Page 1

Re-evaluation of model-based light-scattering

spectroscopy for tissue spectroscopy

Condon Lau

Obrad Šc ´epanovic ´

Jelena Mirkovic

Sasha McGee

Chung-Chieh Yu

Massachusetts Institute of Technology

George R. Harrison Spectroscopy Laboratory

77 Massachusetts Avenue

Cambridge, Massachusetts 02139

Stephen Fulghum Jr.

Newton Laboratories

23 Cummings Park

Woburn, Massachusetts 01801

Michael Wallace

Mayo Clinic

Department of Gastroenterology and Hepatology

4500 San Pablo Road

Jacksonville, Florida 32224

James Tunnell

University of Texas at Austin

Department of Biomedical Engineering

1 University Station, C0800 Austin

Texas 78712-0238

Kate Bechtel

Michael Feld

Massachusetts Institute of Technology

George R. Harrison Spectroscopy Laboratory

77 Massachusetts Avenue

Cambridge, Massachusetts 02139

E-mail: msfeld@mit.edu

Abstract. Model-based light scattering spectroscopy ?LSS? seemed a

promising technique for in-vivo diagnosis of dysplasia in multiple or-

gans. In the studies, the residual spectrum, the difference between the

observed and modeled diffuse reflectance spectra, was attributed to

single elastic light scattering from epithelial nuclei, and diagnostic

information due to nuclear changes was extracted from it. We show

that this picture is incorrect. The actual single scattering signal arising

from epithelial nuclei is much smaller than the previously computed

residual spectrum, and does not have the wavelength dependence

characteristic of Mie scattering. Rather, the residual spectrum largely

arises from assuming a uniform hemoglobin distribution. In fact, he-

moglobin is packaged in blood vessels, which alters the reflectance.

When we include vessel packaging, which accounts for an inhomo-

geneous hemoglobin distribution, in the diffuse reflectance model, the

reflectance is modeled more accurately, greatly reducing the ampli-

tude of the residual spectrum. These findings are verified via numeri-

cal estimates based on light propagation and Mie theory, tissue phan-

tom experiments, and analysis of published data measured from

Barrett’s esophagus. In future studies, vessel packaging should be in-

cluded in the model of diffuse reflectance and use of model-based LSS

should be discontinued. © 2009 Society of Photo-Optical Instrumentation Engineers.

?DOI: 10.1117/1.3116708?

Keywords: spectroscopy; biomedical optics; cancer; light scattering spectroscopy;

diffuse reflectance spectroscopy; vessel packaging.

Paper 08128RRR received Apr. 17, 2008; revised manuscript received Feb. 9, 2009;

accepted for publication Feb. 10, 2009; published online Apr. 14, 2009.

1Introduction

Improving early detection is the key to managing cancer,

since the results of treatment are much more favorable when

the cancer is diagnosed at an early, preinvasive stage. To ad-

dress this, our laboratory has developed trimodal spectroscopy

?TMS?, a technique that combines three spectroscopic

modalities—diffuse reflectance spectroscopy ?DRS?, intrinsic

fluorescence spectroscopy ?IFS?, and light scattering spectros-

copy ?LSS?. DRS measures the spectrum of diffusely reflected

light returning from the tissue and provides information about

tissue scattering, blood concentration, and blood oxygenation.

IFS measures tissue autofluorescence spectra and provides the

relative concentrations of native tissue fluorophores, such as

collagen and NADH. In the TMS studies,1–3LSS was as-

sumed to measure single elastic light scattering from epithe-

lial nuclei, from which their size distribution could be deter-

mined. In this work, we use the term LSS to refer to the

specific model-based method employed in those studies, al-

though there are other similarly named methods/techniques

that have been developed and used to study single scattering

in epithelial nuclei4–6and other cell organelles.7–9

TMS has shown promise for diagnosing early cancer in a

variety of organs, and multipatient, multiorgan studies indi-

cate that LSS was an important predictive component of

TMS. Backman et al. applied LSS to detection of early cancer

in bladder, colon, and other tissues in vivo.10They obtained

100% sensitivity and 100% specificity in distinguishing ab-

normal from normal tissue in bladder and colon. Müller et al.

employed TMS in the oral cavity, and obtained 96% sensitiv-

ity and 96% specificity in separating cancerous and dysplastic

tissues from normal tissue.3With LSS alone, they were able to

obtain 92% sensitivity and 97% specificity for the same clas-

1083-3668/2009/14?2?/024031/8/$25.00 © 2009 SPIE

Address all correspondence to Michael Feld, George R. Harrison Spectroscopy

Laboratory, Massachusetts Ave, Cambridge, MA 02139 United States of

America; Tel: 617/253-7700; Fax: 617/253-4513; E-mail: msfeld@mit.edu

Journal of Biomedical Optics 14?2?, 024031 ?March/April 2009?

