Autologous fat grafting is increasingly used for breast augmentation and reconstruction.1–5 Fat grafts are easily available, biocompatible, cause low donor-site morbidity, and give grafted sites a natural appearance. However, fat grafting is generally considered an unpredictable procedure,6 with long-term retention commonly varying between 10% and 80%.7–14 Much work has been done to optimize this procedure; however, the clinical practice has advanced faster than the supporting science. Fat grafting can be considered in 4 phases: harvesting, processing, reinjecting, and managing the recipient site.15 To determine the optimal surgical methods for harvesting, processing, and reinjecting, Gir et al6 completed an extensive literature review. Their results show the variability of current surgical techniques with current literature only supporting general principles and not any specific technique. Furthermore, no experimental or theoretical studies have analyzed how the different surgical methods alter the microenvironment surrounding the graft or how the microenvironment affects graft retention.
In this context, we define a model as a conceptual and mathematical representation of a phenomenon that has occurred in the past in an attempt to predict how it will occur in the future as specific variables change. Modeling has been critical for many advances in plastic surgery. Our group has modeled both skin expansion and the mechanical forces involved in vacuum-assisted closure devices.16,17 These models have helped enhance our understanding of the biological effects and medical uses of mechanical forces. Modeling provides the theoretical framework for testing theories. This study aims to identify the role of the recipient site in fat grafting and create a model to serve as a scientific basis to analyze the variables related to the recipient site and graft retention.
Grafted fat initially lacks vascular support and must receive oxygen and nutrients by diffusion from nearby capillaries until neovascularization occurs.18 Oxygen seems to be the critical molecule required for cell survival. Low oxygen partial pressures in the center of the graft can lead to cell necrosis. Attempts to improve graft retention have largely been based on the “cell survival theory,” which states that long-term graft volume consists primarily of grafted adipocytes that have survived the entire procedure.15 This theory has generally been accepted18,19 and has directed most efforts to maintaining adipocytes viability through improved harvesting, processing, and reinjecting techniques.19–21 Studies supporting the cell survival theory claim that the “viable zone” (40% adipocyte survival) reaches as far down as 0.2 cm from the periphery of the grafted tissue.22 These conclusions are based mostly on morphological observations with H&E staining. However, judging adipocyte health by shape or nuclear appearance can be misleading, and histologic sections are too thin to show most nuclei of healthy adipocytes.23 Moreover, the “cell survival theory” may fail to get to the complex phenomena occurring in fat grafting. Fat grafts are not pure aggregates of adipocytes, but a mixture of adipocytes, preadipocytes, endothelial cells, pericytes, stem cells, fibroblasts, inflammatory cells, and matrix.
Using immunostain for perilipin, a method for determining adipocyte viability,24 Eto et al23 in the Yoshimura Lab tested the cell survival theory and concluded that a dynamic remodeling of grafted adipose tissue (AT) occurs. In hypoxic cell cultures, they demonstrated that adipocytes cannot survive more than 1 day of severe ischemia-mimicking conditions (1% O2 with no serum), whereas adipose-derived stromal cells (ASCs) remained viable for up to 72 hours. In a second experiment, the inguinal fat pad of a mouse was grafted to the scalp. Only the peripheral area (surviving zone; <0.03 cm from the edge) of the graft had a high survival rate of both adipocytes and ASCs. In a deeper (regenerating) zone, most adipocytes did not survive more than 1 day, but ASCs survived and eventually provided new adipocytes. By day 3, the number of proliferating cells increased, and by day 7, they found an increased thickness of the zone with viable adipocytes. At the center of the graft, no AT survived, and macrophages removed the dead cells25; this was named the “necrotic zone.”
