Recent Advances and Future Perspectives in the Use of Machine Learning and Mathematical Models in Nephrology

We reviewed some of the latest advancements in the use of mathematical models in nephrology. We looked over 2 distinct categories of mathematical models that are widely used in biological research and pointed out some of their strengths and weaknesses when applied to health care, especially in the context of nephrology. A mechanistic dynamical system allows the representation of causal relations among the system variables but with a more complex and longer development/implementation phase. Artificial intelligence/machine learning provides predictive tools that allow identifying correlative patterns in large data sets, but they are usually harder-to-interpret black boxes. Chronic kidney disease (CKD), a major worldwide health problem, generates copious quantities of data that can be leveraged by choice of the appropriate model; also, there is a large number of dialysis parameters that need to be determined at every treatment session that can benefit from predictive mechanistic models. Following important steps in the use of mathematical methods in medical science might be in the intersection of seemingly antagonistic frameworks, by leveraging the strength of each to provide better care.

Phosphorus Removal in Low-Flux Hemodialysis, High-Flux Hemodialysis, and Hemodiafiltration

Phosphorus removal by hemoelimination procedure is a important mechanism to maintain phosphorus level in acceptable level in patients on dialysis. Phosphorus is removed by both diffusion and convection, but in clinical practice, it is not possible to differentiate the contribution of this two transport modalities. We used Gutzwiller formula to quantify the amount of removed phosphorus and compared it in low-flux hemodialysis (LFHD), high-flux hemodialysis (HFHD), and on-line hemodiafiltration (HDF). There were no significant differences in phosphorus predialysis concentration, duration of procedure, processed blood volume and ultrafiltration, e.g., factors, which could possibly influence phosphorus elimination. All three tested dialysis modes also did not differ in urea dialysis dose (Kt/V) as a parameter of small molecular weight removal (LFHD, 1.50 ± 0.04 vs HFHD, 1.5 ± 0.06 vs HDF, 1.5 ± 0.05). The amount of removed phosphorus in LFHD, HFHD, and HDF was 34.0 ± 1.2, 37.8 ± 1.6, and 38.3 ± 1.4 mmol, respectively. Statistically significant increase in phosphorus removal was seen only with use of high-flux membrane (HFHD and HDF) when compared with the low-flux one. No difference was, however, found between HFHD and HDF. It can thus be concluded that phosphorus removal in all three dialysis modes is a predominantly diffusive issue and contribution of convection to it is minor to negligible.

Evaluation of a pseudo-one-compartment model for phosphorus kinetics by later-phase dialysate collection during blood purification

PURPOSE

Phosphorus removal is a major issue to assess for physicians engaging in hemodialysis. A pseudo-one-compartment model was reported as a novel model for phosphorus kinetics. We aimed to evaluate the adequacy of this model from the standpoint of the total mass of removed phosphorus during prolonged treatment.

METHODS

Dialysate was collected during 6-h hemodialysis and hemodiafiltration treatment in 5 patients. Later-phase (from 4 to 6 h) dialysate was collected separately. Mobilization clearance (K(m)) and dialyzer clearance (K) were calculated by simple arithmetic operations utilizing stable serum phosphorus concentrations in this later phase. Volume of the accessible compartment (V(0)) was estimated by a fitting method. Amounts of removed phosphorus were calculated with these parameters and compared with measured values. The best sampling time points during treatment were also assessed, when the parameters were determined by serial serum phosphorus concentrations alone.

RESULTS

Pearson's correlation coefficient (R) between calculated and measured values of removed phosphorus was 0.991 and the concordance correlation coefficient (ρ) was 0.987. When K(m), K and V(0) were determined by serial serum concentrations alone, including those at 0, 1, 4, and 6 h, the calculated mass of removed phosphorus had high R (0.974-0.975) or ρ (0.966-0.972) with the measured values.

CONCLUSIONS

We confirmed that a pseudo-one-compartment model is useful for the estimation of removed phosphorus mass during prolonged blood purification by collecting dialysate. When the parameters are determined by a fitting method using serial serum concentrations alone, sampling at 0, 1, 4, and 6 h seems to be adequate.