Advisor:  Dr. Jennifer

Committee:  Dr. Margaret Cheney, Dr. Patrick Shipman, Dr. Marlis Rezende

Title: An Inverse Problem and Multi-Compartment Lung Model for the Estimation of Lung Airway Resistance throughout the Bronchial Tree

Abstract: Mechanical ventilation is a vital treatment for patients with respiratory failure, but mechanically ventilated patients are also at risk of ventilator-induced lung injury. Optimal ventilator settings to prevent such injury could be guided by knowledge of the airway resistance throughout the lung. While the ventilator provides a single value estimating the total airway resistance of the patient, in reality the airway resistance varies along the bronchial tree. Multiple literature sources reveal a wide range of clinically used values for airway resistance along the bronchial tree, motivating an investigation to estimate the values of airway resistance in the alveolar tree and the relationship to disease state.

In this work, we introduce a multi-compartment asymmetric lung model based on resistor-capacitor circuits by using an analogy between electric circuits and the human lungs. A method for solving the inverse problem of computing the vector of airway resistance values in the alveolar tree is presented. The method uses a linear least squares optimization approach with several constraints. First, a symmetric lung model that makes use of parameters supplied by the mechanical ventilator of patients with acute respiratory distress syndrome (ARDS) is used. We then generalize the model to an asymmetric lung model. The asymmetric model takes regional information data from electrical impedance tomography, a medical imaging technique, and converts them to time dependent lung airway volumes. The linear least squares optimization inverse problem is embedded in an iterative method to update unknown parameters of the forward problem for the asymmetric case