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Difficulty: HardNephrology

A 64-year-old woman is brought to the emergency department by her family due to profound weakness and confusion. She has had 5 days of severe, voluminous watery diarrhea. Her medical history includes type 2 diabetes mellitus and hypertension. On examination, blood pressure is 82/50 mm Hg, heart rate is 118/min, and respiratory rate is 24/min. She has dry mucous membranes, flat neck veins, and delayed capillary refill.

Laboratory studies show:
Serum Na+Na^+: 140 mEq/L
Serum K+K^+: 3.2 mEq/L
Serum Cl−Cl^-: 112 mEq/L
Serum HCO3−HCO_3^-: 8 mEq/L
Blood urea nitrogen: 54 mg/dL
Serum creatinine: 2.8 mg/dL (baseline 0.9 mg/dL)
Serum lactate: 5.2 mmol/L (Normal: 0.5-1.0 mmol/L)
Serum albumin: 4.0 g/dL

Assuming a reference anion gap of 12 mEq/L and a normal serum bicarbonate of 24 mEq/L, what is this patient's calculated delta ratio (also known as the Δ/Δ\Delta/\Delta ratio)?

Answer: 0.5

Answer

0.5
The correct answer is 0.5. This patient presents with hypovolemic shock (hypotension, tachycardia, poor perfusion) secondary to severe watery diarrhea, leading to an elevated lactate level. Therefore, she has a mixed acid-base disorder: a high anion gap metabolic acidosis (HAGMA) from lactic acidosis, and a normal anion gap metabolic acidosis (NAGMA) from gastrointestinal bicarbonate losses. The delta ratio is used to uncover this mixed disorder. It is calculated by dividing the excess anion gap (ΔAG=20−12=8\Delta AG = 20 - 12 = 8) by the bicarbonate deficit (ΔHCO3−=24−8=16\Delta HCO_3^- = 24 - 8 = 16). The resulting ratio of 0.5 falls between 0.4 and 0.8, which is the classic diagnostic range for a mixed HAGMA and NAGMA.

Step-by-Step Solution

1
Calculate the serum anion gap.
2020 mEq/L
Determines the presence and magnitude of unmeasured anions contributing to the acidosis.
2
Calculate the ΔAG\Delta AG.
88 mEq/L
Quantifies the excess gap above the normal baseline (20−1220 - 12).
3
Calculate the ΔHCO3−\Delta HCO_3^-.
1616 mEq/L
Quantifies the total deficit of bicarbonate below the normal baseline (24−824 - 8).
4
Divide ΔAG\Delta AG by ΔHCO3−\Delta HCO_3^-.
0.50.5
Provides the delta ratio, which identifies complex mixed acid-base disorders.

Key Concept

In patients with a high anion gap metabolic acidosis (HAGMA), the delta ratio (ΔAG/ΔHCO3−\Delta AG / \Delta HCO_3^-) is calculated to identify concurrent concealed acid-base disorders. A ratio < 0.8 indicates a concurrent normal anion gap metabolic acidosis (NAGMA), which in this patient is due to severe diarrhea.
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Topics

Nephrology

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