Published

May 16, 2025

Author

Nicolas Vachicouras

Why did I write this article?

Soft, ultrasoft, flexible, ultraflexible, thin, ultrathin, stretchable… These are just a few of the many terms you’ll encounter if you start exploring the (very deep) rabbit hole of implantable brain-computer interfaces (BCIs). They are often used interchangeably even though they refer to very different, and sometimes ill-defined, mechanical and geometrical properties of brain interfaces. Worse, these critical concepts are often misunderstood or overlooked entirely.

Brain interfaces are as complex as rocket science. Designing and building them demands knowledge across a wide range of disciplines: mechanical and electrical engineering, chemical engineering, electrochemistry, physics, biology, and more. Even after more than a decade in the field, I still find myself using differential equations and complex numbers regularly. That’s one of the reasons I love this work.

To make matters more challenging, all these disciplines are interconnected. For example, mechanical and geometrical properties don’t just impact surgical delivery and biocompatibility, they also affect the electrical and electrochemical behavior of the device.

So welcome to the first article in a series dedicated to unpacking the key technical elements of brain interfaces. I am starting with mechanical properties, because after 15 years working on implantable BCIs, I am more convinced than ever that they are both the most crucial and most poorly understood design factor for building safe, and therefore scalable, interfaces

Who should read this article?

If you are building, using, or investing in implantable brain interfaces, you need a solid grasp of the fundamentals, especially those that aren’t immediately obvious from a slide deck or product demo.

Neurotechnology is inherently interdisciplinary. Engineers, doctors, neuroscientists, and investors must collaborate together, yet they all come from different worlds. Go too superficial and you lose critical nuance. Go too deep and you risk alienating your audience. I will aim for the right balance by explaining what I believe are the most important mechanical and geometrical factors in enough depth to understand their clinical and technical impact.

This article is meant to be a foundational resource. I couldn’t find a single clear, holistic explanation of these topics to send to interested stakeholders, so I decided to write one. If you are an engineer, student, or curious hobbyist, I hope this gives you a strong base to build on. If you are an investor, I hope it provides a new lens through which to evaluate the next generation of neurotechnology companies.

To any experts reading this: I have necessarily simplified or skipped some details in the interest of clarity. Please feel free to share feedback. I'm always looking to improve this article for its intended audience.

For those who want to dive a bit deeper in this subject I also recommend reading this review:

Lacour, Stéphanie P., Grégoire Courtine, and Jochen Guck. "Materials and technologies for soft implantable neuroprostheses." Nature Reviews Materials 1, no. 10 (2016): 1-14.

Even though the focus here is on selected mechanical and geometrical properties, I will touch on how these aspects connect with broader device characteristics. I plan to explore these other dimensions in future articles, with the aim of building a comprehensive guide to key design principles in implantable BCIs.

Key foundational concepts

Before we dive into mechanical properties, we need to agree on two basic, but crucial, definitions. Each of these could warrant an article on its own, but I’ll keep it short and focused on what matters for understanding brain interface mechanics.

What is a brain interface?

When I say “brain interface,” I am referring specifically to the part of the device that is in direct contact with neural tissue, typically made of passive components like conductors and insulators. It does not usually include active elements like chips, batteries, or wireless modules.

Electrically, the brain interface performs one or both of the following:

• Recording: converting ionic brain signals into electronic currents (read mode)
• Stimulation: converting electronic currents into ionic flows (write mode)

A complete BCI system includes upstream (or downstream) electronics, like amplifiers, ADCs (Analog-to-Digital Converters), power delivery, and communication modules, but here we focus solely on the interface at the tissue level, because:

• It determines surgical access and invasiveness
• It drives biocompatibility and long-term safety
• It sets the reliability limits of the entire system

Most brain interfaces can be divided into four core components:

1. Electrode sites

The exposed conductive pads that make direct contact with brain tissue. These are the points of current injection or sensing.

2. Substrate

The structural base that defines the shape, thickness, and mechanical properties. This is what we mostly refer to when we discuss “mechanics.”

3. Interconnects (tracks)

Conductive lines that route electrical signals from the electrode sites to the connector (or vice-versa for stimulation).

4. Connector region

The transition zone where the brain interface connects to active electronics. Often includes wire-bonds, pins, or cables.



When we talk about mechanical properties, we mainly refer to the substrate material, as it usually dominates the entire mechanical properties of the device. However, it is important that the other components integrate well with the substrate material and to keep in mind that these can also impact the overall mechanical properties of the device. We will see below in which cases this can become a problem if not properly designed.

💡 When you hear people talk about “graphene electrodes”, or “PEDOT:PSS electrodes” or “platinum arrays,” remember: they are referring to the conductive layer, not the whole structure. The substrate still defines the overall mechanical behavior and that’s the focus of this article.

