A kit of parts for an apparatus for liposuction and lipofilling of adipose tissue, said kit of parts comprising: An extraction unit comprising a liposuction device having: (a) a substantially linear, hollow, elongated cannula with an inner lumen extending along a longitudinal axis, X, from a first inlet end (1 i), provided with one or several openings for drawing adipose tissue into said lumen, to a second, outlet end, located at the opposite end of the elongated body, said cannula being coupled by means of fixing means (1 c) to, (b) a powered handpiece suitable for imparting a given movement to the inlet end of the cannula, a separation unit, comprising a vessel, provided with separation means, for separating in a retentate volume_a selected portion of adipose tissue from liquids and other undesired solids, a re-injection unit comprising a lipofilling device comprising a cannula as defined in point (a) supra, coupled to a handpiece; a vacuum pump suitable for creating a vacuum in the lumen of the cannula of the liposuction device sufficient for drawing adipose tissue out of a location of a body, a re-injection piston pump suitable for driving said selected portion of adipose tissue from the vessel to the lumen of the cannula of the lipofilling device under sufficient pressure for injecting said selected portion of adipose tissue into a location of a body, and tubing for connecting the various elements of the kit of parts together such as to form an apparatus for liposuction and lipofilling of adipose tissue, characterized in that, the powered handpiece of the liposuction device is suitable for imparting to the inlet end (1 i) of the cannula a vibrational movement comprising a first, linear component of a back and forth reciprocal movement along the longitudinal axis, X, at a frequency of 10 to 500 Hz and a second, orbital component about the longitudinal axis, X, and in that, the kit-of-parts further comprises a three-way valve having a first, aspiration position, suitable for bringing the retentate volume of the vessel of the separation unit in fluid communication with said re-injection piston pump, and a second, injection position, suitable for bringing the re-injection piston pump in fluid communication with the lipofilling device. An extraction unit comprising a liposuction device having: (a) a substantially linear, hollow, elongated cannula with an inner lumen extending along a longitudinal axis, X, from a first inlet end (1 i), provided with one or several openings for drawing adipose tissue into said lumen, to a second, outlet end, located at the opposite end of the elongated body, said cannula being coupled by means of fixing means (1 c) to, (b) a powered handpiece suitable for imparting a given movement to the inlet end of the cannula, (a) a substantially linear, hollow, elongated cannula with an inner lumen extending along a longitudinal axis, X, from a first inlet end (1 i), provided with one or several openings for drawing adipose tissue into said lumen, to a second, outlet end, located at the opposite end of the elongated body, said cannula being coupled by means of fixing means (1 c) to, (b) a powered handpiece suitable for imparting a given movement to the inlet end of the cannula, a separation unit, comprising a vessel, provided with separation means, for separating in a retentate volume_a selected portion of adipose tissue from liquids and other undesired solids, a re-injection unit comprising a lipofilling device comprising a cannula as defined in point (a) supra, coupled to a handpiece; a vacuum pump suitable for creating a vacuum in the lumen of the cannula of the liposuction device sufficient for drawing adipose tissue out of a location of a body, a re-injection piston pump suitable for driving said selected portion of adipose tissue from the vessel to the lumen of the cannula of the lipofilling device under sufficient pressure for injecting said selected portion of adipose tissue into a location of a body, and tubing for connecting the various elements of the kit of parts together such as to form an apparatus for liposuction and lipofilling of adipose tissue,