Nephrology Practice Questions — USMLE Step 2 CK — Page 3

Question 41Question →

A 68-year-old man with a history of severe chronic obstructive pulmonary disease (COPD) is brought to the emergency department by his wife due to worsening shortness of breath, profound fatigue, and confusion. According to the wife, the patient has had severe, large-volume, watery diarrhea for the past four days. His temperature is $37.2^\circ\text{C}$ ( $99.0^\circ\text{F}$ ), blood pressure is $100/60$ mm Hg, pulse is $112$ /min, and respiratory rate is $24$ /min. Physical examination reveals dry mucous membranes, decreased skin turgor, and diminished breath sounds bilaterally with a prolonged expiratory phase.

Laboratory results are as follows:

Test	Result
Sodium	$136$ mEq/L
Potassium	$3.1$ mEq/L
Chloride	$112$ mEq/L
Bicarbonate	$14$ mEq/L
Blood urea nitrogen	$42$ mg/dL
Creatinine	$1.6$ mg/dL
Albumin	$4.0$ g/dL

Arterial blood gas analysis on room air:

Test	Result
pH	$7.14$
pCO $_2$	$43$ mm Hg
pO $_2$	$62$ mm Hg

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

Mixed normal anion-gap metabolic acidosis and respiratory acidosis

Uncompensated normal anion-gap metabolic acidosis

Mixed high anion-gap metabolic acidosis and respiratory acidosis

Normal anion-gap metabolic acidosis with appropriate respiratory compensation

Mixed high anion-gap metabolic acidosis and respiratory alkalosis

Show answer & explanation

Answer: Mixed normal anion-gap metabolic acidosis and respiratory acidosis

Answer

Mixed normal anion-gap metabolic acidosis and respiratory acidosis

The correct interpretation involves a multi-step analysis. First, the patient has severe acidemia (pH 7.14). The low bicarbonate (14 mEq/L) identifies a primary metabolic acidosis, which is clinically consistent with his history of severe diarrhea (intestinal loss of bicarbonate). Calculating the anion gap [136 - (112 + 14) = 10 mEq/L] confirms a normal anion-gap metabolic acidosis (NAGMA). To determine if respiratory compensation is appropriate, Winter's formula must be applied: Expected pCO2 = (1.5 × HCO3-) + 8 ± 2. In this patient, Expected pCO2 = (1.5 × 14) + 8 ± 2 = 29 ± 2 mm Hg. The patient's actual pCO2 is 43 mm Hg, which is significantly higher than the expected target of 27-31 mm Hg. Because the patient is retaining more CO2 than expected (due to his severe underlying COPD), he has a superimposed, concomitant respiratory acidosis.

Step-by-Step Solution

1

Evaluate the pH to determine the primary acid-base direction.

The pH is 7.14, which indicates significant acidemia.

Establishing acidemia or alkalemia is the mandatory first step in acid-base interpretation.

2

Examine the serum bicarbonate (HCO3-) and pCO2 to identify the primary disorder.

The serum bicarbonate is markedly low at 14 mEq/L, confirming a primary metabolic acidosis. This is clinically consistent with massive bicarbonate loss from severe diarrhea.

A low pH driven by a low bicarbonate defines metabolic acidosis.

3

Calculate the serum anion gap (AG).

AG = Na+ - (Cl- + HCO3-) = 136 - (112 + 14) = 136 - 126 = 10 mEq/L.

Determining the anion gap (normal 8-12 mEq/L) is required to categorize the metabolic acidosis. An AG of 10 mEq/L indicates a normal anion-gap (hyperchloremic) metabolic acidosis.

4

Apply Winter's formula to determine the expected respiratory compensation (expected pCO2).

Expected pCO2 = (1.5 × 14) + 8 ± 2 = 21 + 8 ± 2 = 29 ± 2 mm Hg (Range: 27 to 31 mm Hg).

Winter's formula determines if the lungs are adequately blowing off CO2 to compensate for the metabolic acidosis.

5

Compare the expected pCO2 to the measured pCO2.

The measured pCO2 is 43 mm Hg. Because the measured pCO2 (43) is significantly higher than the expected pCO2 (27-31), there is an additional primary respiratory acidosis.

When actual pCO2 exceeds expected pCO2 in a metabolic acidosis, a superimposed respiratory acidosis is present. The patient's severe COPD prevents adequate hyperventilation.

Key Concept

Acid-base interpretation using Winter's formula to identify mixed acid-base disorders in patients with underlying lung disease.

Question 42Question →

A 54-year-old man is brought to the emergency department by paramedics after being found stuporous in a local park. Beside him, paramedics found several empty bottles of antifreeze. His temperature is $36.5^\circ\text{C}$ ( $97.7^\circ\text{F}$ ), blood pressure is $105/65\text{ mmHg}$ , pulse is $98/\text{min}$ , and respirations are $14/\text{min}$ . Physical examination reveals a lethargic patient who arouses to painful stimuli but is unable to answer questions. Cardiopulmonary examination is unremarkable.

The following laboratory results are obtained:

Laboratory Test	Result
Serum sodium	$138\text{ mEq/L}$
Serum potassium	$4.8\text{ mEq/L}$
Serum chloride	$100\text{ mEq/L}$
Serum bicarbonate	$12\text{ mEq/L}$
Blood urea nitrogen	$24\text{ mg/dL}$
Serum creatinine	$1.5\text{ mg/dL}$

Arterial blood gas analysis on room air reveals:

Parameter	Result
pH	$7.15$
PaCO2	$35\text{ mmHg}$
PaO2	$88\text{ mmHg}$

Which of the following best describes this patient's primary acid-base disturbance(s)?

High anion gap metabolic acidosis with appropriate respiratory compensation

High anion gap metabolic acidosis with a concurrent respiratory alkalosis

High anion gap metabolic acidosis with a concurrent respiratory acidosis

Normal anion gap metabolic acidosis with a concurrent respiratory acidosis

Mixed high anion gap and normal anion gap metabolic acidosis

Show answer & explanation

Answer: High anion gap metabolic acidosis with a concurrent respiratory acidosis

Answer

High anion gap metabolic acidosis with a concurrent respiratory acidosis

The correct answer accurately identifies a mixed acid-base disorder. First, the low pH (

7.15

) and low serum

HCO_3^-

(

12\text{ mEq/L}

) establish a primary metabolic acidosis. Next, calculating the anion gap (

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

) yields

138 - (100 + 12) = 26\text{ mEq/L}

. An anion gap greater than 14 indicates a high anion gap metabolic acidosis (HAGMA), which is highly consistent with this patient's presentation of likely antifreeze (ethylene glycol) toxicity. To determine if the respiratory response is appropriate, Winter's formula is applied: Expected

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

. For this patient, the expected

PaCO_2 = (1.5 \times 12) + 8 \pm 2 = 26 \pm 2\text{ mmHg}

(range

24-28\text{ mmHg}

). The measured

PaCO_2

is

35\text{ mmHg}

, which is significantly higher than the expected range. An inappropriately elevated

PaCO_2

in the setting of a metabolic acidosis indicates a concurrent primary respiratory acidosis. This mixed disorder is classically seen in severe toxic alcohol ingestions due to CNS depression resulting in profound hypoventilation.

Step-by-Step Solution

1

Determine the primary acid-base disturbance based on pH and

HCO_3^-

.

The pH is

7.15

(acidemia) and serum

HCO_3^-

is

12\text{ mEq/L}

(low), indicating a primary metabolic acidosis.

Establishing the initial primary disorder is the first step in analyzing any arterial blood gas.

2

Calculate the anion gap to classify the metabolic acidosis.

Anion gap =

Na^+ - (Cl^- + HCO_3^-) = 138 - (100 + 12) = 26\text{ mEq/L}

. Since this is

> 14\text{ mEq/L}

, it is a high anion gap metabolic acidosis (HAGMA).

HAGMA has a specific differential diagnosis (e.g., MUDPILES) that is distinct from normal anion gap metabolic acidosis.

3

Calculate the expected

PaCO_2

using Winter's formula to check for respiratory compensation.

Expected

PaCO_2 = (1.5 \times 12) + 8 \pm 2 = 26 \pm 2\text{ mmHg}

(range:

24\text{ to }28\text{ mmHg}

).

To determine if the body is appropriately compensating via hyperventilation or if a secondary respiratory disorder exists.

4

Compare the calculated expected

PaCO_2

with the measured

PaCO_2

.

The measured

PaCO_2

(

35\text{ mmHg}

) is greater than the expected compensatory range (

24-28\text{ mmHg}

).

An inappropriately high

PaCO_2

in the setting of severe metabolic acidosis indicates a concurrent primary respiratory acidosis.

Key Concept

In a patient with metabolic acidosis, an inappropriately elevated

PaCO_2

compared to the calculated expected value using Winter's formula indicates a concurrent primary respiratory acidosis.

