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

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 (β_H+) and [H⁺] curve shift at 40 mmHg ([H⁺]₄₀). Model findings were: 1) in severe hypoproteinemia, hemoglobin enhances buffering (decreases β_H+), whereas albumin compromises it, resulting in an almost unchanged β_H+; [H⁺]₄₀ decreases (alkalemia) due to hypoalbuminemia. 2) Severe hyperalbuminemia greatly increases both β_H+ 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, β_H+, [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.

Optimizing antimicrobial use: challenges, advances and opportunities

An optimal antimicrobial dose provides enough drug to achieve a clinical response while minimizing toxicity and development of drug resistance. There can be considerable variability in pharmacokinetics, for example, owing to comorbidities or other medications, which affects antimicrobial pharmacodynamics and, thus, treatment success. Although current approaches to antimicrobial dose optimization address fixed variability, better methods to monitor and rapidly adjust antimicrobial dosing are required to understand and react to residual variability that occurs within and between individuals. We review current challenges to the wider implementation of antimicrobial dose optimization and highlight novel solutions, including biosensor-based, real-time therapeutic drug monitoring and computer-controlled, closed-loop control systems. Precision antimicrobial dosing promises to improve patient outcome and is important for antimicrobial stewardship and the prevention of antimicrobial resistance.

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.

A mathematical model to investigate the effects of intravenous fluid administration and fluid loss

The optimal fluid administration protocol for critically ill perioperative patients is hard to estimate due to the lack of tools to directly measure the patient fluid status. This results in the suboptimal clinical outcome of interventions. Previously developed predictive mathematical models focus on describing the fluid exchange over time but they lack clinical applicability, since they do not allow prediction of clinically measurable indices. The aim of this study is to make a first step towards a model predictive clinical decision support system for fluid administration, by extending the current fluid exchange models with a regulated cardiovascular circulation, to allow prediction of these indices. The parameters of the model were tuned to correctly reproduce experimentally measured changes in arterial pressure and heart rate, observed during infusion of normal saline in healthy volunteers. With the resulting tuned model, a different experiment including blood loss and infusion could be reproduced as well. These results show the potential of using this model as a basis for a decision support tool in a clinical setting.

A mechanistic physicochemical model of carbon dioxide transport in blood

A number of mathematical models have been produced that, given the Pco₂ and Po₂ of blood, will calculate the total concentrations for CO₂ and O₂ in blood. However, all these models contain at least some empirical features, and thus do not represent all of the underlying physicochemical processes in an entirely mechanistic manner. The aim of this study was to develop a physicochemical model of CO₂ carriage by the blood to determine whether our understanding of the physical chemistry of the major chemical components of blood together with their interactions is sufficiently strong to predict the physiological properties of CO₂ carriage by whole blood. Standard values are used for the ionic composition of the blood, the plasma albumin concentration, and the hemoglobin concentration. All K_m values required for the model are taken from the literature. The distribution of bicarbonate, chloride, and H⁺ ions across the red blood cell membrane follows that of a Gibbs-Donnan equilibrium. The system of equations that results is solved numerically using constraints for mass balance and electroneutrality. The model reproduces the phenomena associated with CO₂ carriage, including the magnitude of the Haldane effect, very well. The structural nature of the model allows various hypothetical scenarios to be explored. Here we examine the effects of 1) removing the ability of hemoglobin to form carbamino compounds; 2) allowing a degree of Cl^- binding to deoxygenated hemoglobin; and 3) removing the chloride (Hamburger) shift. The insights gained could not have been obtained from empirical models.

NEW & NOTEWORTHY

This study is the first to incorporate a mechanistic model of chloride-bicarbonate exchange between the erythrocyte and plasma into a full physicochemical model of the carriage of carbon dioxide in blood. The mechanistic nature of the model allowed a theoretical study of the quantitative significance for carbon dioxide transport of carbamino compound formation; the putative binding of chloride to deoxygenated hemoglobin, and the chloride (Hamburger) shift.

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.

