INSTITUTE OF PHYSICS PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY Phys. Med. Biol. 48 (2003) 357–370 PII: S0031-9155(03)53741-1 Poly(vinyl alcohol) gels for use as tissue phantoms in photoacoustic mammography Alexei Kharine1 , Srirang Manohar1, Rosalyn Seeton, Roy G M Kolkman, René A Bolt, Wiendelt Steenbergen and Frits F M de Mul Biophysical Techniques Group, Faculty of Applied Physics, University of Twente, PO Box 217, 7500AE Enschede, The Netherlands E-mail: W.Steenbergen@tn.utwente.nl Received 20 September 2002 Published 22 January 2003 Online at stacks.iop.org/PMB/48/357 Abstract Materials for solid photoacoustic breast phantoms, based on poly(vinyl alcohol) hydrogels, are presented. Phantoms intended for use in photoacoustics must possess both optical and acoustic properties of tissue. To realize the optical properties of tissue, one approach was to optimize the number of freezing and thawing cycles of aqueous poly(vinyl alcohol) solutions, a procedure which increases the turbidity of the gel while rigidifying it. The second approach concentrated on forming a clear matrix of the rigid poly(vinyl alcohol) gel without any scattering, so that appropriate amounts of optical scatterers could be added at the time of formation, to tune the optical properties as per requirement. The relevant optical and acoustic properties of such samples were measured to be close to the average properties of human breast tissue. Tumour simulating gel samples of suitable absorption coefficient were created by adding appropriate quantities of dye at the time of formation; the samples were then cut into spheres. A breast phantom embedded with such ‘tumours’ was developed for studying the applicability of photoacoustics in mammography. 1. Introduction Recent years have seen many research efforts in developing optical imaging of tissue into a diagnostic modality, with a thrust in mammography, as an alternative to conventional radiological techniques. Several embodiments of optical mammographs using near-infrared light (NIR) have been showcased in this regard, which can broadly be classified into timedomain (Grosenick et al 1999, Hebden et al 2001) and frequency-domain (Fantini et al 1997, 1 These authors contributed equally to the work. 0031-9155/03/030357+14$30.00 © 2003 IOP Publishing Ltd Printed in the UK 357 358 A Kharine et al McBride et al 2001) techniques. These techniques have demonstrated that changes in blood flow, oxygen consumption and physiology—fundamental changes associated with tumour growth—can be detected using NIR light (Pogue et al 2001). The intrinsic non-ionizing nature of the light used furnishes a safer modality compared with x-ray mammography. Additionally, the techniques hold potential for spectrally discerning the signatures of malignant tissue vis-á-vis benign growth (Tromberg et al 2000), a capability not shared by x-ray techniques. However, there are inherent difficulties in obtaining sharp images with a high spatial resolution at higher depths, accruing from the fact that the nature of light propagation in tissue is highly scattering. Medical ultrasonography on the other hand is a well-established clinical procedure, which is routinely employed as an indispensable adjunct to conventional x-ray mammography. Compared with light, ultrasound is scattered much less by tissue and therefore lends itself to a higher imaging resolution. Ultrasound, however, has limitations in sensitivity resulting in many false negatives, which discourages its being used for detection (Sabel and Aichinger 1996). Recent developments have attempted to combine the intrinsic contrast of tumours to NIR light in optical imaging, with the high resolution possible with ultrasound imaging, in a variety of hybrid techniques. These include photoacoustic (PA) imaging (Hoelen et al 1998, Oraevsky et al 2002, and references therein), ultrasound-modulated tomography (Wang and Ku 1998, Hisaka et al 2001), combined ultrasound and NIR diffusive light imaging (Zhu et al 1999) etc. In contrast to the other techniques, photoacoustics is intrinsically composite in the sense that the ultrasound is generated internally by the absorption of pulsed laser light. In this, non-radiative deexcitation of the absorbed optical energy takes place with the release of localized heat. The local thermal expansion that results produces pressure transients. When illuminated with pulsed laser light, a tumour site by virtue of its higher absorption with respect to the healthy background tissue, due to angiogenesis (Carmeliet and Jain 2000), will act as a source of bipolar photoacoustic pulses (Oraevsky et al 2002, and references therein). This ultrasound propagates with minimal distortion to the surface where it is detected using appropriate wideband detectors. The time-of-flight, amplitude and peak–peak time of the bipolar PA pulse possess