Original Research—Facial Plastic and Reconstructive Surgery
Biomechanics of the Rhombic Transposition Flap Shelby G. Topp, MD1, Scott Lovald, PhD2, Tariq Khraishi, PhD3, and Curtis W. Gaball, MD1
Otolaryngology– Head and Neck Surgery 2014, Vol. 151(6) 952–959 Ó American Academy of Otolaryngology—Head and Neck Surgery Foundation 2014 Reprints and permission: sagepub.com/journalsPermissions.nav DOI: 10.1177/0194599814551128 http://otojournal.org
Sponsorships or competing interests that may be relevant to content are disclosed at the end of this article.
Received May 16, 2014; revised August 8, 2014; accepted August 22, 2014.
Abstract Objective. To develop a computational model of cutaneous wound closures comparing variations of the rhombic transposition flap.
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Study Design. A nonlinear hyperelastic finite element model of human skin was developed and used to assess flap biomechanics in simulated rhombic flap wound closures as flap geometric parameters were varied. Setting. In silico. Methods. The simulation incorporated variables of transposition angle, flap width, and tissue undermining. A 2-dimensional second-order Yeoh hyperelastic model was fit to published experimental skin data. Resultant stress and strain fields as well as local surface changes were evaluated. Results. For the rhombus defect, closure stress and strain were minimized for the transposition flap with a distal flap angle of 30° by recruiting skin from opposing sides of the defect. Alteration of defect dimensions showed that peak stress and principal strain were minimized with a square defect. Likelihood of a standing cutaneous deformity was driven by the magnitude of angle closure at the flap base. Manipulation of the transposition angle reoriented the primary skin strain vector. Asymmetric undermining decoupled wound closure tension from strain, with direct effects on boundary deformation. Conclusions. The model demonstrates that flap width determines the degree of secondary tissue movement and impact on surrounding tissues. Transposition angle determines the orientation of maximal strain. Local flap design requires consideration of multiple factors apart from idealized biomechanics, including adjacent ‘‘immobile’’ structures, scar location, local skin thickness, and orientation of relaxed skin tension lines. Finite element models can be used to analyze local flap closures to optimize outcomes. Keywords rhombic flap, local flap, transposition flap, wound closure, finite element, skin flap, cutaneous wound, hyperelastic
he rhombic flap, as initially described by Limberg in 1946,1 is a commonly used transposition flap for closure of cutaneous wounds in reconstructive surgery. Beyond the basic geometry, experimental determination of flap dynamics, including closure force vectors and tension distribution, has been described by Larrabee et al2 in an in vivo porcine model. Variations of the traditional rhombic flap have been described, adapting flap design to specific wound characteristics while minimizing distortion of surrounding structures. The classic Limberg design applies to a rhombus-shaped defect with internal angles of 60° and 120° with all edges of equal length. The donor skin flap is designed with an apical angle of 60°, matching the defect. The flap margin is oriented as an extension of the short diagonal of the defect, defining its arc of rotation. The Limberg flap may create a standing cutaneous deformity, or ‘‘dog-ear’’ deformity at the flap base, due to compressive forces. The Dufourmental modification of the rhombic flap was first described in 19643 as a modification for defects not conforming to the 60° to 120° rhombus, primarily differing from the Limberg in its arc of rotation and orientation of donor site closure. The flap is again designed with an apical angle equal to that of the internal defect angle, but the rotation axis of the flap is based from an edge that lies on a line
1 Naval Medical Center, San Diego, Department of Otolaryngology, San Diego, California, USA 2 Exponent, Incorporated, Menlo Park, California, USA 3 University of New Mexico Mechanical Engineering Department, Albuquerque, New Mexico, USA
The views expressed in this article are those of the author(s) and do not necessarily reflect the official policy or position of the Department of the Navy, Department of Defense, or the US government. This article was presented as a poster at the 2011 AAO-HNSF Annual Meeting & OTO EXPO; September 11-14, 2011; San Francisco, California. Corresponding Author: Shelby G. Topp, MD, Department of Otolaryngology–Head and Neck Surgery, Naval Medical Center, San Diego, 34800 Bob Wilson Dr, San Diego, CA 92134, USA. Email: [email protected]
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bisecting the short diagonal of the defect and a line paralleling the defect edge. The Webster flap is another well-described rhombic variation4 that employs a flap with apical angle of 30° along with a W-plasty at the flap base of rotation. This design is intended to minimize the risk of standing cutaneous deformity by limiting closure lines to a maximum rotation arc of 30°. In addition, since the transposed flap volume incompletely fills the defect, it relies on secondary tissue movement from the opposing wound edge to establish closure and distributes closure tension more evenly along the suture line. The implicit biomechanical principles underlying these and other wound closure efforts are 3-fold: (1) skin behavior under tension and during healing is determined by its particular thickness, collagen orientation, vascularity, subcutaneous attachments, and muscle force vectors; (2) surface distortion and impact on surrounding structures are determined by the distribution of wound closure forces, degree of skin undermining, and intrinsic skin elasticity; and (3) tension along a wound closure line leads to unfavorable scarring and increased risk of healing complications.5 It is with these principles in mind that models have been developed to advance our understanding of tension and deformation associated with flap closures. The biomechanical properties of skin have been studied extensively in human and animal models,6-12 and it has been shown to have complex viscoelastic, anisotropic, nonlinear characteristics. Multiple specimen-specific factors such as subject age, skin location, thickness, and directional collagen orientation greatly influence skin behavior. Mathematical models have been applied to approximate skin properties, with considerable work in recent years using finite element modeling. Pioneering work applying finite element models to cutaneous flaps was described by Larrabee13-16 and has been extended by others.17-23 Initial work used linear elastic material modeling for skin and soft tissue, but more recently hyperelastic and viscoelastic properties have been incorporated to better match the observed biomechanics of skin. The current work describes a novel hyperelastic finite element model of wound closure that refines our understanding of factors that affect clinical outcomes and assists rhombic flap closure design.
