Plasma volume response patterns and a physiologic model of ultrafiltration in hemodialysis.

BACKGROUND: Ultrafiltration (UF) is an essential process of restoring fluid homeostasis during hemodialysis (HD). Fluid shifts across the extracellular compartments during UF, predominantly across the capillary interface and between the macro- and microcirculation. A mismatch between UF and transcapillary fluid transport can lead to hemodynamic instability leading to cardiac morbidity. We wished to study intradialytic fluid transport characteristics and their variation during UF to identify factors that govern variability in transcapillary fluid movement in HD. METHODS: Twenty-two patients undergoing stable HD sessions were studied to measure and monitor absolute blood and plasma volume throughout UF. A computational mathematical model of predicted plasma volume decay during UF was analyzed with respect to the intradialytic real-time data profile. Pre- and post-dialysis fluid status was assessed using multifrequency bioimpedance spectroscopy. Serum electrolytes, osmolality, and total protein concentration were measured pre- and post-dialysis and during the intradialytic phase. RESULTS: Two distinct profiles of PV responses were detected. 60% of the patients presented plasma volume decline, characterized by a high percentage of volume decrease during the first hour, and a subsequent slower decrease with early rebound. The model was modified to achieve a proper fit of these volume profiles, assuming time-dependent changes in selected parameters governing the refilling flow. CONCLUSIONS: Although the modified model could more accurately fit the data, the new parameter values often fell outside of a physiologically acceptable range, suggesting that other factors not included in the classic description of transcapillary fluid transport might be the cause of the observed patterns.

Modeling acid-base balance during continuous kidney replacement therapy.

Clinical studies have suggested that use of bicarbonate-containing substitution and dialysis fluids during continuous kidney replacement therapy may result in excessive increases in the carbon dioxide concentration of blood; however, the technical parameters governing such changes are unclear. The current work used a mathematical model of acid-base chemistry of blood to predict its composition within and exiting the extracorporeal circuit during continuous veno-venous hemofiltration (CVVH) and continuous veno-venous hemodiafiltration (CVVHDF). Model predictions showed that a total substitution fluid infusion rate of 2 L/h (33% predilution) with a bicarbonate concentration of 32 mEq/L during CVVH at a blood flow rate of 200 mL/min resulted in only modest increases in plasma bicarbonate concentration by 2.0 mEq/L and partial pressure of dissolved carbon dioxide by 4.4 mmHg in blood exiting the extracorporeal circuit. The relative increase in bicarbonate concentration (9.7%) was similar to that in partial pressure of dissolved carbon dioxide (8.2%), resulting in no significant change in plasma pH in the blood exiting the CVVH circuit. The changes in plasma acid-base levels were larger with a higher infusion rate of substitution fluid but smaller with a higher blood flow rate or use of substitution fluid with a lower bicarbonate concentration (22 mEq/L). Under comparable flow conditions and substitution fluid composition, model predicted changes in acid-base levels during CVVHDF were similar, but smaller, than those during CVVH. The described mathematical model can predict the effect of operating conditions on acid-base balance within and exiting the extracorporeal circuit during continuous kidney replacement therapy.

Transcapillary Refilling Rate and Its Determinants during Haemodialysis with Standard and High Ultrafiltration Rates.