Estimated Time:1m 30s

Question 43Question →

A 42-year-old woman is evaluated in the emergency department for severe, colicky left flank pain radiating to the groin and gross hematuria. For the past year, she has experienced progressive generalized muscle weakness, persistent dry eyes, and a dry mouth. Blood pressure is 120/76 mm Hg, and pulse is 88/min. Laboratory studies show:

Laboratory Test	Result
Serum sodium	$139$ mEq/L
Serum potassium	$2.8$ mEq/L
Serum chloride	$115$ mEq/L
Serum bicarbonate	$14$ mEq/L
Serum creatinine	$1.1$ mg/dL
Arterial pH	$7.27$
Arterial $PaCO_2$	$29$ mm Hg
Arterial $PaO_2$	$98$ mm Hg

Urinalysis	Result
pH	$6.8$
Blood	Large
Protein	Trace

A non-contrast CT of the abdomen and pelvis reveals a 5-mm calculus in the left ureter and bilateral medullary nephrocalcinosis. Which of the following is the most likely primary pathophysiologic mechanism responsible for this patient's laboratory and imaging findings?

Impaired apical hydrogen ion secretion in the distal tubule

Defective sodium-bicarbonate cotransport in the proximal tubule

Decreased epithelial sodium channel activity in the cortical collecting duct

Increased gastrointestinal loss of bicarbonate-rich fluids

Accumulation of unmeasured organic anions due to decreased glomerular filtration

Show answer & explanation

Answer: Impaired apical hydrogen ion secretion in the distal tubule

Answer

The primary pathophysiologic mechanism is impaired apical hydrogen ion secretion in the distal tubule (Type 1 Renal Tubular Acidosis).

The correct option identifies the defect seen in Type 1 (distal) RTA: an inability of the

\alpha

-intercalated cells in the distal tubule to secrete hydrogen ions. This defect leads to a normal anion gap metabolic acidosis, profound hypokalemia (as the kidney wastes potassium in an attempt to retain sodium without exchanging hydrogen), and a persistently alkaline urine (pH > 5.5). The combination of alkaline urine and hypocitraturia creates an environment highly susceptible to calcium phosphate precipitation, leading to bilateral medullary nephrocalcinosis and urolithiasis. Furthermore, Type 1 RTA is classically associated with autoimmune diseases, specifically Sjögren syndrome and rheumatoid arthritis, perfectly matching the patient's sicca symptoms and joint history.

Step-by-Step Solution

1

Calculate the serum anion gap to classify the metabolic acidosis.

AG = Na^+ - (Cl^- + HCO_3^-) = 139 - (115 + 14) = 10

mEq/L.

An anion gap between 8 and 12 mEq/L indicates a normal anion gap metabolic acidosis (NAGMA), ruling out etiologies like lactic acidosis, ketoacidosis, and uremia.

2

Evaluate the respiratory compensation using Winter's formula.

Expected

PaCO_2 = (1.5 \times 14) + 8 \pm 2 = 29 \pm 2

mm Hg. The measured

PaCO_2

is

29

mm Hg.

Confirming appropriate respiratory compensation ensures there is no mixed acid-base disorder (e.g., concurrent respiratory alkalosis or acidosis) complicating the clinical picture.

3

Analyze the serum potassium and urine pH in the context of a NAGMA.

The patient has severe hypokalemia (

2.8

mEq/L) and an inappropriately alkaline urine (pH

6.8

).

In the setting of NAGMA, a high urine pH (

> 5.5

) and hypokalemia specifically point toward a distal renal tubular defect (Type 1 RTA), as the kidney fails to excrete

H^+

.

4

Integrate the clinical and imaging findings to confirm the etiology.

The patient has signs of Sjögren syndrome (dry eyes/mouth, muscle weakness from hypokalemia) and nephrocalcinosis with kidney stones.

Type 1 RTA is highly associated with autoimmune diseases like Sjögren syndrome and uniquely causes nephrocalcinosis/calcium phosphate stones due to alkaline urine and low urinary citrate.

Key Concept

Type 1 (distal) renal tubular acidosis presents with a normal anion gap metabolic acidosis, hypokalemia, urine pH > 5.5, and nephrocalcinosis, often in the setting of autoimmune disorders like Sjögren syndrome.

Question 44Question →

A 28-year-old woman, who is 14 weeks pregnant, is brought to the emergency department after 4 days of intractable nausea, vomiting, and diffuse abdominal pain. She has a history of type 1 diabetes mellitus and has not taken her insulin for the past 48 hours due to her inability to tolerate oral intake. She reports profound weakness and lightheadedness when standing. Her temperature is 37.1°C (98.8°F), blood pressure is 92/58 mm Hg, heart rate is 122/min, and respiratory rate is 26/min. Physical examination shows dry mucous membranes and diminished skin turgor.

Laboratory studies:

Serum Chemistries
Sodium	140 mEq/L
Potassium	3.2 mEq/L
Chloride	86 mEq/L
Bicarbonate	18 mEq/L
Blood urea nitrogen	42 mg/dL
Creatinine	1.6 mg/dL
Glucose	480 mg/dL

Arterial Blood Gas (Room Air)
pH	7.48
$pCO_2$	25 mm Hg
$pO_2$	98 mm Hg

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

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

Chronic respiratory alkalosis with appropriate metabolic compensation

High anion gap metabolic acidosis and respiratory alkalosis only

High anion gap metabolic acidosis and metabolic alkalosis only

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

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

This patient has a triple acid-base disorder. First, despite the alkalemic pH (

7.48

), the anion gap is massively elevated at

36

mEq/L calculated as

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

or

140 - (86 + 18)

. This indicates a severe high anion gap metabolic acidosis (HAGMA), consistent with diabetic ketoacidosis. Second, the delta-delta gap must be assessed to uncover hidden metabolic disorders. The delta anion gap (

\Delta AG

) is

36 - 12 = 24

. Subtracting this from a normal bicarbonate of

24

mEq/L yields an expected bicarbonate of

0

mEq/L if HAGMA were the only metabolic disorder present. Because the measured bicarbonate (

18

mEq/L) is significantly higher than this expected value, a massive concurrent metabolic alkalosis is present, consistent with her history of intractable vomiting. Finally, Winter's formula (

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

) is used to calculate the appropriate respiratory compensation for the measured bicarbonate. The expected

pCO_2

is

1.5 \times 18 + 8 = 35 \pm 2

mm Hg. The patient's actual

pCO_2

of

25

mm Hg is substantially lower than this range, revealing an additional, tertiary primary respiratory alkalosis.

Step-by-Step Solution

1

Calculate the Anion Gap (AG) to screen for a primary metabolic acidosis regardless of the pH.

AG = Na^+ - (Cl^- + HCO_3^-) = 140 - (86 + 18) = 36

mEq/L.

An anion gap > 12 mEq/L confirms the presence of a High Anion Gap Metabolic Acidosis (HAGMA), which in this patient is driven by diabetic ketoacidosis.

2

Calculate the delta-delta gap to identify any hidden concurrent metabolic disorders.

\Delta AG = 36 - 12 = 24

. The Expected

HCO_3^-

(if HAGMA were the only metabolic process) =

24 - 24 = 0

mEq/L. Since Measured

HCO_3^-

(18 mEq/L) > Expected

HCO_3^-

(0 mEq/L), a concurrent metabolic alkalosis is present.

The patient's severe vomiting has generated a profound metabolic alkalosis, which is independently raising the bicarbonate level above what would be expected from the HAGMA alone.

3

Apply Winter's formula to the measured bicarbonate to evaluate the expected respiratory compensation.

Expected

pCO_2 = 1.5 \times HCO_3^- + 8 \pm 2 = (1.5 \times 18) + 8 = 35 \pm 2

mm Hg (Range: 33 to 37 mm Hg).

This establishes the appropriate physiological

pCO_2

response to the patient's current bicarbonate level.

4

Compare the patient's actual

pCO_2

to the expected

pCO_2

.

The measured

pCO_2

(25 mm Hg) is significantly lower than the expected range (33 to 37 mm Hg).

Because the actual

pCO_2

is lower than expected, a concurrent primary respiratory alkalosis is present, likely multifactorial due to pregnancy (progesterone effect), abdominal pain, and dehydration.

Key Concept

Diagnosis of triple acid-base disorders requires sequential calculation of the anion gap, delta-delta gap, and Winter's formula to uncover hidden metabolic and respiratory derangements that may be masked by a deceptively normal or alkaline pH.

Question 45Question →

A 72-year-old woman is brought to the emergency department from a skilled nursing facility due to severe lethargy and altered mental status over the past 24 hours. Facility staff report she has had multiple episodes of voluminous, watery diarrhea for the past 3 days after completing a course of clindamycin for a cellulitis infection. Her medical history is significant for advanced chronic obstructive pulmonary disease (COPD) requiring home oxygen, hypertension, and heart failure with preserved ejection fraction.

