Finite Element Analysis is a frequently used tool to investigate the mechanical performance of structures under load. Here we apply its use to modeling the biomechanics of the zebrafish jaw.
Skeletal morphogenesis occurs through tightly regulated cell behaviors during development; many cell types alter their behavior in response to mechanical strain. Skeletal joints are subjected to dynamic mechanical loading. Finite element analysis (FEA) is a computational method, frequently used in engineering that can predict how a material or structure will respond to mechanical input. By dividing a whole system (in this case the zebrafish jaw skeleton) into a mesh of smaller ‘finite elements’, FEA can be used to calculate the mechanical response of the structure to external loads. The results can be visualized in many ways including as a ‘heat map’ showing the position of maximum and minimum principal strains (a positive principal strain indicates tension while a negative indicates compression. The maximum and minimum refer the largest and smallest strain). These can be used to identify which regions of the jaw and therefore which cells are likely to be under particularly high tensional or compressional loads during jaw movement and can therefore be used to identify relationships between mechanical strain and cell behavior. This protocol describes the steps to generate Finite Element models from confocal image data on the musculoskeletal system, using the zebrafish lower jaw as a practical example. The protocol leads the reader through a series of steps: 1) staining of the musculoskeletal components, 2) imaging the musculoskeletal components, 3) building a 3 dimensional (3D) surface, 4) generating a mesh of Finite Elements, 5) solving the FEA and finally 6) validating the results by comparison to real displacements seen in movements of the fish jaw.
Sonlu Elemanlar (FE) modelleme hesaplama hesaplamak ve bir yapı 1 etkiyen suşları büyüklüğünü ve konumunu harita olabilir bir mühendislik tekniğidir. Modeli "Sonlu Element" bir örgü ile temsil edilen 3D yapı oluşur ve analiz Sonuç örgü, mekanik büyüklük ve konum elemanlarının yapısı ve sayısı da dahil olmak üzere bir dizi faktöre tarafından yönetilir yükler ve malzeme özellikleri. Malzeme özellikleri yükün belli bir türü altında bir malzemenin davranış bazı yönlerini tanımlamak; Örnek gerildiğinde Poisson oranı, uzunluğu bir malzemenin genişliği oransal azalma tarif ise Young modülü (E) malzemenin elastikiyetini açıklanmaktadır. FE modelleme 'yapısı hakkında hesaba benzersiz giriş verileri alarak model üzerinde değiştirme, stres, baskı ve gerilme oyunculuk da dahil olmak üzere değişkenler çeşitli hesaplamak için kullanılabilir; S şekil, konum ve yüklerin büyüklüğü ve özgül malzeme özellikleri.
FE modelleme yaygın mühendislik 2 ve giderek 3, ortopedik ve paleontolojik uygulamaları 4 kullanılır. Gelişmede biyomekanik kuvvetler hücresi tepkilerini 5-8 aktif hale getirmek için birçok hücrede bir uyarıcı olarak işlev gördükleri bilinmektedir ve organ sistemlerini geliştirmek içinde göreli konumları ve mekanik uyarıcılara büyüklüğünü hem de tahmin etmek yararlıdır, ancak, şu anda FE modelleme az kullanılan olmuştur Zebra balığı gelişimi için.
Hem kıkırdak ve kemik mechanosensitive malzeme olduğu gösterilmiştir. Örneğin, in vitro olarak bir sıkıştırma gerilimi kemik oluşumu 9 için gerekli olduğu gösterilmiştir edilmiş olmasına rağmen, kondrojenik yolunu aktive olduğu bulunmuştur. FE analizi (FEA) fo kemiğin sırasında iskelet elemanları üzerinde etki gösterenler dahil, biyolojik örnekler üzerinde etkili suşları modellemek için istismar edilmiştirım 10. Teorik biyomekanik güçler 11,12 maruz kalmıştır ve civciv diz eklemi morfolojilerinden 8 sırasında mevcut suşları desen göstermek için sonra diğer kalkınma uygulamaları eklem şeklini tahmin etmek kullanımını da kapsar.
Bu protokol gelişmekte olan dokulara mekaniğini anlamak için bir bakış açısıyla konfokal görüntüleri 3 boyutlu yüzeyler, kafesleri ve Sonlu Elemanlar modellerinin üretilmesi deneyim paylaşımı amaçlanıyor. Biz de in vivo gerçek eklem değiştirme bilgileri yakalayan rağmen FE modelleri doğrulayarak yollarını göstermektedir. Biz bir örnek olarak Zebra balığı çene kullanırken aynı teknikler kas-iskelet sistemi yapısı üzerinde 3D bilgiler konfokal veya multiphoton görüntüleme ile elde edilebilir olan herhangi bir küçük bir biyolojik sistemde kullanılabilir.
