a uniform distribution of

identical scattering and absorbing particles is char-

acterized by the scattering and absorption coeffi-

cients, respectively

ms rss (2)

ma rsa (3)where ss and sa are the cross sectional areas of the

scattering and absorption particles, respectively,

which describe the propensity to scatter and absorb.

r is the number density of scattering and absorption

particles in the sample medium. The standard units

of for ms and ma are cm1.

Different terminologies are often used to represent

the ms and ma when individual techniques are used to

separate absorption and scattering, despite the fact

that they often share the same underlying optical

definitions. The absorption coefficient is defined asthe probability of photons being absorbed, while the

scattering coefficient is defined as the probability

of photons being scattered. The reciprocal of ms is

the scattering mean free path, representing the

average distance a photon travels between consecu-

tive scattering events. The reciprocal of ma is the

absorption mean free path, representing the average

distance a photon travels between consecutive

absorption events. Absorption and scattering coeffi-

cients together are often referred to as the optical

coefficients or the optical properties of a sample

medium.

Diffusion Approximation to the RTE

Due to the multiply scattering events that occur when

NIR light interacts with turbid media, the diffusion

approximation is commonly used to simplify the RTE.

The diffusion approximation is applicable to situations

where scattering dominates the light propagation

process. In the diffusion process, the particles (in the

current case, photons) move through a medium in aseries of steps of random length and direction (i.e.,

random walk). Each step begins with a scattering

event that is equally likely to be taken in any direction.

In the diffusion approximation, the scattering

event in RTE is described by the reduced scattering

coefficient m0s, which is related to the previouslydefined parameters by

m0s 1 gms (4)

where g is the anisotropy factor, describing theangular distribution of SPF between ^s0 and ^s inEq. (1). The anisotropy factor is zero for isotropic

scattering. A nonzero g value is representative ofanisotropic scattering, in which total forward scatter-

ing is described by g 1, while total backwardscattering is described by g 1. As it can be seenin Figure 1, a scatterer with a g in the range of 0 to 1means it is more likely to forward-scatter the incident

photons, while a scatter with g ranging from 1 to 0indicates it is more likely to backward-scatter the

incident photons. Pharmaceutical solids are reported

to demonstrate substantial forward scattering within

the NIR wavelength region.2

After introducingm0s, the light propagation beha-vior in a sample with optical properties ma, ms, and

g 6 0 can be alternatively described by the samesample with optical properties ma, m

0s, and g 0.

Alternatively stated, the reflectance and transmit-

Figure 1. The angular distribution of SPF for g 0.9,0.5, 0.1, 0.2, 0.5, and 0.8, assuming the light impingesupon the center of the polar plot from the left.

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 12, DECEMBER 2010 DOI 10.1002/jps

4768 SHI AND ANDERSON


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tance for a sample with optical properties ma, ms, and

g 6 0 are the same as those for the same sample withoptical properties ma, m

0s, and g 0. This is referred to

as the Similarity Principle in tissue optics.34

Therefore, the optical properties needed to describe

light propagation behavior in turbid media are

simplified to ma and m0s.

Based on the first-order expansion in the unitvector ^s, the diffusion equation is obtained as follows;the detailed derivation can be found elsewhere.3,35,36

@

@tfr; t Dr2fr; t macmfr; t Qr; t (5)

In the diffusion approximation, the properties of

photon movement in the medium are contained in the

diffusion constant, D 1=3ma m0s. fr; t is thefluence rate, which is the light intensity per unit area

at position (r) at a given time (t). F(r, t) is the netintensity vector (i.e., diffuse photon flux), which is the

photon energy per unit area in the direction of ^s. cmsymbolizes the speed of light in the sample medium.

In order for the diffusion approximation to the RTE

to describe the light propagation behaviors in turbid

media, the following assumptions are typically

considered.

m0s=ma m0s, also known as the albedo (v0), isclose to unity, that is, when the absorption of the

medium is low. If scattering is not dominant, the

photon migration behavior cannot be appropri-

ately described by the random walk. Then the

diffusion approximation to RTE also does notstand.37

The point of interest is far from sources or bound-aries. A common criterion is the distance

between the light source and detector is larger

than 10 times the mean free path of the photons

in the sample. This indicates that the diffusion

approximation to RTE is only suitable for

describing photon migration behaviors that

experience large numbers of scattering events

with small scattering angles, in comparison with

photons experiencing a few scattering events

with large scattering angles.

22

The sample medium has to be offinite thickness.If the sample becomes thinner to the point where

its thickness is comparable to the effective pene-

tration depth 1=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

3mama m0sp

, the diffusion

approximation will break down as a result of

the increased relative importance of potential

photonphoton interactions.34

Monte Carlo simulation

Many situations of practical interest involve a

variety of light sources, multiple sample types, and

complex illumination geometries. These situations

typically require assumptions regarding individual

boundary conditions and parameters to generate a

closed form analytical solution to the RTE (Eq. 1).

Thus, analytical solutions for realistic scenarios are

complicated at best (if an analytical solution even

exists). For cases when the analytical solution is not

available, the problem can be approached usingnumerical techniques. The most widely used

approach for radiative transfer theory is Monte

Carlo (MC) simulation method-based photon migra-

tion.

Monte Carlo refers to the city in Monaco, where

the primary attractions are casinos that offer games

of chance. The random behavior in games of chance

is similar to how MC simulation statistically

samples the probability distribution for the photon

migration parameters, such as step size, scattering

direction, internal reflection/out of boundary, etc.

These parameters are simulated using functions of

random number generators. Because of these func-

tions, individual photon movement can be traced

step-by-step through the sample medium, and the

distribution of light (i.e., reflectance and/or trans-

mittance) in the system can be recorded from these

individual photon trajectories. As the number of

photons in the simulation grows toward infinity, the

MC simulation for the light distribution approaches

an analytical solution to the RTE. The actual

number of photons necessary for a realistic result

depends on the specifics of the simulation and which

quantities one desires to determine. As few as 3000

photons may be adequate for determining diffusereflectance from a sample, while more than 100000

may be required for a complex three-dimensional

simulation.3

There are several advantages to using the MC

method to describe photon migration behavior.3,4

First, the initial large-scale applications of MC

methods were radiative transfer problems involving

neutron transport. Thus, the MC approach is well

suited for problems involving light transport in turbid

media because a photon can be treated as a neutron

particle whose propagation behaves according to the

rules of radiative transport. Second, the algorithms

for implementing the basic elements of an MC

simulation are straightforward. Third, the technique

possesses a great deal of flexibility and is widely

applicable to practical transport problems. Through

the use of corresponding mathematical relationships,

MC simulation has the ability to simulate virtually

any source, detector, and sample boundary condition,

as well as any combination of sample optical proper-

ties. Finally, the MC approach can be used for any

albedo and SPF.