information regarding the location, absorption and dimensions of the source, thereby permitting a reconstruction of the tumour site. In order to validate the feasibility of these techniques, understand deficiencies such as the limits of detection, and generally prepare the technique for the transition from laboratory to clinic, requires the use of stable and reproducible inanimate objects—phantoms—which simulate the properties of tissue relevant to the technique. The literature abounds with descriptions of phantoms for purely optical (Pravdin et al 2002, and references therein) and purely ultrasonic techniques (Madsen et al 1998, and references therein), but similar reports for the hybrid techniques have been lacking. Phantoms specific to these techniques are singular in that they must possess both the optical and the acoustic attributes of human tissue. In this paper, we describe a material that is suitable as a breast phantom for use in photoacoustics, but equally applicable to the previously mentioned techniques as well. The phantom medium is based on poly(vinyl alcohol) (PVA). This is a polymer of considerable interest, owing to the myriad applications in the pharmaceutical and biomedical fields (Hassan and Peppas 2000). Poly(vinyl alcohol) must be in the form of a rigid gel in order to be useful for most applications. An aqueous solution of PVA will in due succession congeal into a gel upon standing at room temperature, but this possesses low mechanical strength and will not be able to support its own weight. A variety of procedures have been adopted to achieve gel reinforcement by enhancing the cross-linking between the polymer chains to build up a higher dimensional network structure. One mechanism which avoids additives and complex Poly(vinyl alcohol) gels for use as tissue phantoms in photoacoustic mammography 359 procedures is that of physical cross-linking. In this, simple freezing and de-freezing of an aqueous solution of PVA results in a gel whose mechanical strength progressively increases with the number of freezing–de-freezing cycles (Peppas 1975). Such physically cross-linked gels were recently employed as couplants between ultrasound sources and body parts for the purposes of administering ultrasonic wave therapies, and have been studied for ultrasonic wave propagation (Nambu et al 1990). An attendant phenomenon to rigidification is an increasing turbidity from the clear solution state, with an increasing number of these cycles. Thus one of the strategies adopted to develop a photoacoustic phantom based on PVA was to utilize the light scattering that is concomitant to the formation of the mechanically rigid gel, and optimize the number of freezing–de-freezing cycles to obtain optical properties characteristic of tissue. A second strategy was to obtain a rigid yet transparent gel; a host to which scatterers/absorbers could be added at the time of formation. In both cases, the acoustic properties would also have to be found admissible to suit that of tissue. 2. Preparation 2.1. Method I PVA with a degree of hydrolysis greater than 99%, and an average molecular weight (MW) of 85 000–140 000 (Sigma-Aldrich, catalog nr 36 314–6), was used to prepare aqueous solutions. A PVA concentration of 20% by weight in solution was obtained by heating the appropriate amounts of PVA and demineralized water over a temperature bath at 95 ◦ C for 2 h. Continuous gentle stirring is required to ensure homogeneity and promote dissolution of the PVA. The solution was allowed to stand for a few hours to allow any air bubbles to migrate to the surface from where they can be skimmed off. The solution was then cast in the required moulds and refrigerated at −20 ◦ C for 12 h. Subsequently, the frozen solution was thawed at room temperature for 12 h. This constituted one freezing–thawing cycle. It was observed that a mechanically rigid and optically turbid gel was obtained. It was also observed that the gels experienced an enhancement in strength and an increase in turbidity with subsequent freezing and thawing cycles. It is believed that the process of freezing and thawing, in addition to formation of cross-links by hydrogen bonding between the hydroxyl groups on the PVA chains, also promotes the formation of crystallites in the amorphous matrix (Hassan and Peppas 2000). These serve as additional cross-links to hold the three-dimensional structure together. Such partially crystallized, cross-linked PVA specimens acquire a high mechanical strength since the mechanical load can be supported along the crystallites of the three-dimensional structure. The number, size and stability of the crystallites is increased with the number of freezing and thawing cycles. One of the mechanisms explaining the origin of the turbidity has been that of phase separation in the gel. The structure of the gel may be understood to be composed of three distinct phases: a water phase with a low PVA concentration, an amorphous phase and a crystalline phase (Hassan and Peppas 2000). When refrigerated, the water freezes over, with an accompanying large volume expansion. This leads to the formation of large pores; the resulting refractive index fluctuations in the medium due predominantly to the presence of these pores lead to the observed turbidity. 