Each color indicates a different thickness, as shown in the figure key. Best-fit trend lines (in this case logarithmic) are shown as dotted lines of the same color for each L-strut thickness. For an explanation of yield strength, see the Yield Strength subsection in the Methods section.
Each color indicates a different width, as shown in the legend on the right. Best-fit trend lines (in this case exponential) are shown as dotted lines of the same color for each L-strut width. For an explanation of yield strength, see the Yield Strength subsection in the Methods section.
The green wire frame represents actual data points collected from experiments, and the colored surface represents estimated yield strengths. For an explanation of yield strength, see the Yield Strength subsection in the Methods section.
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Liu YF, Messinger K, Inman JC. Yield Strength Testing in Human Cadaver Nasal Septal Cartilage and L-Strut Constructs. JAMA Facial Plast Surg. 2017;19(1):40–45. doi:10.1001/jamafacial.2016.1180
Copyright 2016 American Medical Association. All Rights Reserved.
What factors correlate with yield strength in nasal septal cartilage, and what is the association between L-strut width and thickness in determining yield strength?
In this laboratory modeling study of human cadavers, L-strut thickness was the only factor significantly associated with nasal septal cartilage yield strength. L-strut thickness was more important than L-strut width in determining yield strength.
Septorhinoplasty surgeons should consider the thickness of potential L-struts when determining the amount of cartilaginous septum to harvest and graft.
To our knowledge, yield strength testing in human nasal septal cartilage has not been reported to date. An understanding of the basic mechanics of the nasal septum may help surgeons decide how much of an L-strut to preserve and how much grafting is needed.
To determine the factors correlated with yield strength of the cartilaginous nasal septum and to explore the association between L-strut width and thickness in determining yield strength.
Design, Setting, and Participants
In an anatomy laboratory, yield strength of rectangular pieces of fresh cadaver nasal septal cartilage was measured, and regression was performed to identify the factors correlated with yield strength. To measure yield strength in L-shaped models, 4 bonded paper L-struts models were constructed for every possible combination of the width and thickness, for a total of 240 models. Mathematical modeling using the resultant data with trend lines and surface fitting was performed to quantify the associations among L-strut width, thickness, and yield strength. The study dates were November 1, 2015, to April 1, 2016.
Main Outcomes and Measures
The factors correlated with nasal cartilage yield strength and the associations among L-strut width, thickness, and yield strength in L-shaped models.
Among 95 cartilage pieces from 12 human cadavers (mean [SD] age, 67.7 [12.6] years) and 240 constructed L-strut models, L-strut thickness was the only factor correlated with nasal septal cartilage yield strength (coefficient for thickness, 5.54; 95% CI, 4.08-7.00; P < .001), with an adjusted R2 correlation coefficient of 0.37. The mean (SD) yield strength R2 varied with L-strut thickness exponentially (0.93 [0.06]) for set widths, and it varied with L-strut width linearly (0.82 [0.11]) or logarithmically (0.85 [0.17]) for set thicknesses. A 3-dimensional surface model of yield strength with L-strut width and thickness as variables was created using a 2-dimensional gaussian function (adjusted R2 = 0.94). Estimated yield strengths were generated from the model to allow determination of the desired yield strength with different permutations of L-strut width and thickness.
Conclusions and Relevance
In this study of human cadaver nasal septal cartilage, L-strut thickness was significantly associated with yield strength. In a bonded paper L-strut model, L-strut thickness had a more important role in determining yield strength than L-strut width. Surgeons should consider the thickness of potential L-struts when determining the amount of cartilaginous septum to harvest and graft.
Level of Evidence
The structural integrity of the nose is determined by the sum of many individual components, each contributing through its intrinsic properties based on biochemical constitution, its shape, and its interactions with surrounding structures. Therefore, to understand the mechanics of the nose as a whole, one must have an appreciation of each rudimentary unit. One of the most important such units that has been thoroughly studied yet still poses many questions is the cartilaginous nasal septum (CNS).1
The mechanical properties of the CNS are determined by the intrinsic properties of septal cartilage and its size and shape. The size cannot be easily changed, but the shape is frequently manipulated in septoplasty and rhinoplasty. The general dogma of such surgical procedures mandates that a minimum width of 10 to 15 mm of caudal and dorsal CNS must be preserved to prevent nasal collapse, resulting in an L-shaped cartilage remnant called the L-strut.2-4 However, the thickness of the CNS and how it contributes to septal strength have been relatively neglected in the literature.3,5 Surgeons frequently remove cartilage from the septum, creating L-struts, and augment the CNS by using spreader grafts and caudal or dorsal struts. Spreader grafts change the dimensions of the septum in the sagittal plane, and caudal or dorsal struts alter its thickness. Therefore, an appreciation of the interplay between changing L-strut width and changing L-strut thickness is vital to our understanding of nasal strength after surgical modification.
