The set of phantoms with varying scattering and absorption imitated
CHAPTER 5 . TISSUE PHANTOMS
Alexander B.Pravdin
, Svetlana P.Chernova
(Saratov State University,
Russia), Theodore G.Papazoglou
(FORTH-IESL, Greece), Valery
V.Tuchin
(Saratov State University, Russia)
5.1 INTRODUCTION
We are currently witnessing a steady growth of interest in optical methods for medical diagnostics and treatment. The reason for this growth is that optical methods have the advantage of being inherently noninvasive.
Many research groups are working on the theoretical foundation and measuring techniques that allow for the reconstruction of tissue intrinsic optical properties from optical (spectral) signals that are measured on the surface of the biological objects. The detection and localization of optical inhomogeneities, such as tumors or hematomas, deep within the tissue is one example. Another example is the development of light-based therapeutic methods (selective tissue ablation, PUVA, PDT etc.), which needs the assessment of intensity (fluence) fields within the tissue or organ that is treated.
However, the evaluation of measuring techniques and validation of theoretical predictions on light propagation in tissues is hardly possible in direct experiments on actual bioobjects. One encounters a wide variations of morphological and biochemical parameters that are beyond the control of experimentator. If diagnostics equipment is to be used on a day-to-day routine basis, stable and reproducible calibration methods need to be developed. For this purpose stable and reproducible test-objects that mimic tissue optical characteristics are needed.
Since the late eighties 1–7 , various models of actual tissue, which mimic the optical or structural properties of tissue, have been developed for many different areas of optical diagnostics. Tissue models have been developed for tissue fluorescence spectroscopy 8–17 , noninvasive glucose monitoring 18–20 , oxygenation monitoring and oxymetry 21–23 , optoacoustics 20,35,36 , pulsed photothermal measurements 37,38 , ex vivo measuring of optical properties of tissues 39,40 , Doppler-flowmetry 41–43 , measuring of polarization degree decay 44,45 , and quantitative detection of fluorophores (including photosensitizers) in tissues 15,16,46 . In addition, tissue phantoms exists for diffuse reflectance measurements in steady-state 7,23–28 ,the time-domain 24,29–32 , and the frequency-domain 33,34 . Tissue phantoms also play an important role in studies concerned with imaging of tissue using time resolved transmittance 47,48 , steady-state reflectance 49,50 , polarization gating 51 , frequency-domain optical tomography 52 , time-resolved fluorescence 53 , and cw optical tomography 54 . Finally, tissue-like phantoms have also been taken up in the researches connected with therapeutical implementation of optical radiation; among of them being light dosimetry 6,55 , laser ablation 56 , and
PDT 9,16,57 .
5.2 GENERAL APPROACH TO PHANTOM DEVELOPMENT
Light propagation in optically inhomogeneous, turbid media, such as biological tissues, which are predominantly light scattering in the visible range, is commonly described by the Boltzmann transport equation. The equation accounts for optical properties of the tissue in the form of absorption coefficient
a
, scattering coefficient
s
, and scattering phase function. These quantities form the basis of phantom modeling. The light propagation in an artificial medium is considered similar to that in actual tissue when
s
,
a
, and anisotropy factor (as an approximation for phase function), g, of the phantom are similar to the values found in a natural object. In soft tissues typical values for the coefficients are
a
0.5 to 5.0 cm
–1
,
s
0.2 to 400 cm
–1
, and
0.8< g <0.99 in visible and NIR ranges.
When the problem under study allows the use of the diffusion approximation to Bolzmann equation, and the shape of the phase function is not essential, modeling of only two parameters,
a and the transport scattering coefficient,
s
' =
s
(1–g), provides the necessary light transport similarity. For some purposes the similarity of the optical properties of phantom and tissue may be on the level of equal values of the diffusion coefficient, D=
a
/
eff
2 ,
eff being the effective attenuation coefficient, and
eff
2 = 3
a
[
a
+
s
(1–g)]. On this basis scaled phantom models can be developed, in which scattering and absorption of light proceed in the same manner as in tissue, but over larger dimensions 58 .
When the task is to model the tissue with complex architecture, or even a whole organ, or to prepare the test-object for evaluation of imaging techniques, the "macroscopic" geometry of the natural object should be reproduced in phantom. One of the most commonly encountered feature is a layered tissue structures. Multilayered phantoms have been developed in the past to mimic, for example, the skin 27,37 ,the human head 23,24,49 , the cervix 10 .
When phantoms of complex structures are developed, the refractive indices of layers (inclusions) should be accounted for, as a mismatch at the interfaces may influence the light propagation within tissue. The value of refractive index also plays an important role when the tissue-air interface is modeled. The accepted typical values for soft tissues are –1.33-1.50
59 .
A straight-forward approach to modeling optical properties of tissue is to reproduce scattering and absorption coefficients independently by mixing relevant proportions of purely scattering (no absorption in wavelength region of interest) and purely absorbing media. The latter being predominantly dyes that have negligible scattering, because they are dispersed on molecular level
(no mesoscopic inhomogenities of refractive index).
Phantoms developed for the use in fluorescence studies also contain fluorescent dyes, which may be photosensitizers or natural fluorophores. The criteria of quantification of fluorophores to be added are based on their absorption coefficients at the excitation wavelength and the spectral fluorescence yields 8,13 .
Both scatterers and absorbers / fluorophores are suspended in an appropriate transparent host medium (ground material) which forms the volume of phantom. The demand on the optical properties of the host
material, apart from being nonscattering and nonabsorbing, is that the value of refractive index is close to a value found in actual tissue.
In deciding on a host for a particular phantom, the issue of component compatibility should be taken into consideration. This is important because some commonly used scatterers are colloidal systems and may aggregate in an inappropriate diluent, and some particles, e.g.
polystyrene microspheres, may dissolve in organic solvents. Besides chemical stability, stable spectroscopic properties should be considered, since the absorbers and fluorophores may be markedly influenced by solvent / matrix effects.
According to the mechanical properties of the host used, tissue phantoms can be divided in two classes, liquid and solid phantoms. Liquid phantoms, in which scatterers and absorbers are mixed in correct diluent, are rather easy to prepare, however don't allow making of samples of realistic complexity 8 .
Such phantoms have been commonly used in modeling of infinite or semiinfinite media with absorption, scattering and (optionally) fluorescence. The advantages of a liquid phantom is the easy movement of fluence or radiance detectors within the phantom volume.
In solid phantoms the host material serves as a mechanical basis. Typical host materials are polymers 8,30,37,41,48,57 and aqueous gels 8–10,29,31,34,35,38,47 . The ability of these materials to hold the desired shape provides the opportunity of manufacturing geometrically complex inhomogeneous phantoms. This goes as far as to mimic whole organs, by cutting and stacking slabs or use of moulding techniques. One of the advantages of such solid media is a near perfect refractive index matching at interfaces for the absence of walls or partitions. Furthermore, the aggregation and the sedimentation of scattering particles, which is a common problem in liquid phantoms, is not a problem in solid phantoms; the hardness of the host material does not allow for movement of the scattering particles.
However, dyes that are dissolved in a polymer or gel matrix may diffuse unabstructured from one slab to another, thus reducing the stability of the phantom optical parameters. To circumvent this problem along with the problem of spectral shifts caused by interactions of absorbers and fluorophores with other components of phantom, it has been suggested to substitute absorbing and fluorescing particles suspended in host material for the dyes 8 .
In the systematic design of tissue phantoms it is important that the optical parameters of the sample be predictable from the individual characteristics of its constituents and from the system composition. The practical implementation of the method places additional constraints 8 . For example physical parameters of the phantom system should be temporally stable. This concerns not only optical parameters but mechanical stability (evaporation of solvents, aging of polymers, degradation of constituents by bacteria) as well.
Furthermore, the preparation process should, as far as possible, be simple, quick, and safe.
5.3 SCATTERING MEDIA FOR PHANTOM PREPARATION
Calculations based on Mie theory are conventionally performed to predict scattering properties of particle suspensions that mimic the actual scattering by tissues. Although Mie theory is strictly applicable only in the case of some regular-shaped particles, its predictions are often considered acceptable for the particles of irregular shape. The theory yields the scattering cross-section,
s
(cm 2 ) and scattering anisotropy g. For non-absorbing particles these two parameters are given by 60
s
(
2
0
/ 2
n
0
2
) n
1
( 2 n
1 )( a n
2 b n
2
), (5.1) g
2
0
n
0
2 s
n
1
2 n
1 n ( n
1 )
Re( a n b
* n
)
n
1 n ( n
2 ) n
1
Re( a n a
* n
1
b n b
* n
1
)
,
(5.2) where b a n n
( )
n
( m
)
m
n
( m
n
n
( m
)
m
n
( m
n
, (5.3) m
( m ) n
( )
n
( m )
n
( ) m
n
( m ) n
( )
n
( m )
n
( )
, (5.4) m
n p n
0
;
2
rn
0
0
, (5.5) r – radius of spherical scattering particles (cm),
0
– light wavelength in vacuum (cm),
n
,
n
,
‘ n
,
‘ n
– Ricatti-Bessel functions of the first or second kind, n
0
– refractive index of ground (host) material, n p
– refractive index of scattering particle material, and * denotes the complex conjugate.
When all scattering events can be treated independently from each other
(the volume fraction of scatterers should not exceed 1 – 10%), the scattering coefficient (cm
–1
) can be expressed with scattering particles density (cm
–3
s
as
s
=
s
, where
is the
). In the case of absorbing particles a complex refractive index has to be considered and the relevant Mie theory expressions yield
s
,
a
(absorption cross-section which gives
a
=
a
), and g.
