Focusing on Presbyopia Correction with Simulation

Presbyopia is an eye disorder that results in the loss of the near vision. The World Health Organization (WHO) says that “uncorrected presbyopia is the most common cause of visual impairment” — and it becomes more prevalent as we get older, with an onset at around 45 years old.

While we’re young, visual accommodation helps our eyesight to naturally adapt its distance of focus for far and near objects. Among other factors, the crystalline lens of the eye is able to change its shape through a complex biomechanical process that causes far vision to be passive and near vision to be active. However, as we age, geometric changes happen in the lens. The growth of the lens and the mechanical property change of the lens (the lens gets stiffer) cause the ciliary ring to be pushed forward. Lens compliance is affected more and more until the amplitude of deformation is almost nonexistent between far and near vision. The lens’ shape increases, and its equivalent refractive power and overall diameter decrease to the point that, in cases of presbyopia, the most accommodated shape ends up being the far vision.

Anatomy of a human eye for the near and far vision, with the main structures involved in the accommodation process labeled. Image courtesy Kejako.

While corrective lenses, such as eyeglasses, are the safest and most reliable way to address vision problems associated with presbyopia, they do not address every problem associated with the presbyopia — and not everyone likes wearing spectacles.

Reading glasses have been around for quite a while to help correct visual impairment from disorders like presbyopia. This painting, called the “Glasses Apostle”, was painted by Conrad von Soest in 1403. Image in the public domain in the United States, via Wikimedia Commons.

Some people choose to undergo refractive surgery to address this type of near-vision loss. Currently, this surgery is invasive and can still come with visual compromises — patients may experience vision that produces a glare or halo or have problems seeing in dim lighting. Further, many in vivo imaging technologies available for these procedures are not able to accurately account for every factor or practical clinical measurement in the visual accommodation process.

Left: Halos at night. Right: Glare at night. Images courtesy Kejako.

To address these limitations as well as the root problem of presbyopia, David Enfrun, Aurélien Maurer, and Charles-Olivier Zuber at Kejako developed a 3D parametric mechanical model of the human eye as well as an optical evaluation technique using the COMSOL® software. According to Enfrun, cofounder and CEO of Kejako, the research team "decided to approach ophthalmology with an antiaging mindset," so they turned to simulation in order to look for a "biomechanical alternative to reading glasses and heavy surgeries." With their model, the team can use a reverse engineering technique to deduce nonmeasurable properties from in vivo imaging.

Modeling Solutions to the Age-Old Problem of Presbyopia

Because the visual accommodation process is so complex, simplifications are often made when it comes to modeling the eye and its components. For instance, many models are axisymmetric and do not account for the natural variability of the organs of the eye. The models focus on either the accommodation’s mechanical or optical aspects, meaning only a few of the eye components are modeled and material properties are approximated rather than taking real behaviors into account.

In vivo technologies for ophthalmology have contributed greatly to advances in 3D modeling, but each type has its pros and cons:

• Magnetic resonance imaging (MRI) provides the best results (low distortion, high resolution) for internal geometry but is hard to use outside of labs
• Optical coherence tomography (OCT) helps retrieve info on the optical axis but induces some spatial distortions
• Ultrasound biomicroscopy (UBM) gets images of nontransparent eye parts but induces high spatial distortions

After making corrections and extrapolating information from in vivo imaging, some material properties are still difficult to measure. What’s more, nonmeasurable properties are often essential when trying to correct presbyopia, such as the stiffness and the refractive index distribution in the crystalline lens.

Setting Up an Optomechanical Model of the Human Eye

In an effort to obtain this important data, the Kejako research team built a model of their own using the Nonlinear Structural Materials Module, Structural Mechanics Module, and Ray Optics Module; add-on products to the COMSOL Multiphysics® software.

First, they developed and validated a complete 3D nonaxisymmetric model of the human eye’s accommodation that includes the main organs involved in the visual accommodation process. Since the validated model proved capable of simulating presbyopia progression, the researchers were able to further develop the model geometries, including accounting for both nearsighted and farsighted geometries.

The parametric optomechanical model of the human eye developed by Kejako. Image courtesy Kejako.

The research team also used the CAD Import Module to prepare the model geometries based on an OCT scan of a relatively young eye belonging to a 22-year-old patient. While they used this imaging as a basis for their model, the researchers will eventually be able to help customize patient procedures by importing each patient’s biometry data into the model so they can “have an exact representation of each patient’s eye and its actual presbyopia stage.”

This could significantly advance presbyopia treatment, as according to Maurer, the current implant market is “like a ready-to-wear shop for shoes: a bunch of different sizes.” However, each person’s eye is different; the distances between components and their individual shapes creating a unique combination. In addition, Zuber says that not all patients at a given age are experiencing the same stage of presbyopia when it comes to lens hardening, and the lens properties are not “evenly distributed among patients.” Using simulation could help create optimized laser treatments that fit each person’s needs. As Maurer explains, “the combination of imaging, simulation, and laser enables us to make a patient-specific treatment.”

The OCT imaging provided the team with geometries in the optical axis for two optical stimuli: 0D for far vision and 6D for near vision. Measured in diopters, these geometries indicate the power of the lens and its ability to focus light on the retina. They used additional measurements and properties from validated experiments and reference data. The researchers were then able to submit the sample tissue to both mechanical and optical tests to increase their ability to obtain more material properties. The model was considered ready once the unaccommodated geometry entered a tolerance of +/-5% with the far vision measurement. (For more details, take a look at Kejako’s research paper, which was presented at the COMSOL Conference 2017 Rotterdam.)

OCT imaging of the subject (left) alongside a CAD simulation (right). Images courtesy Kejako.

Deducing the Refractive Index for 2 States of Vision

To model the refraction of the lens, the researchers used the Wall Distance interface to create a repartition of the refractive index that follows the deformation of the lens during accommodation. The team’s goal was to compute the refractive index and its spatial distribution for both farsighted vision and nearsighted vision conditions.

In their first study (“Test A”), they prepared the geometry to account for these extreme conditions, hypothesizing that the refractive index is homogeneous in the lens. They then applied a two-parameter function to the generated distance field to create a gradient of refractive index (GRIN) that lined up with natural optical properties.

Left: A GRIN measured with MRI. Image from S. Kasthuriranagan et al., “In Vivo Study of Changes in Refractive Index Distribution in the Human Crystalline Lens with Age and Accommodation“, 2018. Right: Simulation showing 3D cuts of the distance gradient generated with the Wall Distance interface. Image courtesy Kejako.

The second study they prepared (“Test B”) focused on the model of the GRIN. By running parametric sweeps, the researchers sought to extract a unique couple of parameters for the GRIN that match both vision states.

Map of a GRIN that matches the two states of vision. Image courtesy Kejako.

Evaluating the Simulation Results

After examining the overall simulation, the researchers were able to verify that their results for the 3D parametric human eye model geometry were consistent with scientific literature. For instance, the far-vision data has a less than 3% difference in the lens position and shape. In addition, the researchers found that the results for the individual studies are consistent with validated data. The values they obtained in Test A are well within the range of the equivalent measurements from verified studies, and the GRIN results in Test B are consistent for both visual conditions.

Based on these two studies, the team found some surprising results that helped inform their research and reverse engineering capabilities. For instance, contrary to their hypothesis that the refractive index is homogeneous in the lens, the results for Test A show that a unique homogeneous refractive index matching the amplitude of the patient’s stimuli (0 to 6D) could not be found. In addition, when the far-vision-matching homogeneous refractive index is used for near vision, it induces an accommodation amplitude of 4.35D instead of 6D — the homogeneous refractive index value needs to be much higher when computed for near vision.

Based on their GRIN model results, the researchers also found something interesting concerning the natural optical structure: The human eye will induce a nonlinear response to try to maximize the optical power of the lens tissue. As shown below, to achieve the same maximal value of the plateau, the gradient induces bigger changes than the maximal values.

Effect of two different GRIN intensity parameters with the same plateau value in the far vision. Image courtesy Kejako.

Furthermore, due to the natural optical structure, the eye has a greater range of focus with a lower maximal value of the refractive index. Shown below is a schematic of the GRIN acting as a multiplicative factor for the accommodation. For each state of vision, the lens tissues move with the accommodation. The optical configuration for far vision is clearly quite different than the configuration for near vision. By inducing this nonlinear response, the GRIN contributes to improving the amplitude of vision.