We sought to examine how the width and thickness of the L-strut quantitatively contribute to L-strut strength. First, we tested the strength of small rectangular pieces of human cadaveric septal cartilage to determine the factors correlated with strength. Then, we used a septal cartilage substitute to perform a large number of mechanical experiments on anatomically correlated L-shaped struts of various widths and thicknesses. Finally, we mathematically modeled the strength of the L-strut based on the width and thickness. The study dates were November 1, 2015, to April 1, 2016.
No living humans were evaluated in this study. Therefore, it was exempt from institutional review board approval according to Loma Linda University human subject research guidelines.
In engineering, yield strength (YS) is defined as the stress (force applied to an object) at which a material begins to deform plastically such that when the stress is released the material is not able to return to its original shape. We used YS as a measure of the CNS strength in this study. Yield strength was measured with a force gauge (Mark-10 Series 5; Mark-10 Corporation) by placing one end of test objects in the vise grip of a manual force stand (Mark-10 ES20; Mark-10 Corporation) and compressing the other end with a circular plate. Materials were compressed at a rate of 0.25 mm/s. A stress-strain curve was generated for each compression test, and the first point at which the stress decreases with continuous compression was determined to be YS, recorded to the nearest 0.5 N.
Nasal septal quadrangular cartilages were sharply harvested from 12 unembalmed, fresh human cadavers less than 48 hours after death as atraumatically as possible, with borders of bone attached to prevent damage from fracture at the bony cartilaginous junction (BCJ). As many rectangular pieces as possible were cut from these septa, but each was large enough to allow for adequate YS testing. The pieces were held along a straightedge in the force stand vise grip. A total of 95 cartilage pieces were tested. The dimensions of each piece were measured with a digital caliper (0.01-mm resolution; Neiko Tools).
Multipurpose copy paper (Boise; Packaging Corporation of America) with thicknesses of 0.10 and 0.15 mm were bonded together using spray adhesive (HDX; The Home Depot) (1-minute set time and 10-minute cure time) and compressed with an 11.3-kg flat weight overnight. Two hundred forty model L-struts with thickness ranging from 0.5 to 4 mm were constructed. They were cut into right-angled, L-shaped pieces, with the long limb measuring 30 mm and the short limb measuring 20 mm to correlate with previous investigations of nasal septal anatomy.6 Widths of L-strut limbs were carved in a range of 5 to 20 mm. Yield strength in each L-strut was obtained in the same manner as cadaver cartilage, except that the L-struts were held at the distal end of the 2 limbs in the vise grip while the junction of the limbs was compressed. This method simulates L-struts in vivo, in which the dorsal limb is “fixed” to the keystone area, the caudal limb is fixed to the nasal crest of the maxilla, and force is applied to the nasal tip in the sagittal plane.
Basic statistical analysis, multiple regression, and 2-dimensional and 3-dimensional graphing were performed using software programs (Excel 2013; Microsoft Corporation and OriginPro 2015; OriginLab Corporation). Multiple regression was performed in a step-up manner, adding variables one at a time to maximize the correlation coefficient (R2) while maintaining the significance of each variable. Residuals plots were constructed to assure appropriate fit. Surface fitting was performed using a model (Gauss2D in OriginPro 2015; OriginLab Corporation) with the following equation:
where X, Y, and Z are variables and all other components are constants determined by the data used for fitting. Means (SDs) are reported. Significance was established at the P < .05 level. P values and 95% CIs were calculated using multivariate regression.
The mean (SD) age of the 12 cadavers was 67.7 (12.6) years, and half of them were female. Race/ethnicity was not recorded. The mean (SD) [range] dimensions and YS of the 95 cut pieces of cadaver nasal septal cartilage were as follows: 1.3 (0.5) (range, 0.8-3.2) mm for thickness, 6.0 (1.2) (range, 3.4-9.1) mm for width, 6.2 (1.5) (range, 3.4-10.2) mm for length, and 4.7 (4.9) (range, 0.5-21.5) N for YS. Multiple regression using width, length, and thickness as the factors correlated with YS revealed L-strut thickness to be the only significant variable in the following resultant regression equation: y = −2.62 + 5.54x, where y is YS (in newtons) and x is thickness (in millimeters). Both the y-intercept of −2.62 (95% CI, −4.99 to −0.26; P = .03) and the coefficient for the thickness of 5.54 (95% CI, 4.08-7.00; P < .001) were significant in the equation. The adjusted R2 correlation coefficient was 0.37.