BACKGROUND: Achieving euvolaemia using ultrafiltration (UF) during haemodialysis (HD) without inducing haemodynamic instability presents a major clinical challenge. Transcapillary refill is a key factor in sustaining the circulating blood volume (BV) during UF, which is in turn predicted by the rate of refilling. However, absolute plasma refilling rate (PRR), its determinants and variability with UF rate (UFR), have not been reported in the literature. METHOD: We studied paired HD sessions (n = 48) in 24 patients over 2 consecutive mid-week HD treatments. Plasma refilling was measured using real-time, minute-by-minute relative BV changes obtained from the integrated BV monitoring device during UF. A fixed bolus dilution approach at the start of HD was used to calculate absolute BV. The first control HD session was undertaken with a standard UFR required to achieve the prescribed target weight, while during the second study session, a fixed (high) UFR (1 L/h) was applied, either in the first (n = 12 patients) or in the final hour (n = 12 patients) of the HD session. Participants' had their hydration status measured pre- and post-HD using multifrequency bioimpedance (BIS). Blood pressure was measured at 15-min intervals and blood samples were collected at 7 intervals during HD sessions. RESULTS: The mean PRR during a standard 4-hr HD session was 4.3 ± 2.0 mL/kg/h and varied between 2 and 6 mL/kg/h. There was a mean time delay of 22 min (range 13.3-35.0 min) for onset of plasma refilling after the application of UF irrespective of standard or high UFRs. The maximum refilling occurred during the second hour of HD (mean max PRR 6.8 mL/kg/h). UFR (beta = 0.60, p < 0.01) and BIS derived pre-HD overhydration index (beta = 0.44, p = 0.01) were consistent, independent predictors of the mean PRR (R2 = 0.49) in all HD sessions. At high UFRs, PRR exceeded 10 mL/kg/h. The total overall plasma refill contribution to UF volume was not significantly different between standard and high UF. During interventions no significant haemodynamic instability was observed in the study. CONCLUSION: We describe absolute transcapillary refilling rate and its profile during HD with UF. The findings provide the basis for the development of UF strategies to match varying PRRs during HD. An approach to fluid removal, which is tailored to patients' refilling rates and capacity, provides an opportunity for more precision in the practice of UF.

Evaluating hydrogen ion mobilization during hemodialysis using only predialysis and postdialysis blood bicarbonate concentrations.

INTRODUCTION: The hydrogen ion (H+) mobilization model has been previously shown to provide a quantitative description of intradialytic changes in blood bicarbonate (HCO3) concentration during hemodialysis (HD). The current study evaluated the accuracy of different methods for estimating the H+ mobilization parameter (Hm) from this model. METHODS: The study compared estimates of the H+ mobilization parameter using predialysis, hourly during the HD treatment, and postdialysis blood HCO3 concentrations (Hm-full2) with those determined using only predialysis and postdialysis blood HCO3 concentrations assuming steady state conditions (Hm-SS2) during the midweek treatment in 24 chronic HD patients treated thrice weekly. RESULTS: Estimated Hm-full2 values (0.163 ± 0.079 L/min [mean ± standard deviation]) were higher than, but not statistically different (p = 0.067) from, those of Hm-SS2 (0.152 ± 0.065 L/min); the values of Hm-full2 and Hm-SS2 were highly correlated with a correlation coefficient of 0.948 and a mean difference that was small (0.011 L/min). Further, the H+ mobilization parameter values calculated using only predialysis and postdialysis blood HCO3 concentrations during the first and third HD treatments of the week were not different from those calculated during the midweek treatment. CONCLUSIONS: The H+ mobilization model can be used to provide estimates of the H+ mobilization parameter without the need to measure hourly intradialytic blood HCO3 concentrations.

Effect of time-dependent dialysate bicarbonate concentrations on acid-base and uremic solute kinetics during hemodialysis treatments.

Recent studies have suggested benefits for time-dependent dialysate bicarbonate concentrations (Dbic) during hemodialysis (HD). In this clinical trial, we compared for the first time in the same HD patients the effects of time-dependent changes with constant Dbic on acid-base and uremic solute kinetics. Blood acid-base and uremic solute concentration were measured in twenty chronic HD patients during 4-h treatments with A) constant Dbic of 35 mmol/L; B) Dbic of 35 mmol/L then 30 mmol/L; and C) Dbic of 30 mmol/L then 35 mmol/L (change of Dbic after two hours during Treatments B and C). Arterial blood samples were obtained predialysis, every hour during HD and one hour after HD, during second and third treatments of the week with each Dbic concentration profile. Blood bicarbonate concentration (blood [HCO3]) during Treatment C was lower only during the first three HD hours than in Treatment A. Overall blood [HCO3] was reduced during Treatment B in comparison to Treatment A at each time points. We conclude that a single change Dbic in the middle of HD can alter the rate of change in blood [HCO3] and pH during HD; time-dependent Dbic had no influence on uremic solute kinetics.

Mathematical modelling of bicarbonate supplementation and acid-base chemistry in kidney failure patients on hemodialysis.