2.2. Method II It was demonstrated by Hyon and Ikada (1987) that if the freezing of the water phase in the interstitial regions between the PVA chains and crystallites was avoided, while the sample was 360 A Kharine et al cooled strongly, then it would be possible to obtain a transparent gel. The cooling to −20 ◦ C is required to promote crystallite formation and is unavoidable. It was therefore proposed to inhibit freezing by the addition of appropriate miscible organic solvents to water. It was shown particularly that dissolving PVA in a mixture of water and dimethylsulphoxide (DMSO), the latter having the effect of depressing the freezing point of the water phase to below −20 ◦ C, yielded highly transparent and mechanically strong gels (Hyon et al 1989). The resulting gels were shown from scanning electron microscope (SEM) studies to be more homogeneous, with smaller pore sizes compared with the ‘freeze-thaw’ turbid gels; the resulting spatial variation of refractive index in the medium is smaller, explaining the transparency. Additionally, the crystallization process which involves structural rearrangements can continue to proceed during cooling since the solution state exists without freezing over; the strength of the gel is high. The procedure followed for the preparation of the transparent hydrogels was based on that described by Hyon et al (1989). PVA of the same grade described earlier is dissolved in a 80:20 mixture of DMSO and water, to obtain a PVA solution of 15% concentration by weight. The mixture is gently stirred while being maintained at 140 ◦ C for 2 h in a temperature bath. The solution is poured in appropriate containers and allowed to stand for a while, to allow the air bubbles that may have been trapped to migrate to the surface, before refrigerating at −20 ◦ C for 24 h. The resulting transparent gel samples are then immersed in water to remove the organic solvent. The water is continuously agitated and regularly recharged to promote a thorough exchange of DMSO in the gel with water, to yield the PVA hydrogels. The resulting hydrogels were seen to possess excellent transparency. As mentioned earlier, it is proposed here to use the transparent gel as the host to which scatterer and absorber particles are to be added. The addition of the correct proportion of these media should impart to the host the required optical properties suggestive of tissue, in particular those of breast tissue. The optical properties of breast tissue from in vivo measurements (Tromberg et al 2000, Suzuki et al 1996) in the visible and NIR yield the following quantities, relevant to the design of the phantom: reduced scattering coefficient (µ′s ) ≈ 0.6–1.3 mm−1 ; absorption coefficient (µa) ≈ 0.005–0.017 mm−1; mean cosine (g) of the scattering angle (θ ) ≈ 0.9 (Cheong et al 1990). Under simplifying assumptions, that the scatterers in the non-absorbing medium are homogeneous dielectric spheres and the electromagnetic field incident on each sphere is a plane wave, single-particle Mie scattering theory can be used to calculate the extinction crosssection of the added spheres. This is possible with a knowledge of the relative refractive index (m), between that of the sphere (ns ) and the host (n0 ); and the aspect ratio (a) which is the ratio of the sphere circumference (2πa) and the light wavelength (λ) in the medium, where a is the radius of the sphere. The refractive index (n0 ) of the transparent gel was measured as 1.366 at 589 nm (see section 3.1.3). This is close to the value of the refractive index obtained for human tissue (Tuchin 2000, p 42). It is known from Mie theory that the scattering introduced by micron-sized spheres is largest if a and λ are of the same order. The reduced scattering coefficient (µ′s ) increases with the relative refractive index (m); anisotropy (g) is maximal when m approaches 1. It is proposed to use a wavelength of 1064 nm from an Nd:YAG laser as the light source in the photoacoustic experiments, since light penetration in human tissue is high at this wavelength (Tromberg et al 2000), a feature that is crucial in mammography owing to the large amount of breast tissue that would be encountered by the light. At this wavelength, it was decided to use borosilicate glass microspheres with a radius of 1 µm, and possessing a refractive index of 1.56 at 589 nm. With this available data, Mie calculations to determine the extinction cross-section (Cext ) of