Nephrology Practice Questions — USMLE Step 2 CK — Page 4

Question 61Question →

Emergency medical services transport a $65$ -year-old man from a long-term care facility to the hospital due to acute-onset confusion, fever, and severe abdominal pain. His past medical history is significant for alcohol-associated cirrhosis with refractory ascites, which is managed with high-dose furosemide and spironolactone. Upon arrival, his temperature is $39.2^\circ$ C ( $102.6^\circ$ F), blood pressure is $80/50$ mm Hg, heart rate is $122$ /min, and respiratory rate is $28$ /min. Abdominal examination reveals severe distension, diffuse tenderness, and involuntary guarding. Laboratory results are as follows:

Laboratory Test	Result
Sodium	$132$ mEq/L
Potassium	$3.1$ mEq/L
Chloride	$82$ mEq/L
Bicarbonate	$16$ mEq/L
Blood urea nitrogen	$45$ mg/dL
Creatinine	$2.2$ mg/dL
Lactate	$7.5$ mmol/L

Arterial blood gas (room air):

Parameter	Result
pH	$7.50$
pCO $_2$	$21$ mm Hg
pO $_2$	$68$ mm Hg

Based on the clinical presentation and laboratory results, which of the following sets of acid-base disorders is present in this patient?

High anion gap metabolic acidosis, metabolic alkalosis, and respiratory alkalosis

High anion gap metabolic acidosis and respiratory alkalosis

High anion gap metabolic acidosis, normal anion gap metabolic acidosis, and respiratory alkalosis

High anion gap metabolic acidosis and metabolic alkalosis

Normal anion gap metabolic acidosis, metabolic alkalosis, and respiratory alkalosis

Show answer & explanation

Answer: High anion gap metabolic acidosis, metabolic alkalosis, and respiratory alkalosis

Answer

The correct answer is the set containing a high anion gap metabolic acidosis, a metabolic alkalosis, and a respiratory alkalosis.

The patient's ABG shows an alkalemia (pH >

7.45

) driven by hypocapnia (pCO

_2

<

40

mm Hg), indicating a primary respiratory alkalosis. This is clinically consistent with hyperventilation due to severe sepsis and fever. Next, calculating the anion gap (AG): AG = Na

^+

- (Cl

^-

+ HCO

_3^-

) =

132 - (82 + 16) = 34

mEq/L. Since the normal AG is

12

mEq/L, an AG of

34

confirms the presence of a high anion gap metabolic acidosis (HAGMA), resulting from lactic acidosis due to septic shock. Finally, to check for a third disorder, a delta-delta calculation is performed. The

\Delta

AG is

34 - 12 = 22

. The corrected HCO

_3^-

= measured HCO

_3^-

+

\Delta

AG =

16 + 22 = 38

mEq/L. Because the corrected HCO

_3^-

(

38

mEq/L) is significantly greater than the normal baseline (

24

mEq/L), there is a concurrent metabolic alkalosis. This is clinically explained by the patient's ongoing use of high-dose loop diuretics for his cirrhosis. Therefore, a triple acid-base disorder is present.

Step-by-Step Solution

1

Analyze the pH to determine the primary acid-base disturbance.

The pH is

7.50

, indicating alkalemia.

Establishing the primary disturbance helps anchor the subsequent interpretation.

2

Evaluate the pCO

_2

and HCO

_3^-

to identify the driver of the alkalemia.

The pCO

_2

is markedly low at

21

mm Hg, and the HCO

_3^-

is low at

16

mEq/L. The low pCO

_2

explains the alkalemia, confirming a primary respiratory alkalosis.

Respiratory alkalosis in this patient is driven by hyperventilation secondary to sepsis and fever.

3

Calculate the anion gap (AG) to check for a metabolic acidosis.

AG = Na

^+

- (Cl

^-

+ HCO

_3^-

) =

132 - (82 + 16) = 34

mEq/L.

An AG >

12

mEq/L indicates a high anion gap metabolic acidosis (HAGMA), driven here by lactic acidosis from septic shock.

4

Perform a delta-delta calculation to unmask any hidden third disorder.

\Delta

AG =

34 - 12 = 22

. Corrected HCO

_3^-

= measured HCO

_3^-

(

16

) +

\Delta

AG (

22

) =

38

mEq/L.

Because the corrected HCO

_3^-

(

38

mEq/L) is significantly greater than the baseline of

24

mEq/L, there is a concurrent metabolic alkalosis, likely secondary to loop diuretic therapy.

Key Concept

Diagnosis of triple acid-base disorders using the anion gap and delta-delta calculations.

Alternative Method

Instead of using the corrected bicarbonate formula, the delta ratio (

\Delta

AG /

\Delta

HCO

_3^-

) can be used.

\Delta

AG =

34 - 12 = 22

.

\Delta

HCO

_3^-

=

24 - 16 = 8

. The delta ratio is

22 / 8 = 2.75

. A delta ratio greater than

2.0

confirms the presence of a concurrent metabolic alkalosis.

Estimated Time:2m 0s

Question 62Question →

A 54-year-old man with a history of severe alcohol use disorder is admitted to the intensive care unit with acute necrotizing pancreatitis. Over the past 72 hours, he has experienced intractable vomiting and an inability to tolerate any oral intake. On physical examination, the patient is lethargic. Mucous membranes are extremely dry, and skin turgor is poor. Vital signs show a blood pressure of 88/50 mmHg, a pulse of 118/min, and a respiratory rate of 22/min.

Laboratory studies reveal the following:

Variable	Value
Sodium ( $Na^+$ )	138 mEq/L
Potassium ( $K^+$ )	3.1 mEq/L
Chloride ( $Cl^-$ )	92 mEq/L
Bicarbonate ( $HCO_3^-$ )	16 mEq/L
Blood urea nitrogen (BUN)	45 mg/dL
Creatinine	2.1 mg/dL
Albumin	1.6 g/dL
Lactic acid	6.2 mmol/L

The physician evaluates the patient's acid-base status. Assuming a baseline normal anion gap of 12 mEq/L and a normal serum bicarbonate of 24 mEq/L, what is the patient's calculated delta ratio ( $\Delta\text{AG}/\Delta\text{HCO}_3^-$ ) after appropriately correcting the anion gap for his hypoalbuminemia?

Show answer & explanation

Answer: 3

Answer

3.0

This patient has an elevated anion gap metabolic acidosis secondary to profound lactic acidosis (from tissue hypoperfusion) and likely starvation ketoacidosis. Concurrently, his intractable vomiting introduces a primary metabolic alkalosis. To accurately quantify this mixed disorder, the delta ratio must be calculated. First, the measured anion gap is calculated as

138 - (92 + 16) = 30

mEq/L. Because albumin is a major circulating unmeasured anion, severe hypoalbuminemia (1.6 g/dL) falsely lowers the measured anion gap. The corrected anion gap is

30 + 2.5 \times (4.0 - 1.6) = 36

mEq/L. The

\Delta\text{AG}

is

36 - 12 = 24

mEq/L. The change in bicarbonate (

\Delta\text{HCO}_3^-

) is

24 - 16 = 8

mEq/L. The delta ratio is

24 / 8 = 3.0

. A delta ratio greater than 2.0 indicates that the bicarbonate is higher than expected, confirming a concurrent metabolic alkalosis (from vomiting).

Step-by-Step Solution

1

Calculate the measured anion gap (AG).

138 - (92 + 16) = 30 mEq/L.

The standard anion gap is necessary to identify the presence of unmeasured anions (e.g., lactate).

2

Correct the anion gap for hypoalbuminemia.

30 + 2.5 \times (4.0 - 1.6) = 30 + 2.5 \times 2.4 = 30 + 6.0 = 36 mEq/L.

Albumin is a major unmeasured weak acid. In severe hypoalbuminemia, the measured anion gap is falsely lowered and must be corrected to reveal the true extent of the metabolic acidosis.

3

Calculate the change in anion gap (

\Delta\text{AG}

).

36 - 12 = 24 mEq/L.

This value represents the excess unmeasured anions above the baseline normal value of 12 mEq/L.

4

Calculate the change in bicarbonate (

\Delta\text{HCO}_3^-

).

24 - 16 = 8 mEq/L.

This determines how much the serum bicarbonate has fallen from the normal baseline of 24 mEq/L due to buffering.

5

Calculate the delta ratio.

24 / 8 = 3.0.

The delta ratio compares the rise in unmeasured anions to the fall in bicarbonate, helping to identify mixed acid-base disorders.

Key Concept

In patients with high anion gap metabolic acidosis, the measured anion gap must be corrected for hypoalbuminemia before calculating the delta ratio to accurately identify mixed acid-base disorders.

