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Non-Gaussian diffusion restriction effects in intravoxel incoherent motion imaging acquired at b-values below 1000 $$$\tt s/mm^{2}$$$

Hajime Tamura¹, Hideki Ota², Tatsuo Nagasaka², Naoko Mori², and Shunji Mugikura²

¹Tohoku University School of Medicine, Sendai, Japan, ²Tohoku University Hospital, Sendai, Japan

Synopsis

To know how much the intravoxel incoherent motion (IVIM) parameters deduced by a bi-exponential model are affected by neglecting non-Gaussian diffusion restriction effects, we performed Monte-Carlo simulations: fitting the bi-exponential model to simulated data containing the diffusion restriction effects. The results showed that non-Gaussian diffusion restriction effects may considerably affect estimation of IVIM parameters even when data acquired with low b-values (b≤1000 s/mm²) are used. This should be taken into account when interpreting the results of IVIM analyses based on the bi-exponential model.

INTRODUCTION

Non-Gaussian diffusion restriction effects are not clearly visible when low b-values (b≤1000 s/mm²) are used in clinical MRI. Therefore, the restriction effects are usually neglected for intravoxel incoherent motion (IVIM) imaging with b-values less than 1000 s/mm² and a simple bi-exponential signal decay model is used¹:$$ S(b)=S(0)\left\{fe^{-bD^{*}}+(1-f)e^{-bD}\right\}, \quad (Equation\quad 1)$$ where S denotes the signal intensity; b, the b-value; f, the flowing blood (perfusion) fraction; D^*, the pseudo-diffusion coefficient of vascular compartment; D, the apparent diffusion coefficient of non-vascular compartment. However, the accuracy of parameters (f, D, D^*) estimated by fitting the bi-exponential model to IVIM data that contain non-Gaussian diffusion restriction effects has not been investigated systematically. The purpose of this study is to know how much the estimated parameters are affected by the non-Gaussian diffusion restriction effects.

METHODS

We numerically simulated IVIM data containing non-Gaussian diffusion restriction effects. We adopted the diffusion kurtosis as an indicator of the restriction effects. Theoretical IVIM signals were generated using the diffusion kurtosis model²:$$ S(b)=S(0)\left\{fe^{-bD^{*}}+(1-f)e^{(-bD+Kb^{2}D^{2}/6)}\right\}, \quad (Equation\quad 2)$$ where K denotes the diffusion kurtosis. The signal intensities were calculated for 10 b-values (b≤500-1000 s/mm², Table 1) with ranges of parameters: K = 0-1.5, f = 0.03-0.1, D^* = 6-20 µm²/ms, and D = 0.8-1.5 µm²/ms. S(b)'s were calculated 1024 times for each set of parameters with adding Rician noise randomly so that the signal-to-noise ratio was 100 for the signal at b = 0.

D was estimated by non-linear least squares using the simulated data of b≥400 s/mm² where the first term in Equation 1 is assumed to be negligibly small. Then f and D^* were calculated using the data of b≤80 s/mm² and the estimated D above. f and D^* were constrained as 0 < f < 0.5, and 3<D^*<50 µm²/ms. We also calculated the apparent diffusion coefficient for a single-exponential decay model (ADC) as$$ADC = \log\left[S(0)/S(b_{max})\right]/b, \quad (Equation\quad 3)$$ where b_max is the maximum b in the set of 10 b-values.

The estimated parameters were compared with ground-truth values using box and whisker plots.

RESULTS

The estimated D decreased successively with both K and b_max. The estimated values were 0.66-0.82 of the ground truth at K = 1.0 and b_max = 1000 s/mm² and 0.49-0.75 of the ground truth at K = 1.5 and b_max = 1000 s/mm². Though the estimated D^* showed the same tendency as D, the precision was poor. The estimated f increased successively with both K and b_max. The estimated values of f were 1.8-2.2 of the ground truth at K = 1.0 and b_max = 1000 s/mm² and 2.1-4.9 of the ground truth at K = 1.5 and b_max = 1000 s/mm². The estimated ADC showed both the perfusion (the first term of the bi-exponential model: Equation 1 or 2) and the restriction effects. Figure 1-3 show box and whisker plots of the estimated D, D^* and f for D = 0.8 µm²/ms, D^* = 10 µm²/ms, and f = 0.05. Figure 4 shows the box and whisker plot of estimated ADC for the same D, D^* and f as above.