Finite multilayer representation of the GRIN with decomposition in equivalent lenses for each layer. Image courtesy Kejako.

Deducing nonmeasurable properties like the ones above could lead to important developments in eye care, such as the prevention and correction of presbyopia. The Kejako researchers quickly understood the value of this ability in the ophthalmology field. After developing and validating their model, they opened an internal department dedicated to answering research and development questions that their tools and simulations can help answer.

The Future of Simulation in Eye Care

In the future, simulation could help the team learn more information, such as what effect laser treatment has on a patient’s amplitude of accommodation. The reverse engineering technique could also come into play in their plans to determine the mechanical properties of a lens from elastography imaging.

Already, their model results have helped answer some questions about visual accommodation. Soon, the researchers hope their model will not be limited to visual accommodation and can be used in diagnostics and the optimization of personalized medical procedures as well. To accomplish this, the team is working on improving the eye model so that they can simulate potential solutions for treating presbyopia.

Enfrun explains that they’re further developing the model for lab testing by “increasing the physical interpretation of what can happen in lab testing,” whether ex or in vivo (currently, the researchers are testing ex vivo feasibility). With improvements like this, the model could reduce the number of biological (e.g., in vivo) tests needed, which was one of the team’s goals. Enfrun says they chose simulation “as a tool for us to understand the visual accommodation process without further ex vivo/in vivo testings.”

For more information about the 3D full-eye model, you can read the research paper by clicking the button below:

Learn even more about Kejako’s optomechanical modeling research on pages 6–9 of Multiphysics Simulation 2018.

What Is Photoacoustics?

In basic terms, photoacoustics is when light induces vibrations in matter. The effect occurs when light pulsed onto the surface of a material generates heat. The heat causes the lighted area of the material to expand, which sends a pressure wave through the solid material.

A simple representation of the photoacoustics process.

Bell’s Photophone Leads to an Unintentional Discovery

Alexander Graham Bell discovered photoacoustics by accident when he was working on the development of the photophone, a followup to his recently developed telephone that operated via modulated sunlight instead of electricity.

You would operate a photophone by speaking into its transmitter toward a mirror placed inside of it. The vibrations of your voice would then cause similar vibrations in the mirror. Next, sunlight was directed into the mirror to capture the vibrations and project them into the photophone’s receiver. The vibrations would then be turned back into audible sound.

An illustration of the photophone. Image is in the public domain, via Wikimedia Commons.

Out of all of his innovations, Bell was most proud of the photophone. The rest of the world didn’t feel the same. For one, the device didn’t work when it was cloudy or rainy (obviously, as it needed sunlight). In an article in The New York Times from August 1880, the photophone was even ridiculed:

“Does Prof. Bell intend to connect Boston and Cambridge…with a line of sunbeams hung on telegraph posts[?]…There is something about Professor Bell’s photophone which places a tremendous strain on human credulity.”

Despite its stunted success, Bell made an unintentional discovery through the photophone. He observed that when he illuminated a solid material with a rapidly pulsed beam of modulated light, it caused an acoustic frequency to emit at the same frequency as the beam of light. Bell called the effect “photophonic phenomena” or “radiophony”; what we now know as photoacoustics.

The Revival of Photoacoustics in Research

Photoacoustics research fell by the wayside for a few decades, perhaps due to the unpopularity of the photophone or the scientific community’s focus on other areas of study. A gradual revival of interest in photoacoustics began in the late 1930s, spanning from Russia to Germany to the U.S.

An early example of photoacoustics research came about in France within the biomedical field. In 1964, a pulsed laser light was directed into the eyes of a rabbit to study its retinas. Don’t worry — the rabbit wasn’t harmed and the laser only caused it to blink a few times.

“Photoacoustics? I thought you said ‘carrot sticks!’”

The first in vivo photoacoustics study took place a few decades later, in 1993, when a pulsed laser was used to produce an image of a human finger. Moving into the 21^st century, photoacoustics has become more accepted as a biomedical research method. (Ref. 1)

Investigating Photoacoustic Effects with Simulation

Nowadays, the photoacoustics effect and photoacoustic imaging are useful for nearly any application area that involves generating images of opaque material samples. Using acoustics modeling software, it’s possible to study this phenomenon and optimize devices that rely on it.

Photoacoustic effects can be solved by the thermoviscous acoustics equations, which account for the acoustic perturbations in pressure, velocity, and temperature. Thermoviscous acoustics are involved in the study of many different devices, including:

• Condenser microphones
• Miniature loudspeakers
• Hearing aids
• Mobile devices
• MEMS structures

Application areas that involve thermoviscous acoustics: vibrating micromirrors, acoustic mufflers, perforates, and condenser microphones (clockwise from top left).

Specialized Thermoviscous Acoustics Features in the COMSOL® Software

By adding the Acoustics Module to the COMSOL Multiphysics® software, you gain access to the Thermoviscous Acoustic, Frequency Domain interface, which can be used to simulate photoacoustic effects. This interface includes predefined functionality for modeling thermoviscous acoustics phenomena and solving the full linearized compressible Navier-Stokes, continuity, and energy equations for a fluid. This is useful because the thermoviscous acoustics equations are complex and can be difficult to solve “by hand”. In addition, because of the large 3D domains involved, a typical photoacoustics model may involve many degrees of freedom, taking up valuable computational memory and time.

Consider the Photoacoustic Resonator example model, in which a pulsating laser heats a gas, which causes it to expand and contract, creating pressure waves. A well-designed photoacoustic resonator can be used as a sensor for measuring the material parameters of a gas; for instance, a system’s resonance frequency depends on the gas inside.

Geometries of the resonator (left) and heat source (right) for a photoacoustic resonator model.

To find the frequency in the resonator, you can add the Thermoviscous Acoustic, Frequency Domain interface as well as a Heat Source domain feature, which accounts for heat generated by the pulsating laser. Boundary conditions applied to the model geometry (which, in this example, is based on the published research referred to in the model documentation) include the:

• Slip condition (for the velocity field)
• Adiabatic condition (for the temperature)

These two boundary conditions mimic the standard Pressure Acoustics boundary conditions to avoid any viscous or thermal boundary layers at the walls (the layers are insignificant here).

The laser beam energy distribution is given by a Gaussian with the standard deviation — which, in this model, is 1/100 of the resonator radius. By using a boundary layer mesh, only a small section along the longitudinal axis of the geometry requires fine mesh elements to resolve the laser pulse width. The rest of the geometry can employ a coarser and computationally efficient mesh.

Using a boundary layer mesh saves computational memory and modeling time.

The COMSOL® software solves the model to find the frequency response, pressure, and sound pressure level. In addition, an eigenfrequency study is performed, which shows that the pulsating laser excites the symmetric eigenmodes, not the asymmetric ones.

The pressure (left) and sound pressure level (right) of a photoacoustic resonator.

Other Applications of Photoacoustic Methods

Making Strides in Medical Diagnostics

Photoacoustics combines the capabilities of optical and acoustical imaging. This combination offers the best of both worlds in terms of biomedicine, as it makes photoacoustic imaging a multiscale, high-resolution, and noninvasive technique.

A video showing photoacoustic imaging of a tumor in human breast tissue. Video file by M. Toi et al. and licensed under CC BY 4.0, via Wikimedia Commons.

Some potential applications of photoacoustics for biomedicine (Ref. 2) include:

• Generating images of vasculature that show the level of oxygen in the blood vessels
• Photoacoustics-based mammography systems for more accurate results and a patient-friendly experience
• Locating cancerous tumors without any interaction that could alter the cancer’s course of action

Understanding How Plants Grow

Photoacoustics sheds light on the three main phenomena that occur within plants and algae during the process of photosynthesis:

1. The photothermic signal, or the thermal expansion tissues, liquids, and gases undergo via light
2. The photobaric signal, or the increase in pressure due to a burst in gaseous oxygen from the light on the plant surface
3. Electrostriction, which is when a plant changes in either volume or spatial conformation

One major benefit of photoacoustics for this type of research is that measurements can be performed in vivo. Researchers can study photosynthesis in a living plant, enabling them to see how herbicides, soil toxicity, and more affect plants in real time.

Photoacoustics can be used to analyze different types of plants and algae.

