Approximately 1% of infants are born extremely preterm and underweight and are prone to respiratory distress and subsequent morbidity. Typical treatments for respiratory distress in late preterm and term infants, such as non-invasive pressure support, are less effective in preterm infants. Invasive mechanical ventilation applied as a last resort causes trauma, leading to ventilator-induced lung injury (VILI). Maternal infection, such as chorioamnionitis, can cause prenatal and neonatal lung infection, inflammation, and often very preterm birth. Inflammation is expected to stiffen the lungs with increased resistance and lowered compliance, but exceptions occur. A complete picture of the mechanisms of stiffening remains unknown. In an attempt to elucidate this information, we applied custom parameter inference and image analysis procedures to a neonatal rat model of chorioamnionitis and VILI, incorporating subject-specific pressure-volume measurements and histology. Numerical optimizations on a nonlinear compartmental model identified key parameter differences between healthy and unhealthy groups that may suggest mechanisms of VILI in infected respiratory systems. Combined analyses of the two strategies identified new correlations between model parameters, imaging metrics, and inflammatory markers from the data, suggesting that mathematical approaches provide an important path towards understanding VILI and infection.