Question 63Question →

A $72$ -year-old man is brought to the emergency department from a long-term care facility due to altered mental status. Facility staff report that the patient has experienced intractable vomiting and an inability to tolerate oral intake for the past $48$ hours. His past medical history includes hypertension, benign prostatic hyperplasia, and mild cognitive impairment. Upon arrival, his temperature is $38.8^\circ\text{C}$ ( $101.8^\circ\text{F}$ ), blood pressure is $88/54\text{ mm Hg}$ , pulse is $118\text{/min}$ , and respirations are $28\text{/min}$ . Physical examination reveals dry mucous membranes, delayed capillary refill, and diffuse abdominal rigidity with severe rebound tenderness.

Laboratory Test	Result
Sodium	$145\text{ mEq/L}$
Potassium	$3.1\text{ mEq/L}$
Chloride	$90\text{ mEq/L}$
Bicarbonate	$20\text{ mEq/L}$
Blood urea nitrogen	$48\text{ mg/dL}$
Creatinine	$2.4\text{ mg/dL}$
Lactate	$9.5\text{ mmol/L}$

Arterial Blood Gas (Room Air)	Result
pH	$7.43$
$PaCO_2$	$31\text{ mm Hg}$
$PaO_2$	$78\text{ mm Hg}$

Based on the laboratory data provided, which of the following combinations of primary pathophysiologic processes best explains this patient's complete acid-base status?

Tissue hypoperfusion, loss of gastric hydrochloric acid, and primary central respiratory stimulation

Tissue hypoperfusion, loss of gastric hydrochloric acid, and appropriate respiratory compensation

Tissue hypoperfusion and appropriate respiratory compensation only

Tissue hypoperfusion and primary central respiratory stimulation only

Loss of gastric hydrochloric acid and primary central respiratory stimulation only

Show answer & explanation

Answer: Tissue hypoperfusion, loss of gastric hydrochloric acid, and primary central respiratory stimulation

Answer

The correct option is the one that identifies tissue hypoperfusion, loss of gastric hydrochloric acid, and primary central respiratory stimulation.

The correct answer accurately identifies a triple acid-base disorder by systematically applying the anion gap, the delta-delta analysis, and Winter's formula. First, the patient has a primary high anion gap metabolic acidosis (HAGMA) due to lactic acidosis from tissue hypoperfusion (Anion Gap =

35

). Second, applying the delta-delta analysis reveals an expected bicarbonate of

1\text{ mEq/L}

, but the actual bicarbonate is

20\text{ mEq/L}

. This massive discrepancy indicates a concurrent primary metabolic alkalosis, secondary to loss of gastric hydrochloric acid from severe vomiting. Finally, utilizing Winter's formula, the expected

PaCO_2

for a bicarbonate of

20\text{ mEq/L}

is

38 \pm 2\text{ mm Hg}

. The patient's actual

PaCO_2

is

31\text{ mm Hg}

, which represents an independent, primary respiratory alkalosis driven by central respiratory stimulation (SIRS/sepsis).

Step-by-Step Solution

1

Calculate the Anion Gap (AG).

AG = Na^+ - (Cl^- + HCO_3^-) = 145 - (90 + 20) = 35

.

An

AG > 12

indicates the presence of a primary high anion gap metabolic acidosis (HAGMA). In this case, the highly elevated lactate (

9.5\text{ mmol/L}

) due to tissue hypoperfusion is the driver.

2

Perform a Delta-Delta (

\Delta-\Delta

) analysis to evaluate for hidden metabolic disorders.

\Delta AG = 35 - 12 = 23

. Expected

HCO_3^- = 24 - \Delta AG = 24 - 23 = 1\text{ mEq/L}

. The actual

HCO_3^-

is

20\text{ mEq/L}

.

Because the actual bicarbonate (

20\text{ mEq/L}

) is drastically higher than the expected bicarbonate (

1\text{ mEq/L}

), a concurrent primary metabolic alkalosis is present, driven by the loss of gastric hydrochloric acid from intractable vomiting.

3

Calculate the expected respiratory compensation using Winter's formula.

Expected

PaCO_2 = (1.5 \times HCO_3^-) + 8 \pm 2 = (1.5 \times 20) + 8 = 38 \pm 2\text{ mm Hg}

(range

36-40

).

The patient's actual

PaCO_2

is

31\text{ mm Hg}

. Because

31 < 36

, the patient is hyperventilating beyond physiologic compensation. This indicates a third independent disorder: a primary respiratory alkalosis, likely driven by central respiratory stimulation secondary to sepsis and an acute abdominal emergency.

Key Concept

Diagnosis of triple acid-base disorders requires a systematic three-step approach: calculating the anion gap, performing a delta-delta analysis, and applying Winter's formula.

Alternative Method

Instead of subtracting the delta gap from a normal bicarbonate level, the delta ratio (

\Delta AG / \Delta HCO_3^-

) can be utilized. A ratio

> 2.0

confirms the presence of a concurrent metabolic alkalosis.

Estimated Time:2m 0s

Question 64Question →

A 32-year-old man comes to the clinic due to 5 days of severe, watery diarrhea. He recently returned from a trip to Southeast Asia. The patient reports having 8 to 10 loose bowel movements daily. He has been drinking plain water but has not consumed any food or electrolyte solutions. His temperature is 37.1°C (98.8°F), blood pressure is 108/64 mm Hg, and pulse is 104/min. Physical examination shows dry mucous membranes and decreased skin turgor. Laboratory studies show the following:

Laboratory Test	Result
Sodium	138 mEq/L
Potassium	3.2 mEq/L
Chloride	115 mEq/L
Bicarbonate	15 mEq/L
Blood urea nitrogen	28 mg/dL
Creatinine	1.2 mg/dL

Based on these findings, which of the following acid-base disturbances is most likely present in this patient?

Normal anion gap metabolic acidosis

High anion gap metabolic acidosis

Metabolic alkalosis

Primary respiratory acidosis

Primary respiratory alkalosis

Show answer & explanation

Answer: Normal anion gap metabolic acidosis

Answer

Normal anion gap metabolic acidosis

This patient's clinical presentation of severe diarrhea has led to significant fluid and electrolyte loss. The serum chemistry shows a low bicarbonate level (

15 mEq/L

), which defines a metabolic acidosis. The next essential step in evaluating any metabolic acidosis is to calculate the serum anion gap using the formula:

AG = Na^+ - (Cl^- + HCO_3^-)

. For this patient, the calculation is

138 - (115 + 15) = 8 mEq/L

. A normal anion gap is generally between 8 and 12 mEq/L. Therefore, this patient has a normal anion gap metabolic acidosis (NAGMA). This is physiologically consistent with his history of profuse diarrhea, which causes direct gastrointestinal loss of bicarbonate. To maintain electroneutrality, the kidneys retain chloride, resulting in the observed hyperchloremia (

115 mEq/L

).

Step-by-Step Solution

1

Identify the primary disturbance by evaluating the serum bicarbonate level.

The serum bicarbonate is low (15 mEq/L).

A low bicarbonate level in the setting of severe diarrhea strongly suggests a primary metabolic acidosis.

2

Calculate the serum anion gap to classify the metabolic acidosis.

The formula is

AG = Na^+ - (Cl^- + HCO_3^-)

. Calculation:

138 - (115 + 15) = 138 - 130 = 8 mEq/L

.

Differentiating between high and normal anion gap metabolic acidosis is essential for identifying the underlying etiology.

3

Correlate the calculated anion gap with the patient's clinical presentation.

The anion gap of 8 mEq/L is normal. Diarrhea is a classic cause of normal anion gap metabolic acidosis.

Severe diarrhea leads to direct gastrointestinal loss of bicarbonate, which the kidneys compensate for by retaining chloride, resulting in a hyperchloremic, normal anion gap metabolic acidosis.

Key Concept

Severe diarrhea causes direct gastrointestinal loss of bicarbonate, resulting in a hyperchloremic, normal anion gap metabolic acidosis.

Estimated Time:1m 0s

Question 65Question →

A 68-year-old man with a history of type 2 diabetes mellitus and chronic obstructive pulmonary disease (COPD) is brought to the emergency department by his daughter due to lethargy and confusion. The daughter reports that he has had severe nausea and vomiting for the past 3 days and has been unable to eat or take his usual medications, including insulin. On physical examination, the patient is lethargic and oriented to person only. His temperature is 37.2°C (99.0°F), blood pressure is 90/60 mm Hg, pulse is 115/min, and respiratory rate is 24/min with shallow breaths. Mucous membranes are extremely dry, and skin turgor is decreased. Pulmonary examination reveals prolonged expiration with bilateral wheezes and decreased breath sounds.

Laboratory results are as follows:

Arterial blood gas (room air):
$pH$ : 7.25
$PaCO_2$ : 50 mm Hg
$PaO_2$ : 55 mm Hg
$HCO_3^-$ : 21 mEq/L

Serum chemistry:
$Na^+$ : 140 mEq/L
$K^+$ : 4.8 mEq/L
$Cl^-$ : 90 mEq/L
$HCO_3^-$ : 21 mEq/L
Blood urea nitrogen: 45 mg/dL
Creatinine: 2.2 mg/dL
Glucose: 450 mg/dL
Albumin: 4.0 g/dL

Urinalysis is strongly positive for ketones.

