on skin expansion
TRANSCRIPT
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Research Paper
On skin expansion
Djenane C. Pamplonaa,n, Raquel Q. Vellosoa, Henrique N. Radwanskib
aLaboratory of Membranes and Biomembranes, PUC-Rio, Rio de Janeiro, BrazilbIvo Pitanguy Institute of Plastic Surgery, Rio de Janeiro, Brazil
a r t i c l e i n f o
Article history:
Received 22 January 2013
Received in revised form
18 March 2013
Accepted 26 March 2013
Available online 19 April 2013
Keywords:
Characterization of human skin
Finite elements
Skin expansion
Biomembranes
Skin expanders
Elastic foundation
Constitutive equation
nt matter & 2013 Elsevie.1016/j.jmbbm.2013.03.023
to: Laboratory of Membr47.: [email protected],
a b s t r a c t
This article discusses skin expansion without considering cellular growth of the skin. An
in vivo analysis was carried out that involved expansion at three different sites on one
patient, allowing for the observation of the relaxation process. Those measurements were
used to characterize the human skin of the thorax during the surgical process of skin
expansion. A comparison between the in vivo results and the numerical finite elements
model of the expansion was used to identify the material elastic parameters of the skin of
the thorax of that patient. Delfino's constitutive equation was chosen to model the in vivo
results. The skin is considered to be an isotropic, homogeneous, hyperelastic, and
incompressible membrane. When the skin is extended, such as with expanders, the
collagen fibers are also extended and cause stiffening in the skin, which results in
increasing resistance to expansion or further stretching. We observed this phenomenon
as an increase in the parameters as subsequent expansions continued. The number and
shape of the skin expanders used in expansions were also studied, both mathematically
and experimentally. The choice of the site where the expansion should be performed is
discussed to enlighten problems that can lead to frustrated skin expansions. These results
are very encouraging and provide insight into our understanding of the behavior of
stretched skin by expansion. To our knowledge, this study has provided results that
considerably improve our understanding of the behavior of human skin under expansion.
& 2013 Elsevier Ltd. All rights reserved.
1. Introduction
The present work intends to describe and raise considera-tions about the surgical procedure of skin expansion. Skinexpansion is a physiological process based on the ability ofhuman skin to increase its superficial area in response to astress (Van Rappard et al., 1988). The surgical procedure isperformed by implanting skin expanders under the subcuta-neous tissue. Skin expanders are silicon bags of different shapesand sizes, which are infiltrated with a saline solution. The skinrelaxes after a period of time, and if the imposed deformation is
r Ltd. All rights reserved.
anes and Biomembranes/
[email protected], djen
maintained, the resulting stress, and consequently the internalpressure, decreases. The physiology of skin expansion considersboth the stretching of the skin and the relaxation process used toobtain an extra flap of skin that possesses the required char-acteristics. For example, skin expansions are used to reconstructburned areas and breasts after mastectomy as well as to hidescars and defects. Several papers have been published on thebehavior of the skin due to expansion. Beauchene et al. (1989)presented an animal experiment performed on 24 animals thatexpanded the skin of the peritoneal cavity for 32 days. Theauthors concluded that the skin tension increased dramatically
CTC, Marques de São Vicente 225, 22451-900 RJ, Brazil.
[email protected] (D.C. Pamplona).
Fig. 1 – Expansion in the stomach.
