Advertisement

Clinical Approach to Assessing Acid-Base Status: Physiological vs Stewart

  • Horacio J. Adrogué
    Affiliations
    Department of Medicine, Section of Nephrology, Baylor College of Medicine, Houston, TX

    Department of Medicine, Division of Nephrology, Houston Methodist Hospital, Houston, TX
    Search for articles by this author
  • Bryan M. Tucker
    Affiliations
    Department of Medicine, Section of Nephrology, Baylor College of Medicine, Houston, TX

    Department of Medicine, Division of Nephrology, Houston Methodist Hospital, Houston, TX
    Search for articles by this author
  • Nicolaos E. Madias
    Correspondence
    Address correspondence to Nicolaos E. Madias, MD, Department of Medicine, St Elizabeth's Medical Center, 736 Cambridge St, Boston, MA 02135.
    Affiliations
    Department of Medicine, Tufts University School of Medicine, Boston, MA

    Department of Medicine, Division of Nephrology, St Elizabeth's Medical Center, Boston, MA
    Search for articles by this author
      Evaluation of acid-base status depends on accurate measurement of acid-base variables and their appropriate assessment. Currently, 3 approaches are utilized for assessing acid-base variables. The physiological or traditional approach, pioneered by Henderson and Van Slyke in the early 1900s, considers acids as H+ donors and bases as H+ acceptors. The acid-base status is conceived as resulting from the interaction of net H+ balance with body buffers and relies on the H2CO3/HCO3 buffer pair for its assessment. A second approach, developed by Astrup and Siggaard-Andersen in the late 1950s, is known as the base excess approach. Base excess was introduced as a measure of the metabolic component replacing plasma [HCO3]. In the late 1970s, Stewart proposed a third approach that bears his name and is also referred to as the physicochemical approach. It postulates that the [H+] of body fluids reflects changes in the dissociation of water induced by the interplay of 3 independent variables—strong ion difference, total concentration of weak acids, and PCO2. Here we focus on the physiological approach and Stewart's approach examining their conceptual framework, practical application, as well as attributes and drawbacks. We conclude with our view about the optimal approach to assessing acid-base status.

      Key Words

      • The physiological approach quantitates the dominant buffer pair in blood (H2CO3/HCO3), evaluates the plasma anion gap, measures the secondary responses to primary acid-base perturbations, and fulfills both the chemical and pathophysiological tasks for assessing acid-base status.
      • Criticisms of the physiological approach include lack of independence of plasma [HCO3] from PCO2, failure to quantitate buffers other than HCO3, and variability of plasma anion gap stemming from changes in albumin levels—criticisms that are convincingly rebutted.
      • The physicochemical approach measures strong ion difference, total concentration of weak acids, and PCO2 (its 3 independent variables) allowing assessment of acid-base status, including [H+] and [HCO3] of plasma (both considered dependent variables).
      • Criticisms of the physicochemical approach include its exclusive anchoring in chemistry, lack of experimental demonstration that the independent variables cause the changes in [H+], absence of a biological mechanism that senses and regulates strong ion difference, and precarious reliability resulting from multiple laboratory measurements.
      Definition of acid-base status relies on accurate measurement of acid-base variables and their appropriate assessment.
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      Currently, 3 approaches are utilized for the assessment of acid-base variables.
      • Adrogué H.J.
      • Gennari F.J.
      • Galla J.H.
      • Madias N.E.
      Assessing acid-base disorders.
      • Berend K.
      Diagnostic use of base excess in acid-base disorders.
      • Kurtz I.
      • Kraut J.
      • Ornekian V.
      • Nguyen M.K.
      Acid-base analysis: a critique of the Stewart and bicarbonate-centered approaches.
      • Rastegar A.
      Clinical utility of Stewart’s method in diagnosis and management of acid-base disorders.
      • Siggaard-Andersen O.
      • Fogh-Andersen N.
      Base excess or buffer base (strong ion difference) as measure of a non-respiratory acid-base disturbance.
      The physiological or traditional approach was pioneered by Henderson and Van Slyke in the early 1900s.
      • Henderson L.J.
      The theory of neutrality regulation in the animal organism.
      ,
      • Van Slyke D.D.
      • Wu H.
      • McLean F.C.
      Studies of gas and electrolyte equilibria in the blood. V. Factor controlling the electrolyte and water distribution in the blood.
      Thereafter, Astrup and Siggaard-Andersen introduced the base excess approach in the late 1950s.
      • Astrup P.
      A simple electrometric technique for the determination of carbon dioxide tension in blood and plasma, total content of carbon dioxide in plasma, and bicarbonate content in “separated” plasma at a fixed carbon dioxide tension (40 mmHg).
      ,
      • Siggaard-Andersen O.
      • Engel K.
      • Jorgensen K.
      • Astrup P.
      A micro method for determination of pH, carbon dioxide tension, base excess and standard bicarbonate in capillary blood.
      Finally, in the late 1970s, Stewart proposed the homonymous approach that was subsequently amended by his followers and is also referred to as the physicochemical approach.
      • Stewart P.A.
      Independent and dependent variables of acid-base control.
      • Fencl V.
      • Leith D.E.
      Stewart’s quantitative acid-base chemistry: applications in biology and medicine.
      • Constable P.D.
      Clinical assessment of acid-base status: comparison of the Henderson-Hasselbalch and strong ion approaches.
      • Kellum J.A.
      Disorders of acid-base balance.
      • Corey H.E.
      Stewart and beyond: new models of acid-base balance.
      Here we focus on the physiological approach and Stewart's approach examining their conceptual framework, practical application, as well as attributes and drawbacks.

      Physiological Approach

      Determinants of Acidity

      The physiological approach espouses the concepts of Brønsted and Lowry which consider acids as H+ donors and bases as H+ acceptors.
      • Lowry T.M.
      The uniqueness of hydrogen.
      ,
      • Brönsted J.N.
      The acid base function of molecules and its dependency on the electric charge type.
      The acid-base status is conceived as resulting from the interaction of net H+ balance with body buffers. This approach relies on the H2CO3/HCO3 buffer pair for assessing acid-base status. It is rooted in the isohydric principle, which establishes that the equilibrium [H+] is determined by the concentrations of all body buffers (eg, H2CO3/HCO3, H2PO4/HPO42−, proteinH+/protein) and their dissociation constants. Changes in [H+] entail redistribution of H+ among all buffer pairs such that the ratio of each pair conforms to identical acidity. Consequently, evaluation of a single buffer pair allows definition of the prevailing acid-base status. Selection of the H2CO3/HCO3 pair is based on its abundance, physiological importance, and independent regulation of its components.
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Astrup P.
      A simple electrometric technique for the determination of carbon dioxide tension in blood and plasma, total content of carbon dioxide in plasma, and bicarbonate content in “separated” plasma at a fixed carbon dioxide tension (40 mmHg).
      ,
      • Siggaard-Andersen O.
      • Engel K.
      • Jorgensen K.
      • Astrup P.
      A micro method for determination of pH, carbon dioxide tension, base excess and standard bicarbonate in capillary blood.
      ,
      • Gennari F.J.
      • Galla J.H.
      Acid-base chemistry and buffering.
      ,
      • Adrogué H.J.
      • Madias N.E.
      Measurement of acid-base status.
      Because H2CO3 is difficult to measure and its concentration is small, it is quantitated by CO2 tension (PCO2). The relationship between pH and H2CO3/HCO3 pair is embodied in the Henderson-Hasselbalch equation,
      pH=pKa+log([HCO3]/αPCO2),


      where pH is –log10 [H+] expressed in mol/L, pKʹa is –log10 Kʹa, and α is the solubility coefficient of CO2. Its nonlogarithmic form is the Henderson equation,
      [H+]=24×PCO2/[HCO3],


      where [H+] is expressed in nEq/L, PCO2 in mm Hg (respiratory component), and [HCO3] in mEq/L (metabolic component) (Table 1). Blood gas analyzers measure pH and PCO2 from which plasma [HCO3] is calculated. Proximity of measured venous total CO2 concentration, [TCO2] (∼95% of which is bicarbonate), with the derived [HCO3] supports the reliability of the data. Notably, clinicians are usually first alerted to acid-base disorders through abnormalities of venous [TCO2].
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Gennari F.J.
      • Galla J.H.
      Acid-base chemistry and buffering.
      ,
      • Adrogué H.J.
      • Madias N.E.
      Measurement of acid-base status.
      Table 1Assessment of the Metabolic Component of Acid-Base Status and Classification of Acid-Base Disorders According to the Physiological Approach
      Assessment of the Metabolic Component of Acid-Base Status
      ParameterDerivationComments
      Plasma [HCO3]Measured blood pH and PCO2Assessment requires evaluation of plasma AG (corrected for plasma albumin levels)
      Classification of Acid-Base Disorders
      DisorderPrimary changeExpected secondary response
      Metabolic acidosis↓ [HCO3]↓ PCO2 ∼ 1.2 × Δ[HCO3]
       Normal-AG acidosis
       High-AG acidosis
      Metabolic alkalosis↑ [HCO3]↑ PCO2 ∼ 0.7 × Δ[HCO3]
      Respiratory acidosis↑ PCO2
       Acute↑ [HCO3] ∼ 0.1 × ΔPCO2
       Chronic↑ [HCO3] ∼ 0.5 × ΔPCO2
      Respiratory alkalosis↓ PCO2
       Acute↓ [HCO3] ∼ 0.2 × ΔPCO2
       Chronic↓ [HCO3] ∼ 0.4 × ΔPCO2
      Abbreviation: AG, plasma anion gap, [Na+] − ([Cl] + [HCO3]).
      The mean slope of the expected secondary response to chronic respiratory acidosis was previously taken as 0.35 mEq/L per mm Hg but has been adjusted to 0.5 mEq/L per mm Hg on the basis of 2 recent studies.
      • Martinu T.
      • Menzies D.
      • Dial S.
      Re-evaluation of acid-base prediction rules in patients with chronic respiratory acidosis.
      ,
      • Gonzaléz S.B.
      • Menga G.
      • Raimondi G.A.
      • Tighiouart H.
      • Adrogué H.J.
      • Madias N.E.
      Secondary response to chronic respiratory acidosis in humans: a prospective study.

