A 58-year-old man with COPD presents with dyspnea and hypoxemia (SpO₂ 88% on room air). Arterial blood gas shows PaO₂ 55 mmHg, PaCO₂ 52 mmHg, pH 7.32. Clinical examination reveals decreased breath sounds bilaterally with prolonged expiration. Which investigation is most appropriate to quantify the degree of ventilation-perfusion mismatch and guide oxygen therapy?