Fasting means that a person must, in obedience to the commands of Allah, refrain, from the time of Adhan for Fajr prayers up to Maghrib, from the things which invalidate the fast.
To further explain, just before dawn a column of whiteness rises upwards from the east. It is called the first dawn. When this whiteness spreads, it is called the second dawn, and the prime time for Fajr prayers. It is exactly the time to refrain from the things which invalidate the fast. Maghrib is the time when the redness in the eastern sky appearing after sunset disappears in the horizon. This is the beginning of Maghrib time and the end of the time for imsak.
Therefore, as per the foregoing explanation, there is no imsak time other than the time between the Adhan for Fajr prayers and the Adhan for Maghrib prayers.
The grand jurists have said that in order to ensure that one has been fasting throughout this time, he should, as a matter of precaution, begin abstaining a little earlier than the Adhan for Fajr prayers, and continue to refrain for a little after Maghrib, from acts which invalidate a fast.
What follows below is an answer to a similar question from Grand Ayatollah Khamenei:
Question: Given that the cities are developing and becoming larger every day and it is not possible to ascertain the exact time of Fajr, kindly let us know about the exact time of imsak for Fast and Fajr prayer.
Answer: The believers are asked to exercise precaution about imsak and the time for Fajr prayer. So, they should refrain from invalidating things from Adhan time as declared by the media and should offer their Fajr prayers five to six minutes after the Adhan for Fajr prayers.
 - Tawzih al-Masail (with annotation by Imam Khomeini), vol.1, pg.88.
 - Ibid, vol.1, pg.411
 - Khomeini, Sayyid Rohullah Musavi, Tawzih al-Masail (by Imam Khomeini), pg.164, issue No.730, First, 1436 A.H.
 - Tawzih al-Masail (with annotation by Imam Khomeini), vol.1, pg.440; Khamenei, Sayyid Ali, Answers to Jurisprudential Questions, pg. 73, Office of Grand Ayatollah Khamenei in Qom, Qom, Iran, First, 1424 A.H.