A sample MC protocol for simulation-based photon

migration is illustrated in Figure 2.38




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TECHNIQUES USED FOR SEPARATINGABSORPTION AND SCATTERING IN NIRS

Integrating Sphere-Based Reflectance andTransmittance Measurement

The integrating sphere-based approach, reported by

Fricke and coworkers is the first documented method

for the separation of NIR absorption and scattering in

pharmaceutical samples.2831 Measurement of dif-

fuse reflectance (Rd) and diffuse transmittance (Td)provides access for deconvolution of analytical

equations to determine ma and m0s.

Instrumentation

Integrating sphere-based approaches can be gener-ally classified into two different instrument set-ups.34

The first set-up uses a single integrating sphere for

both the reflectance and transmittance geometries

(Fig. 3A). The incident light can be either a collimated

beam or diffuse irradiation. The measurement viadiffuse irradiation is less accurate than that made

with collimated irradiation as a result of the high

background signal of the diffuse source in the

reflectance measurement.34

The other set-up consists of a double integrating

sphere system (Fig. 3B), where the sample is placed in

a common port between two spheres. One of the main

advantages of using a double sphere is to increase

signal in both spheres over the single-sphere case,

which is a result of the cross talk between the two

spheres.34 Additionally, the double sphere provides

the opportunity to determine Rd and Td simulta-neously. This instrument configuration has not yet

been applied to pharmaceutical samples.

In the integrating sphere-based approach, the

measurement is designed to obtain values of both

Rd and Td. Therefore, the sample must have a finitethickness, which is dependent on the optical proper-

ties of the sample. If the sample is too thick, notenough signal will be detected in Td. If the sample istoo thin, however, the assumption of the diffusion

approximation will be violated as a result of

individual photons interfering with each other.34

It has been suggested that performing a complete

calibration of the experimental set-up using samples

of known absorption and scattering properties over

the range of those anticipated for samples and

wavelengths of interest is essential to obtain accurate

measurements of Td and Rd.34 Thus, both single-

sphere and double-sphere systems require calibration

using standard samples to characterize the method

accuracy (i.e., percentage deviation from known

values of the standards) in order to further correct

the estimated ma and m0s.

Mathematical Approaches to Determinela andl0s

Fricke and coworkers were the first to develop the

closed-form equations for Rd and Td, and they usedthese equations to determine the optical properties of

pharmaceutical samples.2831 The detailed deriva-

tions can be found elsewhere.30 Briefl y, a three-flux

approximation was applied to derive the measured

Figure 2. Schematic diagram of Monte Carlo simulation.

The figure was adapted from Wang et al.38

Figure 3. Integrating sphere based reflectance and

transmittance measurements. (A) Single sphere measure-

ment. (B) Double sphere measurement. The figure was

adapted from Wilson.34




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quantities of transmission (Td) and reflectance (Rd).The three-flux approximation represents the three

surfaces through which light propagates: transmit-

tance, reflectance, and side scatter (as described in

Mathematical Approaches to Determine ma and m0s

Section).

Td v0

; t0

cg

F

aT

1 2=3k ekt

0 bT1 2=3k e

kt0 3et0 TF

et0 TF(6)

Rd v0; t

0

cg

F

aR

1 2=3k bR

1 2=3k 3

5 3e2toRF

e2t0RF(7)

The formulae for calculating constants c, g, k, aT, bT,aR, bR, A, and B in Eqs. (6) and (7) can be foundelsewhere.30 In addition, F, TF, and RF are experi-mental constants, representative of the impinging

flux of the light source, the transmission and

reflectance coefficient of the supporting layer on

which the Td and Rd measurements of the powdersample were measured. Except for F, TF, and RF, therest of constants shown in the right side of Eqs. (6)

and (7) are functions of the scaled albedo v0 and thescaled optical depth (t).30 The v0 and t

are

defined as

v0 v01 g

1 v0g (8)

t t1 v0g (9)where t m0tx, m0t m0s ma, and x represents thephoton position along the depth-axis of the sample.

Since Eqs. (6) and (7) express the diffuse reflectance

and transmittance as a nonlinear function ofv0 andt

, nonlinear regression tools (e.g., NewtonRaphson

method) are typically applied to fit the measured Rd

and Td profiles in order to estimate the v0 and t

.Subsequently, the reduced scattering coefficient m0sand absorption coefficient ma can be determined using

Eqs. (8) and (9).29 Since the determined optical

coefficients are typically normalized by the sample

density, the resultant units for the optical coefficients

determined by this approach are m2/kg.

Related Pharmaceutical Applications

Fricke and coworkers conducted a series of studies

in which they utilized the integrating sphere-

based approach to determine optical coefficients of

pharmaceutical powder samples within the infrared

(IR) and NIR ranges.28,29,31

The first paper addressed the general information

of absorption and scattering properties of pharma-

ceutical powders in the IR range,29 which was later

confirmed in the NIR range.31 The inter-relationship

between the absorption and reduced scattering

coefficients for specific materials was investigated.It was found that an inverse correlation between the

reduced scattering and absorption coefficient existed

for the sample materials (e.g., lactose and micro-

crystalline cellulose powder), in which a peak in the

absorption coefficient always corresponded to a valley

in the reduced scattering coefficient. The inverse

relationship between the absorption and reduced

scattering coefficients was also confirmed using a

theoretical Mie calculation.29

The wavelength dependences of the optical coeffi-

cients were also explored. The reduced scattering

coefficient gradually decreased with increasing wave-

lengths (and absorption). Further, the absorption

coefficients showed wavelength dependence due to

specific absorption bands within certain wavelength

ranges. The wavelength dependence of the reduced

scattering coefficient was also found to be material

dependent. The reduced scattering coefficients of

lactose and microcrystalline cellulose powder were

found to vary over the observed wavelength range,

while the reduced scattering coefficients of paraceta-

mol and ascorbic acid powder were relatively

constant. Given the wavelength dependency of

scattering, Fricke and coworkers pointed out the

potential invalidity in the commonly used scatteringcorrection methods, such as multiplicative scattering

correction (MSC) and standard normal variate (SNV),

which assume constant scattering across the wave-

length axis.

