  Modelling ultrasound speckle has generated considerable interest for its
ability to characterize tissue properties. As speckle is dependent on the
underlying tissue architecture, modelling it may aid in tasks like segmentation
or disease detection. However, for the transplanted kidney where ultrasound is
commonly used to investigate dysfunction, it is currently unknown which
statistical distribution best characterises such speckle. This is especially
true for 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 are the first to investigate these
two aims. N=821 kidney transplant recipient B-mode images were automatically
segmented into the cortex, medulla, and central echogenic complex using a
neural network. Seven distinct probability distributions were fitted to each
region. The Rayleigh and Nakagami distributions had model parameters that
differed significantly between the three regions (p <= 0.05). While both had
excellent goodness of fit, the Nakagami had higher Kullbeck-Leibler divergence.
Recipient age correlated weakly with scale in the cortex (Omega: rho = 0.11, p
= 0.004), while body mass index correlated weakly with shape in the medulla (m:
rho = 0.08, p = 0.04). Neither sex, primary disease, nor donor type
demonstrated any correlation. We propose the Nakagami distribution be used to
characterize transplanted kidneys regionally independent of disease etiology
and most patient characteristics based on our findings.
