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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.

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Microneedles fabricated with two-photon polymerization:
Credit: Royal Society of Chemistry

I first covered ACerS member Roger Narayan’s work in the field of two-photon polymerization a little more than a year ago in a story for ACerS’ membership magazine, the Bulletin. For several years, Narayan, a professor in the Joint Biomedical Engineering Department that is connected with NC State’s College of Engineering and the University of North Carolina at Chapel Hill, has been examining the use of this rapid prototyping approach using ceramic–polymer hybrid materials to create patient-specific microscale medical prostheses, scaffolds for tissue engineering and microscale medical devices.

One of set of applications he has been working on, in particular, is using two-photon polymerization to create arrays of fine microneedles. (Conceptually, Narayan’s polymerization process is like a 3D ink jet process that builds up structures on the nanoscale.)

Recently, Narayan coauthored a paper on the novel use of microneedles to deliver quantum dots into the skin. “Our findings are significant, in part, because this technology will potentially enable researchers to deliver quantum dots, suspended in solution, to deeper layers of skin. That could be useful for the diagnosis and treatment of skin cancers, among other conditions,” Narayan says in a news release from NCSU.

QDs, sometimes called “artificial atoms,” are semiconductor materials that fall into the category of nanocrystals, and they contain a variable number of electrons that occupy well-defined, discrete quantum states.

This groups is attracted to the use of QDs because of their ability to serve as fluorophores and also work as drug delivery vehicles. QD-based fluorescent probes can be engineered to be superior to organic dye fluorophore by being brighter and having better photostability (can fluoresce after one hour of continuous excitation), signal-to-noise ratio, emission ranges and fluorescent lifetimes. Researchers report they can use their intense fluorescence to track individual molecules.

Sample quantum dot with bio coating. Credit: Histesh R. Patel

At this point, Narayan and the other researchers just are using the microneedles on pig skin and can capture images of the quantum dots entering the skin using multiphoton microscopy. Although this work is still preliminary, these images allow the researchers to verify the basic effectiveness of the microneedles as a delivery mechanism for quantum dots.

The hope is that multiphoton microscopy will have clinical applications using real-time imaging materials such as the quantum dots for faster diagnosis of cancers or other medical problems.

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Credit: Bok Yeop Ahn and Jennifer A. Lewis.

As you can see above, ACerS Fellow Jennifer Lewis and her team at the University of Illinois at Urbana-Champaign have figured out how to make intriguing and beautifully simple (yet complex) origami structures by bending and folding planar lattices. The lattices are made by extruding “inks” of ceramic, metal or polymeric materials using a precise, direct-write method.

In general, beads of inks are laid down in a particular pattern and allowed to partially dry. They are then trimmed, folded and finally annealed to complete the structure.

Direct writing of lattice. Credit: Bok Yeop Ahn and Jennifer A. Lewis.

But this makes it sound much too easy. In fact, Lewis,  Bok Yeop Ahn, David Dunand and others in her team faced significant materials and technical challenges. In a University press release, Lewis says, “Most of our inks are based on aqueous formulations, so they dry quickly. They become very stiff and can crack when folded.”

She says the challenge, then, was to find a solution that would render the printed sheets pliable enough to manipulate, yet firm enough to retain their shape after folding and annealing. The answer came by combining  wet-folding origami techniques (where paper is partially wetted to enhance its foldability) with special inks containing a mixture of fast- and slow-drying solvents.

The combination yields a lattice that can can be partially dry but flexible enough to fold through multiple steps. The origami crane - requiring 15 steps – allows them to demonstrate the agile possibilities of their methods.

For Lewis, a professor of materials science and engineering and the director of the university’s Frederick Seitz Materials Research Laboratory, these structures have a serious side. “By combining these methods, you can rapidly assemble very complex structures that simply cannot be made by conventional fabrication methods,” Lewis says.

Practically speaking, this technique could provide an alternative to existing “rapid prototyping” approaches to build scaffolds for tissue engineering. There are limits to rapid prototyping, which builds 3D structures by laying down layer after layer of material, due to the sagging of lower layers or compressing under their own weight.

Lewis’ team’s method could create light, strong structures that can be bent, folded and rolled out of lattices  formed from nearly any pattern. Stents, bone-repair scaffolds, biomedical devices or even catalytic substrates are possible.

Samples of stents and other structures. Credit: Bok Yeop Ahn and Jennifer A. Lewis.

Dunand says the next step is to try larger and much smaller structures and test ink compositions that would contain other ceramic and metallic materials.

“We’ve really just begun to unleash the power of this approach,” Lewis said.

A short video providing a closer look at some of the structures is available here.

Adding . . . Advanced Materials published a paper on this work, and if you look in the comments, the editor of the magazine has kindly posted a link for a free download of the paper.

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