# An approach to complex acid-base problems

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## Abstract

### OBJECTIVE

To review rules and formulas for solving even the most complex acid-base problems.

### SOURCES OF INFORMATION

MEDLINE was searched from January 1966 to December 2003. The search was limited to English-language review articles involving human subjects. Nine relevant review papers were found and provide the background. As this information is well established and widely accepted, it is not judged for strength of evidence, as is standard practice.

### MAIN MESSAGE

An understanding of the body’s responses to acidemia or alkalemia can be gained through a set of four rules and two formulas that can be used to interpret almost any acid-base problems. Physicians should, however, remember the “golden rule” of acid-base interpretation: always look at a patient’s clinical condition.

### CONCLUSION

Physicians practising in acute care settings commonly encounter acid-base disturbances. While some of these are relatively simple and easy to interpret, some are more complex. Even complex cases can be resolved using the four rules and two formulas.

## Résumé

### OBJECTIF

Passer en revue les règles et formules qui permettent de résoudre même les problèmes acido-basiques les plus complexes.

### SOURCES DE L’INFORMATION

Une recherche limitée aux articles de revue de langue anglaise portant sur des sujets humains a été effectuée dans MEDLINE entre janvier 1966 et décembre 2003. Les neuf articles pertinents repérés ont servi de base au présent travail. Comme cette information est bien fondée et généralement reconnue, sa valeur probante n’a pas été estimée, contrairement à la coutume.

### PRINCIPAL MESSAGE

L’utilisation de quatre règles et deux formules pour interpréter la plupart des problèmes acido-basiques permet de mieux comprendre les réponses de l’organisme à l’acidose ou à l’alcalose. Le médecin doit toutefois se rappeler la règle d’or de l’interprétation acido-basique: toujours tenir compte de la condition clinique du patient.

### CONCLUSION

Le médecin qui pratique dans un contexte de soins aigus est confronté à des déséquilibres acido-basiques. Si certains cas sont relativement simples et faciles d’interprétation, d’autres sont plus complexes. Ces derniers cas peuvent toutefois être résolus à l’aide des quatre règles et deux formules.

### EDITOR’S KEY POINTS

- Acid-base disturbances can be conveniently understood using four rules and two formulas. Rule 1. Metabolic acidosis: 1.2(∆⇓Hco
_{3}^{–}) = ∆⇓Pco_{2}; Rule 2. Metabolic alkalosis: 0.6(∆⇑Hco_{3}^{–}) = ∆⇑Pco_{2}; Rule 3. Respiratory acidosis and alkalosis: 0.4(∆Pco_{2}) = ∆Hco_{3}^{–}; Rule 4. Anion gap: ∆⇑anion gap = ∆⇓Hco_{3}^{–}; Formula 1. Anion gap: anion gap = [Na^{+}] – ([Hco_{3}^{–}] + [Cl^{–}]); Formula 2. Osmolar gap: osmolar gap = measured osmolality minus calculated osmolality - Solve most problems by asking: What is the anion gap? (formula 1); does the anion gap equal the base deficit? (rule 4); and what is the osmolar gap? (formula 2).
- Remember the “golden rule” of acid-base interpretation: always look at a patient’s condition.

## Case 1

A 19-year-old woman came into the local emergency department with nausea and epigastric pain of several hours’ duration. She recently found out she is unexpectedly pregnant and is quite upset with her unsupportive partner.

Her vital signs reveal moderate tachycardia and tachypnea, but she is normotensive. On examination, she is distressed, her chest is clear on auscultation, and her abdomen is soft with mild epigastric tenderness. An arterial blood gas (ABG) analysis has the following results: Pao

_{2}= 93 mm Hg, Paco_{2}= 25 mm Hg, Hco_{3}^{–}= 25 mEq/L, pH = 7.57. What is the acid-base disturbance?A few hours later she begins to vomit blood-streaked emesis and looks ill. A repeat ABG has the following results: Paco

_{2}= 29 mm Hg, Hco_{3}^{–}= 29 mEq/L, pH = 7.62. What is the acid-base disturbance now?Much later she gets drowsy and hypotensive. Repeat examination of her vital signs now shows marked hypotension. A third ABG reveals the following: Paco

_{2}= 31 mm Hg, Hco_{3}^{–}= 9 mEq/L, pH = 7.12. What is the acid-base disturbance now, and what is a possible diagnosis?

Physicians practising in acute care settings commonly encounter patients with acid-base disturbances. While some of these are relatively simple and easy to interpret, some, such as the case described above, can be complicated. Keep in mind that, as cases get more intricate, they also become more interesting and challenging.

