Mean thickness (in millimeters) and percentages relative to overall mean thickness of 1.45 mm are labeled for all points. Rows of 4 points each from top to bottom indicate posterior dorsal, anterior dorsal, anterior caudal, posterior caudal regions. ASA indicates anterior septal angle; PSA, posterior septal angle.
Lines are labeled for widths (mm), and odds only from 9 to 15 mm. The dashed line represents the spring constant of a 1.45-mm-thick dorsal or caudal arm with a width of 15 mm (2.209 N/m).
Nicholas Paul, Kelton Messinger, Yuan F. Liu, Daniel I. Kwon, Cherine H. Kim, Jared C. Inman. A Model to Estimate L-Strut Strength With an Emphasis on Thickness. JAMA Facial Plast Surg. 2016;18(4):269–276. doi:10.1001/jamafacial.2016.0136
To perform and teach septorhinoplasty, one must have a principled understanding of the mechanics of the nasal septum. The thickness of the L-strut and how it changes septal strength have not been adequately quantified, yet calculating septal strength based on changes to thickness and size is vital in maintaining lasting nasal strength and integrity.
To establish standards for the nasal septal cartilage thickness, dorsal and caudal septum length, and Young’s modulus. To provide a basis for quantitative, operative decision making, a mathematical model of L-strut strength is presented based on changes in thickness and width.
Design, Setting, and Participants
Nasal septal cartilages from 30 fresh cadavers were used to measure thickness at clinically relevant points and length of dorsal and caudal L-strut arms. The Young modulus was directly measured using a force gauge. Statistical analyses were performed to compare thicknesses in anatomically relevant areas. Using a cantilevered beam construct, the spring constant of the L-strut dorsal and caudal arms were estimated individually with width and thickness as variables.
Main Outcomes and Measures
Thickness, dorsal and caudal length, and the Young modulus of nasal septal cartilage. Spring constants of dorsal and caudal L-strut arms with different combinations of thickness and width.
The mean (SD) age at death of the 30 cadavers was 79.2 (13.6) years (range 50-97 years). Of these, 17 (57%) were male, and 13 (43%) were female. The mean (SD) nasal septal cartilage thickness in the 30 cadavers was 1.45 (0.54) mm. Mean (SD) thickness of points along the 2-mm L-strut line was 1.49 (0.56) mm and was significantly thicker than points along the 5-mm L-strut line (mean [SD] thickness, 1.29 [0.52] mm) but significantly thinner than points along the 15-mm L-strut line (mean [SD] thickness, 1.68 [0.53]). Mean (SD) thicknesses of the posterior dorsal and caudal cartilage points were 1.52 (0.45) mm and 1.71 (0.69) mm and were significantly thicker than the anterior dorsal and caudal points (mean [SD] thickness, 1.28 [0.42] mm and 1.31 [0.44] mm, respectively). Mean (SD) dorsal and caudal L-strut arm lengths were 21.9 (3.7) mm and 20.9 (3.5) mm, respectively. The mean (SD) Young modulus was 2.03 (1.3) MPa. A model was generated demonstrating the thickness required to maintain a desired strength at a given dorsal or caudal arm width.
Conclusions and Relevance
Although thickness was not uniform throughout the nasal septum, there is a predictable pattern. Thickness of the L-strut contributes more to septal strength than does L-strut width. The model generated in this study can be used in planning, performing, or teaching the applied mechanics of septorhinoplasty.
Level of Evidence
The nasal septum is the primary contributor to the structural integrity of the nose.1 Therefore, preserving an adequate dorsocaudal L-strut of the quadrangular cartilage is fundamental to septorhinoplasty.2,3 The L-strut must be strong enough to withstand the forces of gravity, the nasal soft tissue envelope, and minor trauma, such that deforming forces do not doom the nose to collapse.
