Computational protocol: In vivo cranial bone strain and bite force in the agamid lizard Uromastyx geyri

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Protocol publication

[…] Strain gage outputs were filtered and processed in IGOR Pro 4.0.4 (WaveMetrics, Inc., Lake Oswego, OR, USA) using custom-written software and calibration files produced during the recording sessions. The strain data (strain being a dimensionless unit, ε, that represents change in length over original length, ΔL/L) were converted to με. The strain tracings (along with simultaneous video/videofluoroscopy and electromyograms) were examined to identify movement artifacts; these sequences were not included in the analysis. The magnitude of the maximum (ε1) and minimum (ε2) principal strains were calculated for every cycle recorded (); mean and peak principal strains recorded at each gage site in each experiment are recorded in and supplementary material Tables S1–S3, sorted by bite location, food type and behavior. ε1 is the largest tensile (or occasionally least negative) strain and usually registers as a positive value; ε2 is the largest compressive (or occasionally least tensile) strain and usually registers as a negative value. The orientation of ε1 relative to the A-element of the strain gage was calculated for each cycle (the orientation of ε2 is orthogonal to that of ε1), as was the ratio of maximum to minimum principal strains |ε1/ε2|; values are presented in supplementary material Tables S1–S3. Shear strain (γ), which is equal to ε1–ε2, was also calculated for each cycle.To facilitate comparisons between gage sites and experiments, strain orientations presented in all tables and figures (and used in statistical analyses) were calculated with the skull in right lateral view (thus, left side strains are seen from ‘below’). Strain orientations were calculated relative to the axes shown in ; the reference axis (horizontal) is aligned with the palate in lateral view and is directed anteriorly whereas the vertical axis is perpendicular to this and points dorsally. By convention, positive values are rotated counterclockwise from the reference axis (vectors rotated clockwise from the axis are negative). Custom software within IGOR Pro 4.0 was used to convert strain orientations and magnitudes to vectors within polar coordinates. Vector plots (), in which the orientations and relative magnitudes of ε1 and ε2 during all recorded bites (as well as sorted by bite location, food type and behavior) are displayed, were created using Adobe Illustrator CS 5.1 (Adobe Systems Incorporated, San Jose, CA, USA). [...] To quantify the effects of various factors on strain magnitude and orientation, data from left and right gage sites were sorted by bite location (front, working side or balancing side), food type (greens, Mazuri pellets or force transducer) and feeding behavior. Missing data indicate that no strains were recorded for a particular bite location, food type or behavior.Principal strain orientations are axial circular data in which an ε1 orientation of 0 deg is equal to 180 deg (and thus 90 deg is not a sensible mean). These data cannot be analyzed using traditional statistics. Quantitative analyses of in vivo principal strain orientations were performed in Oriana 3.13 (Kovach Computing Services, Anglesey, UK). In order to conduct these analyses, all angle data had to be converted to positive values (e.g. −30 deg was converted to 330 deg prior to analysis). Additionally, Oriana converts all axial data to values between 0 and 180 deg. Readers are urged to note these changes when comparing descriptive statistics from supplementary material Tables S1–S3 with circular statistics from supplementary material Tables S4–S6.Descriptive circular statistics (supplementary material Tables S4–S6) were produced for ε1 orientations at each gage site, with data grouped by bite location, food type and behavior. Groups containing a single data point (see supplementary material Tables S1–S3) were excluded from statistical analyses. The statistics presented here include: the mean angle of the vectors (μ) relative to the reference axis describe above; the length of the mean vector (r) ranging from 0 to 1, which is a measure of angular dispersion with values closer to 1 indicating that individual observations are clustered more closely around the mean (length of mean vector is not the mean magnitude of ε1); the concentration (k), which measures the departure of the distribution from a uniform distribution (or perfect circle) and was calculated using published formulas (; ); the circular variance (V), which is calculated as V=1−r, and is equivalent to its linear counterpart; the circular standard deviation (S), calculated as S=[−2×ln(r)]1/2; the standard error of the mean; and the 95% and 99% confidence intervals derived from standard error. Additionally, Rayleigh's test of uniformity and Watson's U2-test were used to determine whether data are derived from a von Mises distribution (continuous probability distribution on a circle, not to be confused with von Mises stress). To determine whether ε1 strain orientations changed as strain magnitude increased, circular–linear correlation coefficients were calculated between ε1 orientation and magnitude () (supplementary material Tables S4–S6). To determine whether the distribution of ε1 angles differ significantly with changes in bite location, food type or feeding behavior, ε1 orientations recorded within each gage were compared using a non-parametric Mardia–Watson–Wheeler test or a parametric Watson–Williams F-test (supplementary material Tables S7–S9). (These tests determine whether two or more distributions are identical; significant differences between distributions will lead to a large W test statistic and low probability of distributions being identical.)Mixed-model ANOVAs were used to investigate the effect of bite location, food type and feeding behavior on principal and shear strain magnitudes, and principal strain orientations in JMP 8 (SAS Institute, Cary, NC, USA) using the restricted maximum likelihood method, with individuals as random effects and food, behavior and their interaction as fixed effects (supplementary material Table S10). Because strain magnitude distribution was skewed, data were log-transformed to normalize them. Separate analyses were run for right and left gages; gage sites and behaviors with few data points were excluded. Because bite location was identified in only a third of all cycles, separate mixed-model ANOVAs were conducted for bite location with individuals as random effects (supplementary material Table S11). Tukey post hoc comparisons of differences in means were carried out. Significance was assessed at α=0.05. Angular data were analyzed using the CircStat () toolbox in MATLAB (MathWorks, Natick, MA, USA). Analyses were performed in the same groupings as above; however, because we cannot include individual variation as a random effect, we tested each individual independently. The effect of food type and behavior was analyzed using the Harrison–Kanji test (supplementary material Table S12). Depending on the concentration parameter, κ, two different statistics were used [χ2 and F for large κ; when κ is small, the interaction effect is not reported; see Harrison and Kanji ()]. To test the effect biting side on strain orientation, we used the Watson–Williams test (supplementary material Table S13). […]

Pipeline specifications

Software tools Adobe Illustrator, CircStat
Application Miscellaneous
Organisms Alligator mississippiensis