British ffournal of Plastic Surgery (197’0, zS, 3oo-3 ~4 CLOSURE OF RHOMBOIDSKIN DEFECTS: THE FLAP~, Foran’. OF LIMBERG AND DUFOURMENTEL ~s shownin rotated thr.c ~=: By G. D. LISTER, M..B., F.R.C.S.(Ed.& Eng.) areaP ,-x~ and T. GIBSON,D.Sc.,/VLB., F.R.C.S.(Ed. &Glasg.) thesepoints in turn de~ Westof ScotlandRegional Plastic andOral Surgery Unit, ~onsideratie CanniesburnHospital, Bears&n,Glasgow ¢xtensibilit) at right ang IN excising the majority of skin lesions, surgeonscreate an elliptical as at righta can be closed directly. As the lesions increase in size, however, there comes wheneither the long axis of the ellipse becomestoo long for the local cosmetic result, or the short axis too wide to permit direct suture. In instances the excisional outline maybe replanned and closure obtained with flap, until of course the defect becomesso large that cover can only be imported skin. Designingsuch local flaps, particularly whenthe secondarydefect is to directly, can tax the skill of the most experienced plastic surgeon. Only trial and error does he learn intuitively to judge the maximumtension under can suture the pardy devascularised flap and the absolute limits to which stretch the surroundingskin ; the art of designing such flaps takes long to is hard to teach. There are, however,2 exceptions to whichwe wouldlike to draw the flaps designed by Limberg(I 946, 1966, and 1967) and by Dufourmentel to close rhomboid defects. A rhombusis an equilateral parallelogram and regarded as an" ellipse with straight sides .". Rhomboidexcision has so over elliptical excision particularly whenthe defect is to be closed with a For example,less normalskin needsto be excised in the long axis, the design and of a straight-sided flap is far simpler than that of the round flap and rhomboid lends itself to the technique recommendedby Borghouts(1964) of histological lion of the specimen margins to check mmourclearance. The Limbergflap and the Dufourmentelflap are different in design and and will be described and discussed separately.
THE !LIMBERG FLAP its ownlenl The flap which Limbergdesigned for a rhomboid defect is one extension classical studies on transposed triangular flaps. Thus in Figures I and 2 the t~pthe skin dosed by interchanging the unequal flaps TLWand UVW.The design may ~houldif regarded as a rhomboidflap XUVWof the same size and shape as the defect into primary it is to be rotated. Fig.4, a). The flap whenused singly is suitable for closure only of rhomboid ° ° ° withthe po: angles of 60 and I2O ; in this paper such a defect is called a 60 rhomboid. ttowever,v rhombusis thus composedof 2 equilateral triangles and the short axis is length as each side. &rthe rho: In constructing the flap (Fig. I) the short diagonal is extended in one Lirnbe direction by its ownlength to the point V. A further incision VWparallel to anglesand equal to each of the sides completes the design. It will be evident that the l.imberg’s: UWis also equal to the short diagonal[ of the defect and therefore to all other modelsprc in the plan. All attractive aspect of this Limbergflap is that, oncethe len ~aut,slight: diagonal has been determined, the. remainder of the design maybe completed by ~hornboid calipers set to that length. 3oo CLOSURE OF RHOMBOID SKIN DEFECTS 301 For any given 6o° rhomboiddefect there are theoretically 4 Limbergflaps available FLAPS shownin FigUreo3. Oncethe most appropriate flap has been chosen and raised it is --~ ,hrou~h 6o and placed in the defect (Fig. 2). It will be seen that U and totat~u " o ~ a~proximatedin closing the secondary defect. If Nllows that the ease with which ~k~tsmrn dcpendscan be apposed on the relativedeterm~es availabfiky whether or andnot ex[ensib~itythe design isof appropriatethe skin. A ;major t~s ~nsiderafion. in planing should therefore be to seek out the d~ecfion of maxim~ ~tensibilit~ xn t~e skin ~r2und,~defect (gibso~ et ~l., z~69~. This line is usually right angmsto ~anger s ~mes~umson et at., ~97~) ana on merace it maybe regarded ~tical ~ at right angles to the crease ~es. It maybe readily determ~edclinically by pic~g ,~erecomes ii local z. In ained with be %ctis to Only on under to~ which long to mentel )gram and as some =l wit_ha local~i ~ design and [rhomboid ex’~i~ .lstologlcal ex~ ;ign and appli~~ V