Four bonded paper L-strut models were constructed for every possible combination of the width and thickness, for a total of 240 models. The 20-mm-wide L-struts were essentially 20 × 30-mm rectangles. The mean (SD) measured YS varied from 12.6 (1.4) N for the smallest L-strut (5-mm wide by 0.5-mm thick) to 372.9 (22.0) N for the largest L-strut (20-mm wide by 4-mm thick).
Holding thickness constant, L-strut width was plotted against the mean YS, as shown in Figure 1. The same was done for L-strut thickness vs YS while holding width constant, as shown in Figure 2. Best-fit modeling using either linear, logarithmic, or exponential trend lines is also shown in each of these figures. The mean (SD) R2 was highest using logarithmic (0.82 [0.11]; range, 0.61-0.97) or linear (0.85 [0.17]; range, 0.50-0.99) trend lines for L-strut width vs YS when width was held constant, and it was highest using exponential (0.93 [0.06]; range, 0.86-0.99) trend lines for L-strut thickness vs YS when thickness was held constant.
A factorial experiment with surface fitting was performed using L-strut width and thickness as variables simultaneously to estimate YS based on the bonded paper L-strut data, as shown in Figure 3 (adjusted R2 = 0.94). Estimated values of bonded paper L-strut YS based on the modeling are listed in the Table as percentages of the classic “minimum” 10-mm-wide L-strut with 1.5-mm thickness (based on the mean septal thickness found in our group’s previous study).7
Surgical treatment of the nasal septum should be anchored on a solid foundation of physical and mechanical understanding of septal structure. Although studies have been performed to model the strength of the CNS, the focus has been on the sagittal dimensions, with thickness assumed to be constant.3,8,9 Our group has shown in a previous study7 that thickness not only varies greatly (from 0.32-4.50 mm; mean, 1.45 mm) but also has an important role in determining the elastic strength of the CNS. In the present study, we sought to explore and model the CNS YS, which is a different way to look at strength. Yield strength cannot simply be derived from size, shape, and properties of a material using an equation but must be measured through experimentation.
To our knowledge, YS has never been tested in human nasal septal cartilage.10 However, we believe that it is an important aspect of the nasal mechanics to understand. Most septal literature focuses on tensile strength, which is determined using the elastic modulus by Young, an intrinsic property of a material, although tensile strength does not provide any information on the limits of stress that the CNS can endure. Therefore, if knowledge is available about what combinations of the width and thickness are required to obtain a certain YS, the surgeon is more in control of septal strength when performing septorhinoplasty.
Why did we choose to use a substitute material to model the L-strut? If we had performed mechanical testing on cadavers as we did in the 240 bonded paper models, too many specimens would have been required because each septal cartilage could produce only one L-strut, which after YS testing would no longer be adequate for further experiments. This method would not have been the best use of valuable resources when our objective could have been demonstrated by other means. Furthermore, thicknesses of L-struts vary among individuals, so analysis solely based on cadaver L-strut studies would be difficult.5,7,11 We chose paper because it is inexpensive, reproducible, and easily modified to create the desired dimensions in L-strut width and thickness. It also has stiffness but tangible elasticity, similar to cartilage.
Of the 3 dimensions of a rectangular piece of fresh cadaveric nasal cartilage, we discovered that L-strut thickness was the only factor significantly correlated with YS. This finding does not mean that the other 2 dimensions do not contribute to YS. However, it signifies that per unit change (in millimeters) thickness is much more important in determining YS. This result has important implications for septal surgery. Historically, our understanding of nasal septal strength has been based to such an extent on L-strut width that we have ignored L-strut thickness in the assessment of residual septal strength after portions of the CNS are removed. Given the variability in septal thickness, we should perhaps measure the thickness of potential residual cartilage before creating the L-strut solely based on residual width.7
The reason why actual L-shaped models were constructed to again test YS is that YS is also dependent on the architecture of an object. We wanted to confirm the significance of thickness in an L-shaped (vs rectangular) strut with force applied in a direction to simulate real-life stress, as well as to provide a model in which different combinations of L-strut width and thickness can be used to obtain a desired YS. Unfortunately, there is no ratio or equation that allows for the direct derivation of septal cartilage L-strut YS from bonded paper L-strut YS. Given that YS is partly based on the intrinsic property of a material, we suspect that YS of septal cartilage is associated with that of paper by some ratio relating the intrinsic material properties of each. Therefore, the mathematical influence of L-strut width and thickness on YS in bonded paper L-struts should hold true for cartilage L-struts. In other words, YS in the CNS L-struts should increase exponentially with increases in thickness as demonstrated in the bonded paper L-struts (Figure 2), but it should increase only linearly or logarithmically with increases in L-strut width (Figure 1).
