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A modified tri-exponential model for multi-b-value diffusion-weighted imaging to detect the strictly diffusion-limited compartment and its initial application in grading and differential diagnosis of gliomas
Qiang Zeng1, Biao Jiang2, Jianmin Zhang1, Feina Shi3, Fei Dong2, and Chenhan Ling1

1Department of Neurosurgery, Second Affiliated Hospital of Zhejiang University College of Medicine, Hangzhou, People's Republic of China, 2Department of Radiology, Second Affiliated Hospital of Zhejiang University College of Medicine, Hangzhou, People's Republic of China, 3Department of Neurology, Second Affiliated Hospital of Zhejiang University College of Medicine, Hangzhou, People's Republic of China

Synopsis

In this study, we focused on the strictly diffusion-limited compartment with extremely low ADC. Because of the negligible signal attenuation of this compartment, the ADC of this compartment was set as zero. By adding this compartment to the two-compartment model, we presented a modified tri-exponential model. The AICcs of this model were found to be lower than the bi-exponential model and the conventional tri-exponential model, indicating this model is the best. Additionally, the parameters derived from this model, especially the fraction of the strictly diffusion-limited compartment (f0), showed potential clinical value in distinguishing the grade of malignancy of tumors.

Introduction

In order to detect the real distribution of water diffusion in tissues, many models have been developed 1-3, including multi-compartment models. Both the two-compartment model and models with more compartments face many challenges 4-10. Previous studies have indicated the existence of the strictly diffusion-limited compartment with extremely low ADC in tissues and even cells 10-14. However, the existing models do not contain this compartment. The signal attenuation of this compartment is negligible at normal b-values. Hence, the ADC of this compartment could be set to zero mathematically. By adding this compartment to the two compartments model and setting the ADC of this compartment as zero, we developed a modified tri-exponential model (see equation [1]). According to our hypothesis, the strictly diffusion-limited compartment represents water molecules strictly limited in microstructures, such as intracellular organelles and myelin sheath. Hence, f0 represents the volume fraction of these microstructures. Our first study was to compare this new model with the bi-exponential model and the conventional tri-exponential model. Secondly, we also performed an initial study to apply this model in grading and differential diagnosis of gliomas.

S=S0*(f0+fslow*e-ADCslow*b+ffast*e-ADCfast*b) [1]

where f0+fslow+ffast=1, f0 is the fraction of the strictly diffusion-restricted compartment, and fslow and ffast are corresponding fractions of ADCslow and ADCfast.

Methods

Firstly, multi-b-value diffusion-weighted imaging (DWI) with 17 b-values up to 8000 s/mm2 were achieved from 6 volunteers. The DWI images with the first 16 b-values were used for curve fitting. The corrected Akaike information criterions (AICcs) were calculated to determine the best model. Then the signal intensities at b = 8000 s/mm2 were predicted, and the errors between the predicted and measured values were squared to form the squared predicted errors (SPEs). This index was used to identify whether models could accurately predict the signal attenuation at ultra-high b-value. Secondly, we performed a retrospective study based on our prospectively collected database for gliomas. 18 low-grade gliomas (LGG), 45 high-grade gliomas (HGG) and 5 primary central nervous system lymphomas (PCNSL), who underwent a pre-operative DWI with 9 b-value up to 3000 s/mm2, were enrolled in this study. Parametric maps were derived from the modified tri-exponential model. The receiver operating characteristic and the Pearson rank correlation were used for statistical analysis.

