In order to visualize restricted diffusion, the present study developed a novel method called ‘apparent diffusion coefficient (ADC) subtraction method (ASM)’ and compared it with diffusion kurtosis imaging (DKI). The diffusion-weighted images of physiological saline, in addtion to bio-phatoms of low cell density and the highest cell density were obtained using two sequences with different effective diffusion times. Then, the calculated ADC values were subtracted. The mean values and standard deviations (SD) of the ADC values of physiological saline, low cell density and the highest cell density phantoms were 2.95±0.08×10^{−3}, 1.90±0.35×10^{−3} and 0.79±0.05×10^{−3} mm^{2}/sec, respectively. The mean kurtosis values and SD of DKI were 0.04±0.01, 0.44±0.13 and 1.27±0.03, respectively. The ASM and SD values were 0.25±0.20×10^{4}, 0.51±0.41×10^{4} and 4.80±4.51×10^{4} (sec/mm^{2})^{2}, respectively. Using bio-phantoms, the present study demonstrated that DKI exhibits restricted diffusion in the extracellular space. Similarly, ASM may reflect the extent of restricted diffusion in the extracellular space.

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) (

Recent techniques such as diffusion kurtosis imaging (DKI) (

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.

A microcuvette (halbmikro 1.5 ml; Greiner Labortechnik Manufacturing Ltd., Greiner, Germany) was installed in a phantom container that had an outer diameter of 9.5 cm in length, 14 cm in width and 7 cm in height (

As bio-phantom, Jurkat cells were used, which were purchased from Bio Resource Center (Tsukuba, Japan). For cell culture, 10% fetal bovine serum (Filtron Pty Ltd., Victoria, Australia) and 1% penicillin-streptomycin-neomycin (Gibco; Thermo Fisher Scientific, Inc., Waltham, MA, USA) were added to RPMI-1640 medium (pH 7.4; Gibco; Thermo Fisher Scientific, Inc.). The incubation was carried out at 37°C with 5% CO_{2}. The number of cells with a diameter >8 µm was counted with an electric cell counter (Coulter Electronics Ltd., Luton, UK) prior to bio-phantom preparation, since the diameter of the majority of Jurkat cells is >8 µm, with the mean diameter being 9.6 µm (^{8} cells/ml. Upon treatment, the cells were enclosed in gellan gum (P-8169; Sigma-Aldrich; Merck KGaA, Darmstadt, Germany). Two types of bio-phantom were prepared. One was a pellet-like high cell density phantom, and the other was a low cell density phantom fixed with gellan gum. Each bio-phantom was enclosed in a phantom container.

A 3.0T MRI system (MAGNETOM Prisma VE11C; Siemens AG, Munich, Germany) was used, which had a 20-channel head/neck coil. The image analysis software used was Image J (National Institutes of Health, Bethesda, MD, USA) (

A phantom container was installed in a self-constructed bio-phantom heating device, which was formed of ethylene-vinyl acetate copolymer and was connected to a circulating thermostatic chamber (Thermo-Mate BF-41; Yamato Scientific Co., Ltd., Tokyo, Japan). The temperature of the bio-phantom was adjusted to ~37°C, similarly to human body temperature.

For real-time phantom temperature measurements, an optical fiber thermometer (Fluoroptic™ m3300, Luxtron Co., Santa Clara, CA, USA) was installed in the micro-cuvette during MRI.

^{2}. For RESOLVE-modify, the b-values were set to 4 points: 0, 500, 1,000 and 10,000 sec/mm^{2} (

In the above formula, γ is the gyromagnetic ratio of protons and G is the gradient magnetic field strength. The effective diffusion time of RESOLVE-basic and RESOLVE-modify were 39.3 and 46.0 msec, respectively. The extension of the effective diffusion time has an upper limit. The effective diffusion time of this modification sequence is elongated until this limit. Imaging of both DKI and ASM was performed 5 times for the high cell density phantom and 9 times for the low cell density phantom.

DKI image analysis software DKE version 2.6 is published on the website of the Medical University of South Carolina (

In the above formula, S is signal intensity and S_{0} is the signal intensity when the b-value is 0 sec/mm^{2}. The b-values used are shown in

The ADC values (ADC_{b} and ADC_{m}) were calculated for RESOLVE-basic using the 3 b-values: 0, 500 and 1,000 sec/mm^{2}, and for RESOLVE-modify using the above 3 b-values from 0 to 1,000 without 10,000 sec/mm^{2}. The formula used to calculate ASM is shown in Equation 3. As the variation of ADC values increases when ADC values are high, the absolute difference between ADC values (ADC_{b} and ADC_{m}) is divided by ADC_{b} value three times in ASM to adjust the variation of ADC values.