Fro. i. Design of a Limberg flap. STUXrepresents a 60° rhomboid defect. SU is extended by ,ts ox :~ ;:ngth to V. "qW is then drawn parallel and equal to UX. Note that the distance between any 2 adjacent points in the design is identical. ~ne extension c and 2 the defee~jli~ : design may .a~.~ ~p the skin between finger and thumb. Havingfi~und that line, the points U and W :he defect into *h0uldif possible be placed on it ; they lie on the sameline as one of the sides of the primary defect and ~ flaps can be designed in this fashion for any one 6o° rhomboid omboid defe~~ Fig. 4, A). If the lesion is circular, the rhomboidcan be rotated giving ~ moreflaps 6o° rhomboid. "*’ith the points U and Win the sameline of maxim,amextensibility (Figs. 4, B and 4, c). ttowever, whenthe shape of the lesion already determinesthe positioning of the rhom- ~ort axis is the Midthese remarksare not appropriate and one selects the most suitable flap available ’.’or the rT, omboidso positioned. ~ded in one or gr parallel to Limbergpointed out that movingany flap inwflves but 2 processes, opening wound ingles and closing woundangles. Closing a woundangle produces a dog-ear or, in !ent that the dii~ I.imberg’s more precise term, a standing cone. Openingan angle in Limberg’spaper : to all other models produces a lying cone. This cannot forra in skin ; what usually occurs is a ~he length of th~ :aut, slightly depressed area around the angle. If for exampleone were to close the )e completed by.~ :homboiddefect shownin Figure I directly, dog-ears would form at points T and X 302 BRITISH JOURNALOF PLASTIC SURGERY and depressed areas at S and U. By adding the rhomboid flap for closure avoids any movementof angles T and S. This can bc of cosmetic value, i~ the deformations aroundthe other angles can bc placed in less obtrusive
v
B C LME FIG. 12. A, the flap designed in Figure I has been cut and transposed into the defect. post-operatively. C, z weeks post-operatively.
PRACTICALAPPLICATIONS Excisional Surgery. In most cases it is possible to decide in advance skin lesion will require elliptical excMonand direct closure, excision with closure or excision and distant skin cover. Fro. 4. \V Where doubt exists about the practicabilky of direct closure k is wise to Fig. I) lie, only the lesion with appropriate clearance as the initial step. If apposition then ~a ~e so s that direct closure is feasible further excision to create an ellipse suitably long to CLOSURE OF RHOMBOID SKIN DEFECTS 303 losure [ue, ;lV~
FIG. 3. In theory a choice of 4 Limberg flaps is available for any 6o° rhomboid defect.
LME
LME __ J__~ _ ~tefect. B, 6
vance a with local t;I..~. 4. With roughly circular lesions the rhombus should be so positioned that points U and W is wise to rlg: I) lie on the line of maximumextensibility. There are ~ possible ways in which the rhombus ;ition then ~n t~e so sited (A and B) and thus 4 flaps of this kind are available (C). This of course is bly long to applicable if the shape of the lesion dictates the position of the rhombus. 304 BRITISH JOURNAL OF PLASTIC SURGERY
Fro. 5. A, Two alterna- tive Limberg flaps have been designed. The 2 others theoretically avail- able would encroach upon the ear. B, Direct closure ~va8 felt to involve sutur- ing under undue tension. C, The more suitable flap was chosen, cut, transposed and sutured, (D and E) with good result.
the formation of permanent dog-ears is performed. If direct closure is form inapplicable no normal tissue has been discarded needlessly and a flap designed can be cut and rotated into position (Fig. 5). At the other extreme of applicability, it may be found that U and W .~ :s. 6. Adefect in the formof a parallel- :,r:am, havingacute angles of 60° and long ~,3~ twice that of the short, cart be closed ,.:.~., Limbergflaps. The 5 possible designs are shown. A
OSLlreJS ad a flap B C U and W ~" "- A parallelogram defect created by excision of a rodent ulcer closed by ~ Limbergflaps. Any distortion of the eyebrowor irregularity of the hairline was avoided by the choice of flaps. 306 BRITISH JOURNAL OF PLAsTIc SURGERY approximated even after undermining. The flap must then be replaced measured a~ alternative means of skin cover found. With a little experience, however, limbs pointi Occurs. should 2 sh~ The Simultaneous Use of 2 Limberg Flaps. Any defect which can be positio.n,,an as a parallelogram the long side of which is twice as long as the short side, is crc’:. :. angles of which are 6o°, may be closed with 2 Limberg flaps. ulcer o’~ occurred. On oc~ FiG. 8. A circular defect may undesirable be considered as a hexagon. Gillies fan f Each side equals the radius of the original circle in length. FIG. 9- All equilateral hexagons are made up of three 6o° rhom- boids. Three Limberg flaps can be constructed to close a hexagonal defect. Preferably the peripheral limbs should point in the same direction. FIG. IO. Construction where 2 of the flaps have peripheral limbs pointing towards one another. This may be necessary anatomic- ally, but the angle closed at A is 12o° and will produce a dog-ear.
