Sisan, F. M.; Joya, C.; Situ, A.; Silver, S.; Akbarullah, S.

Traditional gas exchange metrics, such as the alveolar-arterial (A - a) gradient ({Delta}P), fail to account for systemic oxygen extraction or ventilatory adequacy, thereby limiting their diagnostic precision in complex respiratory or circulatory pathologies. We propose and derive the corrected oxygenation gradient (COG), a novel formula that incorporates the A - a gradient, systemic oxygen extraction (CvO2/CaO2), and ventilatory adequacy (PaCO2 normalization). Complete mathematical proofs of continuity, differentiability, and boundary behaviors are provided. Simulations across physiological and pathological ranges illustrate logical behavior. COG appropriately scales with hypercapnia and tissue hypoxia, offering a single index sensitive to integrated oxygenation status. COG represents a theoretically rigorous and physiologically intuitive tool for characterizing gas exchange inefficiency.