Vital signs are:
Temperature: 37.8°C (100.0°F)
Heart rate: 112/min
Blood pressure: 90/60 mm Hg
Respiratory rate: 26/min
Oxygen saturation: 88% on her baseline 2 L/min nasal cannula.

Physical examination reveals dry mucous membranes and delayed capillary refill. Lung auscultation demonstrates diffusely decreased breath sounds with prolonged expiration and scattered end-expiratory wheezes. The patient is somnolent but arousable to physical stimuli.

Serum chemistry results are as follows:
Sodium: 135 mEq/L
Potassium: 3.1 mEq/L
Chloride: 110 mEq/L
Bicarbonate: 14 mEq/L
Blood urea nitrogen: 42 mg/dL
Creatinine: 1.6 mg/dL (baseline 0.9 mg/dL)

Arterial blood gas analysis (on 2 L/min oxygen) reveals:
pH: 7.19
$PaCO_2$ : 38 mm Hg
$PaO_2$ : 58 mm Hg

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

Normal anion gap metabolic acidosis with appropriate respiratory compensation

High anion gap metabolic acidosis with appropriate respiratory compensation

Normal anion gap metabolic acidosis and concurrent respiratory acidosis

High anion gap metabolic acidosis and concurrent respiratory acidosis

Primary respiratory acidosis with appropriate metabolic compensation

Show answer & explanation

Answer: Normal anion gap metabolic acidosis and concurrent respiratory acidosis

Answer

Normal anion gap metabolic acidosis and concurrent respiratory acidosis

The correct answer identifies two simultaneous acid-base disorders. First, the patient's severe diarrhea has resulted in a profound loss of bicarbonate, leading to a metabolic acidosis. The anion gap is calculated as

Na^+ - (Cl^- + HCO_3^-) = 135 - (110 + 14) = 11

mEq/L, which falls squarely into the normal range (8-12 mEq/L), confirming a normal anion gap metabolic acidosis (NAGMA). Second, to determine if the respiratory compensation is appropriate, Winter's formula must be applied: Expected

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

. For this patient, Expected

PaCO_2 = (1.5 \times 14) + 8 = 29 \pm 2

mm Hg. The patient's actual measured

PaCO_2

is 38 mm Hg. Because the actual

PaCO_2

is significantly higher than the expected range of 27-31 mm Hg, the patient has a concurrent respiratory acidosis. This failure to adequately ventilate is highly consistent with impending respiratory failure in a patient with severe underlying COPD who is fatiguing under the stress of acute hypovolemic shock.

Step-by-Step Solution

1

Analyze the pH to determine the primary disturbance.

The pH is 7.19 (acidemia). The

HCO_3^-

is 14 mEq/L (low) and the

PaCO_2

is 38 mm Hg (near normal). The primary disturbance is metabolic acidosis.

A low pH driven by a low bicarbonate indicates a primary metabolic acidosis.

2

Calculate the serum anion gap (AG).

AG =

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

=

135 - (110 + 14) = 135 - 124 = 11

mEq/L.

Determining the anion gap distinguishes between bicarbonate loss (normal AG, 8-12 mEq/L) and unmeasured acid accumulation (high AG, >12 mEq/L). The patient's diarrhea has caused a normal AG metabolic acidosis.

3

Calculate expected respiratory compensation using Winter's formula.

Expected

PaCO_2 = (1.5 \times 14) + 8 \pm 2 = 21 + 8 \pm 2 = 29 \pm 2

mm Hg (range 27-31 mm Hg).

This determines if the respiratory system is appropriately compensating for the metabolic acidosis.

4

Compare actual

PaCO_2

to expected

PaCO_2

.

Actual

PaCO_2

(38 mm Hg) is greater than Expected

PaCO_2

(27-31 mm Hg).

Because the actual

PaCO_2

is higher than expected, there is inadequate ventilation, indicating a concurrent (superimposed) respiratory acidosis. This is likely due to diaphragmatic fatigue secondary to her underlying COPD and acute illness.

Key Concept

Acid-base analysis requires calculating the anion gap to categorize metabolic acidosis, followed by Winter's formula to uncover hidden secondary respiratory disorders; a 'normal' absolute PaCO2 value is highly abnormal in the setting of severe metabolic acidosis.

Question 46Question →

A 68-year-old woman is brought to the emergency department by her son due to progressive lethargy and confusion over the past 24 hours. The son reports that she has experienced severe, watery diarrhea and intractable vomiting for the last 4 days following a suspected foodborne illness. Her past medical history is significant for severe chronic obstructive pulmonary disease (COPD) requiring home oxygen therapy. Upon arrival, her temperature is $37.1^\circ$ C ( $98.8^\circ$ F), blood pressure is $82/50$ mmHg, heart rate is $124$ /min, and respiratory rate is $28$ /min. Physical examination reveals a somnolent patient with profoundly dry mucous membranes, decreased skin turgor, and diffuse bilateral wheezing.

Laboratory studies reveal:

Test	Result
Sodium	$140$ mEq/L
Potassium	$3.1$ mEq/L
Chloride	$86$ mEq/L
Bicarbonate	$14$ mEq/L
Blood urea nitrogen	$62$ mg/dL
Serum creatinine	$2.8$ mg/dL
Albumin	$4.0$ g/dL
Lactate	$7.4$ mmol/L

An arterial blood gas obtained on room air shows:

Parameter	Result
pH	$7.11$
PaCO $_2$	$45$ mmHg
PaO $_2$	$58$ mmHg

Which of the following combinations most accurately characterizes this patient's acid-base status?

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

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

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

High anion gap metabolic acidosis and respiratory acidosis only

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

Show answer & explanation

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

Answer

The patient's acid-base status is best characterized by a high anion gap metabolic acidosis, a metabolic alkalosis, and a respiratory acidosis.

The correct combination characterizes a classic triple acid-base disorder. First, the anion gap is

40

mEq/L (

140 - (86 + 14)

), diagnosing a high anion gap metabolic acidosis (HAGMA) secondary to lactic acidosis from shock. Second, calculating the delta gap (

40 - 12 = 28

) and adding it to the measured bicarbonate (

14 + 28 = 42

) yields an expected bicarbonate greater than

24

mEq/L, confirming a concurrent metabolic alkalosis (from intractable vomiting). Finally, Winter's formula predicts a PaCO

_2

of

27-31

mmHg. The measured PaCO

_2

of

45

mmHg is inappropriately high, confirming a superimposed respiratory acidosis due to COPD exacerbation and respiratory muscle fatigue.

Step-by-Step Solution

1

Analyze the primary disturbance.

The pH is

7.11

(acidemia) and the HCO

_3^-

is

14

mEq/L (low). This indicates a primary metabolic acidosis.

Identifying the primary direction of pH and matching it with the appropriate buffer system change establishes the baseline disorder.

2

Calculate the anion gap (AG).

AG = Na

^+

- (Cl

^-

+ HCO

_3^-

) =

140 - (86 + 14) = 40

mEq/L. Since

40

>

12

, a high anion gap metabolic acidosis (HAGMA) is present.

An elevated anion gap confirms the presence of unmeasured anions, in this case, lactate due to tissue hypoperfusion.

3

Calculate the delta gap (

\Delta

AG) and expected bicarbonate.

\Delta

AG =

40 - 12 = 28

mEq/L. The patient's expected HCO

_3^-

(if HAGMA were the only metabolic disorder) is: Measured HCO

_3^-

+

\Delta

AG =

14 + 28 = 42

mEq/L. Since

42

is significantly greater than a normal HCO

_3^-

of

24

, a concurrent metabolic alkalosis is present.

The delta-delta ratio or expected bicarbonate calculation uncovers hidden metabolic disorders. In this patient, vomiting induced a severe metabolic alkalosis that partially masked the severity of the bicarbonate drop from the HAGMA.

4

Calculate expected respiratory compensation using Winter's formula.

Expected PaCO

_2

=

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

mmHg. The measured PaCO

_2

is

45

mmHg.

Winter's formula determines if the respiratory response to metabolic acidosis is adequate. Since the measured PaCO

_2

(

45

mmHg) is higher than the expected range (

27-31

mmHg), there is an uncompensated accumulation of CO

_2

, indicating a superimposed respiratory acidosis.

Key Concept

Diagnosis of a triple acid-base disorder requires sequential calculation of the anion gap, the delta-delta gap (or expected bicarbonate), and Winter's formula.

Estimated Time:3m 0s

Question 47Question →

A $27$ -year-old man presents to the urgent care clinic complaining of diffuse abdominal pain, nausea, and extreme thirst that began yesterday. He acknowledges missing several doses of his prescribed long-acting insulin. On physical examination, his respiratory rate is $28/\text{min}$ with deep, labored breathing. A distinct fruity odor is noted on his breath. Laboratory results are as follows:

Serum sodium: $138 \text{ mEq/L}$
Serum chloride: $100 \text{ mEq/L}$
Serum bicarbonate: $10 \text{ mEq/L}$

Arterial blood gas (room air):
pH: $7.22$
$pCO_2$ : $23 \text{ mm Hg}$
$pO_2$ : $96 \text{ mm Hg}$

Based on the provided laboratory values, which of the following is the most accurate interpretation of this patient's acid-base status?