FtG. 8
teukoplakiao that no furtt > which was n: a commonb Altho,u.~hit FIG. 9 FIG. IO flap of~uc~ have -. a d/ There are 5 possible constructions (Fig. 6) ; the choice will depend i’:;;2erP, anatomy and the availability of skin. A clinical example is shown in Figure 7. and free skir The Simultaneous Use of 3 Limberg Flaps. A circular defect closely backs while to the form of a hexagon, the length of the radius equalling the length of each becauseof tl: sides (Fig. 8). All such equilateral hexagons are made up of three ° ts divided in 3 Limberg flaps can therefore be designed to close the defect (Fig. 9). In this and further the calipers are invaluable ; set to the radius of the circular defect 18 7CLOSUREOF RHOMBOIDSKIN DEFECTS 3O replaced tneasured and markedand the design completed. The flaps should have the peripheral however, limbs-19ointing in the same direction as in Figure 9. Only in s pecial circumstances ~hould~ share a commonbase (as at a in Figure IC.) since, whenthey are rotated into h can be ~POScritionan angle of ~:zo° is closed and a pronouncedand probablypermanent dog-ear rt side, andi ¯~ eared.. In, the case illustrated. in Figure ~, excision andg rafting of radlonecrotlca " " ulcer , .: back had previously been performed,but the graft failed and further necrosis ~x-currcd. "fhe ulcer was again excised and successfhlly closed with 3 Limbergflaps. On occasion closure of a defect may be quite feasible technically but mayhave ar defect undesirable results. In the case shownin Figure ~:z the patient had previously had a S a Gillies fan flap rotated at the left angle of his mouthand nowpresented with active the radius :le in length. ateral hexagons hree 60° rhom-~ nberg flaps can: :lose a hexagonal y the peripheral int in the same ion. ~ction where s one another. essary anatomic- ;e closed at A is’ ~duce a dog-ear.i~
Flc,. z t. A, A circular radionecrotic ulcer of the back was excised as an equilateral hexagon and 3 I.i:. flaps designed as in Figure xo. B, The defect excised and the flaps cut. C, Flaps tran- sposed and sutured with, later, (D) sound healing.
l,’ukoplakia of the opposite commissure.While excMon was indicated, it was important :hat no further narrowing of the mouthshould result. Three Limbergflaps, one of ahich was mucosal, gave an acceptable solution. The 2 skin flaps were designed with A ~ commonbase, however,and this resulted in the ,creation of a dog-ear as predicted. ¯ }tthoughit cannot be easily appreciated in black and white photographs,the use of the FIG. IO :Up of buccal mucosaserved to reconstitute the vermilion in a mannerwhich would rill depend on bare been difficult to achieve by other means. wn in Figure 7. 1 .,. IVebs. Moderatedegrees of finger webbing are usually treated by release :ct closely ¯ nd flee skin graft or by Z-plasty. However,a free graft has certain inherent draw- -, length of each Ncks while a Z-plasty maynot introduce sufficient tissue into the line of the web aree° 6o because of the limitation in length of the central limb. It was noted that, whena web ~Fig. 9). In ’-~ divided in the midline (Fig. ~3) and the fingers separated, the defect is rhomboid defect 18 a~adfurther that there is frequently sufficient skin on the sides of the fingers adjacent the we favoris
In o l~ave ,k-sign ar :rodthe f. ~upplyis .my of
,:k~cd ~’~ndar, readih hair =any di£ :F~n witk The
~mcourag,
FIG.12. A, Excisionof leukoplakiaof the .commissureis planned.Two skin flaps and(B) ~re a mucosalflap designed.C, The2 skin flaps witha commonbase as in FigureI I has resultedin a dog-ear.D, Furthernarrowing of the stomahas beenavoided by reconstructingthe vermilion’ If co commissurewith the buccalmucosal flap. :~ults CLOSUREOF RHOMBOIDSKIN DEFECTS 309
Wthe web to supply a Limbcrg flap large enough to give good correction. The limiting factor is again the amountof skin available, but this is easily assessed in advance.
