Orthognathic and cranial surgery planning

Posted by Richard Baxter | 29 Oct, 2025

Polygonica is an ideal toolkit for developing surgical planning and orthotic design applications. The SDK provides a wide range of algorithms for working directly with raw scan data without the need for complex, time consuming and expensive reverse-engineering operations. But, if reverse-engineering is absolutely necessary, Polygonica also provides a range of mesh preparation tools that provide faster and easier segmentation for BREP-surface creation.

In this blog we’ll explore two common medical workflows focused on creating custom implants, based on meshes created from a patient’s CT scan.

Orthognathic surgery planning
Craniomaxillofacial surgery planning

An image of a skull in which the jaw bones have been cut and realigned, held in place by 3D printed strip implants. — Left: Jaw realignment with 3D printed strip implants. Right: A craniomaxillofacial skull cap implant protecting damaged and missing bone beneath.

A skull model in which a large hole in the cranium has been closed by a custom 3D-printed implant. — Left: Jaw realignment with 3D printed strip implants. Right: A craniomaxillofacial skull cap implant protecting damaged and missing bone beneath.

As always, the blog is supported by accompanying video demonstrations, and the code for the reference app is available to Polygonica customers and evaluees on an unsupported basis. Please feel free to get in touch via the contact page.

Orthognathic Surgery Planning

Medicine loves to use long complex words which baffle and bemuse. And I love a digression.

According to Google, ‘ortho’ is from the Greek for straight, and ‘gnathos’ is from Greek for ‘lower jaw’. At least that’s the simple explanation. I suspect the real derivation is even more complex.

So orthognathic surgery covers all types of surgery designed to correct misalignment in the jaw region. One specific variant is malocclusion, or poor bite alignment, which is more commonly corrected using braces and aligners. In more severe cases surgery may be necessary.

Mal-occlusion derives from the Latin for bad or incorrect, and occlusion is from the Latin for ‘shut up, close up’. At some point in the middle of the 19th Century occlusion was adopted by the dental profession to specifically refer to how the teeth in the maxilla (Latin, ‘upper jaw’) and teeth in the mandible (also Latin, ‘jawbone’, ‘used for chewing’) meet.

So we could just say upper jaw, lower jaw and bad bite, but it just doesn’t sound as cool.

End of digression.

Orthognathic surgery generally involves cutting the skull and jaw such that the bones can be moved to ‘straighten’ the alignment, then anchoring the adjusted bones in place using metal plates.

In many cases the metal plates are standard pre-manufactured parts, which the surgeon then bends so that they fit into place.

With the advent of scanning and 3D printing, custom parts can now be manufactured. In this blog we’ll cover using Polygonica in both workflows.

Cutting the skull and jaw

In order to adjust the misaligned parts of the skull and jaw, the surgeon needs to cut through the bones so that the parts can be moved around with respect to each other. The implants will then stabilize the parts in the new position.
As shown in the videos at the end of the blog, Polygonica’s mesh Boolean is ideal for modelling these cutting steps in surgical planning software.

The image shows a transparent skull model with a cuboid cutting tool mimicking the cut performed by a surgeon to allow for realignment. — Left: Mimicking a cut operation by the surgeon. Right: Another cut, in a more complex region.

The original skull model, before alignment. — Left: The original scan of the patient's skull. Right: After the surgeon has cut and realigned the jaw.

A skull model after a surgeon has made cuts and realigned the jaw. — Left: The original scan of the patient's skull. Right: After the surgeon has cut and realigned the jaw.

The split parts can then be manually selected and transformed into the appropriate position.

Using shrinkwrap to create a smooth surface across gaps

After the surgeon has realigned the bones, there might be significant differences in the bone heights on either side of a gap that needs to be secured using a printed implant.

Whilst the profiles required to smoothly bridge such large gaps could be manually specified by the surgeon during planning, this is inefficient. We want to find a way to automatically bridge such gaps without creating unnecessary large concavities in the implant strips.

Polygonica’s shrinkwrap helps solve this problem by providing a tight and accurate wrap around the surface of the bone scan, and a smooth, almost convex, bridge across the large gaps. An example based on the complex ankle joint of an animal is shown below.

An image of a complex joint between two mesh models of bones. — Left: Two mesh models of a complex ankle joint. Right: The shrinkwrap result forming a smooth join after the maximum concave angle setting is used.

The bones have been joined by a smooth shrinkwrap which is only shallowly concave. — Left: Two mesh models of a complex ankle joint. Right: The shrinkwrap result forming a smooth join after the maximum concave angle setting is used.

Before creating the implants a shrinkwrap of the entire skull is generated to provide smooth surfaces across the cuts made by the surgeon.

A shrinkwrapped mesh of a skull model created from the skll model after the surgeon has performed cuts and jaw realignmment. The shrinkwrap has smoothly covered over the gaps. — Left: The cut and realigned version of the skull. Right: After shrinkwrapping the realigned version of the skull, the shrinkwrap provides a smooth surface bridging the cuts, on which it is easy to place strip implants.

Creating a custom 3D printed implant direct from the scan

The workflow for generating the custom implant for the strips is quite similar to generating dental aligners, guides and crowns, which we’ve covered in previous blogs:

For orthognathic strips the following approach is taken:

Identify the locations on the scan for the implant, in this case by the surgeon selecting anchor points directly on the skull model
The selected points are joined using Polygonica’s geodesic path finding, and then Polygonica’s radial curve offset is used to inflate the curve across the surface of the shrinkwrapped version of the model to create the outer and inner, boundary loops. Using the shrinkwrap ensures the resultant strip smoothly bridges more significant gaps.
New edges are imprinted into the mesh along the offset curves so that the faces that lie on the surface inside the offset curve can be retrieved. This is where the implant will lie on the surface – or it can be adjusted so it lies slightly above it.
These faces form a continuous sheet, which is then thickened using Polygonica’s spherical 3D offset to create the implant itself. In practice the cylindrical strip anchors are created separately from the strips that join them, and then the results are joined together using Polygonica’s mesh Boolean.
Remesh the strip to improve the quality of the faces in the mesh that will be printed
Smooth the outer surfaces of the mesh.
Boolean subtract cylindrical holes where screws will be inserted. An appropriate screw thread could be subtracted – we just haven’t done that in this demo.