Recent studies support this “host replacement theory.” Rigamonti et al26 suggest that 4.8% of preadipocytes are replicating at any time, and 1–5% of adipocytes are replaced each day. When mouse AT oxygenation reaches less than 65% of baseline, adipocytes undergo apoptosis in 24 hours; however, ASCs can survive for multiple days in severe hypoxia.27 Hypoxia is known to enhance ASC proliferation.28,29 Injured adipocytes release fibroblast growth factor-2, which stimulates ASC proliferation and hepatocyte growth factor, contributing to the regeneration of AT.30 The retention of grafted fat largely depends on the distance metabolites must travel to reach the center of the graft and on the depths of the surviving and regenerating zones.
MATERIALS AND METHODS
We searched Pubmed for original articles with the term “fat grafting” in the title or abstract to determine which aspects of the microenvironment surrounding fat grafts affect retention. We modeled the relationship between oxygen consumption by metabolizing fat tissue and oxygen delivery via diffusion for grafted fat cylinders of varying radii. We called this the “Microribbon Model.”
In a steady state, oxygen delivery matches oxygen consumption, and oxygen must diffuse off erythrocytes, through the capillary walls, through the extracellular space, and into the grafted cells. To optimize the potential for oxygen delivery, the vascular perfusion must be functioning properly, and several articles propose that an increased interstitial fluid pressure (IFP) during fat grafting might restrict perfusion. To determine the physiological plausibility of this hypothesis, we modeled the relationship between fluid accumulation, IFP, and perfusion. We called this the “Fluid Accommodation Model.”
To study how the information from the first 2 models can be used to optimize the fat grafting procedure, we explored which existing fat grafting procedures were attempting to optimize the variables in our models. Although several articles emphasized a biological approach with cytokines and stem cells, only external volume expansion (EVE) emphasized enhancing oxygen delivery. Therefore, we modeled how EVE could prepare the recipient site to allow the critical variables in the first 2 models to be optimized during fat grafting. We called this the “EVE Effect Model.” The information from these models comes from our calculations derived from established equations, relationships, and constants.
The literature to date concludes that oxygen delivery seems to be the most crucial molecule for fat graft survival. The thickness of the exterior rim of viable cells in multicell spheroids increases linearly with the theoretical oxygen diffusion distance.31 Oxygen diffusion is the limiting variable in determining cell survival in spheroids.32 Therefore, it seems that the core principle of fat graft survival is that oxygen concentration at any point in a graft is a function of the oxygen concentration of the surrounding capillaries, the diffusion rate of oxygen to reach that point in the tissue, the distance from the oxygen source, and the metabolic rate. In other words, at every point within a fat graft, there is a race between the rate at which oxygen is needed by the cells and the rate at which oxygen can be delivered by the capillaries and diffused through the AT.
According to standard principles in physiology, the metabolic rate of a given section of AT is directly proportional to its volume (V). However, the diffusion rate of any substance is directly proportional to the surface area (SA) over which diffusion takes place, and the SA:V ratio of any interior section of a cylinder is (2/radius). Therefore, as the radius of a cylindrical injection of AT increases, the SA:V ratio decreases, and oxygen’s diffusion rate cannot meet the tissue’s metabolic needs. In addition, diffusion is related to the square of the distance between the oxygen source and where it is consumed. When the distance is increased by a factor of 2, the delivery of oxygen is decreased by a factor of 4.
Using diffusion and metabolism equations and biological and physical constants,31–37 we modeled the theoretical borders between the surviving, regenerating, and necrotic zones for fat grafts of different radii (Appendix 1) (Fig. 1). According to the Microribbon Model in standard human conditions, the largest fat microribbon with no necrotic zone would have a radius of 0.16 cm. Such a graft would have a surviving zone of 0.03 cm and a regenerating zone of 0.13 cm. As graft radius increases beyond this point, the necrotic zone grows rapidly.
