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.

Physicochemical properties of abnormal blood acid-base buffering.

This paper describes two new features 1) development of physicochemically based, two-compartment models describing acid-base-state changes in normal and abnormal blood and 2) use of model results to view and describe physicochemical properties of blood, in terms of Pco2 as the causative independent variable and effected [H+] changes as the dependent variable. Models were derived from an in vitro experimental study, where normal blood was made both hypoproteinemic and hyperalbuminemic and then equilibrated with CO2. Strong-ion gap (SIG) values were selected to match model and experimental pH. The effect of individual physicochemical factors affecting blood acid-base-state were evaluated from their induced changes on buffer curve linearized slope (ßH+) and [H+] curve shift at 40 mmHg ([H+]40). Model findings were: 1) in severe hypoproteinemia, hemoglobin enhances buffering (decreases ßH+), whereas albumin compromises it, resulting in an almost unchanged ßH+; [H+]40 decreases (alkalemia) due to hypoalbuminemia. 2) Severe hyperalbuminemia greatly increases both ßH+ and [H+]40, hence, compromising buffering and causing a severe acidemia. 3) Pco2-induced changes in the electrical-charge concentration of hemoglobin are the principal factor responsible for maintaining normal buffering characteristics in hypoproteinemia and hyperalbuminemia. 4) SIG values are a third Pco2-independent characteristic of blood acid-base state and 5) the quantities, ßH+, [H+]40, and SIG, derived from a [H+] vs. Pco2 perspective, are a more informative and intuitive way to characterize blood acid-base state.NEW & NOTEWORTHY This study represents the most up-to-date, physicochemical, multi-compartment computer model of the processes involved in determining the acid-base buffering state of blood. Previous models lack this capability, notably by being single compartment and/or lacking electroneutrality and osmotic constraints. Model results, analyzed from a different perspective of dependent [H+] changes resulting from independent Pco2 changes, provide a new set of Pco2-independent parameters, characteristic of blood buffering properties.

Mechanisms of Blood pH Changes in Venovenous Extracorporeal Membrane Systems: Roles of Hemoglobin-Ion Binding and Donnan Equilibrium.

An equilibrium model was developed to understand interrelated, physicochemical mechanisms leading to blood pH and electrolyte distribution changes in patients because of venovenous extracorporeal membrane oxygenation (ECMO) and carbon dioxide removal. The model consists of plasma and red cell compartments between which water and small ions can move to establish an equilibrium state. Governing forces are as follows: 1) ionic electroneutrality in each compartment; 2) osmotic equilibrium between compartments; 3) mass balance of small ions other than bicarbonate; 4) oxygen (O 2 )-dependent hemoglobin (Hb)-Cl binding in red cells; 5) albumin binding to Cl - , Ca 2+ , and Mg 2+ in plasma; and 6) chemical equilibria of carbonates and phosphates in each compartment. The model was constructed and validated using recent clinical ECMO inlet and exit blood-pH and electrolyte concentration data. The model closely described pH and electrolyte concentration changes in both states, which validated the model. The model was then used to predict CO 2 and O 2 saturation-induced changes in pH and electrolyte concentrations. It was found that O 2 -dependent Hb-Cl binding had a much lesser effect on blood acid-base status changes and electrolyte shifts during ECMO than previously thought. The model showed that the Cl-shift and Gibbs-Donnan equilibrium effects, characterized by pH and electrolyte distribution changes during ECMO, were primarily caused by changes in pH-induced electrical charge on mainly Hb and other constrained ions in red cells. These insights can improve understanding of the same factors acting when blood traverses the lung.

Peritoneal physicochemical transport mechanisms: Hypotheses, models and controversies.

This study answers criticisms by Waniewski et al. of the recent paper by Wolf on peritoneal transport kinetic models. Their criticisms centre on the accuracy of the data used for model fits, the hypothesis presented, which involves changes in glucose membrane parameters at high peritoneal glucose concentration and on the necessary techniques required to achieve accurate model parameter estimation. In response, this article shows that (1) the mean values previously captured from graphical depictions of Heimburger et al. are not different than those captured from the recent Waniewski et al. graphs, (2) a much simpler hypothesis is proposed, which centres on intraperitoneal pressure-induced lymph flow during the dialysis dwell and (3) the finding that the new model predictions, with only two constant parameter values, as estimated by the Powell algorithm, give a closer fit than the Waniewski model, which uses many time-varying parameters. The current findings again bring into question of the validity of their vasodilation hypothesis, leading to transient changes in capillary surface area during the dwell.