FIG. 13. A, Midline in- cision of a finger web burn contracture resulted in a rhomboid defect when the fingers were separated. B, A flap designed on the adjacent finger was cut, transposed and sutured into place (C).
DISCUSSION In our experience of over 5° cases in which the Limberg flap has been used, we have found it safe, reliable and versatile. One great merit of its geometrically precise design and the fact that only one measurement is needed to construct both the defect and the flap, is that it is so easily taught. The trainee has the assurance that the blood ~upply is adequate and that the edges to be apposed will fit together precisely without any of the adjustment so often required in placing other flaps ; in other words, the ttap vi!! " work". ¯ ,, :.major limitation of the Limberg flap is that the secondary defect must be closed directly and flap placement cannot be eased by the use of free grafts on the ~condary defect ; the size depends directly on the awdlability of skin in the area. A further limitation, commonto all local flaps, is that the correct quality of skin maynot be readily available, for exampleafter excision of lesion’,; of or near the eyelids and close to hair margins. At the same time because the Limberg flap can be designed in so raany different directions, it is more often possible to construct a flap of the right skin than with less versatile designs. The final scar follows a slightly bizarre line whichcannot all be lost in crease lines, but ;., ~aost cases the quality of the scar has been good without spreading or hyper- :ropl:. ad the result has certainly been better than that obtainable by the simplest ~hernadve, a full thickness graft. Theoretically the shape of the Limberg flap should encourage the formation of a raised " trap-door " scar. Whether the increased tension ~mposedon the flap prevents this is not known,but we have only seen it on one occasion, ,s and (B) one :~here a rather small flap was used. esulted in If correctly executed and if good primary healing occurs, the Limbergflap produces the vermilion :esults which, for colour and texture match and overall[ appearance, are excellent. 310 BRITISH JOURNAL OF PLASTIC SURGERY THE DUFOURMENTEL FLAP may prov Whereas the Limberg flap can only be constructed for a 6o° rhomboid dosed Dufourmentel flap, " ’ le lambeau en L pour losange ’ dit ’ LLL’ ", can, in used for any rhomboid. The rhombus is thus composed of two isosceles unlike the Limberg construction, the short axis of the defect need not equal its sides. The procedure may be regarded again as transposition of two flaps or more obviously the rotation of an irregular quadrilateral flap into a defect. In planning the Dufourmentel flap, the short diagonal LN (Fig. 14) other of the adjacent sides of the defect KNare extended and the angle so! bisected by a line (NQ) equal in length to each of the sides of the defect. line (QR) is then drawn parallel to the long axis of the defect and again equals each side of the defect. Calipers are: of some use in constructing the flap incisions are of equal length, l:.ut a protractor is necessary to place the accurately. Once raised, the flap KNQRis transposed into the defect. in Figure 15, 4 Dufourmentel flaps can be planned for any rhomboid the 4 angles of the defect come to equal one another, as the rhomboid shape of a square, flaps may be designed at each of the 4 angles giving 8 (Fig. 16). The merit of placing the equivalent points N and R in the line of extensibility has already been discussed in considering the Limbergflap. complicated with the Dufourmentel design ; indeed, on initial consideration, to be quite impractical, since the relationship of the baseline of the trian defect varies as the shape of the rhomboid varies. However, as the geometrical of the design given as an appendix to this paper shows, the angle between axis of the flap (NR) and the short axis of the defect (LN) changes by degrees from 15o° as the acute angle of the defect varies from 6o° to 9o°. Thisi may be ignored and, in practice, having determined the line of maximumskin bility, points N and R may be placed upon it and the short axis of the angle of I5o° to that line. Tiffs applies only to those cases in which the the rhombusis not dictated by the shape of the lesion. As the acute angle of the defect falls below 6o°, the Dufourmentel flap progressively wider than the primary defect. Little is to be gained therefore use of the flap in these circumstances and direct closure is to be preferred. As the acute angle of the defect increases from 6o°, the defect becomes wider than the flap and when it reaches a square the short axis of the flap is quarters the length of the short axis of the defect. It is in this range that the clinical value.
