Multiscale analysis of simultaneous uptake of two reactive gases in the human lungs and its application to methemoglobin anemia

• Multiscale modeling of simultaneous uptake of two reactive gases in human lungs.
• We divide the human lung into micro (RBCs), meso (capillaries), macro (lung) scales.
• Liapunov–Schmidt scheme of bifurcation theory used to reduce model dimension.
• Model applied to a binary system of oxygen (O2) and nitric oxide (NO) to study the disease – methemoglobinemia.
• We simulate disease conditions, critical levels of NO (∼203 ppm) and oxygen therapy and briefly discuss methylene blue therapy.

We present a novel multiscale modeling and simulation methodology for quantifying the simultaneous uptake of two reactive gases in the human lungs, and apply it to predict pulmonary hypoxemia in patients suffering from methemoglobin anemia (resulting from excess inhaled nitric oxide (NO)). We start with the convection–diffusion–reaction equations at each scale of the lung and apply a spatial averaging technique (based on Liapunov–Schmidt method of the classical bifurcation theory) to obtain low-dimensional multiscale models. Our simulations for methemoglobin anemia show that while breathing in room air, the O2 saturation in the patient's hemoglobin falls to below 94% at 50 ppm NO, and above 203 ppm, NO causes severe hypoxemia by reducing the O2 saturation to below its critical value of 88%. We predict that patients respond to O2 therapy up to inhaled NO levels of 271 ppm, above which they are candidates for methylene blue therapy.