Mathematical modelling of proled haemodialysis

In healthy individuals, the removal of uid and toxic catabolic waste products is a continuous 24 hour process. When the kidneys fail, uid is retained and the accumulation of some important ions, such as those of potassium and hydrogen, may become life threatening. For many patients with severe loss of kidney function dialysis is the only means of preventing excessive uid gain and the accumulation of toxic chemicals in the blood (see, for example, [3] for an introduction to treatment of Chronic Renal Failure). Haemodialysis is the transport of water, ions and middle molecules (up to the size of albumin) across the arti cial membrane separating the patient plasma volume and the dialysis machine uid (the dialysate) using both passive diusion and pressure-driven ultraltration. In contrast to healthy kidney function, haemodialysis is an intermittent treatment: patients typically dialyse for 4-6 hours, 3 times a week. During each session, 3-4 litres of uid is removed along with catabolic end-products, and osmotically active solutes. The short duration and intermittent nature of haemodialysis means that most patients experience large and acute swings in body uid volume, ion and solute composition not normally encountered in health. These changes can result in signicant intra- and interdialytic morbidity. Indeed, intradialytic morbidity is recorded in around 30 % of all haemodialysis treatments. In a signicant number of patients, the underlying problem is the rapid removal of water and osmotically active sodium chloride which can lead to severe hypotension or the overhydration and swelling of brain cells. While this is an age-wide problem, it is particularly prevalent in the growing population of elderly haemodialysis patients, many of whom also have impaired cardiac function. One practice aimed at reducing the incidence of volume-related interdialytic morbidity is proled haemodialysis in which the rate of water removal and/or the dialysis machine sodium concentration are varied with time according to a predetermined prole designed to prevent the wide uctuations i