Building Finite Element Models to Investigate Zebrafish Jaw Biomechanics

The overall goal of this modeling technique is to simulate the mechanical environment experienced by developing zebrafish jaws. This method can help answer key questions in the musculoskeletal field, such as, how do patterns of mechanical load change over time? And, how do these loads stimulate cell behavior.

The main advantage of this technique is that it allows us to analyze patterns of gene expression and changes to cell behavior in the context of the mechanical environment. This method can provide insight into skeletal development. It can also be applied to any other biological structure that experiences mechanical load, such as the skeletal elements in higher vertebrates, or the cardiovascular system.

Generally, individuals new to this method may struggle, because the terminology and software assume a background in engineering. To visualize the shape of the skeletal elements, quantify muscle, and identify the exact placement of the muscle attachments, immunostain the fish at the appropriate age for skeletal myosin and type II collagen. First, fix a fish larva in 4%paraformaldehyde and PBS for one hour.

Then, wash the fixative off using two PBT washes. Next, dehydrate the larva in 50%methanol and PBT for five minutes, followed by 100%methanol for five minutes. The larvae can then be stored in 100%methanol until needed.

When needed, rehydrate the larva in 50%methanol and PBT for five minutes. Then, wash it in PBT for five minutes. Now, permeabilize the larva with 0.25%trypsin and PBT on ice for five to six minutes.

Then, wash it in PBT for five minutes and repeat the PBT wash three more times. Before applying the antibodies, block the larva for two to three hours in 5%serum and PBT. Then, incubate the larva in the recommended dilution of rabbit anti-type II collagen and mouse anti-myosin antibodies with 5%serum and PBT.

Perform this incubation for one hour at room temperature, or overnight at four degrees Celsius. After applying the primary antibodies, wash the larva in PBT a total of six times for 15 minutes per wash. After the PBT washes, apply a 5%serum and PBT block for one or two hours.

Now, apply the secondary antibodies, henceforth keeping the preparation in the dark as much as possible. Use fluorescently-labeled anti-mouse and anti-rabbit secondary antibodies in 5%serum and PBT. After applying the secondary antibodies, wash the larva in PBT six times for 10 minutes per wash.

Any larva that is stained as described, or expresses fluorescent tags, can now be imaged using a confocal microscope as follows. Take a confocal image stack of the region of interest using the 10x objective lens with about 2.5x digital zoom. Excite the green and red channel using a 488-nanometer laser and a 561-nanometer laser.

Then, take 512-square-pixel images using a z-plane interval of 1.3 microns with three line averages. About 100 z sections will fill the stack. Export the data as a TIFF image stack.

Open the TIFF image stack and view all the channels in the appropriate software. Right-click on the cartilage channel, select orthoslice, and create. Then, right-click on the cartilage channel and select Image Processing, Smoothing And Denoising, select the image filter, and toggle smoothing Gaussian.

In the project view, right-click on the filtered image and select image segmentation, and then edit new label. Create a new label for each material, such as cartilage and joint. Then, select the cartilage region of the image using the magic wand tool with the all slices toggle on, and use the brush tool to remove noise from the outlines.

Next, select the joint region with the brush tool, and assign it to the joint component and repeat action throughout the joint. To smooth multiple slices at once, select Segmentation from the top menu, and select Smooth labels. Then, to produce a 3D surface render of the component, right-click on the image and select Generate Surface.

Now, click on the rendered surface, and save the data as an HMASCII file for the meshing software. 3D mesh generation is a critical step in generating a good model. You need to compromise between a mesh that represents the true shape of the structure you are trying to model, without including so much detail that you introduce problem elements, such as ones with too small or too large an angle.

To generate the mesh, import the 3D model into a capable software package. To generate a two-dimensional mesh of the cartilage and joint surfaces, use the shrinkwrap tool under the 2D menu. Choose an element size between 1.5 and 2.5.

A range of differently-sized surface meshes can be made to carry out 3D mesh optimization. In order to ensure that the mesh is continuous between the joint and cartilage surfaces, any elements on the boundary must share common nodes. To achieve this, remove the inner surface of the joint, leaving a hollow tube.