This article reviews rules and formulas for solving even the most complex acid-base problems. It describes how to use these rules and formulas to work through cases. By the end of the article, readers should be able to answer the three questions posed in the case above and resolve almost any acid-base question, no matter how complex.

## Sources of information

A computer-assisted search of the scientific literature (MEDLINE) from January 1966
to December 2003 was carried out using National Center for Biotechnology Information
PubMed search engines. Search terms included “acid-base analysis,” “acid-base
disorders,” “arterial blood gas,” and “metabolic acidosis.” Given the nature of the
topic, searches were limited to English-language review articles involving human
subjects. More than 200 papers were initially found and their abstracts, where
available, were reviewed. From these papers, nine relevant review articles were
selected to provide background information.^{1}^{-}^{9} As this information is well
established and widely accepted, it is not judged for strength of evidence, as is
standard practice.

## Acid-base interpretation

An in-depth knowledge of acid-base physiology is not essential for solving acid-base
problems. For those who wish, a detailed discussion of it can be found in
Costanzo.^{10} An understanding of renal and
pulmonary responses to acidemia or alkalemia can be gained through a set of rules
and formulas (**Table 1**) that can be used to interpret acid-base abnormalities. Reading the
following cases, you will see that you can solve acid-base problems without paying
much attention to pH values. Above all, remember the “golden rule” of acid-base
interpretation: always look at the patient. Some patients could be really ill,
despite results that are not much different from normal values. And, conversely,
patients who are relatively stable despite abnormal arterial blood gas (ABG) results
might still need close observation, but only conservative therapy.

## Rule 1. Metabolic acidosis

In pure metabolic acidosis, every 1 mEq/L decrease in serum bicarbonate should lead
to a compensatory decrease of 1.2 mm Hg in Pco_{2}. This
change in CO_{2} should occur very quickly, and anything greater or less
than this predicted change should lead you to consider an accompanying respiratory
acid-base derangement. Rule 1 can be mathematically represented as
1.2(∆⇓Hco_{3}^{–}) =
∆⇓Pco_{2}.

## Case 2

A 56-year-old man with a history of diabetes mellitus and alcoholism presents after having eaten no food and taken no insulin for the last 3 days and drinking “lots” of alcohol. He is hypotensive, tachycardic, and markedly tachypneic (respiratory rate 36). He smells strongly of acetone and is dehydrated, and clinical findings are consistent with left lower lobe pneumonia. Results of ABG testing are: Pao

_{2}= 68 mm Hg, Paco_{2}= 17 mm Hg, Hco_{3}^{–}= 6 mEq/L, and pH = 7.30. What is the acid-base abnormality?

Using rule 1, the answer is that he has metabolic acidosis with an appropriate
respiratory response. His bicarbonate level is low, likely because of a combination
of prolonged alcohol intake, starvation, and ketone production (the acetone on his
breath). To attempt to correct his pH, he hyperventilates and exhales his
Pco_{2} down to 17, almost as low as it can go. His pH
approaches normal but does not quite get there. Renal and respiratory compensatory
mechanisms can almost, but never completely, correct an abnormal pH level.

What would this patient’s acid-base profile be if his respiratory rate were 14
breaths/min and his Paco_{2} were 29 mm Hg? What might
his pH be? The answer is that he would have metabolic acidosis and concomitant
respiratory acidosis. Although his Paco_{2} is low at 29, it is not
as low as it should be. He is actually hypoventilating relative to his needs,
possibly due to pneumonia and fatigue. His pH is in fact 6.99, potentially life
threatening. He not only needs standard therapy with fluids and insulin for
ketoacidosis, but might very well require ventilatory support. If his
Paco_{2} were to rise to 40, still a “normal” value, his pH
would plummet to 6.75, and he would die.

## Rule 2. Metabolic alkalosis

With pure metabolic alkalosis, every 1 mEq/L increase in serum bicarbonate should
result in a compensatory rise in Pco_{2 }of 0.6 mm Hg.
This increase in CO_{2} should occur very quickly, and again, anything
greater or less than this should lead you to think of an associated respiratory
abnormality. This rule can be mathematically represented as
0.6(∆⇑Hco_{3}^{–}) =
∆⇑Pco_{2}.

## Case 3

A 44-year-old woman presents with 24 hours of unremitting emesis. She is dehydrated and hypotensive. Tests of her ABG show the following values: Pao

_{2 }= 104 mm Hg, Paco_{2}= 46 mm Hg, Hco_{3}^{–}= 34 mEq/L, and pH = 7.49. What is the acid-base disturbance here?