Iatrogenic changes to the L-strut are poorly understood. The dogma of L-strut preservation has dictated that one should always leave an L-strut with dorsal and caudal widths of a minimum of 10 to 15 mm.4 However, the L-strut is a 3-dimensional structure, with each dimension contributing to its strength. Not only have there been few studies examining the validity of this minimum L-strut width, but the contribution of L-strut thickness has been largely neglected.4,5 Therefore, decisions on L-strut width and degree of cartilage grafting (ie, thickness augmentation) seem to be largely arbitrary.
Studies emphasizing a minimum L-strut width make the assumption of a septum with uniform thickness throughout, such as 2 mm in some studies.4,6 However, Mowlavi et al5 demonstrated significantly different thicknesses at the septal base, dorsum, center, and anterior regions, ranging from a mean of 1.2 to 2.7 cm, a more than 2-fold difference. It follows then, to ask, how do variations in L-strut thickness relate to septal strength with iatrogenic changes in L-strut width?
We sought to answer this question by establishing standards for septal thickness, width, length, and elastic (Young) modulus using cadavers; to determine significant patterns of thickness in different regions of the nasal septum; to introduce a clinically relevant way to conceptualize the L-strut by treating its dorsal and caudal arms separately; and to present a simplified model to estimate septal strength based on L-strut thickness and width.
Thirty fresh cadaver heads less than 48 hours postmortem were dissected. The nasal quadrangular cartilages were harvested as atraumatically as possible by bisecting the nasal soft tissues in the sagittal plane. The cartilages were sharply cut with a border of septal bone still attached to prevent damage to the septal cartilage incurred by fracturing the bony-cartilaginous junctions. This research was exempt from our institutional review board because no living subjects were studied. Scientific and ethical protocols of the Loma Linda School of Medicine Anatomy Department were followed.
Stiffness, a measure of strength, is defined as the ability of an object to return to its original shape after deformation by a given force and removal of that force. Stiffness of septal cartilage is important because it is a direct measure of how well it can withstand the constant forces around it and the forces introduced when objects physically deform the nose, in that greater stiffness is equivalent to greater resistance against these forces. L-strut stiffness is dependent on its structure, composed of dimensions and shape; and its elasticity, an intrinsic property of septal cartilage that can be characterized by its Young modulus. Therefore a model that incorporates all of these variables is needed to measure the stiffness of the L-strut.
The cartilaginous nasal septum can be thought of as a plate suspended at its border by attachments along the bony-cartilaginous junctions posteriorly and inferiorly. When the posteroinferior septum is excised in septal surgery, essentially the core of the plate is removed, leaving an L-strut with attachments only in 2 areas, the keystone area and the anterior nasal spine. To calculate stiffness by continuing to model the leftover septum as such—an L-shaped plate with 2 attachments—is complex and potentially less clinically useful as dorsal and caudal L-strut arms are frequently managed separately with regard to dorsal and caudal strut carving and augmentation. Therefore, a solution to simplify the calculation would be to conceptualize the L-strut as 2 separate, rectangular beams, each cantilevered at a single attachment. In other words, the dorsal arm of the L-strut is a beam cantilevered from the keystone area, and the caudal arm is a beam cantilevered from the anterior nasal spine. This model allows the strength of the dorsal and caudal arms to be calculated individually, which may be more practical given that the width of each arm can be different, and the type of strut used to modify the thickness of each arm can be variable. Furthermore, this method gives a more conservative estimate of the full strength of the L-strut because it does not take into consideration the attachment of the dorsal and caudal arms to each other anteriorly, which would otherwise increase the stiffness of each individual arm.
To model a cantilevered beam, stiffness can be measured by the spring constant, k, in Newton per meter (N/m), in the Euler-Bernoulli beam equation as:
k = Ewt3/(4l3)
where E is the Young modulus, w is the width of a cantilevered beam, t is its thickness, and l is its length.6,7Figure 1 demonstrates these measurements as related to the L-strut. This equation can be used to model a force vector applied in the coronal plane toward the L-strut dorsal and caudal arms. Thus, any force beside one that is directed exactly in the sagittal plane at the septal tip would have a component force vector in the coronal plane and can be modeled.
