A soft deformable tissue-equivalent phantom for diffuse optical tomography

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1 INSTITUTE OF PHYSICS PUBLISHING Phys. Med. Biol. 51 (2006) PHYSICS IN MEDICINE AND BIOLOGY doi: / /51/21/013 A soft deformable tissue-equivalent phantom for diffuse optical tomography Jeremy C Hebden, Ben D Price, Adam P Gibson and Gary Royle Department of Medical Physics & Bioengineering, University College London, Gower Street, London WC1E 6BT, UK Received 1 August 2006, in final form 8 September 2006 Published 16 October 2006 Online at stacks.iop.org/pmb/51/5581 Abstract A recipe is presented for the manufacture of highly compressible phantoms for diffuse optical tomography. The recipe is based on polyvinyl alcohol (PVA) slime, a viscoelastic fluid which readily deforms under moderate pressure. Scattering particles and absorbing compounds can be added to provide a uniform material with stable and reproducible optical properties. A linear relationship between the concentration of scattering particles (either titanium dioxide or microspheres) and the transport scatter coefficient is demonstrated. Phantoms of an arbitrary size and shape may be produced by containing the slime within a thin latex shell, and a stability over a period of at least 3 months has been established. The deformable phantoms may be used to test and calibrate optical tomography systems designed for use on patients with irregular or variable geometries. 1. Introduction Measurements of the transmittance of near-infrared light across tissue can be used to monitor changes in blood volume and oxygenation (Ferrari et al 2004). By making multiple measurements between pairs of points over the surface of a volume of tissue, it is possible to produce images which display the spatial variation in these physiological parameters. This is the basis of diffuse optical tomography, which is being widely explored as a means of generating functional maps of the brain and of detecting disease in the adult female breast (Gibson et al 2005). The development of optical imaging techniques, like that of any other medical diagnostic modality, has relied upon appropriate phantoms whose physical properties and geometries are matched to those of human tissues. Measurements on phantoms are used to evaluate the performance of systems and to validate imaging algorithms. The propagation of light through tissue can be characterized by the refractive index n, the absorption coefficient µ a, the scatter coefficient µ s, and the scattering phase function P( ). Although variations in refractive index at the cellular scale give rise to considerable scatter, the macroscopic variation in the refractive index is small, typically varying between /06/ $ IOP Publishing Ltd Printed in the UK 5581

2 5582 J C Hebden et al those of water (1.33 at 800 nm) and fat ( 1.5). The absorption and scatter coefficients, representing the probabilities of a photon being absorbed and scattered per unit length of travel respectively, can vary by orders of magnitude depending on the tissue type and the optical wavelength. The scattering phase function, which describes the distribution of scattering angles, is usually assumed to be independent of the initial and final directions (represented by unit vectors and, respectively), and therefore only depends on the angle θ between them. This assumption is probably reasonable for most tissues, although may not hold for those consisting of aligned fibres (e.g. muscle and brain white matter) where light will have a tendency to propagate along the fibre direction (Hebden et al 2004). When measuring multiply scattered light, e.g. through biological tissue, the precise form of the phase function is less relevant and can be represented by g, the mean cosine of the scattering angle θ. For diffuse optical tomography, where the statistical nature of diffuse light rather than individual photons is considered, a further simplifying assumption can be made that scatter can be characterized by a single parameter known as the transport scattering coefficient µ s = µ s(1 g). This implies that scatter can be considered isotropic over distances larger than 1/µ s, known as the transport scattering length. During the past 20 years, a broad variety of materials have been proposed to mimic the optical properties of biological tissues. For testing imaging systems and algorithms in the laboratory, fluid-based phantoms are often the most appropriate. Fluids allow small solid targets of contrasting optical properties to be placed within them, and to be moved in and out to represent a regional change in blood volume and/or oxygenation. Most fluid phantom materials have been water-based, with appropriate absorption provided by inks, food colouring agents or industrial dyes. A popular and inexpensive source of scattering for such phantoms has been intralipid, an intravenous nutrient consisting of an emulsion of phospholipids micelles and water. The optical properties of intralipid have been well characterized (van Staveren et al 1991, Flock et al 1992), and a 1% intralipid concentration (of solid by volume) provides a medium with a transport scatter coefficient of roughly 1 mm 1 at near-infrared wavelengths. Although the value of g for intralipid solutions is generally less than that of most biological tissues, this is usually not a significant concern for diffuse optical imaging applications where the separation between sources and detectors is typically much larger than the transport scattering length. When it has been desirable to model the scattering characteristics (i.e. µ s and g) more accurately, phantoms based on a suspension of latex microspheres (Hebden 1992) in water have been employed. For microspheres of a specific diameter, refractive index and concentration, the scattering coefficient and phase function can be precisely determined using Mie theory (Bohren and Huffman 1983). A combination of polystyrene microsphere sizes in appropriate concentrations has also been used to mimic specific tissue phase functions (Passos et al 2005). Other fluid phantoms have been produced using milk (Wilson et al 1989) and non-dairy creamer (Linford et al 1986) as scattering agents. A major disadvantage of fluid phantoms is that they require a barrier of solid material to contain the fluid and to separate regions of different optical properties. Other disadvantages are that they are often unstable over a prolonged period, and they are difficult to transport. The use of solid phantoms avoids these problems, and researchers have advocated various alternative recipes for generating them. The optical properties of tissue have been simulated using a highly scattering plastic known as Delrin (Berg et al 1996), RTV rubber (Jiang et al 2003), colouring pigment in paraffin wax (Srinivasan et al 2002), ink and intralipid in agar (Cubeddu et al 1997), haemoglobin and intralipid in gelatine (De Grand et al 2006), cosmetic powder and aluminium oxide particles in silicone rubber (Lualdi et al 2001), dye and titanium dioxide particles in polyester resin (Firbank and Delpy 1993), dye and quartz glass spheres in polyester resin (Sukowski et al 1996) and dye and amorphous silica spheres in epoxy resin