Methods Institutional review board approval was not required for this study, since no human subject or patient data were used.
Geometry Creation The skin was modeled as a 2-dimensional planar geometry in ANSYS 11.0 software (ANSYS, Canonsburg, Pennsylvania) in keeping with previously published skin models.17,20,24 The base flap was a classic rhombic repair of a defect with 60° to 120° interior angles. The a angle was defined as the flap near-margin angle measured from an extension of the defect short diagonal; this is the angle modified in the original Dufourmental flap. The b angle is the distal flap angle, which defines the flap width for a given height. This
parameter is defined as 60° in the Limberg flap and 30° in the Webster modification. The model allows modification of each of these variables, all shown in Figure 1. After creation of a base model, the areas were meshed using 8-node SHELL 281 elements (ANSYS). The element size was iteratively determined by altering the number of nodes until the difference in principal stress results converged to within 1%.
Material Properties The material properties of skin were modeled as hyperelastic, incompressible, isotropic, and time independent. A second-order Yeoh hyperelastic model was fit to experimental data of excised porcine skin strips provided by Wexler et al.9 For the Yeoh model, C10 = 0.017207, C20 = 0.19287, and d1 = d2 = 0. Explicit validation was performed by mimicking a previously described in vivo study on the displacement of human scalp skin performed by Raposio and Nordstro¨m25 and modeled by Gambarotta et al.8
Boundary Conditions Outer boundaries of the modeled region were held fixed during closure. Outcome measures of interest assessed after closure included the first principal stress (closure tension in the primary tension/compression direction), first principal strain, Z-direction strain (indicating likelihood of standing cutaneous deformity), and forces along the closure line. Closure line forces were assigned a primary, secondary, and tertiary value for different zones of tension. The primary value is defined as that along the sides that are advanced to close the initial defect, the secondary value is that along the donor site closure line, and the tertiary value is that required to close the remaining edge of the defect. Regions for primary, secondary, and tertiary forces are labeled in Figure 1.
Results Base Model Results The model was solved for the base rhombic flap. Figure 1 shows the total displacement of all points in the skin after closure, relative to their initial location. Figure 2 depicts the first principal strain and stress after defect closure. These measures are commonly used as predictive failure criteria in materials engineering modeling and describe the magnitude and directionality of strain and stress. The strain field in the left panel is a good indicator of the degree of surface deformation of the skin flap and surrounding tissue. The peak deformation occurs at the vertex of the donor site closure. The highest strains in this region are from 40% to 50%. Accordingly, the right panel shows peak stress in the same region, indicating that the tension at the suture line is highest there. These findings are in effect a precisely modeled depiction of rhombic principles introduced in the animal model of Larrabee et al.2 Notably, the directional strain vector is oriented parallel to and superimposed upon the original defect margin, validating traditional teaching principles for
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Figure 1. (A) Model variable configuration. (B) Surface displacement (mm) for the base rhombic flap. Regions for primary, secondary, and tertiary forces are denoted as ‘‘1,’’ ‘‘2,’’ and ‘‘3,’’ respectively.
Figure 2. (A) Meshed starting defect. (B) First principal strain. (C) First principal stress (MPa) in the base rhombic analysis.
rhombic flap design with respect to natural skin lines of maximal extensibility (LME). Figure 3 shows the Z-direction strain in the flap and surrounding tissue. The Z-direction strain, oriented orthogonal to the plane of flap rotation, represents increases or decreases in skin thickness. The zones of high positive strain demonstrate compression of the skin, identifying areas at risk for standing cutaneous deformity. The central region of negative strain indicates skin stretching and thinning.
Flap Design Variables Defect Height. Figure 4A, B shows the increase in peak first principal strain and all closure line forces for a rhombic flap repair using the Limberg flap orientation (eg, a = 0) as the defect long diagonal is increased from an initial 15 3
Figure 3. Z-direction component of strain for the base rhombic analysis.
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Figure 4. (A) Peak first principal strain and peak Z-strain in the skin as the defect height is increased. (B) Primary, secondary, and tertiary stitch force as the defect height is increased. See Supplemental Appendix A available at otojournal.org for the raw data.
