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

Mechanisms of whole body, respiratory, acid-base buffering: a first computer-model test of three physicochemical, acid-base theories

Acid-base disorders are currently analyzed and treated using a bicarbonate-centered approach derived from blood studies prior to the advent of digital computers, which could solve computer models capable of quantifying the complex physicochemical nature governing distribution of water and ions between fluid compartments. An alternative is the Stewart approach, which can predict the pH of a simple mixture of ions and electrically charged proteins; hence, the role of extravascular fluids has been largely ignored. The present study uses a new, comprehensive computer model of four major fluid compartments, based on a recent blood model, which included ion binding to proteins, electroneutrality constraints, and other essential physicochemical laws. The present model predicts quantitative respiratory acid-base buffering behavior in the whole body, as well as determining roles of each compartment and their species, particularly compartmental electrically charged proteins, largely responsible for buffering. The model tested an early theory that H+ was conserved in the body fluids; hence, when changing Pco2 states, intracellular buffering could be predicted by net changes in bicarbonate and protein electrical charge in the remaining fluids. Even though H+ is not conserved in the model, the theory held in simulated respiratory disorders. Model results also agreed with a second part of the theory, that ion movements between cells and interstitial fluid were linked with H+ buffering, but by electroneutrality constraints, not necessarily by some membrane-related mechanisms, and that the strong ion difference (SID), an amalgamation of ionic electrical charges, was approximately conserved when going between equilibrium states caused by Pco2 changes in the body-fluid system.NEW & NOTEWORTHY For the first time, a physicochemically based, whole body, four-compartment, computer model was used to study respiratory whole body acid-base buffering. An improved approach to quantify acid-base buffering, previously used by this author, was able to determine contributions of the various compartmental fluids to whole body buffering. The model was used to test, for the first time, three fundamental theories of whole body acid-base homeostasis, namely, H+-conservation, its linkage to ion transport, and strong ion difference conservation.

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.

Impact of the nature of the capillary wall on plasma refilling during hemodialysis

OBJECTIVES

Our aim was to clarify the impact of the nature of the capillary wall, defined by the contribution of large (LP), small (SP), and ultrasmall (UP) pores, on plasma refilling in a hemodialysis session.

METHODS

This study included data from 78 patients. The relative blood volume change (ΔBV%) was monitored using a Crit-Line monitor. A bioimpedance device was used to measure extracellular and intracellular fluid volumes, and the excess fluid mass (M_ExF) was calculated. We simulated blood volume change (sΔBV%) based on a three-pore model. Hydraulic permeability of the capillary wall (LpS) and fractional contribution of LP to LpS (α_LP) were determined by fitting sΔBV to ΔBV. The total refilling volume (TV_ref) was calculated from the total ultrafiltration volume and total blood volume change. Values were standardized to a body surface area of 1.73 m² and are denoted by the subscript BSA.

RESULTS

LpS and α_LP were 3.09 (2.32, 4.68) mL/mmHg/min and 0.069 (0.023, 0.109), respectively. The standardized regression coefficient (β) of the ultrafiltration rate (UFR_BSA) and initial excess fluid mass (M_ExF,_BSA,0) by multiple linear regression analysis of TV_ref,BSA without (Model 1) and with (Model 2) α_LP were as follows: UFR_BSA, 0.714/<0.001 (β/p); M_ExF,_BSA,0, 0.247/<0.001 (Model 1); UFR_BSA, 0.799/<0.001; M_ExF,_BSA,0, 0.066/0.237; and α_LP, -0.327/<0.001 (Model 2).

CONCLUSIONS

The impact of volume overload (M_ExF,_BSA,0) on plasma refilling became insignificant with the addition of α_LP in the model, suggesting that the nature of the capillary wall described by inter-endothelial gaps (LP) may have a greater impact on plasma refilling than volume overload.