From the above expressions in can be easily seen that the particle characteristics governing its scattering properties are radius, r, and refractive
r n p index, n p
. The controlling parameters are the ratios and , which
0 n
0 implies the dependence of
s
and g for given scatterers on radiation wavelength and host material used.
Calculations based on Mie theory 8 predict that the transport scattering n p coefficient rises steeply when departs from unity (Fig. 1a). The n
0 symmetry about n p n
0
1 suggests a use of dispersions with n p
1 as n
0 scattering media in phantoms. Such media may be, for example, the foams, provided a size of bubbles can be controlled under preparation. If n p
is close to n
0
, sufficiently large particles (r>5λ) scatter light mostly in the forward direction, and the anisotropy factor g approaches 1 (Fig. 1b). Figure 1c shows that the transport scattering coefficient of suspensions with the constant volume fraction of particles becomes maximum when particle dimension is comparable (or of the same order) with light wavelength. Sections of the characteristic surfaces by r = const planes in Figs.1c,d reveal the wavelength dependence of scattering parameters. In calculations, n o
and n p
were assumed independent of
0
, thus spectral variations of
s
' and g are connected only with the influence of parameter
in Mie formulae.
Scattering by particles that are smaller or comparable in size with the wavelength is spectrally dependent. The transport scattering coefficient decreases with
0
. In case of large-diameter scatterers,
s
' is nearly constant.
The spectral dependence of the scattering anisotropy parameter for different size particles is similar. The scattering characteristic of large particles show almost no dependence on wavelength, while the scattering characteristics of particles with diameters comparable to the wavelength or smaller show a strong dependence on the wavelength.
Actual biological tissues usually show high values of g (typical for large particles) as well as a steep increase of transport scattering coefficient towards shorter wavelength (typical for small-size scatterers). This observation can not be modeled using a monodisperse particles suspension.
Therefore, several authors have suggested that a mixture of large and small particles may be better suited to describe real tissue 8,61 .
When a mixture of particles or a suspension with broad-banded size distribution is employed, effective transport parameters of the scattering medium may be expressed, following Ref.
8 , in terms of average values weighted by volume fractions of particles of different size:
s
3
4 c
p i
i
( 1
r i
3 g i
)
, (5.6)
g
i
i
g
i r r i i
3
3
, where c p
is the fraction of suspension volume occupied by particles;
i
is the volume fraction of particles of radius r i
, calculated as r i
3 i
r i
3 i i
i
being the relative number of particles of radius r i
in suspension;
si
– scattering cross-section for particles of radius r i
;
;
(5.7) g i
– scattering anisotropy factor for particles of radius r i
.
Fig. 1. Scattering properties calculated using Mie theory for nonabsorbing spherical particles: a,b – at
0
= 633 nm; c,d – at n p
/n
0
= 1.07
8 .
The most common scattering media used in tissue phantom manufacturing, especially in preparation of liquid systems, are fat emulsions
(Intralipid, Nutralipid, Liposyn) for intravenous feeding of patients 7,8,11,12,16,19,23–27,29,33,37,46,47,54,58,62–65 . These products contain soybean oil, egg phospholipids, and glycerol and are the suspensions of roughly spherical fat droplets dispersed in water. In Ref.
62 the formulation of 10% Intralipid
(Kafi Pharmacia) is cited as:
Table 5.1.
Composition of 10% Intralipid 62 purified soybean oil 10 g purified egg phospholipids 1.2 g anhydrous glycerol water
2.2 g upto 100 ml of solution
Since these emulsions are produced for medical application and not as optical standards, their properties may vary with different batches and the measured optical properties may vary from one research group to another.
The mean size of scattering oil droplets in Intralipid – 10% has been estimated in Ref.
66 as 402 – 426 nm, but in Ref.
67 it was found that over 75% of droplets in Intralipid had diameters equal or less than 125 nm.
As a systematical construction of phantom requires the individual optical properties of its components to be known beforehand, a number of measurements using different methods has been performed to determine parameters of scattering media. In Ref.
24 for 1% v/v concentration of
Intralipid (Liposyn 20%) at 633 nm the following values were listed:
s
' =
14.0
0.5 cm technique);
s
–1
(measured by frequency-domain diffuse reflectance
= 71 cm
–1
(determined with collimated transmission measurements), thus g = 0.8 was adopted;
a
= 0.005 cm
–1
(determined with video reflectometry apparatus).
Based on comparison between experimental dependencies of absorption length, transport length, and anisotropy factor on wavelength for 2% v/v solution of Intralipid–10% and Mie theory the use of the following useful approximation 68 was suggested over 400 – 1000 nm region:
s
' (
) (cm
–1
)
1.6
10 3
–1
; g (
)
1.1 – 0.58
10
–3
.
Optical properties for different concentrations of Intralipid–10% at 1064 nm were obtained with integrating sphere and collimated transmission measurements followed by inverse adding-doubling calculations 58 :
s
a
/ % (cm
–1
/ %) = 1.30
/ % (cm
–1 g = 0.5
0.02,
/ %) = 0.054
0.047;
0.02;
where absorption coefficient is corrected for water absorption (see Fig.2). a b
Fig.2. The absorption and scattering coefficients (a), and scattering anisotropy factor (b) at 1064 nm for varying concentrations of water suspension of Intralipid 10% 58 .
Authors of Ref.
23 accepted the approximate value of 5
8 cm
–1 for
s
' of
0.5% Intralipid in NIR range and supposed that
s
' increased proportionately to Intralipid concentration (in the cited work the 0.5%
2% concentration range was used).
Optical properties of pure Intralipid (10% solids; Kibavitrum, Inc.) were determined 64 using steady-state optical measurements of collimated transmission and total diffuse reflectance from semi-infinite layer of both pure Intralipid and Intralipid with known amount of India ink added. The results are depicted in Table 5.2.
Table 5.2.
Optical properties of Intralipid 10% 64 wavelength,
(nm) absorption coefficient,
a
(cm
–1
) scattering coefficient,
s
(cm
–1
) anisotropy factor, g
488
633
0.07
0.02
617
313
0.80
0.71
1064 0.10 78 0.68
In Fig. 3 spectral dependencies of absorption (
a
) and scattering (
s
') coefficients for 1% Lyposyn are shown 33 . Spectra were obtained using frequency-domain in vivo spectrometer. The increase of absorption at the wavelengths exceeding 700 nm most probably results from water absorption.
Authors of Ref.
33 mention that the values of reduced scattering coefficient are in 10 – 15% agreement with the published results obtained using CW spectroscopy. These 10-15% are within the batch-to-batch variability of
Lyposyn.
In constructing liquid tissue phantom for fluorescence measurements for 1% v/v Intralipid scattering coefficients of 79 and 47 cm
–1
11 ,
were adopted at
514 and 635 nm, respectively. For the analogous Intralipid solution containing one percent solids (this term is often used with relation to
Intralipid despite the disperse phase in this case being liquid oil) the optical properties at 633 nm were determined 7 . Using collimated transmission method the value of 34.4
0.1 cm
–1
for total attenuation coefficient,
t
, was obtained. An added absorber technique gave small
a
= 0.011 scattering coefficient was assumed to be equal to
t
0.001 cm
–1
. The
because of negligibly
a
. The direct measurement of scattering phase function by goniometry gave g = 0.68.
This low value of g, as compared with most actual tissues, illustrates the general feature of Intralipid; while reproducing well scattering coefficients of tissue,
s
, it underestimates the anisotropy factor. Thus, using Intralipid, one has to select the
s value which gives the transport scattering coefficient,
s
'=
s
(1–g), equivalent to that of the tissue. By doing so we obtain the phantom that models the fluence field within the tissue only on the level of diffusion approximation or the principle of similarity 69 . In other words, we consider the fluence distributions in the tissue and the phantom when these
two scattering and absorbing media have the same
a
and
s
', but not the complete set of optical parameters (
a
,
s
, and g). To make the value of scattering anisotropy parameter of Intralipid-based phantoms closer to the figures for actual tissue, a fraction of large particles ( e.g.
1 – 10
m diameter
SiO
2
particles 9 ) may be added. This scarcely affects the wavelength dependence of anisotropy factor but enhances the value of g.
Fig. 3. Wavelength dependencies of absorption and scattering coefficients for 1% Lyposyn 33 , obtained using frequency-domain spectrometer.
While liquid Intralipid phantoms are in general stable during a short measurement, it should be kept in mind that Intralipids are colloidal systems, and considerable changes in pH or ion content of dispersive medium (diluent) may provoke aggregation of scatterers over time.
In preparation of solid Intralipid–based phantoms 8 it was observed that transport scattering coefficients of Intralipid in gel strongly depended on the amount of gelling agent For example, 2% w/w of agarose caused
s
' reduction by 30% as compared to a water suspension. Authors of Ref.
8 suggested that the effect may be caused either by the increased temperature during gel preparation or by structural changes of the scatterers induced by interactions with agarose.
Other scatterers frequently used in construction of tissue-like phantoms are micron–sized polystyrene latex spheres 13,14,18,30,35,36,38–40,42,43,45,50,70 .
Compared with Intralipid these products provide much better optical standard.
In general, commercially available latexes have a narrow size distribution and the needed information about distribution may be obtained from the
manufacturer. Formulae of Mie theory can be used for calculating the scattering properties of spheres suspensions, provided that condition of independent scattering is observed.