For example, researchers used photoacoustics to analyze the efficiency of photosynthesis in phytoplankton, as well as its biomass. Doing so enabled them to see how the presence or absence of different nutrients affected the plant samples with studies that were faster, easier, and more direct than other methods. (Ref. 3)

Detecting Molecular Gas Remotely

Photoacoustic spectroscopy (PAS) is an ultrasensitive way to detect trace amounts of molecular gas flow in a sample of air. This is useful for monitoring pollution levels, detecting chemical agents and explosives, as well as monitoring illegal drug manufacturing sites.

In PAS, a laser beam is tuned to the specific absorption feature of a gas and swept through the sample at the speed of sound, which generates acoustic waves. The signal is amplified without a resonate chamber, enabling the gas to be detected remotely, and at very trace amounts. PAS is so sensitive that it has even detected the molecular flow of gas at 50 parts per trillion! (Ref. 4)

Investigating Hidden Features in Artwork

We’ve talked about how photoacoustics can be used in medicine, biology, and gas detection, but it also has a place in the art world. Photoacoustic microscopy (PAM) is the use of photoacoustics to uncover hidden features in works of art, such as the original sketch lines of a painting. This method can penetrate opaque layers of paint without damaging the artwork, unlike optical imaging and other methods.

PAM utilizes a conventional optical microscope with an inverted lens. A laser is pulsed at the inverse side of a painting (the blank side of the canvas) to reveal the patterns underneath. To test the process, researchers created mock versions of famous paintings to see how red, blue, and green paint — as well as sketching materials such as pencil and charcoal — respond to PAM.

This type of research could be used to verify the authenticity of valuable artwork and even answer some of the art world’s greatest mysteries. If Leonardo Da Vinci wrote the name of Mona Lisa’s subject on the famous painting, for instance, we could use this method to find out her true identity!

Next Step

Get a closer look at the specialized features and functionality for acoustics modeling by clicking the button below:

References

1. S. Manohar and D. Razansky, “Photoacoustics: a historical review“, Advances in Optics and Photonics, vol. 8, no. 4, pp. 586–617, 2016.
2. K. Kincaid, “Optoacoustic Imaging/Photoacoustics: The wide-ranging benefit of photoacoustic commercialization”, BioOptics World, 17 Feb. 2016; https://www.bioopticsworld.com/articles/print/volume-9/issue-2/biooptics-features/optoacoustic-imaging-photoacoustics-the-wide-ranging-benefit-of-photoacoustic-commercialization.html.
3. Y. Pinchasov-Grinblat and Z. Dubinsky, “Photoacoustics: A Potent Tool for the Study of Energy Fluxes in Photosynthesis Research“, Artificial Photosynthesis, ed. M. Najafpour, InTech, pp. 257–271, 2012.
4. C.M. Wynn et al., “Dynamic photoacoustic spectroscopy for trace gas detection“, Applied Physics Letters, vol. 101, no. 18, 2012.

ISFETs: Applications, Benefits, and Design Considerations

ISFETs are similar in design to metal-oxide-semiconductor field-effect transistors (MOSFETs), and they offer several advantages over other pH sensors. For one, ISFETs are made of silicon, hence they are more durable than other options, which are typically made of glass. This is especially advantageous for quality testing in the food, medical, pharmaceutical, and environmental fields, where broken glass could lead to contamination and setbacks.

ISFETs can handle extreme acid and alkaline pH levels and they are also small, lightweight, fast, and have a high sensitivity. These qualities are useful for applications that require portability and high performance, including:

• Monitoring beer fermentation
• Manufacturing dairy products like cheese, milk, and yogurt
• Analyzing soil for herbicides, chemicals, and other toxic chemicals
• Handheld drug detection devices

Schematic of a typical ISFET. Image by Huijunan — Own work. Licensed under CC BY-SA 4.0, via Wikimedia Commons. Though not shown explicitly in the drawing, the black wires are understood to penetrate the yellow-orange insulators to make connections with the n+ source and drain regions.

Despite their many benefits, ISFETs also have a few drawbacks, such as drift and temperature sensitivity. They also have a limited dynamic range and can produce high levels of noise. In addition, the minimum voltage required for an ISFET to operate (i.e., the threshold voltage) can vary. These factors impact ISFET accuracy and stability and cause a need for frequent adjustments, which makes them unsuitable for biosensing applications (such as DNA analysis) and processing circuitry.

In order to account for these factors, engineers must accurately analyze ISFET designs while taking into account the chemical reactions and electromagnetics phenomena, and more. The COMSOL Multiphysics® software, along with the Semiconductor Module and either the Microfluidics Module or a chemical engineering add-on module, provides features to do just that.

For details on the available add-on products for modeling ISFETs, check out the COMSOL® product suite).

Modeling an ISFET with the COMSOL® Software

The ISFET example highlighted here consists of two domains:

1. Semiconductor
2. Electrolyte

The semiconductor domain is similar to that of a MOSFET, but an ISFET uses an electrolyte rather than a metal gate. The electrolyte domain contains hydrogen and hydroxide ions, in addition to a pair of generic anions and cations as in this similar model: Diffuse Double Layer model.

You can find more information about this example in the Simulation of an Ion-Sensitive Field-Effect Transistor (ISFET) tutorial. The accompanying documentation provides detailed instructions for setting up and solving the model, and the MPH-file is available for download if you have a COMSOL Access account and valid software license.

You can couple the semiconductor and electrolyte domains after modeling each domain individually. The electric potential from the electrolyte is applied on the oxide surface of the semiconductor domain, and the displacement field from the semiconductor side is applied on the boundary of the electrolyte domain.

The electric potential in the ISFET.

The resulting coupled system is nonlinear, so you need to use a series of studies to solve the problem.

The first three studies solve for the:

1. Electrolyte domain
2. Semiconductor domain
3. Coupled system in different scenarios

A fourth study is then used to show how the ISFET performs under normal operation, when a feedback circuit maintains a constant drain current. To save time, this circuit does not need to be modeled explicitly. Instead, you can use a global equation to simulate the effect of the feedback circuit.

Evaluating the Simulation Results

Starting with the study of the electrolyte domain, you can see the electrolyte potential along its center. The results can be compared to a 1D approximation formula (Ref. 1 in the model documentation). As shown below, the general curve of the results is in good agreement with the 1D approximation.

The electrolyte potential of the ISFET model (solid curves) and 1D approximation (dotted curves).

Next, you can evaluate the operation of the ISFET. The left plot below indicates the response of the ISFET when the drain current is controlled by the applied gate voltage, while the right plot demonstrates the effect of three different pH values on the drain current-drain voltage curve, with the gate voltage fixed. These results help a designer to determine the best operating point for the ISFET.

Left: The drain current of the ISFET as a function of the applied gate voltage. Right: The drain current for a pH value of 3, 7, and 11.

Once the operating point is chosen, the sensitivity curve can be extracted by simulating the ISFET in the constant-current mode with a feedback circuit as described above. The slope of this curve matches that of the reference paper (Ref. 1 in the model documentation).

The sensitivity of the ISFET.

Using a model like this one, engineers can study ISFET sensor designs and improve their performance for various applications.

Next Step

Want to try this ISFET model for yourself? Click the button below to head to the Application Gallery. There, you can find detailed documentation and the MPH-file for the example.

Taking a Closer Look at MOS Capacitors

A MOS capacitor (MOSCAP) contains three main parts:

1. A semiconductor body or substrate
2. An insulator film
3. A metal electrode (or gate)

There are two main types of MOSCAPs: surface channel and buried channel designs. The design used depends on the application.

A MOSCAP. Image by Brews ohare — Own work. Licensed under CC BY-SA 4.0, via Wikimedia Commons.

In general, MOS structures are used in silicon planar devices to generate capacitance measurements, helping engineers to understand the working principles of these devices. MOSCAPs specifically are used in charge-coupled devices (CCDs) for medical and imaging technology applications. Typically, they serve as components in MOS transistors, commonly used semiconductor devices found in integrated circuits and components like microprocessors.

To ensure MOSCAPs function properly, engineers need to predict their behavior. The Semiconductor Module, an add-on to COMSOL Multiphysics, provides multiple methods for analyzing MOSCAPs.