Additionally, the authors investigated the effect of

particle size on the optical coefficients. It was

demonstrated that the reduced scattering coefficient

was inversely related to particle size in both the IR

and NIR ranges; smaller particle size led to a larger

reduced scattering coefficient. Meanwhile, the

absorption coefficient was also found to increase

when particle size was reduced, especially within the

IR range where strong absorption bands are

located.29 The correlation between the absorption

coefficient and particle size diminished in the NIR

range, except for large particle size difference, such as

that observed for 90mm versus 490mm ascorbic acid

powder.31 Fricke and coworkers attributed the

relationship between the absorption coefficient and

particle size to the decreased hidden mass in the small

particles, which results in a corresponding increase in

absorption. The hidden mass was defined as the

portion of material contributing to the total mass

but not contributing to absorption. For example,




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absorption is much stronger for several small

particles having the same mass as a single large

particle, which is a consequence of the decreased

hidden mass of the former.29,31

Given the effects of particle size on the optical

coefficients, especially for the absorption coefficient,

Fricke and coworkers realized its potential impact on

the quantitative analysis of powder mixtures.29

Theauthors cautioned that the development of a proper

calibration for a two-component mixture, subsequent

spectral analysis of unknown mixtures may contain

significant errors. They postulated that this might be

due to a change in the degree of agglomeration (owing

to humidity), which alters the particle size distribu-

tion of the mixture and leads to differences in the

absorption intensity and both optical coefficients.29

However, the authors did not address any potential

solutions to the variability in the absorption coeffi-

cient as a result of physical variation (e.g., particle

size) and its potential effect on prediction errors in

future samples.

The same group of researchers applied the

extracted absorption and reduced scattering coeffi-

cients to enhance the prediction capability of a

method for determining the amount of active

ingredient in two-component mixtures containing

paracetamol and lactose.28 Since MSC treats scatter-

ing as a wavelength-independent phenomenon, MSC

was used only on wavelength regions that were

independent of scattering (i.e., wavelength ranges for

which constant reduced scattering coefficients of the

powder mixture were observed). Partial least squares

modeling resulted in a more accurate (lower RMSEC)model compared to MSC applied to the entire

wavelength region. Additionally, an artificial neural

network (ANN) was trained to build a calibration

model between separated absorption coefficients and

paracetamol concentrations. The ANN-derived model

showed significantly lower RMSEC and RMSEP

compared to the PLS calibration. Burger et al.

attributed the enhanced performance of the ANN to

its capacity to model nonlinear relations. The

application of an ANN was justifiable as a certain

degree of nonlinearity was found between absorption

coeffi

cient and paracetamol concentration.

Measurements of Remission, Absorption, andTransmission Fractions through Layers of Material ofDifferent Thicknesses

Separation of absorption and scattering was reported

for diffuse reflectance measurements of pharmaceu-

tical samples of different thicknesses.32,33 An inte-

grating sphere is typically used to acquire the

measurement. The difference compared to the

approach used in the section of Integrating Sphere-

Based Reflectance and Transmittance Measurement

is that here, only reflectance is used; no transmittance

component is involved. Instead of estimating the

absorption and reduced scattering coefficients, a

simplified solution of the KubelkaMunk (KM)

function describing light flux into and from samples

was used to calculate the KM absorption (K) andscattering (S) coefficients. The following equationswere used to describe the relation between S and K

within diffuse reflectance measurements.

S 2:303d

R11 R21

logR11 R1R0

R1 R0

(10)

K 2:3032d

1 R11 R1 log

R11 R1R0R1 R0

(11)

Here, R0 denotes the spectrum measured at a definedsample thickness (d) and R

1denotes the measure-

ment of the same sample with an optically infinite

thickness. As it can be seen from Eqs. (10) and (11), Kand S can be directly calculated from the reflectance

measurements. Although the coefficients K and S used in KM

theory are not directly comparable with ma and m0s,

they are related through the relationship expressed

in Eq. (12).17,21,29

K

S 8

3

ma

m0s

(12)

The sole pharmaceutical application of the optical

coefficients determined by this method was reported

in terms of hard model constraints for multivariate

curve resolution.33 Multivariate Curve Resolution is a

group of chemometric algorithms that help resolvemixtures by determining the number of constituents,

their spectral profiles and their estimated concentra-

tions when no prior information is available about the

nature and composition of these mixtures. The

dataset contained NIR spectra of pharmaceutical

tablets compressed at 31, 156, and 281 MPa. The

spectra of the tablets compressed at 31 MPa were

used for calibration, while the remaining spectra

were reserved for validation. It was found that

multivariate curve resolution-alternating least

squares (MCR-ALS), using the background informa-

tion of KM scattering and absorption coefficients,was comparable in calibration, but superior in

validation, when compared to PLS modeling without

any spectral pretreatment. The study also showed

slightly better validation performance for optical

coefficients-based MCR-ALS, compared to pure com-

ponent spectra based MCR-ALS and PLS modeling on

extended multiplicative scattering correction (EMSC)

preprocessed spectra. Moreover, only three samples

were necessary for a reliable and robust calibration

when optical coefficients-based MCR-ALS was

applied, despite the fact that strong changes in the

scattering behavior were expected.




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Time-Resolved Spectroscopy (TRS)

Absorption and scattering properties of a turbid

medium can be estimated by measuring the temporal

dispersion of a short light pulse as it propagates

through the medium. Such measurements have long

been of interest in atmospheric research. For

example, Weinman and Shipley39 used the time

dependence of a transmitted pulse to deduce theoptical thickness of clouds. This method was first

developed for medical applications, but it has since

been extended to other fields, such as pharmaceutics

and agriculture. It uses picoseconds laser pulses to

irradiate a sample. The light signal diffusively

remitted by the sample at a given distance from

the irradiation point is then temporally recorded. The

temporal shape of the pulse is altered by absorption

and scattering events as it passes through the sample.