The refractive index of latex is given by n = 1.583 (at 514.5 nm) 70 ; (n =
1.59
45 ). When a phantom for the use with different wavelengths is developed, the spectral dependencies of refractive index should be known. For polystyrene and water, data for the refractive indices in visible were extrapolated into NIR region using approximation by a Cauchy fit of the form: n(
) = n
0
+ n
2
/
2 + n
4
/
4 + n
6
/
6 , with the following parameters for
taken in nanometers: water polystyrene n
0
1.3199
1.5626 n
2 n
4 n
6
6.876
10 3 –1.132
10 9 1.11
10 14
1.169
10 3 –1.125
10 9 1.72
10 14
Mie calculations performed in Ref.
70 for two samples of polystyrene spheres suspended in water for 514.5 nm yielded the following: particle diameter
(
m) volume fraction of particles (C p
)
s
' (cm
–1
)
0.205
0.460
0.01798
0.00013
0.01665
0.00013
83
73 g
0.875
0.962
Refraction index 1.583 was taken for particles and 1.336 for water. In Ref.
43 the calculations for particles embedded in gelatin gel (assumed value of host refractive index was 1.35) for wavelength of 632.8 nm gave: particle diameter
(
m) scattering cross-section (cm 2 ) anisotropy factor
0.21
0.48
1.05
3.3
10
–11
1.35
10
–9
2.412
10
–5
0.36
0.81
0.92
Scattering parameters for 0.9
m spheres, taken as 10% suspension, in ultraviolet region (
= 335 nm) are reported in Ref.
36 :
s
has the value 6090 cm
–2
, and g is 0.918, what corresponds to reduced scattering coefficient,
s of 500 cm
–1
.
',
Being colloidal systems, polystyrene spheres suspensions may undergo aggregation, which will affect their scattering properties. Dense suspensions need sonication before phantom preparation and stirring of liquid phantoms before each measurement.
In preparation of solid phantoms, sonication of warm gels with scatterers before casting is also advisable. The addition of surfactant (0.1% by weight of sodium dodecyl sulfate) in order to ensure long-term stability of suspension
was reported in literature 70 . Polystyrene particles proved to be stable in hydrophilic enviroment 8 . Therefore, these particles are suitable for the use as constituents of solid phantoms on the base of hydrophilic gels (gelatin, agarose, agar-agar), while organic solvents and monomers that are employed in elaborating of polymer-based solid phantoms may dissolve the spheres.
Mineral particles are anticipated to be stable both in hydrophilic and hydrophobic environment, and are used as scattering medium in various solid phantoms (TiO
2
10,23,24,31,32,34,39,49,55,57 ; SiO
2
47,71 ; talc 56 ). The drawback that constrains the employment of these scatterers in liquid phantoms is their high specific weight, which causes rapid sedimentation of particles in a nonviscous host.
In Table 5.3 relative refractive indices for nonabsorbing mineral particles embedded in solid host are presented.
Table 5.3.
Relative refractive indices of massive mineral particles in aqueous gel
(n = 1.33) and polyorganosiloxane rubber (n = 1.40) 8 substance in aqueous gel in rubber
SiO
2
–Al
2
O
3
BaSO
4
MgO*
–Al
2
O
3
1.10
1.20
1.23
1.31
1.33
1.04
1.14
1.17
1.24
1.26
TiO
2
** 1.95 1.86
*MgO may be unstable in hydrophilic media as it reacts with water yielding magnesium hydroxide.
** Nanoparticles of TiO
2
are known to catalyze photodestruction of some dyes.
In Ref.
31 layered tissue phantoms were designed to experimentally test simulation results obtained with time-resolved Monte Carlo code. Tissue layers with defined scattering properties were generated by addition TiO
2 powder into gelatin gel. The particles exhibited Gaussian distributed sizes with a mean value of 280
m and full width at half-maximum of 80
m. In
Ref.
39 TiO
2
particles of three orders of magnitude smaller diameters (d = 0.3
m) were suspended in an epoxy resin host. In modeling of optical properties of atheromatous plaque at 1064 nm and 1300 nm, ground talc, with average particle size of 30 – 40
m, dispersed in 2% agar-agar gel was used 56 .
The reduced scattering coefficient of TiO
2
powder (Fisher Chemical,
Boston, Massachusetts) suspended in 7% gelatin gel was measured at 690 nm using a diffuse reflectance instrument 55
0.2g of TiO
2 per 20ml of the gel the
s
. For the sample that contained
' value of 14
2 cm
–1
was obtained. On the series of samples, the linear increase of reduced scattering coefficient with the rise of TiO
2
concentration was observed (see Fig. 4).
The samples were prepared by mixing the components in boiling phosphate buffer and casting after 2 min stirring. In separate measurements the samples were checked for the homogeneity of the reduced scattering
coefficient. The variation of
s
' appeared to be less than
10% within one sample, the intersample variation being also
10% 55 .
For nonabsorbing spherical particles the scattering properties,
s
' and g, are uniquely determined, using Mie theory, by n p
/n
0
and particle size. But the effective values and their spectral dependencies for the mixtures of particles, when scatterers are made out of different substances and have different dimensions, may be adjusted to the desired figures. It has been demonstrated 8 that even binary mixture allows construction of scattering media with distinct
s
' wavelength dependencies and practically coincident scattering anisotropy factors. Fig. 5 demonstrates the results of Mie theory calculations for two binary mixtures of monodisperse mineral particles.
Fig. 4. Reduced scattering coefficient at 690 nm vs TiO
2
content.
TiO
2 powder was added to the mixture of 7% gelatin and
0.0002% India ink solution in 20 ml of phosphate buffer saline 55 .
Along with massive mineralic scatterers the porous spherical
-Al
2
O
3 particles were applied in the preparation of tissue-like phantom 8 . Particles had diameters of 5.3
m
1.0
m with nearly symmetrical size distribution. 10 nm diameter pores occupied 65% of the particle volume and, as it was assumed that the pores were filled with polyorganosiloxane. The effective refractive index, n eff
, of such "impregnated" particles was calculated by
Bruggeman theory: c por n
2 p
n
2 eff n
2 p
2 n
2 eff
( 1 c por
) n n
2
0
n
2
0
2 n eff
2 eff
0 , (5.8)
where n p
– refractive index of massive
-Al
2
O
3
, n
0
– refractive index of host rubber, c por
= 0.65 – volume fraction of pores in particles.
The value of n eff
= 1.52 at 546 nm was obtained and used in phantom characterization.
Fig. 5. Spectral dependencies of scattering parameters of binary mixtures of nonabsorbing particles 1:19; a – mixture of: 0.1
m particles, n p
/n
0
= 1.85
(corresponds to TiO
2
in polyorganosiboxane); 5
m particles, n p
/n
0
= 1.25
(corresponds to Al
2
O
3
in polyorganosiboxane). b – 3:7 mixture of: 0.1
m particles, n p
/n
0
= 1.25; 5
m particles, n p
/n
0
= 1.25
8 .
In Ref.
27 an example of the scattering system with n p
1 was realized. n
0
Hollow microspheres with the external diameter of 1
m were embedded in polyvinylalcohol films. In dehydrated state the cavities of spheres are filled with gas (n gas
1). The calculations based on Mie theory were performed for the 0.8
m diameter spheres, with n p
= 1, in the host material with n
0
= 1.53.
The following parameters were obtained 27 :
s
(cm 2 )
= 633 nm
1.116
10
–8
= 780 nm
0.997
10
–8 g 0.8447 0.8359
Cow milk has also been applied to a number of phantom measurements 1,44,51,72,73 . The system of scattering particles of milk comprises
two subsystems: i . emulsion of fat spheres and ii . colloidal protein particles.
The size of spheres falls into the range 0.5
20
m. Most of the particles have a diameter of 2
4
m (concentration 3
10- cm
–3
). Dimensions of protein fraction are distributed within 0.02 - 1
m range as follows: 0.02
0.04
m – 30%; 0.04
0.08
m – 30%; 0.08
0.15
m – 30%; 0.15
1
m –
10% 44 . In phantom preparations both whole and skimmed milk are used. Their scattering properties should differ, because in the last case the fraction of large particles, which impart a higher g value and a weaker wavelength dependence, is removed. Optical properties of homogenized whole milk
(3.5% fat) and the milk diluted with water was estimated in visible and NIR region using a time-resolved transmittance method in Ref.
72 Here the refractive index of the suspensions was taken to be n = 1.33, and the sample thickness was 2 cm: volume fraction of milk, % estimation for
s
'
(cm
–1
) estimation for
a
(cm
–1
)
6
12
25
5
10
18
< 0.015
< 0.015
< 0.015
50
100
30
46
< 0.015
< 0.015
Based on the measurements of total transmittance, diffuse reflectance, and collimated transmittance the optical properties of undiluted milk (3.5% fat) were obtained over the wavelength range of 700 – 1100 nm 73 . The refractive index of the milk at 650 nm was found to be n = 1.36. Experimental data were processed using an inverse
-Eddington method (IDE), and an inverse Monte
Carlo method combined with small-angle approximation of the radiative transfer theory (IMC + SAA). The results for 880 nm are presented in Table
5.4.
Table 5.4.
Optical properties of undiluted milk 73 sample
a
(cm
–1
)
s
(cm
–1
) g thickness (mm) IDE IMC+SAA IDE IMC+SAA IDE IMC+SAA
0.1
0.2
0.5
7.86
4.75
1.88
0.93
0.95
0.69
140.2 140.3 0.7222 0.831
127.2 129.2 0.736 0.800
128.2 129.5 0.765 0.766
At the wavelength of 700 nm the scattering properties of milk obtained in
Ref.
73 are close to the estimations in Ref.
72 .