3 A soft phantom for diffuse optical tomography 5583 (Firbank et al 1995). Recently, Spirou et al (2005) described a novel design of solid phantom which mimics both the optical and acoustic properties of tissues. Their phantom is based on polyvinyl chloride-plastisol mixed with titanium dioxide powder and a black plastic colouring agent. Phantoms used to test or calibrate imaging systems built for patient studies are often required to simulate the patient geometry, which can vary quite considerably. For example, optical tomography of the infant brain at UCL requires a phantom which can fit precisely within the same probe-supporting helmet as worn by the infants (Hebden et al 2002). Similarly, some optical mammography systems involve compressing the breast to a thickness which depends on the patient (Grosenick et al 2005, Taroni et al 2005). Therefore, a phantom which can mimic the mechanical properties of soft tissues and/or can be moulded into a desired shape to exactly fit the same optical array geometry as used for the patient would be of significant benefit. To meet this need, we have developed a phantom which can be easily compressed and deformed, and with optical properties which are reproducible and stable over a period of several months. 2. Phantom design 2.1. Materials The principal component of the phantom is polyvinyl alcohol (PVA) slime, a slow-flowing viscoelastic non-newtonian fluid which becomes significantly more viscous and brittle when subject to a shear stress. The slime is optically clear and colourless, and therefore to provide the required amount of scatter and absorption, the slime is mixed with scattering particles (e.g. titanium dioxide or polystyrene microspheres) and an appropriate quantity of water-soluble dye or ink. The slime is then enclosed within a flexible latex shell of a suitable size and shape Recipe PVA slime. Slime is generated when PVA is mixed with a solution of sodium tetraborate decahydrate (known as borax). PVA is a polymer of the vinyl alcohol unit (C 2 H 3 OH). When dissolved in water, these units link up to form long chains. When borax is added to the PVA solution, the chains of PVA cross-link to form the viscoelastic slime. The cross-linking is weak, so the links continually form and break under the weight of the gel, allowing it to flow slowly. However, subject to a sudden force the material will become brittle and snap apart. Both PVA and borax are obtainable as dry powders, which require dissolving separately in water, to obtain concentrations of about 4% by weight. Because PVA does not dissolve easily (requiring heating of the water and a considerable amount of stirring), we saved time by purchasing a PVA solution ( PVA Clear, Alec Tiranti Ltd., London). Borax powder is widely available from general stores as a cleaning agent. When the two solutions are added, the consistency of the resulting slime depends on their ratio. A PVA:borax ratio of 5:2 was found to produce the most satisfactory, deformable medium Scattering particles. Because of its high viscosity, uniform mixing of any substance directly within slime is difficult. Therefore, scattering or absorbing materials were added in equal concentrations to the separate PVA and borax solutions, distributing as evenly as possible using an electrical stirrer for up to 30 min. However, vigorous mixing in air inevitably produces bubbles, and any bubbles in the slime will cause additional and irreproducible scattering. Two mechanisms were introduced into the phantom preparation to avoid this. First, electrical