15-mm square, maintaining a fixed short diagonal. The flap starting volume in these analyses is set to match the defect. Peak first principal strain is predictably increased as the defect area requiring coverage increases. Closure line stress is shown to be minimized in the square defect. On the other hand, the Z-direction strain reaches a nadir for the 60° to 120° rhombus defect. Figure 5 shows strain contours for a square defect, a 60° to 120° defect (defect height = 26 mm), and a defect with a height of 40 mm. The contours illustrate the increase in strain as the defect height is increased. The contour showing a defect height of 40 mm has a large region of high strain over 40%.
Flap Transposition Angle. variable of flap transposition angle, defined as the a angle, was assessed. Figure 6 compares the vector change in the strain contours for the 60° to 120° rhombus defect closed with a angles of 0° and 50°. These closures create a thin uniaxial strain area that is rotated to a degree approximately commensurate with the a angle. Figure 6A (0°) shows the high strain pattern aligned along the axis of the defect near margin, while Figure 6B (50°) shows the high strain vector rotated more in line with the defect short diagonal and nearly perpendicular to the donor site closure. Flap Width. The variable of flap width was altered, removing the constraint of equal donor and defect volume. Figure 7A shows the 60° to 120° rhombus closed with a 30° b flap, with recruitment of tissue from opposing sides of the defect to accomplish closure. The contours show a more condensed high-strain region in comparison to previous figures. The strain field is not oriented uniaxially as before but instead is shown to distribute circumferentially, as would be expected with the secondary tissue movement engendered by the smaller flap volume. Figure 7B shows a 30° a/30° b flap used to close a 60° to 120° rhombus defect.
Figure 8 shows the results of a test analysis that was performed to demonstrate the effects of changing a angle (eg, per the Dufourmental modification) in a tissue field with nonuniform directional distensibility. With the predictable rotation of the strain field seen with change in the a angle, it was hypothesized that an appropriately oriented a angle could be advantageous when there was, for example, more tissue unrelated to fixed structures and available for undermining in the horizontal direction of Figure 6. The test analysis created a model with an undermined height of 50 mm and an undermined width of 100 mm. As expected, the peak first principal strain decreased steadily as the a angle was increased to align the strain vector with the maximally distensible skin orientation.
Discussion Local flap wound closure can present a challenging reconstructive puzzle that has not been fully characterized using controlled biomechanical methods. Computational modeling of flap closures allows for analysis from a purely mechanical perspective, minimizing the variability seen in clinical and animal studies. A number of computational models have been developed to address wound closure. Most of these studies have assumed a linear model to describe the material behavior of the skin,13-16,18,26 while others have used more sophisticated material modeling strategies.8,27-29 The current model expands on previous work by using a nonlinear hyperelastic material model and simulation of the loading, skin closure, and relaxation of various rhombic defects. The magnitude and orientation of final closure tension are determined with varying flap geometries. This model demonstrates the differences in stress and strain patterns between different rhombic closure designs, including the traditional Limberg flap along with the Dufourmental and Webster modifications. The study goes further to
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Figure 5. Strain field in (A) square defect, (B) 60° to 120° rhombus defect, and (C) a defect with height increased to 40 mm.
Figure 6. The 60° to 120° rhombus defect is shown with an a angle of (A) 0° and (B) 50°.
Figure 7. A 60° to 120° rhombus defect with a 30° b angle flap is shown in two states with an a angle of (A) 0° and (B) 30°.
explore combinations of design parameters of these particular flaps to identify an ‘‘optimized’’ flap design with regard to closure force and stress and strain in the surrounding skin. By applying this simulation to regions bordered by immovable or distortable facial landmarks such as the eye or nose, the findings can be used to aid in planning proper placement and orientation of defect closures. The stress and strain fields in Figure 2 highlight the focality of peak closure tension and are in agreement with prior rhombic flap analyses in identifying the donor limb closure site as the place most at risk for tension-related complications such as wound breakdown or scar widening.2,28
The results in Figure 5 demonstrate the effect of elongating the defect. If the goal of a particular flap design is to minimize compromise of local blood supply by minimizing tension, a simple square defect is desirable. The simulation demonstrates a remarkable increase in stress and strain as the height of the defect is increased from the square configuration. If, on the other hand, the goal is to minimize dog-earing along the suture line and need for subsequent additional excision and longer scar line, there is some utility in increasing the defect height to approximate the internal rhombus angles proposed by Limberg.1 The model found no
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utility in elongating the defect height beyond that of the traditional 60° to 120° rhombus. The analyses of a and b angle manipulation demonstrated clear effects on properties of the final closure. Increasing the a angle will always, holding all other parameters constant, increase the closure force along the defect side of the closure line due to a larger skin connection between the flap and the surrounding skin and less ‘‘directional sharing’’ of strain. In cases of thicker skin and a large defect, increasing the a angle could become undesirable. In cases where ‘‘wide’’ (x-axis direction in the figures) undermining is possible, the a angle closure force effect is mitigated. Perhaps the most striking effect demonstrated with a angle manipulation is its impact on the orientation of the primary strain vector. This factor is highly clinically relevant, as facial wound location is often not under the surgeon’s control, as seen in Mohs and cancer reconstructions. The ability to orient the