1. What would be the signs that would convince him that his son is doomed and there's nothing he can do?
Hi Patrick! I am happy to help with your question.
#1: What would be the signs that the son is going to die?
Essentially the scenario you've set up would be death from hypovolemic shock (the son is bleeding out). Or, organ dysfunction from crush injury. But, let’s stick with hypovolemic shock as it will work well in this scenario.
What would be more concerning to the father and trained ER doctor would be his signs of shock--- this would lead to his death. I'm going to use the medical words because this is how your ER doctor would think and then I'll put what they mean in parenthesis.
I think one thing that helps is to understand the symptoms in light of the injury. When you're bleeding out, you're losing blood. Blood carries oxygen. So the body compensates by trying to circulate those remaining red blood cells faster.
Shock is your body's inability to meet its oxygen demands (hypovolemic shock is one type of shock.) So, initial signs of hypovolemic shock are: tachycardia (increased heart rate to circulate the blood faster), tachypnea (increased breathing rate to load more oxygen on the cells that remain), complaints of thirst, pallor (pale skin-- circulating red blood cells gives you your color) and diaphoresis (sweating). Also, diminished, weak, rapid peripheral pulses. Peripheral pulses are those at your wrist (radial) and feet (pedal). This would progress to central pulses--those in your neck (carotid) and groin (femoral)--- being weak and thready.
In kids (this is my area of specialty)-- the blood pressure will be normal initially because kids can do really well at compensating for shock up to a point.
So-- hypotension (or low blood pressure) is then an ominous sign. One way a trained ER doctor can estimate what his son’s blood pressure is is by palpating his pulses.
As his shock progresses, his level of consciousness will begin to wan. He'd have periods of being coherent-- then unresponsive (depending on how fast you'd want this death to occur). The brain is oxygen hungry so when it doesn't have enough-- you become unconscious.
His ultimate sign of impending death will actually be bradycardia (low heart rate-- less than 60 beats/minute) progressing to asystole (no heart beat). This is how kids generally die. The child would become unconscious. His breathing would slow/stop. His heart rate would slow then stop. Pupils will dilate and become unresponsive to light.