Acid-base regulation by the kidneys is largely missing in end-stage renal disease patients undergoing hemodialysis (HD). Bicarbonate is added to the dialysis fluid during HD to replenish the buffers in the body and neutralize interdialytic acid accumulation. Predicting HD outcomes with mathematical models can help select the optimal patient-specific dialysate composition, but the kinetics of bicarbonate are difficult to quantify, because of the many factors involved in the regulation of the bicarbonate buffer in bodily fluids. We implemented a mathematical model of dissolved CO2 and bicarbonate transport that describes the changes in acid-base equilibrium induced by HD to assess the kinetics of bicarbonate, dissolved CO2, and other buffers not only in plasma but also in erythrocytes, interstitial fluid, and tissue cells; the model also includes respiratory control over the partial pressures of CO2 and oxygen. Clinical data were used to fit the model and identify missing parameters used in theoretical simulations. Our results demonstrate the feasibility of the model in describing the changes to acid-base homeostasis typical of HD, and highlight the importance of respiratory regulation during HD.

Validity of the hydrogen ion mobilisation model during haemodialysis with time-dependent dialysate bicarbonate concentrations.

BACKGROUND: The hydrogen ion (H+) mobilisation model has been previously shown to accurately describe blood bicarbonate (HCO3) kinetics during haemodialysis (HD) when the dialysate bicarbonate concentration ([HCO3]) is constant throughout the treatment. This study evaluated the ability of the H+ mobilization model to describe blood HCO3 kinetics during HD treatments with a time-dependent dialysate [HCO3]. METHODS: Data from a recent clinical study where blood [HCO3] was measured at the beginning of and every hour during 4-h treatments in 20 chronic, thrice-weekly HD patients with a constant (Treatment A), decreasing (Treatment B) and increasing (Treatment C) dialysate [HCO3] were evaluated. The H+ mobilization model was used to determine the model parameter (Hm) that provided the best fit of the model to the clinical data using nonlinear regression. A total of 114 HD treatments provided individual estimates of Hm. RESULTS: Mean ± standard deviation estimates of Hm during Treatments A, B and C were 0.153 ± 0.069, 0.180 ± 0.109 and 0.205 ± 0.141 L/min (medians [interquartile ranges] were 0.145 [0.118,0.191], 0.159 [0.112,0.209], 0.169 [0.115,0.236] L/min), respectively; these estimates were not different from each other (p = 0.26). The sum of squared differences between the measured blood [HCO3] and that predicted by the model were not different during Treatments A, B and C (p = 0.50), suggesting a similar degree of model fit to the data. CONCLUSIONS: This study supports the validity of the H+ mobilization model to describe intradialysis blood HCO3 kinetics during HD with a constant Hm value when using a time-dependent dialysate [HCO3].

Calculation of the Gibbs-Donnan factors for multi-ion solutions with non-permeating charge on both sides of a permselective membrane.

Separation of two ionic solutions with a permselective membrane that is impermeable to some of the ions leads to an uneven distribution of permeating ions on the two sides of the membrane described by the Gibbs-Donnan (G-D) equilibrium with the G-D factors relating ion concentrations in the two solutions. Here, we present a method of calculating the G-D factors for ideal electroneutral multi-ion solutions with different total charge of non-permeating species on each side of a permselective membrane separating two compartments. We discuss some special cases of G-D equilibrium for which an analytical solution may be found, and we prove the transitivity of G-D factors for multi-ion solutions in several compartments interconnected by permselective membranes. We show a few examples of calculation of the G-D factors for both simple and complex solutions, including the case of human blood plasma and interstitial fluid separated by capillary walls. The article is accompanied by an online tool that enables the calculation of the G-D factors and the equilibrium concentrations for multi-ion solutions with various composition in terms of permeating ions and non-permeating charge, according to the presented method.

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.

Does the plasma refilling coefficient change during hemodialysis sessions?

The filtration coefficient in the Starling equation is an important determinant of plasma refilling during hemodialysis. A method for calculating from clinical data an estimate of the filtration coefficient, called the refilling coefficient, was proposed in the past. The assumption behind this method was that the only drive for refilling is the increase in plasma oncotic pressure, and the remaining Starling forces have negligible effect. The refilling coefficient was observed to decrease during hemodialysis, and this was interpreted as a change in the filtration coefficient. The purpose of our study was providing an alternative explanation for the behavior of the refilling coefficient and, using clinical data and mathematical modeling, to predict the values of the immeasurable Starling forces and provide the theoretical basis for the interpretation of the refilling coefficient as the filtration coefficient. Blood volume and bioimpedance data from 23 patients undergoing hemodialysis were used to calculate the refilling coefficient according to the original formulation and to fit a two-compartment model of protein and fluid transport. The changes in the other Starling forces were non-negligible, ranging from 19% to 60% of plasma oncotic pressure. The results showed that the decrease observed in the refilling coefficient is likely caused by neglecting important changes in the Starling forces while deriving the equation for the refilling coefficient. When these Starling forces were taken into account, constant filtration coefficient and dynamic refilling coefficient provided an equivalent description of the data in most cases. However, this was not true for a subgroup of sessions, which suggests that additional factors may also be responsible for the observed decrease in the refilling coefficient.