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sification. Georgakoudi et al. used TMS in the cervix and

were able to distinguish between squamous intraepithelial le-

sions ?SILs? and non-SILs with 92% sensitivity and 90%

specificity.2With LSS alone, they were able to perform the

same distinction with 77% sensitivity and 83% specificity.

Georgakoudi et al.1employed TMS in Barrett’s esophagus

and obtained 100% sensitivity and 100% specificity in distin-

guishing high grade dysplasia from low grade dysplasia and

nondysplastic Barrett’s. Wallace et al.11used LSS alone in

Barrett’s esophagus and found that dysplasia could be distin-

guished from nondysplastic tissue with 90% sensitivity and

90% specificity. These studies show that LSS, especially in

combination with DRS and IFS, offers promise for diagnosing

early cancer.

The LSS modality employed in the previous studies is

model based. In model-based LSS, a residual spectrum is ob-

tained by fitting a model of diffuse reflectance to the observed

diffuse reflectance spectrum.12This residual spectrum was at-

tributed to single elastic light scattering from epithelial nuclei,

and a Fourier-transform-based LSS diagnostic algorithm, de-

veloped by Perelman et al.12and Backman et al.10, analyzed it

as such to extract nuclear size and density from the

wavelength-dependent oscillatory structure.13However, re-

cent experimental and theoretical work in our laboratory indi-

cates that this picture is incorrect, and analysis of larger clini-

cal datasets of cervical, oral, and Barrett’s esophagus spectra

failed to reproduce the results obtained in the original

studies1–3using model-based LSS. In actuality, the residual

spectrum arose primarily from inaccurate modeling of the he-

moglobin absorption features in the DRS spectrum. Hemoglo-

bin, a very strong tissue absorber at 420 nm, is contained in

blood and confined to the blood vessels. It is thus “packaged”

in small regions of the tissue, and this alters the apparent

hemoglobin absorption spectrum.14

In this work, we provide proof for these claims using nu-

merical estimates based on light propagation and Mie theory,

and measurements of reflectance from physiological tissue

phantoms. We then analyze the Barrett’s esophagus clinical

reflectance data of Georgakoudi et al.1, with and without ves-

sel packaging, to evaluate the role of vessel packaging on

DRS fitting. Vessel packaging is a model developed by

Svaasand et al. that accounts for the effects of inhomogeneous

hemoglobin distribution on diffuse reflectance.14–16We con-

clude by simulating tissue reflectance spectra to show that the

Fourier-transform analysis applied to residual spectra is not

robust.

2

In this section we employ numerical analysis with light propa-

gation and Mie theory13to estimate the magnitude and wave-

length dependence of single elastic light scattering from epi-

thelial nuclei relative to the total reflectance. The single

scattering contribution is estimated in a background of total

reflectance that adds uncertainty to any measurement. A real-

istic model of light scattering in tissue, first proposed by Per-

elman et al.,12is evaluated, and the amplitudes and spectral

shapes of predicted light scattering signals are obtained for

later comparison with those acquired in the clinical studies.

Light scattering in epithelial tissue can be modeled by the

two-layer tissue model of Fig. 1?a?. The lower layer is a semi-

infinite diffusive scattering layer with reduced scattering co-

efficient ?s? ?mm−1? and absorption coefficient ?a?mm−1?,

modeling subepithelial tissue. The thin upper layer, represent-

ing the epithelium, is composed of spherical scatterers ?cell

nuclei? of diameter d ??m? and number density ? ?mm−3?,

with index of refraction mismatch m relative to the surround-

ing medium. The implementation of Perelman’s model pre-

sented in this work assumes a single size of epithelial scatter-

ers. This assumption has minimal impact on the final light

scattering spectra, because the effect of a distribution of scat-

terer sizes is similar to the effect of averaging scattering sig-

nals measured within a finite solid angle, which is included in

the model.

