Measurement of mass attenuation coefficient of polyvinyl alcohol (PVAL) as breast tissue equivalent material in the photon energy range of 16.61–25.26 keV

Medical physics phantom is commonly designed to mimic physical properties of human tissue. Phantom is widely used to provide quantitative and qualitative information upon its interaction with ionizing radiation in medical imaging, radiation dosimetry and treatment planning procedures. This study was carried out to fabricate a potential medical physics phantom material for mammography using polyvinyl alcohol (PVAL). The mass attenuation coefficients (μ/ρ ) of the PVAL gel samples were calculated based on the measurement of attenuation coefficient studies with low photon energy. The gel samples were prepared at 4 concentrations (5, 10, 15 and 20 %) of PVAL solution. Single photon beam transmission in the energy range between 16.61 and 25.26 keV was used to determine the μ/ρ of the PVAL gel. The low photon energy was chosen as the effective energy used in mammography is in a range between 17.5 to 22.6 keV. This was achieved by using the X-ray fluorescent (XRF) configuration. The experimental μ/ρ were compared with theoretical values of water and breast tissue calculated by using the XCOM computer program. The measured value of μ/ρ of the PVAL gels agreed with the XCOM values of water and breast tissue. The 5% and 10% PVAL gel samples were the closest to water while the 20% PVAL was the closest to breast tissue.


Introduction
The quality control (QC) and dosimetry studies are periodically conducted in medical physics to develop new techniques and to investigate new methodologies to continuously improve patient care. Most of these works cannot be carried out on human beings because they require the use of ionizing radiation which is harmful to human tissue. As a result, tissue mimicking materials referred to as phantoms are used in many applications of medical physics works such as medical imaging, dosimetry studies, quality assurance tests and radiotherapy. Phantoms could be anatomical or geometrically designed, with the former completely representing the anatomical structure of the body while the later are constructed to represent geometrical shapes [1].
Generally, water is known to be an excellent phantom material because the body is largely composed of water and the physical and attenuation properties of water mimic the human tissue to a large extent. As water exists in the liquid state, it is not convenient for use as a phantom material in most imaging and dosimetry studies hence the need for solid phantom materials like Perspex, polystyrene, epoxy,  [2][3][4]. Researchers have used several materials to fabricate breast tissue equivalent phantoms [4,5].
Poly (vinyl alcohol) (PVAL) is a non-toxic industrial compound which is commonly used to prepare adhesives, food packaging or for children's craft projects (slime). However, by using the appropriate amount of PVAL and water solution, this material can be easily formed into a gel possessing tissuemimicking properties [6]. PVAL has a mass density of 1.19 g/cm 3 which is close to the density of water and perspex which are commonly used as standard phantom materials. In addition, PVAL gels are solid and yet compressible, which makes it a likely suitable material for breast phantoms. The / is an important parameter used to characterize the absorption and scattering of ionizing radiation in tissue. Many authors have studied the / of different elements and compounds of biological and dosimetry materials [7][8][9][10]. Breast is a soft tissue, composed of adipose and fibro glandular tissue in various proportion depending on the density of the breast. Breast calcifications and tumours appear similar to breast tissue on mammograms, hence, the need for low energy x-ray in mammography examinations to illustrate early stage of breast cancer. To the best our knowledge, there is no literature on the / of water-based PVAL gel in the mammography energy range.
The XCOM program provided by the National Institute of Standards and Technology NIST [11] is a software that can be used to determine the / of elements and compounds that are of dosimetric interest at different energies. This study was carried out to fabricate potential breast tissue equivalent phantoms using water-based PVAL gel, and to evaluate their / in the photon energy range of 16.61 -25.26 keV using the x-ray fluorescence (XRF) configuration. The experimental results obtained will be compared with the theoretical values of water and breast tissue (75 % muscle and 25 % fat referred to as Breast 1 or young age breast by some authors) [9,12,13]. The theoretical values will be calculated using the NIST XCOM program.

