In Francisco Torrent-Guasp's models it seems like the suction phase (Trainini, 2020) force is from contraction of some segment of the band. Jorge Carlos Trainini has mapped hyaluronan throughout the heart (Trainini, 2021), and according to Mark Knepper (Knepper, 2003), compressed hyaluronan binds sodium, between its carboxyl groups (see image below), and when it relaxes, it forcibly relaxes from electrostatic repulsion between the carboxyl groups, and, also from osmotic pressure as it releases the bound sodium ions, that are osmotically active, forcing relaxation of heart. Maybe this is what causes the suction phase and maybe the contraction-model that Torrent-Guasp suggested was wrong. Or, I don't get their explanation. Could be both factors but I don't get theirs.

Also the vacuum in the pericadrial sac, same mechanism as in pleural cavity, forcing the suction phase once myocardium no longer contracting, could be one mechanism for the suction phase in the 3-stage heart.

The video below shows the suction at the suction phase,

The suction mechanism provides the pressure gradient for aortic regurgitation from aortic insufficience.

References

Knepper, M. A., Saidel, G. M., Hascall, V. C., & Dwyer, T. (2003). Concentration of solutes in the renal inner medulla: interstitial hyaluronan as a mechano-osmotic transducer. American journal of physiology. Renal physiology, 284(3), F433–F446. https://doi.org/10.1152/ajprenal.00067.2002

Trainini, J., Lowenstein, J., Beraudo, M., Trainini, A., Llabata Mora, V. and Wernicke, M. (2020). Myocardial torsion: Anatomo-functional interpretation of cardiac mechanics. Editorial Biblos.

Trainini, J. (2021). Hyaluronic acid in the heart. J Tre Bio Res.