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 (Jv,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, JpMAX. From the data we estimated JpMAX and two other parameters linked to transcapillary transport of fluid and protein: the capillary filtration coefficient Lp and its large pores fraction αLP. In an Expanded model one more generic solute was included to evaluate the impact of the number of substances appearing in the equation describing Jv,ISIC. RESULTS: In the baseline model, median values (interquartile range) of estimated parameters were: Lp: 11.63 (7.9, 14.2) mL/min/mmHg, αLP: 0.056 (0.050, 0.058), and JpMAX: 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, αLP: 0.046 (0.038, 0.052), and JpMAX: 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 JpMAX indicating that this parameter is highly sensitive to the number of species modeled, and that the value of JpMAX should be interpreted only in relation to this factor.

Phosphate equilibration rate and daily clearance in patients on CAPD, CCPD and APD.

BACKGROUND: Criteria for how to assess removal rate of inorganic phosphorous (iP) in peritoneal dialysis (PD) and whether iP removal differs between different PD modalities are debated. METHODS: In a cross-sectional study, 73 prevalent patients on continuous ambulatory PD (n = 16), continuous cyclic PD (n = 8) or automated PD (n = 49) with mean age 54 (range, 18-87) years, 46 males, underwent standard peritoneal equilibration test (PET) and 24-hour collection of dialysate with measurements of iP, urea and creatinine in all samples and bags. There were 11 slow, 53 average, and 9 fast transporters. RESULTS: D/P ratios for iP and creatinine at 4 h of PET were strongly correlated (ρ = 0.86, p<0.0001). Allocation of patients into slow, average and fast transporters according to D/P ratios for iP and creatinine was essentially similar. Whereas the weekly peritoneal clearance of iP (30.8 ± 16.6 L/wk) was lower than that of creatinine (38.4 ± 14.9 L/wk), clearances were strongly correlated (ρ = 0.89, p<0.0001). The correlation between peritoneal weekly clearance of iP and urea KT/V was however weak (ρ = 0.56, p<0.0001. CAPD patients had higher iP clearance than APD patients, 43.2 ± 14.9 versus 24.7 ± 13.4 L/wk (p<0.05); however, serum iP concentrations did not differ. CONCLUSIONS: Creatinine is a good surrogate marker for phosphate removal, both as assessed by PET and by 24 hours' clearance, in different PD modalities. Therefore, a separate PET scale for phosphate may not be needed. iP removal was greater with CAPD than APD but serum phosphate levels did not differ.

Changes of peritoneal transport parameters with time on dialysis: assessment with sequential peritoneal equilibration test.

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.

Modelling Transcapillary Transport of Fluid and Proteins in Hemodialysis Patients.

BACKGROUND: The kinetics of protein transport to and from the vascular compartment play a major role in the determination of fluid balance and plasma refilling during hemodialysis (HD) sessions. In this study we propose a whole-body mathematical model describing water and protein shifts across the capillary membrane during HD and compare its output to clinical data while evaluating the impact of choosing specific values for selected parameters. METHODS: The model follows a two-compartment structure (vascular and interstitial space) and is based on balance equations of protein mass and water volume in each compartment. The capillary membrane was described according to the three-pore theory. Two transport parameters, the fractional contribution of large pores (αLP) and the total hydraulic conductivity (LpS) of the capillary membrane, were estimated from patient data. Changes in the intensity and direction of individual fluid and solute flows through each part of the transport system were analyzed in relation to the choice of different values of small pores radius and fractional conductivity, lymphatic sensitivity to hydraulic pressure, and steady-state interstitial-to-plasma protein concentration ratio. RESULTS: The estimated values of LpS and αLP were respectively 10.0 ± 8.4 mL/min/mmHg (mean ± standard deviation) and 0.062 ± 0.041. The model was able to predict with good accuracy the profiles of plasma volume and serum total protein concentration in most of the patients (average root-mean-square deviation < 2% of the measured value). CONCLUSIONS: The applied model provides a mechanistic interpretation of fluid transport processes induced by ultrafiltration during HD, using a minimum of tuned parameters and assumptions. The simulated values of individual flows through each kind of pore and lymphatic absorption rate yielded by the model may suggest answers to unsolved questions on the relative impact of these not-measurable quantities on total vascular refilling and fluid balance.