5.4. LIGHT ABSORBING MEDIA FOR PHANTOM PREPARATION
Light absorption by tissue is modeled in phantoms by reproducing the value of absorption coefficient,
a
. In most cases when the phantoms are employed, it is sufficient to give an account of light propagation at one wavelength. This makes a variety of dyes, which may be considered as candidates for the use in phantoms, very wide. Such dyes should have conspicuous absorbance at the wavelength of interest and be soluble in the host material. Besides, the dyes should meet the general requirements of stability, safety, and phantom component compatibility.
Common microscopy stains which are easily available and widely used in laboratories absorb in visible and NIR spectral region. They are water soluble.
Because of this, these dyes are often used in the preparation of water-base liquid phantoms and the solid phantoms based on aqueous gels.
Semi-infinite liquid phantoms with methylene blue as an absorber were used in measurements of angular radiance in turbid absorbing media at 630 nm 62 . The stock solution of the dye in distilled water at the concentration of 1 mg
ml
–1
was added to water + 10% Intralipid mixtures at different proportions to vary the absorption coefficient of the medium. The formulations employed are as follows:
10% Intralipid Methylene blue solution
Distilled water
I
II
3.2%
6.0%
0.5%
0.4%
96.3%
93.6%
III 1.9% 0.2% 97.9%
Measured radiance dependency on viewing angle of detector within the phantom I overlapped the radiance obtained in Monte Carlo simulations with the following parameters:
a
= 0.95 cm
–1
,
s
= 150 cm
–1
, g = 0.975
62 .
Measurements on a series of liquid phantoms (Intralipid in phosphate buffered saline) with an increasing amount of Evans blue as an absorber have been performed to check the validity of the method of spatially resolved steady-state diffuse reflectance spectroscopy. Absorption properties of pure solution of Evans blue were measured using a spectrophotometer 25 .
Spectrophotometry is a conventional technique for the isolated characterization of the dyes which are used in phantoms. The specific absorption of the dyes dissolved in the host medium is measured at the chosen wavelengths. Then these data are used for the prediction of light absorption properties of turbid phantoms loaded with the dyes.
Indocyanine green has been employed as near infrared (NIR) absorber in preparation of gelatin gel-based layered solid phantoms. These layered phantoms were used in testing reconstruction techniques for time-resolved measurements. The phantom incorporated two layers of gelatin. The scattering and absorption properties of the layers were controlled by the amounts of Intralipid and indocyanine green introduced into the gel. The reduced scattering coefficients was
s coefficients at 752 nm were varied from
' = 10 cm
–1
, and the absorption a
= 0.12 cm
–1
to 0.36 cm
–1 29 .
In the case of aqueous gel-based phantoms, it is advisable to conduct the measurements of optical properties of absorbing dyes not on its stock solution
but on the scatterer-free gel + absorber samples, as a binding of absorber to the gelling agent (usually polypeptide or polysaccharide) macromolecules may result in pronounced spectral shift.
A liquid semi-infinite phantom with a dye as absorber was used for experimental validation of a forward-adjoint fluorescence model. The optical properties of the aqueous phantom medium were controlled by the contents of a fluorophore (endogenous tissue (cell) fluorophore NADH was used), a scatterer (suspended polystyrene microspheres), and an absorber (Ethyl orange) 14 . The principle of fluorescence measurements places additional constraints on the absorber. The absorber should not fluoresce under the excitation wavelength used in the experiment. Ethyl orange was tested with
351 nm argon-ion laser radiation used for NADH fluorescence excitation 14 and was found to have negligible fluorescence. The optical mean free path was measured on a stock solution of each component with a spectrometer modified to a narrow-beam geometry. Fluorescent emission of NADH at
470
5 nm (but not at the emission spectrum maximum at 540 nm) was recorded because the absorption of both NADH and Ethyl orange practically does not depend on the wavelength over this spectral interval 14 .
Several groups have used in liquid and solid tissue phantoms the microscopy stain trypan blue. In a series of papers 16,19,50 , polarization properties of diffuse reflectance were studied on semi-infinite liquid turbid samples. The feasibility of video imaging using polarized light reflectometry has been demonstrated in 50 on human skin scaled phantom (3.5 mm of phantom corresponded to
1 mm of skin) prepared on the base of water, polystyrene spheres (0.9
m dia), and trypan blue. The optical properties were determined at 633 nm and 792 nm using video reflectometry and diffusion theory for analysis:
g
s a
'
a
s g
s
'
633 nm
0.20 cm
–1
69.8 cm
–1
0.913 cm
–1
6.073 cm
–1
792 nm
0.02 cm
2518 cm
–1
–1
0.939 cm
–1
6.86 cm
–1
In Ref.
74 similar phantoms have been used in video measurements of the polarized component of backscattered light at 442 nm and 792 nm. For the phantom prepared from water suspension of 900
m polystyrene spheres with trypan blue added, the optical properties appeared to be:
442 nm
0.04 cm
0.93
10.7 cm
–1
–1
792 nm
0.02 cm
0.89
5.1 cm
–1
–1
Estimated optical properties of human skin at 792 nm
0.4 cm
–1
—
15 cm
–1
Trypan blue also has been added yielding
s
' = 10 cm
–1 and
a
19 to Intralipid solution in distilled water
= 0.1 cm
–1
. The changes in the polarization patterns induced by glucose have been studied using this phantom.
In Ref.
26 13 liquid tissue-simulating phantoms have been employed for the evaluation of the accuracy of spatially resolved absolute diffuse reflectometry. To prepare the phantoms, different amounts of trypan blue were successively added to Intralipid solutions of different concentration. The
"true" optical properties of the samples were measured independently by the frequency-domain technique. The values of the transport scattering coefficient were between 5 and 10 cm
–1 between 0.02 and 1 cm
–1 and of the absorption coefficient
at 633 nm. For each solution the absorption coefficient of trypan blue was determined using conventional spectrophotometry.
Solid semi-infinite scattering and absorbing phantoms with known optical properties have been used to test the algorithms for obtaining optical properties of a turbid material from pulsed photothermal radiometry data 38 .
In those studies, the aqueous gel was chosen as the host material, because its thermal diffusivity is practically equal to the thermal diffusivity of most soft tissues. Varying amounts of polystyrene microspheres colloid and
Trypan blue dye were added to the melted collagen gel, yielding the samples with absorption coefficient ranged from 20 to 144 cm
–1 and reduced scattering coefficient from 0 to 150 cm
–1 at 627 nm. The absorption of the dye stock solution was measured with conventional spectrophotometer. The scattering properties of the polystyrene microspheres were calculated with Mie theory.
There are some particular problems, e.g.
the measurements in infrared spectral region, the studies of fluorescence excitation and emission spectra, the manufacturing of the phantoms on the base of hydrophobic host, which impose the additional requirements upon the properties of the absorber to be used in the phantom. This leads to the employment of extended list of the dyes other than common microscopy stains.
The validity of the methodology that combined integrating sphere measurements and the Monte Carlo inversion technique for determination of near-infrared optical properties of ex vivo human skin and subcutaneous tissues was estimated using liquid and solid phantoms containing infrared dyes as absorbers 39 . One series of experiments in the 650 – 1000 nm spectral interval was performed on liquid samples made of aqueous suspension of 1.27
m polystyrene spheres with infrared dye, S109564 Zeneca. The absorption coefficient of the solution was estimated from the known absorption spectra of the dye, and the reduced scattering coefficient was calculated from Mie theory. In the liquid samples placed between glass coverings, the edge effects may distort the homogeneity of the optical coefficients. To eliminate this hindrance, the solid phantoms on the base of "Araldite" epoxy resin, with 0.3
m TiO
2
particles as scatterers and Project 900 NP dye (Zeneca specialties
Manchester, UK) as a NIR absorber, were substituted for the liquid phantoms 39 . In Ref.
41 , the water soluble infrared absorber IRAWS1 (provided by Zeneca specialties) was used to provide absorption,
a
= 1 – 0.5 cm
–1
, in the solid polyvinyl alcohol-based phantom at the often used wavelength of
780 nm.
To demonstrate the validity of the dual-wavelength time-gated spectroscopy for determining the concentration of absorber in turbid media, liquid phantoms for transmission-mode measurements at 782 nm and 831 nm were prepared 48 . Greenish brown ink (Chugai Kasei) used as a pure absorber was added into 420 ml of 1% aqueous Intralipid–20% suspension in 0.07 ml steps up to 0.56 ml total volume of ink.
The absorption coefficients of ink solutions of various concentrations were premeasured using a spectrophotometer. The measurements gave absorption coefficients for a series of phantoms in ranges from 2.45
10
–2
to
2.94
10
–1
cm
–1
at 782 nm and from 3.10
10
–2
to 1.85
10
–1
cm
–1
at 831 nm. The determined values for water absorption: 2.45
10
–2
cm
–1
at 782 nm and
3.10
10
–2
cm
–1
at 831 nm are accounted for 39 .
The multilayered 2% agar gel phantoms with Intralipid–10% as a standard scattering element and a soluble dye, safranin, as absorber were used in the study of the total reflection of light from neonatal skin and the pattern of light distribution within layered tissue 27 . The concentration of absorber and scatterer was scaled down, which allowed modeling of light behavior in thin layers of actual skin on the large-scale gel phantoms.
As the optical properties of a layer can be expressed via the dimensionless quantities of albedo,
s
/(
a
+
a
), optical thickness, (
a
+
s
)d, and anisotropy, g, the behavior at various wavelengths can be reproduced using the same experimental wavelength. In Fig.6, the observed distribution of 633 nm light within the layered gel structure is depicted. To the right, the scale of corresponding dimensions in the skin at 460 nm is shown. Different layers of the phantom corresponded to the layers of actual skin, which optical characteristics are summarized in Table 5.5.