This Microribbon Model correlates well with experimental data. When multicell spheroids were cultured in excess medium, the spheroids ceased to expand at a radius of 0.15 cm.38 Carpaneda and Ribeiro22 suggest that, in humans, only the region 0.15 cm from the edge of a fat graft retains a significant percent of its volume. Current successful method descriptions suggest a 0.13-cm limit for the radius of reinjected fat.39,40 Multiple studies report negative correlation between fat graft particle width and retention percentage.8,15,25,41 Long-term fat graft retention requires small volumes of fat to be diffusely distributed into a well-vascularized recipient site through well-separated tunnels.1,4,8,41–43 If the microinjections are not diffusely distributed in the recipient site, they will coalesce, forming particles too wide to survive.25,39,40
Fat graft survival is also largely dependent on the vasculature’s ability to delivery oxygen blood through the capillaries surrounding the graft.39,40,44,45 Several surgeons have suggested that injecting too much fat into a small recipient site can increase IFP enough to constrict capillaries, inducing ischemia in the grafted tissues.5,15,39,40,45 Guyton46 demonstrated that, for up to a certain volume, interstitial fluid can accumulate in a tissue without significant IFP increase, but beyond that range, any additional fluid causes drastic IFP increases, quickly reaching levels associated with compartment syndrome.47 Milosevic et al48 also demonstrated that capillary perfusion decreases with increasing IFP. Therefore, it is recognized that fluid accumulation can lead to increased IFP and that increased IFP can lead to decreased capillary perfusion.
Using these relationships, we modeled the change in relative capillary perfusion as a function of IFP and interstitial fluid accumulation to determine if increased IFP during fat graft is enough to limit capillary perfusion and oxygen delivery (Fig. 2). According to this Fluid Accommodation Model, a given tissue compartment can accommodate about 60% of its weight in interstitial fluid before reaching a critical IFP (IFPC) of 9 mm Hg, beyond which, any additional fluid causes a drastic IFP increase and capillary perfusion decrease. It is important to recognize that this 60% accommodation is a generalized estimation, which will change with differences in the compliance of tissues; therefore, the IFP could be monitored intraoperatively if excess fat injections could be a possibility.39,40 This IFPC closely correlates with recent suggestions of IFP-based fat grafting stop points of 9–10 mm Hg.39,40,49,50 Increased IFP may also inhibit retention of grafted cells by mechanical compression, which induces apoptosis and regulates cytokine release.51 Therefore, interstitial volume, compliance, and vascularity determine how many microribbons of fat can be dispersed before increasing IFP enough to significantly reduce perfusion and cell survival.
Mechanical forces can induce angiogenesis, adipogenesis, and increased subcutaneous tissue thickness and compliance.16,39,40,45,52–58 Our group previously studied the mechanism behind EVE’s effects54 and found that the macroscopic swelling is likely due to deformation of the extracellular matrix, which induces tension on the cells anchored to extracellular matrix fibers. This micromechanical strain is transferred to the cytoskeleton,59 where it acts as a gate-control signal to induce proliferation.60 EVE-induced ischemia activates the hypoxia inducible factor -1α/vascular endothelial growth factor pathway to induce vascular remodeling, angiogenesis, and cell proliferation.55 Adipogenesis can be induced by lymphedema or water-rich empty proteinaceous matrices.61–69 Inflammation promotes these processes.70
Khouri et al56 developed a suction-based EVE bra (BRAVA) that noninvasively induces long-term breast growth in humans.71 It uses cyclical forces, which have a greater effect than continuous forces.16 Daily BRAVA-use induces temporary edema and angiogenesis and sustained increases in subcutaneous tissue thickness and compliance.39,45,56 Once fat grafting to the breast was more accepted and understood, BRAVA was proposed for application in preparation for fat grafting. Pre-expansion and resultant augmentation had a strong linear correlation (R2 = 0.87), and pre-expansion allowed significantly more AT to be grafted and retained than what was reported in a meta-analysis of 6 other published reports on fat graft breast augmentation without pre-expansion (P < 0.00001).45 Preoperative expansion also has several clinical applications in breast augmentation and reconstruction (Khouri et al, unpublished data, 2014).5,39,40,45,49,72,73
To understand the effectiveness of EVE devices for fat grafting, we must consider the ratio of grafted fat to recipient site volume. If the original recipient site is 100 mL and noncompliant, and 30 mL of AT are to be grafted, there is no need for pre-expansion because, with a 30% increase, the AT can be diffusely microinjected. If the original recipient site is 100 mL, and the volume of AT to be grafted is 90 mL, this 90% increase cannot be done without overcrowding, which would cause coalescence, increased IFP, reduced perfusion and oxygen delivery, thinner surviving and regenerating zones, and significant volume loss (Fig. 3A). However, our EVE Effect Model predicts that a tight 100-mL recipient site can be transformed into a compliant 300-mL site and, according to the Starling equation, cause edema influx. Because the fat microribbons can be diffusely dispersed into the pre-expanded tissue, less coalescence occurs and more AT can be grafted before reaching IFPC. As IFP increases, the Starling equation dictates that interstitial fluid is reabsorbed, allowing IFP to quickly return to baseline levels (Fig. 3B).
