Relationship between kurtosis and bi-exponential characterization of high b-value diffusion-weighted imaging: application to prostate cancer

Background: High b-value diffusion-weighted imaging has application in the detection of cancerous tissue across multiple body sites. Diffusional kurtosis and bi-exponential modeling are two popular model-based techniques, whose performance in relation to each other has yet to be fully explored. Purpose: To determine the relationship between excess kurtosis and signal fractions derived from bi-exponential modeling in the detection of suspicious prostate lesions. Material and Methods: This retrospective study analyzed patients with normal prostate tissue (n = 12) or suspicious lesions (n = 13, one lesion per patient), as determined by a radiologist whose clinical care included a high b-value diffusion series. The observed signal intensity was modeled using a bi-exponential decay, from which the signal fraction of the slow-moving component was derived (SFs). In addition, the excess kurtosis was calculated using the signal fractions and ADCs of the two exponentials (KCOMP). As a comparison, the kurtosis was also calculated using the cumulant expansion for the diffusion signal (KCE). Results: Both K and KCE were found to increase with SFs within the range of SFs commonly found within the prostate. Voxel-wise receiver operating characteristic performance of SFs, KCE, and KCOMP in discriminating between suspicious lesions and normal prostate tissue was 0.86 (95% confidence interval [CI] = 0.85 - 0.87), 0.69 (95% CI = 0.68-0.70), and 0.86 (95% CI= 0.86-0.87), respectively. Conclusion: In a two-component diffusion environment, KCOMP is a scaled value of SFs and is thus able to discriminate suspicious lesions with equal precision. KCE provides a computationally inexpensive approximation of kurtosis but does not provide the same discriminatory abilities as SFs and KCOMP.