Fig. 6. The distribution of 633 nm light observed in phantom model of skin 27 .
Table 5.5.
Optical properties of skin layers at 460 nm 27
Layer
a
(cm
–1
)
s
(cm
–1
) g thickness
Pigmented 14 370 0.9
(mm)
65 epidermis
Papillary dermis
Venous plexus
Reticular dermis
5
18
5
370
333
440
0.9
0.9
0.9
55
50
1000
In Ref.
65 , the series of experiments to demonstrate the ability of laser induced spectroscopic techniques for quantitative estimation of tissue chromophores concentration was carried out on liquid and agar gel-based scattering and absorbing phantoms. Liquid phantoms were prepared by diluting stock Intralipid solutions with distilled water to the concentrations of
Intralipid from 1% to 20%. Commercially available red dye, Carmine – E120, and green dye, Chlorophyll – E140, were used as light absorbers
(chromophores). The optical properties,
a
,
s
, g, and
s
', of the phantoms at
543 and 633 nm were calculated from the integrating sphere reflectance / transmittance measurements using Kubelka-Munk theory.
The development of a phantom suitable for testing the method of hematoporphyrin derivative quantification in tissue by fluorescence measurement using dual-wavelength excitation and dual-wavelength detection required an absorber that absorbs excitation light much better than the fluorescent one 46 . As the two wavelengths, 405 and 435 nm, were used for excitation, and fluorescence was recorded over 550 – 725 nm region, the food colorant European Sunset (E110) was chosen as an absorbing component.
The 1 mg/ml solution of the dye has absorption coefficients of 28 cm cm
–1
–1
and 34
, at 405 and 435 nm respectively, and only of
0.1 cm
–1
at 560 – 700 nm.
This was determined with a standard spectrophotometer. Because the laser dye DCM, that was introduced into the phantom to imitate tissue autofluorescence also absorbs light, the concentration of European Sunset was decreased accordingly.
When manufacturing the tissue simulating phantoms for the study of the effect of photosensitizer (Photofrin) photobleaching on the surface fluorescence signal, authors of Ref.
57 used, as an absorbing component of the styrene resin phantom, a dye (Lewiscraft, # 88204) which had absorption in the region of Photofrin's fluorescence emission. At 630 nm (one of the photosensitizer's fluorescence peaks) absorption coefficient of phantom, including absorption by both dye and sensitizer, was measured as 0.19
0.04 cm
–1
. At the same time, in the development of standard samples for the noninvasive evaluation of sulphanated aluminum phthalocianine concentration in tissue, only the scattering coefficient of the samples was adjusted to that of tissue, and tissue absorption over 630 – 700 nm region was considered negligible 16 .
The methodology of correction of internal absorption effect in fluorescence emission and excitation spectra was tested in measurements on liquid scattering phantoms containing fluorophore and nonfluorescent dye producing absorption in excitation and emission spectral regions 12 . In experiments for emission spectra correction, proflavine (3.6-diamino
acridine) hemisulfate dihydrate was used as fluorophore. A triphenylmethane dye, Basic Fuchsine (Pararosaniline chloride), was used as a nonfluorescent absorber. Absorption spectrum of Basic Fuchsine (maximum at
540 nm) overlaps both absorption (maximum at
460 nm) and emission (maximum at
503 nm) spectra of proflavine + DNA complex.
The complex of proflavine fluorescent dye with DNA was used in order to prevent the interaction of fluorophore with absorber and scatterer, which might lead to resonant energy transfer and formation of nonfluorescing complexes. Positively charged planar molecules of 3,6-diaminoacridines are known to intercalate between the base pairs and bind strongly to DNA, while positively charged but nonplanar molecules of the triphenylmethane dyes can not totally intercalate into DNA macromolecule. This results in space separation of the two dyes. All solutions containing DNA (and corresponded control solutions without fluorophore) were prepared in 0.15 M phosphate buffer saline. In experiments for excitation spectra correction, the solution of
Kiton Red 620 (Sulforhodamine 620, laser grade) dye in deinonized water was used as fluorophore. In these experiments, Basic Fuchsine was employed, because its absorption spectrum overlaps absorption (excitation) spectrum of
Kiton Red. In preparation of all phantoms, Intralipid 10% aqueous solution was diluted in proper proportion to obtain the phantom medium with necessary photon mean free path. Basic Fuchsine was added to the phantoms in the concentrations from 0.09 mM to 0.6 mM.
As an individual group of absorbing phantom components inorganic ions may be considered. An aqueous solution of potassium chromate (K
2
CrO
4
) has been used in the study of laser-induced transient stress in nonscattering solutions and turbid aqueous gels and laser ablation of clear homogeneously absorbing liquid 36 . According to 36 , K
2
CrO
4
offers the following advantages over solutions of organic dyes: i . potassium chromate solution absorbs over visible and near-UV regions; ii . the solution practically does not fluores, thus the total absorbed light energy is converted into heat; iii . being photochemically stable, this solution retains its optical properties at high laser irradiance.
A water solution of K
2
CrO
4
at the concentration of 0.035 g/cm 3 had an absorption coefficient of approximately 1000 cm
–1
at 355 nm 36 . A series of solution concentrations were obtained by dilution of starting solution with distilled water. Before experiments the solutions were filtered through 0.22
m filter to avoid effects of dust and microbubbles.
In order to obtain a medium more closely reproducing optical and thermomechanical properties of soft tissues, aqueous gel phantoms were developed 36 . The samples were prepared with gelatin gel (5% w/w gelatin in water for clear phantoms and 10% w/w gelatin in water for turbid phantoms) colored with potassium chromate. The absorption coefficient of such gels was assumed to be the same as in the potassium chromate solutions used in gel preparation. Polystyrene microspheres were added to the gels at concentrations of approximately 2%, which gave
s
' = 99 cm
–1
. In the samples, the ratio of the transport scattering to the absorption coefficient was
81.5. This is a typical figure for biological tissues, for which values from 70 to 100 over the 600 – 1000 nm spectral interval have been reported 36 .
In the case of complex systems incorporating K
2
CrO
4
, the issue of chemical compatibility and stability should be considered. The chromate ion is a strong oxidizing agent that may be reduced, e.g.
by alcohol, changing its color from yellow to bluish-green.
Water solutions of another inorganic salt, CuSO
4
, have been employed as absorbing component in liquid phantoms. Steady-state measurements of transmission under infinite–boundary conditions were performed using these phantoms. From the measurement results the optical diffusion coefficient in a homogenous highly absorbing turbid medium was determined 63 . CuSO
4
was chosen as an absorber of the phantom, because CuSO
4 is nonfluorescent
(same as for K
2
CrO
4
) and does not induce any alteration in the scattering coefficient of Intralipid during measurements. Measurements were performed at 809 nm, near the maximum of CuSO
4
absorption in NIR; the value of 27.6 cm
–1
M
–1
was obtained for CuSO
4
aqueous solution at 809 nm by conventional spectrophotometry 63 .
We have already mentioned that the diffusion of dye within gel media is a shortcoming of macroscopically inhomogeneous phantoms reproducing morphological structures. In such phantoms partitions between the volumes
(more often – the layers) of different optical properties are avoided in order to provide refraction index matching. The molecular diffusion coefficient of
2
7
-dichlorofluorescin diacetate (DCFDA), whose oxidized form absorbs
(peak at 485 nm) and fluoresces (peak at 528 nm) in visible, in 7% gelatin gel prepared on phosphate buffered saline has been measured at room temperature using CCD camera coupled to fluorescence microscope 55 . On 3 mm-thick layer of gelatin gel containing DCFDA and bensoporphyrin derivative monoacid used as photosensitizer of DCFDH oxidation, CW laser
690 nm radiation was focused into 2 mm–diameter spot producing the initial region of oxidized, and thus fluorescent, DCFDA localization. The fluorescent image of the spot obtained in fluorescence microscope was then captured by CCD camera for a series of time points after the irradiation. The full width at half magnitude (FWHM) border of the spot expanded from 2 mm to 3 mm diameter in approximately one hour. The FMHM vs time dependency was then fitted to a diffusion equation to give the value of 2.5
10
–
5 mm 2 /s for molecular diffusion coefficient of the dye. It was concluded 55 that those results showed that the diffusion of the molecules would not result in a large redistribution of the fluorophore within one hour. The effects of the diffusion also could be minimized by refrigeration of the sample.
The problem of dye diffusion within gel can be alleviated to some extent by the implementation of pigments instead of the dyes. The pigments are present in a system as insoluble particles contrary to dyes, which are dispersed on molecule level. On the other hand, the particles being the inhomogenities of mesoscopic dimensions produce light scattering in the phantom, thus, strictly speaking, the pigments can not be considered independent light absorbers.
One of the readily available and widely used pigments is India ink, the suspension of lampblack particles in aqueous medium. According to Ref.
75 the suspension is a mixture of small (0.1
m) and large (1.0
m) particles.
As there did not appear to be a water-soluble, nontoxic molecular absorber for 1064 nm, India ink was used in developing liquid tissue phantoms for measurements at this wavelength 58 . Optical properties of the ink were determined in a series of ink suspensions in deionized water, concentrations ranging from 0.05 to 0.5% by volume. On each suspension the measurements of collimated (total) and diffuse transmission and diffuse reflectance were made. From those data the optical properties of the samples were calculated using inverse adding-doubling method. The results are shown in Fig. 7, a linear fit being applied to the data. The average optical properties of India ink at 1064 nm are summarized in Table 5.6.
