The selection of optimal positive end expiratory pressure (PEEP) levels during ventilation therapy of patients with ARDS (acute respiratory distress syndrome) remains a problem for clinicians. One particular mooted strategy states that minimizing the energy transferred to the lung by mechanical ventilation could potentially be used to determine the optimal PEEP level. This minimization could potentially be undertaken by finding the minimum range of dynamic elastance. In this study, we compare an adapted Gauss-Newton method with the typical gauss newton method in terms of the level of agreement obtained in elastance-pressure curves across different PEEP levels in 10 patients. The Gauss-Newton adaptation effectively ignored characteristics in the data that are un-modelled. The adapted method successfully determined regions of the data that were un-modelled, as expected. In ignoring this un-modelled behavior, the adapted method captured the desired elastance-pressure curves with more consistency than the typical least-squares Gauss Newton method.