DISCUSSION

The IVIM parameters estimated by fitting the bi-exponential model to the data generated with relatively low b-values (b≤1000 s/mm²) were shown to be considerably affected by non-Gaussian diffusion restriction effects (K =0.5-1.5) that have been reported on human tissue.^3,4 Although decreasing b_max would alleviate the effects, precision of the estimated parameters are degraded for the smaller b_max. Because the K’s have been known to be greater for malignant tumors than for benign tumors,^5,6 the D’s estimated with the bi-exponential model may be smaller for malignant tumors than for benign tumors even when the actual D’s are the same. Similarly, the f’s estimated based on the bi-exponential model may be larger for malignant tumors than for benign tumors even when the actual f’s are the same.

CONCLUSION

Non-Gaussian diffusion restriction effects may considerably affect estimation of IVIM parameters even when low b-values (b≤1000 s/mm²) are used. D may be underestimated and f may be overestimated when using the bi-exponential model. This should be taken into account when interpreting the results of IVIM analyses based on the bi-exponential model.

Acknowledgements

This work was supported by JSPS KAKENHI Grant Number 15K09914.

References

1. Federau C. Intravoxel incoherent motion MRI as a means to measure in vivo perfusion: A review of the evidence. NMR in Biomed. 2017;e3780.

2. Iima M and Le Bihan D. Clinical Intravoxel Incoherent Motion and Diffusion MR Imaging: Past, Present, and Future. Radiology 2016;278(1):13-32.

3. Lätt J, Nilsson M, Wirestam R, et al. Regional values of diffusional kurtosis estimates in the healthy brain. J. Magn. Reson. Imaging 2013;37(3):610–618.

4. Wurnig M, Kenkel D, Filli L, et al. A Standardized parameter-free algorithm for combined intravoxel incoherent motion and diffusion kurtosis analysis of diffusion imaging data. Invest Radiol. 2016;51(3):203-210.

5. Cauter S, Veraart J, Sijbers J, et al. Gliomas: Diffusion kurtosis MR imaging in grading. Radiology 2012;263(2):492-501.

6. Iima M, Kataoka M, Kanao S, et al. Intravoxel incoherent motion and quantitative non-Gaussian diffusion MR imaging: evaluation of the diagnostic and prognostic value of several markers of malignant and benign breast lesions.Radiology 2017:162853. https://doi.org/10.1148/radiol.2017162853.

Figures

Table 1. Sets of 10 b-values adopted in this study varying the maximum b-values 500 to 1000 s/mm².

Figure 1. Box and whisker plots of estimated D’s using the data of D = 0.8 µm²/ms, D^* = 10 µm²/ms, and f = 0.05 with various Kurtosis (K) and sets of b-values. The each set has 10 b-values with the maximum b-value (b_max) of 500-1000 s/mm² (Table 1). The horizontal line indicates the ground truth. The estimated D’s decrease successively with both K and b_max as low as 0.73 of the ground truth at K = 1.5 and b_max = 1000 s/mm².

Figure 2. Box and whisker plots of estimated D^*’s from the data of D/D^*=0.8/10 µm²/ms, and f = 0.05 with various Kurtosis (K) and sets of b-values. The each set has 10 b-values data with the maximum b-value (b_max) of 500-1000 s/mm² (Table 1). The horizontal line indicates the ground truth. The estimated D^*’s tend to decrease successively with K or b_max.

Figure 3. Box and whisker plots of estimated f’s from the data of D/D*=0.8/10 µm²/ms, and f = 0.05 with various Kurtosis (K) and sets of b-values. The each set has 10 b-values data with the maximum b-value (b_max) of 500-1000 s/mm² (Table 1). The horizontal line indicates the ground truth. The estimated f’s increase successively with both K and b_max as large as 2.2 of the ground truth at K = 1.5 and b_max = 1000 s/mm².

Figure 4. Box-and-whisker plots of ADC’s calculated by Equation 3 in the text using the data of D/D*=0.8/10 µm²/ms, and f = 0.05 with various Kurtosis (K) and pairs of b-values: b = 0 and the maximum b-value (b_max) of 500-1000 s/mm². The horizontal line indicates the ground truth. The estimated ADC’s decrease successively with K or b_max. The ADC’s are overestimated at K = 0 and underestimated at K≥1.0 and b_max≥800 s/mm². The overestimation is caused by “perfusion effect” (the first term of the bi-exponential model: Equation 1 or 2 in the text).

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)

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