Ex vivo experiment
Strain gauges are electrical components that experience changes in length as changes in resistance. This property can be used to measure strain on a surface. In order to accurately measure the orientation of maximum principal strain, a strain gauge must comprise of multiple measuring grids. Rectangular rosette gauges have three grids orientated at 45 ° to one another, and are available in stacked or planar configurations. Because of their larger size, planar rosettes are rarely used in vivo as they are more invasive (Herring et al. 2001; Thomason et al. 2001; Ross et al. 2011), and obviously their size prohibits their use on smaller specimens (Rayfield, 2011). However, in this experiment, where the bones are large and invasion is not an issue, planar rosettes are preferred for two reasons, as follows. (i) Resistance is also affected by heat. Bone is a poor thermal conductor, and gauges in a stacked configuration may overheat, causing their reporting of strain to drift (Tech Note TN-515; Vishay Measurements Group, Basingstoke, UK). (ii) Bone is a heterogeneous material. Larger gauges will average strain over a larger area, meaning that small heterogeneities in the bony material will not overtly influence the reporting of local strain. In this experiment, 16 planar rosette gauges (C2A-06-062LR-350; Vishay Micro-Measurements, Basingstoke, UK) were used.
Gauges were attached to locations on the skull of a modern domestic pig (Sus scrofa; Fig. 1A). The skull was manually defleshed with a scalpel, and the gauge sites prepared: periosteum was removed with pumice powder and the site cleaned with alcohol, before applying the gauges with cyanoacrylate adhesive (M-Bond 200; Vishay Micro-Measurements, Basingstoke, UK). The gauges were then covered with a waterproof silicon rubber coating for protection (3140 RTV Coating; Dow Corning, Midland, MI, USA). Strain was recorded by the 16 gauges using an amplifier (5100B; Vishay Micro-Measurements, Basingstoke, UK), and converted to principle strains and orientations using StrainSmart 4.01 software (Vishay Measurements Group, Basingstoke, UK). Preliminary drift tests were conducted for all gauges before loading. When each new gauge was connected, it was left unloaded for 30 min, to assess whether the gauges were thermally drifting. Over 30 min, the average thermal drift on the gauges was 11.58 με. The standard deviation from the mean unloaded strain gives an indication of the noise on the gauges, which was 2.00 με. During these drift tests, it was noticed that one of the strain grids on G1 (on the dorsal premaxilla) was drifting by 59 με and, as a result, the gauge had trouble zeroing and reporting stable strain. For this reason, results from G1 were not considered further.
Figure 1. (A) A CT-derived 3D model of the pig specimen showing gauge locations, and FE loading and constraints simulating (B) diagram of loading details in experiment. (C) Photograph of experimental set-up, and (D) closer photo of load application. G, gauge; M1, 1st molar tooth; TMJ, temporomandibular joint.
Download figure to PowerPoint
A custom-built aluminium testing rig was designed to apply loads representing the temporalis and the combined masseter/zygomaticomandibularis muscles (Fig. 1). Mastication is a complex muscular process (Herring & Scapino, 1973), which would be impossible to replicate accurately ex vivo. As a validation, the objective of the model was not to replicate in vivo loading, but to test how accurately FE reported experimentally derived strains; hence it was decided that a simpler approximation would provide a scenario that is easy to replicate both experimentally and in the computational analysis, while also applying a similar load to that which the structure is adapted for. As a static load was applied here, the intricacies of muscle activation patterns were not considered, nor were the presence of functional units within the muscles that do not all activate contemporaneously. Despite being active with the masseter during jaw adduction in vivo, the medial pterygoid was not included for practical reasons, as attaching experimental loading to the pterygoid tubercle from which the muscle arises was problematic. It has been shown that the dominant source of masticatory loading in the pig skull is from the masseter (Herring et al. 2001), thus this omission was considered justifiable.
The specimen was supported bilaterally by aluminium bars at the temporomandibular joints (TMJ) and bilaterally at the 1st molar teeth (M1). Loads were applied to the attachment sites of the masseter and temporalis muscles. Thin (1 mm) steel strips were attached to the zygomatic arch with 3.5-mm bolts, and to the temporal bone using 3.5-mm self-tapping screws. These steel strips were tied with non-slipping bowline knots to hanging balances [HCB 100K200 (masseter) and HCB 50K100 (temporalis), Kern & Sohn GmbH, Balingen, Germany] using 3-mm low-stretch polyester cord (3 mm Magic Speed, LIROS GmbH, Berg, Germany). In the case of the loads from the temporalis, these passed over low-friction pulleys (Size 1 upright block, Barton Marine Equipment, Kent, UK) to apply the desired line-of-action determined from dissection. The hanging balances were then attached to rigging screws (6 mm Fork Bottlescrew; Sea Sure, Hampshire, UK). Manually tightening the screws applied tension without twisting, which was recorded by the hanging balances to a precision of 1 N. During the experiment, the specimen was kept moist by applying a 50 : 50 mixture of glycerine and water between each loading.
