The Nagahama line (長浜派) of the Ryōi Shintō-ryū (良移心当流) would use a number of different written permutations of Shintō-ryū (as an abbreviated term instead of Ryōi Shintō-ryū). Amongst these were the:

Shintō Yawara 神当和, Shintō-ryū Yawara 心當流和, Shintō Yawara 心當和, Shintō Yawara 神富柔, & Shintō-ryū 心當流.

In the 'Kenpō Gokui Atemi Sappô Kappō Meikai' by Fujita Seiko (1958), he describes the 'Shintō-ryū Atemi no Zu' and provides the illustration as above.

Whether this is part of that same Shintō-ryū line or not is difficult to say with absolute certainty, but it is consistent with what we know about the Ryōi Shintō-ryū. The Shintō-ryū 心當流 Mokuroku (目録) refers to the Godai (五大 - five elements) of: 木 Wood, 火 Fire, 土 Earth. 金 Metal & 水 Water

and the In’yō no Maki (陰陽之巻) deals with the interchange between Yin & Yang.