Principles of Hemodialysis
Kidney function in patients with partial or complete renal failure is insufficient to adequately remove excess electrolytes (salts) and waste metabolites generated through ordinary metabolism. As a result, the concentrations of these species will build in the body to toxic levels unless something is done to help remove them.
The major source of waste metabolites is the liver since this is where most of the energy conversion processes in the body take place. The end products of carbohydrate and fat metabolism tend to be water and carbon dioxide, both of which can be lost from the body through respiratory processes (breathing). The end products of protein metabolism, however, are generally eliminated through the kidneys. Urea is the largest mass of waste metabolite produced in the liver from protein metabolism and is generally used as a marker of renal function because it is present in large quantities in the blood and is easily measured.
A schematic diagram of a typical hollow-fiber dialyzer is shown in the figure at the left. The dialyzer consists of a bundle of semi-permeable hollow fibers (tubes) surrounded by a hard plastic casing (shell). The fibers are potted into the casing with an impermeable glue at either end. Fluid distribution caps are then glued into place. Blood can then flow into one fluid distribution cap, along the interior of the fiber (tube-side) to the exit distribution cap, and thence out of the dialyzer. Dialysate, basically distilled water with an electrolyte and pH composition similar to that of blood plasma, flows counter-current to the blood on the outside of the fibers (shell-side).
Chemical species that are in the blood and not in the dialysate and that are of sufficiently small molecular size to pass across the semi-permeable membrane, can diffuse from the blood side to the dialysate side under a concentration difference (potential driving force) between the blood side concentrations (high) and dialysate side concentrations (low). As in all potentials drive fluxes thermodynamic settings, species will move from areas of high potential (concentration) to areas of low potential (concentration). The overall mass transfer equation that describes the steady-state (meaning all entering and exiting compositions of the blood stream and the dialysate stream remain constant with time) counter-current operation of the dialyzer is
where M i : mass transfer rate of species i, mmol/min
K : overall mass transfer parameter, mL/min/m2
A : membrane area, m2
(DC i) lm : log mean concentration difference of species i, mmol/mL
and Kd : dialyzer clearance = KA, mL/min.
For counter-current flow as depicted in the figure
where Cb : blood concentration, mmol/mL
Cd : dialysate concentration, mmol/mL
subscript i : stream inlet
subscript o : stream outlet
The overall mass transfer coefficient, Kd, is what is termed a “lumped parameter” that takes into consideration the mass transfer resistances due to fluid flow on the blood side of the hollow fiber, mass transfer resistance due to diffusion through the membrane of the hollow fiber, and mass transfer resistance due to fluid flow on the dialysate side of the hollow fiber. Since species diffusion depends upon molecular weight (or more correctly, molecular size), the overall mass transfer coefficient will be species dependent. Also, species diffusion through the membrane will depend upon species size and permeability of the membrane to that species. Membranes are typically designed to limit the size of molecules that can transfer across them by diffusive mechanisms. This is especially important in dialysis applications where we want to remove low molecular weight metabolic byproducts from the blood stream while retaining larger molecules such as peptides and proteins.
In practice, the dialyzer clearance is used to describe dialyzer performance because of the membrane area in any particular dialyzer is fixed. Similar comments as for the overall mass transfer coefficient apply to the dialyzer clearance.
Copyright © 2001, John F Patzer II
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