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.

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.

Are transient changes in capillary surface area required to explain peritoneal transport in renal failure patients?

BACKGROUND: Waniewski postulated a transient increase in peritoneal capillary surface area to fit their model predictions to experimental data of Heimburger measured in renal failure (RF) patients undergoing peritoneal dialysis (PD) but with only a 3.86% glucose dialysis fluid. The present aim is to propose a new mathematical model of the patient PD procedure that could closely fit the complete Heimburger measurement set without this postulate. METHODS: The three-pore model of Rippe was used to describe transient changes in peritoneal volume and solute concentrations during a PD dwell. The predialysis, RF patient, plasma solute concentrations were assumed to remain constant during the dwell. The model was validated using the 3.86% glucose Heimburger measurements. Permeability surface area product parameters were chosen to match only the end-dwell peritoneal fluid glucose concentration and the end-dwell amounts of urea, creatinine, and Na+ removed from this simulated patient group. Then, this model was used to predict additional measurements by Heimburger on two other patient groups dialyzed with glucose concentrations of 2.27% and 1.36%, respectively. Parameters were unchanged when simulating these other patient groups. RESULTS: To match the shape of the transient changes in drained volume and dialysis fluid glucose concentration for the 3.86% glucose group, it was necessary for only one parameter, the effective radius of glucose, to vary linearly in proportion to the dialysis fluid glucose concentration. This description was unchanged in the other two groups. CONCLUSION: Postulated transient increases in peritoneal capillary surface area were unnecessary to predict the entire Heimburger measurements.

Physicochemical Models of Acid-Base.

Physicochemical models have played an important role in understanding, diagnosing, and treating acid-base disorders for more than 100 years. This review focuses on recent complex models, solved using computers, and shows how these models provide new understanding and diagnostic approaches in acid-base disorders. These advanced models use the following physicochemical principles: (1) chemical equilibrium, (2) conservation of mass, (3) electroneutrality, and (4) osmotic equilibrium to describe the steady-state distribution of H2O and ions in the four major body-fluid spaces, cells, interstitium, plasma, and erythrocytes, and show how this distribution is changed by fluid infusions and losses through renal and gastrointestinal physiological processes. Illustrations of model use with a new comprehensive diagnostic approach are the understanding of an important clinical situation, saline acidosis, and the diagnosis of a patient with diabetic ketoacidosis. This new approach predicts a patient's whole-body base excess and partitions this value into 10 individual values, producing the disorder. These data and other data produced by the diagnostic model described in this review provide much more extensive insight than previous approaches.

Hemoglobin-Dilution Method: Effect of Measurement Errors on Vascular Volume Estimation.

The hemoglobin-dilution method (HDM) has been used to estimate changes in vascular volumes in patients because direct measurements with radioisotopes are time-consuming and not practical in many facilities. The HDM requires an assumption of initial blood volume, repeated measurements of plasma hemoglobin concentration, and the calculation of the ratio of hemoglobin measurements. The statistics of these ratio distributions resulting from measurement error are ill-defined even when the errors are normally distributed. This study uses a "Monte Carlo" approach to determine the distribution of these errors. The finding was that these errors could be closely approximated with a log-normal distribution that can be parameterized by a geometric mean (X) and a dispersion factor (S). When the ratio of successive Hb concentrations is used to estimate blood volume, normally distributed hemoglobin measurement errors tend to produce exponentially higher values of X and S as the SD of the measurement error increases. The longer tail of the distribution to the right could produce much greater overestimations than would be expected from the SD values of the measurement error; however, it was found that averaging duplicate and triplicate hemoglobin measurements on a blood sample greatly improved the accuracy.

Hyperglycemia-induced hyponatremia: Reevaluation of the Na+ correction factor.