closure force vector with respect to the LME and surrounding structures can prominently influence the favorability of the result. If a proposed rhombic flap closure and resultant strain/deformation field is superimposed upon a defect, the impact on distortable structures, such as the nasal ala, lip, and eyelid, may be estimated. In areas of the neck that are far from these structures, more consideration is given to orientation and visibility of scars and less given to strain. Another finding of note is the relatively minor impact of a angle on Z-direction strain and risk of standing cutaneous deformity. Conventional descriptions of the Dufourmental flap mention the advantage of reduced dog-earing due to the smaller angle of rotation. The model results, however, demonstrate that the Z-direction strain is insensitive to a angle and is primarily determined by the defect dimensions and the angle closed at the flap base. These analyses suggest that the utility of a angle manipulation (and thus Dufourmental-style flaps) is in orienting the strain field of the closure to lie in a direction to better take advantage of natural skin extensibility and to avoid distorting immovable structures. In a traditional Limberg flap, the direction of highest strain is approximately aligned to the defect margin, with highest magnitude at the vertex of the donor site closure. Increasing the a angle will rotate this high-strain field to a commensurate degree (Figure 6). The surgeon can exploit this principle to both orient the long axis of the rhombic defect and manipulate the a angle of the flap closure in cases where the amount of extensibility is directionally dependent. Reduction of the b angle affected peak strain and stress, largely through recruitment of tissue from opposing wound edges. The high-strain region transitioned from a relatively elongated uniaxial field to a more condensed tridirectional conformation (Figure 7). This outcome distributes closure forces and would be expected to lessen the compromise of vascularity. It reduces the overall deformation of skin and adjacent facial structures (eyes, mouth) by capitalizing on
Figure 8. (A) Strain and (B) stitch force are shown as the a angle of a 60° to 120° rhombus defect was increased in an asymmetrically undermined area. The undermined area for this particular analysis was height = 50 and width = 100. See Supplemental Appendix B available at otojournal.org for the raw data.
low-stress regions of the force-displacement curve in all directions and limits the amount of tissue undermining necessary in any particular direction. As depicted in Figure 7, the 30° b flap minimized peak principal strain and stress for closure of the 60° to 120° rhombus. In terms of traditional flap designs, this outcome confirmed that in the simplest case, a Webster flap design and a 60° to 120° rhombus defect are the ideal configurations for the rhombic closure. An optimization procedure confirmed this finding. There were a number of limitations to this study. The model incorporated flaps similar to the published Webster design but did not include the W-plasty component that is employed to eliminate zones of angle closure .30°. The anticipated effect of this is primarily confined to the Z-direction strain in the defect apex where the W-plasty is often included. Results for the peak first principal stress and strain are not likely to be significantly affected. It is noted that a W-plasty can be added to any of the Webster-style rhombic designs considered in this study to enhance the Z-direction strain minimization but generally requires an elongation of the starting defect dimensions. Further possible refinements to this model include assessment of orthotropic material properties and viscoelastic, time-dependent
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components. The incorporation of asymmetric undermining in the above simulation partly displays the influence of directional skin distensibility. Analogous work is currently ongoing to analyze other flap designs such as the rotation and monopedicle advancement flaps.
Conclusions The current study provides a number of biomechanically based guidelines for clinicians to improve rhombic flap design. Enlargement of a square or rhombic defect to obtain idealized starting dimensions is not found to be beneficial toward reducing peak tensile strain in the flap. The utility of Dufourmental-style flaps is in orienting the strain field of the closure to lie in a direction to better take advantage of natural skin extensibility and to avoid distorting structures such as the eye, nasal ala, and lip. Narrowing the donor flap distributes closure strains to surrounding tissues, which can be a benefit or detriment, depending on clinical circumstances. The contribution of directional distensibility, either from extended undermining or intrinsic skin properties, should not be discounted and in many cases may be the most powerful single variable driving overall closure tension. The best idealized closure configuration in the current model was a 60° to 120° rhombus defect with an a = 0°/ b = 30° flap. In the uncomplicated case, this is the best configuration given its low stitch force and condensed strain field that is much less directionally dependent than those of the other configurations. The a angle can be increased in cases where undermining is asymmetric or directional distensibility and laxity is present. Burrow’s triangles and W-plasty additions can be superimposed on the discussed flaps to further modify these results and control scar location. Authors’ Note Authors SGT and CWG are military service members. This work was prepared as part of their official duties. Title 17, USC, §105 provides that ‘‘copyright protection under this title is not available for any work of the United States Government.’’ Title 17, USC, §101 defines a US government work as a work prepared by a military service member or employee of the US government as part of that person’s official duties.
Author Contributions Shelby G. Topp, study design, analysis of results, manuscript preparation; Scott Lovald, study design, model creation, analysis of results, manuscript preparation; Tariq Khraishi, study design, model creation, analysis of results; Curtis W. Gaball, study design, analysis of results, manuscript preparation.
Disclosures Competing interests: None. Sponsorships: None. Funding source: Naval Medical Center, San Diego (no role in study).
Supplemental Material Additional supporting information may be found at http://otojournal .org/supplemental.
