A mathematical model for lactate transport to red blood cells

A simple mathematical model for the transport of lactate from plasma to red blood cells (RBCs) during and after exercise is proposed based on our experimental studies for the lactate concentrations in RBCs and in plasma. In addition to the influx associated with the plasma-to-RBC lactate concentration gradient, it is argued that an efflux must exist. The efflux rate is assumed to be proportional to the lactate concentration in RBCs. This simple model is justified by the comparison between the model-predicted results and observations: For all 33 cases (11 subjects and 3 different warm-up conditions), the model-predicted time courses of lactate concentrations in RBC are generally in good agreement with observations, and the model-predicted ratios between lactate concentrations in RBCs and in plasma at the peak of lactate concentration in RBCs are very close to the observed values. Two constants, the influx rate coefficient C (1) and the efflux rate coefficient C (2), are involved in the present model. They are determined by the best fit to observations. Although the exact electro-chemical mechanism for the efflux remains to be figured out in the future research, the good agreement of the present model with observations suggests that the efflux must get stronger as the lactate concentration in RBCs increases. The physiological meanings of C (1) and C (2) as well as their potential applications are discussed.