      Simple Acid-Base Disorders and Secondary Responses

      The physiological approach recognizes 4 simple acid-base disorders (Table 1). A simple disorder is defined by a primary abnormality in either plasma [HCO3] or blood PCO2 and the appropriate secondary response in the other. Simple disorders are metabolic or respiratory in nature. The former is expressed by primary changes in [HCO3] and include metabolic acidosis, a primary reduction in [HCO3], and metabolic alkalosis, a primary increase in [HCO3]. Respiratory acid-base disorders are expressed as primary changes in PCO2 and include respiratory acidosis, a primary increase in PCO2, and respiratory alkalosis, a primary decrease in PCO2.
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Winters R.W.
      Terminology of acid-base disorders.
      • Elkinton J.R.
      Acid-base disorders and the clinician.
      • Mehta A.N.
      • Emmett M.
      Approach to acid-base disorders.
      The secondary response to a primary change in [HCO3] or PCO2 is directional to the initiating abnormality (ie, both increase or decrease), tends to minimize the change in acidity prompted by the primary abnormality, and is an integral part of the simple disorder (Table 1). We discourage referring to secondary responses as compensatory because animal studies showed that occasionally they fail to protect pH or even worsen it. These secondary responses have been quantitated in animals and humans, and absence of the appropriate response signals coexistence of an additional simple disorder.
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Brackett Jr., N.C.
      • Cohen J.J.
      • Schwartz W.B.
      Carbon dioxide titration curve of normal man. Effect of increasing degrees of acute hypercapnia on acid-base equilibrium.
      • Arbus G.S.
      • Hebert L.A.
      • Levesque P.R.
      • Etsten B.E.
      • Schwartz W.B.
      Characterization and clinical application of the “significance band” for acute respiratory alkalosis.
      • Adrogué H.J.
      • Madias N.E.
      Influence of chronic respiratory acid-base disorders on acute CO2 titration curve.
      • Madias N.E.
      • Adrogué H.J.
      Influence of chronic metabolic acid-base disorders on the acute CO2 titration curve.
      • Schwartz W.B.
      • Brackett Jr., N.C.
      • Cohen J.J.
      The response of extracellular hydrogen ion concentration to graded degrees of chronic hypercapnia: the physiologic limits of the defense of pH.
      • Gennari F.J.
      • Goldstein M.B.
      • Schwartz W.B.
      The nature of the renal adaptation to chronic hypocapnia.
      • Brackett Jr., N.C.
      • Wingo C.F.
      • Muren O.
      • Solano J.T.
      Acid-base response to chronic hypercapnia in man.
      • Krapf R.
      • Beeler I.
      • Hertner D.
      • Hulter H.N.
      Chronic respiratory alkalosis. The effect of sustained, sustained hyperventilation on renal regulation of acid-base equilibrium.
      • Madias N.E.
      • Bossert W.H.
      • Adrogué H.J.
      Ventilatory response to chronic metabolic acidosis and alkalosis in the dog.
      • Bushinsky D.A.
      • Coe F.L.
      • Katzenberg C.
      • et al.
      Arterial PCO2 in chronic metabolic acidosis.
      • Galla J.H.
      Chloride-depletion alkalosis.
      • Andersen O.S.
      • Astrup P.
      • Bates R.G.
      • et al.
      Statement on acid-base terminology. Report of the ad hoc Committee of the New York Academy of Sciences Conference, November 23-24, 1964.
      • Adrogué H.J.
      • Madias N.E.
      Secondary responses to altered acid-base status: the rules of engagement.

      Mixed Acid-Base Disorders

      A mixed acid-base disorder denotes the simultaneous occurrence of 2 or more simple disorders. Mixed disturbances can also result from 2 or more forms of a simple disturbance having a different time course (eg, acute on chronic respiratory acidosis) or pathogenesis (eg, high- and normal-anion-gap metabolic acidosis). The impact on blood pH of the coexisting disorders can be additive or offsetting.
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Mehta A.N.
      • Emmett M.
      Approach to acid-base disorders.
      ,
      • Rastegar A.
      Mixed acid-base disorders.

      Plasma Anion Gap

      The unmeasured anions or anion gap (AG) in venous blood is an essential tool to assessing plasma [HCO3]. The AG is calculated using the following equation:
      AG=[Na+]([Cl]+[HCO3])


      In clinical practice, [TCO2] is substituted for [HCO3]. The utility of AG centers on differentiating metabolic acidosis into normal-AG (hyperchloremic) metabolic acidosis and high-AG (normochloremic) metabolic acidosis (Fig 1) (Table 2).
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Mehta A.N.
      • Emmett M.
      Approach to acid-base disorders.
      ,
      • Kraut J.A.
      • Madias N.E.
      Serum anion gap: its uses and limitations in clinical medicine.
      Figure thumbnail gr1
      Figure 1Comparison of the plasma electrolyte patterns of the normal state, normal-AG (hyperchloremic) metabolic acidosis, and high-AG (normochloremic) metabolic acidosis. Abbreviation: AG, anion gap.
      Table 2Utility of the Relationship Between ΔAG and Δ[HCO3] in the Evaluation of Metabolic Acidosis and Mixed Acid-Base Disorders
      DisorderpHPaCO2[HCO3]AGΔ[HCO3]ΔΑG[HCO3]cComments
      Normal7.404024100024
      Normal-AG metabolic acidosis7.0917510−1905↓[HCO3], nl AG, &. ↓pH define normal-AG acidosis; PaCO2 is ↓ & appropriate for Δ[HCO3]: data consistent with normal-AG acidosis
      High-AG metabolic acidosis7.1620727−171724↓[HCO3], ↑AG, & ↓pH define high-AG acidosis; ΔAG matches Δ[HCO3]; [HCO3]c is nl: PaCO2 is ↓ & appropriate for Δ[HCO3]; data consistent with high-AG acidosis
      High-AG and normal-AG metabolic acidosis7.26231017−14717↓[HCO3], ↑AG, & ↓pH define high-AG acidosis; ΔAG < Δ[HCO3]; [HCO3]c is subnormal; PaCO2 is ↓ & appropriate for Δ[HCO3]; data consistent with high-AG acidosis and normal-AG acidosis
      High-AG metabolic acidosis and metabolic alkalosis7.33291528−91833↓[HCO3], ↑AG, & ↓pH define high-AG acidosis: ΔAG > Δ[HCO3]; [HCO3]c is higher than nl; PaCO2 is ↓ & appropriate for Δ[HCO3]; data consistent with high-AG acidosis and metabolic alkalosis
      High-AG metabolic acidosis and chronic respiratory acidosis7.11652020−41030↓[HCO3], ↑AG, & ↓pH define high-AG acidosis; ΔAG > Δ[HCO3]; [HCO3]c is higher than nl; PaCO2 is increased rather than decreased, data consistent with high-AG acidosis and chronic respiratory acidosis
      Abbreviations: AG, anion gap; [HCO3]c, [HCO3] value after correcting for the ΔΑG.
      PaCO2, mm Hg; [HCO3] and AG, mEq/L.
      The mean value of normal AG is ∼10 mEq/L. When available, baseline AG can be used for optimal assessment of its current value. Albumin accounts for up to 75% of normal AG; other contributors include organic acids (eg, lactate, urate), phosphate, and sulfate.
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Mehta A.N.
      • Emmett M.
      Approach to acid-base disorders.
      ,
      • Kraut J.A.
      • Madias N.E.
      Serum anion gap: its uses and limitations in clinical medicine.
      • Adrogué H.J.
      • Brensilver J.
      • Madias N.E.
      Changes in the plasma anion gap during chronic metabolic acid-base disturbances.
      • Madias N.E.
      • Ayus J.C.
      • Adrogué H.J.
      Increased anion gap in metabolic alkalosis: the role of plasma protein equivalency.
      Accordingly, correction of AG for abnormal albumin levels entails subtracting or adding 2.5 mEq/L for each 1 g/dL of albumin below or above the normal value of 4.5 g/dL (eg, normal AG of 10 mEq/L becomes 5 mEq/L when albumin is 2.3 g/dL, but it increases to 15 mEq/L when albumin is 6.8 g/dL). Changes in pH elicit small, directional changes in the anionic charge of albumin and the concentration of organic acids, and thus the AG.
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Kraut J.A.
      • Madias N.E.
      Serum anion gap: its uses and limitations in clinical medicine.
      • Adrogué H.J.
      • Brensilver J.
      • Madias N.E.
      Changes in the plasma anion gap during chronic metabolic acid-base disturbances.
      • Madias N.E.
      • Ayus J.C.
      • Adrogué H.J.
      Increased anion gap in metabolic alkalosis: the role of plasma protein equivalency.
      • Figge J.
      • Mydosh T.
      • Fencl V.
      Serum proteins and acid-base equilibria: a follow-up.
      Such changes are ignored in clinical practice.
      If the AG is larger than normal (ΔAG), the patient has high-AG metabolic acidosis. In such conditions, retained H+ (eg, lactic acid) reduce [HCO3] (Δ[HCO3]), whereas retained acid anions increase AG (1:1 stoichiometry). The ΔAG/Δ[HCO3], known as delta/delta (Δ/Δ), informs whether the increased AG fully or partially accounts for the decreased [HCO3]. If ΔAG amounts to 50% of Δ[HCO3], ie, Δ/Δ = 0.5, high-AG metabolic acidosis accounts for 50% of the hypobicarbonatemia, and the remaining 50% is attributed to a hyperchloremic hypobicarbonatemic disorder (normal-AG metabolic acidosis or respiratory alkalosis). Adding the ΔAG to the prevailing [HCO3] allows estimation of the baseline [HCO3] (Table 2).
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Mehta A.N.
      • Emmett M.
      Approach to acid-base disorders.
      ,
      • Kraut J.A.
      • Madias N.E.
      Serum anion gap: its uses and limitations in clinical medicine.
      ,
      • Adrogué H.J.
      • Wilson H.
      • Boyd III, A.E.
      • Suki W.N.
      • Eknoyan G.
      Plasma acid-base patterns in diabetic ketoacidosis.
      As a word of caution, the 1:1 stoichiometry between ΔAG and Δ[HCO3] represents an approximation that can be modified substantially by several factors, including the space of distribution of H+ and acid anion as well as the generation of new bicarbonate and the excretion of the acid anion by the kidneys.
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Mehta A.N.
      • Emmett M.
      Approach to acid-base disorders.
      ,
      • Kraut J.A.
      • Madias N.E.
      Serum anion gap: its uses and limitations in clinical medicine.
      ,
      • Adrogué H.J.
      • Wilson H.
      • Boyd III, A.E.
      • Suki W.N.
      • Eknoyan G.
      Plasma acid-base patterns in diabetic ketoacidosis.
      Notably, a high AG could reflect other causes, including laboratory error, dehydration, severe hyperphosphatemia, anionic paraproteins, and infusions of anionic antibiotics (eg, carbenicillin) or sodium metabolites (eg, lactate, acetate).
      • Mehta A.N.
      • Emmett M.
      Approach to acid-base disorders.
      ,
      • Kraut J.A.
      • Madias N.E.
      Serum anion gap: its uses and limitations in clinical medicine.

      Clinical Application

      To identify the primary or dominant acid-base disorder, one can first evaluate plasma [HCO3]. A high value indicates metabolic alkalosis or the secondary response to respiratory acidosis. If alkalemia is present, metabolic alkalosis is the dominant disorder, whereas acidemia points to respiratory acidosis. Conversely, low [HCO3] indicates metabolic acidosis or the secondary response to respiratory alkalosis. If acidemia is present, metabolic acidosis is the dominant disorder, whereas alkalemia denotes respiratory alkalosis.
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Mehta A.N.
      • Emmett M.
      Approach to acid-base disorders.
      Plasma [HCO3] is further evaluated by examining the AG. An increased AG, especially if >5 mEq/L, points to high-AG metabolic acidosis. Utilization of ΔAG/Δ[HCO3] aids evaluation of metabolic acidosis and mixed disorders (Table 2).
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Mehta A.N.
      • Emmett M.
      Approach to acid-base disorders.
      ,
      • Rastegar A.
      Mixed acid-base disorders.
      ,
      • Kraut J.A.
      • Madias N.E.
      Serum anion gap: its uses and limitations in clinical medicine.
      The appropriateness of the secondary response to the primary disorder is judged by applying the empirically obtained slopes (Table 1).
      • Martinu T.
      • Menzies D.
      • Dial S.
      Re-evaluation of acid-base prediction rules in patients with chronic respiratory acidosis.
      ,
      • Gonzaléz S.B.
      • Menga G.
      • Raimondi G.A.
      • Tighiouart H.
      • Adrogué H.J.
      • Madias N.E.
      Secondary response to chronic respiratory acidosis in humans: a prospective study.
      ,
      • Mehta A.N.
      • Emmett M.
      Approach to acid-base disorders.
      ,
      • Adrogué H.J.
      • Madias N.E.
      Secondary responses to altered acid-base status: the rules of engagement.
      If the calculated value falls within ±3 mEq/L for [HCO3] and ±5 mm Hg for PaCO2 of the expected value, it is considered appropriate; if not, an additional disorder must be present.
      • Adrogué H.J.
      • Madias N.E.
      Secondary responses to altered acid-base status: the rules of engagement.
      Clinicians should be mindful that a given set of acid-base values is never diagnostic of a specific acid-base disorder (eg, mixed disorders can mimic a simple disorder); clinical correlation is always required to establish the correct diagnosis.
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Adrogué H.J.
      • Madias N.E.
      Secondary responses to altered acid-base status: the rules of engagement.
      Detection of mild disorders can be challenging because pH values can fall near or within the normal range. Interpretation of acid-base data of patients on mechanical ventilation should recognize that PaCO2 is set by the procedure; thus, it can alter pre-existing acid-base status or interfere with the expression of the secondary response to future metabolic acid-base disorders.
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Adrogué H.J.
      • Madias N.E.
      Secondary responses to altered acid-base status: the rules of engagement.