Which of the following best describes this patient's primary acid-base disturbances?

High anion gap metabolic acidosis, metabolic alkalosis, and respiratory acidosis

High anion gap metabolic acidosis and respiratory acidosis

High anion gap metabolic acidosis and metabolic alkalosis

Non-anion gap metabolic acidosis and respiratory acidosis

Respiratory acidosis and metabolic alkalosis

Show answer & explanation

Answer: High anion gap metabolic acidosis, metabolic alkalosis, and respiratory acidosis

Answer

High anion gap metabolic acidosis, metabolic alkalosis, and respiratory acidosis

This patient has a triple acid-base disorder. First, the anion gap is significantly elevated at 29 mEq/L (

140 - (90 + 21) = 29

), confirming a primary high anion gap metabolic acidosis (HAGMA), driven by diabetic ketoacidosis. Second, Winter's formula (

1.5 \times 21 + 8 = 39.5

) predicts a

PaCO_2

of roughly 39.5 mm Hg. The patient's actual

PaCO_2

is 50 mm Hg; this relative hypercapnia confirms a superimposed primary respiratory acidosis (due to COPD exacerbation and hypoventilation). Finally, analyzing the delta-delta reveals a hidden third disorder. The

\Delta AG

is 17 (

29 - 12 = 17

). Adding this to the measured bicarbonate yields a corrected bicarbonate of 38 mEq/L (

21 + 17 = 38

). Because this value is well above the normal 24-26 mEq/L, there is a concurrent primary metabolic alkalosis, perfectly consistent with his 3-day history of severe vomiting.

Step-by-Step Solution

1

Assess the primary pH disorder.

The patient has an arterial

pH

of 7.25, indicating acidemia.

Establishing the initial direction of the pH abnormality is the first step in acid-base interpretation.

2

Calculate the serum anion gap (AG).

AG = Na^+ - (Cl^- + HCO_3^-) = 140 - (90 + 21) = 29

An AG greater than 12 indicates the presence of a primary high anion gap metabolic acidosis (HAGMA). In this patient, the HAGMA is secondary to diabetic ketoacidosis (hyperglycemia, positive ketones) and potentially lactic acidosis/uremia.

3

Determine if respiratory compensation is appropriate using Winter's formula.

Expected\ PaCO_2 = 1.5 \times HCO_3^- + 8 \pm 2 = 1.5(21) + 8 = 39.5 \pm 2

(Range: 37.5 to 41.5 mm Hg). The measured

PaCO_2

is 50 mm Hg.

Because the measured

PaCO_2

(50 mm Hg) is significantly higher than the expected compensated

PaCO_2

(39.5 mm Hg), there is a concurrent primary respiratory acidosis. This is clinically consistent with the patient's COPD exacerbation and respiratory fatigue.

4

Calculate the delta gap and corrected bicarbonate to check for a third disorder (Delta-Delta).

\Delta AG = Measured\ AG - Normal\ AG = 29 - 12 = 17

.

Corrected\ HCO_3^- = Measured\ HCO_3^- + \Delta AG = 21 + 17 = 38 mEq/L

.

The corrected

HCO_3^-

represents what the bicarbonate would be if the anion gap metabolic acidosis were resolved. A corrected

HCO_3^-

> 26 mEq/L indicates a concurrent primary metabolic alkalosis, which is clinically explained by the patient's 3 days of severe vomiting (loss of gastric

HCl

).

Key Concept

Diagnosis of triple acid-base disorders requires sequential calculation of the anion gap, expected respiratory compensation (Winter's formula), and the delta-delta gap.

Alternative Method

Instead of the additive Delta-Delta calculation (

Measured\ HCO_3^- + \Delta AG

), the Delta Ratio (

\Delta AG / \Delta HCO_3^-

) can be used.

\Delta AG = 29 - 12 = 17

.

\Delta HCO_3^- = 24 - 21 = 3

. Delta Ratio =

17 / 3 = 5.6

. A Delta Ratio > 2.0 strongly indicates a concurrent metabolic alkalosis.

Estimated Time:3m 0s

Question 66Question →

Match each classic urinalysis sediment finding with its most likely underlying renal pathology.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Muddy brown granular casts match with Acute tubular necrosis; RBC casts match with Glomerulonephritis; WBC casts match with Acute pyelonephritis; Fatty casts match with Nephrotic syndrome; Broad waxy casts match with Advanced chronic kidney disease.

Urinalysis sediment provides crucial diagnostic information in nephrology. Casts take the shape of the distal tubules and collecting ducts where they form. Their composition directly reflects the underlying renal pathology: necrotic cells (muddy brown) in ATN, red blood cells in glomerulonephritis, white blood cells in tubulointerstitial inflammation, lipids in nephrotic syndrome, and dense, degenerated material (broad waxy) in dilated tubules of chronic kidney disease.

Step-by-Step Solution

1

Identify the cellular composition of the muddy brown granular cast.

Recognize that it contains necrotic tubular cells, pointing to Acute tubular necrosis.

Ischemia or nephrotoxins cause death of tubular cells which slough into the lumen and form casts.

2

Evaluate the significance of RBC casts.

Link RBC casts to Glomerulonephritis.

RBCs entering the tubules through a disrupted glomerular basement membrane get trapped in Tamm-Horsfall mucoprotein, forming casts.

3

Determine the origin of WBC casts.

Associate WBC casts with Acute pyelonephritis.

WBC casts confirm that the inflammation/infection is located within the kidney (tubulointerstitium) rather than the lower urinary tract.

4

Connect fatty casts to their pathophysiologic state.

Match fatty casts with Nephrotic syndrome.

Heavy proteinuria is accompanied by hyperlipidemia and lipiduria, leading to lipid droplets and oval fat bodies in the urine.

5

Understand the formation of broad waxy casts.

Link broad waxy casts to Advanced chronic kidney disease.

Decreased urine flow through dilated tubules in end-stage renal disease allows time for casts to become dense, waxy, and unusually broad.

Key Concept

Urinalysis Sediment Pathologies

Estimated Time:1m 0s

Question 67Question →

A 24-year-old man is brought to the emergency department by his roommate due to confusion, rapid breathing, and ringing in his ears after intentionally ingesting an unknown quantity of pills. On physical examination, temperature is 37.8°C (100.0°F), blood pressure is 110/70 mm Hg, pulse is 112/min, and respiratory rate is 28/min. The lungs are clear to auscultation. Laboratory studies show the following:

Serum sodium: 142 mEq/L
Serum potassium: 4.1 mEq/L
Serum chloride: 104 mEq/L
Serum bicarbonate: 14 mEq/L

Arterial blood gas analysis on room air reveals:
pH: 7.43
pCO2: 21 mm Hg
pO2: 98 mm Hg

Based on these findings, which of the following best describes this patient's acid-base status?

Mixed high anion gap metabolic acidosis and primary respiratory alkalosis

High anion gap metabolic acidosis with appropriate respiratory compensation

Mixed high anion gap metabolic acidosis and primary respiratory acidosis

Mixed non-anion gap metabolic acidosis and primary respiratory alkalosis

Primary respiratory alkalosis with appropriate metabolic compensation

Show answer & explanation

Answer: Mixed high anion gap metabolic acidosis and primary respiratory alkalosis

Answer

Mixed high anion gap metabolic acidosis and primary respiratory alkalosis

This patient has a mixed high anion gap metabolic acidosis and primary respiratory alkalosis. The anion gap is calculated as

142 - (104 + 14) = 24

mEq/L (normal: 8-12 mEq/L), indicating a primary high anion gap metabolic acidosis (HAGMA). In primary metabolic acidosis, the lungs compensate by hyperventilating to decrease pCO2. To determine if this respiratory compensation is appropriate, Winter's formula is used: Expected pCO2 =

(1.5 \times 14) + 8 \pm 2 = 29 \pm 2

mm Hg (range 27-31 mm Hg). The patient's actual pCO2 is 21 mm Hg, which is significantly lower than the expected range. A measured pCO2 lower than the expected compensatory pCO2 indicates the presence of a concurrent primary respiratory alkalosis. This mixed acid-base disorder is the classic presentation of salicylate toxicity (which causes a direct stimulation of the medullary respiratory center followed by an accumulation of organic acids).

Step-by-Step Solution

1

Calculate the serum anion gap to identify if a metabolic acidosis is present.

Anion Gap =

142 - (104 + 14) = 24

mEq/L.

An elevated anion gap (> 12 mEq/L) establishes the diagnosis of a primary high anion gap metabolic acidosis (HAGMA).

2

Calculate the expected pCO2 to evaluate the respiratory response to the metabolic acidosis.

Expected pCO2 =

(1.5 \times 14) + 8 \pm 2 = 29 \pm 2

mm Hg (range: 27-31 mm Hg).