2 Ways to Simulate a MOSCAP

The 1D MOSCAP model used in these examples is grounded on the right endpoint and has an oxide-silicon interface at the left endpoint. To better study the oxide-silicon interface, engineers can refine the mesh at this point via a user-controlled mesh. There is also a uniform doping and Shockley-Read-Hall recombination applied throughout the modeling domain. In addition, to make the model setup process easier, engineers can use the material data for silicon that is available directly in COMSOL Multiphysics.

Using a model like this one, researchers can analyze MOSCAP behavior in many different ways, such as with the two methods briefly discussed below.

Tip: The methods featured here are explained with step-by-step instructions in the documentation for these examples, which is linked to at the end of this post.

Method 1: Voltage Sweep

In the first example, the model domain is 1 mm thick and the MOSCAP is simulated using a voltage sweep with a Stationary study step for the initial condition as well as a Time-Dependent study step for the sweep.

When using this functionality, it’s possible to study the MOSCAP behavior under a linear voltage ramp. Here, the voltage ramp ranges from -2 to 1 V. It has a low-frequency slew rate of 10^-3 V/s and a high-frequency slew rate of 10³ V/s.

Method 2: Small-Signal Analysis

Engineers may also want to run a small-signal analysis to determine differential capacitance values at an array of DC bias points in a MOSCAP design.

As of COMSOL Multiphysics® version 5.3a, there are two features in the Semiconductor Module that can be used in semiconductor models. The first is the Semiconductor Equilibrium study step, which can be used to study systems in equilibrium and to produce initial conditions for nonequilibrium systems. There’s also the Quasi-Fermi level formulation, which helps engineers deal with highly nonlinear systems of equations when modeling semiconductor devices in extreme conditions, like very low temperatures.

The Semiconductor Equilibrium study step in the COMSOL® software.

These features are demonstrated in the small-signal analysis model of the MOSCAP. As a result, this method can examine an array of linear DC bias voltages ranging from -2 V to 1 V. At the same time, it can account for a small-scale harmonic perturbation of 1 mV that has a frequency of 10^-3 Hz for the low-frequency case and 10⁴ Hz for the high-frequency case. The model used in this example has a domain thickness of 10 um.

MOSCAP Simulation Results

Both of these simulation methods can be used to calculate low- and high-frequency C-V curves, which are important for analyzing MOSCAP designs. You can see these curves in the images below for both versions of the MOSCAP model. Both methods generate similar C-V curve results.

C-V curves for the voltage sweep (left) and small-signal analysis (right).

We found that the behavior seen in both plots matches what is typically seen in textbooks, such as the plot in Reference 1 in the model documentation. As such, these models highlight the ability of the Semiconductor Module to reach an accurate solution when using alternative methods.

Next Steps

To try the examples discussed in this blog post, click the links below. Doing so will take you to the Application Gallery, where you can download the PDF documentation with step-by-step instructions. If you have a valid software license, you can also get the related MPH-files by logging into your COMSOL Access account.

• MOSCAP 1D
• MOSCAP 1D Small Signal

Learn more about semiconductor simulation on the COMSOL Blog:

• Learning Quantum Mechanics Concepts with Double-Barrier Structures
• Computing the Band Gap in Superlattices with the Schrödinger Equation

The original version of this post was written by Alexandra Foley and published on July 15, 2013. It has since been revised with additional details, animations, and an updated version of the featured model.

The Doppler Effect, Explained

One of the most common ways we experience the Doppler effect in action is the change in pitch caused by either a moving sound source around a stationary observer or a moving observer around a stationary sound source. When the sound source is stationary, the sound that we hear is at the same pitch as the sound emitted from the sound source.

Sound waves propagating from a stationary sound source in a uniform flow (this corresponds to the source moving at constant speed).

When the sound source moves, the sound we perceive changes. Going back to the ambulance example, when an ambulance drives past us, the siren sounds different than it would if we were standing right next to it. The moving ambulance has a different pitch as it approaches, when it is closest to us, and as it passes us and drives away.

As the ambulance moves toward us, each successive sound wave is emitted from a closer position than that of the previous wave. Because of this change in position, each sound wave takes less time to reach us than the one before. The distance between wave crests (the wavelength) is thereby reduced, meaning that the perceived frequency of the wave increases and the sound is perceived to be of a higher pitch. Conversely, as a sound source moves away, waves are emitted from a source that is farther and farther away. This creates an increased wavelength, a decreased perceived frequency, and a lower pitch.

The situation is mirrored when we drive by the siren of an ambulance that is parked. In this instance, the observers (us) move toward the source (the siren) and the sound waves reach us from closer and closer positions as we move.

Visualizing Another Example of the Doppler Effect

Another example of the Doppler effect that is easy to visualize involves waves on a water surface. For instance, a bug rests on the surface of a puddle. When the bug is stationary, it moves its legs to stay afloat. These disturbances propagate outward from the bug in spherical waves.

When the bug starts moving across the water, the water flow around the bug changes. The waves appear closer together when we look at the bug swimming toward us (eek!) and farther apart as it swims away (phew!) The animation above shows the principle for waves (ripples) on water, which move much slower than the speed of sound. The slower speed is why, in this instance, the Doppler effect can be seen with the naked eye.

Simulating the Doppler Effect

By using the COMSOL Multiphysics® software and the add-on Acoustics Module, you can simulate the Doppler effect and measure the change in frequency for a source moving at a certain velocity. Let’s assume that the air surrounding the sound source (the ambulance, in this case) is moving with a velocity of V = 50 m/s in the negative z direction. We also assume that the observer of the sound is standing 1 m from the ambulance as it passes by. In the figure below, we can see the change in the pressure as the ambulance approaches and passes an observer.

In this plot, the distance of the ambulance from the observer is represented on the x-axis. The solid line represents the pressure perceived by the observer of an approaching ambulance and the dashed line shows the pressure as the ambulance gets farther away.

From this plot, we can see how the amplitude of the wave (or pressure) drops off at a faster rate when the ambulance is moving away from an observer compared to when it approaches. The change in the amplitude of the wave depicts how the siren becomes quieter as the ambulance moves away. The rate at which the sound level decreases as the ambulance recedes is much faster than the rate at which the sound becomes louder as the ambulance approaches (as shown in the graph above).

To look at this effect in a different way, we can visualize the sound pressure level around the sound source (remember, the source is effectively moving in the positive z direction).

The sound pressure level around the sound source is represented by colors and contour lines. You can see how the outermost contour runs from well inside the physical domain to the perfectly matched layer, showing that the sound is greater below the source than above it.

Other Examples of the Doppler Effect

The Doppler effect is apparent in many other phenomena. One common example is Doppler radar, in which a radar beam is fired at a moving target. The time it takes for the beam to bounce off the target and return to the transmitter can provide information about a target’s velocity. Doppler radar is used by police to identify people driving faster than the speed limit.

The Doppler effect is also used in the field of astronomy to determine the direction and rate at which a star, planet, or galaxy moves compared to Earth. By measuring the change in the color of electromagnetic waves — called redshift or blueshift — an astronomer can determine a celestial body’s radial velocity. If you notice a star that appears red, it is quite far from Earth — and a visible sign that the universe is expanding!

Other applications that take advantage of the Doppler effect include meteorological forecasts, sonar, medical imaging, blood flow measurement, and satellite communication.

Next Steps

Click the button below to try simulating the Doppler effect. With a COMSOL Access account and valid software license, you will be able to download the MPH-file for the example featured in this blog post.

Additional Resources

• Learn about the man who discovered the Doppler effect in this blog post on Christian Doppler
• Explore the Acoustics Module

What Is a Shape Memory Alloy?

A shape memory alloy is a material that undergoes a phase transformation when it experiences a mechanical stress or temperature change. When the conditions return to normal, the SMA “remembers” its original shape and reverts to it.

Watch the video for a closer look at shape memory behavior!

The two crystal structures of SMA materials are known as austenite and martensite. Austenite is the SMA’s structure at higher temperatures, while martensite is the structure at lower temperatures. The transformation from austenite to martensite or vice versa is the cause of this “memory” behavior.

The basic phase transformation process in an SMA.

Common materials for SMAs include copper-aluminum-nickel and nickel-titanium alloys. The latter is often referred to as nitinol, which refers to its elemental makeup (ni for nickel and ti for titanium) as well as where it was first discovered (nol for Naval Ordnance Laboratory, which we will discuss later in this blog post).

A coil made out of a nickel-titanium alloy, an SMA.

If you search “nitinol” on various ecommerce sites, it is not hard to find SMA wires and other types of memory materials available for purchase.

