Did Jesus's rational soul or His spirit descend into hell? Jesus said on the Cross: "Father into your hands I commend my spirit" (Luke 23:46).

The Apostles' Creed says: "Jesus suffered under Pontius Pilate, was crucified, died, and was buried. And then Jesus descended into hell. On the third day he rose again…"

If Jesus already commended His spirit to the Father and had not yet ascended into Heaven, would it mean that the one who descended to the dead is Jesus's rational soul and not the Spirit that received as His anointing in the Baptism in the river Jordan (Matt. 3:16)?
Article 5 of the Catechism of the Council of Trent says:


  We are not to imagine that His power and virtue only, and not also His soul, descended into hell; but we are firmly to believe that His soul itself, really and substantially, descended thither, according to this conclusive testimony of David: Thou wilt not leave my soul [animam] in hell. (Ps. 15:10).


The "Spirit" of Matthew 3:16 ("…the Spirit of God descending as a dove…") is the Holy Ghost, the 3rd Person of the Holy Trinity. Christ's human soul, which is a creature, is not the Holy Ghost, Who is uncreated.

Also, His divinity remained united to His human body and to His human soul. Cf. St. Thomas Aquinas's question "Whether the whole Christ was in hell?" (Summa Theologica III q. 52 a. 3).