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Biomechanics of the Rhombic Transposition Flap Shelby G. Topp, MD1, Scott Lovald, PhD2, Tariq Khraishi, PhD3, and Curtis W. Gaball, MD1
Otolaryngology– Head and Neck Surgery 2014, Vol. 151(6) 952–959 Ó American Academy of Otolaryngology—Head and Neck Surgery Foundation 2014 Reprints and permission: sagepub.com/journalsPermissions.nav DOI: 10.1177/0194599814551128 http://otojournal.org
Sponsorships or competing interests that may be relevant to content are disclosed at the end of this article.
Received May 16, 2014; revised August 8, 2014; accepted August 22, 2014.
Abstract Objective. To develop a computational model of cutaneous wound closures comparing variations of the rhombic transposition flap.
T
Study Design. A nonlinear hyperelastic finite element model of human skin was developed and used to assess flap biomechanics in simulated rhombic flap wound closures as flap geometric parameters were varied. Setting. In silico. Methods. The simulation incorporated variables of transposition angle, flap width, and tissue undermining. A 2-dimensional second-order Yeoh hyperelastic model was fit to published experimental skin data. Resultant stress and strain fields as well as local surface changes were evaluated. Results. For the rhombus defect, closure stress and strain were minimized for the transposition flap with a distal flap angle of 30° by recruiting skin from opposing sides of the defect. Alteration of defect dimensions showed that peak stress and principal strain were minimized with a square defect. Likelihood of a standing cutaneous deformity was driven by the magnitude of angle closure at the flap base. Manipulation of the transposition angle reoriented the primary skin strain vector. Asymmetric undermining decoupled wound closure tension from strain, with direct effects on boundary deformation. Conclusions. The model demonstrates that flap width determines the degree of secondary tissue movement and impact on surrounding tissues. Transposition angle determines the orientation of maximal strain. Local flap design requires consideration of multiple factors apart from idealized biomechanics, including adjacent ‘‘immobile’’ structures, scar location, local skin thickness, and orientation of relaxed skin tension lines. Finite element models can be used to analyze local flap closures to optimize outcomes. Keywords rhombic flap, local flap, transposition flap, wound closure, finite element, skin flap, cutaneous wound, hyperelastic
he rhombic flap, as initially described by Limberg in 1946,1 is a commonly used transposition flap for closure of cutaneous wounds in reconstructive surgery. Beyond the basic geometry, experimental determination of flap dynamics, including closure force vectors and tension distribution, has been described by Larrabee et al2 in an in vivo porcine model. Variations of the traditional rhombic flap have been described, adapting flap design to specific wound characteristics while minimizing distortion of surrounding structures. The classic Limberg design applies to a rhombus-shaped defect with internal angles of 60° and 120° with all edges of equal length. The donor skin flap is designed with an apical angle of 60°, matching the defect. The flap margin is oriented as an extension of the short diagonal of the defect, defining its arc of rotation. The Limberg flap may create a standing cutaneous deformity, or ‘‘dog-ear’’ deformity at the flap base, due to compressive forces. The Dufourmental modification of the rhombic flap was first described in 19643 as a modification for defects not conforming to the 60° to 120° rhombus, primarily differing from the Limberg in its arc of rotation and orientation of donor site closure. The flap is again designed with an apical angle equal to that of the internal defect angle, but the rotation axis of the flap is based from an edge that lies on a line
1 Naval Medical Center, San Diego, Department of Otolaryngology, San Diego, California, USA 2 Exponent, Incorporated, Menlo Park, California, USA 3 University of New Mexico Mechanical Engineering Department, Albuquerque, New Mexico, USA
The views expressed in this article are those of the author(s) and do not necessarily reflect the official policy or position of the Department of the Navy, Department of Defense, or the US government. This article was presented as a poster at the 2011 AAO-HNSF Annual Meeting & OTO EXPO; September 11-14, 2011; San Francisco, California. Corresponding Author: Shelby G. Topp, MD, Department of Otolaryngology–Head and Neck Surgery, Naval Medical Center, San Diego, 34800 Bob Wilson Dr, San Diego, CA 92134, USA. Email: [email protected]
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bisecting the short diagonal of the defect and a line paralleling the defect edge. The Webster flap is another well-described rhombic variation4 that employs a flap with apical angle of 30° along with a W-plasty at the flap base of rotation. This design is intended to minimize the risk of standing cutaneous deformity by limiting closure lines to a maximum rotation arc of 30°. In addition, since the transposed flap volume incompletely fills the defect, it relies on secondary tissue movement from the opposing wound edge to establish closure and distributes closure tension more evenly along the suture line. The implicit biomechanical principles underlying these and other wound closure efforts are 3-fold: (1) skin behavior under tension and during healing is determined by its particular thickness, collagen orientation, vascularity, subcutaneous attachments, and muscle force vectors; (2) surface distortion and impact on surrounding structures are determined by the distribution of wound closure forces, degree of skin undermining, and intrinsic skin elasticity; and (3) tension along a wound closure line leads to unfavorable scarring and increased risk of healing complications.5 It is with these principles in mind that models have been developed to advance our understanding of tension and deformation associated with flap closures. The biomechanical properties of skin have been studied extensively in human and animal models,6-12 and it has been shown to have complex viscoelastic, anisotropic, nonlinear characteristics. Multiple specimen-specific factors such as subject age, skin location, thickness, and directional collagen orientation greatly influence skin behavior. Mathematical models have been applied to approximate skin properties, with considerable work in recent years using finite element modeling. Pioneering work applying finite element models to cutaneous flaps was described by Larrabee13-16 and has been extended by others.17-23 Initial work used linear elastic material modeling for skin and soft tissue, but more recently hyperelastic and viscoelastic properties have been incorporated to better match the observed biomechanics of skin. The current work describes a novel hyperelastic finite element model of wound closure that refines our understanding of factors that affect clinical outcomes and assists rhombic flap closure design.