Winter's formula determines the expected compensatory pCO2 for a given HCO3- in primary metabolic acidosis.

3

Compare the actual measured pCO2 with the expected pCO2.

Actual pCO2 (21 mm Hg) is less than the expected range (27-31 mm Hg).

When actual pCO2 is lower than the expected compensatory pCO2, it indicates the presence of an independent, concurrent primary respiratory alkalosis.

Key Concept

The evaluation of acid-base disorders requires calculating the anion gap to identify primary metabolic acidosis and applying Winter's formula to determine if the respiratory response is appropriate or if a concurrent primary respiratory disorder exists.

Question 68Question →

A 65-year-old woman with a history of severe chronic obstructive pulmonary disease (COPD) is brought to the emergency department due to worsening shortness of breath, productive cough, and confusion over the past 3 days. She has also had decreased oral intake. Her temperature is 38.6°C (101.5°F), blood pressure is 90/55 mm Hg, pulse is 120/min, and respiratory rate is 28/min. Physical examination reveals bilateral diffuse wheezing and coarse crackles at the right lung base.

Laboratory studies show:
Serum sodium: 140 mEq/L
Serum potassium: 4.2 mEq/L
Serum chloride: 102 mEq/L
Serum bicarbonate: 14 mEq/L
Blood urea nitrogen: 35 mg/dL
Serum creatinine: 1.8 mg/dL (baseline 0.9 mg/dL)
Serum lactate: 4.5 mmol/L (normal: 0.5-2.2 mmol/L)

Arterial blood gas analysis on room air reveals:
pH: 7.21
$pCO_2$ : 36 mm Hg
$pO_2$ : 58 mm Hg

Which of the following best describes this patient's current acid-base disturbance?

High anion gap metabolic acidosis with appropriate respiratory compensation

Normal anion gap metabolic acidosis with appropriate respiratory compensation

High anion gap metabolic acidosis with concurrent respiratory acidosis

High anion gap metabolic acidosis with concurrent respiratory alkalosis

Normal anion gap metabolic acidosis with concurrent respiratory acidosis

Show answer & explanation

Answer: High anion gap metabolic acidosis with concurrent respiratory acidosis

Answer

High anion gap metabolic acidosis with concurrent respiratory acidosis

The patient's anion gap is

140 - (102 + 14) = 24

mEq/L, confirming a high anion gap metabolic acidosis. Applying Winter's formula, the expected

pCO_2

is

(1.5 \times 14) + 8 \pm 2 = 29 \pm 2

mm Hg (range 27-31 mm Hg). Because the patient's actual

pCO_2

(36 mm Hg) is higher than the expected range, she has a concomitant primary respiratory acidosis, likely secondary to underlying COPD and respiratory fatigue from her severe infection.

Step-by-Step Solution

1

Calculate the serum anion gap to determine the primary metabolic disorder.

Anion gap =

140 - (102 + 14) = 24

mEq/L.

An elevated anion gap (>12 mEq/L) indicates a primary high anion gap metabolic acidosis, which in this patient is likely due to lactic acidosis secondary to tissue hypoperfusion and sepsis.

2

Use Winter's formula to calculate the expected

pCO_2

for the degree of metabolic acidosis.

Expected

pCO_2 = (1.5 \times 14) + 8 \pm 2 = 27

to

31

mm Hg.

Winter's formula determines if the respiratory compensation (hyperventilation) is appropriate for a simple metabolic acidosis.

3

Compare the expected

pCO_2

to the patient's measured

pCO_2

.

Measured

pCO_2

(36 mm Hg) is greater than the expected range (27-31 mm Hg).

An inappropriately elevated

pCO_2

indicates inadequate alveolar ventilation, diagnosing a concurrent primary respiratory acidosis. This is common in patients with severe COPD and respiratory fatigue.

Key Concept

In a patient with metabolic acidosis, Winter's formula (

1.5 \times HCO_3^- + 8 \pm 2

) is used to calculate the expected

pCO_2

. If the measured

pCO_2

is higher than expected, there is a concurrent primary respiratory acidosis.

Question 69Question →

Following $2$ days of fever, progressive confusion, and abdominal pain, a $55$ -year-old man is brought to the emergency department. He has a known history of alcohol-associated cirrhosis and diuretic-refractory ascites, for which he takes furosemide and spironolactone. His temperature is $38.6^\circ\text{C}$ ( $101.5^\circ\text{F}$ ), blood pressure is $88/54$ mm Hg, pulse is $112$ /min, and respirations are $24$ /min. Physical examination reveals scleral icterus, a distended abdomen with shifting dullness, and diffuse abdominal tenderness to palpation. Asterixis is present.

Laboratory studies show:
Sodium: $140$ mEq/L
Potassium: $2.9$ mEq/L
Chloride: $105$ mEq/L
Bicarbonate: $20$ mEq/L
Blood urea nitrogen: $42$ mg/dL
Creatinine: $1.9$ mg/dL
Albumin: $1.0$ g/dL
Lactate: $5.2$ mmol/L

Arterial blood gas on room air:
pH: $7.51$
PaCO $_2$ : $26$ mm Hg
PaO $_2$ : $85$ mm Hg

Which of the following best characterizes this patient's primary acid-base disturbances?

Normal anion gap metabolic acidosis and respiratory alkalosis

High anion gap metabolic acidosis and respiratory alkalosis

High anion gap metabolic acidosis, metabolic alkalosis, and respiratory alkalosis

Normal anion gap metabolic acidosis, metabolic alkalosis, and respiratory alkalosis

High anion gap metabolic acidosis, metabolic alkalosis, and respiratory acidosis

Show answer & explanation

Answer: High anion gap metabolic acidosis, metabolic alkalosis, and respiratory alkalosis

Answer

The correct answer is high anion gap metabolic acidosis, metabolic alkalosis, and respiratory alkalosis.

The correct answer is high anion gap metabolic acidosis, metabolic alkalosis, and respiratory alkalosis. This patient's calculated anion gap is 15 mEq/L, which might appear normal or borderline depending on the laboratory reference range. However, adjusting for his severe hypoalbuminemia (1.0 g/dL) yields a corrected anion gap of 22.5 mEq/L, confirming a high anion gap metabolic acidosis (lactic acidosis due to sepsis from spontaneous bacterial peritonitis). Calculating the delta gap reveals an excess anion gap of 10.5 mEq/L. Subtracting this from a normal bicarbonate of 24 mEq/L gives an expected bicarbonate of 13.5 mEq/L. Since his actual bicarbonate (20 mEq/L) is higher than expected, a concurrent metabolic alkalosis is present (diuretic-induced contraction alkalosis). Finally, Winter's formula predicts an expected PaCO2 of 38 mm Hg. The actual PaCO2 is 26 mm Hg, indicating a concurrent primary respiratory alkalosis.

Step-by-Step Solution

1

Calculate the uncorrected anion gap (AG) using the formula

\text{Na}^+ - (\text{Cl}^- + \text{HCO}_3^-)

.

140 - (105 + 20) = 15

mEq/L.

To screen for an unmeasured anion accumulation (normal range is approximately

8-12

mEq/L).

2

Correct the calculated anion gap for the patient's severe hypoalbuminemia.

Add

2.5

mEq/L to the AG for every

1.0

g/dL the albumin is below

4.0

g/dL. Corrected AG

= 15 + [2.5 \times (4.0 - 1.0)] = 15 + 7.5 = 22.5

mEq/L.

Albumin is a major unmeasured anion; severe hypoalbuminemia falsely lowers the calculated AG, masking a primary high AG metabolic acidosis. The corrected AG of

22.5

mEq/L confirms a high anion gap metabolic acidosis (due to lactic acidosis from sepsis).

3

Calculate the delta-delta gap (

\Delta\text{AG} / \Delta\text{HCO}_3^-

) to check for a concurrent metabolic disorder.

Excess AG

= 22.5 - 12 = 10.5

mEq/L. Expected

\text{HCO}_3^- = 24 - 10.5 = 13.5

mEq/L. The patient's actual

\text{HCO}_3^-

is

20

mEq/L.

Since the actual

\text{HCO}_3^-

(

20

mEq/L) is significantly higher than the expected

\text{HCO}_3^-

(

13.5

mEq/L), there is a secondary process adding bicarbonate to the serum. This confirms a concurrent metabolic alkalosis (likely contraction alkalosis from diuretic use).

4

Assess the respiratory compensation using Winter's formula.

Expected PaCO

_2

= (1.5 \times 20) + 8 = 38 \pm 2

mm Hg. The actual PaCO

_2

is

26

mm Hg.

Since the actual PaCO

_2

(

26

mm Hg) is much lower than the expected PaCO

_2

(

36-40

mm Hg), a primary respiratory alkalosis is also present (driven by hyperventilation from sepsis and hepatic encephalopathy).