Fully compensated high anion gap metabolic acidosis

Mixed high anion gap metabolic acidosis and primary respiratory alkalosis

Mixed high anion gap metabolic acidosis and primary respiratory acidosis

Uncompensated high anion gap metabolic acidosis

Fully compensated normal anion gap metabolic acidosis

Show answer & explanation

Answer: Fully compensated high anion gap metabolic acidosis

Answer

Fully compensated high anion gap metabolic acidosis

The correct interpretation is a fully compensated high anion gap metabolic acidosis. The patient's low pH (

7.22

) and low bicarbonate (

10 \text{ mEq/L}

) demonstrate a metabolic acidosis. The anion gap is elevated at

28 \text{ mEq/L}

. To determine if the respiratory compensation is adequate, Winter's formula (

Expected\ pCO_2 = 1.5 \times [HCO_3^-] + 8 \pm 2

) is applied. In this case,

(1.5 \times 10) + 8 = 23 \text{ mm Hg}

. Because the measured

pCO_2

(

23 \text{ mm Hg}

) falls exactly within the expected range, the patient is fully compensated and does not have a secondary acid-base disturbance.

Step-by-Step Solution

1

Determine the primary disorder from the pH and bicarbonate.

pH is

7.22

(acidemia) and

HCO_3^-

is

10 \text{ mEq/L}

(low), confirming a primary metabolic acidosis.

Establishing the initial direction of the pH and the primary driver is the first step in acid-base analysis.

2

Calculate the anion gap to classify the metabolic acidosis.

AG = Na^+ - (Cl^- + HCO_3^-) = 138 - (100 + 10) = 28 \text{ mEq/L}

. The normal range is

8-12 \text{ mEq/L}

, so this is a high anion gap metabolic acidosis.

Metabolic acidosis must be categorized into normal or high anion gap to narrow the differential diagnosis (e.g., DKA in this patient).

3

Use Winter's formula to assess if respiratory compensation is appropriate.

Expected

pCO_2 = 1.5 \times [HCO_3^-] + 8 \pm 2

. Thus, Expected

pCO_2 = (1.5 \times 10) + 8 = 15 + 8 = 23 \pm 2

(range

21-25 \text{ mm Hg}

).

If the measured

pCO_2

falls outside the expected range, a secondary respiratory disorder is present.

4

Compare expected and measured

pCO_2

.

The measured

pCO_2

is

23 \text{ mm Hg}

, which perfectly matches the expected value.

This confirms there is no concurrent respiratory acidosis or alkalosis, meaning the condition is a simple, fully compensated high anion gap metabolic acidosis.

Key Concept

In patients with metabolic acidosis, the primary disorder must be classified using the anion gap, and appropriate respiratory compensation must be verified using Winter's formula to rule out mixed acid-base disorders.

Estimated Time:1m 0s

Question 48Question →

Microscopic examination of urine sediment is a critical diagnostic tool in evaluating renal pathology. Match each classic urinary cast finding with its most likely associated underlying pathophysiology or clinical condition.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Red blood cell casts match with Glomerular inflammation (Glomerulonephritis). Muddy brown granular casts match with Ischemic or toxic tubular injury (Acute tubular necrosis). White blood cell casts match with Tubulointerstitial inflammation (Acute interstitial nephritis). Fatty casts match with Heavy proteinuria and altered lipid metabolism (Nephrotic syndrome).

Each urinary cast has a specific mechanism of formation that points to the underlying renal pathology. Red blood cell casts signify glomerular inflammation. Muddy brown granular casts denote necrotic tubular injury. White blood cell casts reflect tubulointerstitial inflammation. Fatty casts occur when severe proteinuria causes compensatory hyperlipidemia, leading to lipiduria.

Step-by-Step Solution

1

Identify the etiology of red blood cell casts.

RBC casts form when red blood cells leak through a damaged glomerular basement membrane and get trapped in Tamm-Horsfall mucoprotein in the tubules.

Understanding the origin of RBC casts links them directly to glomerulonephritis.

2

Identify the etiology of muddy brown granular casts.

These casts are made of necrotic epithelial cells from the renal tubules.

This pathophysiologic mechanism characterizes acute tubular necrosis (ATN).

3

Identify the etiology of white blood cell casts.

WBCs enter the tubules during severe interstitial inflammation or infection.

This links WBC casts to acute interstitial nephritis (AIN) or pyelonephritis.

4

Identify the etiology of fatty casts.

Heavy proteinuria in nephrotic syndrome triggers hepatic lipoprotein synthesis, leading to lipiduria and fatty cast formation.

This mechanism connects fatty casts directly to nephrotic syndrome.

Key Concept

Interpretation of urinary casts is essential for differentiating the causes of acute kidney injury and intrinsic renal disease.

Question 49Question →

A 22-year-old woman with a history of type 1 diabetes mellitus presents to the emergency department with a 1-day history of nausea, vomiting, and diffuse abdominal pain. She missed several doses of her insulin because she was not feeling well. Her temperature is $37.2^\circ C$ ( $99.0^\circ F$ ), blood pressure is $105/65$ mmHg, heart rate is $118/min$ , and respiratory rate is $26/min$ . Physical examination reveals dry mucous membranes and diffuse abdominal tenderness without rebound or guarding.

Laboratory studies show:

Laboratory Study	Result
Serum sodium	$140$ mEq/L
Serum potassium	$4.5$ mEq/L
Serum chloride	$104$ mEq/L
Serum bicarbonate	$12$ mEq/L
Blood glucose	$450$ mg/dL
Serum creatinine	$1.2$ mg/dL

Which of the following is the expected arterial partial pressure of carbon dioxide ( $pCO_2$ ) if appropriate respiratory compensation has occurred in this patient?

12

mmHg

20

mmHg

26

mmHg

32

mmHg

40

mmHg

Show answer & explanation

Answer: $26$ mmHg

Answer

The expected arterial

pCO_2

is

26

mmHg.

The correct expected arterial

pCO_2

is

26

mmHg. This patient presents with diabetic ketoacidosis, which causes a primary anion gap metabolic acidosis. In the presence of a metabolic acidosis, the physiological response is hyperventilation to decrease arterial

pCO_2

and normalize the blood pH (respiratory compensation). The appropriate degree of respiratory compensation is calculated using Winter's formula: Expected

pCO_2 = 1.5 \times [HCO_3^-] + 8 \pm 2

. Using the patient's serum bicarbonate of

12

mEq/L, the expected

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

mmHg. A measured

pCO_2

within the range of

24

to

28

mmHg indicates a simple metabolic acidosis with appropriate compensation.

Step-by-Step Solution

1

Calculate the anion gap and identify the primary acid-base disturbance.

Anion Gap =

140 - (104 + 12) = 24

. The patient has an elevated anion gap metabolic acidosis (diabetic ketoacidosis).

Identifying the primary disturbance dictates which compensation formula to use.

2

Apply Winter's formula to determine expected respiratory compensation.

Expected

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

.

Winter's formula predicts the expected

pCO_2

response to a primary metabolic acidosis.

3

Calculate the specific expected value for this patient.

Expected

pCO_2 = (1.5 \times 12) + 8 = 18 + 8 = 26

(Range:

24 - 28

mmHg).

Plugging in the patient's bicarbonate level of

12

mEq/L yields the target compensation.

Key Concept

Winter's formula for predicting appropriate respiratory compensation in primary metabolic acidosis

Question 50Question →

Match each patient's clinical presentation with the most likely acid-base and electrolyte profile expected on their laboratory evaluation.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The presentations match as follows: Hyperemesis with hypokalemic metabolic alkalosis; Diarrhea with normal anion gap acidosis and low urine pH; Ethylene glycol with high anion gap acidosis; and Type 1 RTA with normal anion gap acidosis and high urine pH.

Understanding the pathophysiology of fluid and electrolyte losses allows for accurate prediction of laboratory panels. Vomiting depletes HCl leading to alkalosis; lower GI losses deplete HCO3- leading to normal AG acidosis with appropriate compensation; toxic alcohols introduce unmeasured anions leading to high AG acidosis; and distal tubular defects prevent H+ secretion leading to normal AG acidosis with inappropriately alkaline urine.

Step-by-Step Solution

1

Determine the primary mechanism of acid-base disturbance for each clinical scenario.

Vomiting loses H+ and Cl-. Diarrhea loses HCO3- and K+. Antifreeze adds unmeasured toxic acids. Sjogren syndrome causes distal tubular dysfunction (Type 1 RTA).