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at the time of inflation but fell to almost the control values at theend of 32 days and the skin thickness, which initially decreased,returned to normal by the end of the experiment. Silver et al.(2003), in an overview on the mechanobiology underlying skingrowth, affirm that the tension in the skin affects the skinbiology and is responsible for the growth of the skin becausetensile stresses applied to skin appear to stimulate cellulargrowth. Buganza Tepole et al. (2011) established a new computa-tional model for stretch-induced skin growth during tissueexpansion. To model skin growth, the authors adopted themultiplicative decomposition of the deformation gradient intoan elastic and a growth portion. The growth was characterizedas an irreversible, stretch-driven, transversely isotropic processparameterized in terms of a single scalar-valued growth multi-plier, the in-plane area growth. The analysis was performed bynumerically simulating the process of gradual tissue expanderinflation. In particular, they compared the spatiotemporal evolu-tion of the area growth, elastic strains, and residual stresses forfour commonly available tissue expander geometries. Zollneret al. (2012) presented a continuum model for skin growth thatsummarizes the underlying mechanotransduction pathwayscollectively in a single phenomenological variable, the strain-driven area growth. To simulate the process of tissue expansionin an anatomically exact geometry, they created a finite elementmesh from three-dimensional computer tomography images ofa child. They only modeled the tissue expander implicitly bycontrolling the expander pressure. However, the interplaybetween the mechanics and the biology during tissue expansionremains unquantified. The authors maintain that, during expan-sion, the epidermis (0.06 to 1mm) undergoes significant thicken-ing and the dermis (1 to 4mm) and subcutaneous tissuebecomes significantly thinner. Although there is some tensiontransfer to the epidermis, the maximum tension occurs in thedermis, which explains why there is a significant thinning of theskin in some models, including Pamplona and Carvalho (2012).The highlighted studies indicate that skin growth and itsthickness during the expansion process are controversial issuesthat requiremore research to clarify the process. In this research,the measured pressure inside the skin expander dropped dra-matically in the first days and even in the first hours ofexpansion, due to the viscoelastic properties of the skin. Thisdiscontinuity in the stresses levels during the studied expansionprocess is the principal reason for not considering the growth ofthe skin in this model. We attributed this skin behavior torelaxation due to viscoelastic properties and not due to structuralor molecular changes. In real tissue expansion, the externalcontrol parameter is the expander volume, not the internalpressure. Some simulations display creep under constant load-ing, but clinical tissue expansion may display relaxation underconstant deformation instead; therefore, these models do notaccount for the fact that the tensile stress varies due torelaxation. In practice, it can be seen that if an expansion isfrustrated in the initial steps, it stops before the expectednumber of expansions, and after the skin expander is removed,there is no extra flap of skin. The skin returns to its original size.When the skin expansion is completed, at the moment of thesurgery, the skin immediately recovers part of the expandedsurface area, given that, it is necessary to consider the need of20–30% of extra tissue due to the dog ear, and mechanicalrecovery of the skin (Padam, 2009; Bhandari, 2009). It appears
that only one to two months after the reconstruction, the skingains its original thickness. The site of the expansion can be veryimportant for attaining the extra flap of skin (Pamplona andMota, 2012). The present article suggests the type, number andvolume of skin expanders necessary to obtain the extra amountof skin to repair a certain medical problem and also proposes aconstitutive equation to describe and predict the behavior of theexpanded skin. We also show the importance of the site chosenfor the expansion to assure that the whole procedure can besuccessfully accomplished.
2. Planning the skin expansion
Skin expansions are usually performed near the places wherethe skin is required to provide skin of the same color, texture,sensibility and structure as the skin to be removed, such as inthe cases of scars, burns and so on. The question that isconstantly raised during expansion is whether it will createenough skin; in other words, whether the achieved expansionis adequate to resurface the defect (Padam, 2009). Thesequestions can be answered if one knows how much newtissue is required for the reconstruction in a given conditionand if this required tissue (surface area) can be calculated inrelation to the volume injected under of the expanded tissue.Additionally, the site of expansion can be very important toattain the extra flap of skin (Pamplona and Mota, 2012). Skinexpanders are silicone bags of several shapes (circular,square, oval, croissant and rectangular) and internal volumesthat are implanted under the subcutaneous tissue in differentparts of the body. Through an incision, the surgeon insertsthe skin expander and its valve under the skin. After theincision is closed, a saline solution, which should be equiva-lent to 10% of the nominal volume of the skin expander(Radwanski, 2012), Vn, is injected into the skin expander usinga needle in the implanted valve. Some days after the surgery,the process of expansion begins, and in this way the processof cicatrization is guaranteed. During the skin expansionprocedure, a certain volume of saline solution is injected intothe expander every week. As the solution is injected, the skinexpands due to the increase of pressure inside the expanderproducing stresses in the skin and, consequently pain in thepatient. Because of the viscoelastic properties of the skin, theskin relaxes after some time, diminishing the pressure insidethe expander and, the pain of the patient. After a week, thereis no measurable pressure inside the expander. Fig. 1 shows acomplete expansion in the stomach with a croissant skinexpander.
