Our Gemara on Amud Aleph tells us that one should prepare and organize his prayers (Shemoneh Esre). Though strictly speaking, this was referring to periodic prayers such as Yamim Tovim and also when they didn’t have easy access to siddurim, the point is well taken that in regard to quality of prayer, preparation is key.
I would like to make a few comments about preparing for prayer while we are on the topic. Prayer requires focus and concentration. The ability to stay focused on prayer is an essential skill that takes time and effort to learn. It also benefits from a realistic and structured approach as I’ll explain shortly. What we know about the mind and meditation can inform us about the benefits but also the process necessary to build prayer ability.
Authors and researchers, Matthieu Ricard, Antoine Lutz and Richard J. Davidson, in "Mind of the Meditator", state the following:
Neuroscientists have now begun to probe what happens inside the brain during the various types of meditation. Wendy Hasenkamp, then at Emory University, and her colleagues used brain imaging to identify the neural networks activated by focused-attention meditation. ... Advanced meditators appear to acquire a level of skill that enables them to achieve a focused state of mind with less effort. These effects resemble the skill of expert musicians and athletes capable of immersing themselves in the 'flow' of their performances with a minimal sense of effortful control. ...
In our Wisconsin lab, we have studied experienced practitioners while they performed an advanced form of mindfulness meditation called open presence. In open presence, sometimes called pure awareness, the mind is calm and relaxed, not focused on anything in particular yet vividly clear, free from excitation or dullness. The meditator observes and is open to experience without making any attempt to interpret, change, reject or ignore painful sensation. We found that the intensity of the pain was not reduced in meditators, but it bothered them less than it did members of a control group. Compared with novices, expert meditators' brain activity diminished in anxiety-related regions -- the insular cortex and the amygdala -- in the period preceding the painful stimulus. The meditators' brain response in pain-related regions became accustomed to the stimulus more quickly than that of novices after repeated exposures to it. Other tests in our lab have shown that meditation training increases one's ability to better control and buffer basic physiological responses -- inflammation or levels of a stress hormone -- to a socially stressful task such as giving a public speech or doing mental arithmetic in front of a harsh jury.
About 15 years of research have done more than show that meditation produces significant changes in both the function and structure of the brains of experienced practitioners. These studies are now starting to demonstrate that contemplative practices may have a substantive impact on biological processes critical for physical health."
While davening is something far more than meditation alone, the ability to be in a focused mindful state is a prerequisite for successful prayer. Here are two key points from Shulkhan Arukh (OC 93:1, and 98:1) that make this clear:
One should wait one [halakhic] hour before he rises to pray [the Amidah] in order to focus his heart to the Omnipresent. And [one should wait] one [halakhic] hour after the prayer, so that it should not seem like a burden to him, that he is quick to leave it.
(Halakha Lemaase we do not do this, see Mishna Berura and other commentaries. However, the essential matter is that a successful Shemoneh Esre is something that requires practice, concentration and preparation.)
And so did the pious ones and the men of action, who would seclude themselves and concentrate on their prayers until they would cast off their physicality and strengthen [their] mental power, until nearly arriving at the level of prophecy. And if another thought comes to one in the midst of the prayer, one should be silent until the thought is eliminated. And one should think about things that humble the heart and concentrate it on one's Father in Heaven, and not think about things that contain levity. Ramah: Before prayer, one should think about the loftiness of God who is raised up and the lowliness of humanity, and remove all human pleasures from one's heart (Ri, beginning of chapter "Ein Om'din" [Berachot Chapter 5] ).
Source "Mind of the Meditator" author: Matthieu Ricard, Antoine Lutz and Richard J. Davidson
https://www.scientificamerican.com/article/neuroscience-reveals-the-secrets-of-meditation-s-benefits/
date: https://www.scientificamerican.com/
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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