By analyzing the modified temporal shape of the

pulse, the optical properties of that sample can be

deduced.

Instrumentation

The basic instrument set-up of TRS requires a

picoseconds laser pulse, a sample interface (either

reflectance or transmittance), and a photon-counting

system to record the temporal spreading. The most

recent instrument set-up was developed by the Lund

Institute of Technology, Sweden.24 This system

utilizes an index-guided crystal fiber for light delivery

and a streak camera, which is necessary to achieve

the temporal resolution. The optic arrangement of

this system is presented in Figure 4.24 The laser pulseis focused into a 100 cm long index-guiding crystal

fiber (ICF). Due to the optical behaviors of an ICF,

light pulses with approximately the same temporal

width as the laser are accessible with a spectral width

spanning from 500 nm to at least 1200 nm. In contrast

to a single photon counting system, this system uses a

streak camera to provide a unique combination of a

relatively short acquisition time with high spectral

and temporal resolution. The system measures a700 nm wavelength region with a spectral resolution

of 5 nm. The system has a total temporal range of

2.1 ns with resolution of 4.5 ps.

Since time resolution must be on the order of tens of

picoseconds, the major limitation for the current TRS

system is the expensive instrument set-up, including

both the pulsed laser and the photon-counting

detector.34 Also, the system is limited by its current

wavelength range, which is relatively narrow com-

pared to that of the NIR region.23 The primary reason

for this limitation is the lack of commercially

available efficient photon cathode materials for

streak tubes that operate in the NIR range.


The analytical equations for TRS were initially

derived from tissue optics. It was developed by

Patterson et al.40 for either reflectance measurements

of a semi-infinite homogenous medium or reflectance/

transmittance measurements of a finite medium. To

date, all reported pharmaceutical applications of TRS

involved finite media.

After using specific boundary conditions on the

diffusion approximation to the RTE (Eq. 5), the

expressions for the reflectance R(d, t) and transmit-tance T(d, t) at a specific time (t) for a sample with

Figure 4. Optical arrangement of TRS. The figure was reproduced, with permission,

from Abrahamsson et al.24




9/18

finite thickness (d), such as a pharmaceutical tablet,are

Rd; t 4pDc1=2t3=2expmact

(

z0exp z20

4Dct

2d z0exp 2d z0

2

4Dct

" #

2d z0 exp 2d z02

4Dct

#" ) 13Td; t 4pDc1=2t3=2 expmact

(

d z0exp d z02

4Dct

" # d z0

exp d z02

4Dct

" # 3d z0 exp 3d z0

2

4Dct

" #

3d z0exp 3d z02

4Dct

#" )14

where c represents the speed of light propagation inthe sample medium, D stands for the diffusionconstant, and z0 1 gms1.

As can be seen in Eqs. (13) and (14), measurement of

either reflectance or transmittance allows for a direct

estimate of ma and m0s. In order to deconvolve these

two equations and extract the optical coefficients,

multiple methods have been reported, including non-

linear regression (Levenberg-Marquardt algorithm,

LMA),22,24 least-square support vector machine (LS-

SVM)26 and other linear approaches, that is, MAx-

imum Determination for Solving Time-REsolved

Spectroscopy Signal (MADSTRESS).25 Nonlinear

regression is the most commonly used method among

pharmaceutical applications.22,24 In mathematics and

computing, LMA generates a numerical solution to a

problem by minimizing a function, which generally

nonlinear, over a space of parameters specific to

function. LMA can also be used as a (nonlinear) least-

squares curve-fitting algorithm. Abrahamsson et al.

applied LMA to determine the optical coefficients of

phantom samples and compared this method to the

measurements acquired using integrating sphere-

based approaches. A phantom sample is a type of lipid

emulsion (Intralipid, SigmaAldrich, St. Louis, MO)with known optical properties in the short NIR

wavelength range. Phantom samples havebeenwidely

used as standards in tissue optics to characterize

method accuracy. Abrahamsson et al.24 concluded that

the two methods offered comparable results.


The first application of TRS to pharmaceutical

samples was published by Johansson et al.23 Trans-

mittance mode was used to acquire measurements of

a 3.5 mm-thick tablet. Based on the temporal

spreading and an assumed refractive index, the

degree of scattering within the tablet matrix, in

terms of the total optical path length, was determined

to be 2025 cm. This indicated that very strong

multiple scattering events took place within the

sample. Monte Carlo simulation and a corresponding

comparison with the experimental data estimated the

reduced scattering coefficients of the tablet to be onthe order of 500 cm1 at 790 nm.

The same group of researchers published a second

paper focusing on the application of extracted reduced

scattering coefficients from TRS to enhance the

quantitative analysis of pharmaceutical tablets

through scatter correction.22 Pharmaceutical tablets

produced at different compression forces and various

granule sizes were used. Multiple comparisons were

performed between the scattering-corrected spectra

and raw NIR spectra using different calibration and

validation datasets. When compared to raw NIR

scans, the scatter-corrected spectra resulted in lower

RMSEPs across all of the evaluated conditions.

In addition, Abrahamsson et al.27 utilized the slope

of the time dispersion curve from the time-resolved

measurement to determinethe chemicalconcentration

of binary compacts containing iron oxide and micro-

crystalline cellulose. When compared to traditional

transmission-based NIRS, the time-resolved measure-

ment resulted in a fivefold increase in accuracy for the

determination of iron oxide concentration. Further,

due to the direct relationship between the slope of time

dispersion curve and light absorption, the calibration

model based on the time-resolved measurement

reliably predicted the concentration of iron oxidein samples with physical properties outside those

included in the calibration set.