Key Concept

Identifying a triple acid-base disorder requires stepwise calculation: correcting the anion gap for albumin, evaluating the delta gap, and applying Winter's formula.

Estimated Time:3m 0s

Question 70Question →

A 52-year-old man is brought to the emergency department by ambulance after being found obtunded in his garage. His medical history is significant for major depressive disorder and alcohol use disorder. He is unresponsive to verbal stimuli but localizes to pain. Vital signs are within normal limits except for a respiratory rate of $24/\text{min}$ . Laboratory evaluation reveals the following:

Test	Result
Sodium ( $Na^+$ )	$138 \text{ mEq/L}$
Potassium ( $K^+$ )	$4.5 \text{ mEq/L}$
Chloride ( $Cl^-$ )	$100 \text{ mEq/L}$
Bicarbonate ( $HCO_3^-$ )	$12 \text{ mEq/L}$
Blood urea nitrogen (BUN)	$28 \text{ mg/dL}$
Creatinine	$1.4 \text{ mg/dL}$
Glucose	$144 \text{ mg/dL}$
Serum ethanol	Undetectable
Measured serum osmolality	$320 \text{ mOsm/kg}$

Arterial blood gas on room air shows a pH of $7.22$ , $PCO_2$ of $26 \text{ mm Hg}$ , and $PO_2$ of $92 \text{ mm Hg}$ .

Based on these laboratory results, what is the patient's calculated serum osmolar gap?

Show answer & explanation

Answer: 26

Answer

26

The patient's osmolar gap is

26 \text{ mOsm/kg}

. This is calculated by taking the measured osmolality (

320 \text{ mOsm/kg}

) and subtracting the calculated osmolality (

294 \text{ mOsm/kg}

). The formula for calculated osmolality is

(2 \times Na^+) + (\text{Glucose}/18) + (\text{BUN}/2.8)

. This elevated gap, alongside a high anion gap metabolic acidosis (

138 - (100 + 12) = 26

), strongly suggests toxic alcohol ingestion, such as methanol or ethylene glycol, given the clinical context of obtundation and negative ethanol levels.

Step-by-Step Solution

1

Calculate the expected serum osmolality.

Calculated osmolality =

294 \text{ mOsm/kg}

.

The calculated osmolality requires serum sodium, glucose, and BUN. The formula is

2[Na^+] + \frac{\text{Glucose}}{18} + \frac{\text{BUN}}{2.8}

.

2

Calculate the osmolar gap.

Osmolar gap =

26 \text{ mOsm/kg}

.

The osmolar gap is the difference between the measured serum osmolality (

320 \text{ mOsm/kg}

) and the calculated serum osmolality (

294 \text{ mOsm/kg}

).

Key Concept

The serum osmolar gap is used to detect the presence of unmeasured osmotically active substances (such as toxic alcohols). It is calculated by subtracting the calculated serum osmolality from the measured serum osmolality.

Question 71Question →

A $38$ -year-old man is brought to the emergency department by emergency medical services after his roommate found him unresponsive. The roommate reports that the patient was severely depressed about a recent job loss and had been drinking a large amount of homemade, illicitly distilled liquor (moonshine). On arrival, the patient is difficult to arouse. His temperature is $36.5^\circ\text{C}$ ( $97.7^\circ\text{F}$ ), blood pressure is $105/65$ mm Hg, pulse is $92$ /min, and respiratory rate is $8$ /min.

Laboratory results are as follows:
Sodium: $142$ mEq/L
Potassium: $4.8$ mEq/L
Chloride: $102$ mEq/L
Bicarbonate: $12$ mEq/L

Arterial blood gas analysis on room air reveals:
pH: $7.12$
$\text{PaO}_2$ : $65$ mm Hg
$\text{PaCO}_2$ : $38$ mm Hg

Which of the following best describes this patient's current acid-base status?

Normal anion gap metabolic acidosis and concurrent respiratory acidosis

Elevated anion gap metabolic acidosis and concurrent respiratory acidosis

Elevated anion gap metabolic acidosis with appropriate respiratory compensation

Primary respiratory acidosis with compensatory metabolic alkalosis

Normal anion gap metabolic acidosis with appropriate respiratory compensation

Show answer & explanation

Answer: Elevated anion gap metabolic acidosis and concurrent respiratory acidosis

Answer

Elevated anion gap metabolic acidosis and concurrent respiratory acidosis

The correct answer accurately synthesizes the data. The acidemia (pH

7.12

) and low bicarbonate (

12

mEq/L) indicate a metabolic acidosis. The anion gap is elevated at

28

mEq/L (

\text{Normal: } 8-12

mEq/L). Based on Winter's formula, the expected

\text{PaCO}_2

is

26 \pm 2

mm Hg. The patient's actual

\text{PaCO}_2

is

38

mm Hg. Since

38

mm Hg is greater than the expected maximum of

28

mm Hg, the patient has a superimposed respiratory acidosis, likely secondary to CNS depression and hypoventilation from severe intoxication.

Step-by-Step Solution

1

Identify the primary acid-base disorder.

Primary metabolic acidosis.

The patient is acidemic (pH

7.12

) with a severely low bicarbonate level (

12

mEq/L), establishing a primary metabolic acidosis.

2

Calculate the anion gap to classify the metabolic acidosis.

The anion gap is

28

mEq/L, which is elevated.

Anion Gap =

\text{Na} - (\text{Cl} + \text{HCO}_3^-) = 142 - (102 + 12) = 142 - 114 = 28

mEq/L. A normal gap is

8-12

mEq/L. The elevated gap suggests ingestion of unmeasured toxic anions, such as methanol or ethylene glycol from the illicit liquor.

3

Apply Winter's formula to determine expected respiratory compensation.

Expected

\text{PaCO}_2

is

26 \pm 2

mm Hg (range:

24-28

mm Hg).

Expected

\text{PaCO}_2 = 1.5 \times [\text{HCO}_3^-] + 8 = 1.5 \times 12 + 8 = 18 + 8 = 26

. This formula predicts how much the patient should hyperventilate to compensate for the metabolic acidosis.

4

Compare the measured

\text{PaCO}_2

to the expected

\text{PaCO}_2

.

The measured

\text{PaCO}_2

(

38

mm Hg) is significantly higher than the expected range (

24-28

mm Hg).

Because the measured

\text{PaCO}_2

is higher than the calculated compensatory response, the patient is inadequately exhaling

\text{CO}_2

(hypoventilation, consistent with a respiratory rate of

8

/min). This confirms a concurrent primary respiratory acidosis.

Key Concept

Identifying a mixed acid-base disorder requires determining the primary disturbance, calculating the anion gap, and applying Winter's formula to evaluate the adequacy of the respiratory response.

Question 72Question →

An unresponsive 58-year-old man is brought to the emergency department by paramedics. His partner reports that the patient missed his last two scheduled hemodialysis sessions due to severe winter weather and transportation issues. Over the past 12 hours, he became progressively short of breath before losing consciousness. On arrival, he is in severe respiratory distress. His temperature is 36.8°C (98.2°F), blood pressure is 185/110 mmHg, pulse is 112/min, and respirations are 28/min and labored. Physical examination reveals prominent jugular venous distention and diffuse coarse crackles throughout both lung fields.

Laboratory evaluation reveals the following:

Laboratory Test	Result
Serum sodium	135 mEq/L
Serum potassium	6.4 mEq/L
Serum chloride	96 mEq/L
Serum bicarbonate	14 mEq/L
Blood urea nitrogen	92 mg/dL
Serum creatinine	9.8 mg/dL
Arterial pH (room air)	7.10
Arterial $pCO_2$	48 mmHg
Arterial $pO_2$	52 mmHg

Which of the following best describes this patient's primary acid-base disturbances?

High anion gap metabolic acidosis and a primary respiratory acidosis

High anion gap metabolic acidosis with appropriate respiratory compensation

High anion gap metabolic acidosis and a primary respiratory alkalosis

Normal anion gap metabolic acidosis and a primary respiratory acidosis

Pure primary respiratory acidosis with appropriate metabolic compensation

Show answer & explanation

Answer: High anion gap metabolic acidosis and a primary respiratory acidosis

Answer

The patient has a mixed acid-base disorder consisting of a high anion gap metabolic acidosis (due to uremia) and a primary respiratory acidosis (due to pulmonary edema).

This patient's labs demonstrate a profound acidemia (pH 7.10) driven by a severe reduction in bicarbonate (14 mEq/L), confirming a primary metabolic acidosis. The anion gap is elevated at 25 mEq/L (

135 - (96 + 14)

), pointing to a high anion gap metabolic acidosis secondary to uremic toxin retention from missed hemodialysis sessions. To determine if there is a mixed disorder, Winter's formula must be applied: Expected

pCO_2 = (1.5 \times 14) + 8 \pm 2 = 29 \pm 2

mmHg. The patient's actual

pCO_2

is 48 mmHg, which is substantially higher than the expected maximum of 31 mmHg. This inappropriate retention of carbon dioxide signifies a concomitant primary respiratory acidosis, which is clinically consistent with his physical exam findings of severe respiratory distress, hypoxia (

pO_2

52 mmHg), and crackles indicative of flash pulmonary edema from volume overload.