the microspheres were performed using the Monte Carlo package (de Mul et al 1995). Poly(vinyl alcohol) gels for use as tissue phantoms in photoacoustic mammography 361 The extinction cross-section is Cext = Cabs + Cscat , where Cabs and Cscat refer to the absorption and the scattering cross-sections respectively. With Cabs being nominally zero, Cscat ≈ Cext . The anisotropy factor (g) was also determined within the framework of Mie theory calculations. The required reduced scattering coefficient (µ′s ) is related to Cscat and the number density (N) as µ′s = (1 − g)Cscat N. (1) With required µ′s chosen to be 1 mm−1 , Cscat calculated as 4.0511 µm2 , and g calculated as 0.9, N can be determined as 2.4 ×106 microspheres/mm3. The dimensions and density of the scattering particles, available from the manufacturer’s data sheets, allow for the determination of the mass of scatterers to be added. With this suitable amounts of borosilicate glass microspheres were added to the PVA dissolved in the mixed solvent of DMSO and water. Stirring was maintained continuously to disperse aggregations of the scatterers and to ensure homogeneity of the mix. The temperature of the solution was maintained at 140 ◦ C for 2 h. The same procedure with regard to the casting, refrigerating and solvent-exchange with water as detailed earlier was followed to yield gels of the required turbidity. 3. Characterization 3.1. Optical property measurements 3.1.1. Total attenuation coefficient. The total attenuation coefficient (µt ) of the samples was measured using a spectrophotometer (Shimadzu UV–3101 PC, Tokyo) using unscattered light through the sample. This was possible with the addition of an aperture stop (1 mm diameter) in the sample-side light beam path of the instrument, in combination with a microcell sample holder provided with masks of dimension (1× 1) mm. The aperture stop was positioned in front of the detector exit to line up along the optical axis of the empty sample holder as the point at which maximum light transmittance was obtained. The baseline was recorded in this position. A thin slice of the sample (100–120 µm) sandwiched between two microscope cover slides was fixed immediately behind the empty sample holder, as shown in figure 1(a). By this arrangement only that portion of the incident beam which did not suffer scattering or absorption was detected (van Staveren et al 1991). The validity of the Beer–Lambert law was assumed to be applicable. The transmission of the samples was recorded between 800 nm and 1200 nm. Experiments were repeated for three specimens of each sample to obtain the scatter about the mean value. 3.1.2. Average cosine of scattering angles. In order to predict the propagation of light in tissue, it is important to know the average angle (θ ) by which photons are scattered, since this along with the scattering coefficient (µs) and absorption coefficient (µa ) determines the penetration depth of light. The measure of this is in terms of g, the average cosine of the scattering angles or anisotropy factor, g = cos(θ ). For g = 1, all radiation travels along the forward incident direction, and for g = 0 scattering is entirely isotropic. Scattering in human tissue is strongly forward-directed (Cheong et al 1990) and recent human breast tissue in vitro measurements (Ghosh et al 2001) have yielded a value of g = 0.86 at 632.8 nm. The angular relationship between the incident direction of radiation and the scattered direction is the scattering phase function p(θ ); this and hence g, can be experimentally determined using a goniophotometer. A schematic of the instrument used is shown in figure 1(b). The angular 362 A Kharine et al (a) (b) Figure 1. (a) Schematic of modifications in sample side of spectrophotometer to determine the total attenuation coefficient (µt (λ)) by collimated transmission measurements. (b) Schematic of goniophotometer for studying scattering phase function (p(θ )) and determining anisotropy factor (g). dependence of the light scattered from a pencil beam by a thin slice (around 100 µm) of the specimen is measured by rotating a detector in a plane around the sample. Further details regarding the instrumentation are provided in Bolt and de Mul (2002). The light source is a He–Ne laser operating at 632.8 nm, under the assumption that g depends negligibly on the wavelength, so that the results may be extended to 1064 nm. 3.1.3. Refractive index. Refractive indices of the samples were measured using an Abbe refractometer (Carl Zeiss, Jena). The refractometer was calibrated using the provided test piece. The experiments were repeated for three specimens of each sample, and the average refractive index for the samples determined at 589 nm. 3.2. Acoustic property measurements 3.2.1. Acoustic velocity and attenuation coefficient. The insertion technique (Bamber 1997) was employed to