The Kidneys Are Not All Normal: Transplanted Kidneys and Their Speckle Distributions

Modelling ultrasound speckle to characterise tissue properties has generated considerable interest. As speckle is dependent on the underlying tissue architecture, modelling it may aid in tasks such as segmentation or disease detection. For the transplanted kidney, where ultrasound is used to investigate dysfunction, it is unknown which statistical distribution best characterises such speckle. This applies to the regions of the transplanted kidney: the cortex, the medulla and the central echogenic complex. Furthermore, it is unclear how these distributions vary by patient variables such as age, sex, body mass index, primary disease or donor type. These traits may influence speckle modelling given their influence on kidney anatomy. We investigate these two aims.

B-mode images from n = 821 kidney transplant recipients (one image per recipient) were automatically segmented into the cortex, medulla and central echogenic complex using a neural network. Seven distinct probability distributions were fitted to each region's histogram, and statistical analysis was performed.

The Rayleigh and Nakagami distributions had model parameters that differed significantly between the three regions (p ≤ 0.05). Although both had excellent goodness of fit, the Nakagami had higher Kullbeck-Leibler divergence. Recipient age correlated weakly with scale in the cortex (Ω: ρ = 0.11, p = 0.004), while body mass index correlated weakly with shape in the medulla (m: ρ = 0.08, p = 0.04). Neither sex, primary disease nor donor type exhibited any correlation.

We propose the Nakagami distribution be used to characterize transplanted kidneys regionally independent of disease etiology and most patient characteristics.