Sample preparation
In order to investigate the / of the water-based PVAL gel samples, cylindrical gels of various thicknesses were required. Sixteen samples were fabricated in all. Four thicknesses for each concentration of PVAL gel were produced. The PVAL used was obtained from Sigma Aldrich with average molecular weight of 85,000 -124000 and 99+ % degree of hydrolysis.
The American College of Radiology (ACR) has established a scheme called BIRADS which stands for Breast Imaging Reporting and Data System. BIRADS has classified breast density on mammography into 4 categories in terms of the amount of fibro glandular and adipose tissue present in the breast. Category 1 breast is almost entirely fat (< 25% fibro glandular tissue), category 2 contain scattered areas of fibro glandular tissue (25 -50% fibrous tissue), category 3 breast are heterogeneously dense (50 -75% fibro glandular tissue) and category 4 is extremely dense breast containing more than 75% fibro glandular tissue [12]. As the amount of fibrous tissue in the breast increases, the sensitivity of the breast to mammography reduces. To mimic these categories of breast tissues, this study set out to fabricate 5, 10, 15 and 20 wt % PVAL gels. This means that for the 5% PVAL gel phantom, PVAL comprised of 5% of the entire weight of the water-based mixture. Same applies to the 10, 15 and 20% PVAL gels. The water based PVAL gel was prepared by dissolving PVAL crystals in deionised water at 90 ºC until a clear solution was obtained. The 5% w/v PVAL solution was prepared by dissolving 20 g of PVAL crystals in 380 ml of deionised water in a 500 ml boiling flask. The round bottomed flask containing the mixture was submerged in water placed on a magnetic hotplate and the flask was held in position by a retort stand. The round bottomed flask had 2 openings. A water-cooled condenser and thermometer were fitted into the openings to minimise water loss and monitor the temperature of the mixture respectively. The mixture was stirred continuously using a magnetic stirrer until the entire crystals dissolved. The solution was put to rest at room temperature for 2 hours to cool and eliminate bubbles. Various amounts of the solution were poured into four plastic moulds of height = 33 mm, diameter = 59 mm and volume = 90232.7 mm 3 to obtain 4 different thicknesses of phantoms. The same procedure was followed to prepare the 10, 15 and 20 % PVAL gel. The moulds containing the PVAL solution were placed in a freezer at -20 ºC for 12 hours, after which the frozen gels were thawed at room temperature; this is called one freeze thaw cycle (FTC). The phantoms were subjected to 2 FTCs to attain the elasticity of breast tissue [14]. Phantoms were stored in deionized water at 5 ℃ after the fabrication process was completed to avoid stiffness. The phantoms are considered stiff or rigid when they become dried and are no longer flexible, this can affect the size of the phantom.  An annular 241 Am radioactive source with approximate activity of 100 mCi and peak gamma energy of 59.54 keV was used to irradiate high purity metal targets to produce XRF photons. The metal targets used, and their corresponding energies were Niobium (Nb), Molybdenum (Mo), palladium (Pd), and tin (Sn) that produced Kα1 florescent x-rays of 16.61, 17.47, 21.17 and 25.27 keV respectively. The photon intensities were measured with a Low-Energy Germanium detector (LEGe). The signals were collected into a spectroscopy amplifier and multichannel analyzer (MCA). The XRF system was duly calibrated before measurements were taken. When a monoenergetic X-ray beam travels through an absorbing medium of thickness t, the intensity of the beam would be reduced as a result of attenuation. This can be evaluated by using the Beer-Lambert's law given by the equation: with I is the final photon intensity, I0 is the initial photon intensity and µ is the linear attenuation coefficient in which can be obtained by rearranging equation (1) as follows:

Sample preparation
The mass attenuation coefficient is obtained by dividing equation (2) by the density, of the sample: Furthermore, the theoretical values of the / of water and breast were calculated using the NIST XCOM software for the mentioned energy range, this is to present a comparison between the measured values and theoretical or XCOM values of the / of water and breast. The XCOM values will serve as a reference standard.

Results and discussion
The / of the 4 PVAL samples were compared to the theoretical values of the / of water and breast tissue calculated from XCOM as seen in Table 2. Based on the XCOM standard reference, it was found that all fabricated phantoms were equivalent to water and breast tissue. The phantom made with 5% PVAL showed results of being the most equivalent to water and phantoms made with 20% PVAL being the most equivalent to breast tissue. Table 2. The measured mass attenuation coefficients of PVAL gel samples based on characteristic xray energy of the metal plates.
Chi square (χ²) test was carried out to measure the level of discrepancy between the experimental values of the PVAL samples and the XCOM value of water as shown in table 2. A small value of the χ² function indicates that the experimental value agrees well with the actual or XCOM value. The χ² function is given by equation (4): with yi is the observed or experimental values, xi is the theoretical or XCOM values and σ is the standard deviation from the actual value.   From Table 3, it was observed that the phantom made with 5% PVAL has the lowest χ² value and therefore the closest to water. This is followed closely by phantoms made with 10, 15 and 20 % PVAL in that order, indicating that as the concentration of PVAL increases, the discrepancy between the value / and the XCOM value of water also increases.

Conclusion
The / of the fabricated water-based PVAL gel phantoms were investigated with the aim of achieving breast phantoms of various densities according to BIRADS classification.  6 5 and10% PVAL measured in the photon energy range of 16.61 -25.26 keV were found to be the closest to the XCOM value of water. On the other hand, the 20% PVAL phantom, which is the closest to XCOM value of breast, could mimic a BIRADS category 3 breasts which contains 50 -75% fibro glandular tissue in the diagnostic energy range. The results indicated the potential of the fabricated PVAL gel materials to be fabricated as phantoms for mammography.