Fig. 7. The absorption and scattering coefficients at 1064 nm for varying concentrations of water suspensions of India ink 58 .
Table 5.6.
Optical properties of India ink (Pelikan, Germany) suspension in water at 1064 nm (ink concentration in %% per volume)
Scattering media
India ink
cm s
/ %
–1
/ %
4.64
2.07
cm a
/ %
–1
/ %
35.99
4.28 g
0.30
0.18
The value for anisotropy is obtained by averaging over the samples with different ink concentrations. In general, the anisotropy of the scatterer suspension should not reveal a dependency on concentration. That was the
case for Intralipid suspensions, Fig.2(b), but for the ink samples the growth of anisotropy factor with concentration is conspicuous, see Fig. 8. Two reasons of such a behavior have been suggested 58 . The first reason is connected with the change of the ink's particle size distribution with the rise of concentration.
The small particles have much lower anisotropy factor than the larger ones.
The albedo of ink suspension increases with the increase of large particles concentration. From Fig.7 it can be seen that
s
grows with the rise of ink concentration. At the higher (0.3 – 0.5%) concentrations of ink, larger particles ( ca 1.0
m) may be strongly influencing the suspension’s anisotropy. At these increased concentrations there may also be a tendency for the particles to coalesce. It was suggested 58 to add a surfactant to ink suspensions to reduce ink particles coalescence.
Fig. 8. The anisotropy at 1064 nm for varying concentrations on India ink water suspension 58 .
The second reason for the nonlinearity of g vs ink concentration dependency may be purely computational. For ink concentrations exceeding
0.2% the diffuse transmission was very weak and insufficient measured signal might not allow the inverse adding-doubling algorithm to arrive at accurate solution for the anisotropy factor value 58 .
India ink suspensions at substantially lower concentrations were used to impart tissue-like absorption properties to gelatin-based optical dosimeters 55 .
The calibration of absorption coefficients of phantoms at 690 nm versus the concentration of India ink in 7% gelatin gel with a fixed TiO
2
(used as scatter) concentration of 0.3 g per 20 ml gel was performed with the use of inverse algorithm matching the data of diffuse reflectance measurements with
Monte Carlo predictions. The results are plotted in Fig. 9. The best fit of obtained points gave
a
= 35
2 cm
–1
/ % per volume of India ink.
Liquid phantoms made of diluted Intralipid (usually up to 1%) or
Lyposin suspensions with India ink added as absorber have been employed in various fields of optical measurements 7,11,15,33,54 . India ink is known to have a relatively constant absorbance over the visible region 75 . It was used as inert absorber simulating the absorption of hemoglobin and melanin, exogenous chromophores presenting in tissue, in phantoms developed for evaluating the fiber-optic bundle for quantitative fluorescence measurement from tissue.
Preliminary measurements gave the value of 50 cm
–1
as an assessment of the absorption coefficient of 1% by volume solution of India ink at 633 nm, the wavelength variation over the 514 – 635 nm spectral region being less than
5% 11,15 .
Fig.9. Absorption coefficient measured in dosimeters with tissue-like optical properties vs India ink content. Ink was added to the mixture of 20 ml of 7% gelatin in PBS and 0.3 g TiO
2
55 .
The adequacy of Monte Carlo simulation of light transport in tissue has been tested on liquid Intralipid + India ink phantoms at 633 nm. But here
India ink was considered as effectively pure absorber. Absorption coefficient of the ink at known dilutions was measured by conventional spectrophotometer. In phantoms, the absorption coefficient was varied in the range of 0.01 <
a
< 2 cm
–1
what corresponded to the optical properties of typical normal tissue 7 .
Solid phantoms incorporating India ink as absorber were used in the studies of light propagation in layered tissues 31,34,37 . The influence of layered tissue structure on time-resolved reflectance data was studied at 780 nm on phantoms mimicking such structure as the skull encapsulating the brain. The layers of the phantoms were made of gelatin gel with TiO
2
as scatterer and
India ink in different concentrations as absorber. Optical properties of the different layers were measured by time-resolved reflectance on homogeneous bulk samples; and in two-layer phantoms the gels with cm
–1
; 0.045 cm
–1
; 0.87 cm
–1
were used 31
a
= 0.50 cm
–1
; 0.04
. The same components (gelatin gel, titania, India ink) were employed in preparation of the layers of two-layered phantoms, with the optical properties in NIR similar to those of soft tissues, for the experimental study of the influence of superficial layer in frequencydomain spectroscopic measurements on strongly scattering media 34 .
A technique of the measurement of subsurface temperature using pulsed photothermal radiometry has been evaluated in experiments on the actual skin and scattering / scattering + absorbing multi-layered gel-based phantoms.
Two types of hydrophilic host media were used: 5% gelatin gel (170
m thick layers) and polyacrylamide gel (70
m thick layers). In both types of gel,
Intralipid served as scattering component and India ink as absorber.
Absorption coefficients were measured on a conventional spectrophotometer before addition of Intralipid and gelling. Irradiation of the samples was performed by the 1-
s pulses at 506 nm. Layers with the following absorption coefficients imparted by the India ink were used in phantoms:
a
= 400 cm
–1
, modeled blood absorption at 577 nm (this wavelength had been chosen for port wine stains treatment);
a
= 300 cm
–1
, reproduced absorption by port wine skin;
a
= 30 cm
–1
, corresponded to absorption within epidermis;
a
= 10 cm
–1
, mimicked absorption by dermis.
Close to India ink are two other pigments used in phantom preparation: carbon powder and graphite powder. The former has been employed as an absorber in liquid phase of three-layer phantom for the study of the effects of layered tissue on NIR imaging. Water suspension of TiO
2
and carbon powder with
s
' = 15 cm
–1
and
a
= 0.1 cm
–1
modeled skull, scalp, and brain tissue 49 .
Graphite powder has been used as absorbing material in silicone-based solid two-layered phantoms with polystyrene spheres as scatterers.
Theoretical results concerning light propagation in two-layered turbid media were confirmed by the results of measurement of time-resolved reflection at
528 nm performed on these phantoms. For the second layers of two phantoms used, the absorption coefficients were determined as
and
a
= 0.19
0.01 cm cm
–1
and
a
= 0.24 cm
–1
–1
, respectively. a
= 0.074
0.005 cm
–1
30 . Measurement of absolute steady-state spatially resolved reflectance at 543 nm 26 gave for those media the values:
a
= 0.09
Most of the mentioned phantoms have been designed to be used at one chosen wavelength. But when the aim is to reproduce, in material model, the light-induced fluorescence of either endogenous (in the case of autofluorescence) or exogenous (often being photosensitizer) fluorophore in actual tissue, relevant conditions of the propagation of both the excitation and emission wavelengths should be modeled. Thus, the phantom for fluorescence measurements should have, over a broad spectral range, the absorption coefficient and scattering coefficient that the tissue under study has. The main chromophore, that is responsible for tissue absorption in visible region, is hemoglobin; and it has been introduced into liquid and solid phantoms in a
form of aqueous solution, as suspension of red blood cells (erythrocytes), and as whole or diluted blood as well.
Gel-based optical phantoms reproducing absorption and scattering characteristics of biological tissues in the broad spectral window (between
400 and 650 nm) have been designed and fabricated for the use in PDT and fluorescence spectroscopy 9 . Such phantoms can be used simultaneously at different wavelengths providing realistic propagation differences characteristic of actual tissue. In those phantoms, the ink and blood served as optical absorbers. While absorption coefficient of the ink was assumed constant between 400 and 650 nm, the erythrocyte suspension provided tissue-like wavelength dependence of the absorption coefficient of the phantom. The effect of erythrocyte suspension absorption on the absorption coefficient of the phantom,
a
=
a
(ink) +
a
(blood), may be evaluated as
a
(blood at 500 nm) = 2.3*C cm
–1
, where C is the erythrocyte concentrate concentration in the phantom, expressed in %% per volume.
a
(blood) wavelength dependence is shown, as blood absorption spectrum, in Fig. 10. The contribution of known concentration of erythrocytes to the phantom absorption coefficient over 300 – 800 nm region can be predicted using right-hand vertical axis. Scattering by the blood cells in the phantom was assumed negligible between 400 and 650 nm. As different batches of erythrocyte concentrate might differ in their optical properties, the absorption of concentrate was checked before phantom preparation; at 500 nm for the light path length of 1 cm it should be equal to 0.9 for a concentration of 1% in physiological saline (0.9 % NaCl). When deviations were revealed, the concentrate concentration was corrected with the physiological saline 9 .
Fig. 10. The absorption spectrum of diluted human blood.
a
is the absorption coefficient of the phantom due to the blood only. The concentration of erythrocyte concentrate, C, is expressed in %% per volume 9 .
In the course of phantom preparation, human erythrocyte concentrate was never added to agarose gel, already loaded with scatterers (silica powder and
Intralipid) and ink solution, until the mixture was cooled to 40 0 C. This temperature is low enough as not to induce a thermal damage of erythrocytes and hemoglobin but sufficient for the gel being still liquid.
Liquid but inhomogeneous phantoms of human tissue have been employed in quantitative analysis of the nature of bluish appearance of vessels. These vessels contain red or dark red blood and are located under skin 28 . Measurements of spatially resolved diffuse reflectance at different wavelengths have been performed on the model blood vessel submerged in highly scattering and weakly absorbing liquid medium. Scattering was imparted to the medium by 20% Lyposin diluted with water to give
s
' = 10 cm
–1
at 633 nm; and absorption of human dermis associated with blood in capillary network was simulated by 0.34% (per volume) oxygenated blood added to the medium.