The Accidental Discovery of Shape Memory Alloys

The discovery of the unique behavior of SMAs is a story in itself. Early research into SMAs took place in the 1930s, when scientists looked into certain unexpected behaviors exhibited by different metals. Swedish chemist Arne Ölander noticed and described a pseudoelastic behavior when observing a gold-cadmium alloy. However, the term “shape memory alloy” did not come into play until a laboratory accident happened around 30 years later…

In the late 1950s and early 1960s, the U.S. Naval Ordnance Laboratory was working on metallurgy research, as described in Ref. 1. A scientist named William J. Buehler was melting and casting bars of nickel titanium. While waiting for the bars to cool, he dropped one of the cooled bars on the concrete floor and noticed that it caused a dull thudding sound. He found this odd and dropped a bar that was still hot, which produced a lighter sound, like a bell. Worried that something had gone wrong in the casting process, Buehler ran to a drinking fountain and cooled the hot nickel-titanium bar under the water. When he dropped the now-cool bar, it produced the thudding sound.

A happy accident: Dropping a nitinol bar on the floor led to the discovery of its unique memory behavior.

The effect was later demonstrated in a Naval Ordnance Laboratory meeting. Buehler’s assistant passed around a thin strip of nickel-titanium alloy that had been stretched, bent, and folded like an accordion. When the object reached Dr. David S. Muzzey, he took out his pipe lighter and heated it. The alloy quickly unfolded and reverted back to the original thin strip shape. After realizing the unique qualities and behaviors of the nickel-titanium alloy under different temperature conditions, the material came to be known as nitinol, an SMA.

More recently, and looking to the future, the development of shape memory materials has moved beyond alloys. Shape memory polymers, and other variations of shape memory materials, have been developed and even released for different commercial uses.

Manufacturing SMAs for Applications Across Industries

The unique behavior of SMAs makes them an attractive choice of material for manufacturing products and components in a wide range of industries. (Ref. 2)

Aerospace

In the aerospace industry, SMAs are used to develop lightweight, quiet, and efficient designs: three factors that are always a point of focus for aircraft. Components such as variable area fan nozzles, vibration dampers, and actuators are created with SMA materials. These devices are austenitic at their normal temperature and then transform to martensitic (and the desired shape) when cooled via temperature change due to airflow around the aircraft or even the ambient temperature change that occurs during a normal flight.

The change in temperature used to induce the phase change can be brought about in different ways. There can be an electronic component that heats the SMA device, or the temperature change can be caused by excess air from the aircraft’s other parts.

A sample of a shape memory material being used in aircraft research and development. Image by Science Museum London/Science and Society Picture Library. Licensed under CC BY-SA 2.0, via Wikimedia Commons.

A more recent technological advancement for shape memory materials in aircraft is wing morphing. SMAs are being used to develop an adaptable aircraft wing that can bend and change shape while in flight.

Automotive

Back on the ground, automotive vehicles also benefit from SMAs, although the reasons have more to do with comfort and ease of use than operation. For example, some cars include an SMA valve for the pneumatic bladders in the seats. At a certain pressure, the lumbar support in a seat contours to the driver or passenger.

SMAs have also been used to build actuators that make vehicle trunks easier to close as well as noise, vibration, and harshness (NVH) valves to control noise and vibration in engines (an important performance indicator in the automotive industry).

Buildings

Building design is another application area in which SMAs are useful. Including SMA rods in concrete beams, for example, can help prestress a bridge or building. On a smaller scale, shape memory materials can be used for reliable pipe fittings in a pipe network.

Medicine

The use of SMAs for biomedical applications can reduce the need for medical intervention in patients. For example, medical stents can be implanted in arteries as a minimally invasive way to improve blood flow in cardiac patients. Microactuators and artificial muscles rely on SMAs for robotic prosthetics, which helps give patients with amputated limbs more freedom of motion.

Stents, a minimally invasive cardiac treatment method, are commonly made out of SMAs. (Note: This image, taken from the Plastic Deformation During the Expansion of a Biomedical Stent tutorial model, does not include SMAs and is purely meant to illustrate the application discussed above.)

On a smaller scale, SMAs are also used in orthodontia, such as braces; and optometry, such as glasses. If glasses frames are made with a shape memory material, they don’t have to be replaced if they get bent out of shape. Instead, they can be heated and return to their original shape.

Other Uses of SMAs

Recently, shape memory materials have been applied to consumer electronics. For instance, autofocus components for smartphone cameras as well as certain mobile antennas can be made out of SMAs.

Certain craft projects and toys also use SMAs. One example is “bendy bracelets”, which are made with a shape memory material that enables them to bend and twist before easily returning to their original bracelet shape. (The Slinky® toy, unfortunately, is made out of a type of steel and won’t return to a tightly wound coil after getting tangled — a common struggle of children everywhere.)

Drawbacks and Design Considerations

When developing a design or component made out of an SMA, there are certain factors and risks to consider. A major drawback of SMAs is the risk of fatigue failure. There are only so many times certain SMAs can be bent and deformed before they return to a shape that’s a bit different from the original one (or they break).

Another drawback is the considerable lag time of the phase change for certain SMAs. If you search for “shape memory alloy” videos online, you can see that the time for the material to return to its original shape can be slow and unpredictable.

Drawbacks such as lag time and fatigue can cause issues during the phase transformation cycle for SMAs.

From a manufacturing standpoint, SMAs can be expensive to produce, which limits their accessibility to manufacturers and consumers. Also, since most of these materials rely on temperature to undergo changes, it could be risky to use SMAs as part of a device that operates under uncontrolled or unstable temperature conditions. An SMA used for an automotive application, for instance, must be able to perform under all possible temperature conditions that a vehicle might experience.

Modeling Shape Memory Alloys in COMSOL Multiphysics®

The mechanics of an SMA are difficult to describe because of the complexity of the phase transformations that take place. This complexity can make modeling SMAs quite the endeavor.

As of version 5.3a of the COMSOL® software, the Nonlinear Structural Materials Module includes two of the most common material models for SMAs: Lagoudas and Souza-Auricchio. Using these material models in your simulation, you are able to define the austenite and martensite properties as well as the phase transformation properties of an SMA. You are also able to easily account for heat transfer in an SMA with a built-in coupling between the Heat Transfer in Solids and Solid Mechanics interfaces.

The Uniaxial Loading of a Shape Memory Alloy tutorial demonstrates using an SMA material model in the COMSOL Multiphysics® software.

In the tutorial model, a nitinol cylinder is subject to axial tension and three separate studies are performed:

1. Parametric sweep, showing the pseudoelasticity effect at different fixed temperatures
2. Prescribed displacement sweep, showing that the pseudoelasticity effect is a partially unloading and partially loading loop
3. Shape memory effect, shown after increasing the temperature

The model indicates that there is a temperature-dependent stress limit for the SMA. When the axial tension reaches the stress limit, the material transforms from the austenite to martensite structure; i.e., a “forward” transformation (deformation) occurs.

Stress and strain of the SMA at different temperatures.

During the unloading of the axial stress, the reverse transformation occurs. This “backward” transformation occurs at a lower stress level than the stress limit for the forward transformation and shows the material returning to its original shape.

The stress and strain curves, which illustrate the shape memory effect in the alloy.

Next Steps

Learn about the specialized features and functionality for mechanical analyses in the Structural Mechanics Module, an add-on to COMSOL Multiphysics, by clicking the button below.

Note: The Lagoudas and Souza-Auricchio material models for SMA also require the Nonlinear Structural Materials Module, an add-on to the Structural Mechanics Module.

References

1. G.B. Kauffman and I. Mayo, “Chemistry and History: The Story of Nitinol: The Serendipitous Discovery of the Memory Metal and Its Applications,” Chem. Educator, 2(2), 1997.
2. J.M. Jani et al., “A review of shape memory alloy research, applications and opportunities,” Materials and Design, 56, 2014.

Slinky is a registered trademark of POOF-SLINKY, LLC.

Advancing Heart Valve Research via Simulation

The four valves in a human heart are flexible enough to both fully open, enabling blood to flow in one direction through the heart, and tightly close, sealing the heart chambers and preventing backflow. However, with valvular heart diseases, the valves do not function properly, which can cause serious cardiac health issues. As a result, studying heart valves is an important research area.