Our EVE Effect Model also predicts that the preoperative cyclical negative pressure treatment increases the host vascular density and diameter, increasing total oxygenated blood delivery, decreasing the mean distance each oxygen molecule must diffuse to reach the center of a grafted microribbon, and accelerating graft revascularization: a major determinant of volume retention (Fig. 4).25,42,73–76
We have presented 3 models to predict how recipient site vascularity, volume, and compliance determine fat graft retention by regulating oxygen delivery via perfusion and diffusion. To the best of our knowledge, this is the first study to mathematically model the essential variables relating to oxygen delivery and graft retention. The information from these models comes from our calculations derived from established equations, relationships, and constants. Our Microribbon Model suggests that any fat injection with a radius greater than 0.16 cm in standard human conditions will have a zone of central necrosis. Our Fluid Accommodation Model suggests that interstitial fluid injections that cause IFP to increase past IFPC will restrict perfusion. Our EVE Effect Model explains how the information from the first 2 models can be used to optimize the fat grafting procedure. It predicts that preoperative EVE increases recipient site vascularity, volume, and compliance, allowing more AT to be successfully grafted. For grafting small volumes of fat into large, compliant, highly vascularized recipient sites, the recipient bed will likely accept the graft even if the surgeon does not specifically consider each of the variables in these models. However, for grafting large volumes of fat into small, restricted, poorly vascularized recipient sites for procedures such as total breast reconstruction, or irradiated tissues, surgeons must optimize each of the variables related to graft retention. None of these models can predict fat graft retention on their own, but taken together, they enhance our understanding of the biological events occurring during fat grafting and allow us harness this knowledge to enhance surgical outcomes.
Modeling provides the theoretical framework for testing theories, so these models require experimental data to be further accepted. To test the Microribbon Model, experiments similar to the ones performed by Eto et al23 would have to be reproduced, but pO2 would have to be measured at various depths within grafts or cylindrical cell cultures of various radii. To test the Fluid Accommodation Model, studies would have to measure IFP, perfusion, and pO2 as fluid is injected into living tissue. To test the EVE Effect Model, a complex set of experiments would be required. More importantly, to truly test the effects of EVE in fat grafting, a large prospective randomized controlled trial should be performed. It is hoped that these studies will lead to long-term prospective studies in humans.
Our models predict the following: that fat injections larger than 0.16 cm in radius will have an area of central necrosis; that, in fat grafting, IFPs greater than 9 mmHg will cause decreased capillary perfusion; and that EVE can enhance tissue volume, vascularity, and compliance, allowing more AT to be successfully grafted.
We thank Kazi Zein Hassan for assisting with figure production and Chenyu Huang, MD, PhD, for assisting with editing the text.
