The power of simulation

The use of electronics both in and outside of the body has been intrinsic to the management of many diseases. The most obvious examples are the range of cardiac implantable electronic devices designed to help control or monitor irregular heartbeats in people with certain heart rhythm disorders and heart failure. Advances in the field have also enabled a new generation of glucose monitors and insulin pumps that make the management of diabetes less of a day-to-day stress for patients. As the ability to fabricate devices that fit more power and capability into a smaller surface area has progressed, so too have research hypotheses pertaining to how we might use electronic components to sense, stimulate, monitor and control biological systems. In order to make those ideas a reality, a number of challenges must be overcome: Finding non-toxic and bioavailable materials, fitting the components required into a small device, collecting and processing data from sensors, convincing the medical community of the benefits. But while none of these barriers are easily surmountable, doing so is dependent on something much simpler – putting the devices on the body.

Nanshu Lu, a professor in the Department of Aerospace Engineering and Engineering Mechanics at the University of Texas at Austin, explains why this seemingly simple conundrum is anything but simple: “Conventional electronics are based on silicon wafers, which are flat and rigid. But the human body has exactly the opposite mechanical properties. It’s very curvilinear and soft.

This means there’s an intrinsic mismatch between the two.” To better understand the limitations of flexible electronics, Lu points to the most recognisable example – foldable smart phones. “They are based on flexible LEDs and circuits, but the limitation of flexible devices is that they are not able to conform to 3D curvilinear surfaces,” she says. In the smartphone example, flexible electronics are able to wrap around a cylinder because they’re able to bend. But, Lu adds, “They are not able to wrap around a spherical surface like the eyeball or an arbitrary surface like the heart.”

Flexible versus stretchable

It’s worth mentioning that researchers have demonstrated bioelectronic capabilities using materials able to adhere to the surfaces of the human body. But these, as Lu explains, are examples of “stretchable” not “flexible” electronics. “Flexible electronics, although well industrialised and very mature in terms of materials and fabrication, are still not fully ready for body conformable electronics,” she says. “On the other hand, stretchable electronics are able to fully conform to 3D curvilinear and arbitrary surfaces, because they can stretch in addition to bending, but their industrialisation is still ongoing and there’s a lot of challenges in fabricating them at scale.”

Another key variable pertains to exactly what you can do with each of these categories of device. Stretchable electronics open up possibilities like muscular strain sensing, for instance, but to engineer such a device requires an appropriate amount of space between the components. “There are some special applications where you need a very high density of electronics over a very limited area,” explains Lu. In this case, components need to be tightly packed together, which means adding stretchable interconnects isn’t an option.

Lu and her collaborator, Ying Li, an associate professor of mechanical engineering at the University of Wisconsin–Madison, joined forces to answer the question of whether it was possible to design a device with all the benefits of a flexible electronic, but could conform to 3D curvilinear surfaces on the body. There are examples in the literature of attempts to do this, Lu says, “but those are from empirical inspirations,” with examples including the truncated icosahedron design of a soccer ball and the petals of a flower. Both having a background in mechanics and the use of mathematical modelling tools, Lu and Li wanted a more objective solution.

To provide a further impetus, in a separate project, Lu and her colleague Dae-Hyeong Kim from Seoul National University designed an ultrathin artificial retina to treat damaged retinas, but were grappling with how to fit it around the eye. “We need thousands of photodetectors over a 1cm diameter spherical cap,” she says. “In that case, we need to have very densely packed active electronics. Flexible electronics for a high-density artificial retina is the most viable approach, but a retina is curvilinear and flexible electronics manufactured on wafers are planar.”

Lu compares the ultra-thin material to a piece of paper to explain how attempting to wrap a flexible sheet around a curvilinear surface like the eyeball results in “buckling”, seen as wrinkling in the paper example. This, she says, is due to the extra material, which can be cut away to improve conformability. “But without a model guiding us, we don’t know how to minimise the removal of the material, or how to maximise the coverage of the device on the spherical surface,” she says. “Therefore, we have to compromise on the number of pixels and the field of view.” When talking about restoring a person’s sight with what could potentially be a better technology than the currently available retinal implants, which produce blurred or distorted images due to their inability to conform to the eye, those sacrifices aren’t really an option. Luckily, Li and his colleagues at the University of Wisconsin- Madison had been building a software package to simulate flexible structures with highly complex geometries and loading conditions, and he was able to apply it to Lu’s problem. “The basic idea is actually pretty simple,” says Li. “We discretise the flexible electronics into a lattice spring network structure to make the simulation much easier and more efficient to handle.” With the modelling software, Li simulated the conformability of circular polymer sheets – which mimic the mechanical properties of flexible electronics – both fully intact and with strategically placed slits, to a plastic hemisphere. Using the same components, the researchers made slits into the polymer sheet according to the parameters for best practice given by the software. The result was an improvement in conformability from 40% to more than 90%. Analysing those results enabled the researchers to derive a readyto- use formula that reveals the underlying physics and predicts the conformability of flexible electronics. “It’s like a digital twin technology,” says Li. “We can build a variety of different models, run the simulation and get the solution.” This process, he adds, can take a matter of minutes or hours depending on the number of models and their complexity.

Considering the hours that go into experimentation with medical devices to reach a workable prototype, it’s not difficult to imagine the benefit that a computational model could bring to the field. This is especially true given the flexibility of the software. “We’re using mathematics and computational tools to provide a very generic guideline for the theoretical study of this kind of challenge,” says Lu. She adds that the mathematical equations within her and Li’s research provide a framework for others to conduct similar experiments by changing the values according to attributes like the radius and thickness of the materials they’re working with. “Our equations can readily give them how many cuts and how long the cuts should be,” she says. These equations are specific to spherical surfaces, but using the software package, “any arbitrary surface can be numerically simulated”, Lu adds.

Part of the significance Lu sees in her and Li’s research is that it could shift the nature of expertise required to design flexible electronics with medical applications. In a field that tends to be dominated by the electrical engineers who design the circuits and mechanical engineers focused on manufacturing them, as well as materials scientists and chemical engineers, she sees the approach she and Li have taken to solve their artificial retina problem as both an outlier and a catalyst. “Our work is the starting point for this line of research,” says Lu. “We need to continue to educate the major players in this field so that they can understand the value of this kind of fundamental research and how they can leverage it without knowing the complicated mathematics and mechanics.”

Just how fundamental the duo’s simulation-based approach will be to the future of flexible electronics remains to be seen, but researchers grappling with similar problems have nothing to lose by trying it out. “The package is already open-source through a GitHub repository,” says Li. “The current name is OpenFSI.”