Using a Human Circulation Mathematical Model to Simulate the Effects of Hemodialysis and Therapeutic Hypothermia

Background: We developed a hemodynamic mathematical model of human circulation coupled to a virtual hemodialyzer. The model was used to explore mechanisms underlying our clinical observations involving hemodialysis. Methods: The model consists of whole body human circulation, baroreflex feedback control, and a hemodialyzer. Four model populations encompassing baseline, dialysed, therapeutic hypothermia treated, and simultaneous dialysed with hypothermia were generated. In all populations atrial fibrillation and renal failure as co-morbidities, and exercise as a treatment were simulated. Clinically relevant measurables were used to quantify the effects of each in silico experiment. Sensitivity analysis was used to uncover the most relevant parameters. Results: Relative to baseline, the modelled dialysis increased the population mean diastolic blood pressure by 5%, large vessel wall shear stress by 6%, and heart rate by 20%. Therapeutic hypothermia increased systolic blood pressure by 3%, reduced large vessel shear stress by 15%, and did not affect heart rate. Therapeutic hypothermia reduced wall shear stress by 15% in the aorta and 6% in the kidneys, suggesting a potential anti-inflammatory benefit. Therapeutic hypothermia reduced cardiac output under atrial fibrillation by 12% and under renal failure by 20%. Therapeutic hypothermia and exercise did not affect dialyser function, but increased water removal by approximately 40%. Conclusions: This study illuminates some mechanisms of the action of therapeutic hypothermia. It also suggests clinical measurables that may be used as surrogates to diagnose underlying diseases such as atrial fibrillation.

Mechanisms of Peritoneal Acid-Base Kinetics During Peritoneal Dialysis: A Mathematical Model Study

To investigate mechanisms of acid-base changes during peritoneal dialysis (PD), a mathematical model was developed that describes kinetics of peritoneal bicarbonate, CO2, and pH during the dwell with both high and low lactate-containing dialysis fluids. The model was based on a previous modification of the Rippe 3-Pore model of water and solute kinetic transport across the peritoneal membrane during the PD dwell. A central feature of the present modification is an electroneutrality constraint on peritoneal-fluid ion concentrations, which results in the conclusion that peritoneal bicarbonate-concentration kinetics are entirely dependent on the kinetics of the other ions. This new model was able to closely predict peritoneal bicarbonate-concentration kinetics during the dwell. Predictions of total peritoneal bicarbonate-mass kinetics were greater than those of porous, transmembrane bicarbonate transport, suggesting that a portion of bicarbonate comes from CO2 transport, both porous and nonporous and then a partial conversion to bicarbonate. Fitting the model to experimental pH data during the dwell, required addition of a peritoneal CO2 mass-conservation constraint, coupled with the description for peritoneal bicarbonate kinetics. Predicted pH kinetics during the dwell, closely mimicked the experimental data. The conclusion was that the mechanisms describing peritoneal bicarbonate and pH kinetics during PD must include 1) electroneutrality of peritoneal fluid, 2) porous transport of bicarbonate and CO2, 3) nonporous transport of CO2, and 4) CO2 conversion to bicarbonate. These mechanisms are quite different and more complex than the bicarbonate-centered, lactate to acid-generation mechanisms previously proposed.

Hemodialysis-induced changes in hematocrit, hemoglobin and total protein: Implications for relative blood volume monitoring

Background

Relative blood volume (RBV) changes during hemodialysis (HD) are typically estimated based on online measurements of hematocrit, hemoglobin or total blood protein. The aim of this study was to assess changes in the above parameters during HD in order to compare the potential differences in the RBV changes estimated by individual methods.

Methods

25 anuric maintenance HD patients were monitored during a 1-week conventional HD treatment. Blood samples were collected from the arterial dialysis blood line at the beginning and at the end of each HD session. The analysis of blood samples was performed using the hematology analyzer Advia 2120 and clinical chemistry analyzer Advia 1800 (Siemens Healthcare).

Results

During the analyzed 30 HD sessions with ultrafiltration in the range 0.7–4.0 L (2.5 ± 0.8 L) hematocrit (HCT) increased by 9.1 ± 7.0% (mean ± SD), hemoglobin (HGB) increased by 10.6 ± 6.3%, total plasma protein (TPP) increased by 15.6 ± 9.5%, total blood protein (TBP) increased by 10.4 ± 5.8%, red blood cell count (RBC) increased by 10.8 ± 7.1%, while mean corpuscular red cell volume (MCV) decreased by 1.5 ± 1.1% (all changes statistically significant, p < 0.001). HGB increased on average by 1.5% more than HCT (p < 0.001). The difference between HGB and TBP increase was insignificant (p = 0.16).

Conclusions

Tracking HGB or TBP can be treated as equivalent for the purpose of estimating RBV changes during HD. Due to the reduction of MCV, the HCT-based estimate of RBV changes may underestimate the actual blood volume changes.