Regarding the MK image, the MK values were determined from three regions of interest (ROI) of 1×4 pixels in the cell part 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 ASM, the signal intensity was determined from four ROIs of 3×3 pixels selected in the cell part of the bio-phantom. For DWI, each b-value was obtained from the imaging of RESOLVE-basic and RESOLVE-modify. The signal intensity was also determined from 8 same-sized ROIs located in the physiological saline portion of the phantom container. 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.

Regarding the ADC_{b}, MK and ASM values, a multiple comparison test using the Steel-Dwass method was performed at a significance level of 5% between saline, low cell density phantom and the highest cell density phantom.

The total number of ROIs used for the calculation of the ADC and ASM values were 112 for physiological saline, 36 for low cell density phantom and 20 for the highest cell density phantom. The values used for the calculation of MK values were 84 for normal saline, 27 for low cell density phantom and 15 for the highest cell density phantom.

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 1.21×10^{8} and 7.41×10^{8} 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} mm^{2}/sec, respectively (_{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 (^{4}, 0.51±0.41×10^{4} and 4.80±4.51×10^{4} (sec/mm^{2})^{2}, respectively (_{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 the present study, the distance of the extracellular space was calculated by Kepler conjecture (^{8} and 7.41×10^{8} 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 (

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 (^{−3} mm^{2}/sec. The range of water diffusion can be obtained by multiplying the ADC value of water, which is 3.0×10^{−3} mm^{2}/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 (

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 (

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.

Not applicable.

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.

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

YY and MK conceived and designed the study, processed the data and wrote the article. YY, MK, IS, AK, BOB, KH, MB, NT, AK, TM, SO, SK and JA performed the experiments. IS, AK, KH, MB and NT edited the article. All authors read and approved the final version of the manuscript.

Not applicable.

Not applicable.

The authors declare that they have no competing interests.

ADC values using RESOLVE-basic. White, gray and black columns indicate physiological saline, low cell density phantom and the highest cell density phantom, respectively. *P<0.05. RESOLVE, readout segmentation of long variable echo-trains. ADC, apparent diffusion coefficient.

Mean kurtosis values. White, gray and black columns indicate physiological saline, low cell density phantom and the highest cell density phantom, respectively. *P<0.05.

ASM values. White, gray and black columns indicate physiological saline, low cell density phantom and the highest cell density phantom, respectively. *P<0.05. ASM, apparent diffusion coefficient subtraction method.

Correlation between the size of intracellular and extracellular spaces and the diffusion observation range using each method. (A) Low cell density phantom. (B) The highest cell density phantom. IC, intracellular space; EC, extracellular space; ADC_{b}, the apparent diffusion coefficient value using RESOLVE-basic; ADC_{m}, apparent diffusion coefficient value using RESOLVE-modify. RESOLVE, readout segmentation of long variable echo-trains.

Imaging conditions of diffusion kurtosis imaging and ASM.

ASM | DKI | ||||
---|---|---|---|---|---|

Parameters | RESOLVE-basic | RESOLVE-modify | DKI-1 | DKI-2 | DKI-3 |

TR (msec) | 8,000 | 8,000 | 6,000 | 6,000 | 6,000 |

TE (msec) | 86 | 106 | 75 | 75 | 75 |

ES (msec) | 0.56 | 0.56 | 0.93 | 0.93 | 0.93 |

FOV (mm) | 120 | 120 | 120 | 120 | 120 |

Matrix | 224×224 | 224×224 | 82×82 | 82×82 | 82×82 |

BW (Hz/pixel) | 399 | 399 | 1,220 | 1,220 | 1,220 |

Averages | 2 | 2 | 1 | 1 | 9 |

Segments | 7 | 7 | 1 | 1 | 1 |

Slice thickness (mm) | 5 | 5 | 5 | 5 | 5 |

Slice number | 1 | 1 | 5 | 5 | 5 |

Phase direction | AP | AP | AP | AP | AP |

δ (msec) | 5.6 | 15.6 | 13.8 | 13.8 | – |

Δ (msec) | 41.2 | 51.2 | 33.5 | 33.5 | – |

Diffusion time (msec) | 39.3 | 46.0 | 28.9 | 28.9 | – |

b-value (sec/mm^{2}) |
0,500,1,000 | 0,500,1,000,10,000 | 0,500,1,000 | 0,500,1,000 | 0 |

Diffusion direction | 3 | 3 | 30 | 30 | – |

Imaging time (min:sec) | 13:28 | 19:06 | 6:24 | 6:24 | 1:12 |

ASM, apparent diffusion coefficient subtraction method; DKI, diffusion kurtosis imaging; RESOLVE, readout segmentation of long variable echo-trains; TR, repetition time; TE, echo time; ES, echo space; FOV, field of view; BW, band width; AP, antero-posterior; δ, motion probing gradient (MPG) pulse duration; Δ, MPG pulse spacing.