Finite-element modeling of time-dependent sodium exchange across the hollow fiber of a hemodialyzer by coupling with a blood pool model

A New Method for Continuous Relative Blood Volume and Plasma Sodium Concentration Estimation During Hemodialysis

OBJECTIVE

Non-invasive sensing and reliable estimation of physiological parameters are important features of hemodialysis machines, especially for therapy customization (biofeedback). In this paper, we present a new method for joint estimation of two important hemodialysis-related physiological parameters-relative blood volume and plasma sodium concentration.

METHODS

Our method makes use of a non-invasive sensor setup and a mathematical estimator. The estimator, based on the Kalman filter, allows merging data from multiple sensors, newly designed as well as onboard, with modeling knowledge about the hemodialysis process. The system was validated on in vitro hemodialysis sessions using bovine blood.

RESULTS

The estimation error we obtained (0.97 ± 0.73% on relative blood volume and 0.47 ± 0.19 mM on plasmatic sodium) proved to be comparable with that of the reference data for both parameters-the system is sufficiently accurate to be relevant in a clinical context.

CONCLUSION

Our system has the potential to provide accurate and important information on the state of a patient undergoing hemodialysis, while only low-cost modifications to the existing onboard sensors are required.

SIGNIFICANCE

Through improved knowledge of blood parameters during hemodialysis, our method will allow better patient monitoring and therapy customization in hemodialysis.

Model of fluid and solute shifts during hemodialysis with active transport of sodium and potassium

Background

Mathematical models are useful tools to predict fluid shifts between body compartments in patients undergoing hemodialysis (HD). The ability of a model to accurately describe the transport of water between cells and interstitium (J_v,ISIC), and the consequent changes in intracellular volume (ICV), is important for a complete assessment of fluid distribution and plasma refilling. In this study, we propose a model describing transport of fluid in the three main body compartments (intracellular, interstitial and vascular), complemented by transport mechanisms for proteins and small solutes.

Methods

The model was applied to data from 23 patients who underwent standard HD. The substances described in the baseline model were: water, proteins, Na, K, and urea. Small solutes were described with two-compartment kinetics between intracellular and extracellular compartments. Solute transport across the cell membrane took place via passive diffusion and, for Na and K, through the ATPase pump, characterized by the maximum transport rate, Jp_MAX. From the data we estimated Jp_MAX and two other parameters linked to transcapillary transport of fluid and protein: the capillary filtration coefficient Lp and its large pores fraction α_LP. In an Expanded model one more generic solute was included to evaluate the impact of the number of substances appearing in the equation describing J_v,ISIC.

Results

In the baseline model, median values (interquartile range) of estimated parameters were: Lp: 11.63 (7.9, 14.2) mL/min/mmHg, α_LP: 0.056 (0.050, 0.058), and Jp_MAX: 5.52 (3.75, 7.54) mmol/min. These values were significantly different from those obtained by the Expanded model: Lp: 8.14 (6.29, 10.01) mL/min/mmHg, α_LP: 0.046 (0.038, 0.052), and Jp_MAX: 16.7 (11.9, 25.2) mmol/min. The relative RMSE (root mean squared error)averaged between all simulated quantities compared to data was 3.9 (3.1, 5.6) %.

Conclusions

The model was able to accurately reproduce most of the changes observed in HD by tuning only three parameters. While the drop in ICV was overestimated by the model, the difference between simulations and data was less than the measurement error. The biggest change in the estimated parameters in the Expanded model was a marked increase of Jp_MAX indicating that this parameter is highly sensitive to the number of species modeled, and that the value of Jp_MAX should be interpreted only in relation to this factor.