The thickness of 30 nasal septal cartilages were measured at locations along L-strut–shaped lines parallel to the dorsal and caudal borders at distances of 2, 5, 10, and 15 mm. These distances were chosen for clinical utility, because the most relevant areas in septal surgery lie within this region. For each dorsal or caudal line, 2 points of measurement were chosen such that the points approximately divide the line into thirds. These points were grouped into anterior dorsal, posterior dorsal, anterior caudal, and posterior caudal, as shown in Figure 2. Thickness was measured with a 0.01-mm-resolution digital caliper (Neico Tools).
The lengths of the dorsal and caudal arms of L-struts were measured from the anterior septal angle to the keystone area and to the anterior nasal spine, respectively.
A Mark-10 Series 5 force gauge was used to measure the force applied to the same 30 cadaveric nasal cartilaginous septa on a Mark-10 ES20 manual force stand (Mark-10 Corporation). The septa were each held between 2 grips on the stand, one attaching to the keystone region and the other to the anterior nasal spine region. Each septum was compressed 1 mm and the Young modulus, E, in MPa was calculated as:
E = (F/A)/(L0-ΔL).
F is the force measured at 1 mm compression (Newton); A is the average cross-sectional area; L0 is the length of the septa between the 2 Mark-10 grips (Mark-10 Corporation); and ΔL is the change in length (1 mm). For context, 5 MPa = 725 lb/in2 (psi). The Young modulus of diamond is about 1600 MPa, gold 100 MPa, lead 12 MPa, polypropylene (plastic containers) 10 to 45 MPa, and human bone 100 to 120 MPa.
Analysis of variance (ANOVA) was used to compare the means of 3 or more variables. Two-tailed Student t tests were used to compare means of 2 variables. All statistics were performed using Microsoft Excel 2013 (Microsoft). Means are reported as mean (SD). Results of statistical analyses were considered to be significant for P values less than .05, except in cases of multiple comparisons where the Holm-Bonferroni method was used to calculate the appropriate significance threshold for the P value.
The mean (SD) age at death of the 30 cadavers was 79.2 (13.6) years (range 50-97 years). Of these, 17 (57%) were male, and 13 (43%) were female.
The mean (SD) overall L-strut cartilage thickness at all points in all cadavers was 1.45 (0.54) mm. The mean (SD) thickness of all anterior and posterior dorsal points was 1.40 (0.45) mm, and the mean (SD) of all anterior and posterior caudal points was 1.51 (0.61) mm (P > .99). The mean thickness at points of interest is shown in Figure 2 and summarized in Table 1.
Mean thicknesses at all septal points were significantly different from one another (ANOVA P < .001). Complete post hoc tests comparing means of all points to one another were not performed, because this would have required 120 paired statistical tests and would produce a high chance of type 1 errors. Instead, the mean thickness of all points along each of the 2-, 5-, 10-, and 15-mm lines were compared with that of all others. The 2-mm line (mean [SD] thickness, 1.49 [0.56] mm) was significantly thicker than the 5-mm line (mean [SD] thickness, 1.29 [0.52] mm; P = .005) and significantly thinner than the 15-mm line (mean [SD] thickness, 1.68 [0.53] mm; P = .01), but not significantly different in thickness from the 10-mm line (mean [SD] thickness, 1.36 [0.46] mm; P = .047, using corrected P < .025 for significance). The 5-mm line was significantly thinner than the 15-mm line (P < .001) but not significantly different in thickness from the 10-mm line (P = .29). The 10-mm line was significantly thinner than the 15-mm line (P < .001).