4 5584 J C Hebden et al 2 Transport Scatter Coefficient (mm -1 ) Concentration of Titanium Dioxide Particles (g l -1 ) Figure 1. The transport scatter coefficient of slime phantom material at 780 nm as a function of concentration of titanium dioxide particles. stirring of each solution was performed within a vacuum chamber. Second, the two solutions were then combined using a syringe to inject the borax below the surface of the PVA. This enabled a uniformly scattering slime to be produced without requiring the two components to be stirred together. Any excess liquid left at the end of this process tends to infuse into the slime if left for a few hours, but otherwise this can be removed without affecting the overall concentration of scattering or absorbing agents within the slime. Three potential scattering agents were evaluated: intralipid, titanium dioxide particles and polystyrene microspheres. On mixing intralipid with the PVA solution, the lipid particles appeared to conglomerate, producing a highly heterogeneous medium. The resulting slime also tended to deteriorate and develop mould on the surface after only a few days. Titanium dioxide particles, purchased as an inexpensive white powder (Alec Tiranti Ltd., London), produced slimes exhibiting highly uniform and reproducible scattering properties. Titanium dioxide is a very effective scatterer because of its very high refractive index (>2.2), and a previous measurement of a similar sample of particles indicated a mean diameter of around 0.3 µm (Firbank and Delpy 1993). The transport scatter coefficient as a function of particle concentration was determined using a method as described in detail by Patterson et al (1989). A series of slimes with different concentrations were prepared. Each slime was generated within a clear-sided rectangular plastic box of dimensions 100 mm 85 mm 44 mm. Optical fibres were coaligned on either side of the box in the centre of each of the largest sides, and the time-resolved transmittance of picosecond pulses of light at 780 nm was measured using a single channel of the time-resolved imaging system described by Schmidt et al (2000). The transport scattering coefficient and the absorption coefficient were determined by performing a least-squares fit of an analytical solution to the time-dependent diffusion equation (for a slab geometry) to the measured temporal distribution of light. While the derived absorption coefficient remained unchanged and roughly consistent with that of water at 780 nm, values of µ s increased in direct proportion to the concentration of titanium dioxide particles, as shown in figure 1. A straight line fit to the data is shown to emphasize the strong linearity. The scatter coefficient as a function of concentration at 780 nm was also calculated by measuring

5 A soft phantom for diffuse optical tomography Transport Scatter Coefficient (mm -1 ) Concentration of Polystyrene Microspheres (g l -1 ) Figure 2. The transport scatter coefficient of slime phantom material at 780 nm as a function of concentration of polystyrene microspheres. the linear attenuation produced by small amounts of particles in water, under conditions of single scatter of light within the sample. From this we derived a value of 0.55 ± 0.02 for the mean cosine of scatter. The scattering efficiency of the particles in water will be virtually identical to that in PVA slime, since measurements confirmed that the refractive index of the PVA slime is consistent with that of water. Samples of titanium dioxide particles from several different suppliers were evaluated, and in each case highly homogenous scattering slimes were produced. However, obtaining a uniform suspension of some samples in the PVA and borax solutions required agitation in an ultrasound bath for 30 min prior to vigorous stirring. As described above, for diffuse optical tomography applications the ability to represent the transport scattering coefficient of tissue is generally sufficient. Nevertheless, if an application requires a phantom material with specific (i.e. tissue-like) values of g and µ s, this can be provided using appropriate microspheres as the scattering agent. We briefly evaluated slime media based on polystyrene microspheres (14 ± 7 µm diameter; refractive index n 1.58 at 780 nm). Thirty minutes of vigorous stirring of the microspheres in the PVA and borax solutions (again in a vacuum) were preceded with a similar period of agitation in an ultrasound bath. A highly homogenous scattering slime was produced, and the transport scatter coefficient as a function of microsphere concentration was determined using the method described above. Although fewer slime samples were evaluated (because of the relatively high concentrations required and the limited supply of comparatively expensive microspheres), the result shown in figure 2 exhibits another linear relationship. The deviation from the linear relationship at the highest concentration is likely due to a departure from the independent scattering regime, which occurs when inter-particle distances become comparable with the wavelength (Ishimaru and Kuga 1982). Theoretical and experimental results presented by Zaccanti et al (2003) demonstrate a significant departure from linearity when concentrations of scattering particles exceed around 2% by volume. Our experimentally derived values of µ s are consistent with those estimated from Mie theory (based on the known distribution of microsphere diameters for the sample), which also predicts a mean cosine of scatter with a tissue-like value of about 0.9. Silica microspheres (1.0 ± 0.05 µm diameter) were also briefly tested, but the comparatively

