If you gain weight after a liposuction, you will tend to develop a "lumpy" look in the liposuctioned areas.
This is because when the liposuction is performed, most fat in those areas is removed, and while at the time of surgery, the area may look like it was pretty smooth, the small amount of remaining fat has ridges bumps and indentations from very small imperfections in the surface of the remaining fat tissue. So when weight is gained, those once tiny imperfections basically get 'inflated' in size. As a result, people who have trouble keeping the weight off, will often go for a second liposuction to 'smooth out' the imperfections in the body fat which got left behind on the first surgery.
Now, if you don't gain weight after the liposuction, that's not an issue. And if you do, it is correctable, but at additional expense.
If you are 'plump' and you liposuction around the waist, and along the inner thigh, etc. then you can achieve a rather hourglass shape. the pic above is a great example of that, although she was rather significantly heavy, and had a tummy tuck as well as liposuction, to get rid of excess skin.
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It is my understanding that the fat removed by liposuction doesn't drastically change if it is transplanted elsewhere in the body. In other words, I wouldn't imagine that it could somehow 'know' exactly where it is under the skin. So if you reinjected that fat in the chest or butt, the fat cells themselves should be relatively oblivious to this change of location. So the transplanted fat should gain/lose weight in a manner similar to before being relocated. I could be wrong though. Some tissues do seem to be able to react and change function in relation to their location in the body.
Traditional fat reinjection involved just sticking the fat directly back into the body. In small amounts this could have a high survival rate, but in larger quantities, many fat cells would die from lack of circulation, as new blood vessels would not grow to supply them quickly enough. Generally the larger the mass of fat reinjected, the more severe this issue. The result would be that to gain 1-2 cup sizes from fat reinjection (200-400cc's or so) as much as half or more of the fat cells would die before any blood supply would grow to supply them. The dead cells would dissolve away, leaving gaps in the transplanted fatty area. The result would be a 'lumpy' uneven augmentation, with about half the original fill amount dissolved away.
This issue of lumpiness is lessened by injecting the fat under a muscle, as the muscle smooths out the result considerably. In the chest that would be similar to a submuscular implant placement, except with reinjected body fat instead of an implant. and in the butt area it could be placed under the "glut" making for a more rounded and squishy butt muscle. Sub muscular placement became the only acceptable way of doing fat reinjection. And it tended to result in very minor augmentation after the death and dissolving of much of the fat tissue.
The new trial method of fat reinjection tries to increase the speed of blood vessel growth in the transplanted fatty tissue, by increasing it's density of stem cells. There's a certain percentage of stem cells present in most body tissues. In the fat which is removed by liposuction, the fat is portioned out, and one portion is set aside to be reinjected. the remainder (about 75% of the fat) is filtered to remove the stem cells from it. After the stem cells are removed, that fat is disposed of. The stem cells are added to the portion of fat which was set aside, and blended in with it. The result is a smaller quantity of fat than was removed (maybe 1/4 as much), but with 4 times the density of stem cells in it. When injected back into the body, this stem cell rich fat grows new blood vessels significantly more rapidly than normal. The result is that 200-400cc's of fat can be reinjected into each breast, with about a 90% survival rate for the fat cells. This means that 90% of the bulk will remain, and the overall appearance is fairly uniform and even.
It can be injected above or below the muscle, and can be used to make a very tailored shape. The limitation is that you only have about 1/4th as much fat to inject as you took out of the body. So it is only of interest to girls who have a noticeable amount of plumpness. It is also being used for correcting minor flaws in breast implant surgeries.
The fat can be put 'on ice' for prolonged periods of time, like semen or eggs, and can be reinjected at a much later date than it is removed. if there is leftover fat at the time of reinjection, that can be stored as well. In theory, the fat reinjection could be broken up into a 2-stage process allowing for a larger quantity of fill, or a higher survival rate of fat cells, either way. Assuming there was enough excess fat tissue to work with that is.
I have not seen specific discussion of it, but there is talk of reinjecting fat using the newer method in a variety of other locations where you normally only see collagen and other fillers. The possibility of lip injections with real body fat has been discussed. ((and on a personal note, it strikes me as the perfect fill material for a injection-based nipple augmentation))
There is also a trial going to test high stem cell fat reinjection breast augmentation in conjunction with a 'brava bra'. The brava bra uses hard breast cups with a vacuum to attempt to suction the breasts to a larger size. It's intended to be worn like 10 hours a day, and over a period of months, result in larger breasts. Users report 0-1 cup sizes of growth with the product. anyway, the thing is, that the vacuum causes temporarily increased vascular capacity (the breast's blood vessels swell somewhat under the vacuum force), and it is thought that this might also help with the blood supply issue with reinjected fat. Plus, there's the possibility of 'minor' additional augmentation using the brava bra.
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One thing about body fat distribution, is that it results from a combination of fat cells and fat cell-size. fat cells can swell to many times their original size, holding body fat in large quantities. Beyond a certain size though, they will divide into two cells, and then grow to hold twice as much. if a person was significantly overweight, for a long period of time (10 years or so), and lost some weight... their remaining fatty tissues would be mostly full of large numbers of relatively small fat cells. compared to someone who just recently gained weight, where the fat cells would be smaller in number, and more bloated in size. Differences like these will affect how the fat behaves as a person gains or looses weight. a high density of small fat cells is very resistant to weight loss, and very prone to growth during weight gain. Meanwhile a low density of swollen fat cells will shrink readily during weight loss, and be reluctant to grow further during weight gain. literally, the more fat you are, and the longer you are fat, the more prone to obesity you become.
If a person were prone to obesity over a long period of time, but lost some weight to become more moderately chubby... they would likely still have some body fat which is very hard to shed, because it's really made up of very densely packed 'empty' fat cells. Thus the stubborn problem areas of weight loss where there seems to be some body fat that won't go away no matter what.
If that dense, low-lipid, fatty tissue were liposuctioned and relocated. It would be very resistant to any further weight loss, but in theory it should be very eager to take in and store dietary fats during weight gain. It strikes me that such a situation could result in weight gain "going straight to her breasts" (or butt, or wherever the fat was reinjected). Just based on the dense quantity of fat cells and their life-mission to uptake bloodstream fat and store it.
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More than half of the body's fat is not in places which can be liposuctioned though. only exterior fat can be suctioned. all the fat inside the torso, under muscles throughout the body, and in the brain (there's fat in the brain's composition), are all not safe to liposuction. And really, the fatty tissues around the major organs is the stuff which causes the most health problems. So, liposuction is not a replacement for a healthy diet & exercise. Really the benefits of liposuction are rather superficial from a body-health perspective. And it can make people think of themselves as being more fit or healthy than they actually are. Also, sometimes liposuction leaves scars of its own, or damages nerves under the skin resulting in numb areas, etc. It's by no means a perfect science.
But it is interesting to think about all the possibilities of moving body fat around in the body, now that it appears they may have figured out a way to do it with a good survival rate for the fat cells. I could see some fairly realistic BE fiction being based on some relatively minor advances beyond what is currently possible.