Results

For the first study, in all white matter ROIs: the AICcs of the modified tri-exponential model were the lowest (p < 0.05, except for one ROI); the SPEs of the bi-exponential model were the highest (p < 0.05). The mean f0, fvery-slow and ADCvery-slow values were ranging 11.9 - 18.7%, 11.9 – 18.3% and 1 – 7 × 10-6 mm2/s respectively in white matter ROIs, and 1.2 - 2.7%, 11.9 - 15.7% and 251 – 445 × 10-6 mm2/s respectively in gray matter ROIs. For the second study, the mean f0 values for PCNSL, HGG and LGG were 13.98%, 6.98% and 3.14% respectively. Four parameters (f0, fslow, ffast and ADCslow) showed ability in distinguishing HGG from LGG (AUC = 0.901, 0.720, 0.829 and 0.813 respectively) and PCNSL from gliomas (AUC = 0.981, 0.652, 0.943 and 0.844 respectively), and showed moderate correlation with the Ki-67 index (r = 0.638, 0.444, -0.595 and -0.518 respectively). Among these parameters, f0 showed the highest clinical value.

Discussion

Firstly, the f0 values were large in white matter, PCNSL and HGG, suggesting the strictly diffusion-limited compartment is a significant component in white matter and high malignant tumors, and the existence of this compartment cannot be explained only by noise. The modified tri-exponential model with lowest AICc is considered as the best among three models. The bi-exponential model was found to be an over-fitting model, while the convention tri-exponential model was found to be an over-fitting model. Besides, ADCvery-slow values were much higher in gray matter than in white matter, which demonstrates that the biological implication for the ADCvery-slow compartment differs among tissues. Models with more compartments may also face this critical limitation. The f0 was consistence with the fraction of myelin sheath in white matter (10 - 20%) 15,16. Higher malignant tumors associate with higher cell density. Besides, swollen organelles have been detected in high malignant tumors 17-20, which may be due to vigorous metabolism and relatively hypoxia. Accordingly, the volume fraction of organelles may have positive correction with tumor malignancy. This may explain why f0 has ability in distinguishing the grade of malignancy of tumors.

Conclusion

The modified tri-exponential model is the best among these three models. The fraction of the strictly diffusion-limited compartment (f0) derived by the new model has important biological implication, and has potential value in distinguishing the grade of malignancy of tumors.

Acknowledgements

This work was supported by the Natural Science Foundation of Zhejiang (Grant number:LY13H180006) and the Medicine and Health Research Foundation of Hangzhou (Grant number: 20140633B25). The authors thank the participants, as well as the MR technicians of our center for necessary modifications to the sequence.

References

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Figures

Figure 1. DWI images achieved with b = 0 (a), 1000 (b), and 8000 s/mm2 (c) from one volunteer. Plots of the average signal-intensity decay of two ROIs as a function of b (d). CG: cingulate gyrus; CCg: genu of the corpus callosum.

Figure 2. The fitting curves of the three models with the first 16 b-values in a typical voxel of white matter (a). The maps of the squared prediction errors (SPE) derived by the bi-exponential model (b), the conventional tri-exponential model (c), and the modified tri-exponential model (d). The unit for SPE is ×10-5.

Figure 3. Images of a 43-year-old man with glioblastoma (a-f), a 32-year-old woman with low-grade astrocytoma (WHO grade II) (g-l), and a 74-year-old man with primary central nervous system lymphomas (m-r). The contrast-enhanced T2-flair images (a, g, m) shown in the first column. The f0 images (b, h, n), fslow images (c, i, o), ffast images (d, j, p), ADCslow images (e, k, q) and ADCfast images (f, l, r) derived by modified tri-exponential model shown in the second, third, fourth, fifth and sixth columns respectively.

Figure 4. The box plots of f0, fslow, ffast, ADCslow and ADCfast in different grades of gliomas and primary central nervous system lymphomas (PCNSL). As grade of gliomas increasing, f0 and fslow had increasing trendency, while ffast and ADCslow had decreasing trendency. *p < 0.05, **p < 0.01 compared with PCNSL; #p < 0.05, ##p <0.01 compared with grade IV gliomas; $$p < 0.01 compared with grade III gliomas.

Figure 5. The linear regress of f0, fslow, ffast, ADCslow and ADCfast with the Ki-67 index (r = 0.638, 0.444, -0.595, -0.518 and -0.300 respectively). Dash lines are the 95% confidence band of the best-fit lines.

Proc. Intl. Soc. Mag. Reson. Med. 25 (2017)
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