Methods Institutional review board approval was not required for this study, since no human subject or patient data were used.
Geometry Creation The skin was modeled as a 2-dimensional planar geometry in ANSYS 11.0 software (ANSYS, Canonsburg, Pennsylvania) in keeping with previously published skin models.17,20,24 The base flap was a classic rhombic repair of a defect with 60° to 120° interior angles. The a angle was defined as the flap near-margin angle measured from an extension of the defect short diagonal; this is the angle modified in the original Dufourmental flap. The b angle is the distal flap angle, which defines the flap width for a given height. This
parameter is defined as 60° in the Limberg flap and 30° in the Webster modification. The model allows modification of each of these variables, all shown in Figure 1. After creation of a base model, the areas were meshed using 8-node SHELL 281 elements (ANSYS). The element size was iteratively determined by altering the number of nodes until the difference in principal stress results converged to within 1%.
Material Properties The material properties of skin were modeled as hyperelastic, incompressible, isotropic, and time independent. A second-order Yeoh hyperelastic model was fit to experimental data of excised porcine skin strips provided by Wexler et al.9 For the Yeoh model, C10 = 0.017207, C20 = 0.19287, and d1 = d2 = 0. Explicit validation was performed by mimicking a previously described in vivo study on the displacement of human scalp skin performed by Raposio and Nordstro¨m25 and modeled by Gambarotta et al.8
Boundary Conditions Outer boundaries of the modeled region were held fixed during closure. Outcome measures of interest assessed after closure included the first principal stress (closure tension in the primary tension/compression direction), first principal strain, Z-direction strain (indicating likelihood of standing cutaneous deformity), and forces along the closure line. Closure line forces were assigned a primary, secondary, and tertiary value for different zones of tension. The primary value is defined as that along the sides that are advanced to close the initial defect, the secondary value is that along the donor site closure line, and the tertiary value is that required to close the remaining edge of the defect. Regions for primary, secondary, and tertiary forces are labeled in Figure 1.
Results Base Model Results The model was solved for the base rhombic flap. Figure 1 shows the total displacement of all points in the skin after closure, relative to their initial location. Figure 2 depicts the first principal strain and stress after defect closure. These measures are commonly used as predictive failure criteria in materials engineering modeling and describe the magnitude and directionality of strain and stress. The strain field in the left panel is a good indicator of the degree of surface deformation of the skin flap and surrounding tissue. The peak deformation occurs at the vertex of the donor site closure. The highest strains in this region are from 40% to 50%. Accordingly, the right panel shows peak stress in the same region, indicating that the tension at the suture line is highest there. These findings are in effect a precisely modeled depiction of rhombic principles introduced in the animal model of Larrabee et al.2 Notably, the directional strain vector is oriented parallel to and superimposed upon the original defect margin, validating traditional teaching principles for
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Figure 1. (A) Model variable configuration. (B) Surface displacement (mm) for the base rhombic flap. Regions for primary, secondary, and tertiary forces are denoted as ‘‘1,’’ ‘‘2,’’ and ‘‘3,’’ respectively.
Figure 2. (A) Meshed starting defect. (B) First principal strain. (C) First principal stress (MPa) in the base rhombic analysis.
rhombic flap design with respect to natural skin lines of maximal extensibility (LME). Figure 3 shows the Z-direction strain in the flap and surrounding tissue. The Z-direction strain, oriented orthogonal to the plane of flap rotation, represents increases or decreases in skin thickness. The zones of high positive strain demonstrate compression of the skin, identifying areas at risk for standing cutaneous deformity. The central region of negative strain indicates skin stretching and thinning.
Flap Design Variables Defect Height. Figure 4A, B shows the increase in peak first principal strain and all closure line forces for a rhombic flap repair using the Limberg flap orientation (eg, a = 0) as the defect long diagonal is increased from an initial 15 3
Figure 3. Z-direction component of strain for the base rhombic analysis.
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Figure 4. (A) Peak first principal strain and peak Z-strain in the skin as the defect height is increased. (B) Primary, secondary, and tertiary stitch force as the defect height is increased. See Supplemental Appendix A available at otojournal.org for the raw data.
