A Model of the Maldistribution of Ventilation and Perfusion, in the Lungs of Heart Failure Patients

The use of mechanical ventilators is widespread within Intensive Care Units, both in patients with normal respiratory function (e.g., post-operative patients) and in subjects with pathologic conditions influencing ventilation mechanics. In particular heart failure, the decreased capacity of the heart to pump blood through the systemic and pulmonary circulation, is clinically known to adversely affect ventilation. Depending on gravity, different areas of the lungs receive different quotas of the pulmonary blood flow, and their alveoli are ventilated to different degrees: the ventilation/perfusion ratio (V/Q) captures this relationship and is normally higher at the apexes and lower at the bases of the lungs (normal distribution of the ratio). Maldistribution of V/Q occurs when these differences are accentuated, and leads to inefficient gas exchange and diminished arterial oxygen saturation. In this work, we introduce a mathematical model of mechanical ventilation and pulmonary blood perfusion, incorporating a representation of the lungs by vertically stacked functional layers. Numerical simulations readily show how progressive degrees of heart pump decompensation are associated with worsening distribution of the ventilation/perfusion ratio, even in the absence of other complicating factors, such as pulmonary edema.