The same analysis was performed comparing the anterior dorsal, posterior dorsal, anterior caudal, and posterior caudal rows of points. The posterior dorsal points (mean [SD] thickness, 1.52 [0.45] mm) were significantly thicker than the anterior dorsal points (mean [SD] thickness, 1.28 [0.42] mm; P < .001) and the anterior caudal points (mean [SD] thickness, 1.31 [0.44] mm; P < .001) and significantly thinner than the posterior caudal points (mean [SD] thickness, 1.71 [0.69] mm; P = .01). The anterior dorsal and anterior caudal points were both significantly thinner than the posterior caudal points (P < .001 and P < .001, respectively) but were not significantly different in thickness from each other (P = .68).
The mean (SD) L-strut dorsal arm length was 21.9 (3.7) mm (range, 14.4-28.5 mm; median 22 mm), and the mean (SD) caudal arm length was 20.9 (3.5) mm (range 12.2-27.3 mm; median 21 mm). The 2 arms were not significantly different from each other in length (P = .38).
The mean (SD) Young modulus measurement was found to be 2.03 (1.30) MPa (range, 0.38-5.91 MPa; median, 1.74 MPa).
The spring constant of a 10- or 15-mm wide dorsal arm that is 21.9 mm long and 1.40 mm thick was calculated as described in the Methods to be 1.326 or 1.989 N/m, respectively. The spring constant of a 10- or 15-mm wide caudal arm that is 20.9 mm long and 1.51 mm thick was found to be 1.914 or 2.871 N/m, respectively.
How the spring constant varies with changes in thickness for a given L-strut dorsal or caudal arm width is demonstrated in Figure 3. This figure models how different combinations of thickness and dorsal or caudal arm width can be paired to achieve a desired spring constant for each arm individually. This data are shown numerically in Table 2 using a dorsal or caudal arm length of 21.9 mm (a longer beam length gives a lower, more conservative spring constant estimate), along with percentages relative to a 15-mm-wide, 21.9-mm-long, 1.45-mm-thick beam. To estimate the strength of the L-strut with a spreader graft, for example, one can add the thickness of the graft to the thickness of the dorsal or caudal arm to be grafted, then use the resulting thickness to look up the strength in Figure 3 or Table 2.
Thickness of the nasal septum has been overlooked in the literature, yet it represents an important contribution to its strength, especially when the area of the nasal septum is decreased in septorhinoplasty and when the L-strut dorsal and caudal arms are augmented with grafting. To our knowledge, there have been only 2 other studies5,8 examining the thickness of the cartilaginous nasal septum, both of which examined the entire quadrangular cartilage, whereas this study focused exclusively on the clinically relevant L-strut region. This study represents the largest septal thickness series to date with 30 fresh cadavers, and it is the first to directly measure all variables needed (eg, thickness, width, length, and the Young Modulus) to obtain a strength estimate for the cartilaginous septum.
Mowlavi et al5 found the mean overall nasal septal cartilage thickness to be 1.8 mm (mean range, 1.2-2.7 mm) in 11 fresh cadavers and Hwang et al8 found it to be 1.58 mm (mean range, 0.74-3.03 mm) in 14 embalmed cadavers. These measurements are similar to our finding of 1.45 mm (mean range, 1.13-1.90 mm) in 30 cadavers. However, all 16 thickness points contained in our data were within the 15-mm L-strut construct, for the sake of clinical utility. The differences in range may be attributable to the technique used for choosing which measurement points on septa should be correlated with one another. We chose our 16 points based on clinically relevant L-strut constructs, whereas Mowlavi et al5 used points on a square grid starting at the posterior caudal septal base and measured at 5-mm intervals, while Hwang et al8 also used grid points divided evenly by 5 in height and length. The anatomic accuracy of using a grid to compare points on septa in this manner is uncertain, as is our method. For instance, the senior author and Lee et al9 demonstrated that there is high variability in septal cartilage shape, size, and geography of the bony-cartilaginous junctions in a sample of 18 nasal septal cartilages. As such, grid points on one septum may be very different in absolute anatomic location from those on another in the technique by Hwang et al, while points may not even exist on one septum compared with another using the technique by Mowlavi et al.5
We found that the nasal septal cartilage was significantly thicker along its border region than in the central region. Figure 2 demonstrates that there is a general pattern of thick to thin and then back to thick going from the dorsal and caudal septum toward the junction of the perpendicular plate and the vomer. Furthermore, the posterior dorsal septum (the keystone area and further posterior) and the septal base were significantly thicker than the anterior septal angle region. These findings are consistent with those of Mowlavi et al5 and Hwang et al8 and have meaningful clinical implications when our septal strength model is also considered. When the central septal cartilage is removed due to deviation in septoplasty surgery or harvested for grafting, there would to be a smaller decrease in septal strength than if the cartilage were to be removed more peripherally, owing to the thickness of the dorsal and caudal septal borders. Perhaps the relative thickness of this border would allow for resection of additional cartilage beyond a 10- to 15-mm-wide L-strut.