1. Coleman SR. Structural fat grafts: the ideal filler? Clin Plast Surg. 2001;28:111–119
2. Kanchwala SK, Holloway L, Bucky LP. Reliable soft tissue augmentation: a clinical comparison of injectable soft-tissue fillers for facial-volume augmentation. Ann Plast Surg. 2005;55:30–35 discussion 35
3. Bucky LP, Kanchwala SK. The role of autologous fat and alternative fillers in the aging face. Plast Reconstr Surg. 2007;120(6 Suppl):89S–97S
4. Khouri R, Del Vecchio D. Breast reconstruction and augmentation using pre-expansion and autologous fat transplantation. Clin Plast Surg. 2009;36:269–280, viii
5. Khouri RK, Smit JM, Cardoso E, et al. Percutaneous aponeurotomy and lipofilling: a regenerative alternative to flap reconstruction? Plast Reconstr Surg. 2013;132:1280–1290
6. Gir P, Brown SA, Oni G, et al. Fat grafting: evidence-based review on autologous fat harvesting, processing, reinjection, and storage. Plast Reconstr Surg. 2012;130:249–258
7. Ersek RA. Transplantation of purified autologous fat: a 3-year follow-up is disappointing. Plast Reconstr Surg. 1991;87:219–227
8. Niechajev I, Sevćuk O. Long-term results of fat transplantation: clinical and histologic studies. Plast Reconstr Surg. 1994;94:496–506
9. Rubin A, Hoefflin SM. Fat purification: survival of the fittest. Plast Reconstr Surg. 2002;109:1463–1464
10. Wolf GA, Gallego S, Patrón AS, et al. Magnetic resonance imaging assessment of gluteal fat grafts. Aesthetic Plast Surg. 2006;30:460–468
11. Zocchi ML, Zuliani F. Bicompartmental breast lipostructuring. Aesthetic Plast Surg. 2008;32:313–328
12. Delay E, Garson S, Tousson G, et al. Fat injection to the breast: technique, results, and indications based on 880 procedures over 10 years. Aesthet Surg J. 2009;29:360–376
13. Park S, Kim B, Shin Y. Correction of superior sulcus deformity with orbital fat anatomic repositioning and fat graft applied to retro-orbicularis oculi fat for Asian eyelids. Aesthetic Plast Surg. 2011;35:162–170
14. Choi M, Small K, Levovitz C, et al. The volumetric analysis of fat graft survival in breast reconstruction. Plast Reconstr Surg. 2013;131:185–191
15. Del Vecchio D, Rohrich RJ. A classification of clinical fat grafting: different problems, different solutions. Plast Reconstr Surg. 2012;130:511–522
16. Chin MS, Ogawa R, Lancerotto L, et al. In vivo acceleration of skin growth using a servo-controlled stretching device. Tissue Eng Part C Methods. 2010;16:397–405
17. Saxena V, Hwang CW, Huang S, et al. Vacuum-assisted closure: microdeformations of wounds and cell proliferation. Plast Reconstr Surg. 2004;114:1086–1096 discussion 1097–1098
18. Billings E Jr, May JW Jr. Historical review and present status of free fat graft autotransplantation in plastic and reconstructive surgery. Plast Reconstr Surg. 1989;83:368–381
19. Rohrich RJ, Sorokin ES, Brown SA. In search of improved fat transfer viability: a quantitative analysis of the role of centrifugation and harvest site. Plast Reconstr Surg. 2004;113:391–395 discussion 396–397
20. Cortese A, Savastano G, Felicetta L. Free fat transplantation for facial tissue augmentation. J Oral Maxillofac Surg. 2000;58:164–169; discussion 169–170
21. Piasecki JH, Gutowski KA, Lahvis GP, et al. An experimental model for improving fat graft viability and purity. Plast Reconstr Surg. 2007;119:1571–1583