Schematic of a heart. Image by Wapcaplet — Own work. Licensed under CC BY-SA 3.0, via Wikimedia Commons.

One recent advancement in heart valve research has been the development of the smallest approved mechanical heart valve in the world. This is an important achievement, as every year, over 35,000 babies in the United States alone are born with congenital heart defects. For some of these newborns, the defects result in malfunctioning heart valves that require surgery to fix.

Of course, the creation of the smallest approved valve is only one example of innovation in heart valve research. This area has also sparked the interest of a team at Veryst Engineering, a COMSOL Certified Consultant who has worked with clients on similar real-world problems. To further advance heart valve research, the team was inspired to create an example model of a heart valve. Such a model could serve as a valuable design tool, providing crucial information to medical researchers.

Modeling the Opening and Closing of a Heart Valve in COMSOL Multiphysics®

As you might expect, modeling a human heart valve can be difficult and computationally expensive. For one, this problem involves strongly coupled fluid-structure interaction (FSI), with a moving and deforming structure interacting with a flowing fluid. In addition, it’s important to accurately account for nonlinear material behavior, contact modeling, and fluid-mesh movement.

To address this challenge, Nagi Elabbasi (a member of the Veryst team) used COMSOL Multiphysics, saying that the software provides a “unique capability to capture all [of] the coupled effects involved.” Using COMSOL Multiphysics, Elabbasi created a simple example to highlight how engineers can overcome the challenges of modeling realistic heart valves and predict their behavior.

In this model, a heart valve opens and closes in response to the fluid flow. Modeling this movement wasn’t easy, with Elabbasi noting that “the main challenges in this model are the closing of the heart valve and accurately representing the material behavior of the valve.” This poses an issue because the fluid mesh can collapse when the heart valve is closed. To avoid excessive mesh distortion, the team opted to use the advanced mesh control features in the COMSOL® software.

Simulation Results for Fluid-Structure Interaction in a Heart Valve

Let’s now take a look at some of the results the team at Veryst obtained from their heart valve model, which analyzes flow patterns, variations, and residence times; flow recirculation around heart valves; and how these factors are affected by the movement of a valve. It’s also possible to use the model to investigate stress and fatigue in the valve material as well as blood pressure, shear stresses, and deformation. The team also found that simulation enabled them to analyze multiple aspects of the heart valve at once, such as the interaction between blood velocity, valve deformation, and von Mises stress in the valve.

The model results (seen below) show that there are dead flow zones around the valve and recirculation in the fluid. Both of these factors are affected by the opening and closing of the valve. In addition, the root of the valve has high stresses. Researchers can use these results to identify potential issues and improve the designs of artificial heart valves. Please note that because this example was made only to demonstrate what you can achieve when modeling heart valves, the results seen here are not completely realistic.

FSI model of a heart valve opening (left) and closing (right).

Multiphysics models can also be used to visualize a heart valve in action, as shown in the example below.

Animation of a heart valve. Animation courtesy Nagi Elabbasi of Veryst Engineering.

Improving the Design of Medical Devices with FSI Modeling

This example shows what medical researchers can achieve by using FSI simulation. Using models like this one, researchers and engineers can predict the behavior of real heart valves, potentially using this information to improve the designs of artificial ones. Elabbasi also mentioned that “FSI modeling should be performed by all medical device companies working on heart valves, providing related products (stents, for example), or analyzing cardiovascular diseases (aneurysms, for example).” The information provided by such simulations will help improve the design of medical devices, making them more effective in treating diseases.

Next Steps

• Check out other medical applications of simulation on the blog:
  • Analyzing the Deformation of a Biomedical Stent with Simulation
  • Analyzing Magnetic Flow Meters for Blood Flow Measurement
  • Finding an Accurate Model to Study Blood Flow Around a Stent

Enhancing Patient Care with RFID Systems

RFID technology is common in many industries. In healthcare, though, there is a major design challenge: size. RFID tags on the smaller end are about the size of a grain of rice, but for cellular-level uses (such as research and diagnostics), the designs need to be even smaller.

A group of Stanford researchers developed an RFID tag that is small enough to be implanted in a cell, such as a skin or cancer cell. The size of the tag is about one-fifth the thickness of a human hair. It works in conjunction with a specialized RFID reader that interprets the data and monitors the cell’s activity in real time. These tiny RFID tags also have the potential to be linked to sensors for advanced biomedical treatment, such as antibody detection and the destruction of cancer cells.

A surgeon implants an RFID microchip into the hand of a doctor. Soon, these tags could be implanted into single cells. Image by Paul Hughes — Own work. Licensed under CC BY-SA 4.0, via Wikimedia Commons.

No matter how good a doctor’s bedside manner is, patients don’t particularly enjoy being poked and prodded in order to get their vital signs taken. At Cornell University, researchers design ultrahigh frequency (UHF) RFID tags that can be used to monitor vital signs, such as heart rate, breathing, and blood pressure, without even touching a patient. The tags, which can be put into hospital wristbands or even sewn into clothes, communicate with an RFID reader that monitors multiple people in range simultaneously. The system relies on back-end software to manage, interpret, and monitor the data. This way, doctors get a clearer picture of each patient’s vital system performance, medical professionals save time and energy taking vitals, and patients are happier.

“Smart fabrics” are one potential application area of RFID systems. Image by Joshua Dickens. Licensed under CC BY-SA 2.0, via Wikimedia Commons.

Sleep disorders and sleep apnea are areas of biomedicine that often go untreated. Although they can lead to myriad health and safety issues, overnight sleep tests are costly and disruptive to a patient’s schedule, and at-home tests can be difficult to use. (I’ve personally undergone an at-home sleep test and it was extremely uncomfortable and awkward to strap the system around my torso, tape the breathing tubes to my face, and keep the monitor on my finger from falling off.)

To offer help in this area, researchers from RADIO6ENSE, the University of Palermo, and the University of Roma developed a passive RFID system for tracking sleep patterns remotely and in real time. The user-friendly passive RFID system involves RFID tags sewn into pajamas that don’t require any batteries and operate on a low power level, making them safe to use as wearables while they accurately collect sleep pattern data.

Considering EMI and EMC in Biomedical RFID Designs

Electromagnetic interference (EMI) and electromagnetic compatibility (EMC) are common phenomena in electromagnetics applications and can be analyzed with, for instance, EMC/EMI testing.

An anechoic chamber is one test facility used to test antennas for EMI/EMC.

EMI is of particular concern when it comes to RFID tags for biomedical applications, as an undesired mutual inductance can occur between devices and negatively affect performance, operation, and reliability. For instance, 2011 research from the National Center for Biotechnology Information says that RFID systems could be affected by contact with water, metal, or other devices (which is completely plausible in a medical scenario) — or RFID tags could negatively affect other medical devices. Additionally, a 2017 FDA report on RFID warns that EMI is a potential hazard when RFID systems interact with other medical devices.

When it comes to a patient’s well-being and safety, “potential hazard” is not a phrase healthcare professionals want to hear. That’s where simulation comes in…

Designing Optimized RFID Components in COMSOL Multiphysics®

Designers of RFID tags for biomedical applications need to account for the performance of tag and reader designs as well as how RFID affects other medical devices and systems. By characterizing a single device, such as an RFID tag, these designers have a good starting point for an EMI analysis. Electromagnetics simulation can be used to compute the mutual inductance of the RFID system design.

Improving Detection and Read Range in UHF Devices

Passive UHF RFID tags, like those mentioned at the beginning of this blog post, are preferred over their low-frequency and high-frequency counterparts because UHF tags can be detected at near and far distances from a reader, and can thus be used for a wide variety of applications. These tags also transfer data at fast rates and are more cost-effective to produce.

To evaluate the detection and read range of a UHF RFID tag, you can use the RF Module, an add-on to the COMSOL Multiphysics® software. RF simulation enables us to determine the default electric field norm, or E-field, for a tag design. This value can be used to predict the ideal placement of tags on a patient as well as the ideal placement of an RFID reader for tracking multiple patients at once.

Analyzing the E-field (left) and far-field radiation pattern (right) of a UHF RFID tag can improve the detection and range of the device.

Simulation analysis can also be used to find the far-field radiation pattern of a tag. For instance, in the model above, we can see that the radiation pattern is nearly the same in every direction on the plane of the tag. These results show that the RFID tag design is optimized for performance and has a long read range.