A method for mapping regional oxygen and CO2 transfer in the lung

This paper presents a novel approach to visualizing regional lung function, through quantitative three-dimensional maps of O2 and CO2 transfer rates. These maps describe the contribution of anatomical regions to overall gas exchange and demonstrate how transfer rates of the two gas species' differ regionally. An algorithm for generating such maps is presented, and for illustration, regional gas transfer maps were generated using values of ventilation and perfusion imaged by PET/CT for a healthy subject and an asthmatic patient after bronchoprovocation. In a sensitivity analysis, compartment values of gas transfer showed minor sensitivity to imaging noise in the ventilation and perfusion data, and moderate sensitivity to estimation errors in global lung input values, chiefly global alveolar ventilation, followed by cardiac output and arterial-venous O2 content difference. Gas transfer maps offer an intuitive display of physiologically relevant lung function at a regional level, the potential for an improved understanding of pulmonary gas exchange in health and disease, and potentially a presurgical evaluation tool.

Benchtop technologies for circulating tumor cells separation based on biophysical properties

Circulating tumor cells (CTCs) are tumor cells that have detached from primary tumor site and are transported via the circulation system. The importance of CTCs as prognostic biomarker is leveraged when multiple studies found that patient with cutoff of 5 CTCs per 7.5 mL blood has poor survival rate. Despite its clinical relevance, the isolation and characterization of CTCs can be quite challenging due to their large morphological variability and the rare presence of CTCs within the blood. Numerous methods have been employed and discussed in the literature for CTCs separation. In this paper, we will focus on label free CTCs isolation methods, in which the biophysical and biomechanical properties of cells (e.g., size, deformability, and electricity) are exploited for CTCs detection. To assess the present state of various isolation methods, key performance metrics such as capture efficiency, cell viability, and throughput will be reported. Finally, we discuss the challenges and future perspectives of CTC isolation technologies.

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.

The ideal crystalloid - what is 'balanced'?

PURPOSE OF REVIEW

This review explores the contemporary definition of the term 'balanced crystalloid' and outlines optimal design features and their underlying rationale.

RECENT FINDINGS

Crystalloid interstitial expansion is unavoidable, but also occurs with colloids when there is endothelial glycocalyx dysfunction. Reduced chloride exposure may lessen kidney dysfunction and injury with a possible mortality benefit. Exact balance from an acid-base perspective is achieved with a crystalloid strong ion difference of 24 mEq/l. This can be done simply by replacing 24 mEq/l of chloride in 0.9% sodium chloride with bicarbonate or organic anion bicarbonate substitutes. Potassium, calcium and magnesium additives are probably unnecessary. Large volumes of mildly hypotonic crystalloids such as lactated Ringer's solution reduce extracellular tonicity in volunteers and increase intracranial pressure in nonbrain-injured experimental animals. A total cation concentration of 154 mmol/l with accompanying anions provides isotonicity. Of the commercial crystalloids, Ringer's acetate solution is close to balanced from both acid-base and tonicity perspectives, and there is little current evidence of acetate toxicity in the context of volume loading, in contrast to renal replacement.

SUMMARY

The case for balanced crystalloids is growing but unproven. A large randomized controlled trial of balanced crystalloids versus 0.9% sodium chloride is the next step.

Dynamic simulation and metabolome analysis of long-term erythrocyte storage in adenine-guanosine solution

Although intraerythrocytic ATP and 2,3-bisphophoglycerate (2,3-BPG) are known as direct indicators of the viability of preserved red blood cells and the efficiency of post-transfusion oxygen delivery, no current blood storage method in practical use has succeeded in maintaining both these metabolites at high levels for long periods. In this study, we constructed a mathematical kinetic model of comprehensive metabolism in red blood cells stored in a recently developed blood storage solution containing adenine and guanosine, which can maintain both ATP and 2,3-BPG. The predicted dynamics of metabolic intermediates in glycolysis, the pentose phosphate pathway, and purine salvage pathway were consistent with time-series metabolome data measured with capillary electrophoresis time-of-flight mass spectrometry over 5 weeks of storage. From the analysis of the simulation model, the metabolic roles and fates of the 2 major additives were illustrated: (1) adenine could enlarge the adenylate pool, which maintains constant ATP levels throughout the storage period and leads to production of metabolic waste, including hypoxanthine; (2) adenine also induces the consumption of ribose phosphates, which results in 2,3-BPG reduction, while (3) guanosine is converted to ribose phosphates, which can boost the activity of upper glycolysis and result in the efficient production of ATP and 2,3-BPG. This is the first attempt to clarify the underlying metabolic mechanism for maintaining levels of both ATP and 2,3-BPG in stored red blood cells with in silico analysis, as well as to analyze the trade-off and the interlock phenomena between the benefits and possible side effects of the storage-solution additives.

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.