# Development of a novel phantom using polyethylene glycol for the visualization of restricted diffusion in diffusion kurtosis imaging and apparent diffusion coefficient subtraction method

- Authors:
- Published online on: September 22, 2020 https://doi.org/10.3892/br.2020.1359
- Article Number: 52

#### Abstract

#### Introduction

Magnetic resonance imaging (MRI) is a widely adopted method used to conduct clinical tumor examination. Specifically, diffusion MRI is utilized for the early diagnosis of tumors and brain infarctions (1-3). The aim of the current study was to evaluate the potential of polyethylene glycol (PEG) phantoms for use as a standard phantom for restricted diffusion in MRI.

In a previous study, Matsuya et al (4) revealed that PEG phantoms may be used as the standard phantom for apparent diffusion coefficient (ADC). ADC, which indicates the average area that a water molecule moves per second, is calculated using diffusion-weighted MR images. In the body, there are two types of water-molecule diffusion (5). The first is free diffusion, which is defined as water-molecule movement in free space without the restriction of barriers. Free diffusion in solution is affected by temperature, viscosity and various other factors. The second type is restricted diffusion, which is defined as water-molecule movement that is impeded by membrane structures of cells in the body (6). ADC accounts for both free and restricted diffusion in MR images.

In recent years, new MR imaging techniques that represent restricted diffusion have been developed. One example of this is diffusion kurtosis imaging (DKI) (7) which has been developed and has been revealed to be as useful as ADC maps in certain clinical trials. A new technique for imaging restricted diffusion has recently been proposed; the ADC subtraction method (ASM) (8).

The current study aimed to evaluate the usability of polyethylene glycol (PEG) phantoms as standard phantoms for restricted diffusion in MRI. It was revealed that PEG phantoms may have the potential to be used as the standard phantoms, not only for ADC, but also for restricted diffusion in DKI and ASM. The current study details these phantoms and provides formulae for calculating PEG concentrations that enable us to create phantoms with arbitrary ADC, DKI and ASM values mimicking various tissues and tumors.

#### Materials and methods

###### Polyethylene glycol (PEG) phantom

The phantom (4) comprised: i) PEG (P3640-500G; Sigma-Aldrich; Merck KGaA) as a diffusion modifier; ii) NaN3 (Katayama Chemical Industry Co., Ltd.) as an antiseptic; and iii) distilled water.

The phantom solution was heated and diluted using distilled water to achieve concentrations of 20, 40, 60, 80, 100 and 120 mM with 0.03% w/w NaN3. The solution was transferred to microcuvettes (Halbmikro 1.5 ml; Greiner Labortechnik Manufacturing Ltd.) and used as the PEG phantoms. Subsequently, the cuvettes were installed in a phantom container (length, 12.5 cm; width, 10.5 cm; and height 9.5 cm) and were immersed in physiological saline (0.9% NaCl).

###### Bio-phantom

A bio-phantom (9) was prepared using Jurkat cells (Bio Resource Center) to ensure that the range of ADC, DKI and ASM values fall within the range of those of the PEG phantoms. Cells were cultured in 10% fetal bovine serum (Filtron Pty Ltd.), 1% penicillin-streptomycin-neomycin (Gibco; Thermo Fisher Scientific, Inc.) and RPMI-1640 medium (pH 7.4; Gibco; Thermo Fisher Scientific, Inc.). The incubation was carried out at 37˚C with 5% CO2. The number of cells with a diameter >8 µm was counted using an electric cell counter (Beckman Coulter, Inc.) prior to bio-phantom preparation, as the diameter of the majority of Jurkat cells is >8 µm (mean, 9.6 µm). After measuring the cell number, the cell solution was condensed to ~0.89 ml, transferred to a micro-cuvette (Halbmikro 1.5 ml; Greiner Labortechnik Manufacturing Ltd.), and centrifuged at 161 x g for 5 min. Thereafter, the supernatant was removed and the resulting bio-phantom was composed of pellet-like cells (density, ~1-8x108 cells/ml).

###### MRI device, image analysis software and statistical analysis software

A 3.0T MRI device (MAGNETOM Prisma VE11C; Siemens AG) was used which had a 20-channel head/neck coil. ImageJ 1.52a (National Institute of Health) was used for image analysis. Diffusional Kurtosis Estimator (DKE) version 2.6 was used for DKI image analysis.