22. Carpaneda CA, Ribeiro MT. Study of the histologic alterations and viability of the adipose graft in humans. Aesthetic Plast Surg. 1993;17:43–47
23. Eto H, Kato H, Suga H, et al. The fate of adipocytes after nonvascularized fat grafting: evidence of early death and replacement of adipocytes. Plast Reconstr Surg. 2012;129:1081–1092
24. Tansey JT, Sztalryd C, Gruia-Gray J, et al. Perilipin ablation results in a lean mouse with aberrant adipocyte lipolysis, enhanced leptin production, and resistance to diet-induced obesity. Proc Natl Acad Sci U S A. 2001;98:6494–6499
25. Smahel J. Experimental implantation of adipose tissue fragments. Br J Plast Surg. 1989;42:207–211
26. Rigamonti A, Brennand K, Lau F, et al. Rapid cellular turnover in adipose tissue. PLoS One. 2011;6:e17637
27. Suga H, Eto H, Aoi N, et al. Adipose tissue remodeling under ischemia: death of adipocytes and activation of stem/progenitor cells. Plast Reconstr Surg. 2010;126:1911–1923
28. Lee EY, Xia Y, Kim WS, et al. Hypoxia-enhanced wound-healing function of adipose-derived stem cells: increase in stem cell proliferation and up-regulation of VEGF and bFGF. Wound Repair Regen. 2009;17:540–547
29. Weijers EM, Van Den Broek LJ, Waaijman T, et al. The influence of hypoxia and fibrinogen variants on the expansion and differentiation of adipose tissue-derived mesenchymal stem cells. Tissue Eng Part A. 2011;17:2675–2685
30. Suga H, Eto H, Shigeura T, et al. IFATS collection: fibroblast growth factor-2-induced hepatocyte growth factor secretion by adipose-derived stromal cells inhibits postinjury fibrogenesis through a c-Jun N-terminal kinase-dependent mechanism. Stem Cells. 2009;27:238–249
31. Franko AJ, Sutherland RM. Oxygen diffusion distance and development of necrosis in multicell spheroids. Radiat Res. 1979;79:439–453
32. Venkatasubramanian R, Henson MA, Forbes NS. Incorporating energy metabolism into a growth model of multicellular tumor spheroids. J Theor Biol. 2006;242:440–453
33. Thomlinson RH, Gray LH. The histological structure of some human lung cancers and the possible implications for radiotherapy. Br J Cancer. 1955;9:539–549
34. Chow DC, Wenning LA, Miller WM, et al. Modeling pO(2) distributions in the bone marrow hematopoietic compartment. I. Krogh’s model. Biophys J. 2001;81:675–684
35. Croll TI, Gentz S, Mueller K. Modelling oxygen diffusion and cell growth in a porous, vascularising scaffold for soft tissue engineering applications. Chem Eng Sci. 2005;60:4924–4934
36. Goossens GH, Bizzarri A, Venteclef N, et al. Increased adipose tissue oxygen tension in obese compared with lean men is accompanied by insulin resistance, impaired adipose tissue capillarization, and inflammation. Circulation. 2011;124:67–76
37. Martin AD, Daniel MZ, Drinkwater DT, et al. Adipose tissue density, estimated adipose lipid fraction and whole body adiposity in male cadavers. Int J Obes Relat Metab Disord. 1994;18:79–83
38. Folkman J, Hochberg M. Self-regulation of growth in three dimensions. J Exp Med. 1973;138:745–753
39. Khouri RK, Rigotti G, Cardoso E, et al. Megavolume autologous fat transfer: part I. Theory and principles. Plast Reconstr Surg. 2014;133:550–557
40. Khouri RK, Rigotti G, Cardoso E, et al. Megavolume autologous fat transfer: part II. Practice and techniques. Plast Reconstr Surg. 2014;133:1369–1377