Fig. 2 – Experimental apparatus.
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2.1. The methodology to choose the number and sizes ofskin expanders
The first step is to measure the amount of superficial area, Sd,of skin required to resurface the defect. To cover the defectsurface, it is necessary to obtain 20% to 30% more tissue byexpansion due to dog ear and skin retraction that occurs afterthe removal of the skin expander. The excess tissue also takescare of the retraction of the skin itself. Therefore, the surfacearea to be obtained by expansion is represented by Sd
* . Thissuperficial area has to be equal or smaller than the size of theflap of skin obtained by expansion using the formulas and tablesthat are developed in this research. Note that the extra flap ofskin, Sf, is the superficial area of the expanded skin minus thebase of the expander because this region must be covered againwith skin
Sf≥Sn
d ¼ 1:3� Sd ð1Þ
The superficial area of the extra flap obviously dependson the amount of injected liquid, which has an internalvolume of Vi.
A rectangular skin expander is a parallelepiped of basea�b and height c. The extra flap of skin, Sf, is related to theinternal volume, Vi, by the following mathematical formula
Sf ¼2� ðaþ bÞ
a� bVi ð2Þ
A round skin expander has a radius a and height h. Unlikethe rectangular skin expander, the relationship betweenSf and Vi is nonlinear for round expanders because the valueof h changes nonlinearly depending on the infiltrated volume.The extra flap of skin, Sf, is related to the internal volume, Vi,by the following formula obtained by Gerolamo Cardomo inhis book Ars Magna (1545)
Sf ¼ π � a2 � β2;
β¼ ð4� Cþ 4�ffiffiffiffiffiffiffiffiffiffiffiffiffiffi4þ C2
pÞ3=2−4
2� ð4� Cþ 4�ffiffiffiffiffiffiffiffiffiffiffiffiffiffi4þ C2
pÞ1=3
C¼−6� Vi
π � a3ð3Þ
The formulas for the extra flap of skin were obtainedmathematically; therefore, it is necessary to verify if theresults obtained are compatible with reality. To do so, anexperimental apparatus was developed with a rigid acrylicbase where two skin expanders were attached. One expanderwas round (Vn of 200 ml), with radius a¼4.8 cm, and heighth¼4.1 cm, and the other was rectangular (Vn of 240 ml), withbase a¼9.6 cm, b¼5.9 cm, and height c¼5.0 cm (see Fig. 2). Alatex membrane covered the skin expanders to simulatethe skin.
The superficial surface was obtained and measured with a3D scanner for every 50 ml of injected liquid. Using thesoftware Rhinoceros 4, the internal volume and superficialarea were obtained. The scanned surfaces can be seen inFigs. 3 and 4.
2.2. Results for choosing the number and sizes of the skinexpanders
The experimentally obtained extra flap of skin, Sfn, is the
measured surface minus the area of the basis of the skin
expander because this surface has to be recovered with skin.The following results enable us to realize the differencesbetween the results obtained by a mathematical formula andthose obtained in a more realistic way with a 3D scanner.Tables 1 and 2 show the comparison between the extra flapmeasured with the scanner (Sf
n) and the extra flap calculatedfrom the formula (Sf) for each injected volume (Vi). The valuemeasured by the scanner when there is no liquid inside theexpander is due to the existing wrinkles on the flat membrane,as seen on the left in Figs. 3 and 4 (for Vi of 0 ml). In reality, theextra flap that can be used for the reconstruction is only 2/3 ofthe obtained area because, as mentioned above, the skinretracts after the removal of the skin expander and flap itselfalso retracts.