Step-by-Step Solution

1

Determine the primary acid-base disturbance by evaluating the arterial pH,

pCO_2

, and serum

HCO_3^-

.

The pH is 7.10 (acidemia). The serum

HCO_3^-

is low (14 mEq/L), indicating a primary metabolic acidosis.

Acidemia with a low bicarbonate level confirms that metabolic acidosis is the primary driving disturbance.

2

Calculate the serum anion gap to classify the metabolic acidosis.

AG = Na^+ - (Cl^- + HCO_3^-) = 135 - (96 + 14) = 25

mEq/L.

An elevated anion gap (> 12 mEq/L) signifies the presence of a high anion gap metabolic acidosis, which in this patient is caused by the accumulation of uremic toxins (missed dialysis).

3

Calculate the expected respiratory compensation using Winter's formula.

Expected

pCO_2 = (1.5 \times 14) + 8 \pm 2 = 29 \pm 2

mmHg (range 27 to 31 mmHg).

Winter's formula determines if the respiratory response (hyperventilation) is adequate for the degree of metabolic acidosis.

4

Compare the actual measured

pCO_2

to the expected

pCO_2

to identify any secondary superimposed disorders.

The actual measured

pCO_2

is 48 mmHg, which is significantly greater than the expected maximum of 31 mmHg.

A

pCO_2

higher than the expected compensated range indicates a concomitant primary respiratory acidosis. Clinically, this makes sense because the patient's volume overload (missed dialysis) has led to flash pulmonary edema, impairing gas exchange and causing

CO_2

retention despite the drive to hyperventilate.

Key Concept

Patients can present with mixed acid-base disorders; failure of appropriate respiratory compensation in metabolic acidosis (calculated via Winter's formula) indicates a superimposed respiratory disorder. In end-stage renal disease, missed dialysis can simultaneously cause uremic metabolic acidosis and respiratory acidosis secondary to volume overload and pulmonary edema.

Estimated Time:1m 30s

Question 73Question →

A previously healthy female collegiate athlete is admitted to the medical intensive care unit shortly after collapsing at the finish line of a summer half-marathon. Emergency medical personnel found her lethargic and disoriented. On arrival, her temperature is 39.4 °C (102.9 °F), blood pressure is 88/54 mm Hg, heart rate is 132/min, and respiratory rate is 26/min. Physical examination reveals dry mucous membranes and diffuse muscle tenderness, but lungs are clear to auscultation.

Initial laboratory studies demonstrate the following:

Laboratory Test	Result
Sodium	138 mEq/L
Potassium	6.2 mEq/L
Chloride	102 mEq/L
Bicarbonate	12 mEq/L
Blood urea nitrogen	58 mg/dL
Creatinine	3.2 mg/dL

Arterial blood gas (on room air):

Parameter	Result
pH	7.12
$pCO_2$	38 mm Hg
$pO_2$	85 mm Hg

Which of the following best describes this patient's current acid-base disturbance?

High anion gap metabolic acidosis and respiratory acidosis

High anion gap metabolic acidosis with appropriate respiratory compensation

High anion gap metabolic acidosis and respiratory alkalosis

Normal anion gap metabolic acidosis and respiratory acidosis

Mixed high and normal anion gap metabolic acidosis

Show answer & explanation

Answer: High anion gap metabolic acidosis and respiratory acidosis

Answer

High anion gap metabolic acidosis and respiratory acidosis

This patient presents with a severe acute kidney injury, likely due to exertional heat stroke and rhabdomyolysis, resulting in an acid-base disturbance. Stepwise analysis is required. First, the anion gap is

138 - (102 + 12) = 24

mEq/L, confirming a primary high anion gap metabolic acidosis (HAGMA). Next, respiratory compensation is evaluated using Winter's formula:

Expected\ pCO_2 = (1.5 \times HCO_3^-) + 8 \pm 2

. For a bicarbonate of 12 mEq/L, the expected

pCO_2

is 24-28 mm Hg. The patient's actual

pCO_2

is 38 mm Hg. Because the actual

pCO_2

is significantly higher than the expected range, she has a concomitant respiratory acidosis. This often occurs when patients develop respiratory muscle fatigue from the work of breathing associated with severe metabolic acidosis (Kussmaul respirations) or from altered mental status.

Step-by-Step Solution

1

Calculate the serum anion gap.

AG = Na^+ - (Cl^- + HCO_3^-) = 138 - (102 + 12) = 24

mEq/L.

Determines the presence of a primary high anion gap metabolic acidosis (HAGMA).

2

Calculate the expected respiratory compensation using Winter's formula.

Expected\ pCO_2 = (1.5 \times 12) + 8 = 26 \pm 2

mm Hg (range 24-28 mm Hg).

Evaluates whether the lungs are adequately compensating for the metabolic acidosis.

3

Compare the actual

pCO_2

to the expected

pCO_2

.

Actual

pCO_2

(38 mm Hg) > Expected

pCO_2

(24-28 mm Hg).

A

pCO_2

higher than expected defines an uncompensated or mixed state with primary respiratory acidosis.

4

Calculate the delta-delta ratio to rule out a third mixed disorder.

\Delta AG / \Delta HCO_3^- = (24 - 12) / (24 - 12) = 1.0

.

A ratio between 1 and 2 confirms a pure high anion gap metabolic acidosis without an additional normal anion gap metabolic acidosis.

Key Concept

In patients with a primary metabolic acidosis, adequate respiratory compensation must be confirmed via Winter's formula; an actual pCO2 higher than the expected value indicates a concomitant respiratory acidosis.

Question 74Question →

A $34$ -year-old woman with a history of type $1$ diabetes mellitus is brought to the emergency department due to severe nausea, diffuse abdominal pain, and intractable vomiting for the past $48$ hours. She reports missing her last three doses of insulin because she was unable to tolerate any oral intake. On physical examination, her blood pressure is $98/60\text{ mm Hg}$ , heart rate is $118\text{ /min}$ , and respiratory rate is $22\text{ /min}$ . Her mucous membranes are remarkably dry, and skin turgor is decreased.

Laboratory testing reveals:

Test	Result
Arterial $\text{pH}$	$7.30$
$\text{pCO}_2$	$29\text{ mm Hg}$
$\text{pO}_2$	$95\text{ mm Hg}$
$\text{Na}^+$	$144\text{ mEq/L}$
$\text{K}^+$	$3.2\text{ mEq/L}$
$\text{Cl}^-$	$94\text{ mEq/L}$
$\text{HCO}_3^-$	$14\text{ mEq/L}$
$\text{Glucose}$	$550\text{ mg/dL}$
$\text{BUN}$	$38\text{ mg/dL}$
$\text{Creatinine}$	$1.6\text{ mg/dL}$

Assuming a normal serum anion gap of $12\text{ mEq/L}$ and a normal serum bicarbonate of $24\text{ mEq/L}$ , calculate the patient's delta ratio ( $\frac{\Delta\text{AG}}{\Delta\text{HCO}_3^-}$ ) to evaluate for the presence of a mixed acid-base disorder.

Show answer & explanation

Answer: 2.4

Answer

The calculated delta ratio is 2.4.

The patient has a primary high anion gap metabolic acidosis secondary to diabetic ketoacidosis (AG =

36

). In an uncomplicated AGMA, for every

1\text{ mEq/L}

rise in the anion gap, the serum bicarbonate should fall by approximately

1\text{ mEq/L}

, yielding a delta ratio between

1.0

and

2.0

. This patient's delta ratio is

\frac{36-12}{24-14} = 2.4

. A delta ratio greater than

2.0

indicates that the bicarbonate has not dropped as much as expected for the amount of acid present. This means there is a concurrent primary metabolic alkalosis adding bicarbonate to the serum, which in this clinical vignette is driven by profound volume contraction and acid loss from intractable vomiting.

Step-by-Step Solution

1

Calculate the measured Anion Gap (AG).

\text{AG} = 144 - (94 + 14) = 36\text{ mEq/L}

.

Establishing the presence of an anion gap metabolic acidosis (AGMA) is the first step in acid-base evaluation.

2

Calculate the Delta Anion Gap (

\Delta\text{AG}

).

\Delta\text{AG} = 36 - 12 = 24\text{ mEq/L}

.

This value represents the excess unmeasured anions contributing to the acidosis.

3

Calculate the Delta Bicarbonate (

\Delta\text{HCO}_3^-

).

\Delta\text{HCO}_3^- = 24 - 14 = 10\text{ mEq/L}

.

This value represents the amount of bicarbonate consumed to buffer the excess acid.

4

Calculate the Delta Ratio.

\frac{\Delta\text{AG}}{\Delta\text{HCO}_3^-} = \frac{24}{10} = 2.4

.