      Stewart's Approach

      Source of H+

      Based on the physicochemical principles of electroneutrality and mass conservation, Stewart examined the determinants of dissociation of water, a process that produces equal amounts of H+ and OH.
      • Stewart P.A.
      Independent and dependent variables of acid-base control.
      ,
      • Stewart P.A.
      How to Understand Acid-Base: A Quantitative Acid-Base Primer for Biology and Medicine.
      ,
      • Stewart P.A.
      Modern quantitative acid-base chemistry.
      Many molecules, when in solution, dissociate into charged particles, ie, cations and anions. Strong ion molecules, such as NaCl, are completely dissociated in solution; thus, only Na+ and Cl exist along with H+, OH, and undissociated H2O. The presence of Na+ and Cl is proposed to impact [H+] and [OH] of the solution. In a neutral solution, like pure water, [H+] = KW = [OH]; in an acidic solution, [H+] > KW > [OH]; and in a basic (alkaline) solution, [H+] < KW < [OH].
      • Stewart P.A.
      The simplest acid-base system: pure water.
      In all cases, [H+] × [OH] = K′W (where K′W is the water ion product, which in pure water at 37°C is 4.4 × 10−14 Eq/L). Quantitation of the impact of [Na+] and [Cl] on [H+] and [OH] is as follows:
      [H+]=KW+([Na+][Cl])2/4([Na+][Cl])/2


      [OH]=KW+([Na+][Cl])2/4+([Na+][Cl])/2


      Stewart proposed that a gap between strong cations and anions in solution, which he named strong ion difference (SID), can be viewed as creating an electrical charge that determines [H+] and [OH]. Examination of these equations demonstrates that if [Na+] and [Cl] are identical, SID is zero (absence of gap), and both [H+] and [OH] remain unchanged and equal to KW. Conversely, if [Na+] > [Cl], a positive SID is present, and [H+] and [OH] change in a reciprocal manner; the larger thepositive SID, the lower the [H+]. The identity of the strong ions is not relevant; it is the value of SID that determines changes in [H+] and [OH].
      • Stewart P.A.
      Independent and dependent variables of acid-base control.
      ,
      • Stewart P.A.
      How to Understand Acid-Base: A Quantitative Acid-Base Primer for Biology and Medicine.
      • Stewart P.A.
      Modern quantitative acid-base chemistry.
      • Stewart P.A.
      The simplest acid-base system: pure water.
      • Stewart P.A.
      Strong ions and the strong ion difference.
      Contrary to strong ion molecules, weak ion molecules only partially dissociate in water; for a weak acid, both parent molecule (AH) and its dissociation products (A and H+) remain in solution. Weak ion molecules, including weak acids and weak bases, function as H+ buffers, whereas strong ion molecules cannot buffer H+; the acid-base behavior of weak ion molecules requires a complicated mathematical analysis.
      • Gennari F.J.
      • Galla J.H.
      Acid-base chemistry and buffering.
      ,
      • Stewart P.A.
      Modern quantitative acid-base chemistry.
      ,
      • Stewart P.A.
      Weak electrolytes and buffers.
      Stewart theorized that 3 independent variables, ie, SID, ATot (concentration of nonvolatile buffers, also called total weak acids), and PCO2, are responsible for all acid-base effects in a flask.
      • Stewart P.A.
      Independent and dependent variables of acid-base control.
      ,
      • Stewart P.A.
      How to Understand Acid-Base: A Quantitative Acid-Base Primer for Biology and Medicine.
      ,
      • Stewart P.A.
      Modern quantitative acid-base chemistry.
      He then extended the proposal to account for the acid-base status of all body fluids.
      • Stewart P.A.
      Whole-body acid-base balance.
      Sodium and chloride, the dominant strong ions in an extracellular fluid, are the primary determinants of SID in plasma. ATot includes the anionic forms of albumin, globulins, and phosphate ([A]) and their undissociated forms ([AH]).
      • Fencl V.
      • Leith D.E.
      Stewart’s quantitative acid-base chemistry: applications in biology and medicine.
      ,
      • Corey H.E.
      Stewart and beyond: new models of acid-base balance.
      ,
      • Stewart P.A.
      Weak electrolytes and buffers.
      ,
      • Lloyd P.
      Strong ion calculator – a practical bedside application of modern quantitative acid-base physiology.
      In practice, globulins are ignored. Electroneutrality requires that SID equal the sum of [HCO3] and [A]. Notably, bicarbonate, the volatile buffer, is considered a dependent variable.
      • Stewart P.A.
      Independent and dependent variables of acid-base control.
      A series of complex equations allows determination of [H+], a dependent variable like bicarbonate.
      • Stewart P.A.
      Independent and dependent variables of acid-base control.
      ,
      • Stewart P.A.
      How to Understand Acid-Base: A Quantitative Acid-Base Primer for Biology and Medicine.
      ,
      • Stewart P.A.
      Modern quantitative acid-base chemistry.
      Stewart's approach was modified thereafter by his followers.
      • Fencl V.
      • Leith D.E.
      Stewart’s quantitative acid-base chemistry: applications in biology and medicine.
      • Constable P.D.
      Clinical assessment of acid-base status: comparison of the Henderson-Hasselbalch and strong ion approaches.
      • Kellum J.A.
      Disorders of acid-base balance.
      • Corey H.E.
      Stewart and beyond: new models of acid-base balance.
      ,
      • Lloyd P.
      Strong ion calculator – a practical bedside application of modern quantitative acid-base physiology.
      A modified strong ion model offers an equation that incorporates the original framework and resembles the Henderson-Hasselbalch equation:
      pH=pKAlogATot/SIDHCO31


      where KA is the effective dissociation constant for human plasma ATot, which equals 7.10 at 37°C.
      • Constable P.D.
      Comparative animal physiology and adaptation.

      Independent Determinants of Acid-Base Status

      Utilization of the physicochemical approach entails calculation of an apparent SID (SIDA) representing the difference between measured strong cations (Na+, K+, Ca++, and Mg++) and strong anions (Cl) (Fig 2).
      • Fencl V.
      • Leith D.E.
      Stewart’s quantitative acid-base chemistry: applications in biology and medicine.
      • Constable P.D.
      Clinical assessment of acid-base status: comparison of the Henderson-Hasselbalch and strong ion approaches.
      • Kellum J.A.
      Disorders of acid-base balance.
      • Corey H.E.
      Stewart and beyond: new models of acid-base balance.
      ,
      • Fencl V.
      • Jabor A.
      • Kazda A.
      • et al.
      Diagnosis of metabolic acid-base disturbances in critically ill patients.
      Some authors include lactate as a strong anion; this addition decreases SIDA in lactic acidosis (Table 3).
      • Kellum J.A.
      Disorders of acid-base balance.
      ,
      • Fencl V.
      • Jabor A.
      • Kazda A.
      • et al.
      Diagnosis of metabolic acid-base disturbances in critically ill patients.
      • Gucyetmez B.
      • Atalan H.K.
      Non-lactate strong ion difference: a clearer picture.
      • Verma A.
      • Qayyum R.
      Non-lactate strong ion difference and cardiovascular, cancer and all-cause mortality.
      Ionized calcium and magnesium are used. The mean value of normal SIDA is 40 mEq/L.
      Figure thumbnail gr2
      Figure 2Schematic depiction of plasma cations and anions in the normal state, normal-AG (hyperchloremic) metabolic acidosis or SID acidosis, and high-AG (normochloremic) metabolic acidosis or SIG acidosis. The numbers associated with ions are concentrations in mEq/L. Abbreviations: AG, anion gap; SIDA, apparent strong ion difference; SIDE, effective strong ion difference; SID, strong ion difference; SIG, strong ion gap. (Adapted with permission from Adrogué et al, © 2009 International Society of Nephrology
      • Adrogué H.J.
      • Gennari F.J.
      • Galla J.H.
      • Madias N.E.
      Assessing acid-base disorders.
      ).
      Table 3Assessment of the Metabolic Component of Acid-Base Status According to Stewart's Approach
      ParameterDerivationComments
      SIDA[Strong cations] – [Strong anions]:
      ([Na+] + [K+] + [Ca++] + [Mg++]) – [Cl]Most commonly used
      ([Na+] + [K+] + [Ca++] + [Mg++]) – ([Cl] + [lactate])Rarely used
      SIDE[HCO3] + [A], whereSIDE is identical to BB
      [A] = [Alb] + [Pi]originally described by
      [HCO3] is derived from measured blood pH and PCO2Singer and Hastings
      [Alb] = [Alb, g/L] × [(0.123 × pH) – 0.631]
      [Pi] = [Pi, mmol/L] × [(0.309 × pH) – 0.469]
      SIGSIDA – SIDEAn estimate of increased
      unmeasured anions, SIG
      resembles ΔAG
      ATot[A] + [AH], whereUsed to define
      [A] = [Alb] + [Pi]hyperalbuminemic acidosis
      [AH] = [Undissociated Alb and Pi]and hypoalbuminemic
      ATot = 2.7 × [Alb, g/dL] + 0.6 × [Pi, mg/dL]alkalosis
      Abbreviations: A, nonvolatile buffer anions; AH, undissociated albumin and inorganic phosphate; Alb, albumin anions; ATot, total concentration of weak acids; BB, base excess; Pi, inorganic phosphate anion; SIDA, apparent strong ion difference; SIDE, effective strong ion difference; SIG, strong ion gap.
      The sum of [HCO3] and [A] (anionic equivalency of albumin and phosphate) represents a second parameter, effective strong ion difference (SIDE), which, in the normal state, is identical to SIDA (Fig 2).
      • Morgan T.J.
      Reducing complexity in acid-base diagnosis—how far should we go?.
      Its calculation requires measurement of blood pH, PCO2, albumin, and phosphate and their incorporation into an equation or nomogram.
      • Corey H.E.
      Stewart and beyond: new models of acid-base balance.
      A third parameter is the strong ion gap (SIG).
      • Jones N.L.
      A quantitative physicochemical approach to acid-base physiology.
      ,
      • Kellum J.A.
      • Kramer D.J.
      • Pinsky M.R.
      Strong ion gap: a methodology for exploring unexplained anions.
      Introduced by Stewart's followers as an estimate of increased unmeasured anions, it is obtained as the difference between SIDA and SIDE (Fig 2). Normally, SIG should be zero, yet in clinical practice, it ranges from –5 to 5 mEq/L. It has been proposed that SIG is a better tool for estimating increased unmeasured anions than AG.
      • Kaplan L.J.
      • Kellum J.A.
      Initial pH, base deficit, lactate, anion gap, strong ion difference, and strong ion gap predict outcome from major vascular injury.
      ,
      • Balasubramanyan N.
      • Havens P.L.
      • Hoffman G.M.
      Unmeasured anions identified by the Fencl-Stewart method predict mortality better than excess anion gap, and lactate in patients in the pediatric intensive care unit.
      However, SIG shares the limitations of AG outlined above although it is spared from the effect of pH.
      • Morgan T.J.
      • Cowley D.M.
      • Weier S.L.
      • Venkatesh B.
      Stability of the strong ion gap versus the anion gap over extremes of PCO2 and pH.
      Computation of ATot requires measurement of albumin and phosphate. The mean value of normal ATot is 15 mEq/L. Blood PCO2, the third independent variable of acid-base status, is measured by blood gas analysis.