This study addresses the clinically important relationship between the decreases in plasma Na+ and the increases in plasma glucose concentrations seen in diabetes and other hyperglycemic syndromes. This plasma 'Na+ correction factor', is generally accepted as 1.6mM Na+ per 100mg% glucose (0.29mM/mM in SI units) assuming osmotic equilibrium, although much larger numbers have been measured in experiments on normal humans. To resolve this controversy, a mathematical model of whole-body fluid-electrolyte balance was used to perform the experiment wherein plasma glucose concentration was increased to diabetic levels and the plasma Na+ concentration changes assessed, without the complications seen in human experiments. The findings, based on osmotic grounds, were that the factor 1) was significantly <1.6, approaching 1 in some cases, 2) depended upon the anthropometry of the subject; it was inversely proportional to the ratio of extracellular to total body water, which increases with higher fat content and 3) was approximately linear up to glucose concentrations of about 800mg%, but decreased up to 10% for higher glucose concentrations. To explain the experimental data, a hypothesis of Na+ sequestration in cells was incorporated in the model, resulting in close prediction of measured transient Na+ changes.

A head to head evaluation of 8 biochemical scanning tools for unmeasured ions.

We aimed to evaluate the sensitivity and specificity of 8 biochemical scanning tools in signalling the presence of unmeasured anions. We used blood gas and biochemical data from 15 patients during and after cardio-pulmonary bypass. Sampling time-points were pre-bypass (T1), 2 min post equilibration with priming fluid containing acetate and gluconate anions (T2), late bypass (T3) and 4 h after surgery (T4). We calculated the anion gap (AG), albumin-corrected anion gap (AGc), whole blood base excess (BE) gap, plasma BE gap, standard BE gap and the strong ion gap (SIG), plus 2 new indices-the unmeasured ion index (UIX) and unmeasured plasma anions according to the interstitial, plasma and erythrocyte acid-base model (IPEua). Total measured plasma concentrations of acetate and gluconate [XA] were proxies for unmeasured plasma anions. [XA] values (mmol/L) were 1.41 (0.87) at T1, 11.73 (3.28) at T2, 4.80 (1.49) at T3 and 1.36 (0.73) at T4. Corresponding [albumin] values (g/L) were 32.3 (2.0), 19.8 (2.6), 21.3 (2.5) and 29.1 (2.3) respectively. Only the AG failed to increase significantly at T2 in response to a mean [XA] surge of >10 mEq/L. At an [XA] threshold of 6 mEq/L, areas under receiver -operator characteristic curves in rank order were IPEua and UIX (0.88 and 0.87 respectively), SIG (0.81), AGc (0.79), standard BE gap (0.77), plasma BE gap (0.71), BE gap (0.70) and AG (0.59). Similar ranking hierarchies applied to positive and negative predictive values. We conclude that during acute hemodilution UIX and IPEua are superior to the anion gap (with and without albumin correction) and 4 other indices as scanning tools for unmeasured anions.

Comprehensive diagnosis of whole-body acid-base and fluid-electrolyte disorders using a mathematical model and whole-body base excess.

A mathematical model of whole-body acid-base and fluid-electrolyte balance was used to provide information leading to the diagnosis and fluid-therapy treatment in patients with complex acid-base disorders. Given a set of measured laboratory-chemistry values for a patient, a model of their unique, whole-body chemistry was created. This model predicted deficits or excesses in the masses of Na(+), K(+), Cl(-) and H2O as well as the plasma concentration of unknown or unmeasured species, such as ketoacids, in diabetes mellitus. The model further characterized the acid-base disorder by determining the patient's whole-body base excess and quantitatively partitioning it into ten components, each contributing to the overall disorder. The results of this study showed the importance of a complete set of laboratory measurements to obtain sufficient accuracy of the quantitative diagnosis; having only a minimal set, just pH and PCO2, led to a large scatter in the predicted results. A computer module was created that would allow a clinician to achieve this diagnosis at the bedside. This new diagnostic approach should prove to be valuable in the treatment of the critically ill.

Whole body acid-base and fluid-electrolyte balance: a mathematical model.