###### Phantom-heating device

The phantom's temperature was adjusted to a temperature close to that of the human body (~37˚) by installing the phantom container in a heating device (constructed in-house) using ethylene-vinyl acetate copolymer. This heating device was connected to a circulating thermostatic chamber (Therm-Mate BF-41; Yamato Scientific Co., Ltd.).

###### Temperature measurement during MRI

An optic fiber thermometer (FLUOROPTICTM m3300; Luxtron Co.) was installed in the microcuvette in the phantom container and was utilized to monitor the phantom's temperature in real time.

###### Imaging conditions

Table I lists the imaging conditions for DKI and ASM. In DKI, single shot-echo planar imaging (SS-EPI) was used in three sequences; DKI-1, -2 and -3.

In ASM, two types of readout segmentation of long variable echo-train (RESOLVE) sequences were used; RESOLVE-basic and -modify. By changing the number of b-values, two types of DWI were obtained for ASM. For RESOLVE-basic sequences the b-values were set to different points; 0, 500 and 1,000 sec/mm2, and for RESOLVE-modify the b-values were set to 4 points: 0, 500, 1,000 and 10,000 sec/mm2 (Table I). As the number of b-values varied, the δ (motion probing gradient (MPG) pulse duration) and Δ (MPG pulse spacing) of both sequences changed. In the equation used to calculate b-values (equation 1), ‘Δ-δ/3’ is termed the effective diffusion time and represents the time during which diffusion phenomena are observed.

Equation 1: b=γ2G2δ2 x (Δ-δ/3)

In the above equation, γ represents the gyromagnetic ratio of protons and G is the gradient magnetic field strength. The 10,000 sec/mm2 b-value for RESOLVE-modify was used to lengthen the effective diffusion time. The effective diffusion times of RESOLVE-basic and RESOLVE-modify were set to 39.3 and 46.0 msec, respectively. Imaging of the PEG phantom was performed 60 times for ADC and ASM and 45 times for DKI.

Image processing of DKI. The DKI analysis software DKE (version 2.6) is available on the website of the Medical University of South Carolina (https://medicine.musc.edu/departments/centers/cbi/dki/dki-data-processing). The DWIs obtained by the imaging of DKI-1, -2 and -3 were processed using DKE to produce a mean kurtosis (MK) image (equation 2), which is a mean value of the spatial direction. By interpolated processing, the voxel size of the MK image becomes 1.0x1.0x1.0 mm.

Equation 2: S=S0 x exp (-b x ADC+b2 x ADC2 x MK/6)

In equation 2, S represents signal intensity and S0 is the signal intensity when the b-value=0 sec/mm2. The b-values used are exhibited in Table I.

###### Image processing of ASM

The ADC values (ADCb and ADCm) were calculated for RESOLVE-basic using the b-values: 0, 500 and 1,000 sec/mm2 and for RESOLVE-modify using the above 3 b-values from 0 to 1,000 sec/mm2 only. The 10,000 sec/mm2 b-value for RESOLVE-modify was not used to calculate the ADCm value. The formula used to calculate ASM is as follows:

Equation 3: ASM=|ADCb-ADCm|/(ADCb)3

###### Image evaluation

For MK images, MK values were determined from 1 region of interest (ROI) of 2x2 pixels in the PEG phantom and from ROIs of the same size in ≤6 areas per image of the physiological saline portion inside the phantom container.

Regarding ADCb and ASM, the signal intensity was determined from one ROI of 6x6 pixels selected in the PEG phantom, and from ROIs of the same size in ≤6 areas for each image of the physiological saline portion inside the phantom container. For DWI, signal intensity was determined from ROIs of 6x6 pixels in the images of RESOLVE-basic and RESOLVE-modify of each b-value. Each signal intensity value was logarithmically transformed. Subsequently, the ADC value for each ROI was calculated using the inverse of the slope and the ASM value was calculated using equation 3.

The total ROIs used for the calculation of the ADCb and ASM values was 74 for physiological saline, 6 for 20 mM, 12 for 40 mM, 6 for 60 mM, 14 for 80 mM, 6 for 100 mM and 16 for 120 mM PEG. The ROIs used for the calculation of MK values were 57 for physiological saline, 6 for 20 mM, 6 for 40 mM, 6 for 60 mM, 9 for 80 mM, 6 for 100 mM and 12 for 120 mM PEG.

To evaluate the same values for the bio-phantom, the MK values were determined from three ROIs of 4x1 pixels in the cellular section inside the bio-phantom, and from ROIs of the same size in 6 areas of the physiological saline portion inside the phantom container.

