🩸 Haemodialysis

The simulator uses the Michaels (or Gotch) equation for countercurrent diffusive clearance: K = Qb * (E - 1) / (E - Qb/Qd), where E = exp(KoA * (1 - Qb/Qd) / Qb). KoA is the dialyzer's overall mass-transfer coefficient (area product) in mL/min, representing how easily the membrane passes solute. When blood and dialysate flows are equal, L'Hopital's rule applies and K = Qb * KoA / (Qb + KoA). Clearance is always less than or equal to blood flow, because blood flow is the ultimate bottleneck on solute delivery to the dialyzer.

URR = 1 - C_final / C0, expressed as a percentage; a target of 65% or more corresponds approximately to Kt/V 1.2 for a typical patient. URR is simpler to measure (just two blood draws per session) but ignores urea generated during the session and convective removal. Kt/V is the more rigorous metric used in clinical trials. In the single-pool model, URR = 1 - e^(-Kt/V), so the two quantities are mathematically linked when generation and ultrafiltration are neglected.

Many people assume that doubling blood flow rate doubles clearance, but this is not the case. At low blood flow rates, clearance rises steeply with Qb because blood spends enough time in the dialyzer for near-complete extraction. At high flow rates, the dialyzer becomes the bottleneck rather than blood delivery: solute passes through so quickly that extraction efficiency (C_in - C_out)/C_in drops. This is why increasing blood flow from 200 to 300 mL/min yields a larger clearance gain than increasing from 400 to 500 mL/min with the same dialyzer KoA.

Frank Gotch and John Sargent introduced Kt/V in 1985 as a reanalysis of the National Cooperative Dialysis Study (NCDS, 1981), which had randomised patients to different dialysis prescriptions. Their urea kinetic modelling showed that the probability of treatment failure correlated strongly with Kt/V, providing the first quantitative adequacy target. The HEMO Study (2002) subsequently confirmed that Kt/V 1.2 per session is the minimum effective dose and that increasing to Kt/V 1.7 does not further improve survival.

Haemodialysis is closely related to peritoneal dialysis (PD), where the peritoneum acts as the semipermeable membrane and dialysate is instilled into the abdomen. Haemofiltration and haemodiafiltration (HDF) add a convective component using high-flux membranes and replacement fluid, removing larger middle molecules more effectively than diffusion alone. At a more fundamental level, the same membrane-transport physics governs reverse-osmosis water treatment, gas exchange in the lung (where O2 and CO2 diffuse down gradients across alveolar membranes), and pharmaceutical drug-release patches.

Modern dialyzers contain up to 15,000 hollow polysulfone or polyethersulfone fibres with an inner diameter of roughly 200 micrometres and a total membrane area of 1.0 to 2.1 m2. High-flux dialyzers with large pore sizes remove beta-2 microglobulin and other middle molecules linked to dialysis-related amyloidosis. Online haemodiafiltration systems generate up to 25 litres of ultrapure substitution fluid per session from reverse-osmosis water, requiring strict endotoxin control. Wearable and implantable artificial kidneys are active engineering research areas aiming to free patients from three-times-weekly clinic visits.

Single-pool Kt/V has known limitations: it does not capture solute rebound after dialysis (addressed by double-pool or equilibrated eKt/V models), ignores protein-bound uraemic toxins such as indoxyl sulfate and p-cresyl sulfate that dialyzers cannot clear efficiently, and uses urea as a surrogate that may not fully represent all uraemic retention molecules. Current research focuses on extended-hours dialysis (nocturnal HD), incremental dialysis prescriptions tailored to residual kidney function, medium cut-off (MCO) membranes that clear albumin-bound toxins, and biomarker panels beyond urea to assess uraemic burden more accurately.