41. Carpaneda CA, Ribeiro MT. Percentage of graft viability versus injected volume in adipose autotransplants. Aesthetic Plast Surg. 1994;18:17–19
42. Coleman SR. Facial recontouring with lipostructure. Clin Plast Surg. 1997;24:347–367
43. Sommer B, Sattler G. Current concepts of fat graft survival: histology of aspirated adipose tissue and review of the literature. Dermatol Surg. 2000;26:1159–1166
44. Baran CN, Celebioğlu S, Sensöz O, et al. The behavior of fat grafts in recipient areas with enhanced vascularity. Plast Reconstr Surg. 2002;109:1646–1651; 1652
45. Khouri RK, Eisenmann-Klein M, Cardoso E, et al. Brava and autologous fat transfer is a safe and effective breast augmentation alternative: results of a 6-year, 81-patient, prospective multicenter study. Plast Reconstr Surg. 2012;129:1173–1187
46. Guyton AC. Interstitial fluid pressure. II. Pressure-volume curves of interstitial space. Circ Res. 1965;16:452–460
47. Styf J, Körner L, Suurkula M. Intramuscular pressure and muscle blood flow during exercise in chronic compartment syndrome. J Bone Joint Surg Br. 1987;69:301–305
48. Milosevic MF, Fyles AW, Hill RP. The relationship between elevated interstitial fluid pressure and blood flow in tumors: a bioengineering analysis. Int J Radiat Oncol Biol Phys. 1999;43:1111–1123
49. Khouri RK, Khouri RK Jr, Rigotti G, et al. Aesthetic applications of brava-assisted megavolume fat grafting to the breasts: a 9-year, 476-patient, multicenter experience. Plast Reconstr Surg. 2014;133:796–807
50. Khouri RK, Rigotti G, Khouri RK Jr, et al. Tissue-engineered breast reconstruction with brava-assisted fat grafting: a 7-year, 488-patient, multicenter experience. Plast Reconstr Surg. In press
51. Renò F, Sabbatini M, Lombardi F, et al. In vitro mechanical compression induces apoptosis and regulates cytokines release in hypertrophic scars. Wound Repair Regen. 2003;11:331–336
52. Agha R, Ogawa R, Pietramaggiori G, et al. A review of the role of mechanical forces in cutaneous wound healing. J Surg Res. 2011;171:700–708
53. Liu PH, Lew DH, Mayer H, et al. Micro-mechanical forces as a potent stimulator of wound healing. J Am Coll Surg. 2004;199:57
54. Heit YI, Lancerotto L, Mesteri I, et al. External volume expansion increases subcutaneous thickness, cell proliferation, and vascular remodeling in a murine model. Plast Reconstr Surg. 2012;130:1–8
55. Lancerotto L, Chin MS, Freniere B, et al. Mechanisms of action of external volume expansion devices. Plast Reconstr Surg. 2013;132:569–578
56. Khouri RK, Schlenz I, Murphy BJ, et al. Nonsurgical breast enlargement using an external soft-tissue expansion system. Plast Reconstr Surg. 2000;105:2500–2514
57. Sutcliffe MC, Davidson JM. Effect of static stretching on elastin production by porcine aortic smooth muscle cells. Matrix. 1990;10:148–153
58. Lujan-Hernandez JR, Lancerotto L, Nabzdyk C, et al. Adipogenesis by External Volume Expansion. March 9, 2014 New York, New York PSRC Annual Meeting
59. Ingber DE. Tensegrity: the architectural basis of cellular mechanotransduction. Annu Rev Physiol. 1997;59:575–599
60. Ingber D. How cells (might) sense microgravity. FASEB J. 1999;13(Suppl):S3–S15
61. Zampell JC, Aschen S, Weitman ES, et al. Regulation of adipogenesis by lymphatic fluid stasis: part I. Adipogenesis, fibrosis, and inflammation. Plast Reconstr Surg. 2012;129:825–834