The blood vessel was modeled by a cylindrical glass tube, which was filled with whole blood. The distance from the top of the cylinder to the surface of the surrounding medium was 1.4 mm. The inner diameter of the tube was 1.2 mm; and the thickness of the glass wall, not considered in calculations, was ca 0.2 mm. Deoxygenated blood was drawn directly from the vein into the heparinized tube, while the sample representing arterial blood was heparinized and shaken in air to yield the oxygenated state.
The reduced scattering coefficients and absorption coefficients of the phantom model, that were used for the Monte Carlo calculations 28 are shown in Table 5.7. The coefficients for Lyposyn were measured using frequency domain diffuse reflectometry. The parameter of scattering anisotropy was set to 0.8; in the case of whole blood the value of 0.99 was used for g.
Table 5.7
Optical parameters for the phantom model 28
Wavelength
, nm
a
Lyposyn plus blood
, cm
–1 s
', cm
–1 a
, cm
–1
Blood
s
', cm
–1
450
500
550
0.85
0.39
0.67
14.2
12.5
11.4
250
115
200
5
5
5
633
700
0.022
0.015
10.0
0.82
5
1.5; 5*
5
5
Coefficients in the last two columns are for oxygenated blood, except for the marked (*) value which is for venous blood with oxygen saturation of
50%. The hematocrit is 40%.
Results of Monte Carlo simulations using known optical coefficients of the tissue phantoms and human blood were compared to the data obtained in on-phantom measurements in order to check experimental technique and
Monte Carlo technique for the problem of the bluish color of veins 28 .
Blood-like liquid component has been employed in the phantom with varied local oxygenation state; and, using optical tomography system, the
images (Fig.11) of the local distribution of oxy- and deoxy-hemoglobin have been obtained from
a
images at two wavelengths, 761 nm and 835 nm 21 .
Fig. 11. Images of oxy and deoxyhemoglobin in the phantom shown in Fig.
10, obtained by the convertation of a set of
a
images (at 761 nm and 835 nm) 21 .
Fig. 12 shows the top view of the phantom made of silicone resin with scatterer added in such concentration as to obtain
a
= 10 cm
–1
.
Trough blood tubes the solution with variable oxygenation was circulated by the peristaltic pump. The solution consisted of erythrocyte suspension (1.5% or 3.0%) in phosphate buffer saline and milk added to give
s
' value of about 10 cm
–1
.
Here and in some optical phantoms described below the choice of erythrocytes or hemoglobin has been determined by the unique alterations of hemoglobin absorption spectra that attend the change of oxygenation state. In
Ref.
21 , the oxygenation state of solution employed in the phantom was adjusted using a nitrogen – oxygen gas system.
Circulation of blood with variable oxygenation state has been employed in a more complicated tissue-like phantom developed for the testing of noninvasive pulse oximeters 22 . Besides the similarity of optical properties, some other criteria were met in the development of this tissue phantom: the material used to construct the body of the phantom was flexible enough to simulate arterial pulsations similar in size and shape to real photoplethysmograms; material was biocompatable; and the ratio (whole blood volume / bloodless tissue volume) was approximately 2.0% in the phantom, basing on the average actual values inherent in tissues.
Fig. 12. Top view of the phantom with variable oxygenation 21 .
The phantom depicted in Fig. 13 was made of semitransparent medical grade silicone elastomer with flesh colored pigment (Fe – Mg – TiO
2
) added so as to simulate lightly pigmented skin. Blood was pumped through fifteen
0.5 mm diameter conduits in the molded silicone. Circulating blood was prepared by suspending packed red blood cells in plasma to obtain a hematocrit of approximately 41%. The blood was thoroughly mixed, and microaggregates of cells were removed by filtration through transfusion filter.
The pH of the blood was adjusted to 7.4
0.1 by the isotonic solution of
NaHCO
3
.
Fig. 13. Schematic representation of tissue phantom for application to transmittance pulse oximetry 22 .
The blood was pumped through the phantom using a pulsatile blood pump. A photoplethysmographic waveform measured from an average size human finger was reproduced in the phantom by adjusting the stroke volume of the pump operating at the stroke rate of 70 strokes / min, the fixed pulsative phase being of 35 percent systole and 65 percent diastole.
In the measurements, the blood was first deoxygenated by passing a mixture of 95% N
2
and 5% CO
2
gas though the disk oxygenator connected in series with the phantom. Then the blood was exposed to room air for brief
periods thus gradually being oxygenated. The temperature of the blood was maintained at 37 0
0.5
0 C.
It has been shown that the tissue phantom allows the controlled and reproducible measurement of the oxygen saturation of arterial hemoglobin, using a pulse oxymeter. The phantom suggested has a potential for assessment of the effect of blood hematocrit, methemoglobin concentration, arterial blood pulsations, blood temperature, and the variations in the peak emission of the LEDs in the optical sensor on the accuracy of pulse oximetry 22 .
While the pulse oximeters operate at the transmission geometry, quantification of the tissue hemoglobin concentration and oxygen saturation in massive organs, such as a skull with the brain tissue, requires the implementation of near-infrared spectrophotometric instruments with a reflection geometry. To validate an instrument of the type and the algorithms which evaluate the cerebral concentration of hemoglobin and oxygen saturation, a liquid phantom mimicking dimensions, shape, and the layered structure of a neonatal head was constructed 23 .
Skin and skull were represented in the phantom by a 3.5 mm thick and 11 cm diameter hemispherical shell which size corresponded to the head of a new born infant of 40 weeks gestational age. The shell was made of transparent silicon rubber with TiO
2
added as scatterer and the dye from
Zeneca, Manchester, UK, as absorber. These constituents provided
s
'
17 cm
–1
and
a
0.5 cm
–1
. The optical sensor of the instrument (NIR spectrophotometer) was placed at the bottom of the hemisphere on the outside of it. Cerebrospinal fluid (CSF) surrounding the brain was mimicked by the
0.5 mm thick layer of polypropylene attached to the surface of the shell above the sensor.
The half sphere served as a container for a liquid component of the phantom. This aqueous solution filling the rubber shell imitated the brain. It had the volume of approximately 200 ml and contained: i 0.5%, 1%, 1.5% or
2% Intralipid providing different levels of scattering; ii physiological saline
(0.9% NaCl); iii 0.5% yeast suspension ; iv 0.15% (maximally) glucose; v 60
mol l
–1
hemoglobin from a packed erythrocyte concentrate. For 0.5%
Intralipid the
s
' value of 5 – 8 cm
–1 was adopted, which is close to
5 cm
–1 for a neonatal brain. During the measurements, the solution was constantly stirred by a mixer in order to prevent sedimentation. Two parameters, temperature and pH, that might influence the oxygen – binding properties of hemoglobin, were kept within a physiological range. Temperature was maintained at 37 0 by a small heater; pH was adjusted by adding the phosphate buffer to the solution. In the measurements, the predeoxygenated solution was reoxygenated using oxygen, until the pO
2
was > 15kPa. Then it was gradually deoxygenated through the oxygen consumption by yeast, for which purpose glucose was added in small steps of 0.05%, until the total deoxygenation was achieved.
Current oxygen concentration in the solution was measured independently using a pO
2
electrode. The readings from the pO
2
monitor were recorded simultaneously with the optical raw data measured at 776.5 nm, 819.9 nm,
871.4 nm and 908.7 nm and the calculated concentrations.
Those on-phantom measurements have shown that the algorithms for the determination of the cerebral concentrations of hemoglobin and oxygen saturation, when applied to the data obtained on a neonatal head phantom with a spherical geometry and layered structure, considerably underestimate the changes in hemoglobin concentration 23 .
Measurements essential towards understanding the light absorption by cerebral blood in various blood vessels were undertook on heterogeneous tissue-vessel models 32 .
The phantom used in the study (Fig. 14) has the structure akin to the tissue model described in Ref.
22 , but the measurements were performed at a reflection geometry.
Fig. 14. The heterogeneous tissue-vessel phantom for NIR time resolved reflectance measurements 32 .
The body of the phantom imitated a low-absorbing tissue and was made of polyster resin with TiO
2
added to give reduced scattering coefficient,
s
'
(back), from 6 to 9.2 cm
–1
; while the absorption coefficient of the medium,
a
(back), was from 0.02 to 0.06 cm
–1
. The cylindrical holes (tubes) simulating the blood vessels made up 18% and 20% of the entire sample volume. The samples with either 3.2 mm diameter holes or 6.4 mm diameter holes were used in the experiments. Absorbing turbid solutions, filled in the tubes, imitated blood in vessels. 0.5% or 1.0% Intralipid was used to ensure the light scattering by the "blood". The aqueous solutions of either methemoglobin or ink served as absorbers 32 .
Methemoglobin (the form of hemoglobin that contains Fe(III)), in alkaline medium, has absorption peaks at 417, 540, and 578 nm, which are close by wavelength to the peaks of oxyhemoglobin but are considerably less intensive 76 . In some cases of phantom preparation, the lack of ability to bind oxygen may give an advantage to methemoglobin over hemoglobin, as the absorption spectrum of the latter depends on the oxygen saturation of phantom medium. In Ref.
32 the methemoglobin solution was made from the hemoglobin by adding the potassium ferricyanide.
The absorption coefficients,
a
(tube), of the methemoglobin or ink turbid solutions at different absorber concentrations were determined separately using time-resolved reflection technique. In time-resolved reflection measurements on the tissue - vessel phantoms at 670 nm, the methemoglobin solutions with the absorption coefficient up to
0.32 cm
–1
were used.