Comparing the change in anion gap to the change in bicarbonate identifies occult mixed metabolic acid-base disorders.

Key Concept

The delta ratio (

\frac{\Delta\text{AG}}{\Delta\text{HCO}_3^-}

) is used to diagnose mixed metabolic acid-base disorders in the setting of a high anion gap metabolic acidosis. A ratio

> 2.0

indicates a concurrent metabolic alkalosis, such as from severe vomiting.

Estimated Time:2m 0s

Question 75Question →

Match each clinical scenario with the primary acid-base disorder it most likely causes.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Diarrhea matches with Normal anion gap metabolic acidosis. Vomiting matches with Metabolic alkalosis. Opiate overdose matches with Respiratory acidosis. Panic attack matches with Respiratory alkalosis.

The diagnosis of primary acid-base disorders requires identifying the underlying pathophysiology. Loss of bicarbonate-rich fluids (such as in severe diarrhea) leads to normal anion gap metabolic acidosis. Loss of hydrogen ions (such as in vomiting) leads to metabolic alkalosis. Decreased alveolar ventilation (such as in opiate toxicity) causes carbon dioxide retention and respiratory acidosis. Increased alveolar ventilation (such as in anxiety or panic attacks) blows off excessive carbon dioxide, causing respiratory alkalosis.

Step-by-Step Solution

1

Analyze the acid-base effect of lower gastrointestinal fluid loss.

Severe diarrhea causes bicarbonate loss, which matches with normal anion gap metabolic acidosis.

Lower GI secretions are rich in bicarbonate, and their loss forces the kidneys to reabsorb chloride to maintain electroneutrality, causing a hyperchloremic (normal anion gap) metabolic acidosis.

2

Analyze the acid-base effect of upper gastrointestinal fluid loss.

Vomiting causes acid loss, which matches with metabolic alkalosis.

Gastric fluid is rich in hydrochloric acid; its loss directly increases serum bicarbonate concentration, leading to alkalosis.

3

Analyze the acid-base effect of central respiratory depression.

An opiate overdose causes hypoventilation, which matches with respiratory acidosis.

A respiratory rate of 6 breaths/min indicates severe hypoventilation, leading to the accumulation of carbon dioxide (PCO2) in the blood.

4

Analyze the acid-base effect of hyperventilation.

A panic attack causes excessive breathing, which matches with respiratory alkalosis.

Hyperventilation drives off carbon dioxide at a rate faster than it is produced by cellular metabolism, causing a primary decrease in PCO2.

Key Concept

Primary acid-base disorders based on classic clinical presentations

Question 76Question →

A 22-year-old man with type 1 diabetes mellitus presents to the emergency department with abdominal pain, nausea, and persistent vomiting for the past 2 days. He reports missing his last several doses of insulin. His vital signs include a heart rate of 118/min and a blood pressure of 90/60 mm Hg. Laboratory studies show the following:

Laboratory Test	Result
Sodium ( $Na^+$ )	142 mEq/L
Potassium ( $K^+$ )	4.5 mEq/L
Chloride ( $Cl^-$ )	92 mEq/L
Bicarbonate ( $HCO_3^-$ )	14 mEq/L
Blood urea nitrogen	35 mg/dL
Creatinine	1.4 mg/dL
Glucose	450 mg/dL

Assuming a normal reference serum anion gap of 12 mEq/L and a normal serum bicarbonate of 24 mEq/L, what is the patient's delta ratio (calculated as the change in anion gap divided by the change in serum bicarbonate)? (Provide the exact calculated decimal value).

Show answer & explanation

Answer: 2.4

Answer

2.4

The delta ratio is used to determine if a mixed acid-base disorder is present in the setting of a high anion gap metabolic acidosis. First, the patient's anion gap is calculated as

Na^+ - (Cl^- + HCO_3^-) = 142 - (92 + 14) = 36

mEq/L. The change in the anion gap (

\Delta AG

) is the calculated gap minus the normal gap:

36 - 12 = 24

mEq/L. The change in bicarbonate (

\Delta HCO_3^-

) is the normal bicarbonate minus the patient's bicarbonate:

24 - 14 = 10

mEq/L. The delta ratio is

\Delta AG \div \Delta HCO_3^- = 24 \div 10 = 2.4

. A ratio greater than 2.0 indicates that the bicarbonate level is higher than would be expected from the buffering of the excess acid alone, implying a concurrent primary metabolic alkalosis (in this case, secondary to the patient's persistent vomiting).

Step-by-Step Solution

1

Calculate the patient's anion gap.

142 - (92 + 14) = 36

mEq/L

The basic anion gap formula is

Na^+ - (Cl^- + HCO_3^-)

.

2

Calculate the change in the anion gap (

\Delta AG

).

36 - 12 = 24

mEq/L

This value represents the excess unmeasured anions above the normal baseline.

3

Calculate the change in serum bicarbonate (

\Delta HCO_3^-

).

24 - 14 = 10

mEq/L

This value represents the amount of bicarbonate consumed by buffering the excess acid.

4

Calculate the delta ratio.

24 \div 10 = 2.4

The delta ratio compares the rise in unmeasured anions to the fall in bicarbonate to help identify mixed acid-base disorders.

Key Concept

Calculation and interpretation of the delta ratio in mixed acid-base disorders

Question 77Question →

A 54-year-old woman is evaluated in the intensive care unit for worsening kidney function. She was admitted four days ago for sepsis secondary to a complicated urinary tract infection and required aggressive fluid resuscitation and vasopressor support. Her urine output has steadily decreased over the past 24 hours.

Current laboratory results are as follows:
Serum sodium: 140 mEq/L
Serum creatinine: 2.1 mg/dL
Urine sodium: 60 mEq/L
Urine creatinine: 30 mg/dL

Based on these findings, what is this patient's fractional excretion of sodium (in percent)?

Show answer & explanation

Answer: 3

Answer

3

The fractional excretion of sodium (FeNa) is 3%. The calculation is derived using the formula

FeNa = (U_{Na} \times P_{Cr}) / (P_{Na} \times U_{Cr}) \times 100

. Plugging in the values gives

(60 \times 2.1) / (140 \times 30) \times 100

, which simplifies to

126 / 4200 \times 100 = 3

. In this clinical context, a FeNa greater than 2% strongly points toward acute tubular necrosis (ATN) induced by previous ischemic shock, confirming intrinsic renal damage rather than a simple prerenal state.

Step-by-Step Solution

1

Identify the standard formula for calculating Fractional Excretion of Sodium (FeNa).

FeNa = \frac{U_{Na} \times P_{Cr}}{P_{Na} \times U_{Cr}} \times 100

This formula relates the clearance of sodium to the clearance of creatinine to differentiate prerenal from intrinsic acute kidney injury.

2

Extract the specific laboratory values from the clinical vignette.

Urine sodium (

U_{Na}

) = 60, Plasma/Serum creatinine (

P_{Cr}

) = 2.1, Plasma/Serum sodium (

P_{Na}

) = 140, Urine creatinine (

U_{Cr}

) = 30.

These variables must be precisely assigned to avoid calculation errors.

3

Substitute the values into the formula and solve.

FeNa = \frac{60 \times 2.1}{140 \times 30} \times 100 = \frac{126}{4200} \times 100 = 0.03 \times 100 = 3

Solving the arithmetic yields the exact physiological percentage.

Key Concept

Calculation of Fractional Excretion of Sodium (FeNa)

Question 78Question →

A 32-year-old woman comes to the clinic for evaluation of profound generalized muscle weakness that has progressively worsened over the past three days. She also reports a one-year history of a gritty sensation in her eyes and feeling like she constantly needs to drink water because her mouth is extremely dry. Last year, she was treated in the emergency department for severe left flank pain, which was attributed to a kidney stone. Vitals are within normal limits. Physical examination reveals a dry oral mucosa and bilaterally enlarged parotid glands. Laboratory results are as follows:

Serum chemistry:
Sodium: $139 \text{ mEq/L}$
Potassium: $2.6 \text{ mEq/L}$
Chloride: $114 \text{ mEq/L}$
Bicarbonate: $13 \text{ mEq/L}$
Blood urea nitrogen: $14 \text{ mg/dL}$
Creatinine: $0.9 \text{ mg/dL}$

Arterial blood gas (room air):
pH: $7.28$
pCO_2: $28 \text{ mmHg}$

Urinalysis:
pH: $6.8$
Specific gravity: $1.010$
Blood: Negative
Protein: Negative
Glucose: Negative

Which of the following is the most likely primary mechanism responsible for this patient's current acid-base and electrolyte derangements?

Impaired apical secretion of hydrogen ions in the collecting duct

Defective reabsorption of filtered bicarbonate in the proximal tubule

Reduced responsiveness of the principal cells to aldosterone

Increased gastrointestinal excretion of bicarbonate-rich fluids

Accumulation of unmeasured endogenous organic anions

Show answer & explanation

Answer: Impaired apical secretion of hydrogen ions in the collecting duct

Answer

The correct answer is impaired apical secretion of hydrogen ions in the collecting duct, which is the pathophysiologic mechanism of Type 1 (distal) renal tubular acidosis.