      Acid-Base Disorders

      Two of the 3 independent variables, SID and [ATot], assess the metabolic component of acid-base status. Metabolic acidosis is defined as a primary decrease in SIDE or a primary increase in [ATot], whereas metabolic alkalosis is expressed by a primary increase in SIDE or a primary decrease in [ATot].
      • Fencl V.
      • Leith D.E.
      Stewart’s quantitative acid-base chemistry: applications in biology and medicine.
      ,
      • Kellum J.A.
      Disorders of acid-base balance.
      The vast majority of metabolic acidosis diagnoses are SIDE acidosis, which is further classified according to SIG levels. In SID acidosis, SIG is normal, and the decrease in SIDE matches the decrease in SIDA. SID acidosis is equivalent to normal-AG (hyperchloremic) metabolic acidosis of the physiological approach. In SIG acidosis, SIG is increased, and SIDA remains normal, whereas SIDE decreases (Fig 2). High [ATot] acidosis primarily reflects hyperalbuminemic acidosis.
      • Figge J.
      • Mydosh T.
      • Fencl V.
      Serum proteins and acid-base equilibria: a follow-up.
      ,
      • Rossing T.H.
      • Maffeo N.
      • Fencl V.
      Acid-base effects of altering plasma protein concentration in human blood in vitro.
      • Fencl V.
      • Rossing T.H.
      Acid-base disorders in critical care medicine.
      • Figge J.
      • Rossing T.H.
      • Fencl V.
      The role of serum proteins in acid-base equilibria.
      The dominant type of metabolic alkalosis is SID alkalosis in which the increase in SIDE matches the increase in SIDA. Low [ATot] alkalosis primarily reflects hypoalbuminemic alkalosis.
      • Figge J.
      • Mydosh T.
      • Fencl V.
      Serum proteins and acid-base equilibria: a follow-up.
      ,
      • Rossing T.H.
      • Maffeo N.
      • Fencl V.
      Acid-base effects of altering plasma protein concentration in human blood in vitro.
      • Fencl V.
      • Rossing T.H.
      Acid-base disorders in critical care medicine.
      • Figge J.
      • Rossing T.H.
      • Fencl V.
      The role of serum proteins in acid-base equilibria.
      • McAuliffe J.J.
      • Lind L.J.
      • Leith D.E.
      • Fencl V.
      Hypoproteinemic alkalosis.
      Secondary ventilatory responses to metabolic disorders are not quantitated in the physicochemical approach.
      Considering the proposed impact of SID on the dissociation of water, the larger the positive SID ([Na+] > [Cl]), the lower the [H+]. Furthermore, changes in water balance alter both [Na+] and [Cl] as well as the gap between these 2 strong ions (SID). Water deficit increases their concentrations and the gap (SID), and it is postulated to lower [H+]; water excess has the opposite effect. Consequently, water deficit is proposed to elicit SID alkalosis, whereas water excess results in SID acidosis.
      The third independent variable, PCO2, assesses the respiratory component of the acid-base status. Respiratory acidosis is defined by a primary increase in PCO2, whereas respiratory alkalosis is expressed by a primary decrease in PCO2. The secondary response to respiratory disorders alters SID, with increases in SID in hypercapnia and decreases in SID in hypocapnia.
      • Stewart P.A.
      Whole-body acid-base balance.

      Clinical Application

      Contemporary practitioners of the physicochemical approach utilize a hybrid framework that incorporates elements of the base excess and physiological approaches.
      • Kellum J.A.
      Disorders of acid-base balance.
      ,
      • Kellum J.A.
      • Moviat M.
      • van der Hoeven J.G.
      Using the Stewart model at the bedside.
      • Kellum J.A.
      Clinical review: reunification of acid-base physiology.
      • Fidkowski C.
      • Helstrom J.
      Diagnosing metabolic acidosis in the critically ill: bridging the anion gap, Stewart, and base excess methods.
      • Seifter J.L.
      Integration of acid-base and electrolyte disorders.
      Data required include blood gases, SIDA, SIDE, SIG, and [ATot] (Table 3). Blood gas determination provides pH, PCO2, plasma [HCO3], and standard base excess (SBE), the latter being the cornerstone of the base excess approach for assessing the metabolic component of acid-base status. Calculation of SIDA, SIDE, SIG, and [ATot] requires a complete set of serum electrolytes, ionized calcium and magnesium, albumin, and phosphate (and possibly lactate). Because ionized magnesium is commonly unavailable, the product of serum magnesium level and 0.7 is used.
      Evaluation of the acid-base status starts with assessment of blood pH. The next step is examination of PCO2 to determine whether the primary disorder is metabolic or respiratory in nature. Assessment of the metabolic component is accomplished by SIDA, SIDE, plasma [HCO3], SBE, [ATot], and SIG. SIG allows differential diagnosis of metabolic acidosis and mixed acid-base disorders.
      • Kellum J.A.
      • Moviat M.
      • van der Hoeven J.G.
      Using the Stewart model at the bedside.
      • Kellum J.A.
      Clinical review: reunification of acid-base physiology.
      • Fidkowski C.
      • Helstrom J.
      Diagnosing metabolic acidosis in the critically ill: bridging the anion gap, Stewart, and base excess methods.
      • Seifter J.L.
      Integration of acid-base and electrolyte disorders.

      Discussion

      Here we examine the attributes and drawbacks of the physiological and physicochemical approaches and offer a rationale for our preference.

      Physiological Approach

      The physiological approach blends the chemistry of acids and bases with the physiology and pathophysiology of acid-base status.
      • Adrogué H.J.
      • Madias N.E.
      Measurement of acid-base status.
      ,
      • Gennari F.J.
      Regulation of acid-base balance: overview.
      It centers on the H2CO3/HCO3 pair, the dominant body buffer. Regulation of H2CO3 reflects the balance between metabolically produced CO2 and its elimination by the lungs; and regulation of [HCO3] reflects the balance between [H+] input and its output by the kidneys.
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Gennari F.J.
      • Galla J.H.
      Acid-base chemistry and buffering.
      ,
      • Adrogué H.J.
      • Madias N.E.
      Measurement of acid-base status.
      ,
      • Gennari F.J.
      Regulation of acid-base balance: overview.
      Blood gas analyzers reliably measure the H2CO3/HCO3 pair.
      • Adrogué H.J.
      • Madias N.E.
      Measurement of acid-base status.
      Calculation of AG requires measurement of routinely obtained venous-blood electrolytes. Albumin levels are needed to normalize AG. Thus, limited and easily available laboratory data allow implementation of the physiological approach.
      • Mehta A.N.
      • Emmett M.
      Approach to acid-base disorders.
      ,
      • Kraut J.A.
      • Madias N.E.
      Serum anion gap: its uses and limitations in clinical medicine.
      Deviations of either component of the buffer pair define the 4 simple acid-base disorders. This approach first recognized the existence of predictable secondary responses allowing recognition of mixed acid-base disorders. Interpretation of the acid-base data is straightforward.
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Mehta A.N.
      • Emmett M.
      Approach to acid-base disorders.
      ,
      • Adrogué H.J.
      • Madias N.E.
      Secondary responses to altered acid-base status: the rules of engagement.
      ,
      • Rastegar A.
      Mixed acid-base disorders.
      The physiological approach has been criticized on grounds that plasma [HCO3] (metabolic component) is not independent of PCO2 (respiratory component).
      • Siggaard-Andersen O.
      Normal values and extreme values.
      ,
      • Severinghaus J.W.
      Acid-base balance nomogram—a Boston-Copenhagen deténte.
      Certainly, these 2 variables impact each other because they represent a single buffer pair. Beyond this chemical interaction, physiological interactions have been empirically described. Changes in PCO2 elicit secondary changes in [HCO3] via titration of nonbicarbonate buffers and modification of renal acidification.
      • Martinu T.
      • Menzies D.
      • Dial S.
      Re-evaluation of acid-base prediction rules in patients with chronic respiratory acidosis.
      ,
      • Gonzaléz S.B.
      • Menga G.
      • Raimondi G.A.
      • Tighiouart H.
      • Adrogué H.J.
      • Madias N.E.
      Secondary response to chronic respiratory acidosis in humans: a prospective study.
      ,
      • Brackett Jr., N.C.
      • Cohen J.J.
      • Schwartz W.B.
      Carbon dioxide titration curve of normal man. Effect of increasing degrees of acute hypercapnia on acid-base equilibrium.
      • Arbus G.S.
      • Hebert L.A.
      • Levesque P.R.
      • Etsten B.E.
      • Schwartz W.B.
      Characterization and clinical application of the “significance band” for acute respiratory alkalosis.
      • Adrogué H.J.
      • Madias N.E.
      Influence of chronic respiratory acid-base disorders on acute CO2 titration curve.
      • Madias N.E.
      • Adrogué H.J.
      Influence of chronic metabolic acid-base disorders on the acute CO2 titration curve.
      • Schwartz W.B.
      • Brackett Jr., N.C.
      • Cohen J.J.
      The response of extracellular hydrogen ion concentration to graded degrees of chronic hypercapnia: the physiologic limits of the defense of pH.
      • Gennari F.J.
      • Goldstein M.B.
      • Schwartz W.B.
      The nature of the renal adaptation to chronic hypocapnia.
      • Brackett Jr., N.C.
      • Wingo C.F.
      • Muren O.
      • Solano J.T.
      Acid-base response to chronic hypercapnia in man.
      • Krapf R.
      • Beeler I.
      • Hertner D.
      • Hulter H.N.
      Chronic respiratory alkalosis. The effect of sustained, sustained hyperventilation on renal regulation of acid-base equilibrium.
      ,
      • Madias N.E.
      • Adrogué H.J.
      • Cohen J.J.
      • Schwartz W.B.
      Effect of natural variations in PaCO2 on plasma HCO3 in dogs: a redefinition of normal.
      ,
      • Madias N.E.
      • Adrogué H.J.
      • Horowitz G.L.
      • Cohen J.J.
      • Schwartz W.B.
      A redefinition of normal acid-base equilibrium in man: carbon dioxide tension as a key determinant of plasma bicarbonate concentration.
      Conversely, disturbances in [HCO3] modify alveolar ventilation resulting in secondary changes in PCO2.
      • Madias N.E.
      • Bossert W.H.
      • Adrogué H.J.
      Ventilatory response to chronic metabolic acidosis and alkalosis in the dog.
      ,
      • Bushinsky D.A.
      • Coe F.L.
      • Katzenberg C.
      • et al.
      Arterial PCO2 in chronic metabolic acidosis.
      ,
      • Adrogué H.J.
      • Madias N.E.
      Secondary responses to altered acid-base status: the rules of engagement.
      Importantly, as animal studies demonstrated, the secondary ventilatory responses to primary changes in [HCO3] alter renal acidification like primary changes in PCO2, thereby impacting [HCO3] (Fig 3).
      • Madias N.E.
      • Schwartz W.B.
      • Cohen J.J.
      The maladaptive renal response to secondary hypocapnia during chronic HCl acidosis in the dog.
      ,
      • Madias N.E.
      • Adrogué H.J.
      • Cohen J.J.
      Maladaptive renal response to secondary hypercapnia in chronic metabolic alkalosis.
      The interdependency of PCO2 and [HCO3] does not undermine the rigor of the physiological approach because the secondary responses to all primary changes have been quantitated (Table 1).
      • Martinu T.
      • Menzies D.
      • Dial S.
      Re-evaluation of acid-base prediction rules in patients with chronic respiratory acidosis.
      ,
      • Gonzaléz S.B.
      • Menga G.
      • Raimondi G.A.
      • Tighiouart H.
      • Adrogué H.J.
      • Madias N.E.
      Secondary response to chronic respiratory acidosis in humans: a prospective study.
      ,
      • Adrogué H.J.
      • Madias N.E.
      Secondary responses to altered acid-base status: the rules of engagement.
      Despite claims to the contrary, no known parameter that evaluates the metabolic component, including SID and SBE, is truly independent of the respiratory component.
      • Adrogué H.J.
      • Gennari F.J.
      • Galla J.H.
      • Madias N.E.
      Assessing acid-base disorders.
      ,
      • Berend K.
      Diagnostic use of base excess in acid-base disorders.
      Figure thumbnail gr3
      Figure 3Pathophysiological basis of the change in plasma [HCO3] in metabolic acidosis and metabolic alkalosis in dogs. Only a fraction of the change in plasma [HCO3] is attributable to the primary metabolic process. The remainder, approximately 40% of the overall change, is caused by adjustments in renal acidification engendered by the associated secondary hypocapnia or hypercapnia. These responses by the kidney are maladaptive because they undermine the salutary effect on blood pH afforded by the ventilatory responses acutely. GI, gastrointestinal. (Based on data from Madias et al.
      • Madias N.E.
      • Schwartz W.B.
      • Cohen J.J.
      The maladaptive renal response to secondary hypocapnia during chronic HCl acidosis in the dog.
      ,
      • Madias N.E.
      • Adrogué H.J.
      • Cohen J.J.
      Maladaptive renal response to secondary hypercapnia in chronic metabolic alkalosis.
      ).
      Another criticism relates to failure of the physiological approach to quantitate buffers other than bicarbonate. Such criticism is invalid because [HCO3] always reflects the contributions of nonbicarbonate buffers. Such contributions are also incorporated in the bicarbonate space, an index utilized for estimating acid or alkali replacement.
      • Adrogué H.J.
      • Brensilver J.
      • Cohen J.J.
      • Madias N.E.
      Influence of steady-state alterations in acid-base equilibrium on the fate of administered bicarbonate in the dog.
      • Adrogué H.J.
      • Madias N.E.
      Management of life-threatening acid-base disorders. (First of two parts).
      • Adrogué H.J.
      • Madias N.E.
      Management of life-threatening acid-base disorders. (Second of two parts).
      Finally, this approach has been criticized about the variability of AG stemming from changes in albumin levels. Adjustment of the AG for albumin overcomes this criticism.
      • Adrogué H.J.
      • Madias N.E.
      Tools for clinical assessment.
      ,
      • Mehta A.N.
      • Emmett M.
      Approach to acid-base disorders.
      ,
      • Kraut J.A.
      • Madias N.E.
      Serum anion gap: its uses and limitations in clinical medicine.
      • Adrogué H.J.
      • Brensilver J.
      • Madias N.E.
      Changes in the plasma anion gap during chronic metabolic acid-base disturbances.
      • Madias N.E.
      • Ayus J.C.
      • Adrogué H.J.
      Increased anion gap in metabolic alkalosis: the role of plasma protein equivalency.
      ,
      • Gabow P.A.
      Disorders associated with an altered anion gap.