Estimation of the absorption coefficient of human blood at 780 nm gives
a
780
= 8 mM * 0.46 cm
–1
mM
–1
= 3.68 cm
–1
, where 8 mM is the assumed hemoglobin concentration in the blood, and 0.46 cm
–1
mM
–1
is the specific absorption of hemoglobin at 780 nm. Basing on this estimation, the measurements at 780 nm were performed with high
a
(tube) values which were provided in the phantoms by ink solutions 32 .
To verify experimentally the theoretic expression relating measured fluorescence to the intrinsic fluorescence coefficient, water-based (phosphatebuffered saline, pH = 7.2) semi-infinite phantoms with identical fluorophore concentration and varying absorption and scattering were used 13 . Hemoglobin extracted from fresh human blood has been employed as an absorbing component. The absorption of hemoglobin covered both excitation and emission bands of Rhodamine 6G (R6G) used as the sole fluorophore in the phantom. The 514 nm line of argon laser was used for fluorescence excitation. In Table 5.8 the composition of the phantoms and the approximate values of their optical properties are shown.
Table 5.8.
Tissue phantom composition 13 .
(
R6G
M)
Polystyrene microspheres
(vol. %)
Hb/HbO
2
(blood vol. %)
s
' at 550 nm
(cm
–1
)
a at 514 nm,
550 nm (cm
–1
)
0.5
0.5
0.16
0.16
8
4
7.5
7.5
12; 17
6.0; 8.4
0.5
0.5
0.5
0.5
0.16
0.48
0.48
0.48
1
8
4
1
7.5
25
25
25
1.5; 2.1
12; 17
6.0; 8.4
1.5; 2.1
The set of phantoms with varying scattering and absorption imitated tissue optical properties over extensive range. The diffuse reflection measured on the phantoms varied from 0.04 to 0.4 at the excitation wavelength and from 0.02 to 0.8 within R6G emission band. That allowed the evaluation of the intrinsic fluorescence recovery method for absorption-dominant, comparable absorption and scattering, or scattering-dominant optical conditions in tissue.
However, the experimental results indicative of Rodamine 6G fluorescence quenching by hemoglobin in solution were obtained. The nonradiative energy transfer was suggested as a possible mechanism of the quenching 13 . Thus, in fluorophore-containing phantoms for fluorescence
measurement, hemoglobin cannot be considered a purely absorbing component and should be used with caution.
Bovine hemoglobin was used as a contrasting absorbing agent in the preparation of human breast phantoms for the evaluation of the capability of laser optoacoustic imaging for the visualization of tumors 35 by water in 10%-gelatin gel,
a
. The absorption
= 0.11 cm
–1
at 1064 nm, and the scattering by polystyrene microspheres or milk,
s
= 2.92 cm effective attenuation coefficient of 1.0 cm
–1
–1
at 1064 nm, resulted in the
at 1064 nm for the bulk body of the phantom (Fig. 15). The spherical phantoms of tumors were made of the same turbid gel but colored with the solution of bovine hemoglobin which gave an absorption coefficient of 0.75 cm
–1
at 1064 nm. That value corresponded to 16% blood content in tissue and was seven fold higher than the
a
of surrounding gel. Breast phantoms were obtained through sequential moulding. Prefabricated hemoglobin-colored spheres were positioned, using nylon white threads, inside the Plexiglas mould where liquid colorless gel at the temperature close to the solidification temperature was then poured 35 . In the phantoms so obtained, there is no partition between volumes with different absorption. On the one hand, this realistically imitates the interface between tumor and surrounding tissue, and on the other allows diffusion of hemoglobin into the body of the phantom, distorting optical characteristics of the structure.
Fig. 15. Schematic diagram of the gelatin-based human breast phantom with highly absorbing spheres simulating tumors. Spheres # 1, 2, 3, 4, 5, and
6 had diameter of 3, 4, 6, 2, 4, and 2 mm, respectively 35 .
The problem of the rapid diffusion of dyes in gels and plastics, as well as the problem of chemical instability of dyes during polymerization and the problem of spectral shifts caused by interaction of dyes with host materials and scatterers, may be overcome by the use of absorbing particles instead of dyes 8 .
The optical properties of the suspension of such particles may be predicted using calculations based on Mie theory. The scattering crosssection,
s
(cm 2 ), and scattering anisotropy, g, of the particles are given by
Eqs. 5.1 and 5.2, respectively, taking into account that, in the case of absorbing particles, the refractive index n p
is a complex quantity. The absorption cross-section of the particles,
a
(cm 2 ), is given by 60
a
(
2
0
/ 2
n
2
0
)
n
1
( 2 n
1
) Re( a n
b n
a n
|
2
| b n
| )
(5.9).
The definitions of the incorporated quantities are given after Eqs. 5.1 and
5.2; n p
has a complex value the imaginary part of which can be expressed from the absorption coefficient of particle material,
:
Im( n p
(
0
))
4
(
Re(
0 n
) p
(
0
0
))
(5.10).
Following Ref.
8 , the absorption coefficient of a suspension of particles with broad-banded size distribution can be expressed in terms of average values weighted by volume fractions of particles of different size:
a
3 C p
4
i
i i r i
3
, (5.11) where
a i
is the absorption cross-section for the particles of radius r i.
The definitions of other quantities are given after Eqs. 5.6 and 5.7.
Mie theory predicts that the scattering by absorbing particles dispersed in a nonabsorbing medium with the refractive index n
0
became a strongly forward-directed resonance scattering when the real part of the refractive index of the particle material is equal to n
0
. For such particles the apparent absorption,
a, is smaller than expected from the absorption coefficient of bulk material,
. For example, 1
m-diameter particles with Re(n p
) = n
0
= 1.6 and
= 10 4 cm
–1
yield only
a
= 4.12
10 3 cm
–1
C p
8 .
It should be kept in mind that Mie theory formulae cited are strictly applicable to spherical particles, nevertheless, the results are often considered acceptable for the systems of particles of irregular shape.
It is evident, that the absorbing particles suspended in the ground material, unlike the dyes dissolved in the host medium, cannot be considered independent absorbers when one calculates the optical properties of a phantom. However, Mie theory allows the evaluation of their contribution to the total scattering. In most cases, the increments in the absorption coefficient
and the reduced scattering coefficient, imparted by the addition of highly absorbing particles, are of the same order of magnitude 8
In practice, metal particles and ground colored glass of optical filters have been suggested as absorbing particles without fluorescence. It has been demonstrated that the filter glass (NG-1, Schott) can be ground, using a ball grinder, into irregularly shaped particles with a typical diameter of 1
m and even ruby can be ground to the particles of 3
m mean size.
Scattering and absorption of metal particles in polyorgansibxane (POS, n
0
=1.40 at 589 nm) were calculated 8 with Mie theory, basing on values of the complex refractive index obtained from literature (see Fig. 16). The comparison of the results of the integrating sphere measurements and Mie calculation for the spherical iron particles with asymmetrical size distribution
(16% of the volume fraction is contributed by the particles with the diameter upto 2.0
m, 50% by the particles with the diameter upto 3.0
m, and 34% by the particles with the diameter upto 3.6
m) is shown in Table 5.9.
Fig. 16. Specific transport scattering and absorption coefficients (C p
is the fraction of suspension volume occupied by particles) of the metallic particles, calculated with Mie theory (the left graph is for the particles with the diameter of 2.5
m, and the right one for the particles with the diameter of
0.1
m). In calculations the refractive index of the host medium was assumed independent on the wavelength. The experimental points for the iron particles were obtained using integrating sphere technique. The scattering anisotropy factor of the large particles is positive and varies from 0.5 to 0.7; for the small particles |g|<0.1
8 .
Table 5.9.
Comparison of the results of integrating sphere measurements
Wavelength, nm and Mie calculation for iron particles in POS 8 .
Method
s
' / C p
, cm
–1 a
/ C p
, cm
–1
546
546
633
633
Mie theory
Measured
Mie theory
Measured
3000 (600) b
3500 (900) a
3000 (600) b
2800 (800) a
4500 (900) b
3800 (200) a
4500 (900) b
3900 (200) a
Errors are given in parentheses in units of the last digit(s) and are: a the upper limit error caused by uncertain refractive index (particle composition); b variations of reported values.
In phantom preparation 8 , the iron particles as well as the scattering particles were dispersed in mixtured POS components. Polymerization in castling moulds took typically less than 30 min at 80 0 C. Short polymerization period at high temperature and favorable orientation of the moulds during solidification favors the homogeneity of the particle distribution within the samples. The sedimentation rate in POS can be estimated as less than 0.1 mm/h even for heavy iron particles. Although the metal microparticles have a high specific surface and iron is a chemically reactive element, no evidence has been found for chemical reactions (other than POS polymerization itself) during POS solidification.
It has been found that the modification of scattering properties takes place when iron particles are introduced into the polymer in combination with
Al
2
O
3
particles. The addition of iron particles causes the 5% decrease of
s
'/C p
for aluminum oxide particles. The alteration was presumed to be related to the slight aggregation between particles of different kinds, however, the inspection by light microscopy showed no obvious aggregates 8 . The iron particles used as an absorbing component in the polymer-based tissue phantoms proved to keep their optical properties during POS polymerization and afterwards over several months 8 .
This work was made possible in part by the Award No. REC-006 of the
U.S. Civilian Research & Development Foundation for the Independent States of the Former Soviet Union (CRDF) and the grant No. 00-15-96667 of the
Russian Basic Research Foundation.
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