Identifying the source of acid gain, acid loss, or bicarbonate loss is the first step in predicting the laboratory profile.

2

Correlate the mechanism with the specific anion gap status and compensatory urinary findings.

Vomiting causes hypochloremic alkalosis. Diarrhea causes normal AG acidosis with appropriate urine acidification. Antifreeze causes high AG acidosis. Type 1 RTA causes normal AG acidosis with failed urine acidification.

Distinguishing between different causes of normal gap acidosis requires evaluating the urinary pH and potassium levels.

Key Concept

Pathophysiology and differentiation of acid-base and electrolyte disturbances.

Question 51Question →

A 54-year-old woman is brought to the emergency department due to 3 days of fever, worsening abdominal pain, and profound lethargy. She has a history of Crohn's disease and underwent an extensive ileal resection two years ago. For the past week, she has had severe, voluminous watery diarrhea and has been unable to tolerate oral fluids. Her temperature is 38.9°C (102.0°F), blood pressure is 86/50 mm Hg, pulse is 122/min, and respirations are 24/min. Physical examination shows dry mucous membranes, decreased skin turgor, and diffuse abdominal tenderness with guarding.

Test	Result
Arterial blood gas (room air)
pH	7.26
$pCO_2$	23 mm Hg
$pO_2$	88 mm Hg
Serum chemistries
Sodium	135 mEq/L
Potassium	3.2 mEq/L
Chloride	105 mEq/L
Bicarbonate	10 mEq/L
Blood urea nitrogen	42 mg/dL
Creatinine	2.3 mg/dL
Lactate	5.5 mmol/L

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

Elevated anion gap metabolic acidosis with appropriate respiratory compensation

Mixed elevated anion gap and normal anion gap metabolic acidosis with concurrent respiratory alkalosis

Normal anion gap metabolic acidosis with appropriate respiratory compensation

Mixed elevated anion gap and normal anion gap metabolic acidosis with appropriate respiratory compensation

Mixed elevated anion gap metabolic acidosis and metabolic alkalosis with appropriate respiratory compensation

Show answer & explanation

Answer: Mixed elevated anion gap and normal anion gap metabolic acidosis with appropriate respiratory compensation

Answer

Mixed elevated anion gap and normal anion gap metabolic acidosis with appropriate respiratory compensation

This patient presents in hypovolemic shock with a severe mixed acid-base derangement. First, calculate the anion gap (AG):

Na^+ - (Cl^- + HCO_3^-) = 135 - (105 + 10) = 20 \text{ mEq/L}

. An AG > 12 confirms a primary elevated anion gap metabolic acidosis (AGMA), which is driven here by lactic acidosis (lactate of 5.5 mmol/L) secondary to tissue hypoperfusion. Second, perform a delta gap calculation to evaluate for additional metabolic disorders. The excess AG is

20 - 12 = 8

. In a pure AGMA, the bicarbonate level should drop by 1 mEq/L for every 1 mEq/L increase in the AG. Therefore, the expected

HCO_3^-

is

24 - 8 = 16 \text{ mEq/L}

. Because the patient's measured

HCO_3^-

(10 mEq/L) is significantly lower than the expected 16 mEq/L, there must be a concurrent process further depleting bicarbonate. This indicates an underlying normal anion gap metabolic acidosis (NAGMA), which aligns clinically with her severe, voluminous diarrhea and history of extensive ileal resection. Finally, calculate the expected respiratory compensation using Winter's formula:

Expected\ pCO_2 = (1.5 \times measured\ HCO_3^-) + 8 \pm 2 = (1.5 \times 10) + 8 \pm 2 = 23 \pm 2 \text{ mm Hg}

. The measured

pCO_2

is exactly 23 mm Hg, indicating that her respiratory compensation is perfectly appropriate for her degree of acidemia.

Step-by-Step Solution

1

Calculate the Anion Gap (AG).

AG = Na^+ - (Cl^- + HCO_3^-) = 135 - (105 + 10) = 20 \text{ mEq/L}

.

An AG > 12 establishes the presence of a primary elevated anion gap metabolic acidosis (AGMA).

2

Calculate the Delta Gap to identify mixed metabolic disorders.

Excess AG =

20 - 12 = 8 \text{ mEq/L}

. Expected

HCO_3^- = 24 - 8 = 16 \text{ mEq/L}

. Measured

HCO_3^-

(10 mEq/L) is less than the expected

HCO_3^-

.

Because the measured bicarbonate is significantly lower than the expected value for a pure AGMA, a concurrent normal anion gap metabolic acidosis (NAGMA) is also present.

3

Calculate expected respiratory compensation using Winter's formula.

Expected

pCO_2 = (1.5 \times 10) + 8 \pm 2 = 23 \pm 2 \text{ mm Hg}

. The measured

pCO_2

is exactly 23 mm Hg.

Since the measured

pCO_2

falls exactly within the expected range, the respiratory response is appropriate, ruling out an independent respiratory disorder.

Key Concept

Interpretation of complex mixed acid-base disorders using the anion gap, delta-delta gap, and Winter's formula.

Question 52Question →

A 32-year-old woman presents to the urgent care clinic with profound weakness and lightheadedness. She reports having large-volume, watery stools up to 8 times a day for the past 4 days after returning from a camping trip. She has not been able to tolerate oral intake due to nausea.

Vital signs show a temperature of 37.1°C (98.8°F), blood pressure of 98/60 mm Hg, pulse of 115/min, and respiratory rate of 22/min. Physical examination reveals dry mucous membranes, flat neck veins, and delayed capillary refill.

Laboratory testing reveals the following:

Test	Result
Sodium	136 mEq/L
Potassium	3.1 mEq/L
Chloride	111 mEq/L
Bicarbonate	15 mEq/L
Blood urea nitrogen (BUN)	30 mg/dL
Creatinine	1.2 mg/dL

Arterial blood gas analysis on room air:

Test	Result
pH	7.26
$pCO_2$	30 mm Hg
$pO_2$	95 mm Hg

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

Normal anion gap metabolic acidosis with appropriate respiratory compensation

Normal anion gap metabolic acidosis with a superimposed respiratory alkalosis

Normal anion gap metabolic acidosis with a superimposed respiratory acidosis

High anion gap metabolic acidosis with appropriate respiratory compensation

Respiratory alkalosis with appropriate metabolic compensation

Show answer & explanation

Answer: Normal anion gap metabolic acidosis with appropriate respiratory compensation

Answer

Normal anion gap metabolic acidosis with appropriate respiratory compensation

This patient has a history of severe diarrhea, which causes profound gastrointestinal loss of bicarbonate, leading to a metabolic acidosis. The step-wise evaluation of her acid-base status confirms this diagnosis:

1. Primary Disorder: The arterial pH is 7.26, indicating acidemia. The serum bicarbonate (

HCO_3^-

) is appropriately decreased at 15 mEq/L, confirming a primary metabolic acidosis.

2. Anion Gap: The serum anion gap is calculated as

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

. For this patient, the gap is

136 - (111 + 15) = 10

mEq/L. Since normal is typically 8-12 mEq/L, she has a normal anion gap metabolic acidosis (NAGMA).

3. Compensation: To determine if her respiratory compensation is adequate, Winter's formula is used: Expected

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

.
Expected

pCO_2 = (1.5 \times 15) + 8 \pm 2 = 30.5 \pm 2

mm Hg.
Because her measured

pCO_2

is exactly 30 mm Hg, her respiratory response falls perfectly within the expected range (28.5 to 32.5 mm Hg). Thus, she has appropriate respiratory compensation with no superimposed mixed acid-base disorders.

Step-by-Step Solution

1

Identify the primary acid-base disorder using the pH and standard laboratory values.

The pH is 7.26 (acidemia). The

HCO_3^-

is low (15 mEq/L).

Matching the low pH with a low bicarbonate level confirms that the primary disturbance is a metabolic acidosis.

2

Calculate the serum anion gap to determine the etiology of the metabolic acidosis.

Anion Gap =

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

=

136 - (111 + 15) = 10

mEq/L.

An anion gap of 10 mEq/L is within the normal range (8-12 mEq/L), indicating a normal anion gap metabolic acidosis (NAGMA), which is consistent with this patient's history of severe diarrhea.

3

Apply Winter's formula to determine if the respiratory compensation is appropriate.

Expected

pCO_2 = (1.5 \times 15) + 8 \pm 2 = 22.5 + 8 \pm 2 = 30.5 \pm 2

mm Hg (range: 28.5 to 32.5 mm Hg).

Because the patient's measured

pCO_2

(30 mm Hg) falls within this expected range, there is purely appropriate respiratory compensation without a superimposed respiratory disorder.

Key Concept

The step-wise approach to acid-base disorders requires identifying the primary disturbance via pH, calculating the anion gap for metabolic acidosis, and utilizing Winter's formula (Expected

pCO_2 = 1.5 \times [HCO_3^-] + 8 \pm 2

) to check for appropriate respiratory compensation.