The surgeon selects anchor points for the strip plate implant on either side of the cut. — Left: The surgeon selects anchor points for the model on the realigned skull model. Right: The implant is created by sheet thickening polygons from the shrinkwrap surface.

A strip implant is create in-place by offsetting and thickening the sheet surface of the shrinkwrap. — Left: The surgeon selects anchor points for the model on the realigned skull model. Right: The implant is created by sheet thickening polygons from the shrinkwrap surface.

In this image the surgeon has selected a more complex strip plate layout on the lower jaw. — Creating a more complex strip plate across the lower jaw.

The complex strip plate has been created to anchor the lower jaw. — Creating a more complex strip plate across the lower jaw.

Placing stock implants using Polygonica

Not all implant workflows use custom 3D printed implants. In many cases surgeons use off-the-shelf implants which are bent into the required shape before being deformed further whilst being screwed into place on the skull.

In this case the implants are not manufactured from the custom meshes created using Polygonica, but a Polygonica-based planning workflow can help the surgeon decide if the parts are the correct size and can be adjusted to the required fit.

Polygonica’s deformation algorithms can be used to simulate bending the strips along the creases provided by the manufacturer.

A linear strip plate is placed above a model in which there is a sinificant kink in the surface below it. — Left: A model of an off-the-shelf strip plate. Right: The strip plate has been bent to fit the surface using Polygonica's vector field deformation.

The strip plate has been bent so it conforms to the kind in the surface — Left: A model of an off-the-shelf strip plate. Right: The strip plate has been bent to fit the surface using Polygonica's vector field deformation.

However, in the live demonstration we’ve chosen to use a uv mapping of the profile of implant strip. This has the advantage that the placement will be visually correct even in regions of high curvature. The imprinted curve can then be moved interactively across the surface to make small adjustments, with a re-imprint step at the end to ensure the mapping of the final location is accurate.

A 2D planar slice through a strip implant placed above the skull model, and also wrapped onto the skull model using a uv wrapping. — Left: A planar slice through an off-the-shelf implant is mapped onto the surface using uv wrapping in order to simulate the deformation that will occur when the surgeon places the part and screws it into place. Right: Placing a more complex implant.

As before, once the profile is imprinted, a model of the strip can be recreated from the mesh surface, showing how the implant is likely to deform when the surgeon screws it into the bone.

Craniofacial, maxillofacial and craniomaxillofacial surgery planning

We’ve already learned from our casual etymology that maxillo refers to the upper jaw. Unsurprisingly facial means just that – ‘related to the face’. Cranial is from the Latin for skull.

So in these workflows we’d expect to be planning surgery anywhere from the upper jaw to the top of the skull. However maxilla is also used as a term to refer to both upper and lower jaws, so craniomaxillofacial surgery seems to cover pretty much anything bone-related and above the neck.

But if I get lots of letters from surgeons correcting me, I’ll be very happy.

Creating a large skull cap implant

In the case we’re demonstrating a large area of bone is missing from one side of the skull. We want the implant to completely cover this area.

A skull model with a large hole in the upper left cranium. — Left: The model created from the patient's scan. There is a large hole in the cranium. Right: The custom designed implant created using Polygonica, including flexibility slots, air holes, screw holes and an embossed label.

Using Registration and Alignment

Our first challenge is to define a surface onto which we can create the implant geometry. As the hole is on one side of the skull, we can take advantage of the fact that skulls are generally symmetrical.

So, first a simple mirror transform is applied to a copy of the skull. This then needs to be aligned with the original. Since the result of the mirror transform and subsequent translation to match origins is heavily dependent on the mesh’s coordinate origin and its relation to the best plane of symmetry, we found it more reliable to use Polygonica’s advanced mesh registration/alignment API, PFSolidRegister. This gives us a close fit of the mirrored model to the original, such that the mirrored surface can be used as the surface from which to create the skull cap.

Should the model have significant asymmetry then, following a rough registration, the function PFTransformCreateFromPoints can be used to select equivalent points on both the original mesh and the mirrored mesh, after which fine registration can be re-run to improve the final fit.

The top of two skull models is shown. The original, in brown, has a large hole in it. The other skull, in orange, is a mirrored version of the first, so the orange region fills the hole. — Left: The orange surface is the mirrored skull model, which fills the hole. Centre: Selecting around the hole on the original model. Right: The implant is created by finding the selected surface region on the mirror model, and thickening it using Polygonica's offseting.

The top of a skull with a hole in it, and a user selection around the hole. — Left: The orange surface is the mirrored skull model, which fills the hole. Centre: Selecting around the hole on the original model. Right: The implant is created by finding the selected surface region on the mirror model, and thickening it using Polygonica's offseting.

Creating and customizing the implant

This gives a rough surface on which to create the skull cap. From here we follow a similar workflow to before:

Manually select points on the mirrored surface around the location of the hole in the original surface
Create and smooth an imprint curve on the copy surface
Emboss edges around the curve
Select faces inside the curve
Offset (sheet-thicken) these faces to create the skull cap
Blend (fillet) the sharp edges
Remesh and smooth top surface of the plate