In the enlightenment era, rationalists like Voltaire and biblical critics like Strauss used to have a field day with this one:

And he came out and went, as was his custom, to the Mount of Olives, and the disciples followed him. And when he came to the place, he said to them, “Pray that you may not enter into temptation.” And he withdrew from them about a stone's throw, and knelt down and prayed, saying, “Father, if you are willing, remove this cup from me. Nevertheless, not my will, but yours, be done.” And there appeared to him an angel from heaven, strengthening him. And being in agony he prayed more earnestly; and his sweat became like great drops of blood falling down to the ground. And when he rose from prayer, he came to the disciples and found them sleeping for sorrow, and he said to them, “Why are you sleeping? Rise and pray that you may not enter into temptation.”

Luke 22:39-46

Sweating blood? What is that, if not the stuff of myths and legends? They ridiculed. They argued that this showed that the gospels did not record real history. But what came next was the discovery of Hematidrosis, a rare condition that can occur during times of extreme emotional or physical terror. When a person experiences severe existential dread, the intense activation of the fight or flight response causes the tiny capillaries surrounding the sweat glands to violently constrict and then rupture. The blood is forced into the sweat ducts, mixing with perspiration and oozing out through intact skin. The psychological environment described in Gethsemane matches the exact textbook criteria required to trigger this condition. Jesus was facing imminent betrayal, torture, and a horrific execution, and His agony is described not just here but also in the other accounts.

Luke uniquely records the sweating of blood, though. In the New Testament, Luke is identified as a physician. He used the specific Greek phrase thromboi haimatos, which means "clots" or "thick drops" of blood. This is a very good fit to Hematidrosis, where blood coagulates as it mixes with heavy sweat. Furthermore, the condition explains why Jesus was so physically weakened later on. Hematidrosis leaves the skin extraordinarily fragile and tender, meaning the subsequent Roman scourging would have torn His flesh apart with catastrophic ease. This explains why Jesus was so quick to die later on, when he was crucified, and why He wasn't able to carry the cross Himself.

So now the tables have turned. These droplets of blood from Jesus' forehead rather point to the historicity of the account, than away from it, as Voltaire and Strauss would have it. How would some first century Jews invent something like this, such that it would happen in circumstances that fit the condition? The answer is that they wouldn't. Luke simply wrote down what actually happened.