Time Series Analysis of Blood Flow in Kidney Graft: On the Emergence of Deterministic Chaos during the Phase of Acute Rejection

Abstract

This study deals with time series analysis of blood flow velocity in the lobar branches of the renal artery of the kidney graft undergoing deterioration of function owing to acute rejection, acute tubular necrosis, acute pyelonephritis or chronic rejection. Both classical and Doppler sonography of kidney graft are not specific nor sensitive enough to distinguish between those clinical entities. Results of this pilot study indicate that the Hurst exponent of the time series of blood flow velocity changes significantly in the clinical course of acute cellular rejection or acute tubular necrosis. The Hurst exponent undergoes a unique temporal evolution indicating the emergence of deterministic chaos during the severe alteration of blood flow in kidney graft. This evolution can be described by the exponential function. Therefore, kidney graft with the underlying complex dynamics can be defined as a dynamic system of the first order.