We provided a basic model of the septum as 2 cantilevered beams held together at the nasal tip. Dividing the L-strut into dorsal and caudal arms and modeling each individually using beam mechanics is a simple and practical way of estimating L-strut strength. We overlook the strength added to each beam by their attachment to each other for sake of simplicity. This also gives a more conservative estimate of strength, as the attachment of the 2 beams inhibit torsion, thereby stabilizing each beam and increasing resistance to deformation. However, analysis of this effect would complicate the model and render it less clinically useful. Although further physical testing and computer modeling are needed to prove the accuracy of applying beam mechanics to the L-strut, prior septal mechanics research has also used this beam model.6,7 As such, the considerable influence of thickness on septal strength can be realized by examining the beam equation: k = Ewt3/(4l3), where k is directly proportional to L-strut width but is proportional to septal thickness cubed. Figure 3 and Table 2 may serve as guides to estimate septal strength for surgeons deciding on how much dorsal and caudal L-strut to preserve and how much grafting is needed to increase thickness. Furthermore, this analysis provides a foundation for teaching the mechanics of the L-strut in a quantifiable way.
As confirmed by our study, the L-strut septum is not of uniform thickness. Therefore, perhaps the best way to use our model is to take the mean thickness of the remaining L-strut dorsal or caudal arms and find the corresponding additional thickness needed for a desired spring constant. A more conservative approach would be to use the thinnest point of the dorsal or caudal beam arm in calculations. In the case where the L-strut is determined to be too weak and there is no more septal cartilage left for augmentation, one may consider sacrificing an additional few millimeters of dorsal or caudal L-strut width to be used for grafting, because a small increase in L-strut thickness can compensate for a larger decrease in width. For example, using Figure 3 and Table 2, one can readily see that a 5-mm dorsal or caudal L-strut with an augmented thickness of 2.5 mm (adding 1 mm to an average thickness of 1.5 mm) is about 50% stronger than a 15-mm-wide, 1.5-mm-thick dorsal or caudal L-strut (3.77 vs 2.45 N/m, respectively).
Because the length of the dorsal and caudal L-strut arms are not usually altered in septoplasty, it was not varied in our modeling for sake of simplicity and practicality. However, if the surgeon finds either arm to be significantly different from 20 mm in length, he or she may elect to use the Euler-Bernoulli beam equation to more accurately calculate the desired spring constant.
We found the Young modulus of septal cartilage L-struts to be about 2 MPa on average, ranging from about 0.4 to 6 MPa. Westreich et al7 found a wide range of values, from 1.82 to 32.76 MPa, while others have cited a mean of 5 MPa.10,11 One possible explanation for the wide variability is the difference in water content in the cartilage being tested. The elastic modulus is an intrinsic property of a material based on its composition. Compositional analysis has shown that septal cartilage is 77.7% water by weight, and water content has been shown to be an important factor in the mechanics of articular cartilage (albeit articular cartilage endures more compressive forces than septal cartilage).12,13 We used fresh cadavers and made an effort to conduct experiments quickly after harvest, while keeping the harvested cartilage moist with water otherwise, which may be why our Young moduli measurements were lower (signifying greater ability to deform with stress).