The molecular composition of the CNS may differ among individuals and is not uniform in different areas of the septum.12 There is a significantly higher collagen content in cephalic than in caudal regions, as well as higher sulfated glycosaminoglycan chains in ventral than in dorsal regions, leading to higher ratios of collagen to sulfated glycosaminoglycan in dorsal than in ventral regions.12 While tensile strength has been shown to be influenced by collagen content, compressive strength is affected by aggrecans content.10 Therefore, there would be deviations in YS among individuals with same-sized L-struts. Furthermore, when centrally harvested CNS is used as spreader grafts to augment the thickness of the L-strut, the composition of the graft would be different from that of the L-strut.
Our study is limited by the difference in the mechanical properties between cadaveric and living nasal septal cartilage. After death and with experimentation, the CNS undergoes some degree of dehydration. Decreases in water content have been shown to change the mechanical properties of bovine cartilage.13 Furthermore, the speed at which force is applied to the CNS can influence its YS owing to the shifting of water at the molecular level.14-16 Therefore, our model may be more representative of the forces exerted on the CNS by the soft-tissue envelope or slow, steady compression than by an external force with a large velocity or acceleration.
An interplay of multiple factors, including the nasal septal perichondrium, upper and lower lateral cartilages, soft-tissue envelope, and BCJ, determines the true strength of the nose.17 For example, decreasing support at the BCJ was found to reduce the maximum tensile stress of cadaver L-struts.3 Furthermore, when force was applied to the nasal tip of cadavers, maximum stress was consistently allocated to the BCJ.8 Although increasing the thickness of the CNS through grafting may increase YS, it does not increase strength at the BCJ. Therefore, if YS of the CNS exceeds that of the BCJ, the septum would fail despite an intact septal cartilage.8,9 This example shows the importance of mechanical modeling and force testing in understanding the foundation of nasal septal strength before surgical modifications should be undertaken.
To achieve a certain YS, Figure 3 and the Table may serve as rough guides of how much of an L-strut to preserve based on what grafts are available to increase the thickness. In some situations, there may be deviations in the CNS close to the caudal and dorsal borders, making it difficult to resect further cartilage without possibly compromising the nasal stability. In such cases, the surgeon may consult the Table to see that if YS greater than or equal to that of a 1-cm-wide and 1.5-mm-thick (similar to the mean thickness of the general population) L-strut is desired, he or she could increase the thickness by 0.5 mm to allow a 5-mm decrease in L-strut width.7 We also anticipate that our experiments and analyses can provide a better foundation for teaching the mechanics of septal surgery in an objective way.
In human cadaver nasal septal cartilage, L-strut thickness was significantly associated with YS. L-strut thickness had a more important role than L-strut width in determining YS in a bonded paper L-strut model.
Corresponding Author: Yuan F. Liu, MD, Department of Otolaryngology–Head and Neck Surgery, Loma Linda University Medical Center, 11234 Anderson St, Room 2586A, Loma Linda, CA 92354 (firstname.lastname@example.org).
Accepted for Publication: July 13, 2016.
Correction: This article was corrected March 23, 2017, to fix axis labels Figures 2 and 3.
Published Online: October 6, 2016. doi:10.1001/jamafacial.2016.1180
Author Contributions: Drs Liu and Inman had full access to all the data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis.
Study concept and design: All authors.
Acquisition, analysis, or interpretation of data: All authors.
Drafting of the manuscript: All authors.
Critical revision of the manuscript for important intellectual content: Liu, Inman.
Statistical analysis: All authors.
Obtained funding: Messinger.
Administrative, technical, or material support: All authors.
Study supervision: Inman.
Conflict of Interest Disclosures: None reported.
Previous Presentation: This study was presented at The Triological Society 119th Annual Meeting at the Combined Otolaryngology Spring Meetings; May 21, 2016; Chicago, Illinois.