Sodium flux during haemodialysis
A problem presented at the Canadian MMSG Toronto 2009.
- Presented by:
- (Renal Division, Brigham and Women's Hospital)
- Participants:
Problem Description
One of the major functions of the kidney is the removal from the circulation of toxic compounds and the maintenance of water and salt balance. Kidney function can be replaced in patients with kidney failure by haemodialysis, an extracorporeal procedure in which blood passes through thousands of hollow fibers made of a semipermeable membrane bathed by a balanced electrolyte solution (“dialysate”). Solutes are cleared through the membrane from the blood to the dialysate, and its concentration varies by both diffusion and convection processes.
Sodium flux during haemodialysis is of significant clinical importance and lends itself to quantitative analysis and modeling. The goal of this project is to develop a mathematical simulation of sodium flux during haemodialysis, with the long-term goal of developing a clinical calculator that enables physicians to prescribe individualized sodium dialysate prescriptions in order to improve the safety of the dialysis procedure.
Specfic Goals:
- Develop a mathematical model of sodium flux that takes into account convection, diffusion, as well as intercompartmental transfer (extra-, intracellular, and interstitial) of water and salt in the body, such as the Gibbs-Donnan effect
- In a patient with a given pre-dialysis sodium concentration, potassium concentration, and extracellular fluid volume, determine the dialysate sodium concentration and ultrafiltration rate needed to achieve metabolic goals (fluid and salt removal)
Download the full problem description
Study Group Report
In this report, we focus on formulating a fundamentally-based model to address this question. We consider the formulation near the membrane at the pore scale in order to determine effective jump conditions in ionic concentrations, electric potential and flow rate based on the membrane properties, and in order to determine whether electroneutrality holds within the pore.
Secondly, we consider the local blood-cell concentration within one of the fibres and how this varies axially within the dialysis cartridge. Lastly, we consider a simple one-dimensional model of the charged species problem and find that advection transport through the membrane is important for sodium transport, but less pertinent for transport of other cation species.