This patient has a normal anion gap metabolic acidosis (Anion Gap =

139 - 114 - 13 = 12 \text{ mEq/L}

) with severe hypokalemia and an inappropriately alkaline urine pH (

6.8

). Coupled with a history of recurrent kidney stones and symptoms highly suggestive of Sjögren syndrome (dry mouth, gritty eyes, parotid enlargement), this presentation is pathognomonic for Type 1 (distal) renal tubular acidosis (RTA).

Type 1 RTA is caused by an inability of the alpha-intercalated cells in the distal collecting duct to secrete hydrogen (

H^+

) ions into the tubular lumen. This primary defect leads to impaired urinary acidification (urine pH is almost always

> 5.5

), decreased bicarbonate regeneration, and obligate potassium wasting (as potassium is secreted in excess to maintain electroneutrality when

H^+

cannot be secreted). The persistently alkaline urine, combined with reduced urinary citrate excretion (hypocitraturia), heavily predisposes these patients to the formation of calcium phosphate kidney stones.

Step-by-Step Solution

1

Calculate the serum anion gap to determine the primary acid-base disorder.

Anion Gap =

Na^+ - (Cl^- + HCO_3^-) = 139 - (114 + 13) = 12 \text{ mEq/L}

. This indicates a normal anion gap metabolic acidosis (NAGMA).

Categorizing the metabolic acidosis as normal vs. high anion gap is the mandatory first step in narrowing the differential diagnosis.

2

Evaluate the serum potassium level in the context of the NAGMA.

The potassium is severely low (

2.6 \text{ mEq/L}

).

Hypokalemia rules out Type 4 RTA (which features hyperkalemia) and points toward gastrointestinal losses or Type 1/Type 2 RTA.

3

Analyze the urinalysis, specifically the urine pH.

The urine pH is

6.8

, which is inappropriately alkaline in the setting of severe systemic acidosis.

A urine pH

> 5.5

during systemic acidemia indicates a failure of distal renal acidification, differentiating Type 1 RTA from diarrhea and Type 2 RTA (which both typically have a urine pH

< 5.5

).

4

Correlate the laboratory findings with the clinical history to identify the underlying mechanism.

The patient has symptoms of Sjögren syndrome (sicca symptoms, parotid enlargement) and a history of kidney stones.

Type 1 RTA is highly associated with autoimmune conditions like Sjögren syndrome and characteristically causes calcium phosphate nephrolithiasis due to alkaline urine and hypocitraturia. The mechanism is a failure of alpha-intercalated cells to secrete

H^+

.

Key Concept

Type 1 (distal) renal tubular acidosis is characterized by a normal anion gap metabolic acidosis, severe hypokalemia, inappropriately alkaline urine (pH > 5.5), and calcium phosphate nephrolithiasis. It is caused by impaired hydrogen ion secretion by the alpha-intercalated cells of the collecting duct.

Estimated Time:1m 30s

Question 79Question →

Match each clinical and laboratory presentation with the most likely underlying pathophysiologic mechanism.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches are: the patient with nephrolithiasis and alkaline urine corresponds to impaired alpha-intercalated cell hydrogen ion secretion; the diabetic patient with hyperkalemia corresponds to aldosterone deficiency or resistance; the normotensive patient with hypocalciuria corresponds to a defect in the distal convoluted tubule sodium-chloride cotransporter; and the hypertensive patient with low renin/aldosterone corresponds to constitutive activation of the collecting duct epithelial sodium channel.

Each presentation aligns with a distinct tubular defect. Distal H+ secretion failure causes Type 1 RTA. Aldosterone deficiency causes Type 4 RTA. Na-Cl cotransporter defects cause Gitelman syndrome. ENaC overactivity causes Liddle syndrome.

Step-by-Step Solution

1

Analyze the acid-base and potassium status for each patient to categorize the broad pathophysiologic mechanism.

Two patients have metabolic acidosis with differing potassium levels (one low, one high), and two have metabolic alkalosis with hypokalemia.

Acid-base and potassium abnormalities act as the primary branching points for diagnosing renal tubular defects.

2

Differentiate the two patients with metabolic acidosis.

The hypokalemic patient with alkaline urine and kidney stones has distal (Type 1) RTA, caused by impaired H+ secretion. The hyperkalemic patient with acidic urine has Type 4 RTA, caused by aldosterone deficiency/resistance.

Urine pH and serum potassium are essential keys to distinguishing subtypes of normal anion gap metabolic acidosis.

3

Differentiate the two patients with metabolic alkalosis.

The normotensive patient with hypocalciuria has Gitelman syndrome (Na-Cl cotransporter defect). The severely hypertensive patient with suppressed renin and aldosterone has Liddle syndrome (ENaC overactivity).

Blood pressure and urine calcium levels distinguish between different causes of hypokalemic metabolic alkalosis.

Key Concept

Pathophysiology and clinical differentiation of renal tubular acidosis (RTA) and hereditary tubulopathies.

Question 80Question →

A 19-year-old college student is brought to the emergency department by her roommate due to agitation, nausea, and ringing in her ears for the past several hours. The roommate states she found several empty bottles of over-the-counter pain relievers on the patient's desk. The patient is breathing rapidly.

Her temperature is $38.1^\circ\text{C}$ ( $100.6^\circ\text{F}$ ), blood pressure is $112/70$ mm Hg, pulse is $118$ /min, and respirations are $28$ /min. Physical examination shows a diaphoretic, anxious young woman. Her lungs are clear to auscultation.

Laboratory studies show:

Laboratory Test	Result
Serum sodium	$142$ mEq/L
Serum potassium	$3.8$ mEq/L
Serum chloride	$105$ mEq/L
Serum bicarbonate	$14$ mEq/L
Arterial pH	$7.42$
Arterial PaO $_2$	$98$ mm Hg
Arterial PaCO $_2$	$21$ mm Hg

Which of the following best characterizes this patient's current acid-base disturbance?

Mixed increased anion gap metabolic acidosis and primary respiratory alkalosis

Primary increased anion gap metabolic acidosis with adequate respiratory compensation

Primary respiratory alkalosis with adequate metabolic compensation

Mixed increased anion gap metabolic acidosis and primary metabolic alkalosis

Primary non-anion gap metabolic acidosis with adequate respiratory compensation

Show answer & explanation

Answer: Mixed increased anion gap metabolic acidosis and primary respiratory alkalosis

Answer

Mixed increased anion gap metabolic acidosis and primary respiratory alkalosis

The patient's laboratory results demonstrate an elevated anion gap of

23

mEq/L (

142 - (105 + 14)

), which confirms the presence of a primary increased anion gap metabolic acidosis. By applying Winter's formula (

1.5 \times [HCO_3^-] + 8 \pm 2

), the expected PaCO

_2

for maximal respiratory compensation is

29 \pm 2

mm Hg. The patient's actual PaCO

_2

is

21

mm Hg. Because the measured PaCO

_2

is lower than the expected compensatory value, there is a concurrent primary respiratory alkalosis. This mixed acid-base disorder is the classic presentation of salicylate (aspirin) toxicity, which both directly stimulates the medullary respiratory center (causing respiratory alkalosis) and uncouples oxidative phosphorylation (causing an accumulation of organic acids and a subsequent metabolic acidosis).

Step-by-Step Solution

1

Calculate the anion gap to check for the presence of a metabolic acidosis.

Anion Gap =

Na^+ - (Cl^- + HCO_3^-)

=

142 - (105 + 14) = 23

mEq/L.

An elevated anion gap (

>12

mEq/L) definitively establishes the presence of an increased anion gap metabolic acidosis, regardless of the overall pH.

2

Calculate the expected respiratory compensation using Winter's formula.

Expected PaCO

_2

=

1.5 \times 14 + 8 = 29 \pm 2

mm Hg.

This determines if the respiratory response is appropriate or if there is a superimposed primary respiratory disorder.

3

Compare the expected PaCO

_2

to the measured PaCO

_2

.

The measured PaCO

_2

(

21

mm Hg) is significantly lower than the expected range (

27-31

mm Hg).

A measured PaCO

_2

that is lower than expected indicates an additional primary respiratory alkalosis.

4

Calculate the delta gap to rule out a third acid-base disorder.

Delta AG =

23 - 12 = 11

. Expected HCO

_3^-

=

24 - 11 = 13

mEq/L. This is very close to the measured

14

mEq/L.

Because the expected and measured bicarbonate values are similar, there is no concurrent metabolic alkalosis or non-anion gap metabolic acidosis.

Key Concept

Salicylate toxicity typically presents with a mixed increased anion gap metabolic acidosis and primary respiratory alkalosis.

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