Patient-Specific Modeling of Multicompartmental Fluid and Mass Exchange during Dialysis

Same therapy, same calcium mobilization? Exploring calcium exchange across body compartments using a patient-specific predictive model

BACKGROUND

Comprehensive, patient-specific models are essential to study calcium deposition and mobilization during dialysis. We aim to develop tools to support clinical prescriptions with a more accurate approach for the prediction of calcium mobilization while also considering major electrolytes and catabolites.

METHODS

We modified a multi-solute model predicting patient-specific dialysis response by incorporating a calcium buffer to represent bone exchanges. Data from four centers, involving 127 patients with six sessions each, were utilized. For each patient, three sessions were allocated for model training (ID123), while the remaining sessions were for validation (PRED456). The normalized root mean square error (nRMSE%) was used to evaluate both descriptive and predictive accuracy. Correlations between initial data and calcium exchanges were also assessed.

RESULTS

The overall nRMSE% for ID123 was 3.92%. For PRED456, it was 3.46% (ranging from a minimum of 1.17% for [Na+] to a maximum of 6.62% for [urea]). The median nRMSE% for plasma calcium varied between 1.13 and 8.32 for SHD sessions, depending on whether Ca_dialysis fluid (Cad) was ≥ or <1.50 mmol/L, respectively. For HDF sessions, the range was between 2.90 and 5.89. A significant and moderate correlation was found between overall calcium removal and the buffer balance. The most robust correlation observed was between the amount of calcium administered via post-dilution fluid and the overall calcium removal in the dialysis filter.

CONCLUSIONS

Identical therapy settings do not uniformly affect calcium mobilization, and our approach offers insight into calcium distribution across body compartments. This understanding will enhance clinical prescription practices.

Can the response to dialysis treatment be predicted by using patient-specific modeling of fluid and solute exchanges? A multicentric evaluation

BACKGROUND

Parametric multipool kinetic models were used to describe the intradialytic trends of electrolytes, breakdown products, and body fluids volumes during hemodialysis. Therapy customization can be achieved by the identification of parameters, allowing patient-specific modulation of mass and fluid balance across dialyzer, capillary, and cell membranes. This study wants to evaluate the possibility to use this approach to predict the patient's intradialytic response.

METHODS

6 sessions of 68 patients (DialysIS© project) were considered. Data from the first three sessions were used to train the model, identifying the patient-specific parameters, that, together with the treatment settings and the patient's data at the session start, could be used for predicting the patient's specific time course of solutes and fluids along the sessions. Na+ , K+ , Cl- , Ca2+ , HCO3 - , and urea plasmatic concentrations and hematic volume deviations from clinical data were evaluated.

RESULTS

nRMSE predictive error is on average equal to 4.76% when describing the training sessions, and only increases by 0.97 percentage points on average in independent sessions of the same patient.

CONCLUSIONS

The proposed predictive approach represents a first step in the development of tools to support the clinician in tailoring the patient's prescription.

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.

Mechanisms of Acid-Base Kinetics During Hemodialysis: a Mathematical-Model Study

This study contrasts the abilities and mechanisms of two physicochemical, mathematical models to predict experimental bicarbonate kinetics, hence, buffer transport, during a hemodialysis (HD) treatment in chronic renal failure patients. The existing Sargent model assumes that the body fluids can be described as a single, homogeneous extracellular fluid (EC) compartment whose volume decreases because of a constant ultrafiltration rate during HD. Bicarbonate and acetate transport between HD fluid and the EC compartment are by convection and diffusion with acetate metabolized in that compartment. The new model formulated in this study assumes the same conditions as Sargent et al., but constrains ion concentrations in the EC to be electrically neutral at all times. This constraint requires inclusion in the EC of other transportable small ions, Na+, K+, Cl- and unidentified, anionic organic acids in addition to an electrical charge on impermeable albumin. The findings are that the new electroneutrality model predicts plasma bicarbonate-concentration kinetics as closely as the Sargent model, but bicarbonate transport is an unlikely mechanism. Rather, the findings are better explained by rapid interconversion of CO2 and bicarbonate in this simplified EC compartment model. The results of this study bring into question the ability of the Sargent et al. hypothesized H+-mobilization model to explain buffer-transport kinetics during HD.

Acid-base kinetics during hemodialysis using bicarbonate and lactate as dialysate buffer bases based on the H+ mobilization model

BACKGROUND

The H⁺ mobilization model has been recently reported to accurately describe intradialytic kinetics of plasma bicarbonate concentration; however, the ability of this model to predict changing bicarbonate kinetics after altering the hemodialysis treatment prescription is unclear.

METHODS

We considered the H⁺ mobilization model as a pseudo-one-compartment model and showed theoretically that it can be used to determine the acid generation (or production) rate for hemodialysis patients at steady state. It was then demonstrated how changes in predialytic, intradialytic, and immediate postdialytic plasma bicarbonate (or total carbon dioxide) concentrations can be calculated after altering the hemodialysis treatment prescription.

RESULTS

Example calculations showed that the H⁺ mobilization model when considered as a pseudo-one-compartment model predicted increases or decreases in plasma total carbon dioxide concentrations throughout the entire treatment when the dialysate bicarbonate concentration is increased or decreased, respectively, during conventional thrice weekly hemodialysis treatments. It was further shown that this model allowed prediction of the change in plasma total carbon dioxide concentration after transfer of patients from conventional thrice weekly to daily hemodialysis using both bicarbonate and lactate as dialysate buffer bases.