It can be seen that the behavior of the expander whenfilled freely is different from when it is confined under themembrane or skin and over a rigid base. For the roundexpander, the difference in size between the measured andthe calculated extra flap is approximately 10%, where thecalculated value is larger. The difference in the results can bemore clearly observed for the rectangular expander becausethe corners of its shape when confined becomes rounded andnot sharp as in a parallelepiped, resulting in a smallersuperficial area.
3. The skin behavior and parameters
Skin expansion is usually performed near the site to bereconstructed and sometimes over fatty tissue. During anumber of weeks, the surgeon injects a certain volume ofsaline solution, Vi, into the skin expander, creating an inter-nal pressure. After a week, the internal pressure is reduced tozero and a new injection is possible. When monitoring theinternal pressure and the injected volume during several skinexpansions, we observed discrepancies depending on the siteof the expansion (Pamplona and Mota, 2012), which is thefocus of this portion of the present work.
Fig. 3 – Scanned surface of the circular expander for the internal volumes of 0 ml (left) and 200 ml (right).
Fig. 4 – Scanned surface of the rectangular expander for the internal volumes of 0 ml (left) and 240 ml (right).
Table 1 – Results for the circular skin expander, relatingthe injected volume (Vi) to the measured extra flap (Sf
*)and the calculated extra flap (Sf).
Vi Sf (cm2) Sf
* (cm2) 2/3Sf* (cm2)
0 0.00 0.00 0.00
50 8.44 5.69 5.63
100 18.76 20.09 12.51
150 44.20 38.83 29.47
200 67.07 59.23 44.71
Table 2 – Results for the rectangular skin expander,relating the injected volume (Vi) to the measured extraflap (Sf
n) and the calculated extra flap (Sf).
Vi Sf* (cm2) Sf (cm
2) 2/3Sf* (cm2)
0 0.00 0.00 0.00
50 22.26 27.36 14.84
100 41.47 54.73 27.48
150 71.21 82.10 47.48
200 94.52 109.46 63.01
240 105.09 131.35 70.06
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3.1. Experimental methodology to measure the skinbehavior
To monitor the skin expansion and check and identify thebehavior of the skin from successive skin expansions, it was
necessary to measure the pressure inside the skin expanderbefore, during, and after the injection of saline solution foreach expansion. For this purpose, an apparatus with apressure sensor coupled to the syringe used to perform theinjection of the liquid was developed, as seen in Fig. 5.
The results that follow are for three expansions in the samepatient, a female 20 years of age. One expansion was in theupper part of the thorax (Vn of 200ml), and the other two wereover the rib cage (Vn of 400ml). The volume related in the resultsis Vn because the nominal volumes of the skin expanders weredifferent, although all three expanders were rectangular
Vn ¼ Vi
Vn: ð4Þ
3.2. In vivo results
Fig. 6 shows that the skin expansion behaved very similarlyin the three sites. However, during the fourth expansion, seenin Fig. 7, the behavior of the first rib cage expander began todiverge from the other two. It is noted that the patient feltuncomfortable after this point, and due to the pain, thisexpansion did not succeed. The curves in both figures wereobtained through polynomial fitting.
Fig. 7 shows the differences in the behavior of the proceduredepending on the implantation site for the skin expander. Thisresult was expected, and the expansion over an elastic founda-tion is discussed in our previous article (Pamplona and Mota,2012).
Fig. 5 – Apparatus developed to measure the pressure inside the skin expander.
0
40
80
120
0.3 0.4 0.5 0.6 0.7
Rib Cage #1Rib Cage #2Thorax
V*-r
atio
of t
he in
filtra
ed v
olt
Fig. 6 – Results from the third skin expansion for all three
expanders, the line is a polynomial fitting for the three
expansions.