Using rule 2, we see that she has metabolic alkalosis from the continuous vomiting
and loss of acid-rich gastric contents. In response to the increase in bicarbonate
(she has a base excess of 10 mEq/L), her body appropriately allows her
CO_{2} to rise in an attempt to return the pH to normal. Although the
metabolic abnormality has evolved over an entire day, the respiratory response can
occur and change quickly. What would the acid-base profile look like if she were
anxious and hyperventilating? What would her acid-base status be if she became
obtunded and began hypoventilating?

If she were to hyperventilate and drive her Paco_{2} down to, say,
26 mm Hg, her pH would be something like 7.67. If she hypoventilated and
allowed her CO_{2} to rise too much to, say, 56 mm Hg, her pH
would be 7.42. Although this value is healthier-looking than before, her clinical
situation has clearly worsened (the golden rule). A normal pH value usually points
to a double acid-base abnormality. Compensatory mechanisms can never quite normalize
the pH.

## Rule 3. Respiratory acidosis or alkalosis

For pure respiratory acidosis, every 1–mm Hg increase in
Paco_{2} should cause the bicarbonate level to rise by 0.4
mEq/L. Conversely, with pure respiratory alkalosis, every 1–mm Hg decrease
in Paco_{2} should result in the
Hco_{3}^{–} falling by 0.4 mEq/L. Any change
in Hco_{3}^{–} greater or less than predicted
*might* point to an accompanying metabolic abnormality. The
situation can get confusing, however, because the kidneys take up to 24 hours to
respond fully to respiratory acidosis or alkalosis. Rule 3 can be mathematically
represented as 0.4(∆Pco_{2}) =
∆Hco_{3}^{–}.

## Case 4

Two patients, both in respiratory distress, present to your hospital when you have only a single ventilator available. Each has a history of emphysema and each wants “everything possible done.” Results of ABG testing of the first patient show Pao

_{2 }= 68 mm Hg, Paco_{2}= 58 mm Hg, and Hco_{3}^{–}= 22 mEq/L. Results for the second patient are Pao_{2 }= 59 mm Hg, Paco_{2}= 75 mm Hg, and Hco_{3}^{–}= 38 mEq/L. All else being equal and based purely on ABG analysis, which patient should get the ventilator?

The first patient clearly has respiratory acidosis: his Paco_{2} is
18 mm Hg greater than normal. Using rule 3, an appropriate renal response
would be to conserve Hco_{3}^{–} and increase it
to about 31 mEq/L. Since his system has not yet done this, we can assume this is
*acute* respiratory acidosis. Note how we can arrive at this
conclusion without even knowing his pH (which, incidentally, at 7.18 supports our
judgment). The second patient has an even greater respiratory acidosis: his
Paco_{2 }is 35 mm Hg higher than normal. Rule 3
tells us that his predicted Hco_{3}^{–} should be
38, exactly as his ABG reveals. Thus he is showing an entirely appropriate metabolic
response to *chronic* hypercapnia. Again, we have reached this
conclusion without knowing his pH (which, in fact, is 7.34). Hence, the first
patient needs the ventilator more than the second. You must, of course, follow the
golden rule and base your decision on clinical grounds.

## Formula 1. The anion gap

The anion gap is equal to the difference between Na^{+} concentration and the
sum of the concentrations of Cl^{–} and
Hco_{3}^{–}. It can be mathematically
represented as anion gap =
[Na^{+}] – ([Hco_{3}^{–}]
+ [Cl^{–}]).

The normal value for the anion gap is less than 10 mEq/L, and under usual circumstances, it is composed of sulfate, phosphate, citrate, and certain plasma proteins. It might become greater with decreased excretion of fixed acids, addition of lactate or ketones, or ingestion of certain toxins.

## Case 5

A 41-year-old man with a history of delirium tremens presents having had multiple seizures. He has been drinking heavily and has neglected to take his anticonvulsant medication for 4 days. He is drowsy but tremulous with fever, tachycardia, and hypertension. Results of ABG tests are Pao

_{2}= 62 mm Hg, Paco_{2}= 3 mm Hg, Hco_{3}^{–}= 13 mEq/L, and pH = 7.17. What is this acid-base disturbance?

He has metabolic acidosis with a base deficit of 11 mEq/L. Using rule 1, you can see
that he also has respiratory acidosis. If he were ventilating appropriately, his
Paco_{2} would be 27 and his pH would be 7.30. As his ABG
results show, however, his Paco_{2} is actually much higher and his
pH much lower. Although his CO_{2} is in the normal range, he looks very
sick (the golden rule).