      Stewart's Approach

      Stewart introduced a mathematically sound physicochemical exercise that established relationships between the constituents of a solution and its acid-base status.
      • Stewart P.A.
      Independent and dependent variables of acid-base control.
      ,
      • Stewart P.A.
      How to Understand Acid-Base: A Quantitative Acid-Base Primer for Biology and Medicine.
      ,
      • Stewart P.A.
      Modern quantitative acid-base chemistry.
      He proposed 3 independent variables, SID, ATot, and PCO2, as determinants of the acidity of the solution. Although he conducted theoretical work in a flask, he concluded that his concepts are applicable to whole organisms.
      • Stewart P.A.
      The simplest acid-base system: pure water.
      • Stewart P.A.
      Strong ions and the strong ion difference.
      • Stewart P.A.
      Weak electrolytes and buffers.
      • Stewart P.A.
      Whole-body acid-base balance.
      ,
      • Seifter J.L.
      Integration of acid-base and electrolyte disorders.
      ,
      • Gunnerson K.J.
      • Kellum J.A.
      Acid-base and electrolyte analysis in critically ill patients: are we ready for the new millennium?.
      • Cove M.
      • Kellum J.A.
      The end of the bicarbonate era? A therapeutic application of the Stewart approach.
      • Rubin D.M.
      Last word on viewpoint: Stewart’s approach to quantitative acid-base physiology should replace traditional bicarbonate-centered models.
      Utilizing SID, his followers described SIG that is proposed to better detect increased unmeasured anions, particularly in critically ill patients.
      • Jones N.L.
      A quantitative physicochemical approach to acid-base physiology.
      ,
      • Kellum J.A.
      • Kramer D.J.
      • Pinsky M.R.
      Strong ion gap: a methodology for exploring unexplained anions.
      SIG assesses excess unmeasured anions without requiring the clinician to adjust for albumin as it is the case for AG.
      The physicochemical approach conforms with the “ionization theory of acidity” introduced by Arrhenius in 1887, thereby returning to the old definitions of cations as bases and anions as acids.
      • Siggaard-Andersen O.
      • Fogh-Andersen N.
      Base excess or buffer base (strong ion difference) as measure of a non-respiratory acid-base disturbance.
      ,
      • Gennari F.J.
      • Galla J.H.
      Acid-base chemistry and buffering.
      These concepts were subsequently rejected by the currently held theory of Brønsted and Lowry. Far from original, SID, Stewart's lead independent variable, is actually identical to buffer base, earlier described by Singer and Hastings.
      • Singer R.B.
      • Hastings A.B.
      An improved clinical method for the estimation of disturbances of the acid-base balance of human blood.
      Stewart proposed a cause-and-effect relationship between “independent” and “dependent” variables, the former altering the dissociation of water, thereby establishing the [H+] of the solution. However, mere description of a mathematically precise relationship does not establish which is the driver (“independent” variables) and which is the consequence (“dependent” variables).
      • Adrogué H.J.
      • Gennari F.J.
      • Galla J.H.
      • Madias N.E.
      Assessing acid-base disorders.
      ,
      • Kurtz I.
      • Kraut J.
      • Ornekian V.
      • Nguyen M.K.
      Acid-base analysis: a critique of the Stewart and bicarbonate-centered approaches.
      ,
      • Siggaard-Andersen O.
      • Fogh-Andersen N.
      Base excess or buffer base (strong ion difference) as measure of a non-respiratory acid-base disturbance.
      ,
      • Adrogué H.J.
      • Madias N.E.
      Assessing acid-base status: physiologic versus physicochemical approach.
      • Bie P.
      Strong ion difference: questionable stewardship.
      • Doberer D.
      • Funk G.-C.
      • Kirchner K.
      • Schneeweiss B.
      A critique of Stewart’s approach: the chemical mechanism of dilutional acidosis.
      • Masevicius F.D.
      • Dubin A.
      Has Stewart approach improved our ability to diagnose acid-base disorders in critically ill patients?.
      Whether a variable is “independent” or “dependent” cannot be resolved through mathematical reasoning; only experimentation can provide the answer. Indeed, the proposal that SID is a main driver of changes in the acidity of body fluids has never been validated. Rather than being causes of acid-base perturbations, changes in SID could be mere consequences of these disturbances.
      • Adrogué H.J.
      • Gennari F.J.
      • Galla J.H.
      • Madias N.E.
      Assessing acid-base disorders.
      ,
      • Kurtz I.
      • Kraut J.
      • Ornekian V.
      • Nguyen M.K.
      Acid-base analysis: a critique of the Stewart and bicarbonate-centered approaches.
      ,
      • Siggaard-Andersen O.
      • Fogh-Andersen N.
      Base excess or buffer base (strong ion difference) as measure of a non-respiratory acid-base disturbance.
      ,
      • Adrogué H.J.
      • Madias N.E.
      Assessing acid-base status: physiologic versus physicochemical approach.
      ,
      • Bie P.
      Strong ion difference: questionable stewardship.
      Empirical observations demonstrating that water dissociation is the mechanism by which SID and [ATot] impact pH are unavailable.
      • Adrogué H.J.
      • Gennari F.J.
      • Galla J.H.
      • Madias N.E.
      Assessing acid-base disorders.
      ,
      • Kurtz I.
      • Kraut J.
      • Ornekian V.
      • Nguyen M.K.
      Acid-base analysis: a critique of the Stewart and bicarbonate-centered approaches.
      ,
      • Siggaard-Andersen O.
      • Fogh-Andersen N.
      Base excess or buffer base (strong ion difference) as measure of a non-respiratory acid-base disturbance.
      ,
      • Adrogué H.J.
      • Madias N.E.
      Assessing acid-base status: physiologic versus physicochemical approach.
      • Bie P.
      Strong ion difference: questionable stewardship.
      • Doberer D.
      • Funk G.-C.
      • Kirchner K.
      • Schneeweiss B.
      A critique of Stewart’s approach: the chemical mechanism of dilutional acidosis.
      • Masevicius F.D.
      • Dubin A.
      Has Stewart approach improved our ability to diagnose acid-base disorders in critically ill patients?.
      • Vaughan-Jones R.D.
      • Boron W.F.
      Integration of acid-base and electrolyte disorders.
      • Adrogué H.J.
      • Gennari F.J.
      Integration of acid-base and electrolyte disorders.
      Additional support has been provided against the concept that changes in SID determine specific [H+].
      • Kurtz I.
      • Kraut J.
      • Ornekian V.
      • Nguyen M.K.
      Acid-base analysis: a critique of the Stewart and bicarbonate-centered approaches.
      ,
      • Vaughan-Jones R.D.
      • Boron W.F.
      Integration of acid-base and electrolyte disorders.
      A recent investigation in pigs with acute respiratory or metabolic acidosis showed that Cl removal via electrodialysis increased [HCO3].
      • Zanella A.
      • Caironi P.
      • Castagna L.
      • et al.
      Extracorporeal chloride removal by electrodialysis: a novel approach to correct acidemia.
      This study was interpreted as validation of Stewart's approach.
      • Cove M.
      • Kellum J.A.
      The end of the bicarbonate era? A therapeutic application of the Stewart approach.
      Yet, a more persuasive explanation is that Cl removal generates HCO3 (via a combination of CO2 with OH), thereby maintaining electroneutrality.
      • Swenson E.R.
      Whither the bicarbonate era.
      Acid-base balance in a flask differs markedly from that in living organisms, where there is continuous addition and subtraction of H+ through dietary intake and metabolic reactions.
      • Adrogué H.J.
      • Gennari F.J.
      • Galla J.H.
      • Madias N.E.
      Assessing acid-base disorders.
      ,
      • Gennari F.J.
      Regulation of acid-base balance: overview.
      ,
      • Bie P.
      Strong ion difference: questionable stewardship.
      ,
      • Vaughan-Jones R.D.
      • Boron W.F.
      Integration of acid-base and electrolyte disorders.
      These processes are exaggerated in disease states. It is currently known that a complex system of H+ pumps and transporters in multiple organs regulates extracellular and intracellular [H+] and [HCO3].
      • Gennari F.J.
      Intracellular acid-base homeostasis.
      ,
      • Moe O.W.
      • Baum M.
      • Alpern R.J.
      Molecular biology of renal acid-base transporters.
      By contrast, Stewart dismissed active H+ transport across biological membranes (eg, gastric epithelium) theorizing that SID can fully account for differences in acid-base composition of body fluids.
      • Bie P.
      Strong ion difference: questionable stewardship.
      Furthermore, there is no experimental validation of an operational link between SID or [ATot] and acid-base transporters.
      • Adrogué H.J.
      • Gennari F.J.
      • Galla J.H.
      • Madias N.E.
      Assessing acid-base disorders.
      ,
      • Bie P.
      Strong ion difference: questionable stewardship.
      ,
      • Vaughan-Jones R.D.
      • Boron W.F.
      Integration of acid-base and electrolyte disorders.
      Stewart dismissed any role of [HCO3] in acid-base balance; yet [HCO3] is a determinant of [ATot], and contemporary application of the physicochemical approach makes use of [HCO3]. The physicochemical approach theorizes that changes in SID drive the regulation of acid-base balance by the kidneys. This thesis has no experimental support. In fact, a wealth of knowledge exists on the biology of acid-base transporters along the renal tubule in health and disease.
      • Bie P.
      Strong ion difference: questionable stewardship.
      ,
      • Moe O.W.
      • Baum M.
      • Alpern R.J.
      Molecular biology of renal acid-base transporters.
