407. Prāṇaḥ प्राणः

Repetitive nāma-s 66 and 320.

Prāṇa is the causal body. It is only the causal body which leads to the formation of subtle and gross bodies. Prāṇa body along with its four derivatives apāna, vyāna, udāna and samāna are responsible for the creation of a being. Here Viṣṇu is adored as the subtlest cause of creation. Prāṇa is also responsible for carrying out different physiological functions of the body for its sustenance.

408. Prāṇadaḥ प्राणदः

Repetitive nāma-s 65, 321.

Prāṇada means the giver of life as discussed in the previous repetitive nāma-s.

A Yogī’s prāṇa is transformed into prāṇana, which means life. This life sustaining force makes the kuṇḍalinī ascend and makes it possible for the Yogī to stay connected with Him perpetually, leading to his liberation.  

Lalitā Sahasranāma 832 is Prāṇadātri. The explanation provided in my book on Lalitā Sahasranāma is given below:

Prāṇa nourishes senses.  Without prāṇa, senses and mind cannot function.  The previous nāma said that She is the chief of prāṇa (possibly embodiment of prāṇa) and this nāma says that She is the giver of prāṇaBrahma Sūtra (II.iv5) says, “prāṇa-s must have originated from the Brahman, since speech is preceded by them.”

Muṇḍaka-Upaniṣad (II.i.8) says, tasmāt sapta prāṇaḥ prabhavanti which means ‘from That (Brahman) seven prāṇa-s (prāṇa here means seven organs - two eyes, two nostrils, two ears, and mouth) have come.  This Upaniṣad confirms the statement of Kaṭha-Upaniṣad referred in the previous nāma. 

Taittirīya-Upaniṣad (I.vii) discusses further on this.  It refers to prāṇa, vyāna, upāna, apāna and samāna the five types of prāṇa-s.  The Upaniṣad calls these five as prāna-pāṇkta (pāṇkta means fivefold) meaning group of prāṇa-s.  This prāna-pāṇkta makes indriya-pāṇkta  function (functional senses). 

Therefore, it is apparent that without prāṇa, senses cannot function.  She gives that ‘vital force’ called prāṇa, without which life is not sustainable. 

When She provides prāṇa to the universe, She becomes Parā-Śakti or parā-prakṛti. Prāṇa is subjective energy or vital force which is derived from the Brahman.  This nāma again reaffirms Her as the Brahman that permeates and sustains.  

409. Praṇavaḥ प्रणवः

Repetitive nāma 957.

Praṇava refers to the sacred syllable OM / ॐ. The sacred mantra consists of A + U + M + bindu (a dot above M) = auṁ / अ + उ + म् = ओं, which is generally written as ॐ. This sacred mantra ॐ is worshipped by all the gods and goddesses. This nāma says that Lord Viṣṇu is in the form of sacred praṇava mantra.

Kṛṣṇa confirms this in Bhagavad Gītā (VII.8), “I am the sacred syllable (OM) of all the Vedas.” Vedas are the breath of Viṣṇu.

410. Pṛthuḥ पृथुः

Pṛthu means expansion. Because of His expansion, the manifestation of the universe takes place. When He uses His Divine Will, the expansion of the Self takes place thereby forming various shapes and forms. He is the cause, and the effect is the universe along with all its existents.

411. Hiraṇyagarbhaḥ हिरण्यगर्भः

Repetitive nāma 70.

Microcosm is the individual soul and Macrocosm is the Brahman. Like microcosm, macrocosm also has four different stages and they are turya or avyakta, Īśvara, hiraṇyagarbha and virāj. The first state of avyakta or turya is beyond the three normal states of human consciousness, active, dream and deep sleep. The second state of Īśvara is the state of God (not the Brahman), where it is associated with māyā. The third state is hiraṇyagarbha, the state of where the constituents of the universe are bound together. If Īśvara is addressed as the cosmic Lord, then hiraṇyagarbha is the Thread-Self or Sūtrātmā, viz. the entire conglomerate of all individual beings into only one entity known as Ekajīva, a step lower than Īśvara. The last one is the virāj who, according to Advaitavedānta, is composed of the waking cosmic Self (viśva) and the waking individual self (vaiśvānara), i.e. it is both the Self and the self in wakefulness. The whole universe is projected through the cosmic energy of hiraṇyagarbha and is endowed with cosmic ego and gets associated with all subtle bodies in the universe collectively.

412. Śatrughnaḥ शत्रुघ्नः

Śatrughna means the destroyer of all inimical forces, working against gods and goddesses. One of the important duties of Viṣṇu is to annihilate the enemies.  Enemies or demons mean the sensory afflictions. He can be realized only when the mind becomes free from sensory impressions of the external world. Attachment to the external world leads to multiplicity of thoughts.  

413. Vyāptaḥ व्याप्तः

He is the One who pervades the entire universe. This nāma says that He is omnipresent. He being the cause, He pervades all the effects. Without cause, effect is not possible. Without Him, life is not possible.

414. Vāyuḥ वायुः

Vāyu means air and by worshipping Him as air, His omnipresence is subtly conveyed.

Bṛhadāraṇyaka Upaniṣad (III.vii.7) talks about air. “He who inhabits air, but is within it, whom air does not know, whose body is air, and who controls air from within is the Internal Ruler, your own Immortal Self.”

415. Adho'kṣajaḥ अधोऽक्षजः

The One, whose vitality always remains upward. In other words, His vitality is not subjected to changes as in the case of gods and other beings. He being the embodiment of prāṇa, the life sustaining force, He is not subjected to modifications.  Brahman alone is beyond modifications, as everything originates from Him and exist in the universe. He is eternal existing as the Self Illuminating Light.

It can also be explained that He can be realized only if one’s sensory organs are turned inwards, thereby disconnecting from the material world.

For further details on Adho'kṣajaḥ please visit Gabriel Pradiipaka (stanza 6).