Final answer:
Prompt celiotomy (laparotomy) in a hemodynamically normal 10-year-old girl with a Grade III splenic injury is mandated by signs of ongoing internal bleeding or hemodynamic instability, which may indicate rapid blood loss requiring immediate surgical intervention.
Step-by-step explanation:
Following a Grade III splenic injury, a hemodynamically normal 10-year-old girl is being observed in the hospital. The scenario that mandates prompt celiotomy (laparotomy) would be evidence of ongoing internal bleeding or hemodynamic instability. These signs could include a drop in blood pressure, tachycardia (rapid heart rate), or a significant continuous drop in hemoglobin levels indicating ongoing blood loss. Moreover, blood loss exceeding 500 ml or more than 7 ml/kg in children, as per the scenario provided, should have appropriate treatment with fluids and potentially blood products available for resuscitation.
The clinical vignettes provided in the context of the question highlight various medical conditions that can arise and require prompt medical attention. For instance, the case of Olivia suggests an infectious response with symptoms consistent with severe systemic infection, potentially meningitis, while the reference to the patient in a motor vehicle accident indicates a scenario where universal donor blood (Type O negative) would be urgently transfused due to the critical nature of the injuries and lack of time to determine the patient's blood type.