Diffusion weighted images (DWIs) have been reported useful for early diagnosis of tumors and cerebrovascular disorders such as cerebral infarction in clinical practice for magnetic resonance imaging (MRI) (1–3). The apparent diffusion coefficient (ADC) map calculated from DWIs is also used clinically, reflecting both free and restricted diffusion. Free diffusion occurs in the absence of a physical barrier and represents the normal distribution of water molecules spreading during a certain time. Restricted diffusion occurs with barriers such as membranes and multiple compartments in living organisms (4).

Recent techniques such as diffusion kurtosis imaging (DKI) (5,6), which analyze the movement of water molecules in restricted diffusion, have been reported. DKI shows restricted diffusion as an index of kurtosis, indicating the degree of deviation from the normal distribution. Recent clinical research indicates that DKI is useful to diagnose acute stage cerebral infarction, glioma, Alzheimer's disease, Parkinson's disease, attention deficit hyperactivity disorder, multiple sclerosis, temporal lobe epilepsy, traumatic brain injury and spinal cord lesions (7–20). Among restricted diffusion imaging techniques, DKI has advantages such as high specificity for restricted diffusion; a small number of b-values, which results in a relatively short imaging time; and quantitative capability. However, it has disadvantages such as the difficulty to understand intuitively the value of the kurtosis, due to the lack of assumption of the biophysical model; the variation in the kurtosis depending on the range of the b-value; and the requirement for specialized software for DKI. For the above reasons, DKI has not been used in routine clinical practice.

The present study developed a novel method to visualize restricted diffusion differently from DKI. Two ADC values with different diffusion times were used, and the difference between them was calculated. This method was referred to as ‘apparent diffusion coefficient (ADC) subtraction method (ASM)’. The purpose of the present study was to compare ASM and DKI in order to examine whether ASM can reveal restricted diffusion using a cell-containing bio-phantom that was developed by our group.

The mean temperature and SD inside the bio-phantom during imaging were 37.2±0.7°C. The cell densities of the low cell density phantom and the highest cell density phantom were 1.21×10⁸ and 7.41×10⁸ cells/ml, respectively. The mean ADC_b and SD values of physiological saline, low cell density phantom and the highest cell density phantom were 2.95±0.08×10⁻³, 1.90±0.35×10⁻³ and 0.79±0.05×10⁻³ mm²/sec, respectively (Fig. 1). As the cell density increased, the ADC_b decreased. A significant difference was observed using the Steel-Dwass method among the 3 groups. The mean MK and SD values of physiological saline, low cell density phantom and the highest cell density phantom were 0.04±0.01, 0.44±0.13 and 1.27±0.03, respectively (Fig. 2). The mean ASM and SD values of physiological saline, low cell density phantom and the highest cell density phantom were 0.25±0.20×10⁴, 0.51±0.41×10⁴ and 4.80±4.51×10⁴ (sec/mm²)², respectively (Fig. 3). In contrast to the ADC_b, the MK and ASM values increased as the cell density increased. Significant differences were observed among the 3 groups for both MK and ASM values.

In the present study, a novel method named ASM was developed and its usefulness was demonstrated experimentally.

DWI is widely used clinically. There are two types of diffusion: Free and restricted, and both are represented by the ADC value. In recent years, imaging techniques such as DKI, which expresses restricted diffusion, have appeared and have been reported to be useful in the clinic. However, the method of imaging restricted diffusion is limited. In the present study, a novel method named ASM was developed and its usefulness was demonstrated experimentally. DKI is an imaging technique that quantitatively reveals how water molecules deviate from free diffusion. DKI has been reported to have more potential to evaluate the actual microstructure in vivo than an ADC map (5,6). Among restricted diffusion imaging techniques, DKI has advantages such as high specificity for restricted diffusion; a small number of b-values, which results in a relatively short imaging time; and quantitative capability. Greater the b-values, the stronger the diffusion weighting, the higher the contrast in pathogenic tissues. In the present study, DKI, which is a diffusion analysis method of non-normal distributions, was considered the standard to evaluate restricted diffusion and was compared with ASM. Numerous clinical studies using DKI have been reported. Hempel et al (27) observed a strong correlation between the grade of glioma and the MK value, stating that the higher the grade, the higher the MK value. Qi et al (28) also reported that the MK value increases as the grade of glioma and cell density increase. Wu et al (29) stated that the ADC value increases, while the MK value decreases, as a result of chemotherapy in cervical non-Hodgkin lymphoma. Wang et al (30) reported that the ADC value is low, while the MK value is high, in bladder tumors compared with bladder inflammation. Barrett et al (31) also stated that ADC values are low while MK values high in prostate cancer compared with normal prostate tissue. These results were similar to those of our study using bio-phantoms.

