A new phantom and empirical formula for apparent diffusion coefficient measurement by a 3 Tesla magnetic resonance imaging scanner

The aim of this study was to create a new phantom for a 3 Tesla (3T) magnetic resonance imaging (MRI) device for the calculation of the apparent diffusion coefficient (ADC) using diffusion-weighted imaging (DWI), and to mimic the ADC values of normal and tumor tissues at various temperatures, including the physiological body temperature of 37°C. The phantom was produced using several concentrations of sucrose from 0 to 1.2 M, and the DWI was performed using various phantom temperatures. The accurate ADC values were calculated using the DWIs of the phantoms, and an empirical formula was developed to calculate the ADC values of the phantoms from an arbitrary sucrose concentration and arbitrary phantom temperature. The empirical formula was able to produce ADC values ranging between 0.33 and 3.02×10−3 mm2/sec, which covered the range of ADC values of the human body that have been measured clinically by 3T MRI in previous studies. The phantom and empirical formula developed in this study may be available to mimic the ADC values of the clinical human lesion by 3T MRI.


Introduction
Diffusion-weighted magnetic resonance imaging (MRI) has been increasingly performed for clinical purposes, including the detection of tumors and cerebrovascular diseases. The apparent diffusion coefficient (ADC) value, which is calculated based on diffusion-weighted imaging (DWI) using several b values, is useful for discriminating whether the lesion is benign or malignant and determining the therapeutic effect of a tumor. Recently, popularized 3 Tesla (3T) MRI devices have shown a performance advantage when calculating accurate ADC values. Several clinical studies have revealed that ADC values from 3T MRI have the diagnostic value as a quantitative parameter (1)(2)(3)(4)(5)(6)(7)(8). However, to the best of our knowledge, there are no reports of an ADC phantom for 3T MRI. With regard to ADC phantoms for 1.5T MRI, Tamura et al (9) reported a phantom that used gelatin and sucrose. While Matsuya et al (10) reported a phantom using polyethylene glycol for 1.5T MRI, and created empirical formulas to calculate polyethylene glycol concentration, which provide arbitrary ADC values at any temperature measurement. In principle, the ADC value of a phantom differs due to its temperature. In the present study, an ADC phantom was developed using sucrose for 3T MRI, which produces arbitrary ADC values due to a range of phantom temperatures (28-39˚C), which includes the physiological body temperature. This is the first temperature-controlled ADC phantom for 3T MRI, which mimics the ADC values of the normal and tumor tissues of the human body. In addition, the developed empirical formula enables the calculation of a sucrose concentration that provides arbitrary ADC values at any phantom temperature.

Correspondence to: Professor Masahiro Kuroda, Department
Preparation for the MRI of sucrose phantoms. Sucrose phantoms were placed into a container filled with 0.9 M sucrose solution and 0.03% (w/w) NaN 3 . The container was able to hold a maximum of 16 phantoms (Fig. 1B).
Heating system. The phantom case container was enclosed in a heating box (Fig. 1C) made of Styrofoam that was produced in-house (Department of Radiological Technology, Graduate School of Health Sciences, Okayama University, Okayama, Japan). The container was heated in the gantry of an MRI scanner via a tube that was connected to a circulating temperature-regulated water bath (Thermo-Mate BF-41; Yamato Scientific Co., Ltd., Tokyo, Japan; Fig. 1D), to maintain the desired phantom temperature during the MRI.
Real-time phantom temperature monitoring. Optical fiber thermometers (Fluoroptic™ thermometer m600; Luxtron Co., Mountain View, CA, USA; Fig. 1E) were placed into the phantoms. The phantom temperature was monitored every 30 sec during the MRI to ensure a constant temperature.

MRI.
A clinical 3T MRI unit (Magnetom Skyra; Siemens, Erlangen, Germany) with a head coil was used for the MRI. DW images were acquired by a three-scan trace, in the phase-encoding, readout and slice-selective directions, via a single-shot echo-planar imaging sequence. The scan parameters were set as follows: 8,000 msec of relation time; 100 msec of echo time; 220x220-mm field of view; 160x112 matrix; b values of 0, 300, 600, 900, 1200, 1500, 1800, 2100, 2400, 2700 and 3000 sec/mm 2 ; a thickness of 5 mm; one excitation number; 26.2-msec diffusion gradient pulse duration (δ); and 47.1-msec diffusion time (Δ), which was the interval between the onset of the diffusion gradient pulses. Each DW image of a maximum of four phantoms was obtained at each ~1˚C interval to cover the physiological body temperature within the range of 28-39˚C.