Laboratory values reveal the following: Na^{+} = 146 mEq/L,
Hco_{3}^{–} = 12 mEq/L, and
Cl^{–} = 112 mEq/L. What is his anion gap? Using formula 1, we
see that his anion gap is 22 (normal value is up to 10). What this means is that he
still has to account for about 12 mEq/L of some unidentified anion in his
extracellular fluid compartment. **Table 2** shows causes of anion gap acidosis.

## Case 6

A 74-year-old man, taking diuretics for heart failure, presents with weakness and diarrhea of 2 days’ duration. On examination he is markedly dehydrated and hypotensive. His ABG results are: Paco

_{2}= 22 mm Hg, Hco_{3}^{–}= 10, and pH = 7.33. Serum biochemical analysis shows the following: Na^{+}= 130 mEq/L, Hco_{3}^{–}= 9 mEq/L, and Cl^{–}= 116 mEq/L. What is his acid-base problem, and what is his anion gap?

This patient has metabolic acidosis with a base deficit of 15 mEq/L. Using rule 1, we
can see that his Pco_{2} should be about 22 mm Hg, so
his ventilatory response to the acidemia is appropriate. Using formula 1, we
calculate his anion gap at 5 mEq/L. Metabolic acidosis with a normal anion gap
arises from bicarbonate loss. **Table 2** lists causes of hyperchloremic metabolic acidosis. The probable causes of
his Hco_{3}^{–} depletion are diarrhea and
chronic diuretic use.

## Rule 4. The base deficit and the anion gap

Metabolic acidosis resulting from any acid gain will be associated with an increase
in unmeasured anions (anion gap). Addition of H^{+} will also deplete
Hco_{3}^{–} as it is buffered. Because each
of the acids listed in **Table 2** dissociates into a single hydrogen ion and its respective anion, every
1–mEq rise in the anion gap should be accompanied by a 1–mEq
fall in bicarbonate. A higher-than-expected
Hco_{3}^{–} should lead you to consider an
additional metabolic alkalosis. This rule can be represented as ∆⇑anion gap =
∆⇓Hco_{3}^{–}.

## Case 7

A 56-year-old man presents with anorexia and unremitting emesis for 4 days. Results of ABG testing are Hco

_{3}^{–}= 18 mEq/L, Paco_{2 }= 30 mm Hg, and pH = 7.40. His biochemistry profile reveals the following: Na^{+}= 130 mEq/L, Hco_{3}^{–}= 18 mEq/L, and Cl^{–}= 89. What is his acid-base disturbance, and what is his anion gap?

This man has metabolic acidosis with a base deficit of about 7 mEq/L. Rule 1 reveals
satisfactory respiratory compensation for the acidemia. Using formula 1, we can
calculate his anion gap at 23 mEq/L. His base deficit is smaller than his anion gap.
How can this be? The answer is quite simple. If he had a preceding metabolic
alkalosis from 4 days of vomiting acid-rich gastric contents, he might have started
with a higher Hco_{3}^{– }concentration before
starvation ketoacidosis set in. **Table 3** lists common causes of metabolic alkalosis.

Note his “dead-on” normal pH of 7.4, despite the elevated anion gap acidosis, compensatory respiratory alkalosis, and initial metabolic alkalosis. A perfectly normal pH strongly suggests a triple acid-base disturbance.

## Formula 2. The osmolar gap

The osmolar gap is equal to the difference between the *measured*
serum osmolarity (osmo_{m}) and the *calculated* serum
osmolarity (osmo_{c}). It can be mathematically represented by the following
formula: osmolar gap = osmo_{m} – osmo_{c}.

The main osmotically active substances in serum are sodium chloride (NaCl), urea, and
glucose (the osmolarity of NaCl is twice that of glucose or urea). Thus, the
calculated serum osmolarity can be derived as: osmo_{c} = 2(Na^{+})
+ glucose + urea.

Substances that increase the osmo_{m} and, hence, the osmolar gap are sugars
other than glucose (which figures in the calculation), and all alcohols. Toxic
alcohols also increase the anion gap (**Table 2**). As a general rule, an anion gap metabolic acidosis with an elevated
osmolar gap is due to a toxic alcohol until proven otherwise.

## Complex metabolic acidosis

With any complex metabolic acidosis, you can work toward a specific diagnosis if you
ask the following three questions. First, what is the anion gap (formula 1)? Second,
does the anion gap equal the base deficit (rule 4)? Third, what is the osmolar gap
(formula 2)? This will allow you to sort through the many causes listed in **Table 2**. And, of course, the golden rule is still important.