Neuman et al14 showed that septal cartilage does not have uniform chemical composition. There was a significant decrease in collagen content from caudal to cephalic regions and an increase in sulfated glycosaminoglycan chains from dorsal to ventral regions, resulting in higher ratios of the former to the latter in dorsal regions than ventral regions. Since mechanical strength and stiffness have been correlated with higher ratios of collagen to glycosaminoglycans, not only is the dorsal region of the cartilaginous septum thicker, but it is biochemically stronger than the central regions. This means that using centrally harvested septal cartilage grafts to thicken the L-strut likely would not be as effective per unit thickness as expected.
Surgery itself on the nasal septum could devascularize the nasal septal cartilage and may lead to a decrease in the strength of the cartilage. Furthermore, the strength of the nasal septum depends on an interplay of multiple factors including contributions from the nasal septal perichondrium, nasal alar cartilages, the soft tissue envelope, and the bony-cartilaginous junctions.7 Mau et al4 discovered that loss of support at the bony-cartilaginous junction greatly reduced the maximum tensile stress of L-strut constructs from cadavers and suggested that leaving additional septal cartilage at the bony-cartilaginous junction toward the superior end of the dorsal septum would be advisable. Lee et al9 also endorsed the idea, citing that maximal stress is consistently allocated to the bony-cartilaginous junction. Hypothetically, adding thickness to the L-strut could increase stiffness of the nasal septum indefinitely. However, when the stiffness of the nasal septum exceeds that of the bony-cartilaginous junction, force would be transmitted to that junction and lead to fracture despite a strong L-strut.9,15 Thus, we are not assuming that the bony-cartilaginous junction is always stiffer than the cartilaginous septum but are isolating the cartilaginous septum to be studied in itself. Stiffness at the bony-cartilaginous junction and its relation to the L-strut requires further research.
The results of this study can serve as a fundamental, mathematical guide in decisions involving L-strut dorsal and caudal arm design and cartilage grafting. We acknowledge that the relationship between L-strut width and thickness is understood by a skilled rhinoplasty surgeon through experience and gestalt, but a more detailed discussion is warranted to provide a basic model for teaching young surgeons that is grounded in biomechanics.
The mean nasal septal cartilage thickness was 1.45 mm, the mean dorsal septum length 21.9 mm, the mean caudal septum length 20.9 mm, and the mean Young modulus was 2 MPa. Although thickness was not uniform throughout the septum, there was a predictable pattern. Thickness of L-strut dorsal and caudal arms contributed more to L-strut strength than did width in our model to estimate strength of septal L-struts based on thickness and width.
Corresponding Author: Yuan F. Liu, MD, Department of Otolaryngology–Head and Neck Surgery, Loma Linda University Medical Center, 11234 Anderson St, Rm 2586A, Loma Linda, CA 92354 (YfangL09@gmail.com).
Accepted for Publication: February 13, 2016.
Published Online: April 14, 2016. doi:10.1001/jamafacial.2016.0136.
Author Contributions: Dr Inman had full access to all of the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis.
Study concept and design: Paul, Messinger, Liu, Kwon, Kim, Inman.
Acquisition, analysis, or interpretation of data: Paul, Messinger, Liu, Kwon, Kim, Inman.
Drafting of the manuscript: Paul, Messinger, Liu, Kwon, Inman.
Critical revision of the manuscript for important intellectual content: Paul, Liu, Kwon, Kim, Inman.
Statistical analysis: Paul, Messinger, Liu, Kim, Inman.
Administrative, technical, or material support: Liu, Kwon, Inman.
Study supervision: Kwon, Inman.
Conflict of Interest Disclosures: None reported.