measure the acoustic properties of the samples. This is a relative measurement method using water as the reference, in which the transmission of ultrasonic longitudinal waves through a solid specimen immersed in water is studied. The experimental configuration comprises an ultrasound source and a detector as represented schematically in figure 2(a). A typical reference signal measured by the detector in water without the sample is shown in figure 2(b). For the measurement of the acoustic velocity, the time shift (T ) in the arrival of the ultrasound pulse with and without the sample in water is measured. With a knowledge of the velocity of sound in water (cw ) and the thickness of the sample (x), the velocity of sound in the sample (cs ) can be calculated as 1 T 1 . = − cs cw x (2) 363 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 -0.5 -0.5 -1.0 -1.0 -1.5 0 (a) 10 20 time (µs) 30 detector output (V) source excitation (V) Poly(vinyl alcohol) gels for use as tissue phantoms in photoacoustic mammography -1.5 40 (b) Figure 2. (a) Schematic of insertion geometry for sound velocity (cs ) and attenuation (αs ) measurement. Dimensions in mm. (b) A typical time-of-flight trace of an ultrasound pulse in water without the sample using the 1 MHz ultrasound source. For the measurement of acoustic attenuation, the same geometry is used, with the amplitude of the acoustic pulse with and without the sample in water being measured. The attenuation (αs ) can then be calculated as αs = αw − 1 {ln As − ln Aw − 2 ln(1 − R)}. x (3) In the above, αi is the attenuation coefficient (cm−1 ) with i = s, w (sample, water), x is the thickness of the slab (cm), Ai is the amplitude of the signal received with i = s, w (sample, water), R is the reflection coefficient at the water–sample interface. R depends on the relative acoustic impedances (z) of water and the sample; z itself depending on the density (ρ) and acoustic velocity (c). A 20% PVA solution was cast in a cuboidal mould (32 × 11 × 28) mm to undergo the freeze–thaw cycles. After each cycle the acoustic measurements were made in a Perspex tank with deionized water at 22 ◦ C as the immersion liquid. The sample was placed in the focus of the transducer at a distance of 20 mm with the detector at a distance of 13 mm from the sample surface. The flat parallel side faces of the sample, with thickness 11 mm, provided the acoustic path during the experiments since the top surface of the gel is not smooth owing to expansion of the free surface in the mould during freezing–thawing. The Videoscan immersion series of transducers (Panametrics NDT, Waltham) with centre frequencies 1.0, 2.25 and 5.0 MHz were used as ultrasound sources in the configuration described above. All the transducers had element sizes 13 mm and focal lengths 20 mm. The detector was a laboratory made PVDF based disc shaped sensor of the type described in Hoelen et al (1999). The transducers were excited with a one cycle burst of a sine wave of the appropriate frequency, with a peak– peak voltage of 2 V, and repetition rate 1 kHz. The excitation was provided by a function generator (Model 33250A, Agilent Technologies, Palo Alto). The signal from the detector was monitored using an oscilloscope (TDS 220, Tektronix, Beaverton), and the data transferred to a PC via a GPIB interface. 3.2.2. Density. The densities of the various samples at room temperature were determined using the standard pycnometer bottle with deionized water as reference. The analytical balance (Sartorius BP 210D, Goettingen) used for making measurements is accurate to 0.0001 g. Densities were measured on five specimens of each sample to determine the 364 A Kharine et al 1064 nm -1 2x 80 3x 4x 5x 6x 60 7x 40 900 1000 1100 8 7x 6 6x 5x 4x 4 3x 2 0 1200 2x 1x 800 900 wavelength (nm) 1000 1100 1200 wavelength (nm) (a) (b) 15 average transmission (%) -1 30 attenuation coefficient µ t (mm ) average transmission (%) 1x 800 1064 nm 10 attenuation coefficient µ t (mm ) 100 14 25 13 µt = 11.89 mm -1 12 20 11 1064 nm 15 800 900 1000 1100 1200 10 wavelength (nm) (c) Figure 3. All curves are obtained as the mean value of measurements on three specimens of each series. The error bars are obtained as the scatter about the average value and are indicated only at the limits of each curve. (a) Wavelength dependence of mean percentage transmission for 120 µm samples prepared using freezing and thawing (method I). The number of freezing–thawing cycles is indicated against each curve. (b) Mean value of the total attenuation coefficient µt as a function of wavelength, for 120 µm samples prepared using method I. (c) Wavelength dependence of average percentage transmission and the total attenuation coefficient µt for a 120 µm sample prepared using method II. scatter in the values obtained. The scatter in the values about the mean value was between 0.1% and 0.5%. 