0
50
100
150
200
0.5 0.6 0.7 0.8 0.9
Rib Cage #1Thorax + Rib cage #2
V*-ratio of the infiltrated volume
Pres
sure
mm
Hg
Fig. 7 – Results from the fourth skin expansion for the three
expanders with polynomial fitting.
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3.3. Numerical methodology to characterize the skinbehavior parameters
To characterize the skin during expansion, it is necessary tomodel the procedure numerically, which can be accom-plished using the commercial finite elements software
program ABAQUS v 6.11. The goal was to identify the para-meters for Delfino's elastic constitutive equation and char-acterize the skin of the thorax for this patient. Theparameters of the constitutive equation for each expansionare not the same because the collagen fibers of the stretchedskin offer more resistance to expansion over the course of theexpansion, as observed by Lim et al. (2008).
To perform the numerical analysis, the finite element meshused was the linear hybrid membrane quadrilateral (M3D4).The control of the volume injected into the skin expander wasessential for modeling this medical procedure, which couldonly be performed in ABAQUS by using fluid finite elements(F3D4). In the fluid elements, the pressure was applied to oneunique node, which is called the reference of cavity node. Thispressure simulated the injection of the fluid into the skinexpander. The middle surface was the reference point for boththe membrane and the fluid elements. In the numericalanalysis, the final geometry of one expansion was used asthe initial geometry for the next expansion, where the stressand pressure were equal to zero because the internal pressuredropped to zero within a week due to the relaxation of the skin.Because the expansions were successive, the thickness ofthe modeled skin changed at the end of each expansion, butnot uniformly, and those values and the geometry wereexported for the new expansion. The results are presented inthe following figures and tables. The boundary was consideredto be simply connected and free to rotate. This boundarycondition was chosen after the careful observation of theexpanded skin to ensure that the skin at the boundary didnot exhibit peeling. The contact between the skin and theexpander was not considered in the numerical model. Skin isconsidered to be homogenous and hyperelastic, although itpossesses properties that are much more complex. This type ofmaterial is characterized through the Strain Energy Density, W,which is a function of the strain invariants I1, I2, and I3.Delfino's exponential function was chosen because it providedthe best fit for these type of data (Pamplona and Carvalho,2012). This equation was initially proposed to describe ahuman artery under several loads and is represented by theexpression in
W¼ cd
e½ðdðI1−3Þ=2Þ−1�n o
ð5Þ
Table 3 – Parameters for characterizing the skin of the thorax
Expansion Initial volume (ml) Final volume
(ml)
Final measu
(mmHg)
4 80 120 90
5 120 160 147
6 160 200 154
Vi-Infiltrated volume (ml)V* -
Pres
sure
(mm
Hg) Pressure (kPa)
Fig. 8 – Results for the best fit from the fourth to sixth skin
expansions, the dots are the measured pressures.
Fig. 9 – Finite elements results for the thicknesses (
Fig. 10 – Finite elements results for the principal stress
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here, c and d are the parameters of the material and I1 is thefirst strain invariant. Although Delfino's material model do notconsider nonlinear stiffening originating from fiber undulation,as the model proposed by Gasser et al. (2006), it was chosen forits simplicity of implementation in ABAQUS. To take thestiffing into account varying material parameters upon expan-sion were considered. The initial thickness of the skin, H¼8mm, was determined by the surgeon performing the surgery.For incompressible materials, such as biological tissues, I3¼1 isused for the third invariant, providing the ratio between theinitial thickness, H, and the final thickness, t.
3.4. The numerical results to characterize the skinbehavior parameters
To numerically model the expansions over the thorax, para-meters c and d for Delfino's constitutive equation, seen
, obtained by Fig. 8.
red pressure Final thickness
(mm)
c (MPa) d
3.96 0.0125 19.75
3.24 0.0380 27.00
2.76 0.1100 20.00
a) 80–120 ml, (b) 120–160 ml, and (c) 160–200 ml.
es (a) 80–120 ml, (b) 120–160 ml, and (c) 160–200ml.
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in Eq. (5), of the thorax were obtained and are shown inTable 3.