Use the F2 function key to access shortcut to Delete Elements menu. Select the elements to delete. Adjust the boundary nodes to match the cartilage surface.

Use a combination of F2, F3, and F6 function keys to delete, move nodes, and create new elements, respectively. Finally, duplicate the cartilage surface at the joint using the collector organize components menu. Use the F2 function key to delete all non-joint elements.

Afterward, perform quality checks by going to the Check elements panel. Check for duplicated elements, insertions, and penetrations in the mesh. If found, edit them using the Tools tab.

Check for dihedral angles using the utility tab found in the model tree option. To generate a 3D mesh from the 2D surface meshes of differing element sizes, use the Tetramesh tool. Compare different mesh sizes, and select the FE model with the lowest mesh size that converges after further simulations, and does not compromise feature definition.

Next, using the Distance tool, transform the mesh so the jaw model is to scale. Ensure the cartilage and joint components are connected in the model by exporting a merged model, or by using ties. Next, apply loads, constraints, and material properties to the FE model to simulate jaw function.

Using the labeled confocal stacks as a guide, define the muscles. First, assign nodes that correspond to the muscle attachment points. Then, create vectors between the nodes that represent the origin and insertion of each muscle.

After all the muscles are defined, create a history loadcollector, and apply a Cload to each muscle. Specify the magnitude in newtons, and assign the associated vector. Then, assign appropriate elastic isotropic material properties, as determined by the literature.

Next, create a boundary loadcollector, and apply some initial constraints on the model. Pick the nodes to constrain, and select a degrees-of-freedom factor similar to the natural range of motion for the muscle defined by those nodes. Now, create a load step for each type of movement to simulate.

Under the analysis menu, select all relevant loads and constraints to simulate the movement being specified. Then, select static from the dropdown menu. When ready, export the model in an appropriate file format, including the mesh, loads, constraints, and material properties.

In this case, the INP format is chosen. Then, load the model into the FE analysis software. Therein, create and execute a job for the model, and analyze output for stress, strain, displacement, and so forth.

Select three to six transgenic zebrafish larvae, and lightly anesthetize the larvae with 0.02%MS-222 until they cease to respond to touch, but their hearts still beat. Then, mount the larvae laterally on cover slips in tepid, 1%low-melting-point agarose in Danieau's solution. Next, carefully remove the agarose from around the head and jaw with forceps.

Then, using a Pasteur pipette, flush fresh Danieau's solution over the head of the larva to remove the anesthetic. Do this until normal mouth movement resumes. Now, use movie-capture software to take fluorescent high-speed videos of the mouth movements.

Film at the highest frame rate for as long as needed to record multiple jaw opening cycles. Later, analyze the maximum displacement of the jaw. Choose the frames that show the jaw open the widest, and measure the distance between the anterior tip of the Meckel's cartilage and the upper jaw.

The upper jaw point corresponds to the tip of the ethmoid plate. Immunostaining for muscle and cartilage, or imaging of transgenic reporters, allows the 3D structure of the jaw to be visualized, along with the associated musculature. By imaging at a high resolution, it was possible to build a model that captures the 3-dimensional shape of the jaw.

The model incorporates loads whose placement and magnitude were derived from the confocal images of muscle and cartilage. From this model, a range of different material properties were tested. Utilizing in vivo displacement seen through high-speed video capture, one model was selected that best replicates that range of motion.

Using the most accurate material properties, loads, and mesh shape data, the FE model was used to explore the best estimate of the mechanical environment experienced during this time frame. For example, magnitudes of the stress were measured. The model can be magnified to see the fine details of the pattern, and then looked at in digital sections to observe the detail in all dimensions.

After watching this video, you'd have a good understanding of how to use confocal imaging to build a physiologically accurate 3D model of a biological structure that is under mechanical load. While attempting this procedure, it's important to remember that this is a linear, elastic model, and cartilage does not behave entirely as a linear material. Other material properties, such as permeability, can be incorporated, but may require further modifications to the mesh.