Frequency-Resolved Spectroscopy (Frequency DomainPhoton Migration, FDPM)

The principle of FDPM involves monitoring the time-

dependent propagation characteristics of multiply

scattered light in turbid media. Briefly, this technique

launches intensity-modulated light onto a multiply

scattering medium via a single point source, anddetects it at other discrete points of known distances

from the incident light. Upon modulating the incidentlight at various modulation frequencies or varying the

source-to-detector distance, the measurements of

phase-shift and amplitude attenuation can be deter-

mined as functions of the optical properties of the

sample medium. The propagation of such a photon

density wave within a turbid medium is influenced by

its absorption and scattering properties and can be

modeled by the diffusion approximation to the RTE.By

solving the diffusion equation with appropriate

boundary conditions, the measurement data (i.e., the

phase-shift and amplitude attenuation) can be used to

determine theoptical properties of the sample medium




10/18

(i.e., the absorption and reduced scattering coeffi-

cients).

Instrumentation

The latest instrument used in FDPM was developed

by Sevick-Muraca et al. This group holds a number of

patents on FDPM instrumentation and their related

applications.1315

As shown in Figure 5,12 modulated light of

modulation frequency v (typically 30200 MHz) is

launched from a monochromatic laser diode, which is

directed to a beam splitter to form reference and

sampling beams. The reference beam is delivered to

a reference photomultiplier tube (PMT) through a

1-mm diameter optical fiber. The sampling beam is

introduced to the sampling medium through a second

1-mm diameter optical fiber whose end is placed

within the sampling medium. A third 1-mm-diameter

fiber is located a distance of r from the point of

illumination to detect the propagated light. Therelative distance between the source and detector

fibers has to be at least 10 times that of the scattering

mean free path to ensure multiple light scattering,

typically 115 cm. The source and detector fibers are

normally maintained in a coplanar geometry. Detec-

tion is accomplished with a second PMT. The two

PMTs are modulated at the same frequency as the

laser diode, with the exception of an additional offset

frequency of Dv 100 Hz. Using the heterodynetechnique, the mixed signals are created to contain

the sum and difference between the signal at the laser

modulation frequency and at 100 Hz higher. Then,

the resulting mixed signals from the PMTs are passed

through two transimpedance amplifiers to filter the

high frequency components, leaving the 100 Hz

signals intact. The remaining phase-shift and ampli-

tude attenuation are then measured. Finally, data

acquisition software is used to acquire the hetero-

dyned signals and record the phase shift (PS),

amplitude (AC), and mean intensity (DC) of the

signal from the sample PMT relative to the referencePMT. The optical properties of the sampling medium

can then be accurately extracted by solving the

equations for PS, AC, and DC as functions ofma andm0s

at the wavelength of the monochromatic laser.

For the above instrument, Sevick-Muraca and

coworkers18 developed two general methods to

determine the optical properties, including multiple

frequency and multiple distance methods; each

method will be discussed in detail in the following

section. Under different experimental conditions,

individual qualification criteria for each method were

developed to assess the accuracy and precision of

FDPM measurements,18 including (1) whether abnor-

mal measurement error exists during the FDPM

experiment; (2) which ranges of modulation fre-

quency and relative distance are suitable for FDPM

experimentation for a given sample; and (3) which

segments of the measurement can be used to generate

accurate and reliable optical properties.

Mathematical Approaches to Determinela

andl0s

Fishkin and Gratton solved the diffusion approxima-

tion to the RTE (Eq. 5) for an infinite and macro-

scopically uniform medium. The outcome was

Figure 5. Schematic diagram of the FDPM setup with the enlarged insert denoting a

powder configuration for multiple scattering of photons. The figure was reproduced, with

permission, from Pan and Sevick-Muraca.12




11/18

expressions for three experimentally determined

quantities: (1) the steady-state photon density or

the time invariant average intensity, the DC compo-

nent, (2) the amplitude of the photon-density oscilla-

tion, the AC component, and (3) the phase shift of the

photon-density wave, the PS component.42,43 These

three quantities are illustrated in Figure 6.42 To

eliminate measurement error at a given v, the

properties of the photon density wave at two different

source-detector separations, namely, r and r0, arenormally measured and compared.43 Thus, the DC,

AC, and PS are normally measured in their relative

quantities, which are expressed as a function of the

optical coefficients as

lnr0

r

DCrel r r03mama m0s

2!

1=2

(15)

lnr0

rACrel

r r0 3mama m

0s

2

!1=2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 vyma

2s 1

24

351=2 16

PSrel r r0

3mama m0s

2 !

1=2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 v

yma

2

s 124 351=2

(17)

lnModrel r r03mama m0s

2

!1=2

ffiffiffi

2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 vyma

2s 1

0@

1A1=2

264

375 18

Eqs. (15)(18) express two general approaches for

extracting the optical coefficients from FDPM mea-

surements: the multiple frequency and multiple

distance methods.

Multiple Frequency (MF) Method. Eqs. (15)(18)

show that at fixed distances between the source and

detector, r and r0, the values of ln[(r/r0)ACrel], PSrel,and ln(Modrel) are nonlinear functions of the modula-

tion frequency. Thus, measurements of DC, AC, andPS (and therefore Mod), which are functions of the

modulation frequency at two fixed source-detector

distances, can be used to estimate the optical

properties via nonlinear regression.Since there are only two unknowns, multiple

combinations of DC, AC, PS, and Mod can be used

to determine ma and m0s. It was found that a regression

approach based on only one type of measurement data

was insufficient to obtain accurate results.18,44 It was

also determined that simultaneous regression of

DC PS, AC DC PS gave comparable results tosimultaneous regression of AC

PS, while simulta-

neous regression of DC AC or Mod PS failed toaccurately estimate the optical properties.18,43

Error associated with the nonlinear regression was

investigated via a Monte Carlo method of erroranalysis.18 The study used a polystyrene colloidal

suspension to determine m0s and compared it with thevalue calculated by Mie theory. Based on the error

analysis, the accuracy and precision of the deter-

mined reduced scattering coefficients obtained via themultiple frequency method were studied and com-

pared at multiple source-detector distances. The

comparison concluded that a minimum relative

distance (r r0) of about 2.5 mm was necessary forreasonable accuracy and precision. If the relative

distance is smaller than this minimum distance

threshold, unsatisfactory accuracy and precision of

the extracted m0s will be induced due to the largeuncertainty in the FDPM measurement.