The optical fiber probe used to deliver light and collect

tissue spectra in vivo1–3consisted of a light delivery fiber sur-

rounded by six collection fibers. All fibers had 200-?m-core

diameters and NA=0.22. The fibers were separated from the

tissue by a 1.5-mm-thick quartz cover piece. During measure-

ment, the probe was placed in contact with the tissue, and

reflectance and fluorescence spectra were acquired. To model

this instrument, we make several simplifications to expedite

computations. First, the light beam incident on the tissue

sample covers the same area as that of the delivery fiber of the

probe, but is assumed to be collimated. Second, the fibers are

assumed to be in direct contact with the tissue. Therefore,

Elastic Light Scattering Analysis

Illumination

1

3

3

d, m, ρ

θ

θ

2

θ

2

50µm

µs’(λ), µa(λ)µs( ), µa( )

1 θ

diffuse

reflectance

(a)(b)(c)

Fig. 1 ?a? Two-layer tissue model describing epithelium and subepithelial tissue. d, m, and ? are the diameter, index mismatch, and number density

of spherical scatterers, respectively. ?s???? and ?a??? are the reduced scattering and absorption coefficients of the lower layer, respectively. ?b?

Backscattering ?labeled 1?. ? is the angle between the incident beam and a backscattered light ray. The irregularly shaped dotted line represents a

light ray entering the diffusive lower layer and re-emerging from the top. ?c? Forward scattering ?labeled 2? and transmission ?labeled 3?. ?1is the

angle between the incident beam and a diffusely reflected light ray exiting the lower layer. ?2is the angle of forward scattering. ? is the angle

between a forward scattered light ray and the incident beam.

Lau et al.: Re-evaluation of model-based light-scattering spectroscopy…

Journal of Biomedical Optics March/April 2009

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light returning from the tissue within collection area A ?the

area on the tissue surface covered by the collection fibers? and

collection solid angle ?c?the solid angle spanned by NA 0.22

fibers? is collected. To mathematically simulate a tissue reflec-

tance measurement, consider the simplified probe described

earlier, placed in contact with the tissue of Fig. 1?a?. Light

entering the tissue can return to the surface in three ways, as

illustrated in Figs. 1?b? and 1?c?. 1. The incident light can be

backscattered from the upper layer ?labeled 1 in Fig. 1?b??.

This light does not enter the lower layer. Light entering the

lower layer is diffusely reflected and can return to the surface

in two additional ways ?dotted and dashed red lines in Fig.

1?c??. 2. It can be scattered in the forward direction before

emerging from the surface ?labeled 2 in Fig. 1?c??. 3. It can

traverse the upper layer on the way up without being scattered

?labeled 3 in Fig. 1?c??. The total reflectance ?fraction of in-

cident light power collected by the probe? R is the sum of the

three contributions:

R = RBS+ RFS+ RT,

?1?

with RBS, RFS, and RTthe reflectance contributions from light

collected from area A on the tissue due to backscattering,

forward scattering, and transmission, respectively.

Perelman et al. derived expressions for the three reflec-

tance terms, which we express in a form specific to our in-

strument.

2.1

Consider Fig. 1?b?, where ? is the angle between a backscat-

tered light ray and the direction of the incident beam. If we

assume RBSto be comprised of only singly backscattered light

returning from within the collection area, it can be expressed

as follows:

Backscattering

RBS??? = ?1 − exp?− ???????

?c

p??,? − ??d?.

?2?

Here, ?, the optical thickness of the upper layer, is equal to the

product of ?, the layer thickness ?assumed to be 50 ?m in the

simulations?, and the total elastic scattering cross section.13

The wavelength is ? ?nm?. The single scattering approxima-

tion is valid when T?1, a reasonable approximation in the

case of tissue epithelium.17The factor 1−exp?−????? is the

fraction of light scattered once while traversing the upper

layer. The phase function of the scatterers in the upper layer

p??,?−?? can be obtained from Mie theory. The integral

over ? gives the fraction of light scattered into the collection

solid angle of the probe.

Figure 2?a? plots RBSfor values of d, m, and ? in the

histological range of interest. Note that the backscattering

spectrum is smooth, with oscillatory wavelength dependent

features having been averaged out by integration over a solid

angle.