With regard to ADCb and ASM, the signal intensity was determined from four ROIs of 3x3 pixels selected in the cellular section of the bio-phantom. The signal intensity was also determined from 8 3x3-pixel ROIs located in the physiological saline portion of the phantom container. For DWI, signal intensity was determined from ROIs of 3x3 pixels in the images of RESOLVE-basic and RESOLVE-modify of each b-value. Each signal intensity value was logarithmically transformed. Then, the ADC value for each ROI was calculated from the inverse of the slope and the ASM value was calculated using Equation 3. The total ROIs used for the calculation of the ADC and ASM values was 12, 24 and 20 for cellularities of 46,522,778, 158,267,558 and 741,367,436 cells/ml, respectively. The ROIs used for the calculation of MK values were 9, 18 and 15 for cellularities of 46,522,778, 158,267,558 and 741,367,436 cells/ml, respectively.

#### Results

The mean temperature and SD inside the bio-phantom was maintained at 37.2±0.7˚C during imaging.

###### ADCb, MK and ASM values of PEG phantoms

An increase in PEG concentration was associated with a decrease in ADCb values (Fig. 1A). Conversely, MK (Fig. 1B) and ASM (Fig. 1C) values increased in line with increasing PEG concentrations. The mean ADCb and SD values of the 0 mM PEG phantom were 2.93±0.06x10-3 mm2/sec, and those for the 120 mM PEG phantom were 0.64±0.01x10-3 mm2/sec. MK values corresponding to the 0 mM and 120 mM PEG phantom were 0.04±0.01 and 1.20±0.14, respectively. The ASM calculations for the 0 mM and 120 mM PEG concentrations yielded 1,412±965 and 63,544±34,965 (sec/mm2)2, respectively.

###### ADCb, MK and ASM values of bio-phantoms

The final cellularity of the bio-phantom ranged from 0.47x108-7.41x108 cells/ml. The mean ADCb and SD values for the bio-phantoms were 2.31±0.05x10-3 mm2/sec for the low-cellularity phantom and 0.79±0.05x10-3 mm2/sec for the high-cellularity phantom (Fig. 2A). MK values ranged between 0.29±0.02 and 1.27±0.03 (Fig. 2B). ASM values ranged between 3,987±3,991 and 48,039±45,071 (sec/mm2)2 (Fig. 2C). The values for the bio-phantoms mostly lie within the range of the values produced for the PEG phantoms. Fig. 2 indicates the correlation between cellularity and ADCb, MK, and ASM values; moreover, all data (except for the highest MK cellularity values) were ascertained to be within the range of the PEG phantom results.

Fig. 3 displays ADCb, MK and ASM images of PEG and bio-phantoms. The ADCb and ASM images provide a higher resolution and less distortion compared with the MK image.

###### Empirical formula for calculating ADCb values of phantoms made using varying PEG concentrations

ADCb values for PEG phantoms with concentrations of 0, 20, 40, 60, 80, 100 and 120 mM were plotted as in Fig. 1A. Using these data points, a regression curve and an empirical formula were constructed facilitating the calculation of the ADCb values from phantoms produced using varying PEG concentrations. The correlation factor (R2) for this approximation was 1.00. The empirical formula to calculate the ADCb value corresponding to any PEG concentration (x) is as follows:

Formula 1: ADCb=a1x4+ a2x3+a3x2+a4x+a5

(a1, 0.0000066786969390685x10-6; a2, -0.0028279562 3507326000x10-6; a3, 0.484704389217086x10-6; a4, -48.0980342756939x10-6; a5, 2,935.33497680997x10-6).

###### Empirical formula for calculating MK values of phantoms made using varying PEG concentrations

MK values for PEG phantoms with concentrations of 0, 20, 40, 60, 80, 100 and 120 mM phantoms were plotted as in Fig. 1B. Using these data points, a regression curve and an empirical formula were created for calculating the MK values of phantoms made with varying PEG concentrations. The correlation factor (R2) for this approximation was 1.00. The empirical formula to calculate the MK value corresponding to any PEG concentration (x) is as follows:

Formula 2: MK=b1x6+b2x5+b3x4+b4x3+b5x2+b6x+b7

(b1, 0.00000000002574679427; b2, -0.000000009958 61887106; b3, 0.00000144033983524861; b4, -0.00009462031 704821070; b5, 0.00263877966804671000; b6, -0.0089848099 7102524000; b7, 0.03857894408353960000).