In the present study, the distance of the extracellular space was calculated by Kepler conjecture (32), with cell densities of the low cell density phantom and the highest cell density phantom of 1.21×10⁸ and 7.41×10⁸ cells/ml, respectively. The Kepler conjecture is a mathematical theorem about sphere packing in three-dimensional Euclidean space, which states that the maximum volume of closely-packed equally-sized spheres is ~74.05% of the total volume of the Euclidean space. The total volume of the spheres in 1 ml is 0.7405 ml, which is 74.05%. Assuming that the cell is a sphere, the volume of one sphere can be determined by dividing the total volume of the spheres by the cell density. The radius of the sphere is calculated from the volume of the sphere. Since the cells are not closely packed in 1 ml, the calculated radius of the sphere is larger than the actual cell radius. Doubling the calculated radius of the sphere indicates the distance between cell centers. The cell diameter minus this distance between cell centers is defined as the distance between cell membranes (extracellular space) to evaluate the volume of the extracellular space. Since the cell diameter used in the present study is 9.6 µm (22), the distance of the extracellular space of the low cell density phantom is 13.1 µm, while that of the maximum cell density phantom is 2.8 µm (Fig. 4). The size of the intracellular space is the cell diameter, i.e. 9.6 µm.

The observation range of the diffusion phenomenon was calculated from the used effective diffusion time. This range changes according to the effective diffusion time. The subtraction of two ADC values via ASM, obtained using different diffusion times, may enable to observe diffusion phenomena in a narrow space. Although the ADC value itself may reflect both free and restricted diffusion, ASM may obtain information on restricted diffusion between cell membranes. The effective diffusion times of RESOLVE-basic and RESOLVE-modify are 39.3 and 46.0 msec, respectively. The Stokes-Einstein equation (33) indicates that water diffusion at 37°C is 3.0×10⁻³ mm²/sec. The range of water diffusion can be obtained by multiplying the ADC value of water, which is 3.0×10⁻³ mm²/sec at 37°C, by the effective diffusion time. Then, the diameter of the range of water diffusion was calculated to be 12.3 and 13.3 µm for ADC_b using RESOLVE-basic and ADC_m using RESOLVE-modify, respectively. ASM may represent the difference between the two diameters, a range of 1.0 µm (Fig. 4).

In our results, the higher the cell density and the narrower the extracellular space, the lower was the ADC value, and conversely, both MK and ASM values increased. Conventionally, DKI is expected to be able to image restricted diffusion, and our data also support that DKI reflects restricted diffusion in the extracellular space. Similarly, ASM may express the extent of restricted diffusion in the extracellular space.

In the present study, the imaging time of ASM (32.5 min in total) was longer than that of DKI (14 min in total). The image quality of DKI is lower than that of ASM. RESOLVE, used in ASM, is reported to improve image quality without distortion and make ADC values accurate (21). The reason for the length of the imaging time of current ASM is the high resolution and the high number of averages and segments to improve the image quality of ASM. If the image quality of ASM is set to be the same as that of DKI, the imaging time of ASM decreases to ~6 min, which is shorter than that of DKI. In the future, it is necessary to develop an ASM sequence for clinical research that shortens the imaging time while maintaining the image quality.

In ASM using RESOLVE-basic and RESOLVE-modify, the present study did not explore the effect of varying each effective diffusion time. If each effective diffusion time used in ASM differs, the degree of restricted diffusion may change. However, the 3.0T devices commonly used clinically have limitations in regard to changing the range of diffusion time remarkably.

In conclusion, using bio-phantoms, the present study clarified that DKI mainly reflects restricted diffusion in the extracellular space. Similarly, ASM may reflect the extent of restricted diffusion in the extracellular space. Future clinical studies are expected to demonstrate the potential of ASM as a useful tool for clinical imaging such as ADC maps.