Question 53Question →

A 45-year-old man is brought to the emergency department by paramedics after being found unresponsive in a park. His medical history is significant for severe alcohol use disorder. On physical examination, he is unarousable and his breath has a fruity odor. Temperature is 36.1°C (97.0°F), blood pressure is 105/65 mmHg, pulse is 102/min, and respiratory rate is 8/min and shallow. Pulse oximetry shows 92% on room air.

Laboratory results are as follows:
Serum sodium: 142 mEq/L
Serum potassium: 4.2 mEq/L
Serum chloride: 98 mEq/L
Serum bicarbonate: 14 mEq/L
Blood urea nitrogen: 28 mg/dL
Serum creatinine: 1.5 mg/dL

Arterial blood gas analysis on room air:
pH: 7.12
$PaCO_2$ : 45 mmHg
$PaO_2$ : 65 mmHg

Which of the following describes the most accurate interpretation of this patient's acid-base status?

High anion gap metabolic acidosis and concurrent primary respiratory acidosis

High anion gap metabolic acidosis with adequate respiratory compensation

High anion gap metabolic acidosis and concurrent primary respiratory alkalosis

Normal anion gap metabolic acidosis and concurrent primary respiratory acidosis

Normal anion gap metabolic acidosis with adequate respiratory compensation

Show answer & explanation

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

Answer

High anion gap metabolic acidosis and concurrent primary respiratory acidosis

The patient presents with acidemia (pH 7.12) and a low serum bicarbonate (14 mEq/L), indicating a metabolic acidosis. To correctly interpret the acid-base status, two main steps are required. First, the anion gap (AG) is calculated:

AG = Na^+ - (Cl^- + HCO_3^-) = 142 - (98 + 14) = 30

mEq/L. A normal AG is typically 8-12 mEq/L; therefore, the patient has a high anion gap metabolic acidosis, likely secondary to alcoholic ketoacidosis given his history. Next, Winter's formula must be applied to determine if the respiratory compensation is adequate: Expected

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

. Using the patient's bicarbonate of 14 mEq/L, the expected

PaCO_2

is

29 \pm 2

mmHg (range 27-31 mmHg). The patient's actual

PaCO_2

is 45 mmHg. Because the actual

PaCO_2

is significantly higher than expected, there is inadequate respiratory compensation, which constitutes a concurrent primary respiratory acidosis. This is clinically consistent with his central nervous system depression and hypoventilation (respiratory rate of 8/min) due to severe alcohol intoxication. Therefore, the correct interpretation is a high anion gap metabolic acidosis with a concurrent primary respiratory acidosis.

Step-by-Step Solution

1

Calculate the serum anion gap.

AG = Na^+ - (Cl^- + HCO_3^-) = 142 - (98 + 14) = 30

mEq/L.

To determine the primary etiology of the metabolic acidosis. A normal AG is typically 8-12 mEq/L. Since 30 > 12, there is a primary high anion gap metabolic acidosis (HAGMA).

2

Calculate the expected

PaCO_2

using Winter's formula.

Expected

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

. Using a bicarbonate of 14 mEq/L, the expected

PaCO_2 = (1.5 \times 14) + 8 \pm 2 = 29 \pm 2

mmHg (range 27-31 mmHg).

To evaluate whether the respiratory compensation for the metabolic acidosis is adequate or if there is a secondary respiratory acid-base disorder.

3

Compare the expected

PaCO_2

with the measured

PaCO_2

.

The measured

PaCO_2

of 45 mmHg is greater than the expected compensatory range of 27-31 mmHg.

A measured

PaCO_2

higher than expected indicates inadequate respiratory compensation, defining a concurrent primary respiratory acidosis (hypoventilation).

Key Concept

Diagnosis of mixed acid-base disorders using the anion gap and Winter's formula

Question 54Question →

A 21-year-old woman is brought to the emergency department by her roommates due to confusion, rapid breathing, and excessive sweating. Her roommates report that she was studying for final exams and seemed highly stressed over the past few days. Upon arrival, the patient complains of a persistent ringing in her ears and nausea. Her temperature is 38.3°C (100.9°F), blood pressure is 110/70 mm Hg, pulse is 118/min, and respirations are 28/min. Physical examination reveals a diaphoretic, agitated patient with clear lungs and a regular heart rhythm.

Laboratory studies show the following:

Serum Chemistry	Result
Sodium	142 mEq/L
Potassium	3.8 mEq/L
Chloride	106 mEq/L
Bicarbonate	16 mEq/L
Blood Urea Nitrogen (BUN)	14 mg/dL
Creatinine	0.9 mg/dL
Glucose	98 mg/dL

Arterial Blood Gas (Room Air)	Result
pH	7.47
$PaCO_2$	23 mm Hg
$PaO_2$	98 mm Hg

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

Mixed primary high anion gap metabolic acidosis and primary respiratory alkalosis

Primary respiratory alkalosis with appropriate metabolic compensation

Primary high anion gap metabolic acidosis with appropriate respiratory compensation

Mixed primary normal anion gap metabolic acidosis and primary respiratory alkalosis

Primary metabolic alkalosis with appropriate respiratory compensation

Show answer & explanation

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

Answer

Mixed primary high anion gap metabolic acidosis and primary respiratory alkalosis

This patient's clinical presentation of tinnitus, hyperventilation, fever, and altered mental status is highly suggestive of salicylate toxicity. The acid-base analysis confirms this. Step 1: The pH of 7.47 indicates alkalemia. Step 2: The low

PaCO_2

of 23 mm Hg indicates a primary respiratory alkalosis. Step 3: Calculation of the anion gap [142 - (106 + 16) = 20 mEq/L] reveals a concurrent high anion gap metabolic acidosis. Step 4: Applying Winter's formula [

1.5 \times 16 + 8 = 32 \pm 2

mm Hg] shows that the actual

PaCO_2

(23 mm Hg) is much lower than the expected compensatory response (30-34 mm Hg). Because the actual

PaCO_2

is lower than expected, an independent primary respiratory alkalosis is confirmed alongside the primary high anion gap metabolic acidosis.

Step-by-Step Solution

1

Evaluate the patient's primary acid-base status using pH.

The pH is 7.47, indicating alkalemia.

Determining the direction of the pH shift identifies the predominant primary acid-base disorder (in this case, an alkalosis).

2

Identify the primary driver of the alkalemia.

The

PaCO_2

is low (23 mm Hg), which aligns with the alkalemia. Therefore, a primary respiratory alkalosis is present.

A primary respiratory disorder is characterized by a

PaCO_2

shift that correlates with the pH shift.

3

Calculate the serum Anion Gap (AG) to screen for hidden metabolic disorders.

AG = Na^+ - (Cl^- + HCO_3^-) = 142 - (106 + 16) = 20

mEq/L.

The normal AG is 8-12 mEq/L. An AG of 20 mEq/L definitively indicates the presence of a primary high anion gap metabolic acidosis, regardless of the overall pH.

4

Apply Winter's formula to determine if the

PaCO_2

is appropriately compensated for the metabolic acidosis.

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

Expected\ PaCO_2 = (1.5 \times 16) + 8 = 32 \pm 2\ mm\ Hg

Comparing the expected

PaCO_2

(30-34 mm Hg) to the actual

PaCO_2

(23 mm Hg) shows that the actual value is significantly lower. This proves the respiratory alkalosis is an independent primary disorder, not just compensation.

5

Synthesize the findings with the clinical presentation.

The patient has a mixed primary high anion gap metabolic acidosis and primary respiratory alkalosis, classic for salicylate (aspirin) toxicity.

Salicylates directly stimulate the medullary respiratory center (causing respiratory alkalosis) and uncouple oxidative phosphorylation (causing lactic acidosis and ketoacidosis, resulting in HAGMA).

Key Concept

Salicylate toxicity classically presents with a mixed primary high anion gap metabolic acidosis and primary respiratory alkalosis, requiring calculation of both the anion gap and Winter's formula for accurate diagnosis.

Question 55Question →

A 54-year-old man is hospitalized for the management of severe pneumonia complicated by sepsis. On hospital day 3, his urine output drops to $200$ mL over a 12-hour period. To evaluate the etiology of his oliguric acute kidney injury, the following laboratory studies are obtained:

Serum sodium: $140$ mEq/L
Serum creatinine: $2.0$ mg/dL
Urine sodium: $56$ mEq/L
Urine creatinine: $40$ mg/dL

What is this patient's fractional excretion of sodium (FENa)? Give your answer as a percentage.