The load was applied with the right masseter (RM)/left temporalis (LT) pair ‘active’, and the left masseter (LM)/right temporalis (RT) pair ‘balancing’. The desired load was RM = 300 N; LT, LM = 200 N, RT = 100 N. This load was an idealised one, based on bite force measurements from pigs of a similar age and weight to the specimen (Bousdras et al. 2006), and the observation from electromyography that, although pigs bite bilaterally, their muscle activation is not symmetrical, with the working-side master and balancing-side temporalis acting together to close the jaw (Herring & Scapino, 1973; Herring & Teng, 2000).
Because there was only space on the amplifier for four rosette gauges to be tested at any time, the gauges were divided into four groups of four (G1–G4, G5–G8, G9–G12 and G13–G16) and the experiment repeated three times for each group, to assess error in the repetition of loading. Gauges were zeroed, and the screws were tightened one at a time by approximately 50 N increments, in the following order: RM, LT, LM, RT. Once the final load was achieved, it was allowed to stabilise for 1 min, then strain was recorded for 2 min. After unloading, the specimen was allowed to recover for 15 min to allow any residual strain to dissipate.
Upon unloading, it was noticed that the hanging balances reported a load still present (mean RM = 20 ± 4 N, LT = 5 ± 2 N, LM = 24 ± 6 N, RT = 2 ± 2 N). Whilst every effort had been made to reduce these effects, this probably represented load that was lost to friction, elasticity and knot-tightening in the cords, as the strain gauges returned to zero following unloading, suggesting that plastic deformation of the bone had not occurred. For each loading, the lost load was recorded and deducted from the experimental load to determine the true load applied by each screw.
The pig specimen (Large White Breed, age approximately 6 months, skull dimensions 247 × 141 × 133 mm) was CT scanned at the Royal Veterinary College on a Picker PQ5000 medical scanner (0.55 mm pixel size, 2 mm slice thickness, 120 kV, 200 mA). Scan data were imported into amira 4.1 (Mercury Computer Systems, USA), and the bony and dental materials were segmented out, generating a stereolithography surface that was imported into HyperMesh 10.0 (Altair Engineering, USA) to generate a specimen-specific FE model.
The surface was ‘cleaned’ to remove mesh errors (free edges, holes, T-connections), and the HyperMesh‘shrink-wrap’ function was used to generate a mesh of good aspect ratio, evenly sized elements (as tested using standard element quality checks in HyperMesh and Abaqus). Following a convergence test (Bright & Rayfield, 2011), a model with 1 749 149 second-order (quadratic 10-noded) tetrahedral elements [modal element size of 0.92 mm, with 10 nodes per element (TET10)] was confirmed to report strain at all gauge sites within 5% (except G7, which was within 12%), and was selected for the analysis. From this mesh, 23 models were created to test sensitivity and validity. These models are summarised in Table 1, and described in detail below.
Table 1. Material properties and loading assignments for all models in the analysis.
|Model||Element type||E (GPa)||ν||Alteration of masseter (°)||Alteration of temporalis (°)|
Initial model (HOM model)
Material properties were assigned initially as isotropic and homogenous. In the absence of data for pigs, the average properties of muscle-bearing human cortical bone from the cranial vault were used (E = 12.5 GPa, ν = 0.35; Peterson & Dechow, 2003). The teeth were modelled as being continuous with bone, and were assigned the same material properties. Debate persists on whether it is necessary to include the PDL in FE models. A validation study by Panagiotopoulou et al. (2011) demonstrated that models of the macaque mandible are relatively insensitive to the presence of the PDL beyond the immediate vicinity on the alveolar region. Conversely, other validation and sensitivity tests (Marinescu et al. 2005; Gröning et al. 2011a) have found that neglecting to model the PDL can result in models that are too stiff and deform differently to models with a PDL. In this study, CT resolution was insufficient to precisely resolve the position of the tooth roots, meaning that the PDL could not be incorporated accurately.
Loads and constraints were applied to replicate the conditions of the ex vivo experiment. Repetition of loading introduced some variation into the experiment, as it was difficult to consistently apply the same load, given that not all the load was successfully transferred to the specimen as mentioned earlier. For this reason, the loads applied to the model were averages of the experimental loads. The final load applied to the model was RM = 282 N [experimental standard deviation (ESD) = 4 N], LT = 195 N (ESD = 2 N), LM = 178 N (ESD = 6 N), RT = 100 N (ESD = 3 N), giving a total model load of 755 N.
Constraints were applied to 25 nodes bilaterally at the TMJ, preventing translation in the x-, y- and z-axes, and to 20 nodes bilaterally at the 1st molar teeth preventing translation in the dorso-ventral (y) axis. Muscle vectors were defined to simulate the lines of action of the cords in the experiment, and the corrected experimental loads were applied via rigid body elements (RBE3 in Abaqus; Fig. 1A).