A cellular compartment was added to our previous mathematical model of steady-state acid-base and fluid-electrolyte chemistry to gain further understanding and aid diagnosis of complex disorders involving cellular involvement in critically ill patients. An important hypothesis to be validated was that the thermodynamic, standard free-energy of cellular H(+) and Na(+) pumps remained constant under all conditions. In addition, a hydrostatic-osmotic pressure balance was assumed to describe fluid exchange between plasma and interstitial fluid, including incorporation of compliance curves of vascular and interstitial spaces. The description of the cellular compartment was validated by close comparison of measured and model-predicted cellular pH and electrolyte changes in vitro and in vivo. The new description of plasma-interstitial fluid exchange was validated using measured changes in fluid volumes after isoosmotic and hyperosmotic fluid infusions of NaCl and NaHCO3. The validated model was used to explain the role of cells in the mechanism of saline or dilutional acidosis and acid-base effects of acidic or basic fluid infusions and the acid-base disorder due to potassium depletion. A module was created that would allow users, who do not possess the software, to determine, for free, the results of fluid infusions and urinary losses of water and solutes to the whole body.

A comprehensive, computer-model-based approach for diagnosis and treatment of complex acid-base disorders in critically-ill patients.

We have developed a computer-model-based approach to quantitatively diagnose the causes of metabolic acid-base disorders in critically-ill patients. We use an interstitial-plasma-erythrocyte (IPE) model that is sufficiently detailed to accurately calculate steady-state changes from normal in fluid volumes and electrolyte concentrations in a given patient due to a number of causes of acid-base disorders. Normal fluid volumes for each patient are determined from their sex, height and weight using regression equations derived from measured data in humans. The model inputs (electrolyte masses and volumes) are altered to simulate the laboratory chemistry of each critically-ill patient. In this process, the model calculates changes in body-fluid volumes, osmolality and yields the individual values of IPE base excess (BE(IPE)) attributed to changes due to: (1) fluid dilution/contraction, (2) gain or loss of Cl(-), (3) hyper- or hypoalbuminemia, (4) presence of unmeasured ions, (5) gain of lactate, (6) gain or loss of phosphate, (7) gain or loss of calcium and magnesium, (8) gain or loss of potassium and (9) gain or loss of sodium. We use critically-ill patient data to show how our new approach is more informative and much simpler to interpret as compared to the approaches of Siggaard-Andersen or Stewart. We demonstrate how the model can be used at the bedside to diagnose acid-base disorders and suggest appropriate treatment. Hence, this new approach gives clinicians a new tool for diagnosing disorders and specifying fluid-therapy options for critically-ill patients.

A mathematical model of blood-interstitial acid-base balance: application to dilution acidosis and acid-base status.

We developed mathematical models that predict equilibrium distribution of water and electrolytes (proteins and simple ions), metabolites, and other species between plasma and erythrocyte fluids (blood) and interstitial fluid. The models use physicochemical principles of electroneutrality in a fluid compartment and osmotic equilibrium between compartments and transmembrane Donnan relationships for mobile species. Across the erythrocyte membrane, the significant mobile species Cl⁻ is assumed to reach electrochemical equilibrium, whereas Na(+) and K(+) distributions are away from equilibrium because of the Na(+)/K(+) pump, but movement from this steady state is restricted because of their effective short-term impermeability. Across the capillary membrane separating plasma and interstitial fluid, Na(+), K(+), Ca²(+), Mg²(+), Cl⁻, and H(+) are mobile and establish Donnan equilibrium distribution ratios. In each compartment, attainment of equilibrium by carbonates, phosphates, proteins, and metabolites is determined by their reactions with H(+). These relationships produce the recognized exchange of Cl(-) and bicarbonate across the erythrocyte membrane. The blood submodel was validated by its close predictions of in vitro experimental data, blood pH, pH-dependent ratio of H(+), Cl⁻, and HCO3⁻ concentrations in erythrocytes to that in plasma, and blood hematocrit. The blood-interstitial model was validated against available in vivo laboratory data from humans with respiratory acid-base disorders. Model predictions were used to gain understanding of the important acid-base disorder caused by addition of saline solutions. Blood model results were used as a basis for estimating errors in base excess predictions in blood by the traditional approach of Siggaard-Andersen (acid-base status) and more recent approaches by others using measured blood pH and Pco2 values. Blood-interstitial model predictions were also used as a basis for assessing prediction errors of extracellular acid-base status values, such as by the standard base excess approach. Hence, these new models can give considerable insight into the physicochemical mechanisms producing acid-base disorders and aid in their diagnoses.