4. Results The wavelength dependences of the transmission of the samples, prepared by methods I and II, are shown in figures 3(a) and (c). From the Beer–Lambert law, the transmission is given by Iτ = exp(−µt d) . (4) I0 In the above τ is the transmission, µt the total attenuation coefficient (mm−1 ), d the sample thickness (mm); Iτ is the collimated transmission and I0 the incident intensity. The wavelength dependences of µt of the samples, prepared by methods I and II, are shown in figures 3(b) τ= Poly(vinyl alcohol) gels for use as tissue phantoms in photoacoustic mammography 365 Table 1. Relevant optical properties of certain samples studied. With the suitability of the seven cycle freeze–thawed sample ascertained from the value of µ′s , subsequent measurements of parameters of method I samples were confined only to these. µs was measured at 1064 nm, g at 632.8 nm and n0 at 589 nm. Sample Scattering coefficient µs (mm−1 ) Scattering anisotropy g Reduced scattering coefficient µ′s (mm−1 ) Refractive index n0 Method I Four cycles Five cycles Six cycles Seven cycles Method II Tissue 5.04 ± 0.25 5.47 ± 0.23 6.11 ± 0.28 6.90 ± 0.38 11.8 ± 0.32 4.28–9.28a – – – 0.91 ± 0.01 0.93 ± 0.01 0.86b – – – 0.62 ± 0.1 0.82 ± 0.1 0.6–1.3c – – – 1.360 ± 0.002 1.366 ± 0.002 1.33–1.55d a Calculated from columns 3 and 4. From Ghosh et al (2001). c From Tromberg et al (2000) and Suzuki et al (1996). d Typically quoted for soft human tissue (Tuchin 2000). b and (c), respectively. The scattering coefficient µs is obtained from µt and the absorption coefficient µa as µt = µs + µa . (5) In order to determine µa , method I samples and transparent method II samples (without scatterers) were melted down into cuvettes and the absorption spectra of the clear solutions recorded. At 1064 nm, µa (method I) = 0.035 mm−1 and µa (method II) = 0.025 mm−1 respectively; µs is calculated using equations (4) and (5). The scattering coefficients of certain samples studied are presented in table 1, juxtaposed with values quoted for human breast tissue. It is seen that for method I samples, µs increases with an increasing number of freeze–thaw cycles to yield for six to seven cycles, a value that approximates that expected of breast tissue. Beyond this, the changes in µs are very slight and do not justify subsequent cycling. With the measured value of g (see further) to obtain µ′s , the suitability of seven cycle freeze–thawed sample is ascertained; subsequent measurements of parameters of method I samples are confined only to these. Also, the value obtained experimentally from the sample prepared using method II matches µs that it is designed for. The measured output voltage V (θobs ) of the photomultiplier tube, representing collected power versus observed angle θobs , for a 100 µm thick specimen prepared by method I is shown in a semilog plot in figure 4(a). The strong forward-directed nature of scattering is evident in the figure. At |θobs | = 63◦ , there is an abrupt fall in the measured output, the signature of total internal reflection occurring at the specimen–glass interface and precluding passage of light to the detector. The raw data require processing to be available as phase function parameters, also taking into consideration certain sources of error intrinsic to the experiment geometry. The protocol followed for correcting the data is based on that described by Jacques et al (1987). The following equations represent a consolidation of corrections to V (θobs ): 
1 cos(θexit )n2s V (θobs ) (6) I (θexit ) = 2 Vdir (1 − r1 )ω cos(θobs ) cos(θobs )ng [1 − r(θexit )] (1 − r2 )   ns θexit = sin−1 sin(θobs ) . ng (7) A Kharine et al 20 2 10 10 -1 -3 -6 -60 -40 -20 0 20 40 observed angle (degrees) (a) 60 -3/2 2 method I: 7 x thickness: 100 µm I=a(1-g )(1+g -2g cos(x)) -2 10 method I: 7 x thickness: 100 µm 0 intensityI(θ) (mW cm sr ) uncorrected PMT voltage (volts) 366 a = 1.98 x 10 -5 15 g = 0.91 ± 0.00594 10 5 0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 exiting angle θ (radians) (b) Figure 4. (a) Semi-log plot of angular dependence of light scattering as voltage output of the photomultiplier tube in the goniophotometer setup for the seven cycle freeze–thawed sample of method I. (b) The experimentally derived scattering phase function obtained by correcting the data obtained. The solid curve is the theoretical fit of the Henyey–Greenstein function to the data. In the above, the final result in the series of corrections is I (θexit ), the radiant intensity of light in W sr−1 with θexit the true angle of exitance; Vdir is the direct on-axis measurement without the sample and taking into account the neutral density filters used to prevent saturation of the PMT; (1 − r1 ) is the correction for specular reflection across the two interfaces between the three media, namely air, glass (microscope slide) and sample