Mathematical Modelling of Profiled Haemodialysis: A Simplified Approach

Abstract

For many renal patients with severe loss of kidney function dialysis treatment is the only means of preventing excessive fluid gain and the accumulation of toxic chemicals in the blood. Typically, haemodialysis patients will dialyse three times a week, with each session lasting 4-6 hours. During each session, 2-3 litres of fluid is removed along with catabolic end-products, and osmotically active solutes. In a significant number of patients, the rapid removal of water and osmotically active sodium chloride can lead to hypotension or overhydration and swelling of brain cells. Profiled haemodialysis, in which the rate of water removal and/or the dialysis machine sodium concentration are varied according to a predetermined profile, can help to prevent wide fluctuations in plasma osmolality, which cause these complications. The profiles are determined on a trial and error basis, and differ from patient to patient. Here we describe a mathematical model for a typical profiled haemodialysis session in which the variables of interest are sodium mass and body fluid volumes. The model is of minimal complexity and so could provide simple guidelines for choosing suitable profiles for individual patients. The model is tested for a series of dialysate sodium profiles to demonstrate the potential benefits of sodium profiling. Next, using the simplicity of the model, we show how to calculate the dialysate sodium profile to model a dialysis session that achieves specified targets of sodium mass removal and weight loss, while keeping the risk of intradia-lytic complications to a minimum. Finally, we investigate which of the model profiled dialysis sessions that meet a range of sodium and fluid removal targets also predict extracellular sodium concentrations and extracellular volumes that lie within “safe” limits. Our model suggests that improvements in volume control via sodium profiling need to be set against potential problems in maintaining blood concentrations and body fluid compartment volumes within “safe” limits.