A binary vascular system was a type of circulatory system in which the blood vessels led to two hearts. Time Lords had a binary vascular system. (TV: Spearhead from Space, et al.)
Characteristics
According to the Twelfth Doctor, a binary vascular system led to extremely high blood pressure in comparison to single-hearted species like humans. (TV: Smile) The Dominator Rago once told Jamie McCrimmon that beings with single hearts were physically weaker than those with two hearts. (TV: The Dominators) Given the multiple hearts, Time Lords also had two sets of pulses, as exhibited by the Thirteenth Doctor. (TV: The Woman Who Fell to Earth) The Seventh Doctor used his knowledge of these pulses to attempt to see if his companion Mel was in fact the Rani in disguise. (TV: Time and the Rani)
When the Fifth Doctor was stabbed in the chest, he survived because his human, single-hearted attacker aimed for the spot where the human heart would be, but the Doctor's two hearts were in a slightly different location. (AUDIO: Son of the Dragon) Scans of the Ninth Doctor's hearts and later those of the Eleventh Doctor and Thirteenth Doctor hearts showed that the hearts changed position during regeneration at some point. (TV: Dalek, The Power of Three, Kerblam!, Resolution)
The Master was plagued with a drumming sound which subsequently drove him mad. These "drums" were said to have been the sound of the heartbeat of a Time Lord. (TV: The Sound of Drums, The End of Time)
The Meta-Crisis Tenth Doctor stated that he could not regenerate due to only possessing a single heart. (TV: Journey's End)
A Gallifreyan in cardiac arrest needed CPR on both hearts; otherwise, it would prove ineffective. (TV: Smith and Jones) Amy Pond used a defibrillator to restart one of the Eleventh Doctor's hearts. (TV: The Power of Three)
Cybermen could detect a binary vascular system, prompting them to take the subject for further analysis, which at least delayed cyber-conversion. (TV: The Age of Steel)
In Time Lords
A Time Lord's regenerative process was intimately linked to his or her hearts. Time Lords from Oldblood Houses had only one heart until they regenerated for the first time; (PROSE: The Man in the Velvet Mask, Christmas on a Rational Planet, AUDIO: Time in Office) the First Doctor was seen to have one heart. (TV: The Edge of Destruction) In contrast, members of Newblood Houses were Loomed with both hearts. (PROSE: Christmas on a Rational Planet)
Regeneration could be completely stopped — and the Time Lord was therefore killed immediately, regardless of how many lives they had left — if both hearts were pierced or shot simultaneously. Andred and Serena were both killed in this manner, (AUDIO: Imperiatrix, PROSE: World Game) while Cavis was permanently killed when, during regeneration, her enemy stabbed both her original heart and the place where the second one would grow. (PROSE: The Shadows of Avalon) Brooke of the Kovarian Chapter carried a regeneration inhibitor firearm capable of producing double blasts to take out a binary vascular system, which she used to kill H-One. (AUDIO: The Furies) Missy recommended eight snipers, with three trained on each of her hearts and two for her brain stem, so that Clara Oswald could feel safe while speaking to her, noting that they'd have to "switch [her] off fast" before she could regenerate. (TV: The Magician's Apprentice)
A Gallifreyan could survive with only one heart, though he or she would be weakened greatly. (PROSE: Managra, TV: The Shakespeare Code, AUDIO: City of Spires) When one of the Third Doctor's hearts momentarily stopped, the Master warned him he was "within an inch of dying." (TV: The Mind of Evil) After the Eighth Doctor's second heart was extracted from his chest, he was unable to process drugs or use his respiratory bypass system, and to compensate, his remaining heart had to beat at a worryingly rapid pulse and was prone to fatigue. (PROSE: The Adventuress of Henrietta Street, Hope, Anachrophobia) During the Last Great Time War, at least one Time Lord spy had her second heart removed from her body. (AUDIO: A Heart on Both Sides) One of the Tenth Doctor's hearts stopped beating while he was recovering from regeneration, (TV: The Christmas Invasion) and the Eleventh Doctor claimed that he wouldn't survive much longer after one of his hearts was stopped by a Shakri cube. (TV: The Power of Three)
When Sabbath implanted the Eighth Doctor's second heart in his own chest, it endowed him with the ability to penetrate "deep time" (ie, travelling further away from his homeworld than should be possible), simultaneously creating a link between the Doctor and Sabbath that meant that the Doctor would survive grievous wounds as his heart was still beating in Sabbath, until Sabbath tore the heart out of his own chest, its "death" allowing the Doctor to grow a new one. (PROSE: The Adventuress of Henrietta Street, Hope, Camera Obscura)
In other species
As Time Lords from an alternate timeline, the Word Lords also had a binary vascular system. (AUDIO: The Word Lord)
In the Mutter's Spiral galaxy, a few monopod species and a drone species had two hearts. (PROSE: Tragedy Day)
The Second Doctor once encountered another double-hearted humanoid species called the Dulcians. His own binary vascular system led the Dominators to believe he was a Dulcian. (TV: The Dominators)
Later, the Eighth Doctor met the Kulan, another race whose overall stamina seemed to be improved over humans by their two hearts. (PROSE: Escape Velocity)
The Kirithons were genetically engineered by the Panjistri to have two hearts. (PROSE: Timewyrm: Apocalypse)
The Apalapucians, residents of Apalapucia, had two hearts. Chen-7, also known as the 1 Day Plague, only affected species with binary vascular systems. (TV: The Girl Who Waited)
The inhabitants of Skale had two hearts. (PROSE: Parallel 59)
When Henry van Statten performed an invasive scan of the Ninth Doctor in 2012, he marvelled at the design and enthusiastically announced he was going to patent it. (TV: Dalek) Humans genetically introduced a second heart many Segments prior to circa 10,000,000. (PROSE: The Ark)
Baris, a fan of the Tenth Doctor, had a second heart fitted so he could resemble him more. (PROSE: The Doctor Trap)