Jacek Waniewski

Ion exchange membranes (IEMs) are permselective membranes that, in principle, only allow the flow of ions with a specific charge sign, opposite to that of the fixed membrane ionic groups (counter-ions). This charge-based selectivity, like the size-based selectivity of classic semipermeable membranes, leads to an uneven distribution of permeating ions on the two sides of the membrane, which allows for ion separation or recovery in various processes in industry or environmental protection. Here, we apply the principles of mass balance, charge neutrality, and equality of electrochemical potentials in the state of thermodynamic equilibrium to provide a simple method for estimating the Gibbs-Donnan factors and the equilibrium concentrations of permeating ions in two compartments separated by an ideal IEM, i.e. an IEM that is not permeable to co-ions. We present the method for the case when the equilibrium concentrations are known in one compartment and need to be estimated in the other compartment as well as for the case when the total masses of ions in both compartments are known and their equilibrium concentrations need to be predicted. For both cases, the presented nonlinear algebraic equations require in general the use of numerical methods to approximate their mathematical solutions, although we present as well some closed solutions for simple cases with ideal ionic mixtures. Based on the extended Debye–Hückel theory, we also provide analogous equations (general and for specific cases) for systems with non-ideal ionic mixtures. The presented method can provide the expected ideal separation effectiveness of an IEM, which can then be used to assess the relative separation effectiveness of a real membrane.

The patterns of cardiovascular response to hemodialysis (HD), including the relative blood volume (RBV) changes, are not fully understood. Here, we present a synthetic dataset of intradialytic profiles of RBV changes simulated using a lumped-parameter, physiologically-based model of the cardiovascular system and the whole-body water and solute kinetics in 5,000 virtual patients with randomly adjusted values of 90 physiological parameters. The dataset (HD-SIM-RBV) includes a wide range of RBV curves varying in shape and magnitude of RBV changes during HD and it may be used to investigate parameters influencing intradialytic RBV profiles as well as to study the possibility of predicting the end-of-dialysis RBV level using RBV data from the initial phase of HD to help guide HD treatment to avoid hemodynamic instability.Clinical Relevance: Mining this dataset may help elucidate the mechanisms of cardiovascular response to hemodialysis.

The general set of equations for the equilibrium of two solutions with a mixture of non-permeating and permeating ions and neutral solutes at each side of a permselective membrane is formulated using the principles of electroneutrality and mass conservation law for each solution, and equilibrium conditions: equality of electrochemical potentials at both sides of the membrane for each permeating solution component. There is at least one permeating neutral chemical species (solvent) in the system. The theory is in general valid for non-ideal solutions. The generalized Gibbs–Donnan (G–D) equilibrium coefficients depend on activities/fractions of all species at one side of the membrane, and charges of ions and partial molar volumes of all species. The equilibrium osmotic pressure across the membrane is also provided by the theory and can be calculated using the ratio of activities (or equivalently the G–D factor) of any permeating neutral solute (including solvent) or the ratios of activities (or equivalently the G–D factors) of any two permeating ions.

The model for perfused tissue undergoing deformation taking into account the local exchange between tissue and blood and lymphatic systems is presented. The Lie symmetry analysis in order to identify its symmetry properties is applied. Several families of steady-state solutions in closed formulae are derived. An analysis of the impact of the parameter values and boundary conditions on the distribution of hydrostatic pressure, osmotic agent concentration and deformation of perfused tissue is provided applying the solutions obtained in examples describing real-world processes.

Background: Traumatic brain injury (TBI) is often associated with cardiac dysfunction, which is a consequence of the brain–heart cross talk. The subendocardial viability ratio (SEVR) is an estimate of myocardial perfusion. The aim of this study was to analyze changes in the SEVR in patients with severe TBI without previous cardiac diseases. Methods: Adult patients treated for severe TBI with a Glasgow coma score p < 0.05) and after 48 h in survivors ( p < 0.01) and its values were significantly lower in nonsurvivors than in survivors at 24, 72, and 96 h from admission ( p < 0.05). The SEVR increased following DC ( p < 0.05). Conclusions: A decreased SEVR is observed in TBI patients. Surgical decompression increases the SEVR, indicating improvement in coronary microvascular perfusion. The results of our study seem to confirm that brain injury affects myocardium function.