Multiple Distance (MD) Method. Eqs. (15)(18)

also show that at a fixed modulation frequency, v, the

values of ln[(r/r0)DCrel], ln[(r/r0)ACrel], PSrel, andln(Modrel) are linear functions of the relative distance

between the detectors (r r0). Thus, the slopes (k) canbe determined from plots of ln[(r/r0)DCrel], ln[(r/r0)ACrel], PSrel, and ln(Modrel) versus (r r0). Subse-quently, simultaneous regression via different com-binations of kDC, kAC, kMod, and kPS can be used toobtain the optical properties of the sample medium.

Comparisons were performed between multiple

combinations of kDC, kAC, kMod, and kPS to determinethe reduced scattering coefficients via the MD methodand those calculated by Mie theory.18 Results

indicated that the reduced scattering coefficients

derived from simultaneous regression of DC PS,AC PS, and AC DC PS agreed well with thetheoretical calculations, but simultaneous fitting of

Figure 6. Time evolution of the intensity from a sinu-

soidally intensity-modulated source. The figure was

adapted from Fishkin and Gratton.42




12/18

DC AC or Mod PS failed to accurately estimatethe reduced scattering coefficients. The results

obtained via MD linear regression were similar tothose obtained via MF nonlinear regression. Thissuggested that PS data combined with DC and/or AC

data provide the most accurate information of the

optical properties. The modulation data (i.e., AC/DC),

however, are not suitable for deriving the opticalparameters, even when they are combined with PS

data.

The uncertainties of determination via the MDmethod were derived from error analysis using

Eqs. (15)(18).45,46 Error analysis was performed to

calculate the precision and accuracy associated with

the of determination of the reduced scattering

coefficient for a polystyrene colloidal suspension

measured at multiple frequencies via the MDmethod. Both precision and accuracy indicated that

a modulation frequency greater than 60 MHz was

necessary to obtain reasonable results.18 If the

modulation frequency is less than the threshold,

unsatisfactoryaccuracy and precisionwill be induced

as a result of the uncertainty associated with the

FDPM measurement.

In general, the MF and MD methods perform

similarly. The most obvious advantage of the MD

method is that the analytical solution for the optical

parameters can be directly derived without nonlinear

regression. Although a study showed that the

accuracy of the MD method was better than that of

the MF method, the precision was worse.18 The

authors suggested combining the two methods to

increase the signal-to-noise ratio and improvethe accuracy and precision for the estimation of the

optical properties. For a MF measurement, the

experiment can be performed at several different

relative distances (called the combined MF method),

while for a MD measurement, the experiment can be

performed at several different modulation frequen-

cies (called the combined MD method). The combined

approaches were found to improve the accuracy and

precision for the estimation of the optical coefficients.


To date, FDPM has been predominately utilized to

separate absorption and scattering in NIR spectral

responses of pharmaceutical samples. A number of

studies were performed by Dr. Sevick-Muraca and

collaborators, where they applied FDPM for the

analysis of particle size in suspensions and powder

media, and for the determination of constituent

concentration in powder mixtures.912,16,1921,47

For particle size analysis, an inversion algorithm

was developed to determine the particle size dis-

tribution (PSD) and volume fraction for noninteract-

ing colloidal suspension samples (


13/18

tration of both excipients and API, especially for

multi-component pharmaceutical matrices. Thus,

multiple wavelengths measurements are necessary

if FDPM is to be widely used for industrial applica-

tions.

Given that FDPM can determine both absorption

and scattering properties (shown by the above

studies), Sevick-Muraca and coworkers16,17,21

pro-posed it as a tool for on-line monitoring of powder

blending, including both the variation of API

concentrations from changes in the absorption

coefficient, and variation in the packing arrangement

of the powder bed from changes in the reduced

scattering coefficient.

In order to apply a noninvasive measurement

(e.g., FDPM) for monitoring powder blending, one of

the key questions to be answered is the size of

sampling volume. The determination of sampling

volume provides a means to directly compare FDPM

with other analytical measurements, for example,

NIRS and HPLC. Mathematical expressions pre-

dicting the sampling volume of FDPM were devel-

oped for infinite and semi-infinite powder beds viaprobability distribution analysis to describe the

propagation of multiply scattered light between a

point source and point detector separated by a

known distance.10 The predicted volume of inter-

rogation was in agreement with that determined by

empirical measurements of FDPM. Based on the

derived equation, the sampling volume of FDPM is

determined by the (1) separation distance between

the incident point source and the point detector; (2)

optical properties of the sample, and (3) modulationfrequency.

The first article using FDPM to monitor powder

blending was published in 2004 by Pan et al.9 In this

article, FDPM was compared to HPLC as an off-line

method to trace the concentration variation of API in

a terazosin powder blend (0.72%, w/w). Thieved

samples were used for both FDPM and HPLC

measurements. Although the off-line sampling pro-

tocol used to monitor powder blending was not ideal,

the paper did present evidence demonstrating the

relationship between sampling volume and blending

variance. Based on the mathematical expression

developed earlier,10 the sampling volume by FDPM

was estimated to be 1.4 cm3, which was shown to be

larger than that determined by both HPLC (0.65 cm3)

and the reported value for optic fiber-based NIR

spectroscopy (


14/18

Instrumentation

The most common instrument set-up measures

diffuse reflectance (R) as a function of the radial

distance (r) on the sample surface (i.e., radiallydiffused reflectance). The initial set-up used in the

field of tissue optics relied on optic-fibers, in which

point or pencil-beam source was used to perpendicu-

larly illuminate sample surface, and diffusively

reflected signals were detected by optical-fibers at a

specified distances from the illumination spot

(Fig. 7).34 Detection could be accomplished using

one single fiber moving radially and measuring

reflectance one radial distance at a time, or using a

linear fiber array picking up signal simultaneously

from different radial distances. With the development

of imaging technology, charge-coupled device (CCD)

cameras have emerged as a means of detecting

radially diffused reflectance.5,5052 The advantage

of using CCD cameras to capture the entire radial

distribution of diffusively reflected signals is to

enhance the signal-to-noise ratio of the reflectance

measurements via spatial image processing (i.e.,signal binning) of equivalent radial distances.50


In the field of tissue optics, a closed form analytical

equation was developed by Farrell and Patterson53 to

correlate the radially diffused reflectance with ma andm0s. However, the derived equation was based on theassumptions and boundary conditions for a semi-

infinite medium, which is not necessarily applicable

for pharmaceutical samples. A semi-infinite homo-

genous medium has optical boundaries that are

infinitely wide, which indicates that the boundaries

are much wider than the spatial extent of the photon

distribution. Therefore, an alternative approach is

needed before SRS can be applied for pharmaceutical

applications.

