Abstract
Background: Non-dimensional analysis is a powerful approach that can be applied to multivariate problems to better understand their behaviour and interpret complex interactions of variables. It is has not been rigorously applied to the parameters that define renal dialysis treatments and may provide insight into the planning of hemodialysis treatments. Methods:Buckingham’s non-dimensional approach was applied to the parameters that define hemodialysis treatments. Non-dimensional groups were derived with knowledge of a mass transfer model and independent of it. Using a mass transfer model, the derived non-dimensional groups were plotted to develop an understanding of key relationships governing hemodialysis and toxin profiles in patients with end-stage renal disease. Results: Three non-dimensional groups are sufficient to describe hemodialysis, if there is no residual renal function (RRF). The non-dimensional groups found represent (1) the number of half-lives that characterize the mass transfer, (2) the toxin concentration divided by the rise in toxin concentration without dialysis for the cycle time (the inverse of the dialysis frequency), and (3) the ratio of dialysis time to the cycle time. If there is RRF, one additional non-dimensional group is needed (the ratio between cycle time and intradialytic elimination rate constant). Alternate non-dimensional groups can be derived from the four unique groups.Conclusions: Physical interpretation of the non-dimensional groups allows for greater insight into the parameters that determine dialysis effectiveness. This technique can be applied to any toxin and facilitates a greater understanding of dialysis treatment options. Quantitative measures of dialysis adequacy should be based on dimensional variables.
Highlights
Since the beginning of clinical hemodialysis by Willem Kolff in the 1940s, much has been written about how to measure dialysis and how much dialysis ought to be given
Application of the Buckingham Pi Theorem to hemodialysis, with the assumption that the system is dependent on only six variables (dialyzer clearance (K), dialysis time (t), toxin volume of distribution (V), toxin concentration (C), cycle time (T) and mass generation (G)), yielded three independent non-dimensional groups, as the variables considered important only contain three fundamental units
This paper has demonstrated the value of nondimensional groups in dialysis, and has illustrated the physical interpretations of these groups
Summary
Since the beginning of clinical hemodialysis by Willem Kolff in the 1940s, much has been written about how to measure dialysis and how much dialysis ought to be given. It remains a difficult area to understand without resorting to calculations which, practically, require a computer. This creates challenges when (1) deciding how patients should be treated and (2) studying the pathophysiology of end-stage kidney failure. Non-dimensional analysis is a powerful approach that can be applied to multivariate problems to better understand their behaviour and interpret complex interactions of variables. It is has not been rigorously applied to the parameters that define renal dialysis treatments and may provide insight into the planning of hemodialysis treatments
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