Fluid and solute transport in poroelastic media is studied. Mathematical modeling of such transport is a complicated problem because of the volume change of the specimen due to swelling or shrinking and the transport processes are nonlinearly linked. The tensorial character of the variables adds also substantial complication in both theoretical and experimental investigations. The one-dimensional version of the theory is less complex and may serve as an approximation in some problems, and therefore, a one-dimensional (in space) model of fluid and solute transport through a poroelastic medium with variable volume is developed and analyzed. In order to obtain analytical results, the Lie symmetry method is applied. It is shown that the governing equations of the model admit a non-trivial Lie symmetry, which is used for construction of exact solutions. Some examples of the solutions are discussed in detail.

The peritoneal equilibration test (PET) is the most widespread method for assessing water and solute transport across the peritoneal membrane. This study compared three methods: traditional PET (t-PET), mini-PET, and modified PET (mod-PET). Non-diabetic adults (n=21) who had been on peritoneal dialysis (PD) for at least three months underwent t-PET (glucose 2.5%-4 h), mini-PET (glucose 3.86%-1 h), and mod-PET (glucose 3.86%-4 h) to determine dialysate-to-plasma concentration ratio (D/P) for creatinine and dialysate-to-baseline dialysate concentration ratio (D/D0) for glucose. Agreement between methods regarding D/P creatinine and D/D0 glucose was assessed using analysis of variance (ANOVA), Pearson's correlation coefficient, and Bland-Altman analysis. D/P creatinine differed between t-PET and mini-PET (P<0.001) and between mod-PET and mini-PET (P<0.01) but not between t-PET and mod-PET (P=0.746). The correlation of D/P creatinine with t-PET vs mod-PET was significant (r=0.387, P=0.009) but not that of t-PET vs mini-PET (r=0.088, P=0.241). Estimated bias was -0.029 (P=0.201) between t-PET and mod-PET, and 0.206 (P<0.001) between t-PET and mini-PET. D/D0 glucose differed between t-PET and mod-PET (P=0.003) and between mod-PET and mini-PET (P=0.002) but not between t-PET and mini-PET (P=0.885). The correlations of D/D0 glucose in t-PET vs mod-PET (r=-0.017, P=0.421) or t-PET vs mini-PET (r=0.152, P=0.609) were not significant. Estimated bias was 0.122 (P=0.026) between t-PET and mod-PET, and 0.122 (P=0.026) between t-PET and mini-PET. The significant correlation of D/P creatinine between t-PET and mod-PET suggested that the latter is a good alternative to t-PET. There was no such correlation between t-PET and mini-PET.

Background: Sequential peritoneal equilibration test (sPET) is based on the consecutive performance of the peritoneal equilibration test (PET, 4-hour, glucose 2.27%) and the mini-PET (1-hour, glucose 3.86%), and the estimation of peritoneal transport parameters with the 2-pore model. It enables the assessment of the functional transport barrier for fluid and small solutes. The objective of this study was to check whether the estimated model parameters can serve as better and earlier indicators of the changes in the peritoneal transport characteristics than directly measured transport indices that depend on several transport processes. Methods: 17 patients were examined using sPET twice with the interval of about 8 months (230 ± 60 days). Results: There was no difference between the observational parameters measured in the 2 examinations. The indices for solute transport, but not net UF, were well correlated between the examinations. Among the estimated parameters, a significant decrease between the 2 examinations was found only for hydraulic permeability LpS, and osmotic conductance for glucose, whereas the other parameters remained unchanged. These fluid transport parameters did not correlate with D/P for creatinine, although the decrease in LpS values between the examinations was observed mostly for patients with low D/P for creatinine. Conclusions: We conclude that changes in fluid transport parameters, hydraulic permeability and osmotic conductance for glucose, as assessed by the pore model, may precede the changes in small solute transport. The systematic assessment of fluid transport status needs specific clinical and mathematical tools beside the standard PET tests.