Show answer & explanation

Answer: 2

Answer

2.0

The correct value is 2.0%. The Fractional Excretion of Sodium (

FE_{Na}

) measures the percentage of filtered sodium that is ultimately excreted in the urine. It is calculated using the formula:

FE_{Na} = \frac{U_{Na} \times S_{Cr}}{S_{Na} \times U_{Cr}} \times 100

. By substituting the patient's specific laboratory values into this formula, we get

\frac{56 \times 2.0}{140 \times 40} \times 100 = \frac{112}{5600} \times 100 = 2.0\%

. In the context of oliguric acute kidney injury, an

FE_{Na}

of

\geq 2\%

points toward an intrinsic renal etiology, which aligns perfectly with acute tubular necrosis secondary to this patient's sepsis.

Step-by-Step Solution

1

Identify the proper formula for calculating the Fractional Excretion of Sodium.

FE_{Na} = \frac{U_{Na} \times S_{Cr}}{S_{Na} \times U_{Cr}} \times 100

This formula helps differentiate between prerenal azotemia and intrinsic renal failure (like acute tubular necrosis).

2

Substitute the patient's serum and urine laboratory values into the equation.

FE_{Na} = \frac{56 \times 2.0}{140 \times 40} \times 100

Applying the specific clinical data provided in the stem.

3

Perform the mathematical calculation.

\frac{112}{5600} \times 100 = 0.02 \times 100 = 2.0

To obtain the final percentage value.

Key Concept

Calculation of Fractional Excretion of Sodium (FENa) to evaluate acute kidney injury

Question 56Question →

A 71-year-old man is brought to the emergency department by emergency medical services due to severe shortness of breath and altered mental status. His past medical history is significant for severe chronic obstructive pulmonary disease (COPD), cor pulmonale, and hypertension. Home medications include inhaled tiotropium, oral furosemide, and lisinopril. His wife reports he has experienced a productive cough with green sputum and a fever for the past three days.

Vital signs include a temperature of 38.5°C (101.3°F), blood pressure of 82/50 mm Hg, heart rate of 118/min, and respiratory rate of 28/min. Oxygen saturation is 84% on room air. On physical examination, he is somnolent but arousable. Jugular venous distention is present. Lung auscultation reveals bilateral diffuse wheezes and coarse rhonchi.

Laboratory results are as follows:

Test	Result
Sodium	$140\text{ mEq/L}$
Potassium	$3.1\text{ mEq/L}$
Chloride	$86\text{ mEq/L}$
Bicarbonate	$30\text{ mEq/L}$
Blood urea nitrogen	$48\text{ mg/dL}$
Creatinine	$1.9\text{ mg/dL}$
Lactate	$6.0\text{ mmol/L}$

Arterial blood gas (room air):

Test	Result
pH	$7.26$
$PaCO_2$	$70\text{ mm Hg}$
$PaO_2$	$50\text{ mm Hg}$
$HCO_3^-$	$30\text{ mEq/L}$

Based on the laboratory results, 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

Metabolic alkalosis and respiratory acidosis

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

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

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

The patient's arterial blood gas shows an acidemia (pH 7.26) with an elevated

PaCO_2

(70 mm Hg), indicating a primary respiratory acidosis (due to COPD exacerbation). Next, calculating the anion gap (AG) reveals a high anion gap metabolic acidosis (HAGMA):

AG = Na^+ - (Cl^- + HCO_3^-) = 140 - (86 + 30) = 24\text{ mEq/L}

(normal 10-14). Finally, to check for a third disorder, the delta gap (

\Delta AG

) is calculated and added to the measured

HCO_3^-

to find the corrected

HCO_3^-

. The

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

. The corrected

HCO_3^- = 30 + 12 = 42\text{ mEq/L}

. Since the corrected

HCO_3^-

is significantly greater than the normal expected value of 24 mEq/L, an independent metabolic alkalosis is present (likely secondary to loop diuretic use). Therefore, this is a triple acid-base disorder.

Step-by-Step Solution

1

Evaluate the pH and PaCO2 to identify the primary acid-base disorder.

The pH is 7.26 (acidemia) and PaCO2 is 70 mm Hg (hypercapnia), indicating a primary respiratory acidosis.

Matching the direction of pH change with the PaCO2 change determines the initial primary respiratory disturbance.

2

Calculate the serum anion gap to evaluate for a high anion gap metabolic acidosis (HAGMA).

AG = Na - (Cl + HCO3) = 140 - (86 + 30) = 24 mEq/L. This indicates a HAGMA is present.

An elevated anion gap (> 12 mEq/L) independently signifies the presence of a HAGMA (in this case, lactic acidosis from sepsis/hypoperfusion), regardless of the overall pH.

3

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

ΔAG = Calculated AG - Normal AG = 24 - 12 = 12 mEq/L. Corrected HCO3- = Measured HCO3- + ΔAG = 30 + 12 = 42 mEq/L.

The corrected bicarbonate reveals what the HCO3- would be without the HAGMA. Since 42 mEq/L > 24 mEq/L, a concurrent metabolic alkalosis is also present (likely from chronic furosemide use).

Key Concept

Stepwise interpretation of complex acid-base disorders, including the identification of a triple acid-base disorder using the anion gap and delta gap calculations.

Estimated Time:2m 0s

Question 57Question →

A 38-year-old mechanic presents to the urgent care clinic complaining of severe flank pain, nausea, and blurry vision that started earlier this morning. He admits to accidentally ingesting a few mouthfuls of a liquid from an unmarked container in his garage while working late last night. His temperature is 36.8°C (98.2°F), blood pressure is 142/88 mm Hg, pulse is 98/min, and respiratory rate is 22/min. Cardiopulmonary examination is unremarkable. Initial laboratory tests reveal the following:

* Serum sodium: $138 \text{ mEq/L}$
* Serum potassium: $4.5 \text{ mEq/L}$
* Serum chloride: $104 \text{ mEq/L}$
* Serum bicarbonate: $14 \text{ mEq/L}$
* Blood urea nitrogen (BUN): $28 \text{ mg/dL}$
* Serum glucose: $126 \text{ mg/dL}$
* Measured serum osmolality: $315 \text{ mOsm/kg H}_2\text{O}$

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

Show answer & explanation

Answer: 22

Answer

22

The calculated serum osmolality is derived using the formula

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

. Substituting the patient's values yields

2 \times 138 + \frac{126}{18} + \frac{28}{2.8} = 276 + 7 + 10 = 293 \text{ mOsm/kg H}_2\text{O}

. The osmolar gap is the measured osmolality minus the calculated osmolality (

315 - 293 = 22 \text{ mOsm/kg H}_2\text{O}

). A normal osmolar gap is typically less than 10-12; an elevated gap in this clinical context strongly supports the diagnosis of toxic alcohol ingestion (e.g., methanol or ethylene glycol).

Step-by-Step Solution

1

Determine the formula for calculated serum osmolality.

Calculated Osmolality = 2 × [Na+] + [Glucose]/18 + [BUN]/2.8

This standard formula accounts for the major osmotically active solutes in the extracellular fluid in the United States unit system (mg/dL).

2

Insert the patient's laboratory values into the formula.

Calculated Osmolality = (2 × 138) + (126 / 18) + (28 / 2.8)

To compute the expected osmolality based on native physiological solutes.

3

Perform the arithmetic for each component.

276 + 7 + 10 = 293 mOsm/kg H2O

Resolving the equation yields the total calculated osmolality.

4

Calculate the osmolar gap.

Measured Osmolality (315) - Calculated Osmolality (293) = 22 mOsm/kg H2O

The osmolar gap represents the presence of unmeasured osmotically active substances, such as toxic alcohols (e.g., methanol, ethylene glycol).

Key Concept

Calculation and clinical application of the serum osmolar gap in evaluating suspected toxic alcohol ingestion.

Question 58Question →

A 25-year-old woman with a history of type 1 diabetes mellitus presents to the emergency department with generalized weakness, nausea, and abdominal pain for the past 24 hours. She has been unable to eat and has missed her last two doses of insulin. Her blood pressure is 110/70 mm Hg, pulse is 115/min, and respirations are 24/min. Physical examination shows dry mucous membranes and a fruity odor to her breath.

Laboratory studies show:
Serum sodium: 140 mEq/L
Serum potassium: 4.8 mEq/L
Serum chloride: 104 mEq/L
Serum bicarbonate: 12 mEq/L
Blood urea nitrogen: 28 mg/dL
Serum creatinine: 1.2 mg/dL
Plasma glucose: 450 mg/dL

Arterial blood gas analysis on room air:
pH: 7.25
pCO2: 26 mm Hg
pO2: 95 mm Hg

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

Primary high anion gap metabolic acidosis with appropriate respiratory compensation

Primary high anion gap metabolic acidosis with concurrent respiratory alkalosis

Primary high anion gap metabolic acidosis with concurrent respiratory acidosis

Primary normal anion gap metabolic acidosis with appropriate respiratory compensation

Mixed high anion gap metabolic acidosis and primary metabolic alkalosis

Show answer & explanation

Answer: Primary high anion gap metabolic acidosis with appropriate respiratory compensation

Answer

Primary high anion gap metabolic acidosis with appropriate respiratory compensation

This patient presents with classic signs of diabetic ketoacidosis, confirmed by a low pH (

7.25

) and low serum bicarbonate (

12

mEq/L), indicating a primary metabolic acidosis. The anion gap is calculated as

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

, which is

140 - (104 + 12) = 24

mEq/L. Because the normal anion gap is

8

to

12

mEq/L, this is a high anion gap metabolic acidosis (HAGMA). To determine if respiratory compensation is appropriate, Winter's formula must be applied: Expected

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

. For this patient, Expected

pCO_2 = (1.5 \times 12) + 8 = 18 + 8 = 26 \pm 2

mm Hg. The measured pCO2 is

26

mm Hg, which falls exactly within this range. Therefore, the patient has a primary HAGMA with appropriate respiratory compensation.