      There is no biological mechanism that senses and regulates SID as a distinct parameter. Furthermore, each of the strong ions that determines SID features its own regulation that has no known relationship with acid-base homeostasis. By contrast, proton sensors identified in several tissues participate in acid-base homeostasis (eg, control of alveolar ventilation, bone function, intermediary metabolism).
      • Vaughan-Jones R.D.
      • Boron W.F.
      Integration of acid-base and electrolyte disorders.
      ,
      • Javaheri S.
      Determinants of carbon dioxide tension.
      • Ludwig M.G.
      • Vanek M.
      • Guerini D.
      • et al.
      Proton-sensing G-protein-coupled receptors.
      • Sun X.
      • Yang L.V.
      • Tiegs B.C.
      • et al.
      Deletion of the pH sensor GPR4 decreases renal acid excretion.
      The structure-function relationship of body proteins is highly dependent on pH, not SID.
      • Yang A.-S.
      • Honig B.
      On the pH dependence of protein stability.
      ,
      • Talley K.
      • Alexov E.
      On the pH-optimum of activity and stability of proteins.
      It is difficult to conceive a regulatory system in which the controller, SID, is massively larger (10−3 Eq/L) than the regulated variable, [H+] (10−9 Eq/L).
      • Bie P.
      Strong ion difference: questionable stewardship.
      In terms of clinical application, the reliability of SIDA, SIDE, and [ATot] is precarious because their determination requires measurement of multiple variables and calculations incorporating several assumptions.
      • Adrogué H.J.
      • Gennari F.J.
      • Galla J.H.
      • Madias N.E.
      Assessing acid-base disorders.
      ,
      • Rastegar A.
      Clinical utility of Stewart’s method in diagnosis and management of acid-base disorders.
      ,
      • Adrogué H.J.
      • Madias N.E.
      Assessing acid-base status: physiologic versus physicochemical approach.
      ,
      • Morimatsu H.
      • Rocktäschel J.
      • Bellomo R.
      • Uchino S.
      • Goldsmith D.
      • Gutteridge G.
      Comparison of point-of-care versus central laboratory measurement of electrolyte concentrations on calculations of the anion gap and the strong ion difference.
      ,
      • Nguyen B.-V.
      • Vincent J.-L.
      • Hamm J.B.
      • et al.
      The reproducibility of Stewart parameters for acid-base diagnosis using two central laboratory analyzers.
      The classification of metabolic disorders is unduly complex, particularly for metabolic acidosis, which can have normal SIDA, low SIDA, normal SIG, high SIG, or high [ATot].
      • Adrogué H.J.
      • Gennari F.J.
      • Galla J.H.
      • Madias N.E.
      Assessing acid-base disorders.
      ,
      • Emmett M.
      Stewart versus traditional approach to acid-base disorders.
      Additionally, [ATot] acidosis and [ATot] alkalosis that allegedly reflect increased and decreased albumin, respectively, are mostly groundless. There is no evidence that the liver regulates albumin to maintain acid-base balance, and changes in albumin concentration do not correlate with pH or PCO2 levels.
      • Adrogué H.J.
      • Gennari F.J.
      • Galla J.H.
      • Madias N.E.
      Assessing acid-base disorders.
      ,
      • Kurtz I.
      • Kraut J.
      • Ornekian V.
      • Nguyen M.K.
      Acid-base analysis: a critique of the Stewart and bicarbonate-centered approaches.
      ,
      • Siggaard-Andersen O.
      • Fogh-Andersen N.
      Base excess or buffer base (strong ion difference) as measure of a non-respiratory acid-base disturbance.
      The physicochemical approach proposes that rapid infusion of isotonic saline causes metabolic acidosis because SID in saline equals zero. This phenomenon is properly explained as “dilution acidosis” resulting from infusion of a bicarbonate-free solution while maintaining a stable PCO2.
      • Adrogué H.J.
      • Gennari F.J.
      • Galla J.H.
      • Madias N.E.
      Assessing acid-base disorders.
      ,
      • Jaber B.L.
      • Madias N.E.
      Marked dilutional acidosis complicating management of right ventricular myocardial infarction.
      Furthermore, the proposal that water excess results in SID acidosis while water deficit causes SID alkalosis is baseless.
      • Siggaard-Andersen O.
      • Fogh-Andersen N.
      Base excess or buffer base (strong ion difference) as measure of a non-respiratory acid-base disturbance.
      ,
      • Adrogué H.J.
      • Gennari F.J.
      Integration of acid-base and electrolyte disorders.
      SIG has been touted as a better tool for assessing increased unmeasured anions than AG.
      • Kaplan L.J.
      • Kellum J.A.
      Initial pH, base deficit, lactate, anion gap, strong ion difference, and strong ion gap predict outcome from major vascular injury.
      ,
      • Balasubramanyan N.
      • Havens P.L.
      • Hoffman G.M.
      Unmeasured anions identified by the Fencl-Stewart method predict mortality better than excess anion gap, and lactate in patients in the pediatric intensive care unit.
      Normalization of AG for albumin and easy availability of lactate have essentially erased any practical advantage of SIG. In fact, SIG estimation requires measurement of many more electrolytes, thereby introducing logistical complexity, requiring larger blood sampling, and increasing the likelihood of erroneous results.
      • Adrogué H.J.
      • Gennari F.J.
      • Galla J.H.
      • Madias N.E.
      Assessing acid-base disorders.
      ,
      • Rastegar A.
      Clinical utility of Stewart’s method in diagnosis and management of acid-base disorders.
      ,
      • Adrogué H.J.
      • Madias N.E.
      Assessing acid-base status: physiologic versus physicochemical approach.
      ,
      • Moviat M.
      • van Haren F.
      • van der Hoeven H.
      Conventional or physicochemical approach in intensive care unit patients with metabolic acidosis.
      Finally, some studies claim certain diagnostic and prognostic advantages of Stewart's approach.
      • Kaplan L.J.
      • Kellum J.A.
      Initial pH, base deficit, lactate, anion gap, strong ion difference, and strong ion gap predict outcome from major vascular injury.
      ,
      • Balasubramanyan N.
      • Havens P.L.
      • Hoffman G.M.
      Unmeasured anions identified by the Fencl-Stewart method predict mortality better than excess anion gap, and lactate in patients in the pediatric intensive care unit.
      ,
      • Kimura S.
      • Shabsigh M.
      • Morimatsu H.
      Traditional approach versus Stewart approach for acid-base disorders: inconsistent evidence.
      However, critical evaluation of these claims discounts such an advantage.
      • Kimura S.
      • Shabsigh M.
      • Morimatsu H.
      Traditional approach versus Stewart approach for acid-base disorders: inconsistent evidence.
      • Dubin A.
      • Menises M.M.
      • Masevicius F.D.
      • et al.
      Comparison of three different methods of evaluation of metabolic acid-base disorders.
      • Cusack R.J.
      • Rhodes A.
      • Lochhead P.
      • et al.
      The strong ion gap does not have prognostic value in critically ill patients in a mixed medical/surgical adult ICU.

      Case Presentation

      Here we present a clinical case and assess the acid-base status according to the 2 approaches. A 65-year-old man with a history of alcohol abuse and liver cirrhosis is brought to the hospital with jaundice, ascites, confusion, and disorientation. He had persistent nausea and vomiting over the preceding week. He was unable to retain any food for the last several days. On examination, he is afebrile, his blood pressure is 92/50 mm Hg, respiratory rate is 22/min, and heart rate is 110/min. He has moderate ascites and 2+ peripheral edema. He is oriented only to person and has asterixis. Laboratory measurements are as follows: An arterial blood sample shows pH 7.65, PaCO2 28 mm Hg, and [HCO3] 30 mEq/L. Plasma electrolytes in venous blood are [Na+] 126 mEq/L, [K+] 2.6 mEq/L, [Cl] 76 mEq/L, [TCO2] 31 mmol/L, [Ca++] 1.1 mmol/L, [Mg++] 0.5 mmol/L, and [Pi] 0.8 mmol/L. Plasma albumin is 2.2 g/dL.
      Applying the physiological approach, we note that blood pH and plasma [HCO3] are both increased indicating that metabolic alkalosis is the dominant acid-base disorder. The expected PaCO2 for the prevailing hyperbicarbonatemia of metabolic alkalosis is 40 + (30–24) × 0.7 = 44.2 mm Hg. Our patient's hypocapnia (PaCO2 28 mm Hg) indicates the coexistence of an additional acid-base disorder, namely respiratory alkalosis. Turning to the plasma AG, it amounts to 19 mEq/L. We would adjust the average normal value of AG from 10 mEq/L to 5 mEq/L considering the patient's hypoalbuminemia. Thus, the estimated ΔAG (ie, excess AG) equals 14 mEq/L (19 – 5) reflecting the accumulation of a large amount of organic anions in plasma. The increased ΔAG points to the coexistence of a third acid-base disorder, namely high-AG metabolic acidosis. In sum, the physiological approach concludes that the patient has a mixed acid-base disorder comprising 3 simple disorders, namely metabolic alkalosis, respiratory alkalosis, and high-AG metabolic acidosis.
      Utilizing Stewart's approach, SIDA is calculated as 55.8 mEq/L (mean normal value, 40 mEq/L). The combination of an alkaline blood pH and an increased SIDA establishes the presence of SID alkalosis. Because SIDE amounts to 38.3 mEq/L, SIG is calculated as 17.5 mEq/L (mean normal value, 0 mEq/L), signifying the coexistence of an additional acid-base disorder, SIG acidosis, owing to the accumulation of a large amount of organic anions. Reflecting the patient's hypoalbuminemia, [ATot] is 8.3 mEq/L (mean normal value, 15 mEq/L). Decreased [ATot] indicates the presence of [ATot] alkalosis (hypoalbuminemic alkalosis). Furthermore, the observed dilutional hyponatremia gives rise to SIDA acidosis that is hidden within the prevailing SID alkalosis. The patient's hypocapnia in conjunction with alkalemia signifies the coexistence of yet another acid-base disorder, respiratory alkalosis. In sum, Stewart's approach concludes that the patient has a mixed acid-base disorder comprising 5 simple disorders, namely SID alkalosis, [ATot] alkalosis (hypoalbuminemic alkalosis), respiratory alkalosis, SIDA acidosis, and SIG acidosis.