PRACTICAL APPLICATIONS As shown above, the Dufourmentel flap has no practical value where angle is less than 6o°. In closing a 6o° rhomboid defect, it has no advantage Limberg flap, although it has been argued in its favour that it has a safer blood than the Limberg flap because its base is wider. Embarrassment of the blood of a Limberg flap, however, is rarely seen anywhere on the body and never on ° o°, One r It is in closing defects the acute angle of which lies between 6o and 9 ° that the Dufourmentel flap is of use. Such defects are not often created as be.ing60 ~ excision is usually possible to convert the defect to a 6o° rhomboid which can bel Dufourme: with the simpler Limberg flap. Where, however, such additional excision is learn and indicated, for example by the proximity of vital structures, then a Dufourme: l.imberg i CLOSURE OF RHOMBOID SKIN DEFECTS 3I~ ~rovide a satisfactory solution. Such a procedure for a defect whichcould not be maYdo~edr directly withoutundue tension is shownin Figure x7- :homboid ", can, in osceles :d not equal ~ 3n of two flap into a (Fig. 14) the angle so .... ¯ ~,~,~.,~ he defect. ~gain equals ing the flap lace the flap le defect. homboid q nboid giving 8 F), I : I fine :rg flap. This nsideration, e triangular te geometrical gle between ages by less FIG. 14 ~O° tO. 9 aaximum skin ds of the which the FIG. 14. Design of a Dufour- mentel flap. LMNKrepresents armentel flap b~ a rhomboid defect. LN and KN are extended and the angle aed therefore thus formed bisected by a line preferred. NQequal to each of the sides of becomes the rhomboid. QR is then drawn of equal length and parallel to F the flap is only the long axis of the defect MK. :ange that the FIG. 15. In theory a choice of 4 Dufourmentel flaps is available for any defect approximating to a 6o° rhomboid. FIG. 16. If the defect is square value where in shape a choice of 8 flaps is no advantage available. ~as a safer blood Fm. 16 mt of the blood DISCUSSION 7 and never on ° o°, ~:~.e major merit of the Limbergflap is the simplicity of the design, all angles ~ 60 and 9 ° °, en created as being 6o or ~zo all sides being equal. This rnakes it easy to learn and apply. The Dufourmentelflap is by no meanscomplicated, but it is certainly more difficult to oid whichcan be i learn and to plan than the Limbergdesign. Indeed, at first sight it.seems that the onal excision is Dufourmentelflap with its angles rarely matchingthose of the defect is inferior to the ,en a Dt Limbergdesign, but this is too superficial a view. In both instances a defect is 312 BRITISH JOURNAL OF PLASTIC SURGERY
closed an, t,znsion; by the en, In its flap!" more the defect obtuse an: the obtus~ become cited by t ~mto h’, The:
corn[" ~i ~cr The ] dderation A B knowledge fortunate age group far-closed cosmetical
As th~ trend has from Figm Varial angle of a:
D by o::c l "aria l C tcadity see With each equal whet FIG. 17. A, A Dufour- Since mentel flap has been de- signed for a planned I44 , the a1 l~.v plotting rhomboid excision having° an acute angle of 75 . B, ~zcs which Direct closure would have involved suturing under considerable tension. l"l,~p,,.,.. Fro. 17. C, The flap was cut, transposed and sut- ured (D) with good result (E). In oth, ~hisis negli CLOSURE OF RHOMBOID SKIN DEFECTS 313 dosedand in closingit thesurrounding skin is stretchedand put under increased t~sion; theangles carefully planned and measured may have changed considerably bythe end of the procedure. " In i,s range of usefulness between60 ° and 9o°,the acute angle of the Dufourmentel lta-; -ws more acute than that of the defect, while the obtuse angle of the flap is moreobtuse than that of the defect. But imagine point L being pulled to point N as the defect is closed ; the acute angle of the flap wouldtend to becomeless acute, the obtuse angle less obtuse, while the acute angle of the defect becomesmore acute and ~he obtuse angle more obtuse. In other words the angles of the flap and the defect becomemuch more congruous. Unfortunately this variation in angle size is compli- cated by the closure of the secondarydefect ; app,’oximatingpoint N to point R would .~rn to have the opposite effects on the angles than bringing L to N. The matter is obviously very complex; even if we had simple reliable methods of rnc:~,.wingextensibility of skin at any one site and the effect of varyingtensions on ~, th, , ..".y, sis and prediction of the exact behaviourof either flap wouldrequire a ,-omputerrather than a plastic surgeon. TheDufourmentel flap is probablythe better design in so far as it takes into con- sideration the effects of increased tension on the skin, but until we have moreprecise knowledgeof the latter both designs are still to someextent empirical. It is perhaps fortunate that the majority of cases in whichthe tlaps have been used are in the older age group and old skin absorbs unequal angles, unequal sides, too-far-opened and too- far-closed angles in a way which makessuch flaps, with their various shortcomings, ~smeticallyso successful.