15-mm square, maintaining a fixed short diagonal. The flap starting volume in these analyses is set to match the defect. Peak first principal strain is predictably increased as the defect area requiring coverage increases. Closure line stress is shown to be minimized in the square defect. On the other hand, the Z-direction strain reaches a nadir for the 60° to 120° rhombus defect. Figure 5 shows strain contours for a square defect, a 60° to 120° defect (defect height = 26 mm), and a defect with a height of 40 mm. The contours illustrate the increase in strain as the defect height is increased. The contour showing a defect height of 40 mm has a large region of high strain over 40%.
Flap Transposition Angle. variable of flap transposition angle, defined as the a angle, was assessed. Figure 6 compares the vector change in the strain contours for the 60° to 120° rhombus defect closed with a angles of 0° and 50°. These closures create a thin uniaxial strain area that is rotated to a degree approximately commensurate with the a angle. Figure 6A (0°) shows the high strain pattern aligned along the axis of the defect near margin, while Figure 6B (50°) shows the high strain vector rotated more in line with the defect short diagonal and nearly perpendicular to the donor site closure. Flap Width. The variable of flap width was altered, removing the constraint of equal donor and defect volume. Figure 7A shows the 60° to 120° rhombus closed with a 30° b flap, with recruitment of tissue from opposing sides of the defect to accomplish closure. The contours show a more condensed high-strain region in comparison to previous figures. The strain field is not oriented uniaxially as before but instead is shown to distribute circumferentially, as would be expected with the secondary tissue movement engendered by the smaller flap volume. Figure 7B shows a 30° a/30° b flap used to close a 60° to 120° rhombus defect.
Figure 8 shows the results of a test analysis that was performed to demonstrate the effects of changing a angle (eg, per the Dufourmental modification) in a tissue field with nonuniform directional distensibility. With the predictable rotation of the strain field seen with change in the a angle, it was hypothesized that an appropriately oriented a angle could be advantageous when there was, for example, more tissue unrelated to fixed structures and available for undermining in the horizontal direction of Figure 6. The test analysis created a model with an undermined height of 50 mm and an undermined width of 100 mm. As expected, the peak first principal strain decreased steadily as the a angle was increased to align the strain vector with the maximally distensible skin orientation.
Discussion Local flap wound closure can present a challenging reconstructive puzzle that has not been fully characterized using controlled biomechanical methods. Computational modeling of flap closures allows for analysis from a purely mechanical perspective, minimizing the variability seen in clinical and animal studies. A number of computational models have been developed to address wound closure. Most of these studies have assumed a linear model to describe the material behavior of the skin,13-16,18,26 while others have used more sophisticated material modeling strategies.8,27-29 The current model expands on previous work by using a nonlinear hyperelastic material model and simulation of the loading, skin closure, and relaxation of various rhombic defects. The magnitude and orientation of final closure tension are determined with varying flap geometries. This model demonstrates the differences in stress and strain patterns between different rhombic closure designs, including the traditional Limberg flap along with the Dufourmental and Webster modifications. The study goes further to
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Figure 5. Strain field in (A) square defect, (B) 60° to 120° rhombus defect, and (C) a defect with height increased to 40 mm.
Figure 6. The 60° to 120° rhombus defect is shown with an a angle of (A) 0° and (B) 50°.
Figure 7. A 60° to 120° rhombus defect with a 30° b angle flap is shown in two states with an a angle of (A) 0° and (B) 30°.
explore combinations of design parameters of these particular flaps to identify an ‘‘optimized’’ flap design with regard to closure force and stress and strain in the surrounding skin. By applying this simulation to regions bordered by immovable or distortable facial landmarks such as the eye or nose, the findings can be used to aid in planning proper placement and orientation of defect closures. The stress and strain fields in Figure 2 highlight the focality of peak closure tension and are in agreement with prior rhombic flap analyses in identifying the donor limb closure site as the place most at risk for tension-related complications such as wound breakdown or scar widening.2,28
The results in Figure 5 demonstrate the effect of elongating the defect. If the goal of a particular flap design is to minimize compromise of local blood supply by minimizing tension, a simple square defect is desirable. The simulation demonstrates a remarkable increase in stress and strain as the height of the defect is increased from the square configuration. If, on the other hand, the goal is to minimize dog-earing along the suture line and need for subsequent additional excision and longer scar line, there is some utility in increasing the defect height to approximate the internal rhombus angles proposed by Limberg.1 The model found no
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utility in elongating the defect height beyond that of the traditional 60° to 120° rhombus. The analyses of a and b angle manipulation demonstrated clear effects on properties of the final closure. Increasing the a angle will always, holding all other parameters constant, increase the closure force along the defect side of the closure line due to a larger skin connection between the flap and the surrounding skin and less ‘‘directional sharing’’ of strain. In cases of thicker skin and a large defect, increasing the a angle could become undesirable. In cases where ‘‘wide’’ (x-axis direction in the figures) undermining is possible, the a angle closure force effect is mitigated. Perhaps the most striking effect demonstrated with a angle manipulation is its impact on the orientation of the primary strain vector. This factor is highly clinically relevant, as facial wound location is often not under the surgeon’s control, as seen in Mohs and cancer reconstructions. The ability to orient the closure force vector with