      Conclusion

      Contrasting the merits and drawbacks of the physiological approach and Stewart's approach led us to conclude that the former is superior with respect to theoretical framework and practical use. We favor the physiological approach because of its rigor, simplicity, and ease of application.

      References

        • Adrogué H.J.
        • Madias N.E.
        Tools for clinical assessment.
        in: Gennari F.J. Adrogué H.J. Galla J.H. Madias N.E. Acid-Base Disorders and Their Treatment. Taylor and Francis, Boca Raton, FL2005: 801-816
        • Adrogué H.J.
        • Gennari F.J.
        • Galla J.H.
        • Madias N.E.
        Assessing acid-base disorders.
        Kidney Int. 2009; 76: 1239-1247
        • Berend K.
        Diagnostic use of base excess in acid-base disorders.
        N Engl J Med. 2018; 378: 1419-1428
        • Kurtz I.
        • Kraut J.
        • Ornekian V.
        • Nguyen M.K.
        Acid-base analysis: a critique of the Stewart and bicarbonate-centered approaches.
        Am J Physiol Ren Physiol. 2008; 294: F1009-F1031
        • Rastegar A.
        Clinical utility of Stewart’s method in diagnosis and management of acid-base disorders.
        Clin J Am Soc Nephrol. 2009; 4: 1267-1274
        • Siggaard-Andersen O.
        • Fogh-Andersen N.
        Base excess or buffer base (strong ion difference) as measure of a non-respiratory acid-base disturbance.
        Acta Anaesthesiol Scand. 1995; 39: 123-128
        • Henderson L.J.
        The theory of neutrality regulation in the animal organism.
        Am J Physiol. 1907; 18: 427-448
        • Van Slyke D.D.
        • Wu H.
        • McLean F.C.
        Studies of gas and electrolyte equilibria in the blood. V. Factor controlling the electrolyte and water distribution in the blood.
        J Biol Chem. 1923; 56: 765-849
        • Astrup P.
        A simple electrometric technique for the determination of carbon dioxide tension in blood and plasma, total content of carbon dioxide in plasma, and bicarbonate content in “separated” plasma at a fixed carbon dioxide tension (40 mmHg).
        Scand J Clin Lab Invest. 1956; 8: 33-43
        • Siggaard-Andersen O.
        • Engel K.
        • Jorgensen K.
        • Astrup P.
        A micro method for determination of pH, carbon dioxide tension, base excess and standard bicarbonate in capillary blood.
        Scand J Clin Invest. 1960; 12: 172-176
        • Stewart P.A.
        Independent and dependent variables of acid-base control.
        Respir Physiol. 1978; 33: 9-26
        • Fencl V.
        • Leith D.E.
        Stewart’s quantitative acid-base chemistry: applications in biology and medicine.
        Respir Physiol. 1993; 91: 1-16
        • Constable P.D.
        Clinical assessment of acid-base status: comparison of the Henderson-Hasselbalch and strong ion approaches.
        Vet Clin Pathol. 2000; 29: 115-128
        • Kellum J.A.
        Disorders of acid-base balance.
        Crit Care Med. 2007; 35: 2631-2636
        • Corey H.E.
        Stewart and beyond: new models of acid-base balance.
        Kidney Int. 2003; 64: 777-787
        • Lowry T.M.
        The uniqueness of hydrogen.
        Chem Ind. 1923; 42: 43-47
        • Brönsted J.N.
        The acid base function of molecules and its dependency on the electric charge type.
        J Phys Chem. 1926; 30: 777-790
        • Gennari F.J.
        • Galla J.H.
        Acid-base chemistry and buffering.
        in: Gennari F.J. Adrogué H.J. Galla J.H. Madias N.E. Acid-Base Disorders and their Treatment. Taylor and Francis, Boca Raton, FL2005: 1-24
        • Adrogué H.J.
        • Madias N.E.
        Measurement of acid-base status.
        in: Gennari F.J. Adrogué H.J. Galla J.H. Madias N.E. Acid-Base Disorders and their Treatment. Taylor and Francis, Boca Raton, FL2005: 775-788
        • Martinu T.
        • Menzies D.
        • Dial S.
        Re-evaluation of acid-base prediction rules in patients with chronic respiratory acidosis.
        Can Respir J. 2003; 10: 311-315
        • Gonzaléz S.B.
        • Menga G.
        • Raimondi G.A.
        • Tighiouart H.
        • Adrogué H.J.
        • Madias N.E.
        Secondary response to chronic respiratory acidosis in humans: a prospective study.
        Kidney Int Rep. 2018; 3: 1163-1170
        • Winters R.W.
        Terminology of acid-base disorders.
        Ann Intern Med. 1965; 63: 873-884
        • Elkinton J.R.
        Acid-base disorders and the clinician.
        Ann Intern Med. 1965; 63: 893-899
        • Mehta A.N.
        • Emmett M.
        Approach to acid-base disorders.
        in: Gilbert S.J. Weiner D.E. Bomback A.S. Perazella M.A. Tonelli M. National Kidney Foundation’s Primer on Kidney Diseases. Elsevier, Philadelphia, PA2018: 120-129
        • Brackett Jr., N.C.
        • Cohen J.J.
        • Schwartz W.B.
        Carbon dioxide titration curve of normal man. Effect of increasing degrees of acute hypercapnia on acid-base equilibrium.
        N Engl J Med. 1965; 272: 6-12
        • Arbus G.S.
        • Hebert L.A.
        • Levesque P.R.
        • Etsten B.E.
        • Schwartz W.B.
        Characterization and clinical application of the “significance band” for acute respiratory alkalosis.
        N Engl J Med. 1969; 280: 117-123
        • Adrogué H.J.
        • Madias N.E.
        Influence of chronic respiratory acid-base disorders on acute CO2 titration curve.
        J Appl Physiol. 1985; 58: 1231-1238
        • Madias N.E.
        • Adrogué H.J.
        Influence of chronic metabolic acid-base disorders on the acute CO2 titration curve.
        J Appl Physiol. 1983; 55: 1187-1195
        • Schwartz W.B.
        • Brackett Jr., N.C.
        • Cohen J.J.
        The response of extracellular hydrogen ion concentration to graded degrees of chronic hypercapnia: the physiologic limits of the defense of pH.
        J Clin Invest. 1965; 44: 291-301
        • Gennari F.J.
        • Goldstein M.B.
        • Schwartz W.B.
        The nature of the renal adaptation to chronic hypocapnia.
        J Clin Invest. 1972; 51: 1722-1730
        • Brackett Jr., N.C.
        • Wingo C.F.
        • Muren O.
        • Solano J.T.
        Acid-base response to chronic hypercapnia in man.
        N Engl J Med. 1969; 280: 124-130
        • Krapf R.
        • Beeler I.
        • Hertner D.
        • Hulter H.N.
        Chronic respiratory alkalosis. The effect of sustained, sustained hyperventilation on renal regulation of acid-base equilibrium.
        N Engl J Med. 1991; 324: 1394-1401
        • Madias N.E.
        • Bossert W.H.
        • Adrogué H.J.
        Ventilatory response to chronic metabolic acidosis and alkalosis in the dog.
        J Appl Physiol. 1984; 56: 1640-1646
        • Bushinsky D.A.
        • Coe F.L.
        • Katzenberg C.
        • et al.
        Arterial PCO2 in chronic metabolic acidosis.
        Kidney Int. 1982; 22: 311-314
        • Galla J.H.
        Chloride-depletion alkalosis.
        in: Gennari F.J. Adrogué H.J. Galla J.H. Madias N.E. Acid-Base Disorders and their Treatment. Taylor and Francis, Boca Raton, FL2005: 519-551
        • Andersen O.S.
        • Astrup P.
        • Bates R.G.
        • et al.
        Statement on acid-base terminology. Report of the ad hoc Committee of the New York Academy of Sciences Conference, November 23-24, 1964.
        Ann Intern Med. 1965; 63: 885-890
        • Adrogué H.J.
        • Madias N.E.
        Secondary responses to altered acid-base status: the rules of engagement.
        J Am Soc Nephrol. 2010; 21: 920-923
        • Rastegar A.
        Mixed acid-base disorders.
        in: Gennari F.J. Adrogué H.J. Galla J.H. Madias N.E. Acid-Base Disorders and their Treatment. Taylor and Francis, Boca Raton, FL2005: 681-696
        • Kraut J.A.
        • Madias N.E.
        Serum anion gap: its uses and limitations in clinical medicine.
        Clin J Am Soc Nephrol. 2007; 2: 162-174
        • Adrogué H.J.
        • Brensilver J.
        • Madias N.E.
        Changes in the plasma anion gap during chronic metabolic acid-base disturbances.
        Am J Physiol. 1978; 235: F291-F297
        • Madias N.E.
        • Ayus J.C.
        • Adrogué H.J.
        Increased anion gap in metabolic alkalosis: the role of plasma protein equivalency.
        N Engl J Med. 1979; 300: 1421-1423
        • Figge J.
        • Mydosh T.
        • Fencl V.
        Serum proteins and acid-base equilibria: a follow-up.
        J Lab Clin Med. 1992; 120: 713-719
        • Adrogué H.J.
        • Wilson H.
        • Boyd III, A.E.
        • Suki W.N.
        • Eknoyan G.
        Plasma acid-base patterns in diabetic ketoacidosis.
        N Engl J Med. 1982; 307: 1603-1610
        • Stewart P.A.
        How to Understand Acid-Base: A Quantitative Acid-Base Primer for Biology and Medicine.
        Elsevier, New York, NY1981
        • Stewart P.A.
        Modern quantitative acid-base chemistry.
        Can J Physiol Pharmacol. 1983; 61: 1444-1461
        • Stewart P.A.
        The simplest acid-base system: pure water.
        in: Kellum J.A. Elbers P.W.G. Stewart’s Textbook of Acid-Base. acidbase.org, Amsterdam, The Netherlands2009: 45-53
        • Stewart P.A.
        Strong ions and the strong ion difference.
        in: Kellum J.A. Elbers P.W.G. Stewart’s Textbook of Acid-Base. acidbase.org, Amsterdam, The Netherlands2009: 55-70
        • Stewart P.A.
        Weak electrolytes and buffers.
        in: Kellum J.A. Elbers P.W.G. Stewart’s Textbook of Acid-Base. acidbase.org, Amsterdam, The Netherlands2009: 71-109
        • Stewart P.A.
        Whole-body acid-base balance.
        in: Kellum J.A. Elbers P.W.G. Stewart’s Textbook of Acid-Base. acidbase.org, Amsterdam, The Netherlands2009: 181-197
        • Lloyd P.
        Strong ion calculator – a practical bedside application of modern quantitative acid-base physiology.
        Crit Care Resuscit. 2004; 6: 285-294
        • Constable P.D.
        Comparative animal physiology and adaptation.
        in: Kellum J.A. Elbers P.W.G. Stewart’s Textbook of Acid-Base. acidbase.org, Amsterdam, The Netherlands2009: 305-320
        • Fencl V.
        • Jabor A.
        • Kazda A.
        • et al.
        Diagnosis of metabolic acid-base disturbances in critically ill patients.
        Am J Respir Crit Care Med. 2000; 162: 2246-2251