Loading direction (LOAD models)
To assess the effects of loading direction, the vector of load application was varied by 2.5 °, 5 ° and 10 ° in the anterior-posterior and medio-lateral directions in the RM, and in the lateral and ventral directions in the RT, resulting in 18 further models (LOAD models, Table 1). Loading was not varied medially in the temporalis because the position of the bone meant that it was not possible for the load to be applied more medially in the experiment. Similarly, the load was not varied dorsally because doing so would have produced a line of action equivalent to the ropes of the experiment intersecting the zygomatic arch. In an earlier paper, Bright & Rayfield (2011) demonstrated that, because of its high resolution, this model could be run satisfactorily using first-order [4-noded (TET4)] elements without notably affecting strains. As models with first-order elements take significantly less time to run, the load sensitivity models were run with 4-noded elements to save time. All other boundary conditions were kept the same as in the HOM model.
Cancellous bone (HET models)
It is recognised that the structure of cancellous bone is less stiff than that of cortical bone, a factor that may be relevant in FEA. Although cortical and cancellous bone could be identified in the CT scans, the fact that these were of relatively low resolution meant that consistently distinguishing cancellous from cortical bone was not possible at all locations, nor could the internal architecture of the cancellous bone be seen. A higher resolution scan, though desirable, was not possible due to the large size of the specimen. To assess the effects of a stiffer cortex surrounding cancellous bone, the outermost layer of elements in the model were defined as a cortical bone shell with the properties of the solid model (E = 12.5 GPa, ν = 0.35) one element thick (0.92 mm), and the remaining internal elements were assigned less stiff material properties to determine whether this would affect the patterns or magnitudes of strain. Bone was over 2 mm thick in all locations. The thinnest bone was in the palate and anterior to the orbit (2.5 mm), and the thickest bone was located around the braincase (10.5–36 mm). Gauges were located on bone at least 5 mm thick. Cortical bone is not universally thick over the whole skull, but these idealised models remove any ambiguity from the results that may be caused by the uneven distribution of real bony material. Currey (2002) cites cancellous bone properties ranging from 0.004 to 0.35 GPa in humans and 0.035 to 7 GPa in non-humans. To encompass this range, values of 6 and 1 GPa were tested, with Poisson’s ratio kept at ν = 0.35. Six gigapascals represents the higher range of values, and is roughly half the stiffness of the cortical bone value used. The value of 1 GPa is closer to the values reported for humans, and was shown by Panagiotopoulou et al. (2010) to give good validation results when using a similar technique on a macaque mandible.
Cancellous bone is also believed to have a lower Poisson’s ratio than cortical bone (ν = 0.2; Dalstra et al. 1993). To test the effects of varying cancellous bone Poisson’s ratio, the HET models were run again, but this time with ν = 0.2. All models used second-order elements, assumed isotropy, and loading was kept as in the HOM model.
Orthotropy is well known from long bones and the mandible across several taxa, and has been demonstrated to be present in the cranium to varying degrees as well (O’Mahony et al. 2000; Zapata et al. 2010; Chung & Dechow, 2011). As material properties vary throughout the skull, and may not be aligned with a standard anatomical axis (Peterson & Dechow, 2003; Wang & Dechow, 2006; Dechow et al. 2010), defining cranial orthotropy in an FE model is considerably difficult, even with detailed measurements of material properties (which were unavailable for this study). For this reason, the effects of orthotropy are not modelled here.
Node sets representing the positions of 16 strain gauges were defined. This allowed the models to be queried precisely for comparison with the experiment, as well as amongst each other. The placement of the gauge sites on the experimental specimen was measured with calipers, and those measurements were repeated in HyperMesh to confirm gauges were positioned correctly. To ensure that sampling of the node sets was not affecting results, these ‘virtual gauges’ were widened by 1 and 2 mm on each edge and compared with the other results.
Membrane elements (M3D6 in Abaqus) were also constructed in the positions of the gauges. These are two-dimensional elements that share nodes with the original node sets, and were constructed with negligible thickness (0.001 mm) and material properties (E = 0.001 GPa, ν = 0.35), so they would move with the underlying model without affecting its results by introducing additional stiffness. This technique allows the reporting of in-plane stresses and strains, to accommodate the fact that FEA applied here is a 3D technique, whereas strain gauges are 2D and only report a projection of 3D strain that could lead to errors in the calculation of principal strains and their orientations. Principal strains and strain orientations from the membrane elements were compared with results from the node sets to assess differences between the two practices. The issue of 3D vs. 2D strain conversions has only been directly addressed once before in the FE validation literature (Ross et al. 2011), using custom-written matlab software for use with strain output from Strand7.
The model was solved in Abaqus 6.8.2 (Dassault Systèmes Simulia, Providence, RI, USA) on desktop PC (Windows 64-bit Vista Business, Intel Xeon x5450 3.00 GHz CPU, 64 GB RAM).