He Wang^{1}, Kaining Shi^{1}, Weibo Chen^{1}, and Guilong Wang^{1}

^{1}Philips Healthcare, shanghai, China, People's Republic of

### Synopsis

**The study developed a methodology to improve the
quality of the multi-b DWIs using the intrinsic multi-exponential pattern. It was
evaluated on a healthy brain and compared with the mono-exponential model. In
addition, its potential value of improving the robustness of IVIM was also
evaluated. According to the results, the multi-exponential method can improve the image quality of the
multi-b DWIs and may become an effective preprocessing way for the non-monoexponential
models.**### INTRODUCTION

Numerous studies of the diffusion of water in brain
tissue and other biological systems have documented a non-monoexponential
behavior of the MR signal as a function of the b-value at fixed diffusion times.
High-quality multi-b Diffusion Weighted Images (DWI) are required to guarantee the
accurate outcomes of the non-monoexponential models, like bi-exponential [1],
stretched-exponential [2], and statistical model [3]. Getting high-quality
multi-b DWIs, especially with high b- values, in the clinically acceptable scan
time has remained a challenge. Increasing the number of acquisitions (NSA) will
improve the signal to noise ratio (SNR), however, it will expend the scan time
as well. In this study, instead of increasing the NSA, we developed a novel
methodology to improve the quality of the multi-b DWIs using the intrinsic
multi-exponential pattern. It was evaluated on a healthy brain and compared
with the mono-exponential model. In addition, its potential value of improving
the robustness of IVIM was also evaluated.

### MATERICALS AND METHODS

The study was performed using
a 3.0-T system (Ingenia, Philips Medical Systems, Best, the Netherlands) equipped
with a dedicated 32-channel phased-array head coil. Diffusion-weighted
images were acquired using the following parameters: 20 axial slices, FOV 240 x
240 mm, matrix 128 x 128, thickness/gap 5/1.5 mm, TE/TR 125/3314 ms. Eleven b-values
included 0, 25, 50, 100, 200, 400, 800, 1200, 2000, 3000, 4000 s/mm2
were measured with three mutually orthogonal diffusion encoded directions plus two
acquisitions.
Generally, the
diffusion-attenuated MR signal can be expressed as a
multi-exponential function given by (1): S(b) = Σy

_{i}exp(-bD

_{i}) (1),
where S is DWI signal intensity, b is the b-value, y
is the desired signal intensity with specific diffusion coefficient D and n is
the number of diffusion components. All the calculations and programs were done
in Matlab R2012b. First, y was obtained by solving the Eq. (1) using nonnegative
least square algorithm [4] with n=100 and D exponentially equispaced from 0.001
to 100 μm2/ms. Then, the new computed DWI (cDWI) with any specified b-value
could be calculated using the Eq. (1) with the known y. For comparison, the
mono-exponential (n=1) was also performed, and one ROI with 8*8 pixels was
drawn in the white matter (see the red square in Fig. 3) to evaluate the errors
of the fitting results. In addition, we compared the calculated IVIM parameters
using the raw DWIs and the multi-exponential cDWIs as well.

### RESULTS

Fig.1 shows the raw DWIs (the 1st row), the
cDWIs using multi-exponetial model (the 2nd row), and
mono-exponential model (the 3rd row). Obviously, the multi-exponetial
model restored the contrasts of the raw DWIs, while the mono-exponential model altered
the contrasts at some b-values (0, 800, 1200, 2000). The fitting results using these
two different models in the white matter are shown in Fig. 2. The result of the
multi-exponential model (χ2
= 68.7) was much better than that of the mono-exponential model (χ2
= 8161.9). The SNR of cDWI with high b-value was higher than the raw DWI (see
Fig. 3) at b-value 3000 s/mm2. The result of the IVIM parameter,
perfusion fraction (F), was shown in Fig. 4. The values of F from the ROI (see the
red square in Fig. 3) were 0.3108±0.0379 (raw DWIs) and 0.3067±0.0246 (multi-exponential
cDWIs) respectively.

### DISCUSSION AND CONCLUSION

In
this preliminary study, the proposed multi-exponential cDWI method presented a good
fitting result, and the image quality was obviously improved at high b-values
(Fig. 3). Although the mono-exponential model could also increase the SNR at
high b-values, it altered the contrasts of DWIs at some b-values in the
meantime. In Fig. 4, the standard deviation in the ROI was decreased after
multi-exponential model was applied, and the image looks smoother on the right
side. The other two IVIM parameters, diffusion coefficient and pseudodiffusion
coefficient, had the similar results (not listed here). Other non-monoexponential
models need to be evaluated in the future work. In conclusion, the
multi-exponential method can improve the image quality of the multi-b DWIs and
may become an effective preprocessing way for the non-monoexponential models.

### Acknowledgements

No acknowledgement found.### References

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