        • Gucyetmez B.
        • Atalan H.K.
        Non-lactate strong ion difference: a clearer picture.
        J Anesth. 2016; 30: 391-396
        • Verma A.
        • Qayyum R.
        Non-lactate strong ion difference and cardiovascular, cancer and all-cause mortality.
        Clin Chem Lab Med. 2021; 59: 403-409
        • Morgan T.J.
        Reducing complexity in acid-base diagnosis—how far should we go?.
        J Clin Monit Comput. 2020; 34: 17-20
        • Jones N.L.
        A quantitative physicochemical approach to acid-base physiology.
        Clin Biochem. 1990; 23: 189-195
        • Kellum J.A.
        • Kramer D.J.
        • Pinsky M.R.
        Strong ion gap: a methodology for exploring unexplained anions.
        J Crit Care. 1995; 10: 51-55
        • Kaplan L.J.
        • Kellum J.A.
        Initial pH, base deficit, lactate, anion gap, strong ion difference, and strong ion gap predict outcome from major vascular injury.
        Crit Care Med. 2004; 32: 1120-1124
        • Balasubramanyan N.
        • Havens P.L.
        • Hoffman G.M.
        Unmeasured anions identified by the Fencl-Stewart method predict mortality better than excess anion gap, and lactate in patients in the pediatric intensive care unit.
        Crit Care Med. 1999; 27: 1577-1581
        • Morgan T.J.
        • Cowley D.M.
        • Weier S.L.
        • Venkatesh B.
        Stability of the strong ion gap versus the anion gap over extremes of PCO2 and pH.
        Anaesth Intensive Care. 2007; 35: 370-373
        • Rossing T.H.
        • Maffeo N.
        • Fencl V.
        Acid-base effects of altering plasma protein concentration in human blood in vitro.
        J Appl Physiol. 1986; 61: 2260-2265
        • Fencl V.
        • Rossing T.H.
        Acid-base disorders in critical care medicine.
        Annu Rev Med. 1989; 40: 17-29
        • Figge J.
        • Rossing T.H.
        • Fencl V.
        The role of serum proteins in acid-base equilibria.
        J Lab Clin Med. 1991; 117: 453-467
        • McAuliffe J.J.
        • Lind L.J.
        • Leith D.E.
        • Fencl V.
        Hypoproteinemic alkalosis.
        Am J Med. 1986; 81: 86-90
        • Kellum J.A.
        • Moviat M.
        • van der Hoeven J.G.
        Using the Stewart model at the bedside.
        in: Kellum J.A. Elbers P.W.G. Stewart’s Textbook of Acid-Base. acidbase.org, Amsterdam, The Netherlands2009: 339-350
        • Kellum J.A.
        Clinical review: reunification of acid-base physiology.
        Crit Care. 2005; 9: 500-507
        • Fidkowski C.
        • Helstrom J.
        Diagnosing metabolic acidosis in the critically ill: bridging the anion gap, Stewart, and base excess methods.
        Can J Anesth. 2009; 56: 247-256
        • Seifter J.L.
        Integration of acid-base and electrolyte disorders.
        N Engl J Med. 2014; 371: 1821-1831
        • Gennari F.J.
        Regulation of acid-base balance: overview.
        in: Gennari F.J. Adrogué H.J. Galla J.H. Madias N.E. Acid-Base Disorders and their Treatment. Taylor and Francis, Boca Raton, FL2005: 177-208
        • Siggaard-Andersen O.
        Normal values and extreme values.
        in: Siggaard-Andersen O. The Acid-Base Status of the Blood. 2nd edition. Williams & Wilkins, Baltimore, MD1964: 26-29
        • Severinghaus J.W.
        Acid-base balance nomogram—a Boston-Copenhagen deténte.
        Anesthesiology. 1976; 45: 539-541
        • Madias N.E.
        • Adrogué H.J.
        • Cohen J.J.
        • Schwartz W.B.
        Effect of natural variations in PaCO2 on plasma HCO3 in dogs: a redefinition of normal.
        Am J Physiol. 1979; 236: F30-F35
        • Madias N.E.
        • Adrogué H.J.
        • Horowitz G.L.
        • Cohen J.J.
        • Schwartz W.B.
        A redefinition of normal acid-base equilibrium in man: carbon dioxide tension as a key determinant of plasma bicarbonate concentration.
        Kidney Int. 1979; 16: 612-618
        • Madias N.E.
        • Schwartz W.B.
        • Cohen J.J.
        The maladaptive renal response to secondary hypocapnia during chronic HCl acidosis in the dog.
        J Clin Invest. 1977; 60: 1393-1401
        • Madias N.E.
        • Adrogué H.J.
        • Cohen J.J.
        Maladaptive renal response to secondary hypercapnia in chronic metabolic alkalosis.
        Am J Physiol. 1980; 238: F283-F289
        • Adrogué H.J.
        • Brensilver J.
        • Cohen J.J.
        • Madias N.E.
        Influence of steady-state alterations in acid-base equilibrium on the fate of administered bicarbonate in the dog.
        J Clin Invest. 1983; 71: 867-883
        • Adrogué H.J.
        • Madias N.E.
        Management of life-threatening acid-base disorders. (First of two parts).
        N Engl J Med. 1998; 338: 26-34
        • Adrogué H.J.
        • Madias N.E.
        Management of life-threatening acid-base disorders. (Second of two parts).
        N Engl J Med. 1998; 338: 107-111
        • Gabow P.A.
        Disorders associated with an altered anion gap.
        Kidney Int. 1985; 27: 472-483
        • Gunnerson K.J.
        • Kellum J.A.
        Acid-base and electrolyte analysis in critically ill patients: are we ready for the new millennium?.
        Curr Opin Crit Care. 2003; 9: 468-473
        • Cove M.
        • Kellum J.A.
        The end of the bicarbonate era? A therapeutic application of the Stewart approach.
        Am J Respir Crit Care Med. 2020; 201: 757-758
        • Rubin D.M.
        Last word on viewpoint: Stewart’s approach to quantitative acid-base physiology should replace traditional bicarbonate-centered models.
        J Appl Physiol (1985). 2021; 130: 2024
        • Singer R.B.
        • Hastings A.B.
        An improved clinical method for the estimation of disturbances of the acid-base balance of human blood.
        Medicine. 1948; 27: 223-242
        • Adrogué H.J.
        • Madias N.E.
        Assessing acid-base status: physiologic versus physicochemical approach.
        Am J Kidney Dis. 2016; 68: 793-802
        • Bie P.
        Strong ion difference: questionable stewardship.
        Acta Physiol. 2021; 233: 1-4
        • Doberer D.
        • Funk G.-C.
        • Kirchner K.
        • Schneeweiss B.
        A critique of Stewart’s approach: the chemical mechanism of dilutional acidosis.
        Intensive Care Med. 2009; 35: 2173-2180
        • Masevicius F.D.
        • Dubin A.
        Has Stewart approach improved our ability to diagnose acid-base disorders in critically ill patients?.
        World J Crit Care Med. 2015; 4: 62-70
        • Vaughan-Jones R.D.
        • Boron W.F.
        Integration of acid-base and electrolyte disorders.
        N Engl J Med. 2015; 372: 389
        • Adrogué H.J.
        • Gennari F.J.
        Integration of acid-base and electrolyte disorders.
        N Engl J Med. 2015; 372: 389
        • Zanella A.
        • Caironi P.
        • Castagna L.
        • et al.
        Extracorporeal chloride removal by electrodialysis: a novel approach to correct acidemia.
        Am J Respir Crit Care Med. 2020; 201: 799-813
        • Swenson E.R.
        Whither the bicarbonate era.
        Am J Respir Crit Care Med. 2020; 202: 906-907
        • Gennari F.J.
        Intracellular acid-base homeostasis.
        in: Gennari F.J. Adrogué H.J. Galla J.H. Madias N.E. Acid-Base Disorders and their Treatment. Taylor and Francis, Boca Raton, FL2005: 25-46
        • Moe O.W.
        • Baum M.
        • Alpern R.J.
        Molecular biology of renal acid-base transporters.
        in: Gennari F.J. Adrogué H.J. Galla J.H. Madias N.E. Acid-Base Disorders and their Treatment. Taylor and Francis, Boca Raton, FL2005: 119-176
        • Javaheri S.
        Determinants of carbon dioxide tension.
        in: Gennari F.J. Adrogué H.J. Galla J.H. Madias N.E. Acid-Base Disorders and their Treatment. Taylor and Francis, Boca Raton, FL2005: 47-78
        • Ludwig M.G.
        • Vanek M.
        • Guerini D.
        • et al.
        Proton-sensing G-protein-coupled receptors.
        Nature. 2003; 425: 93-98
        • Sun X.
        • Yang L.V.
        • Tiegs B.C.
        • et al.
        Deletion of the pH sensor GPR4 decreases renal acid excretion.
        J Am Soc Nephrol. 2010; 21: 1745-1755
        • Yang A.-S.
        • Honig B.
        On the pH dependence of protein stability.
        J Mol Biol. 1993; 231: 459-474
        • Talley K.
        • Alexov E.
        On the pH-optimum of activity and stability of proteins.
        Proteins. 2010; 78: 2699-2706
        • Morimatsu H.
        • Rocktäschel J.
        • Bellomo R.
        • Uchino S.
        • Goldsmith D.
        • Gutteridge G.
        Comparison of point-of-care versus central laboratory measurement of electrolyte concentrations on calculations of the anion gap and the strong ion difference.
        Anesthesiology. 2003; 98: 1077-1084
        • Nguyen B.-V.
        • Vincent J.-L.
        • Hamm J.B.
        • et al.
        The reproducibility of Stewart parameters for acid-base diagnosis using two central laboratory analyzers.
        Anesth Analg. 2009; 109: 1517-1523
        • Emmett M.
        Stewart versus traditional approach to acid-base disorders.
        Anesth Analg. 2016; 123: 1063-1064
        • Jaber B.L.
        • Madias N.E.
        Marked dilutional acidosis complicating management of right ventricular myocardial infarction.
        Am J Kidney Dis. 1997; 30: 561-567
        • Moviat M.
        • van Haren F.
        • van der Hoeven H.
        Conventional or physicochemical approach in intensive care unit patients with metabolic acidosis.
        Crit Care. 2003; 7: R41-R45
        • Kimura S.
        • Shabsigh M.
        • Morimatsu H.
        Traditional approach versus Stewart approach for acid-base disorders: inconsistent evidence.
        SAGE Open Med. 2018; 62050312118801255https://doi.org/10.1177/2050312118801255
        • Dubin A.
        • Menises M.M.
        • Masevicius F.D.
        • et al.
        Comparison of three different methods of evaluation of metabolic acid-base disorders.
        Crit Care Med. 2007; 35: 1254-1270
        • Cusack R.J.
        • Rhodes A.
        • Lochhead P.
        • et al.
        The strong ion gap does not have prognostic value in critically ill patients in a mixed medical/surgical adult ICU.
        Intensive Care Med. 2002; 28: 864-869