A 24-year-old man is brought to the emergency department due to a 2-day history of generalized weakness, excessive urination, and diffuse abdominal pain. He was diagnosed with type 1 diabetes mellitus 10 years ago and recently missed several doses of his insulin regimen. On physical examination, he appears lethargic and his mucous membranes are dry. Laboratory studies reveal a serum bicarbonate level of 12 mEq/L and an arterial blood pH of 7.28. Which of the following is the expected arterial partial pressure of carbon dioxide () in this patient if appropriate respiratory compensation has occurred?
- A8 to 12 mm Hg
- B14 to 18 mm Hg
- 24 to 28 mm HgCevap
- D31 to 35 mm Hg
- E38 to 42 mm Hg
Cevap
24 to 28 mm Hg
The patient is presenting with diabetic ketoacidosis, which causes a primary anion gap metabolic acidosis. This is confirmed by the acidemic pH (7.28) and the depressed serum bicarbonate (12 mEq/L). In response to a primary metabolic acidosis, the body physiologically compensates by increasing alveolar ventilation (Kussmaul respirations) to blow off carbon dioxide. The adequacy of this respiratory compensation is calculated using Winter's formula: . Substituting the patient's bicarbonate level yields: . Adding the standard variance of yields an expected range of 24 to 28 mm Hg. If the measured falls within this range, it represents appropriate simple respiratory compensation.
Adım Adım Çözüm
Anahtar Kavram
Winter's formula for respiratory compensation in metabolic acidosis
Alternatif Yöntem
A quick rule of thumb for estimating the expected in simple metabolic acidosis is that the should roughly equal the decimal digits of the pH. Alternatively, the 'Rule of 15' states that . For this patient, mm Hg, which cleanly falls into the correct 24 to 28 mm Hg range.
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