Rassilon's left Bollock

Okay so firstly, what is regeneration and how does it work. Well before we even get yo that we have to discuss how Gallifreyan blood works (now this is just a theory, but I have done lots of research over the years). So main components of Gallifreyan blood are T-cells, these are the immune system and can asexually reproduce and often specialise (differentiate) into cells very similar to phagocytes and Lymphocytes in humans, which are then used to fight infections; next there is blood cells, biconcave and basically the same as human red blood cells, but not red as the 'hemoglobin' is an orange compound designed to take in oxygen from a different atmosphere to Earths, however that chemical works the same and carries blood the same; next is lindos cells, these are the platelets of the Gallifreyan system and when an injury occurs they clot the blood and work of healing the area, this bloot clotting can also cause the same issues as in humans, with strokes or hypoxia, but still do the job for both external and internal issues; next is something unlike humans, atron carrier cells. These cells carry artron energy which reacts with the enzymes on the surface of the lindos cells to speed up healing.

They are not natural to the body and are placed there when the time lord recieves "rassilon's imprinteur". These cells do not die because the atron they contain keeps them alive, they are modified blood cells with a different compound for storing atron energy. They are made specially for a specific time lord when they graduate, they combine a marrow extract of stem cells with the chemical so they differentiate in certain conditions, causing "imprinteur" cells to specialise. Then the marrow is transferred back into the host body and the cells are rarely rejected. Then everytime the Timelord(TL) is exposed to the vortex or a rift, their atron cells are replenished.

Regeneration however, is caused when a large scale clotting of Lindos cells occurs on a large injury. When this happens loads of the imprinteur cells get stuck behind them and react rapidly, this influx of energy causes artron radiation to damage the DNA, and when the lindos cells repair the damage they repair the damage to the new DNA print, causing a new body. This can go wrong and cause structural changes to the brain, resulting in new personality, limb differences or missing/malformed internal organs.

After regeneration a person's lindos cells are very low, but after an hour the cell count would've doubled in the body's rapid attempt to make enough. This large influx of cells will stay alive for two weeks, creating an "elastic stage" of regeneration where any damage caused after the first hour and before the end of the first two weeks, will repair itself even quicker, albeit at large cost to the already deprived energy and caloric biome of the body. This means limbs that are severed can regrow, not ones however that are not already there, unless the stump is cut off. Please do wait at least a day before acting on the elastic stage otherwise your poor TL will be very exhausted.

So now we've got that out of the way, it's time to discuss Bigeneration. Lindos enzymes are catalysts, which means they react with artron energy causing the increased healing effect, however like other catalysts they have an optimum PH and an optimum temperature. Most importantly, more energy creates a faster reaction, but too high a temperature (please please please try to keep your TLs at 14.6°c) causes the enzyme to denature or at low temperatures, work slower. They also can only be used once, but considering every Lindos cell carries and excretes roughly 5 microlitres of enzyme when its working and about 300,000 work on an area of 1 cm³, there are always enough.

The Doctor Bigenerated because of the Galvanic radiation, which is what also killed him. Galvanic and artron radiation work in tangent with each other, meaning he had more energy to regenerate with. This caused his cells to undergo mitosis faster, raising his already high Lindos (we can assume this because otherwise no Bigeneration could've occurred and it has been documented that they have an abnormally high count. See: sixth doctor regenerating from small head injury due to internal clotting and high lindos cell count causing fast regen), and more artron energy carrier cells to be produced. This would've accelerated regeneration and given enough energy for two separate bodies to be created.

In the Rani's case however, she was exposed to the unfiltered radiation of space. Her bigeneration doesn't exactly make sense from the same point of view as the Doctor's does, but when you factor in the fact that the flux left a lot of background radiation around, including artron energy. In the deep of space its also very likely there could be an undocumented vortex rift nearby that could've also 'supercharged' her atron cells. However in those deep space temperatures, her enzymes would've been damaged severely*, preventing regeneration until she was dethawed. There she would've had enough time to replenish her lindos count (atron surplus would increase the rate of this).

This acceleration of both factors would've caused a Bigeneration in both these two subjects, however whilst it is very unlikely and there has only ever been one case (See:Pandora and Romana) documented, with these factors it is possible.

-Rani has three brain stems like all timelords, so stayed alive by keeping one thawed

Extras:

-* urm my friend corrected me on my enzyme knowledge so here u go

- the penetrative ability of artron is very contradictory. A lot of sources claim it isn't very penetrative hence the separation of vortex and original dimension (can be stopped by 5-10 metres of air), however some say more penetrative than galvanic due to the existence of rifts. This is important when investigating the source of the Rani's artron energy to regenerate as likely she used up the majority of it she had keeping warm in space. Without this energy she could've regenerated so I have considered it to be as penetrative as gamma radiation, hence its need for the imprinteur cells to be contained.