respect to the LME and surrounding structures can prominently influence the favorability of the result. If a proposed rhombic flap closure and resultant strain/deformation field is superimposed upon a defect, the impact on distortable structures, such as the nasal ala, lip, and eyelid, may be estimated. In areas of the neck that are far from these structures, more consideration is given to orientation and visibility of scars and less given to strain. Another finding of note is the relatively minor impact of a angle on Z-direction strain and risk of standing cutaneous deformity. Conventional descriptions of the Dufourmental flap mention the advantage of reduced dog-earing due to the smaller angle of rotation. The model results, however, demonstrate that the Z-direction strain is insensitive to a angle and is primarily determined by the defect dimensions and the angle closed at the flap base. These analyses suggest that the utility of a angle manipulation (and thus Dufourmental-style flaps) is in orienting the strain field of the closure to lie in a direction to better take advantage of natural skin extensibility and to avoid distorting immovable structures. In a traditional Limberg flap, the direction of highest strain is approximately aligned to the defect margin, with highest magnitude at the vertex of the donor site closure. Increasing the a angle will rotate this high-strain field to a commensurate degree (Figure 6). The surgeon can exploit this principle to both orient the long axis of the rhombic defect and manipulate the a angle of the flap closure in cases where the amount of extensibility is directionally dependent. Reduction of the b angle affected peak strain and stress, largely through recruitment of tissue from opposing wound edges. The high-strain region transitioned from a relatively elongated uniaxial field to a more condensed tridirectional conformation (Figure 7). This outcome distributes closure forces and would be expected to lessen the compromise of vascularity. It reduces the overall deformation of skin and adjacent facial structures (eyes, mouth) by capitalizing on
Figure 8. (A) Strain and (B) stitch force are shown as the a angle of a 60° to 120° rhombus defect was increased in an asymmetrically undermined area. The undermined area for this particular analysis was height = 50 and width = 100. See Supplemental Appendix B available at otojournal.org for the raw data.
low-stress regions of the force-displacement curve in all directions and limits the amount of tissue undermining necessary in any particular direction. As depicted in Figure 7, the 30° b flap minimized peak principal strain and stress for closure of the 60° to 120° rhombus. In terms of traditional flap designs, this outcome confirmed that in the simplest case, a Webster flap design and a 60° to 120° rhombus defect are the ideal configurations for the rhombic closure. An optimization procedure confirmed this finding. There were a number of limitations to this study. The model incorporated flaps similar to the published Webster design but did not include the W-plasty component that is employed to eliminate zones of angle closure .30°. The anticipated effect of this is primarily confined to the Z-direction strain in the defect apex where the W-plasty is often included. Results for the peak first principal stress and strain are not likely to be significantly affected. It is noted that a W-plasty can be added to any of the Webster-style rhombic designs considered in this study to enhance the Z-direction strain minimization but generally requires an elongation of the starting defect dimensions. Further possible refinements to this model include assessment of orthotropic material properties and viscoelastic, time-dependent
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components. The incorporation of asymmetric undermining in the above simulation partly displays the influence of directional skin distensibility. Analogous work is currently ongoing to analyze other flap designs such as the rotation and monopedicle advancement flaps.
Conclusions The current study provides a number of biomechanically based guidelines for clinicians to improve rhombic flap design. Enlargement of a square or rhombic defect to obtain idealized starting dimensions is not found to be beneficial toward reducing peak tensile strain in the flap. The utility of Dufourmental-style flaps is in orienting the strain field of the closure to lie in a direction to better take advantage of natural skin extensibility and to avoid distorting structures such as the eye, nasal ala, and lip. Narrowing the donor flap distributes closure strains to surrounding tissues, which can be a benefit or detriment, depending on clinical circumstances. The contribution of directional distensibility, either from extended undermining or intrinsic skin properties, should not be discounted and in many cases may be the most powerful single variable driving overall closure tension. The best idealized closure configuration in the current model was a 60° to 120° rhombus defect with an a = 0°/ b = 30° flap. In the uncomplicated case, this is the best configuration given its low stitch force and condensed strain field that is much less directionally dependent than those of the other configurations. The a angle can be increased in cases where undermining is asymmetric or directional distensibility and laxity is present. Burrow’s triangles and W-plasty additions can be superimposed on the discussed flaps to further modify these results and control scar location. Authors’ Note Authors SGT and CWG are military service members. This work was prepared as part of their official duties. Title 17, USC, §105 provides that ‘‘copyright protection under this title is not available for any work of the United States Government.’’ Title 17, USC, §101 defines a US government work as a work prepared by a military service member or employee of the US government as part of that person’s official duties.
Author Contributions Shelby G. Topp, study design, analysis of results, manuscript preparation; Scott Lovald, study design, model creation, analysis of results, manuscript preparation; Tariq Khraishi, study design, model creation, analysis of results; Curtis W. Gaball, study design, analysis of results, manuscript preparation.
Disclosures Competing interests: None. Sponsorships: None. Funding source: Naval Medical Center, San Diego (no role in study).
Supplemental Material Additional supporting information may be found at http://otojournal .org/supplemental.
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