A Mathematical Model of Respiratory and Biothermal Dynamics in Brain Hypothermia Treatment

Brain hypothermia treatment (BHT) requires proper mechanical ventilation and therapeutic cooling. The cooling strategy for BHT has been mainly discussed in the literature while little information is available on the respiratory management. We first developed a mathematical model that integrates the respiratory and biothermal dynamics to discuss the simultaneous managements of mechanical ventilation and therapeutic cooling. The effect of temperature on the linear approximations of hemoglobin-oxygen dissociation, together with temperature dependency of metabolism, is introduced during modeling to combine the respiratory system with the biothermal system. By comparing its transient behavior with published data, the model is verified qualitatively and then quantitatively. Second, model-based simulation of the current respiratory management in BHT suggests reduction of minute ventilation in reference to cooled brain temperature to stabilize the states of blood and brain oxygenation. Lastly, the relationship between cooling temperature and minute ventilation is approximated by a linear first-order transfer function of static gain 0.61 min^-1degC^-1 and time constant 8.9 h, which is used to develop a feedforward control to tune the mechanical ventilator in concert with temperature regulation of the cooling blanket. Discussion of the model encourages further studies that provide direct evidence from clinical experiments.