Luke 22:44

Luke 22:39-46
39 And he came out, and went, as he was wont, to the mount of Olives; and his disciples also followed him.
40 And when he was at the place, he said unto them, Pray that ye enter not into temptation.
41 And he was withdrawn from them about a stone’s cast, and kneeled down, and prayed,
42 Saying, Father, if thou be willing, remove this cup from me: nevertheless not my will, but thine, be done.
43 And there appeared an angel unto him from heaven, strengthening him.
44 And being in an agony he prayed more earnestly: and his sweat was as it were great drops of blood falling down to the ground.
45 And when he rose up from prayer, and was come to his disciples, he found them sleeping for sorrow,
46 And said unto them, Why sleep ye? rise and pray, lest ye enter into temptation.

This is just moments before He would be betrayed by Judas and arrested. 

verse 44 is not recorded in Matthew, Mark or John.  Only Luke describes the Agony and sweating as great drops of blood.  Perhaps Luke had a better understanding of the agony and stress Jesus went thru and the effects this would have on His body.  After all he was a physician. 

"His sweat was as it were great drops of blood falling down to the ground."  The fact of a “sweat” accompanying an agony is also mentioned by medical writers; Cases of great mental anguish, causing drops of blood to ooze from the body like sweat, are known to medical authorities. Luke makes it plain that the Lord's body was not covered with any kind of ordinary sweat, but that it was covered all over with sweat in the shape of large thick drops, like great drops of blood. 

Matthew Henry's Commentary says... 
Every pore was as it were a bleeding wound, and his blood stained all his raiment. This showed the travail of his soul. He was now abroad in the open air, in a cool season, upon the cold ground, far in the night;  yet now he breaks out into a sweat, which bespeaks the extremity of the agony he was in.  

Hebrews 5:7 who in the days of His flesh, when He had offered up prayers and supplications, with vehement cries and tears to Him who was able to save Him from death, and was heard because of His godly fear. 

Christ is described as being in agony, sweating as drops of blood, vehement cries and tears.  Why was He willing to offer Himself?  verse 42...“not My will, but Yours be done.”  He submitted Himself to the will of His Father.  It was the Father’s will that Jesus be offered up for He was the only sacrifice that could give us redemption and salvation. 

Gal. 1:4  - who gave Himself for our sins, that He might deliver us from this present evil age, according to the will of our God and Father.