6 5586 J C Hebden et al high density of silica (1.96 g cm 3 ) prevents a uniform suspension from being obtained in either component prior to mixing Absorbers. The intrinsic absorption of PVA slime in the nm wavelength region is consistent with that of water, although their spectra differ slightly at higher wavelengths. Additional absorption can be provided by adding water-based dyes and inks, such as those commonly used for fluid phantoms based on intralipid. We evaluated an industrial near-infrared dye (ICI S109564) and Indian ink. To ensure homogeneity within the final phantom, an equal concentration of absorber was added to the PVA and borax solutions separately before mixing. Gentle stirring was sufficient to distribute the absorber within each component, and both absorbers distributed uniformly in the final slime without evidence of bleaching. The concentration of absorber necessary to provide a given absorption coefficient can be determined by applying the Beer Lambert law to measurements of the transmittance as a function of concentration in water (Ferrari et al 2004) Latex shell. To make a compressible phantom with a given geometry, the slime is encased within a latex shell. The shell is made by painting several layers of liquid latex (Alec Tiranti Ltd., London) mixed in the ratio 20:1 with a thickening agent (Scopas latex thickener, Alec Tiranti Ltd., London) on to a non-porous object which has the same shape as that of the required phantom. A minimum of 60 min is required for each layer to dry before adding the next layer. The shell is peeled off the object when the final layer is set. We found that five layers were sufficient to provide a shell which is sufficiently robust to withstand significant handling and compression without damage, but thin enough to ensure that the optical properties of the latex have a negligible influence on phantom measurements. Latex is only mildly absorbing and almost non-scattering at near-infrared wavelengths. Note that it is possible to increase the scatter and/or absorption of the latex shell if desired by adding a quantity of polyester pigment to the liquid latex. When additional mechanical strength is required, the shell can incorporate one or more layers of latex-soaked cotton bandage. However, these should only be used in areas not to be interrogated optically, such as the base or support structure. Completed latex shells were lightly dusted with talcum powder to prevent them from adhering to themselves. After filling a latex shell, it is necessary to fully enclose the slime by adding further latex within the open neck of the shell. Unfortunately liquid latex does not set when in contact with the slime. Therefore, we cut a patch from a latex sheet and joined it to the neck of the shell by overlapping the patch with the neck and coating both surfaces with a layer of liquid latex. The join can be reinforced with latex-soaked bandage if necessary. Care must be taken to prevent slime from contaminating the joined surfaces while also preventing pockets of air from being trapped within the completed phantom. Trapped bubbles of air may be extracted if necessary using a syringe with a fine needle; the needle hole in the latex can be sealed afterwards using a small amount of liquid latex. We created three different types of compressible phantom: slab phantoms, head phantoms and breast phantoms (figure 3). Latex shells for slab phantoms were generated by coating the latex on five sides of a rectangular plastic box. Anthropomorphic breast phantoms were created using a plaster cast of a female breast. The plaster surface was first sealed by brushing with wax dissolved in white spirit. The latex shell of the breast was then attached to a larger rectangular shell representing the chest wall. Finally, infant head phantoms were constructed from shells generated from dolls heads. Major cavities in the doll s head (mouth, ears, eyes, etc) must first be filled with modelling clay. After filling with slime, a latex patch is inserted within the open neck of the head shell and then sealed with liquid latex.