Ensuring the Safety of RFID Systems for Biomedical Use

Consider a model of a basic RFID system, which consists of a reader-transponder with two main parts:

1. Reader with large RF antenna
2. Tag with a printed circuit board antenna

Geometries of a reader (left) and RFID tag (right).

The system works as such: The reader generates an electromagnetic (EM) field that energizes the chip inside the RFID tag. The EM field is altered by the tag’s circuit and the altered signal is recovered by the RFID reader’s antenna.

Using the AC/DC Module, an add-on product to COMSOL Multiphysics, and the Magnetic Fields interface, designers can simulate the inductive coupling between the reader and the tag. By finding the total magnetic flux intercepted by one antenna for current flowing in the system’s other antenna, you can compute the mutual inductance.

The simulation results below show the magnetic flux lines and the magnetic flux intensity between the RFID tag and reader. These results can be used to determine the mutual inductance of the system.

The magnetic flux density of an RFID system.

By finding the mutual inductance of an RFID system, you are able to predict its EMI with other medical devices. What’s more, you can design RFID tags that can be safely used to enhance healthcare in a variety of ways.

Next Steps

Find out what’s possible with the built-in functionality in the RF Module by clicking the button below.

Further Resources

• Try the models featured in this blog post:
  • Modeling of a UHF RFID Tag
  • An RFID System
• Learn more about applying simulation to RFID designs in this blog post: RFID Tag Read Range and Antenna Optimization

Improving Human Health with Biomedical Stents

One common treatment for atherosclerosis is a procedure called percutaneous transluminal angioplasty, which removes or compresses unwanted plaque that has built up in a patient’s coronary artery. This procedure sometimes relies on stents, placed within a blocked artery by an angioplasty balloon.

After reaching the intended location, the balloon inflates the stent, which locks into an expanded position. The balloon is then deflated and removed, while the stent remains in the artery. The expanded stent functions like a scaffold, keeping the blood vessel open and enabling blood to flow normally.

A stent example. Image by Lenore Edman — Own work. Licensed under CC BY 2.0, via Flickr Creative Commons.

Of course, for the angioplasty procedure to be a success, the tools used must perform as intended. If the ends of the stent expand more than its middle — a common defect known as dogboning — the artery can face serious damage. Another potential issue is foreshortening, which makes it challenging to position the stent and can also damage the artery.

To avoid these issues and make the angioplasty a success, it’s necessary to evaluate stent designs. One step in this process is analyzing the deformation experienced by a stent.

Studying the Deformation Process in a Stent Using COMSOL Multiphysics®

For this example, let’s examine a Palmaz-Schatz stent model, the geometry of which is seen below. This model looks at the stress and deformation in a stainless steel stent that is expanded via a radial outward pressure on the tube’s inner surface. (The pressure represents the balloon expansion.) The original diameter of the stent is 0.74 mm, but after the expansion period, the middle section has a diameter of 2 mm.

Thanks to the inherent symmetry of the stent’s geometry, we can minimize the computational costs of this simulation by reducing the size of the model to 1/24 of its original geometry.

The full stent geometry. The reduced geometry used in this example is represented by the darker meshed area.

The Results of the Nonlinear Structural Mechanics Analysis

First, let’s look at the various stresses and strains experienced by the stent during operation. Below, we see the stress distribution in the stent at maximum balloon inflation (left) and the residual stress in the stent after balloon deflation (right). As expected, stress in the stent is reduced after the balloon deflates.

Stress in the stent during balloon expansion (left) and after balloon deflation (right).

Moving on, we analyze how the effects of dogboning (blue) and foreshortening (green) change in relation to pressure during balloon inflation. Using this plot, we can check for potentially harmful effects in the stent design and optimize its performance.

Dogboning and foreshortening in the stent vs. the pressure in the angioplasty balloon.

We also examine the effective plastic strains in the tube at maximum dogboning, as seen in the following image.

Effective plastic strains and deformation at the time of maximum dogboning. The peak value is about 25%.

In regard to the recoil parameters, note that the longitudinal recoil is around −0.9%, the distal radial recoil is about 0.4%, and the central radial recoil is approximately 0.7%. These parameters provide more details on how the stent behaves when the inflated balloon is removed.

Next Step

With the information provided by simulations like this one, engineers can improve the design of stents and optimize their use in biomedical applications. To try this example for yourself, click on the button below.

Further Reading

• Learn about other medical uses of simulation by reading these blog posts:
  • Finding an Accurate Model to Study Blood Flow Around a Stent
  • Analyzing the Mechanical Behavior of Cells for Biological Applications
  • Designing CSRR-Based Sensors to Monitor Chronic Kidney Disease

Benefits of a MEMS-Based Strain Gauge

Strain gauges measure how structures — both manmade and biological — react to an applied strain. These devices are common in the mechanical and civil engineering fields for monitoring the structural health of bridges, detecting soil pressure changes near oil drilling platforms, and testing aircraft components. Strain gauges can even be used to analyze bone structure in humans and animals.

A mechanical strain gauge used to measure the growth of cracks on the Hudson-Athens Lighthouse in New York. Image by Roy Smith. Licensed under CC BY-SA 2.5, via Wikimedia Commons.

In terms of performance, MEMS-based gauges have several advantages over standard foil strain gauges. For one, MEMS sensors have higher strain sensitivity than foil sensors, resulting in more accurate measurements. MEMS-based gauges also have higher fracture strength and can withstand high operating and bonding temperatures, which makes them more durable than their foil counterparts and expands their range of applications.

DETF strain gauges have their own set of distinct advantages:

• Small size
• High sensitivity
• High resolution
• High shock tolerance

To optimize the design of a new DETF sensor, researchers from the School of Engineering Technology at Purdue University used MEMS simulation.

Modeling a DETF Strain Gauge in COMSOL Multiphysics®

The research team created a 3D geometry of a strain gauge with the MEMS Module, an add-on to COMSOL Multiphysics. The model consists of a DETF — including the beams, base, and anchors — and an electrostatic comb drive. The researchers wanted to validate the simulation results, so they used the dimensions of an analytical model when setting up the model’s components.

The DETF strain gauge. Image courtesy A. Bardakas, H. Zhang, and D. Leon-Salas.

The research team used several of the built-in capabilities of the MEMS Module when modeling the strain gauge. The Thin-Film Damping feature was used to compute the forces between solid surfaces and the surrounding air. This effect accounts for the main cause of damping in the DETF.

The team also used the MEMS Module to set up a prestressed frequency analysis. This is important for many MEMS devices, as it helps determine the initial frequency of the device and how the frequency shifts once a load is applied.

Using a parametric sweep, the researchers determined how a range of applied forces affect the gauge without having to manually change the value and recompute the model each time. This enabled them to optimize their design more efficiently. Based on the results of the parametric sweep, the team modified the geometry to ensure that the device could accommodate a range of forces.

Evaluating the Simulation Results

The resonance frequency of the DETF gauge was computed via two methods. Using a frequency analysis, the researchers found a resonance frequency of 84.060 kHz for the model. This is slightly higher than the frequencies found using a fundamental mode analysis (83.263 and 83.271 kHz). This difference is likely because a denser mesh was used for the mode analysis.

Resonance frequency of the DETF strain gauge for different mode shapes. Image courtesy A. Bardakas, H. Zhang, and D. Leon-Salas

The team used the model to optimize the DETF strain gauge design by balancing its sensitivity and structural integrity. Next, they plan to use a two-mask silicon-on-insulator process to fabricate the design. In addition, the researchers plan to investigate strain loss in the device via further analyses and experiments.

Further Reading

• Learn more in the researchers’ full paper: “Design and Simulation of a Microelectromechanical Double-Ended Tuning Fork Strain Gauge“
• Check out other examples of simulating sensor performance:
  • Simulating a MEMS-Based Pressure Sensor Inspired by a Cave Fish
  • Studying the Influence of Concrete Phenomena on Sensor Performance
  • Simulation Delivers Reliable Results for Piezoresistive Pressure Sensors

Biological cells are essential for life as we know it. They not only store and replicate hereditary information in the form of DNA but also are instrumental in biological processes. In most, if not all, of these processes, the mechanical behavior of cells is a main factor in ensuring normal physiological functions.