Peritoneal Fluid Transport rather than Peritoneal Solute Transport Associates with Dialysis Vintage and Age of Peritoneal Dialysis Patients.

During peritoneal dialysis (PD), the peritoneal membrane undergoes ageing processes that affect its function. Here we analyzed associations of patient age and dialysis vintage with parameters of peritoneal transport of fluid and solutes, directly measured and estimated based on the pore model, for individual patients. Thirty-three patients (15 females; age 60 (21-87) years; median time on PD 19 (3-100) months) underwent sequential peritoneal equilibration test. Dialysis vintage and patient age did not correlate. Estimation of parameters of the two-pore model of peritoneal transport was performed. The estimated fluid transport parameters, including hydraulic permeability (LpS), fraction of ultrasmall pores (α u), osmotic conductance for glucose (OCG), and peritoneal absorption, were generally independent of solute transport parameters (diffusive mass transport parameters). Fluid transport parameters correlated whereas transport parameters for small solutes and proteins did not correlate with dialysis vintage and patient age. Although LpS and OCG were lower for older patients and those with long dialysis vintage, αu was higher. Thus, fluid transport parameters--rather than solute transport parameters--are linked to dialysis vintage and patient age and should therefore be included when monitoring processes linked to ageing of the peritoneal membrane.

Kinetics of plasma refilling during hemodialysis sessions with different initial fluid status.

Removal of fluid excess from the plasma volume by ultrafiltration during hemodialysis (HD) is balanced by plasma refilling from the interstitium, driven mainly by the increase in plasma oncotic pressure. We calculated the plasma refilling coefficient (Kr, a parameter expressing the ratio of refilling rate to the increase in oncotic pressure) for nine patients, each undergoing two HD sessions differing by pretreatment fluid status and session time (shorter session, SH, 3.5 h, and longer session, LH, 4.5h). Relative blood volume change was measured online, and solute concentrations were measured regularly during the sessions. The volume of body compartments was measured by bioimpedance. The patients were more volume expanded before LH session (higher initial body mass and total body water). Oncotic pressure was similar for both sessions. The refilling rate, despite higher fluid overload in the LH sessions, was similar for both sessions. The final Kr values stabilized on similar levels (SH: 136.6 ± 55.6 ml/mm Hg/h and LH: 150.7 ± 73.6 ml/mm Hg/h) at similar times, notwithstanding the difference in initial fluid overload between the two groups, suggesting that Kr at dry weight is relatively insensitive to the initial fluid status of the patient.

Can the three pore model correctly describe peritoneal transport of protein?

The three pore model (3PM) includes large pores for the description of protein leak to the peritoneal cavity during peritoneal dialysis. However, the reliability of this description has been not fully tested against clinical data yet. Peritoneal transport parameters were estimated using 3PM, extended 3p model (with estimation of fraction of large pores, ext3PM), ext3PM with modified size of pores and proteins (mext3PM), and simplified two pore (2PM, small and ultrasmall pores) models for 32 patients on peritoneal dialysis investigated using the sequential peritoneal equilibration test (consecutive peritoneal equilibration test [PET]: glucose 2.27%, 4 h, and miniPET: glucose 3.86%, 1 h). Urea, creatinine, glucose, sodium, phosphate, albumin, and IgM concentrations were measured in dialysis fluid and plasma. Ext3PM and mext3PM, with large pore fraction of about 0.14, provided a good description of fluid and small solute kinetics, but their predictions for albumin transport were less accurate. Two pore model precisely described the data on fluid and small solute transport. The 3p models could not describe the diffusive-convective transport of albumin as precisely as the transport of fluid, small solutes, and IgM. The 2p model (not applicable for proteins) was an efficient tool for modeling fluid and small solute transport.