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Mathematical models for evaluation, optimization, and control of artificial kidney therapy

100%

Waniewski J.

2002

tom Vol. 3

IP27--39

Renal replacement therapy involves the control of body pools of water and electrolytes, and removal of small metabolites (urea, creatinine). The correct estimation of "the dose of therapy" and optimisation of the procedure needs quantification of fluid and solute transport during dialysis as well as evaluation of the distribution and exchange of water and solutes within the body. Mathematical models can combine the general physiological knowledge with information about individual patients yielded by clinical measurements. Many of these models (urea model, sodium model, models of peritoneal transport) have been presented to the community of clinical nephrologists in the form of computer programs often supplemented with on-line measuring devices. However, the debate about their meaning and the search for better methods of their application are still vivid.

Uproszczony przepływowy model hemodializy - porównanie z klasycznym modelem dwuprzedziałowym

72%

Korohoda P.

tom T. 13, z. 3/1

1129-1140

W artykule zaproponowano uproszczoną strukturę modelu przepływowego hemodializy, zbliżoną do klasycznego modelu dwuprzedziałowego. W celu przeprowadzenia obliczeń porównawczych umożliwiających ocenę przydatności nowego modelu opracowano metodykę pseudolosowego generowania danych symulujących zabieg dializy. Dla wytworzonego w ten sposób zbioru danych testowych, N — 1000 wykazano, iż oba modele - proponowany i klasyczny - wykazują podobną zdolność odtwarzania zadanych przebiegów stężeń. Dla opisanych wyżej danych wyznaczono zależność między najważniejszymi parametrami obu modeli, wykazując możliwość ich łatwego przeliczania. Wskazano jednak także na pewne różnice w przebiegach uzyskanych za pomocą obu modeli, co stanowi uzasadnienie dalszego badania modeli przepływowych.

In the paper a simplified blood flow model of hemodialysis is sugested, being a modified version of the classical two-compartment model. A method of pseudorandom hemodialysis data generation has been designed to enable relevant comparative study of both models. For such test data, N = 1000, it has been shown that the flow model has very similar capability of modeling the concentration runs, as the classical two-compartment model. For the randomly generated data, the mutual relationship between the crucial model parameters has been shown. Such property makes the convertion between discussed models very simple. However, some differences in the runs obtained from both models were also indicated, which encourages further investigation of the blood-flow models.

Modeling of insulin secretion and insulin mass balance during hemodialysis in patients with and without type 2 diabetes

72%

Schneditz D. , Niemczyk L. , Niemczyk S.

Biocybernetics and Biomedical Engineering

2021

tom Vol. 41, no. 2

391--401

Background: The secretion, distribution, and elimination of insulin in response to a bolus of glucose injected during regular hemodialysis was modeled to quantify the intra-dialytic mass balance of glucose and insulin in patients without (D0) and with type 2 diabetes (D1). Methods: A two-compartment regional blood flow model with shared compartments and dynamics for glucose, insulin and c-peptide was used to identify parameters of insulin and c-peptide co-secretion, first- and second-pass hepatic insulin extraction, as well as insulin-independent and insulin-dependent glucose utilization. Experimental data from a previous study obtained in 21 D0 and 14 D1 were used to identify kinetic model parameters and the fractions of glucose and insulin removed by dialysis. Results: Modeled gains for insulin secretion (ß1 = 0.015 vs. 0.084 L/min, ß2 = 0.004 vs. 0.666 L) were lower in D1, resulting in a lower total insulin secretion (Mi = 6.40 vs. 38.0 nmol). Hepatic insulin extraction was high (Eihep = 0.558 vs. 0.638) and only slightly smaller in D1. The fraction of insulin removed by dialysis (Fid = 0.07 vs. 0.05) was small and comparable between D1 and D0. Modeled gains for insulin-dependent glucose uptake (γ = 0.38 vs. 1.34 L2/nmol/min) were lower whereas those for insulin-independent glucose uptake (λ = 0.14 vs. 0.067 L/min) were higher in D1. The fraction of glucose removed by dialysis (Fgd = 0.31 vs. 0.28) was higher in D1. Conclusion: Apart from expected differences in modeled secretion and glucose utilization in patients with and without diabetes an intravenous bolus of glucose causes only small differences in overall glucose and insulin balance during a typical hemodialysis treatment.