2.2

Consider Fig. 1?c?. Diffusely reflected light from the lower

layer has an approximately Lambertian angular profile. ?1is

the angle between the incident beam and a light ray emerging

from the lower layer. ? is the angle between the incident beam

and a diffusely reflected light ray that is forward scattered by

the upper layer before reaching the tissue surface. ?2is the

forward scattering angle. If we assume only transmission or

single scattering in the upper layer, and that no light leaks into

or out of the collection area during passage through the upper

layer, RFSand RTcan be expressed as follows:

Forward Scattering and Transmission

1.4

1.6x 10

-3

RT

RFS+R

d = 8, m = 1.06

d = 8, m = 1.04

d = 8, m = 1.02

d = 10, m = 1.06

d = 6 m = 1 06d6, m

d = 4, m = 1.06

4

6x 10

-6

S

(b)

(a)

0.8

1

1.2

1.06

0

2

RBS

0

0.005

0.01

1

−

RR

R

(c)

0 40.4

0.6

0.8

1

τ

(d)

400500600700

-0.01

-0.005

Wavelength (nm)

400500600700

0

0.2

Wavelength (nm)

Fig. 2 LSS analysis results computed from histologically relevant epithelial scattering parameters. In the legend, d has units of microns. For all cases

?=8?104mm−3. ?a? Backscattering reflectances. ?b? Sum of forward scattering and transmission reflectances. ?c? Mean-centered normalized

reflectances. ?d? LSS features ?optical thicknesses? of light scattering from the upper layers.

Lau et al.: Re-evaluation of model-based light-scattering spectroscopy…

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RFS??? =1

?RD????1 − exp?− ???????

?c?

2?

cos??1?p??,?

− ?1?d?1d?,

?3?

RT??? =1

?RD???exp?− ??????

?c

cos??1?d?1.

?4?

RDis the fraction of incident light that traverses the upper

layer, is diffusely reflected in the lower layer, and returns to

the tissue surface within the probe collection area. The diffuse

reflectance model of Zonios et al.,18an appropriate extension

of the model developed by Farrell, Patterson, and Wilson,19

provides an analytic solution to RDin terms of ?s????, ?a???,

and the probe’s light delivery and collection areas. The right-

hand side of Eq. ?3?, similar to that of Eq. ?2?, contains the

product of the fraction of light singly scattered and a double

integral term representing the fraction of diffusely reflected

light scattered into the collection solid angle. Equation ?3?

requires a double integral with 1/? and cosine terms, because

the angular distribution of diffuse light returning from the

lower layer within the collection area is assumed to be Lam-

bertian. Similarly, the right-hand side of Eq. ?4? contains the

product of the fraction of transmitted light, exp?−?????, and

an integral representing the fraction of light emitted from the

lower layer entering the collection solid angle.

To compute RD, we model the reduced scattering coeffi-

cient as follows:

?s???? = A??

?0?

−B

+ C??

?0?

−4

.

?5?

The reference wavelength ?0=700 nm. The ?−4term repre-

sents a change in the exponent of the reduced scattering co-

efficient at short wavelengths, which we have observed in

modeling data presented in this and other studies. The absorp-

tion coefficient used, ?a???, was that of hemoglobin, in which

?a??? = cHb

*??1 − ???Hb??? + ??HbO2????,

?6?

where cHb

?mg/mL? in the volume of tissue sampled by light, and ?

=cHbO2/?cHbO2+cHb? is the oxygen saturation. ?Hbis the ex-

tinction coefficient of deoxygenated hemoglobin in units of

mm−1??mg/mL?−1, and ?HbO2is the corresponding extinc-

tion coefficient of oxygenated hemoglobin.20The reduced

scattering and absorption coefficients used in the following

elastic light scattering analysis are: cHb

=0.5, A=1 mm−1, B=0.5, and C=0 mm−1. A, B, C, ?, and

cHb

this work, we introduce one additional spectroscopy param-

eter BVR ?effective blood vessel radius?, describing vessel

packaging. Note that we compute RDhere, assuming a homo-

geneous hemoglobin distribution rather than a packaged dis-

tribution, so we can evaluate the amplitude and spectral shape

of epithelial nuclear scattering signals extracted by model-

based LSS as implemented in previous works.1–3,10–12

Figure 2?b? plots the forward directed reflectance RFS

+RTfor values of d, m, and ? in the histological range of

interest. Note that this quantity is two orders of magnitude

*=cHbO2+cHbis the total hemoglobin concentration

*=1.0 mg/mL, ?

