Topological optimization can be used to custom design prosthetic implants. Credit: Image created by Janet Sinn-Hanlon, Beckman ITG, University of Illinois

Mathematics—the common language of science and engineering—often proves to be the doorway between disciplines. The common ground between a skyscraper, an airplane wing, and facial bones may not seem obvious until one realizes that from a structural perspective, they are all framework systems that must support and transmit loads within certain constraints. By breaking a structure into trusses, nodes, forces, etc., the mathematics transcends the application, and modeling principles can be applied broadly.

A story on the NSF website describes a study that demonstrates the use of topological optimization to “engineer” new faces when facial bones are destroyed by severe injury or disease. The standard surgical approach to craniofacial repair has been to take part of a larger bone from the patient and sculpt it to shape for implantation, an imperfect approach that may leave the patient improved but still significantly deformed.

“The middle of the face is the most complicated part of the human skeleton. What makes the reconstruction more complicated is the fact that the bones are small, delicate, highly specialized and located in a region highly susceptible to contamination by bacteria,” says Glaucio Paulino in the story. Paulino is program director of the mechanics of materials program at the NSF, professor of civil and environmental engineering at the University of Illinois, Urbana-Champaign and one of the PIs on the study.

Topological optimization takes into account limiting factors, such as available space, applied force, load and layout constraints. From the story, “Imagine a building grid in which you can determine where there should be material and where there shouldn’t. Moreover, you can express loads and supports that would affect certain parts of this block of material. Your final result is an optimized structure that fits your established constraints.”

In a PNAS paper (pdf) published in 2010, Paulino and his colleagues from Ohio State University’s School of Medicine demonstrated the feasibility of using the method to custom design a bone replacement for a massive facial injury. In the conclusions of the paper, they also note that the computational algorithms can be expanded to include other critical variables like oxygen levels, surgical flaps, aesthetics and even cost.

(This fascinating 40-second video shows the transformation of a block into a complex upper jaw prosthesis.)

This approach to designing the prosthetic’s structure dovetails very nicely with work already being done in the materials community on additive manufacturing and laser-based manufacturing fabrication of surgical implants.

At the Fraunhofer Institute in Germany, studies are showing that selective laser melting can be used to fabricate a porous polylactide-tricalcium phosphate composite that the body absorbs as natural bone grows into the scaffold. Structures have been assembled that can close openings of up to 25 cm. Selective laser melting is an additive manufacturing process that uses three dimensional CAD renderings to guide a laser beam through a powder bed to melt powders into a dense component.

The Roger Narayan group at the combined UNC-NC State biomedical engineering department is using two-photon polymerization to synthesize polymeric and zirconia shapes for medical applications. Two-photon polymerization uses laser radiation to initiate chemical reactions, polymerization and hardening of a material to build submicrometer structures.

There are commercial examples, too, of rapid prototyping fabrication of customized surgical implants. TMJ Concepts manufactures temporomandibular joint prostheses from titanium using computer numerical control machining based on patient CAT scans.