Numerical methods have also been used to deter-

mine ma and m0s from SRS measurements. For the case

where there is no derived analytical equation

matching the experimental conditions, numerical

simulation (i.e., Monte Carlo simulation-based

photon migration) can be used as an alternative to

estimate the optical coefficients. These techniques

typically involve forward calculation of R(r) over aexpected range ofma and m

0s values, followed by either

iterative interpolation of the measuredR(r) inside thecalculated range to find the optical properties that

yield the smallest interpolation error,52 or prediction

of the optical properties by certain regression

algorithms, such as artificial neural network

(ANN)54 and partial least square (PLS).5,51


Shi and Anderson were the first to explore the

potential applications of SRS in the pharmaceutical

field. They, along with other researchers, published

a series of reports that focused on SRS method

development for pharmaceutical samples,5 the

enhanced understanding that separated optical

coefficients offer to practical uses of NIRS6,7 and

the application of optical coefficients to spectroscopic

analyses under practical conditions.5,8

The authors established a chemical imaging-based

spatially resolved spectroscopic measurement.5 A

chemical imaging system was used to capture both

the spatial and spectral information from the radially

diffused reflectance of pharmaceutical solid samples

(either as powder or tablets). Subsequently, a Monte

Carlo simulation-oriented PLS model was used to

predict the optical coefficients from the measuredradially diffused reflectance. Simulation and reference

correction by Intralipid at 1064nm normalized the

simulated radiallydiffused reflectance such that it was

comparable to the measured counterpart. This com-

parability indicated that the model based on simulated

data could be applied to the radially diffused reflec-

tance measurements to predict the optical coefficients.

The optical coefficients extracted from SRS have

been used to enhance the understanding of practical

applications of NIRS.6 The samples used here were

pharmaceutical powders of various particle sizes or

compacts of various densities. An increase in eitherparticle size or tablet density induced a proportional

change in ma and an inversely proportional change in

m0s. The separated ma and m0s were input into the

Monte Carlo simulation-based photon migration

program to trace the photon absorption behavior

and record the depth of penetration. The consistency

observed between the measured and simulated

results indicated that the ma and m0s were the

dominant factors in the NIR absorbance profile and

the depth of penetration characteristics, respectively.

The combination of optical coefficients determined

by SRS and Monte Carlo simulation-based photon

Figure 7. Optical set-up of SRS. The figure was adapted

from Wilson.34




15/18

migration provides a unique tool to understand the

depth- and radially resolved profiles of NIR radiation

on pharmaceutical samples.7 The depth-/radially

resolved profile exploits the relationship between

the cumulative percentage of reflected information

and the depth/radial distance in a sample matrix.

In silico studies revealed that both the depth- and

radially resolved profiles are nonlinear, indicatingthat portions of the sample close to the point of

interest, along either the depth/the radial distance,

contribute more to the final reflectance than those

further away. The nonlinearity of the profiles is

expected to be dependent on the ma and m0s at their

corresponding wavelength. Additionally, the simu-

lated depth-/radially resolved profile was also applic-

able to chemical imaging systems. The depth and

radial distance corresponding to 95% of the reflected

information were determined to be approximately 150

and 300mm, respectively, for the simulation condi-

tions. These values were larger than the physical size

of a single pixel in any commercially available

chemical imaging system. Thus, the observed infor-

mation from a single pixel was believed to be

representative of the information within a specific

3-D volume. In other words, the reflected intensity

captured in a given pixel of a chemical image is a

weighted average across a specific depth and radial

distance. These results underscore the precautions

that must be taken when interpreting NIR chemical

images.

Based on the enhanced understanding by the above

studies about individual roles of absorption and

scattering in NIRS, the determined ma and m0s weresubsequently applied to spectroscopic analyses under

practical conditions. Due to the wavelength and

absorption dependency of m0s, a m0s-based scattering

correction method was proposed5 as an alternative to

wavelength-independent scattering correction meth-

ods, such as SNV and MSC. When applied to model the

chemical compositions of tablets, them0s-based scatter-ing correction method, termed scattering orthogona-

lization, resulted in superiorcalibrationand prediction

statistics compared to SNV. The enhanced perfor-

mance of scattering orthogonalization was attributed

to its ability to mitigate the physical interferences

while preserving the chemical information. Therefore,

this method is expected to be useful for routine model

calibration and model update procedures as it mini-

mizes changes to the calibration resulting from

physical variations in the samples related to the m0s.Since pure component materials are typically

available in the pharmaceutical industry, both maand m0s of a pure component raw material can be usedto represent interfering signals when predicting the

chemical concentrations of other components within a

powder or tablet mixture. In a recent paper, ma and m0s

were integrated into specific chemometric algo-

rithms.8 For example, net analyte signal (NAS) and

generalized least squares (GLS) were used to simplify

a NIRS multivariate calibration model using only

pure component spectra and concentration values

from one formulation mixture. It was found that the

simplified model was conducive to parsimonious

multivariate models and reached the same or even

lower prediction error than traditional approaches.Thus, optical coefficient-based signal processing is

expected to be beneficial to both calibration and

update efforts during routine NIR spectroscopic

analyses.

COMPARISON AMONG TECHNIQUES USEDTO SEPARATE ABSORPTION AND SCATTERINGIN NIRS

Five categories of techniques have been applied to

pharmaceutical samples to separate absorption and

scattering in NIRS. To simplify the following discus-

sion, these techniques can be reorganized into two

major groups: time and intensity related measure-

ments. TRS and FDPM are both time dependent

measurements, while integrating sphere-based

reflectance and transmittance measurements, mea-

surements through layers of material of different

thicknesses and SRS are intensity based techniques.

The relationship between TRS and FDPM can be

described as follows.48 A broadened pulse will be

observed in the time domain h(t), if an infinitesimallyshort pulse is applied to a turbid scattering medium.