###### Empirical formula for calculating ASM values of phantoms made using varying PEG concentrations

ASM values for PEG phantoms with concentrations of 0, 20, 40, 60, 80, 100 and 120 mM phantoms were plotted as in Fig. 1C. Using these data points, a regression curve and an empirical formula were created for calculating the ASM values of phantoms made with varying PEG concentrations. The correlation factor (R2) for this approximation was 1.00. The empirical formula to calculate the ASM value corresponding to any PEG concentration (x) is as follows:

Formula 3: ASM=c1x6+c2x5+c3x4+c4x3+c5x2+c6x+c7

(c1, -0.0000004118023456; c2, 0.0000866210497676; c3, -0.0018022499380095; c4, -0.5404589664540250; c5, 34.3619915451854000; c6, -423.5577461123460000; c7, 1,411.8674192056000000).

###### Empirical formula for calculating ADCb values of bio-phantoms with any cellularity

ADCb values for bio-phantoms were plotted as in Fig. 2A. Using these data points, a regression curve and an empirical formula were created for calculating the ADCb values of bio-phantoms made with any cellularity. The correlation factor (R2) for this approximation was 1.00. The empirical formula to calculate the ADCb value corresponding to any cellularity (y) is as follows:

Formula 4: ADCb=d1ln(y)+d2

(d1, -552.230079387058x10-6; d2, 12,081.0508279336 00x10-6).

###### Empirical formula for calculating MK values of bio-phantoms with varying cellularity

MK values for bio-phantoms are plotted in Fig. 2B and the data points were used to create a regression curve and an empirical formula for the calculation of MK values of bio-phantoms made with varying cellularity. The correlation factor (R2) for this approximation was 1.00. The empirical formula to calculate the MK value corresponding to varying cellularity (y) is as follows:

Formula 5: MK=e1y2+e2y+e3

(e1, -0.00000000000000000108; e2, 0.00000000226921884 624; e3, 0.18153679067533800000).

###### Empirical formula for calculating ASM values of bio-phantoms with varying cellularity

The ASM values for bio-phantoms are exhibited in Fig. 2C. Using these data points, a regression curve and an empirical formula were created to calculate the ASM values of bio-phantoms made with varying cellularity. The correlation factor (R2) for this approximation was 1.00. The empirical formula to calculate the ASM value corresponding to varying cellularity (y) is as follows:

Formula 6: ASM = f1y2+f2y+f3

(f1, 0.00000000000008320968; f2, -0.0000021617730 7991540; f3, 3,907.60230188793000000000).

#### Discussion

In the present study, it was revealed that polyethylene glycol (PEG) phantoms are able to mimic a wide range of values, not only for the apparent diffusion coefficient (ADC), but also for restricted diffusion. Formulae were constructed in order to calculate PEG concentrations corresponding to arbitrary ADC, mean kurtosis (MK) and ADC subtraction method (ASM) values. The current results indicate that PEG phantoms may be used as a standard phantom for restricted diffusion with the desired MK and ASM values in MRI.

PEG, which is used as the base material for our standard phantom for ADC, MK and ASM, is a safe material and used as a base in many everyday products, including lapactics, skin creams and cosmetic emulsifiers (4). PEG phantom is safer than previously reported ADC standard phantoms-gelatinous substances such as agar (10), agarose (11) and polyacrylamide (12); and liquid solution materials such as ethanol (13), acetone (14-17), Gd-DTPA solution (18) and cupric sulfate solution (19). PEG phantom is also less expensive and easier to make than the previously reported ADC standard phantoms.

Matsumoto et al used a bio-phantom using tumor cells to visualize restricted diffusion (9). Bio-phantoms are complicated to create, time consuming and expensive, and impossible to use for a long time. The PEG phantom is ready to make, cheap and safe and can be stored for a long time.

PEG is a high molecular compound with a structure polymerized by ethylene glycol. Sehy et al (20) revealed that injecting PEG into cells decreased ADC, suggesting its suppressive action on water diffusion. In a previous study, Matsuya et al (4) proposed the use of PEG phantoms as the standard phantom for apparent diffusion coefficient (ADC). Empirical formulae were then constructed to calculate the PEG concentration at any measured temperature to obtain arbitrary ADC values for 1.5T MRI. Following the formulae, any phantoms with arbitrary ADC values can be made to mimic any tumors at any temperature.