*are referred to as the spectroscopy parameters. Later in

larger than RBS. Hence, in the total reflectance, the effect of

forward directed light dominates over backscattering. Also

note that the spectral shape of the forward directed contribu-

tion shows features of hemoglobin absorption at 420 and

550 nm. Furthermore, the impact of different upper layers on

the total reflectance is small, indicating that the presence of

epithelial nuclei has minimal impact on the reflectance mea-

sured.

Perelman et al. define the normalized reflectance as:

R

R¯,

?7?

where R¯is the reflectance in the absence of the upper layer. It

is not possible to isolate the lower layer during an in-vivo

measurement, but R¯can be estimated by fitting the diffuse

reflectance model of Zonios et al.18to R by varying the spec-

troscopy parameters in Eqs. ?5? and ?6?.12For this calculation,

we assume that diffusely reflected light exits the tissue with a

Lambertian angular profile. The residual spectrum is the

wavelength dependent component of R/R¯,12and this signal

was assumed to be due to epithelial nuclear scattering.

We numerically evaluate Eq. ?7? for values of d, m, and ?

in the histological range of interest. The results, shown in Fig.

2?c?, indicate that the amplitudes, defined as half of the peak-

to-peak values of the oscillatory components of the normal-

ized reflectance spectra, are approximately 1% of the total

collected light power. Also, the wavelength dependent fea-

tures of the residual spectra do not have the same frequencies

as the LSS features ?optical thicknesses? of the upper layers,

shown in Fig. 2?d?. It is important to note that a one-percent

residual spectrum obtained from a clinical experiment would

be extremely difficult to detect, given the experimental vari-

ability, which is typically 2 to 3 % of the total signal.2Further,

the fact the residual spectra have different frequencies than

the LSS features, contrary to the requirements set by Perel-

man et al., calls into question the validity of the Fourier-

transform analysis.10,12The residual spectra of Fig. 2?c? are

not in agreement with the LSS features, because the diffusion

reflectance model of Zonios et al. used to obtain R¯does not

properly account for the addition of a nondiffuse scattering

layer on top of a diffuse scattering layer.

3

In this section we present tissue phantom experiments to

verify the findings of the numerical estimates described in the

previous section. The phantoms are very similar to the tissue

model in Fig. 1?a?, with two distinct layers separated by a

100-?m-thick quartz coverslip. The upper layer is 150 ?m

deep and holds polystyrene spheres ?Duke Scientific, Incorpo-

rated? of diameter d, in units of microns, immersed in opti-

cally clear, refractive index matched oil ?Cargille Laborato-

ries? such that m is close to 1. m is varied by using oils of

slightly different refractive indexes. The lower layer consists

of 10% intralipid ?Fresenius Kabi AG? diluted 1:9 with water.

This two-layer model is optically similar to tissue, where epi-

thelial nuclei lie on top of a diffuse reflecting stroma.

To create the upper layer, approximately 0.5 mL of the

spheres solution was placed inside a vacuum chamber. A

Tissue Phantom Experiment

Lau et al.: Re-evaluation of model-based light-scattering spectroscopy…

Journal of Biomedical OpticsMarch/April 2009

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Page 5

pump was used to evacuate air from the chamber until all of

the water had evaporated. Once evaporation was complete,

the spheres were removed from the vacuum chamber and ap-

proximately 0.5 mL of the index matched oil was placed in

the container. The mixture was stirred until the spheres were

homogeneously distributed. Lastly, the mixture was placed

between two quartz coverslips 150 ?m apart to form the up-

per layer.

We used a probe instrument, very similar to the one used to

measure tissue spectra in vivo,1–3to measure reflectance spec-

tra from four phantoms. The upper layer spheres ranged in

diameter from d=10 to 20 ?m, and the refractive index mis-

match m varied from 1.03 to 1.06. For one phantom, only oil

was placed in the upper layer. The measured reflectance spec-

tra, normalized by a measurement of a 99% spectralon stan-

dard ?Labsphere, Incorporated?, are shown in Fig. 3. Even

though the upper layer properties vary considerably, the mea-

sured reflectance spectra are very similar, as was observed in

the previous section ?Fig. 2?b??. This confirms that epithelial

nuclear scattering has minimal impact on the total tissue re-

flectance.