assuming passage of light normal to the interfaces; ω represents the solid angle of collection of the detection fibre including the lens; cos(θobs ) is the correction term for Lambert’s law. The term in braces corrects for the reduction in the solid angle due to refraction at the sample–glass (hemisphere) interface where ni is the refractive index for i = s or g, referring to sample or glass (hemisphere) respectively. Corrections for Fresnel reflection at the sample–glass (hemisphere) interface and specular reflection at the glass(hemisphere)–air boundary are represented by [1 − r(θexit )] and (1 − r2 ), respectively. The angular dependence of the corrected radiant intensity of the scattered light is the equivalent phase function. This must be fitted to an analytical phase function which permits recovery of the parameter g. In practice, it has been found that the Henyey–Greenstein (HG) function or modifications of it can model the scattering phase function of tissue to a good approximation, under the assumption that single scattering is present. The expression depends on g as   1 − g2 . (8) I (θ ) = scale (1 + g 2 − 2g cos θ )3/2 Figure 4(b) shows the experimentally derived phase function, to which the HG function, equation (8), is fitted. The full line is the theoretical fit to the data. The light which emanates unscattered together with the light scattered in the on-axis direction (−1.5◦ < θ < 1.5◦ ) is masked in the fit. An average value of g = 0.91 was obtained for samples prepared by method I; and g = 0.93 for those from method II. The samples are between 100– 120 µm. Identification of θc , the corrected critical angle from figure 4(a), and with ng = 1.51 (for BK-7 glass) yields the refractive index for the sample. This was corroborated with measurements using the Abbe refractometer. The most relevant optical results are presented in table 1, with a range of values quoted for soft human tissue. Poly(vinyl alcohol) gels for use as tissue phantoms in photoacoustic mammography 367 0.4 method I: 7 x 0.1 0.0 -0.1 -0.3 1.6 method II 1.2 0.8 method I: 7 x 0.4 30.91, -0.17267 30.5 Model: a.f a = 0.32; m = 1.16 -1 31.12, 0.318 0.2 -0.2 m 2.0 30.82, 0.29213 attenuation (dB cm ) detector output (V) 0.3 m Model: a.f a = 0.07; m = 1.68 31.21, -0.21181 31.0 31.5 time (µs) 0 1 2 3 4 5 frequency (MHz) (a) (b) Figure 5. (a) Original water-path ultrasound pulse (– – –) juxtaposed with the shifted, attenuated pulse (——) following the insertion of the sample (method I: seven cycle freeze–thawed). The 5 MHz transducer is used as the source. (b) Frequency dependence of mean acoustic attenuation coefficient (αs ), for ( ) seven cycle freeze–thawed gel and ( ) gel prepared by method II. Each αs is obtained as the mean value of measurements on three specimens of each series. The error bars are obtained as the scatter about the mean value. • ◦ Table 2. Relevant average acoustic properties of samples from methods I and II. Only the seven cycle freeze–thawed sample of method I is presented. Sample Density ρ (×103 kg m−3 ) Velocity cs (×103 m s−1 ) Impedance z (×106 kg m−2 s−1 ) Attenuation α (dB cm−1 ) Method I Method II Tissue 1.03 ± 0.02 1.07 ± 0.02 1–1.07b 1.56 ± 0.02 1.58 ± 0.03 1.425–1.575c 1.654 ± 0.05 1.712 ± 0.064 1.425–1.685d 0.19 ± 0.06a 0.62 ± 0.03a 0.5–1.1e a At 1.76 MHz from power-law frequency dependence. See figure 5(b). From Duck (1990), p 137. c From Bamber (1997). d Calculated from columns 1 and 2. e Specified at 1.76 MHz from Duck (1990), p 103. b Figure 5(a) is a representative plot which shows the time shift and the amplitude change suffered by the water-path ultrasound pulse with the insertion of the sample. The acoustic velocity (cs ) is calculated from equation (2), using the velocity of sound in water (cw ) at 22 ◦ C from Lubbers and Graaff (1998). The acoustic attenuation coefficient (αs ) is calculated from equation (3), using the value for water at 22 ◦ C from Greenspan (1972). Figure 5(b) represents a consolidation of the frequency-dependent attenuation coefficients (dB cm−1 ) of the seven cycle freeze–thawed gel, and the gel prepared by method II. The solid lines are power law (af m ) fits to the data. The relevant data from the acoustic studies are presented in table 2, along with densities measured using the pycnometric method and calculated acoustic impedances (kg m−2 s−1 ). From the table, it is clear that most of the acoustic properties of the PVA gel samples match those of human tissue, barring attenuation of samples from method I. 5. Discussion and conclusion The number of cycles of freezing and thawing of the samples prepared by method I has been optimized to seven, to yield a scattering coefficient µs that lies in the range typically quoted 368 A Kharine et al for breast tissue. Henceforth, only these samples are considered for the discussion. The data presented also show that the