Finite Element models have been used to relate the areas of skeletal elements that are under strain with those undergoing bone formation 10, as well as to map the areas under strain during endochondral ossification and joint morphogenesis 8,12,21. Other studies have also been able to apply theoretical growth models to replicate changes during joint development 11,12. Here we show the protocol for building FE models for a relatively simple system, the zebrafish jaw 20. Unlike alternative methods of collecting raw images for the FE models, such as CT scanning 22, confocal imaging of transgenic lines or immunostained zebrafish allows for multiple tissues to be studied. It can, therefore, provide direct information on muscle attachment points in relation to cartilage. Among vertebrate models zebrafish are particularly amenable to genetic and pharmacological manipulation. The generation of FE models for zebrafish craniofacial cartilage now opens up the possibility of further study of the interplay between biomechanics and genetics in joint morphogenesis.
There are a number of critical steps to the process of creating an FE model; the first is generating an accurate three-dimensional representation of the system. This requires imaging at high enough resolution to clearly define boundaries. Note that even with high-resolution imaging to make a good surface one may have to smooth out some regions. Another critical step is defining the correct placement of the load and correct constraints. An insufficiently constrained model will fail to solve and incorrect placement of the loads will cause abnormal movement.
Some processing of the raw data (Figure 2) is necessary as a surface generated from the raw data would be difficult to mesh (Figure 2B). We filtered the data using a Gaussian filter (Figure 2C) and we carried out some manual smoothing of the curves to produce a set of clean outlines that can be converted into a 3D surface. Too much smoothing can produce a "melted" surface that has lost many of its features. Choosing the correct element size is an iterative process as choosing too small an element size creates too large a mesh which is computationally intensive. However, choosing too large an element size will produce a mesh which fails to recapitulate the correct shape of the structure. The correct mesh had the smallest element size that captured the correct shape of the jaw and converged on a correct solution, verified using the jaw displacement. It may also be necessary to modify the material properties or load calculations to better emulate the correct displacement as different ages and species will have substantially different properties.
It is important to remember that there are always limitations to a hypothetical model and assumptions made to run FE models. When only modeling one or a small number of samples it is critical to ensure that a representative sample is chosen as there are likely to be small variations between individuals. As only some of the jaw elements and muscles were included, the model is a simplified version of the zebrafish craniofacial musculoskeletal system. Therefore, constraints had to be positioned to account for where the modelled jaw elements would connect with the rest of the skull and the model was artificially constrained in the center to fix it in 'space'. This artificial constraint did not impact on the interpretation drawn from the models as the ceratohyal itself was not analyzed. The inclusion of more of the craniofacial structure, especially other jaw opening muscles such as the sternohyals and its attached cartilage 23, could have added to the model, but limitations include the ability of larger models to run in the Finite Element software.
Another limitation is that we have not modeled ligament insertion, though this could be achieved by the insertion of springs 8. One other assumption made in this case was that the model would behave linearly. The magnitudes of strains on the models were comparable to those in published models and applied to in vitro cells 10,24, with strains being below +3,500 and above -5,000 µɛ apart from constraint and muscle attachment points. Therefore, the strains at the relevant regions of the model were deemed within a range acceptable for a linear model. Cartilage does not behave entirely as a linear material and has previously been modelled as a poroelastic material, which enabled analysis of the fluid behavior in the model 25. Spreading the muscle attachment points amongst a cluster of local nodes would distribute the peak forces and more accurately represent the muscle insertion for certain muscles.
Use of FE allows an assessment of the strains and stresses acting on a structure. As a technique it is frequently used in many bioscience disciplines including orthopedics, paleontology and more recently developmental biology. Here we describe how to build FEs for the zebrafish lower jaw. In the future these models could be extended to look at the whole jaw, including the palate. Similar techniques could be used to model spinal biomechanics in fish, which to date have mostly been studied by kinematic means.
The authors have nothing to disclose.
LHB was funded by the Wellcome Trust Dynamic Cell PhD programme; KAR was funded by MRC project grant MR/L002566/1 (awarded to EJR and CLH) and CLH was funded by ARUK grant 19479. We would also like to thank the Wolfson Bioimaging facility for imaging advice.
Coll2 | Abcam | ab34712 | Type II collagen antibody – stains all cartilage |
A4.1025 / MF20 | Developmental studies hybridoma bank | A4.1025 | Skeletal mysoin antibody – marks all skeletal muscle |
Low melt agarose | Sigma | A9414-5G | For mounting zebrafish |
MS222 (Ethyl 3-aminobenzoate methanesulfonate ) | Sigma | E10521-10G | To make anaesthetic |
Trypsin | Fisher | T/3760/48 | sample permeablilisation |
Dylight 488Mouse IgG | Thermofisher | 35502 | Secondary antibody |
Dylight 550 Rabbit IgG | Thermofisher | 84541 | Secondary antibody |
SP8/SP5 or SPE confocal | Leica | For imaging | |
LAS Leica capture software | Leica | Imaging software | |
Aviso (version 7.0.0) | FEI Visualization Science Group | 3D image analysis software (Section 2) | |
Hypermesh part of the Hyperworks package (version 10) | Altair Engineering | FE model generating software (Section 4-5) | |
Abaqus (version 6.14) | SIMULIA | FE analysis software (Section 5.7-5.8) |