## Case 8

A 33-year-old woman with a long history of alcoholism presents unresponsive with hypotension, tachycardia, and tachypnea. Her ABG results are Paco

_{2}= 23, Hco_{3}^{– }= 7 mEq/L, and pH = 7.12. Her venous biochemistry profile shows the following: Na^{+}= 142, Cl^{–}= 105, Hco_{3}^{–}= 6, glucose = 8.4, urea = 5.5, osmolarity = 349, and ethanol = 22 mmol/L. How do you work through this woman’s acid-base abnormality?

This patient has marked metabolic acidosis with a base deficit of 20 mEq/L. Rule 1
indicates that she also has an accompanying respiratory acidosis. Her
Pco_{2} should be 16 mm Hg, but it is
23 mm Hg.

Formula 1 shows her anion gap to be 31 mEq/L. As a normal anion gap is up to 10 mEq/L, her anion gap is about 21 mEq/L, which approximates her base deficit, satisfying rule 4. We are unlikely to see any additional metabolic problem. Formula 2 allows us to calculate her osmolar gap; it is markedly elevated at 50 mmol/L. Her ethanol level accounts for only 22 mmol/L of the osmolar gap. Thus, we should strongly suspect that a toxic alcohol is causing her anion gap metabolic acidosis. Additional laboratory tests ultimately show that her lactate and ketone levels are only mildly elevated, but her methanol level is 26 mmol/L. She needs aggressive therapy with hemodialysis or she will die.

## Answer to case 1

The 19-year-old woman came to your local emergency department with nausea and
epigastric pain. An initial ABG analysis showed the following:
Pao_{2} = 93 mm Hg, Paco_{2} =
25 mm Hg, Hco_{3}^{–} = 25 mEq/L, pH =
7.57. What is the acid-base disturbance?

She has respiratory alkalosis: her Paco_{2} is 15 mm Hg
lower than normal. Rule 3 tells us that a proper response by her kidneys would
result in a Hco_{3}^{–} concentration of about 20
mEq/L. She has not yet had sufficient time for this to happen, so we can say she has
acute respiratory alkalosis (note her high pH). A few hours later, repeat ABG tests
show the following: Paco_{2} = 29 mm Hg,
Hco_{3}^{–} = 29 mEq/L, pH = 7.62. What is
the acid-base disturbance now?

She has now developed metabolic alkalosis from the vomiting. Note that her
Hco_{3}^{–} has risen to 29 instead of
decreasing, and her pH is even higher. Rule 2 tells us that if her
Paco_{2} were to rise to 43, as it should, her pH would be much
closer to normal. She still has some respiratory alkalosis. Much later, when she
appears more ill, a third ABG test reveals the following: Paco_{2}
= 31 mm Hg and pH = 7.12. What is the acid-base disturbance now, and what
is a possible diagnosis?

She has now developed metabolic acidosis. Her bicarbonate has plummeted from 29 to 9
mEq/L. **Table 2** lists possible causes. When you calculate her anion gap as very high and her
osmolar gap as very low, the list of possibilities is narrowed.

Finally, rule 1 tells us that her ventilatory response should be to drive her
Paco_{2} down to 22 mm Hg, but it is actually higher. So she
has associated respiratory acidosis, and this is shown by the very low pH.

She eventually admits to having taken a substantial overdose of acetylsalicylic acid (readers will likely have already recognized the characteristic profile of ASA toxicity). Salicylates commonly cause initial respiratory alkalosis, due to direct central nervous system stimulation, followed by metabolic acidosis due to direct toxic effects.

## Conclusion

Using the four rules and two formulas for acid-base problem interpretation, we have worked through several cases and demonstrated their usefulness. Even when cases are complex, they can be solved readily using the rules and formulas.

## Biography

Dr Herd practises in the Department of Emergency Medicine at the Health Sciences Centre in Winnipeg, Man, and teaches in the Section of Family Medicine in the Faculty of Medicine at the University of Manitoba.

## Footnotes

Competing interests: None declared

## References

**College of Family Physicians of Canada**

## Formats:

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- Citation

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*Bear RA, Dyck RF.**Can Med Assoc J. 1979 Jan 20; 120(2):173-82.* - Back to basics: acidosis and alkalosis.[Pediatr Rev. 2004]
*Schwaderer AL, Schwartz GJ.**Pediatr Rev. 2004 Oct; 25(10):350-7.* - Assessment of acid-base disorders. A practical approach and review.[Can Med Assoc J. 1969]
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- An approach to complex acid-base problemsAn approach to complex acid-base problemsCanadian Family Physician. 2005 Feb 10; 51(2)226

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