4Diffuse Reflectance Spectroscopy with and

without Vessel Packaging

Previously, residual spectra measured from tissue and similar

in form to the ones computed earlier were analyzed with the

Fourier-transform analysis10,12to extract scatterer size distri-

bution and number density of upper layer structures from the

wavelength dependent oscillations.13It was assumed that the

scatterers were epithelial nuclei with properties in the range

listed in Fig. 2?b?, and that changes in their properties were

related to cancer progression.12In this section we analyze a

set of reflectance spectra, measured by Georgakoudi et al.,1

from seven high grade dysplasia ?HGD? lesions, seven low-

grade dysplasia ?LGD? lesions, and 22 nondysplastic Barrett’s

?NDB? tissue sites. Figure 4?a? shows a representative reflec-

tance spectrum along with its R¯obtained in the same manner

as R¯in Eq. ?7?. The spectroscopy parameters are varied until

an optimal fit ?defined in the caption of Fig. 4? is obtained.

This is the R¯estimated from the reflectance spectrum assum-

ing a homogeneous hemoglobin distribution in the tissue. In

Fig. 4?b?, we plot the corresponding normalized reflectance

spectrum ?R/R¯−1?. The amplitude of the wavelength depen-

dent component of the normalized reflectance spectrum is ap-

proximately 10% of the total reflectance. This is an order of

magnitude larger than the 1% value computed by elastic light

scattering analysis. Therefore, it is unlikely that the origin of

the observed residual spectra is due to epithelial nuclear scat-

tering.

Up to this point, we have not discovered the true origin of

the 10% residual spectra observed in clinical measurements.

To explore this topic, we consider the incorrect assumption

made so far in this work that the hemoglobin distribution in

tissue is homogeneous. As has been noted by several

researchers,14–16blood is confined within vessels of finite di-

mension, thus creating an inhomogeneous distribution of he-

moglobin. Because hemoglobin is such a strong absorber at

the Soret band ?420 nm?, regions of tissue with blood vessels

can be totally opaque to 420-nm light and be more transpar-

ent to other wavelengths. In bulk tissue, this tends to reduce

the magnitude of the Soret band relative to the weaker hemo-

globin Q bands around 550 nm. Elastic light scattering analy-

sis and corresponding analysis of clinical data suggest that a

physical model that more accurately accounts for hemoglobin

absorption is required to fit the clinical reflectance spectra. To

0.14

0.16

zed)

R (normaliz

0.1

0.12

d = 10, m = 1.06

d = 10, m = 1.03

d = 20, m = 1.03

no spheres

450500550600650

0.08

Wavelength (nm)

Fig. 3 Reflectance spectra measured from tissue phantoms. The verti-

cal axis is the fraction of light energy collected from the phantom

divided by the amount collected from the 99% spectralon. All phan-

toms had approximately 4?104spheres/mm3in the upper layer. For

clarity, hemoglobin has not been added to the lower layer because the

purpose of this phantom is to examine scattering by spheres in the

upper layer.

1.3

x 10

-3

R

1

1.1

1.2

R

Rbar

R

Rbarvp

R

( )(a)

0.9

0.1

0.2

vp

R

1

−

R

R

-0.1

0

Rbarvp

Rbar1/ RR

Rbar1/

RR

1/

−

VP

RR

(b)(b)

400500600700

-0.2

Wavelength (nm)

−

Fig. 4 ?a? Reflectance spectrum ?solid line? measured from Barrett’s

esophagus in vivo along with optimal fits, using the model of Zonios

et al.,18with ?dotted line? and without ?dashed line? vessel packaging

to account for the inhomogeneous hemoglobin distribution. We de-

fine the optimal fit as the R¯???

−R¯???/R¯????2over all possible combinations of spectroscopy param-

eters. For the fit with vessel packaging, e=0.35, and for the fit without

vessel packaging, e=1.01. ?b? Residual spectra resulting from fitting

with ?dotted line? and without ?dashed line? vessel packaging. The

locations of the largest residual features are somewhat arbitrary, as

they depend on R and the exact objective function used in the fit

optimization. This may affect the appearance of residual spectra pre-

sented in other papers, such as in Figs. 3?a? and 3?b? of Perelman

et al.12

that minimizes e=???R???

Lau et al.: Re-evaluation of model-based light-scattering spectroscopy…

Journal of Biomedical OpticsMarch/April 2009

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