Results
Calculation accuracy of ADC values. For each concentration and temperature of the sucrose phantoms, the ADC values were calculated. The 10 sets of ADC values and their R 2 values were obtained by the least-squares method for each set of data from 11 DW images using 11 b values to two DW images using two b values in order of decreasing b value. As an example, Fig. 2 indicates the procedure to calculate the ADC value of a 0.2 M phantom at a temperature of 37.09˚C. Among 10 sets of ADC values and their R 2 values, when the maximum b value decreased to 1,500 sec/mm 2 (Fig. 2E), the R 2 value obtained for the set of data from six DW images using six b values exceeded 0.99 to become 0.9935. According represents the data that were used for the least-squares method to obtain the regression line and the R 2 value. '◊' represents the data that were not used for the least-squares method to obtain the regression line and the R 2 value.
Validation of the accuracy of the empirical formula. Fig. 4A indicates the calculated ADC values using the empirical formula shown as the three-dimensional graph with the correlation among

A B C
ADC values, sucrose concentration and phantom temperature.
The ADC values decreased according to an increase in sucrose concentration and decrease in phantom temperature. Fig. 4B indicates the correlation between the ADC values, which have been used to make the empirical formula, and the ADC values calculated using the empirical formula. The formula appears to mimic well all the ADC values that were initially used to create it. Fig. 4C indicates the correlation between the ADC values measured using the verification phantoms and the ADC values calculated using the empirical formula. In total, 66.67% of the calculated ADC values were less than one SD away from the mean of the measured ADC values of verification phantoms; 97.22% of the calculated ADC values were less than two SDs away from the mean; and 100% of calculated ADC values were less than three SDs away from the mean.

Discussion
To the best of our knowledge, this is the first study to report ADC phantoms for DW images with 3T MRI. ADC phantoms were produced for 3T MRI using sucrose, and an empirical formula was developed to calculate ADC values between 0.33-3.02x10 -3 at arbitrary sucrose concentrations between 0-1.2 M and arbitrary phantom temperatures between 28-39˚C, including the physiological temperature of 37˚C to mimic the normal and tumor tissue of the human body. Sucrose, a large molecule with the formula of C 12 H 22 O 11 , is a safe and inexpensive material, with a concentration that can be easily controlled. The diffusion coefficient of the material (D) was associated with the temperature (t), the viscosity of the medium (η), and the radius of the diffusion molecule (r) using the Stokes-Einstein equation (11): D = kt/6πηr, where k is the Boltzmann constant (1.3805x10 -23 J K -1 ). Therefore, sucrose with a large molecular size of 0.9 nm in diameter was selected as the material for the phantoms to decrease the ADC values (12).
According to the Stokes-Einstein equation, ADC values are affected by the temperature of the objects in question. As the ADC values used in clinical MRI diagnosis are measured for the human body at 37˚C, ADC phantoms that mimic human body tissue should be comparable. Sasaki et al (13) measured the ADC values of bio-phantoms using human Burkitt's lymphoma cells at 37˚C; however, the majority of in vitro studies have performed the ADC measurement at a lower temperature (14)(15)(16). Tamura et al (9) reported an ADC phantom using 10-50% (wt/wt) sucrose for 1.5T MRI, which covers the range of ADC values between 0.2 and 1.8x10 -3 mm 2 /sec for temperatures between 6 and 20˚C. In the pre-examination of the present study, the ADC values were measured at temperatures between 6-39˚C. The R 2 values of the first-order approximation of the correlation between the ADC values and phantom temperature were low for phantoms of high sucrose concentration at temperatures of <27˚C. Therefore, the temperature range of 28-39˚C was used to create the empirical formula.
This empirical formula covered ADC values from 0.672.47x10 -3 mm 2 /sec at a physiological temperature of 37˚C.
The ADC values of the phantoms almost covered the ADC values of the normal and tumor tissues of the human body that are measured clinically by 3T MRI, as summarized in Table I (1,3,(5)(6)(7)(8)(17)(18)(19). Table I indicates the sucrose concentration of the ADC phantoms at 37˚C, which mimic each tissue of the human body using the empirical formula.
One limitation of this study was that the sucrose phantoms produced ADC values due to changes in free diffusion alone. The actual in vivo diffusion in the human body is affected not only by the change of free diffusion, but also various factors, including perfusion and the change of restricted diffusion, due to cellular membrane structures and cell density (20)(21)(22)(23)(24)(25)(26). This new ADC phantom and empirical formula for 3T MRI has the potential to be used in a number of applications.