ADC represents free and restricted diffusion in MR images. In recent years, new MR imaging techniques representing restricted diffusion have been developed. Of these, DKI is often considered the most promising and has been suggested as an alternative to ADC maps in clinical trials (7). A typical DKI protocol consists of a total of 60-70 images; and more data-demanding protocols are also available. Post-DKI data processing also requires significant time, especially in patients requiring urgent attention (e.g., critical cases and children). However, the superiority of DKI imaging supports developing the clinical and preclinical studies for DKI. Recently, faster imaging techniques for DKI have been already developed (21).

In a recent study, ASM was proposed as a new technique for restricted diffusion (8). ASM enables the observation of water-molecule diffusion with a space-separation resolution of 1 µm. ASM also produces a high image quality (without distortion) using readout segmentation of long variable echo-train (RESOLVE) sequences (22). Under the imaging conditions of this study, the resolution of ASM was higher than that of DKI (Fig. 3). If ASM's image quality were set to the same as that of DKI, ASM would take a much shorter imaging time than DKI in this study. The PEG phantom created in the current study is the first reported standard restricted diffusion phantom for DKI and ASM.

The MK values for the bio-phantoms predominantly fall within the range of the values for the PEG phantoms. Although the phantoms in the current study did not cover the upper limit for the bio-phantoms' MK (1.27±0.03), the maximum cell density covered by our phantom was calculated using empirical formula 5 to be 650,892,050 cells/ml.

MK values in clinical studies using 3T MRI have been previously reported for various tumors; for example, MK for grade II glioma is 0.50±0.08(23); for rectal cancer 1.000±0.112(24); for squamous cell carcinoma 0.917±0.144; and for olfactory neuroblastoma 1.209±0.262(25). ADC values for common tumors in clinical studies using 3T MRI vary between 0.62x10-3 mm2/sec (brain lymphoma) and 2.60x10-3 mm2/sec (neoplastic cystic lesions in the pancreas) (26). The current phantom covers the majority of these values and can therefore be used to mimic most common tumor types.

The ASM values of the bio-phantoms fall completely within the range of the values for the PEG phantoms, suggesting the usability of the phantom in the present study for future ASM experiments. To the best of our knowledge, this is the first paper to present a phantom covering ASM values of biological tissue since the advent of ASM.

There are a few limitations to this study. The equations in the present study were constructed according to values acquired using 3T MRI and sequences available for this experiment. Further examination may be necessary to clarify the effect of imaging conditions, such as the type of MRI devices and sequences used, to ensure the reproducibility of the current results. Furthermore, the mechanism by which PEG mimics restricted diffusion is yet to be elucidated, although there is a possibility that PEG molecules exert a limiting effect on the movement of water molecules. The PEG phantom, however, may have limitations in mimicking restricted diffusion beyond a certain point, since it does not have a concrete restricting structure (such as a membrane), but it was revealed to mimic restricted diffusion within a certain range of clinically reported DKI values. Therefore, this technique may prove useful for future experiments as long as the truncated range is accurately accounted for.

Using the newly developed MRI phantom, instead of imaging the actual tumor in the patient's body, a new method for imaging restricted diffusion might be developed by imaging the phantom with the MK value and ADC value of the tumor. Unlike clinical trials with patients, this phantom contributes to safe and cost-effective research. Improvement of imaging methods for future clinical dissemination of restricted diffusion imaging is expected worldwide and we believe this phantom will contribute to such research.

In conclusion, it was revealed that PEG decreased restricted diffusion and this indicates the potential of the PEG phantom as a standard phantom for restricted diffusion MRIs.

#### Acknowledgements

Not applicable.

#### Funding

The present study was partially supported by Grants-in-Aid for Scientific Research (grant nos. C22591335, 15K09924, and 19K0809801) from the Ministry of Health, Labour and Welfare of Japan.

#### Availability of data and materials

The materials and datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

#### Authors' contributions

AKh, YY and MK conceived and designed the study, processed the data and wrote the article. AKh, MK, YY, IS, BOB, KH, MB, NT, KK, KS, HI, AKu, TM, SO, SK and JA participated in conducting the experiments. IS, AKh, KH, MB and NT edited the article. All authors read and approved the final version of the manuscript.

#### Ethics approval and consent to participate

Not applicable.

#### Patient consent for publication

Not applicable.

#### Competing interests

The authors declare that there are no competing interests regarding the publication of the present manuscript.

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