Alternatively, if a sinusoidally modulated light sourceis applied to the same medium, the photon flux at the

detector will also be sinusoidal in time, but the

oscillation will be delayed in phase and amplitude

relative to the source. In essence, the time domain

signal h(t) can be linked to the phase and amplitude bythe Fourier transform such that any information

acquired in the time domain can also be, in principle,

obtained in the frequency domain. However, certain

practical differences between these two techniques do

exist.48 First, typical FDPM measurements using

frequencies of 300 MHz or less are considerably less

expensive than the time-resolved techniques. Second,phase and amplitude measurements can be made in

near-real time such that the influence of time-varying

phenomena can be studied in a sample medium.

Comparatively, the acquisition rate of time-resolved

data collected using a time-correlated single photon

counter is usually limited by electronic constraints

imposed by the count rate. Therefore, while the funda-

mental observations are the same, the underlying

details of the two techniques dictate their applicability.

The integrating sphere-based approach, measure-

ment through layers of material of different

thicknesses and SRS are all intensity based measure-




16/18

ments. The firsttwo techniques detectreflectedsignals

exiting thesample surface and record these signals as a

single magnitude at a given wavelength. This method

is referred to as the total diffuse reflectance measure-

ment.34 SRS, on the other hand, measures radially-

diffused reflectance, which is the individual reflec-

tance signal at a specific radial distance for a given

wavelength. This method is referred to as the localdiffuse reflectance measurement.34

Limited studies have been reported to date to

compare the practical performance of different

techniques across the same sample platform (i.e.,

the same analyte of interest). Swartling et al.55

compared the practical performance of the integrat-

ing sphere-based approach, TRS and SRS for

determining the optical coefficients of a set of tissue

phantom samples. Their study was limited to a

wavelength range of 660785 nm. The integrating

sphere-based method was shown to be the best

approach to estimate the reduced scattering coeffi-

cients. The authors results were supported by

previously reported values for phantom samples.56

The integrating sphere-based method, however, had a

poor limit of detection for determining absorption

coefficients. Comparatively, TRS demonstrated the

capacity to determine low absorption coefficients.

Overall, Swartling et al. concluded that the differ-

ences between the approaches for the determination

of the optical coefficients were minimal.

Sevick-Muraca et al.57 investigated the theoretical

differences between the time dependent measure-

ments (TRS or FDPM) and SRS. The authors

concluded that SRS, unlike TRS and FDPM, doesnot provide direct measurements of photon path

length, and it relies solely on the detection of light

intensity attenuation to describe the absorption and

scattering behaviors. Compared to SRS, TRS, and

FDPM do not measure relative intensity, but rather

absolute time-of-flight and phase delay. Thus, TRS

and FDPM are essentially self-calibrating, and are

not subjected to the measurement errors associated

with the calibration with respect to an external

standard.

In summary, there are two main reasons for the

limited number of studies comparing the practical

performances of the various techniques for separating

absorption and scattering. First, optical set-ups

interrogate different sample volumes.55 For instance,

because of the large source-detector distance, FDPM

may interrogate a larger sample volume compared to

the other techniques. A larger sampling volume

minimizes the potential effects of sample heteroge-

neity on the resultant optical coefficients, leading to

better precision and reduced measurement error. The

effects of inhomogeneity are also mitigated when

transmittance rather than reflectance is used in TRS

as the former often interrogates larger volumes.23

Second, the accuracy of the determined optical

coefficients is dependent upon the mathematical

approaches used. For instance, nonlinear regression

performed on multiple, rather than two, radial

distance points may enhance the robustness of SRS

for extracting the optical coefficients.55

CONCLUSIONS AND PERSPECTIVES

Overall, publications detailing the separation of

absorption and scattering phenomena in NIRS have

improved the current understanding of NIR diffuse

reflectance, especially with regard to the individual

roles of absorption and scattering. The enhanced

understanding has provided and continuously will

offer the basis for improved spectroscopic analyses

under practical conditions.

With the increasing awareness of the importance of

NIRS in PAT, the spectroscopic application with

mechanistic understanding of underlying optical

phenomena is expected to save time and effort when

integrating PAT into pharmaceutical processes,

and enhance the robustness of multivariate models

to provide effective process monitoring and control

to ultimately improve end-product quality. For

instance, a spectral library ofma(l) and m0sl of pure

component materials is expected to provide tremen-

dous leverage for both multivariate calibration and

routine calibration update in pharmaceutical appli-

cations of NIRS. Additionally, upcoming generations

of NIRS instrumentation are expected to integrate

the techniques used in the separation of absorptionand scattering, such as those reviewed in this article,

to delineate NIR absorbance spectra directly into

absorption and scattering profiles, which will simplify

subsequent qualitative and quantitative applications.

In the meantime, improvements to the techniques

used for the separation of absorption and scattering in

NIRS are necessary.

A standard with known ma(l) and m0sl in NIRrange should be developed to improve the accu-

racy of individual measurements and provide a

platform to compare measurements across dif-ferent techniques. The most common standard in

the field of tissue optics is Intralipid. However,

the wavelength range used in tissue optics is

narrow (6001100 nm) compared to that which

is typically used in pharmaceutical applications

(7802500 nm). Therefore, the determination of

ma and m0s for Intralipid over the NIR spectral

range, or the design and measurement of some

new standard, will be essential for continuous

improvement of the techniques reviewed herein.

Many of the individual techniques might alsobenefit from advances in instrumentation.




17/18

For example, the extended wavelength range

covered by TRS or instrumentation offering

simultaneous FDPM measurements over multi-

ple wavelengths, or better yet, a continuous

wavelength range, is expected to improve the

functionally and generality of these techniques

in pharmaceutical applications.

Finally, the idea of applying the separation of

absorption and scattering in NIRS to enhance the

mechanistic understanding of the fundamental opti-

cal phenomena and improve the practical spectro-

scopic analyses is expected to facilitate future

applications of NIRS.

ACKNOWLEDGMENTS

The authors would like to acknowledge Dr. Steve

Short for his skillful scientific and grammatical edit-

ing, which has been helpful in preparing this manu-script.

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