Step-by-Step Solution

1

Identify the primary acid-base disturbance using the pH and serum bicarbonate.

pH is 7.25 (acidemia) and bicarbonate is 12 mEq/L (low), indicating a primary metabolic acidosis.

Determining the primary disorder is the first step in basic acid-base analysis.

2

Calculate the anion gap.

Anion Gap =

140 - (104 + 12) = 24

mEq/L.

Metabolic acidosis must be categorized into high anion gap or normal anion gap to narrow down the differential diagnosis.

3

Calculate the expected respiratory compensation using Winter's formula.

Expected

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

mm Hg.

Calculating the expected pCO2 determines if the physiological respiratory response is adequate or if a secondary respiratory disorder exists.

4

Compare the measured pCO2 to the expected pCO2.

The measured pCO2 (26 mm Hg) is exactly within the expected range (24 to 28 mm Hg).

Because the measured pCO2 matches the expected value, there is appropriate respiratory compensation without a superimposed respiratory disorder.

Key Concept

Evaluation of acid-base disorders using the anion gap and Winter's formula to determine primary disturbances and physiological compensation.

Question 59Question →

A 58-year-old man with a history of chronic alcohol use disorder is brought to the emergency department due to profound weakness and a four-day history of intractable vomiting. He reports being unable to keep any food or fluids down. On physical examination, he appears lethargic and has dry mucous membranes with decreased skin turgor.

Laboratory studies reveal the following:

Serum:
Sodium: 140 mEq/L
Potassium: 3.1 mEq/L
Chloride: 88 mEq/L
Bicarbonate: 14 mEq/L
Blood urea nitrogen: 35 mg/dL
Creatinine: 1.6 mg/dL

Arterial blood gas on room air reveals a pH of 7.32 and a $pCO_2$ of 29 mm Hg. The physician suspects a complex mixed acid-base disorder driven by alcoholic ketoacidosis and protracted emesis.

Assuming a baseline normal anion gap of 12 mEq/L and a baseline normal serum bicarbonate of 24 mEq/L, what is the calculated delta-delta ratio ( $\Delta AG / \Delta HCO_3^-$ ) for this patient?

Show answer & explanation

Answer: 2.6

Answer

2.6

In a patient presenting with a high anion gap metabolic acidosis, calculating the delta-delta ratio is essential to evaluate for mixed metabolic disorders. First, the patient's anion gap is calculated as

140 - (88 + 14) = 38

mEq/L. The

\Delta AG

is the patient's calculated AG minus the normal baseline AG (

38 - 12 = 26

). The

\Delta HCO_3^-

is the normal baseline

HCO_3^-

minus the patient's measured

HCO_3^-

(

24 - 14 = 10

). The delta-delta ratio is

26 / 10 = 2.6

. Because 2.6 is greater than 2.0, this confirms a concurrent metabolic alkalosis superimposed on the high anion gap metabolic acidosis, which perfectly aligns with the clinical history of alcoholic ketoacidosis paired with profound vomiting.

Step-by-Step Solution

1

Calculate the actual anion gap (AG).

AG = 140 - (88 + 14) = 38

mEq/L.

An elevated anion gap confirms the presence of a high anion gap metabolic acidosis (HAGMA).

2

Calculate the delta anion gap (

\Delta AG

).

\Delta AG = 38 - 12 = 26

mEq/L.

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

3

Calculate the delta bicarbonate (

\Delta HCO_3^-

).

\Delta HCO_3^- = 24 - 14 = 10

mEq/L.

This value represents the apparent fall in bicarbonate due to buffering the excess acid.

4

Calculate the delta-delta ratio.

\Delta AG / \Delta HCO_3^- = 26 / 10 = 2.6

.

A ratio greater than 2.0 indicates that the bicarbonate level is higher than expected, revealing a concurrent metabolic alkalosis (e.g., from vomiting) superimposed on the HAGMA.

Key Concept

The delta-delta ratio (

\Delta AG / \Delta HCO_3^-

) is used in the setting of a high anion gap metabolic acidosis to identify hidden mixed acid-base disorders. A ratio > 2.0 indicates a concurrent metabolic alkalosis, whereas a ratio < 1.0 indicates a concurrent normal anion gap metabolic acidosis.

Estimated Time:1m 30s

Question 60Question →

A 32-year-old woman with a history of systemic lupus erythematosus and recurrent kidney stones is evaluated in the clinic for progressive, generalized muscle weakness over the past two weeks. She reports difficulty climbing stairs and rising from a seated position. She denies diarrhea, vomiting, fever, or recent illnesses. Her vital signs are within normal limits. Physical examination reveals symmetric proximal muscle weakness in the bilateral lower extremities with diminished deep tendon reflexes.

Laboratory evaluation shows the following:

Serum chemistry:
Sodium: 140 mEq/L
Potassium: 2.6 mEq/L
Chloride: 114 mEq/L
Bicarbonate: 14 mEq/L
Blood urea nitrogen: 16 mg/dL
Creatinine: 0.9 mg/dL

Arterial blood gas (room air):
pH: 7.26
pCO2: 29 mm Hg
pO2: 96 mm Hg

Urinalysis reveals a pH of 6.8 with no protein or blood.

Based on the provided laboratory data, which of the following statements is most accurate regarding this patient's current acid-base physiological state?

The respiratory system has appropriately responded to a primary loss of serum buffering capacity.

The patient exhibits an inappropriate degree of hyperventilation, indicating a superimposed primary respiratory disorder.

The accumulation of unmeasured endogenous anions is the primary driver of the acidemia.

The measured arterial carbon dioxide level reflects the primary mechanism of the acid-base disturbance.

The arterial blood gas reveals an inadequate ventilatory response, indicating a concomitant respiratory acidosis.

Show answer & explanation

Answer: The respiratory system has appropriately responded to a primary loss of serum buffering capacity.

Answer

The respiratory system has appropriately responded to a primary loss of serum buffering capacity.

The patient's laboratory results demonstrate an acidemic pH driven by low bicarbonate, confirming a primary metabolic acidosis (loss of serum buffers). The anion gap is normal (

12

mEq/L). To assess respiratory compensation, Winter's formula is applied:

\text{Expected pCO}_2 = 1.5 \times 14 + 8 = 29

(range

27-31

mm Hg). Because the patient's actual pCO2 is

29

mm Hg, the respiratory system has mounted a completely appropriate physiological response.

Step-by-Step Solution

1

Evaluate the arterial pH to determine the primary direction of the disturbance.

The pH is 7.26, which is strictly acidemic (normal 7.35 - 7.45).

Establishing acidemia helps differentiate whether subsequent abnormalities are primary drivers or compensatory mechanisms.

2

Examine the serum bicarbonate and pCO2 to identify the primary etiology.

The serum bicarbonate is significantly low at 14 mEq/L, which aligns with the acidemic pH. This indicates a primary metabolic acidosis (loss of serum buffering capacity).

The primary disorder must match the direction of the pH shift.

3

Calculate the serum anion gap to characterize the metabolic acidosis.

\text{Anion Gap} = \text{Na}^+ - (\text{Cl}^- + \text{HCO}_3^-) = 140 - (114 + 14) = 12

mEq/L. This is a normal anion gap.

Differentiating between normal and high anion gap metabolic acidosis is crucial for diagnosing the underlying disease (e.g., Renal Tubular Acidosis vs. Lactic Acidosis).

4

Apply Winter's formula to determine if the respiratory compensation is appropriate.

\text{Expected pCO}_2 = (1.5 \times \text{HCO}_3^-) + 8 \pm 2 = (1.5 \times 14) + 8 \pm 2 = 29 \pm 2

mm Hg. The actual pCO2 is exactly 29 mm Hg.

If the measured pCO2 falls within the calculated expected range, the patient has an appropriately compensated simple metabolic acidosis without any superimposed respiratory disorders.

Key Concept

The physiological diagnosis of a simple, compensated normal anion gap metabolic acidosis requires calculating the anion gap and confirming the adequacy of respiratory compensation using Winter's formula.

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