APPENDIX MATHEMATICAL CONSIDERATIONS IN THE DuFOURMENTEL FLAP Asthe angles of the defect vary so do themeasurements ofthe flap. The general t~¢ndhas been given in thetext, but the mathematical variations arc readily derived fromFigure 18, A. Variationof the Acute Angleof the Flap (/3) with that of the Defect (~.). /3 is one angle of a right-angled triangle the other angle of whichis equal to Y/4. Since y = ~8o-~ .’. /3 = 45+~/4 :~as been plotted on Figure ~8, B. For each degree of changein v., ~ changes by°. one quarter of a degree. Theyare only equal whenboth are 6o Variationof the ObtuseAngle of the Flap (8) ~with that of the Defect (y). It can readily seen that 8 = i8o-7’/4 and this relationship is also plotted on Figure ~8, B. \rith each degree changeof y, 8 varies by one quarter of a degree and the angles are rqual°. whenboth are ~44 Since fi fits = precisely only whenboth are 6o° and 8 fits y only whenboth are ~44, the angles of the flap cannot both equal their respective angles in one construction. };y plotting ~.//3 against y/8 in Figure I8, c it is possible to determinethat the angle ~es .,.vhich give the closest approximationto perfect fit are ~ 5o°, y ~3o° ; /3 58°, 8 ~48°. ~ :~ion of the Angle (0) betweenthe Short Axis of the Defect (a) and that of ~.:!ap,i,5. 0°- can/3/2 be. readily shownto be equal to ~ 8o Substituting/~ -- 45° + e/4 and symplifying 0 = I57½°- ~/8. In other words 0 changesat a rate 8 times slower than ~ and in the clinical range :his is negligible. 314 BRITISH JOURNAL OF PLASTIC SURGERY Variation in Lengths of Short Axes’ of Flaps and Defect. Since the con: madeup of isosceles triangles the same relationship exists between a and b and! ft. In other words a and b are equal when a is 6o°. As 0~ increases towards t short axis of the defect (a) increases at a rate 4 times as rapid as (b).
EVERsin for grafti donorsit the skin a&ieved, skin is ri ~ually o not alwa}
~st-auri, :~r dora,’
0.sTs FIG. I8. A, See appendix. B, ~ By plotting the acute angles of the flap and the defect, ~ and fl against one another a direct re- lationship is shown. A similar relationship is obtained plotting the obtuse angles 7 and 8 against one another. C, If the ratio of the acute angles one to the other, oqfl is plotted against the ratio of the obtuse angles y/8 the value at which these ratios are equal, and therefore at which the angles are most congruent, can be :-’.’-:..7, o.~ ~.o ~.s obtained.
c REFERENCES BORGHOUTS,J. M. H. M. (x964)- Surgical treatment of basal-cell carcinoma and cell carcinoma of the skin. Archivum Chirurgicum Neerlandicum, x6, I9-3o. DUFOURMENTEL,C. (I962). Le fermeture des pertes de substance cutan6e limit&s ~::G. I. lambeau de rotation en L pour losange " dit " LLL ". Annales de Chirut ~ post. 7, 6~-66. :--4 inade DUFOURMENTEL,C. (t963). An L-shaped flap for lozenge-shaped defects. Transactions the Third International Congress of Plastic Surgery, p. 772. Amsterdam: Medical Foundation. GIBSON, T., STARK, H. and EVANS,J. H. (~969). Directional variations of human skin in vivo. ffournal of Biomechanics, ~, 2oi-2o GIBSON, T., STARK, H. and KENEDI, R. M. (~97~)- The4. significance of Langer’s Transactions of the Fifth International Congress of Plastic and Reconstructive p. ~2~3. Melbourne : Butterworths. LIMBERG,A. A. (~946). Mathematical principles of local plastic procedures on the of the human body. Leningrad : Medgis. LIMBERG,A. A. (~966). Design of local flaps. In " Modern Trends in Plastic Surgery Second Edition, ed. by Gibson, T. London : Butterworths. LIMBERG,A. A. (~967). Planimetrie und Stereometrie der Hautplastik. Jena Fischer Verlag.