62. Aschen S, Zampell JC, Elhadad S, et al. Regulation of adipogenesis by lymphatic fluid stasis: part II. Expression of adipose differentiation genes. Plast Reconstr Surg. 2012;129:838–847
63. Harvey NL, Srinivasan RS, Dillard ME, et al. Lymphatic vascular defects promoted by Prox1 haploinsufficiency cause adult-onset obesity. Nat Genet. 2005;37:1072–1081
64. Cronin KJ, Messina A, Knight KR, et al. New murine model of spontaneous autologous tissue engineering, combining an arteriovenous pedicle with matrix materials. Plast Reconstr Surg. 2004;113:260–269
65. Dolderer JH, Abberton KM, Thompson EW, et al. Spontaneous large volume adipose tissue generation from a vascularized pedicled fat flap inside a chamber space. Tissue Eng. 2007;13:673–681
66. Dolderer JH, Thompson EW, Slavin J, et al. Long-term stability of adipose tissue generated from a vascularized pedicled fat flap inside a chamber. Plast Reconstr Surg. 2011;127:2283–2292
67. Abberton KM, Bortolotto SK, Woods AA, et al. Myogel, a novel, basement membrane-rich, extracellular matrix derived from skeletal muscle, is highly adipogenic in vivo and in vitro. Cells Tissues Organs. 2008;188:347–358
68. Kelly JL, Findlay MW, Knight KR, et al. Contact with existing adipose tissue is inductive for adipogenesis in matrigel. Tissue Eng. 2006;12:2041–2047
69. Stillaert FB, Abberton KM, Keramidaris E, et al. Intrinsics and dynamics of fat grafts: an in vitro study. Plast Reconstr Surg. 2010;126:1155–1162
70. Thomas GP, Hemmrich K, Abberton KM, et al. Zymosan-induced inflammation stimulates neo-adipogenesis. Int J Obes (Lond). 2008;32:239–248
71. Schlenz I, Kaider A. The Brava external tissue expander: is breast enlargement without surgery a reality? Plast Reconstr Surg. 2007;120:1690–1691
72. Del Vecchio DA, Bucky LP. Breast augmentation using preexpansion and autologous fat transplantation: a clinical radiographic study. Plast Reconstr Surg. 2011;127:2441–2450
73. Uda H, Sugawara Y, Sarukawa S, et al. Brava and autologous fat grafting for breast reconstruction after cancer surgery. Plast Reconstr Surg. 2013;133:203–213
74. Smahel J, Meyer VE, Schutz K. Vascular augmentation of free adipose tissue grafts. Eur J Plast Surg. 1990;13:163–168
75. von Heimburg D, Lemperle G, Dippe B, et al. Free transplantation of fat autografts expanded by tissue expanders in rats. Br J Plast Surg. 1994;47:470–476
76. Yamaguchi M, Matsumoto F, Bujo H, et al. Revascularization determines volume retention and gene expression by fat grafts in mice. Exp Biol Med (Maywood). 2005;230:742–748
The following formulas model O2 diffusion into a metabolizing cylinder of tissue33:
1. C = C0 − (M/4D)[(R2 − r2) − a2 ln(R2/r2)]
2. a2 = [1 + ln(R2/a2)] = R2 − (Rcrit)2
3. Rcrit = sqrt(4DC0/M)
C = [O2] at a radial distance (r) cm from the center of a cylinder (μmol/mL)
C0 = [O2] at the surface of a cylinder of radius R cm (μmol/mL)
CS = min [O2] at which ASCs can survive (μmol/mL)
CA = min [O2] at which adipocytes can survive (μmol/mL)
M = metabolic rate [μmol/(mL × min)]
D = O2 diffusion coefficient (cm2/min)
Rcrit = largest radius (R) such that ASCs survive throughout the graft (cm)
a = max radial distance (r) at which [O2] = 0 when R > Rcrit (cm)
rma = min distance from center (r) at which adipocytes can survive (cm)
Using these equations and established constants,23,31–34 we calculated that Rcrit = 0.16 cm.
When R = Rcrit, rma = 0.13 cm.