Fig. 8 shows the numerically generated curves from the best-fit parameters c and d for each expansion (shown in Table 3) andthe in vivo measured points for the three expansions. The fittingwas performed minimizing, using the least square method, thedifferences between the results in vivo and the ones obtained bythe finite elements simulation.
Fig. 9 shows the thinning of this skin as the expansionsproceeded and Fig. 10 shows the stresses that the skinunderwent at the end of each expansion in the thorax.
4. Discussion and conclusions
This work shows that the behavior of the expander whenfilled freely is different from when it is confined under amembrane or the skin. For the round expander, the calcu-lated value of the extra flap was approximately 10% greaterthan the measured value. The difference was more clearlyobserved in the rectangular expander because the corners ofits shape became rounded when confined and were not assharp as in a parallelepiped, resulting in a different super-ficial area. The difference for this case was approximately30%. The differences for small amounts of injected liquidwere not considered because there were wrinkles and anuneven deformation. It is very important to note that for thesame volume inserted, for example, 200 ml, the usable extraflap of skin obtained with the rectangular skin expander(63.01 cm2) is one-third greater than that obtained with theround skin expander (44.71 cm2), suggesting that the use ofthe rectangular expander is recommended. To obtain thesame amount of extra flap with the round skin expander, itwould be necessary to inject more liquid and increase thenumber times for the patient to be subjected to the proce-dure, increasing the patient's discomfort and pain.
This research indicated that the site chosen for the skinexpansion is of great importance. An expansion performedover an elastic foundation can be frustrated because theliquid will not expand the skin as expected but will rathercompress the elastic foundation. When this occurs, themeasured pressure inside the skin expander can be smallalthough there is a considerable amount of liquid beinginjected. The finite element portion of this research modeledthe skin expansion of the thorax and characterized the skinwith the parameters of Delfino's constitutive equation, usingthe same methodology of our previous article (Pamplona andCarvalho, 2012). The in vivo measurements showed that theskin relaxed after each expansion because all of the pressuremeasurements inside the expanders were reduced withinone week after the procedure. Although there are recentproposals supporting that tensile stress or the control of theexpander's internal pressure stimulates cellular growth, inreality, the external control parameter is the injected volume.As a result of the viscoelastic property of the skin, thepressure inside the expander drops dramatically in the firstdays and even in the first hours after expansion due torelaxation. This is the principal reason why skin growthwas not considered here, and why relaxation due to viscoe-lastic properties and not due to structural or molecular
changes was used to model the change in the geometry ofthe skin. It is important to note that as the skin is extended,such as with expanders or in other procedures that thin theskin, the collagen fibers are also extended and cause stiffen-ing in the skin, which results in it being more and moreresistant to expansion or further stretching. We observed thisphenomenon as an increase in parameter c of Delfino'sconstitutive equation with subsequent expansions. Theresults presented in this study are very promising in thisfield and extend our understanding of the expansion of skinand other biological tissues. Additional research will providethe optimal type, number, and volume of skin expanders forthe several shapes of skin expanders, as well as the fre-quency of expansions on several anatomic sites, which arefactors necessary to obtain a specified amount of skin for therepair of particular medical problems. The thickness of theskin can be measured using ultrasound techniques at thebeginning and end of each expansion, giving promising cluesto understand the process.
Acknowledgments
We are especially grateful to Professor Ivo Pitanguy and Dr.Henrique N. Radwanski and his staff, who have supportedour projects over the years. Santa Casa da MisericórdiaGeneral Hospital of Rio de Janeiro and the Ivo PitanguyInstitute of Plastic Surgery approved this research. Thefinancial support from Coordination of Improvement forHigher Level Education (CAPES; Grant number E: 0567-2006)and the Brazilian Council for Scientific and TechnologicalResearch (CNPq; Grant number 301832/2009-9) were essentialfor this research. We also extend special thanks for theagreement, support, and enthusiasm of the patients withoutwhom this work would not have been possible.
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