7 A soft phantom for diffuse optical tomography 5587 (a) (b) (c) Figure 3. Soft deformable phantoms representing (a) rectangular slab, (b) infant head and (c) female breast geometries. Each consists of PVA slime contained within a thin latex shell Stability. Phantoms have been stored at room temperature, and their properties have been monitored over a period of 3 months. The mechanical properties of the slime sealed within the latex shells have remained constant, with no evidence of drying out or of bacterial growth. The optical properties of slab phantoms have been measured at regular intervals and found to be constant. Bubbles have occasionally appeared beneath the latex, either due to diffusion of air through the latex or due to dissolved gas coming out of a solution. These can be removed using a syringe needle as described above. Small holes or tears in the latex shell can be repaired by applying a latex patch to the damaged area, using liquid latex as an adhesive. The effective lifetime of the phantoms appears likely to be limited by the rate of deterioration of the latex. Latex has a tendency to discolour (becoming increasingly dark and yellow) after a prolonged period, although the discolouration does not have a significant influence on the overall optical properties of phantoms. More seriously, the latex becomes less elastic and more prone to tear under stress. This deterioration is likely to limit the useful lifetime of a phantom to about 6 months Insertion of regions of optical contrast Homogeneous phantoms are often employed for essential data calibration tasks and for the overall assessment of optical imaging hardware (Hebden et al 2002, Jiang et al 2003, Liet al 2003, Schmitz et al 2000). Nevertheless, tissue-like phantoms are also useful to evaluate imaging performance in terms of contrast, spatial resolution, signal-to-noise ratio and the presence of artefacts. The evaluations of these quantities require phantoms containing internal regions of contrasting and well-defined optical properties at precisely known positions. The confinement and placement of such regions within the body of a slime-based phantom is not straightforward. Slimes containing different concentrations of dye and/or scattering agent will diffuse together over a period of hours when in direct contact, and therefore such regions must be confined. We successfully achieved this by dividing the latex shell into discrete compartments using internal latex boundaries, which can also be used to support one or more isolated slime-filled, latex-encapsulated targets. Although the internal latex boundaries (if made sufficiently thin) do not have a significant influence on the optical properties of the phantom, they can reduce its compressibility. Furthermore, during compression it is difficult to confidently predict the exact positions of internal boundaries and regions relative to any landmarks on the external surface.

8 5588 J C Hebden et al 3. Discussion The phantom recipe presented above provides a soft, tissue-like absorbing and scattering medium which is reproducible and stable over a period of several months. Repeated applications of the recipe have been able to reproduce the desired optical properties (absorption and transport scatter coefficients) with an accuracy of about 5%. The compressibility of the phantom renders it suitable for a range of optical tomography applications where the tissue geometry is either irregular or variable. The recipe can be adapted to accommodate waterbased absorbers with the desired spectral characteristics. Both titanium dioxide particles and polystyrene microspheres have been found to be effective scattering agents. Due to the greater cost of microspheres (particularly samples with narrow, well-defined size distributions), we recommend the former for applications where a match of the transport scattering coefficient is sufficient. The homogenous infant head phantom shown in figure 3(b) was specifically designed to provide the so-called reference measurements for optical tomography of the newborn infant brain (Austin et al 2006; Hebden et al 2002). Data acquired on a reference phantom with precisely known optical properties provide a valuable calibration of the system, and are essential to generate images of the distributions of absorption and scatter within the infant brain. Immediately after an infant scan, the compressible phantom is inserted into the helmet which attaches the optical fibre sources/detector to the infant head. The phantom is easily moulded to a shape close to that of the infant head so that it fits the same arrangement of optical fibre connectors without significant distortion or movement of the helmet. Preliminary tests suggest that it is a more convenient and effective alternative to previous reference phantoms based on intralipid-filled latex shells (Austin et al 2006) and balloons (Hebden et al 2002). A further potential application of compressible phantoms is the assessment and validation of hybrid breast imaging systems which combine optical tomography with conventional (anatomical) imaging methods such as x-ray mammography (Zhang et al 2005), magnetic resonance imaging (Brooksby et al 2003, Ntziachristos et al 2000) or ultrasound (Zhu et al 2003). Not only can our deformable phantoms be compressed like real tissue, but it is a relatively straightforward task to provide a phantom, and any internal regions, with appropriate x-ray and optical properties simultaneously. Such phantoms have already been constructed in our laboratory, and are currently being evaluated. Finally, an alternative method of cross-linking PVA chains without the addition of borax is to subject a PVA solution to a cycle of freezing and thawing. The rigidity of the PVA gel can be progressively increased by additional cycles. This process also has the effect of increasing its optical scattering. Kharine et al (2003) and Devi et al (2005) describe the preparation of PVA gels with excellent tissue-like optical properties as phantoms for photoacoustic imaging and optical elastography, respectively. By adding an agent to prevent freezing of the water content, Kharine et al (2003) also show that transparent rigid PVA gels can be obtained. Thus, by adding appropriate amounts of absorbing and scattering materials during formation, the final optical properties can be accurately controlled. Acknowledgments Support for this work has been generously provided by the EPSRC and by Cancer Research UK. The authors would also like to thank Sidney Chuka for assistance with the preparation of the phantom materials, Kim Amis for advice on the use of casting methods and materials and Zara Frost and Brooke Gaar for supplying the plaster cast used to make the breast phantom.

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