µs of samples prepared by method II can be predicted theoretically, enabling a tailoring of the optical scattering. The strong forward-directed nature of scattering in tissue is also well reproduced in both types of samples. The refractive index of the samples was found to be close to that of water and soft tissue. The density and acoustic velocity, which may also be determined by water content, are substantially approximate to properties of water and that of soft tissue. The acoustic attenuation of method I samples, however, is lower than that of tissue, but this can be corrected for in calculations of acoustic transport in the phantom. These results indicate that the PVA-based hydrogels allow for the design of controlled breast tissue phantoms for use in photoacoustic imaging investigations. The use of these materials is not particularly restrictive to this field and they can be applied to the earlier mentioned hybrid techniques. The most salient advantage of these materials as phantoms, over those based on gelatin, agarose and polyacrylamide (Tuchin 2000, pp 99–108), is their superior mechanical properties. PVA-based gels are rubbery with a high modulus of elasticity. Conventional gels are fragile; they rupture during handling especially for larger-sized phantoms and can disintegrate under pressure. Method II of preparing samples that involves the use of scattering additives to the transparent base material has the advantage that the light-scattering behaviour is adjustable. However, the use of well-defined microspheres entails prohibitive expense for large phantoms mimicking whole organs such as the mamma. Method I on the other hand has no such problems since the turbidity is intrinsic to the procedure of rigidifying the gel by physical processing. It is therefore preferable in the fabrication of large volume phantoms. A caveat in the preparation of such phantoms is that the rates of freezing and thawing are crucial in determining the properties. It is recommended therefore that the optical properties be verified for the rates available for preparation, and that the procedures be followed consistently to obtain reproducibility in properties. Regarding the issue of stability, PVA-based hydrogels undergo desiccation when exposed to air, causing degradation in the properties. For this reason, it is imperative that the gels be stored under water. To prevent dehydration during imaging experiments, several waterproof coatings such as silicone rubber were experimented with, with no success owing mostly to corrosion of the gel by the curing agents required to harden the rubber. Finally, it was decided to employ a layer of ultrasound gel around the sample to retain moisture. PVA gels are also susceptible to proliferation of fungal growth. This can be avoided by storing the phantoms in a 0.01% solution of sodium azide2 . Interestingly, the samples prepared by method II were resistant to fungus, possibly due to remnant DMSO which may possess fungicidal properties. A breast phantom was fabricated using method I, by casting the aqueous PVA solution in a cubical Perspex mould of dimensions (150 × 60 × 180) mm in which tumour-simulating spheres were suspended. Nine ‘tumours’ of diameters 2, 5 and 10 mm were cut from gel samples with absorption coefficients 0.07, 0.13 and 0.25 mm−1 (approximately 2, 4 and 7.5 times that of background) prepared by method II using added absorbers, but without the glass microspheres. The absorber used was EcolineTM 700 black watercolour (Royal Talens, Apeldoorn) which was added to the DMSO solution at the time of dissolving the PVA. An empirical formula was used for determining the amount of dye required for various µa , from the best fit to the experimentally derived graph of absorption versus concentration of the dye in water. There was a small discharge of the dye during the process of DMSO exchange with water, but µa measured from the samples after a few weeks in water matched the values they were designed for. The spheres were suspended using nylon thread at different locations in 2 Sodium azide is injurious to human health, and adequate precautions must be taken while handling the solution. Poly(vinyl alcohol) gels for use as tissue phantoms in photoacoustic mammography 369 the mould. The aqueous PVA solution was then poured in carefully, having been cooled from 95 ◦ C to 45 ◦ C, so as to not soften/melt the inhomogeneities while still remaining mobile enough to be poured. The mould and its contents were put through the freeze–thaw cycles. Various aspects of photoacoustic imaging techniques relevant to mammography are currently being studied using this breast phantom. Acknowledgment The financial support of the European Commission through the project OPTIMAMM (contract QLG1-CT-2000-00690) is gratefully acknowledged. 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