CONCLUSION

The H⁺ mobilization model can predict changes in plasma bicarbonate or total carbon dioxide concentration during hemodialysis after altering the hemodialysis treatment prescription.

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.

Numerical simulations of the microvascular fluid balance with a non-linear model of the lymphatic system

Fluid homeostasis is required for life. Processes involved in fluid balance are strongly related to exchanges at the microvascular level. Computational models have been presented in the literature to analyze the microvascular-interstitial interactions. As far as we know, none of those models consider a physiological description for the lymphatic drainage-interstitial pressure relation. We develop a computational model that consists of a network of straight cylindrical vessels and an isotropic porous media with a uniformly distributed sink term acting as the lymphatic system. In order to describe the lymphatic flow rate, a non-linear function of the interstitial pressure is defined, based on literature data on the lymphatic system. The proposed model of lymphatic drainage is compared to a linear one, as is typically used in computational models. To evaluate the response of the model, the two are compared with reference to both physiological and pathological conditions. Differences in the local fluid dynamic description have been observed using the non-linear model. In particular, the distribution of interstitial pressure is heterogeneous in all the cases analyzed. The resulting averaged values of the interstitial pressure are also different, and they agree with literature data when using the non-linear model. This work highlights the key role of lymphatic drainage and its modeling when studying the fluid balance in microcirculation for both to physiological and pathological conditions, e.g. uremia.

Acid-base homeostasis during hemodialysis: New insights into the mystery of bicarbonate disappearance during treatment

In patients receiving hemodialysis, it has long been recognized that much more bicarbonate is delivered during treatment than ultimately appears in the blood. To gain insight into this mystery, we developed a model that allows a quantitative analysis of the patient's response to rapid alkalinization during hemodialysis. Our model is unique in that it is based on the distribution of bicarbonate in the extracellular fluid and assesses its removal from this compartment by mobilization of protons (H⁺ ) from buffers and other sources. The model was used to analyze the pattern of rise in blood bicarbonate concentration ([HCO₃^- ]), calculated from measurements of pH and PCO₂ , in patients receiving standard bicarbonate hemodialysis. Model analysis demonstrated two striking findings: (1) 35% of the bicarbonate added during hemodialysis was due to influx and metabolism of acetate, despite its low concentration in the bath solution, because of the rapidly collapsing gradient for bicarbonate influx. (2) Almost 90% of the bicarbonate delivered to the patients was neutralized by H⁺ generation. Virtually all the new H⁺ came from intracellular sources and included both buffering and organic acid production. The small amount of added bicarbonate retained in the extracellular fluid increased blood [HCO₃^- ], on average, by 6 mEq/L in our patients. Almost all this rise occurred during the first 2 hours. Thereafter, blood [HCO₃^- ] changed minimally and always remained less than bath [HCO₃^- ]. This lack of equilibrium was due to the continued production of organic acid. Release of H⁺ from buffers is a reversible physiological response, restoring body alkali stores. By contrast, organic acid production is an irreversible process during hemodialysis and is metabolically inefficient and potentially catabolic. Our analysis underscores the need to develop new approaches for alkali repletion during hemodialysis that minimize organic acid production.

A Bayesian approach for the identification of patient-specific parameters in a dialysis kinetic model

Hemodialysis is the most common therapy to treat renal insufficiency. However, notwithstanding the recent improvements, hemodialysis is still associated with a non-negligible rate of comorbidities, which could be reduced by customizing the treatment. Many differential compartment models have been developed to describe the mass balance of blood electrolytes and catabolites during hemodialysis, with the goal of improving and controlling hemodialysis sessions. However, these models often refer to an average uremic patient, while on the contrary the clinical need for customization requires patient-specific models. In this work, we assume that the customization can be obtained by means of patient-specific model parameters. We propose and validate a Bayesian approach to estimate the patient-specific parameters of a multi-compartment model, and to predict the single patient's response to the treatment, in order to prevent intra-dialysis complications. The likelihood function is obtained by means of a discretized version of the multi-compartment model, where the discretization is in terms of a Runge-Kutta method to guarantee convergence, and the posterior densities of model parameters are obtained through Markov Chain Monte Carlo simulation. Results show fair estimations and the applicability in the clinical practice.

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

INTRODUCTION

Hollow fiber models describe the exchange of solutes between blood and dialysate across the membrane of a single fiber of the hemodialysis filter (hemodialyzer). This work aims to develop a new approach to simulate the solute exchange in a hollow fiber in a dynamic and realistic way. Sodium was chosen as our solute of interest due to its importance in hemodialysis as an osmotic regulator.

METHODS

A 2-dimensional (2D) hollow fiber model based on the finite element method (FEM) is coupled to a simple blood pool model to dynamically update the concentration of the solute entering the dialyzer. The resulting coupled model maintains the geometrical detail of the 2D fiber representation and gains a dynamic, blood-side inlet solute concentration. In vitro dialysis sessions were carried out for model validation, by implementing a combination of blood volume loss and/or sodium concentration steps. Plasmatic sodium concentration was recorded by blood gas sampling. Dialysate inlet and outlet conductivities were continuously recorded.

RESULTS

Simulated plasmatic sodium concentration was compared with data from the blood gas samples. A mean error of 1.76 ± 1.03 mM was found for the complete dataset, along with a 3.87 mM maximum error. The simulated outlet dialysate sodium concentration was compared with the recorded outlet dialysate conductivity: a very high correlation was found on the whole dataset (R2 = 0.992).

CONCLUSIONS

Coupling our FEM hollow fiber model to a simple blood pool model proved to be an effective approach for dynamical analysis of the properties of the hemodialyzer.