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Difficulty: HardNephrology

A 52-year-old woman with a history of type 1 diabetes mellitus is brought to the emergency department after 33 days of intractable vomiting and generalized abdominal pain. She ran out of her prescribed insulin 44 days ago. On physical examination, she appears lethargic with dry mucous membranes and decreased skin turgor. Temperature is 37.2∘37.2^\circ C (99.0∘99.0^\circ F), blood pressure is 95/6095/60 mm Hg, pulse is 118118/min, and respirations are 2626/min and deep.

Laboratory studies reveal:

TestResultReference Range
Serum sodium140140 mEq/L136−145136-145 mEq/L
Serum potassium4.84.8 mEq/L3.5−5.03.5-5.0 mEq/L
Serum chloride9292 mEq/L98−10698-106 mEq/L
Serum bicarbonate1414 mEq/L22−2822-28 mEq/L
Blood urea nitrogen4242 mg/dL7−187-18 mg/dL
Serum creatinine1.61.6 mg/dL0.6−1.20.6-1.2 mg/dL
Blood glucose480480 mg/dL70−11070-110 mg/dL

Assume a normal anion gap of 1212 mEq/L and a normal serum bicarbonate of 2424 mEq/L.

What is the patient's calculated delta ratio (also known as the Δ\Delta AG / Δ\Delta HCO 3−_3^- ratio)?

Answer: 2.2

Answer

The calculated delta ratio is 2.2.
The patient's clinical presentation of diabetic ketoacidosis combined with intractable vomiting strongly suggests a mixed acid-base disorder. Diabetic ketoacidosis causes a high anion gap metabolic acidosis (HAGMA), while vomiting induces a metabolic alkalosis due to the loss of gastric hydrochloric acid. To confirm this mathematically, the delta ratio is calculated. The patient's measured anion gap is 140−(92+14)=34140 - (92 + 14) = 34 mEq/L. The change in anion gap (ΔAG\Delta\text{AG}) is 34−12=2234 - 12 = 22 mEq/L. The change in bicarbonate (ΔHCO3−\Delta\text{HCO}_3^-) is 24−14=1024 - 14 = 10 mEq/L. Dividing the ΔAG\Delta\text{AG} by the ΔHCO3−\Delta\text{HCO}_3^- yields a ratio of 2.22.2. In a pure HAGMA, the drop in bicarbonate should be roughly equivalent to the rise in the anion gap (ratio between 1.01.0 and 2.02.0). A delta ratio >2.0> 2.0 indicates that the bicarbonate level has not fallen as much as expected, which confirms the presence of a concurrent metabolic alkalosis.

Step-by-Step Solution

1
Calculate the patient's anion gap (AG).
AG=140−(92+14)=34\text{AG} = 140 - (92 + 14) = 34 mEq/L
Establishing the initial anion gap is necessary to identify the presence of a high anion gap metabolic acidosis and to compute the delta anion gap.
2
Calculate the change in anion gap (ΔAG\Delta\text{AG}).
ΔAG=34−12=22\Delta\text{AG} = 34 - 12 = 22 mEq/L
The numerator of the delta ratio represents how much the anion gap has increased above the normal baseline.
3
Calculate the change in bicarbonate (ΔHCO3−\Delta\text{HCO}_3^-).
ΔHCO3−=24−14=10\Delta\text{HCO}_3^- = 24 - 14 = 10 mEq/L
The denominator of the delta ratio represents how much the bicarbonate has decreased below the normal baseline due to buffering the excess acid.
4
Divide ΔAG\Delta\text{AG} by ΔHCO3−\Delta\text{HCO}_3^-.
Delta Ratio=2210=2.2\text{Delta Ratio} = \frac{22}{10} = 2.2
The resulting ratio categorizes the nature of the acid-base disorder, determining if a concomitant metabolic alkalosis or normal anion gap metabolic acidosis is present.

Key Concept

In a high anion gap metabolic acidosis, calculating the delta ratio (Δ\Delta AG / Δ\Delta HCO 3−_3^-) helps uncover hidden, concurrent mixed acid-base disorders such as a superimposed metabolic alkalosis.

Alternative Method

Instead of using the delta ratio, clinicians frequently calculate the 'corrected bicarbonate' (or expected bicarbonate) by adding the ΔAG\Delta\text{AG} to the patient's measured bicarbonate: 14+22=3614 + 22 = 36 mEq/L. Because this value is significantly higher than the normal 2424 mEq/L, it leads to the exact same clinical conclusion of a superimposed metabolic alkalosis.
Estimated Time:2m 0s
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Nephrology

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