The Importance of Biological Cells

It goes without saying that we would not exist or function without cells. Vertebrates utilize the circulation of red blood cells, erythrocytes, to deliver oxygen to body tissue. Fibroblasts use their contractile machinery to migrate to — and start the healing process of — wounds. The endothelial cells lining our blood vessels serve as filtration barriers. These cells not only rely on biochemical/transport mechanisms but also on their mechanical behavior to ensure normal physiological functions.

The structural entity responsible for providing cellular stiffness is an interconnected network known as the cytoskeleton, visualized in the image below. This cytoskeleton primarily consists of three types of polymerized filaments, each with their own distinct structure and mechanical characteristics:

1. Actin
2. Intermediate filaments
3. Microtubules

This complex foundation provides cells with the ability to adapt their mechanical properties to the environment, both instantaneously and over time.

A fibroblast cell with the cytoskeleton visualized, including actin (blue), intermediate filaments (green), and microtubules (red). Used with permission from Rathje et al. from the paper “Oncogenes induce a vimentin filament collapse mediated by hdac6 that is linked to cell stiffness”.

Both cells and cytoskeletal networks are highly viscoelastic, as you can see in the plot below of a relaxation curve from a cell indentation experiment by atomic force microscopy (AFM).

Force relaxation curve of a fibroblast cell.

Numerous examples exist in which a diseased cell exhibits abnormal mechanical properties, promoting the progression of pathology. The cytoskeleton found in these cells is often found to behave differently compared to healthy cells. For example, cancer cells are known to exhibit significant stiffness variations compared to control cells. In many cases, this can be linked to the cytoskeleton. The intermediate filament network could be collapsing around the nucleus or there could be increased cell spreading (closely linked to the actin cytoskeleton through focal adhesions).

Investigating the Mechanical Behavior of Filaments and Cells

As mentioned, the cytoskeleton is a dynamic entity with the capability of remodeling itself on a time scale from milliseconds to hours. A consequence of this is a pronounced viscoelastic behavior, due to the nature of the constituent networks. For example, a solution of actin filaments behaves like a solid at short time scales and a liquid at longer time scales. This is due to the link between the thermal fluctuations of semiflexible filaments and their propensity to slide between each other; i.e., they are more or less kinematically constrained at short time scales. The temperature is also an important factor, partly because it affects the thermal behavior, but also because of various linking proteins in the solution.

Taken together, the mechanical behavior of this type of underlying polymer network, together with other cell constituents (e.g., cell nucleus and membrane), it is clear that a detailed analysis accounting for all of these factors is nearly impossible. However, it is possible to circumvent this challenge and obtain results by considering the cell at a macroscopic level.

By creating a finite element model in the COMSOL Multiphysics® software, you can essentially ignore the heterogeneous intracellular structure and instead view it as a continuum; i.e., the displacement field is continuous. This is an acceptable approximation if your goal is to quantify the macroscopic cell response to external stimuli.

The computational model described in this blog post is that of a relaxation test. A rigid indenter is pressed into the soft, viscoelastic cell, and the resulting relaxation of the indentation force is measured and compared to experimental data.

Computational Model of a Cell

A model of a cell with typical dimensions is seen below. Note that the domain is created around the centerline. The semicircular section is the cell nucleus, which will also influence the mechanical response. We also create an indenter in the geometry and neglect the cell membrane in this analysis. For simplicity, we perform a 2D analysis by assuming the cell is axisymmetric.

The model is meshed with 2D elements and refined under the indenter.

The choice of material model for the cell cytoplasm and nucleus should reflect both the instantaneous and long-term response of the material. A linear elastic model is far too simple, as cells can typically withstand large strains and exhibit significant strain hardening. For the cytoplasmic response, we can choose a simple hyperelastic material model, the neo-Hookean model, in which stresses and strains are computed from a strain energy density function Ψ on the form

In this form, where the material is assumed (nearly) incompressible, the shear modulus µ, elastic volume ratio J_el, bulk modulus κ, and isochoric first invariant are included. To incorporate the viscoelastic behavior, two generalized Maxwell branches are also included. The nucleus has been found to be mainly elastic and is therefore modeled without viscoelastic branches.

The chosen material parameters are shown in this table:

The bottom of the cell is constrained vertically. While in reality, the cell adheres to the substrate through focal adhesions, this should be a local effect and not significantly influence the force response.

Contact between the indenter and the cell is enforced by a penalty formulation, using the indenter as the source boundary. The indenter domain is prescribed a velocity of 0.1 µm/s, until the total vertical displacement is 4.6 µm. It is subsequently held fixed for the remainder of the analysis, up to a total time of 30 s.

Simulation Results

The local deformation of the cell after indentation is shown in the plot below.

Deformation of the cell under the indenter.

The equivalent von Mises stresses at times 0.5 s and 30 s are shown below. Naturally, the stresses decrease due to stress relaxation because of the inclusion of viscoelastic branches for the cytoplasmic material model.

Stress distribution at 0.5 s (left) and 30 s (right).

The vertical reaction force on the indenter can be extracted from COMSOL Multiphysics and compared with experimental data.

Results for the indentation force of the cell, both experimental (blue) and computed (red).

The relaxation, as measured by experiments, typically exhibits at least two distinct regimes. These values are reasonably well predicted by the simple neo-Hookean model, along with its two viscoelastic branches. It should be noted that the initial indentation regime exhibits severe strain hardening prior to the constant slope (apparent in the plot above).

Final Thoughts on Biomechanical Modeling

As discussed, COMSOL Multiphysics can be easily used to replicate the viscoelastic behavior of cells by (comparatively) simple material models. Naturally, an increasing level of complexity can be obtained by using more complicated material models. In this case, using other hyperelastic models, such as the Mooney-Rivlin or Ogden models, in combination with a greater number of viscoelastic branches may yield even more accurate results. Keep in mind that as more material parameters are needed, more experimental data points must be available for the material in question.

The cell is in reality a far more complex system than modeled here. There is a constant exchange of mechanical and biochemical signals that constantly alter the intracellular structure, cell shape, and locomotion behavior. Suffice to say, modeling the cell as a continuum is a major simplification, but such an approximation can serve us well in many cases. If we were to analyze metastasizing cells, for example, it may be enough to characterize their macroscopic stiffness in order to assess their capability to squeeze through tissue or arteries. In such a case, the stiffness of the cell as a whole in comparison to the obstacle would be the determining factor, not the detailed interactions of, say, the cytoskeleton and cell nucleus.

It should also be mentioned that the cell is not only a complex system but also far from deterministic and not uniquely characterized by a set of geometrical and material parameters. The response between individual cells varies depending on their health, state of locomotion, and cell cycle state, among other factors. To properly assess the mechanical cell response of a cell type experimentally, a greater number of individual cells would need to be probed. However, we are content with evaluating the capability of modeling the response of an individual cell.

In general, not only cells but also other biological materials can often be modeled by utilizing hyperelastic material models. Depending on the particular material and time scale, viscoelastic behavior can also be included. This opens up some interesting opportunities in the field of biomechanical modeling.

For example, a common type of cardiovascular condition is atherosclerosis in which white blood cells accumulate on the arterial wall, reducing blood flow and increasing the risk of a heart attack due to a blood clot. A common procedure to alleviate this condition is angioplasty, when a balloon is inserted into the artery and inflated. A mechanical stent is then often used to stabilize the artery section. Using COMSOL Multiphysics, we could capture the hyperelastic-viscoelastic behavior of the arterial wall, as well as composite characteristics due to collagen fiber directions, and compute the instantaneous and transient development of stresses and strains.

Editor’s note, 8/20/18: The corresponding cell relaxation model file has been added to the Application Exchange. You can find it here.

About the Author

Björn Fallqvist is a consultant at Lightness by Design working with product development based on numerical analysis. He obtained a PhD from the Royal Institute of Technology in 2016, working with developing constitutive models to capture the mechanical behavior of biological cells. His main professional interest and specialization is in the fields of material characterization and using various material models to capture physical phenomena.

References

1. Rathje et al, “Oncogenes induce a vimentin filament collapse mediated by hdac6 that is linked to cell stiffness”, Proceedings of the National Academy of Sciences, 111, pp. 1515–1520, 2014.
2. B. Fallqvist et al., “Experimental and computational assessment of F-actin influence in regulating cellular stiffness and relaxation behaviour of fibroblasts”, Journal of the Mechanical Behavior of Biomedical Materials, Vol 59, pp. 168–184, 2016.