Types of implantable brain interfaces

Looking at what is relevant in the context of this article, I propose categorizing implantable brain interfaces into two broad classes (even though there are many others, such as subcutaneous, intravascular, etc.):

1. Penetrating interfaces

These physically enter the brain tissue. There are two main subtypes:

1. Intra-cortical electrodes: short shanks or threads that reach within 2–4 mm of cortex or grey matter (ex. Utah array from Blackrock Microsystems, Neuralink or Paradromics)
2. Deep brain electrodes: long electrodes (5–7 cm) that reach deep subcortical structures, like the STN (Sub-Thalamic Nucleus), a target for Deep Brain Stimulation (DBS) for Parkinson’s
2. Surface/cortical interfaces (or ECoG)

These rest on the brain surface, either:

1. Epidural: on top of the dura mater (ex. Wimagine device used by Onward Medical)
2. Subdural: beneath the dura mater, above the arachnoid (ex. Precision Neuroscience or Neurosoft Bioelectronics)

This is also a good opportunity to introduce key anatomical elements of the brain, that are shown on the image below.

• Skull (bone)
• Meninges:
• Dura mater
• Arachnoid
• Pia mater
• Brain:
• Grey matter or cortex (outer layer)
• White matter (inner layer)

🧠 Why this matters mechanically:

As we will see in the next chapters, penetrating devices must survive insertion forces and chronic tissue micro-motion without breaking or scarring tissue. Surface devices must conform closely to the brain’s folds and tolerate pulsations, often across much larger areas. The mechanical environment/surroundings are also very different in each case.

Summary

Understanding what a brain interface is, and the different anatomical environments it operates in, is key before diving into mechanical and geometrical properties. Throughout this article, I will mostly be referring to the substrate, and how its mechanical parameters (like thickness, Young’s modulus, and elasticity) affect safety, performance, and scalability.

Key mechanical parameters and why they matter

Below are the four geometric and mechanical parameters that I believe to be the most relevant in the context of brain interfaces:

• Thickness
• Young’s modulus
• Bending stiffness
• Elasticity vs. plasticity

It is important to keep in mind that these mechanical parameters are inter-dependent and they have a different impact depending on the type of brain interfaces (penetrating vs. surface).

Let’s explore each one of them below, and explain their clinical impact.

Note: These are not the only mechanical properties relevant to brain interface design. Ductility, brittleness, yield stress, toughness, tensile strength, and viscoelasticity are just a short list of other mechanical parameters that can play a role. However, the ones discussed above have the most significant impact on device-tissue interaction, ease of implantation, and long-term performance, and are a good starting point for anyone who wants a short, but thorough, introduction to implantable brain interfaces.

Thickness

Thickness is a geometric property that refers to the smallest dimension of a brain interface. It strongly influences other mechanical parameters, especially bending stiffness (discussed next), and plays a key role in how the device interacts with brain tissue during and after implantation.

In planar devices like subdural grids or intra-cortical thread-like probes (e.g. Neuralink or the Neuropixel probe), thickness defines the vertical profile of the structure. For Utah-style or cylindrical DBS electrodes, the analogous dimension is the shank or shaft diameter.

Typical values for brain interface thickness range from 1 µm to 1 cm, though most devices fall within 5 µm to 1.5 mm. To provide some context, I made an image that provides an overview of the range of thicknesses used in various brain interface technologies (picture is by far not exhaustive - I mostly used devices where data on material thickness was available).

A naive reader might be tempted to draw conclusions only by looking at this image, but as you will understand by reading this article: this is useless. Thickness does not tell you the whole story. First of all, thickness requirements are very different for penetrating devices (such as threads or needles) compared to surface electrodes (such as ECoGs). Moreover, thickness doesn’t provide much information if we don’t know what type of materials we are talking about. A polyimide-based device that is 80 µm thick can be 2 times more “flexible” (term to be defined in the upcoming chapters) than a 25 µm silicon shank, even though it is 3 times thicker. Moreover, some technologies are not restrained to only one thickness. For example, at Neurosoft Bioelectronics we build brain interfaces of various thicknesses depending on the use cases.

Impact of thickness on tissue response

Thickness, as other mechanical parameters we will see below, impacts the tissue response of brain interfaces. A good resource I recommend to better understand tissue response to chronically implanted brain interfaces is the following: Polikov, Vadim S., Patrick A. Tresco, and William M. Reichert. "Response of brain tissue to chronically implanted neural electrodes." Journal of neuroscience methods 148, no. 1 (2005): 1-18.

Penetrating electrodes

For penetrating electrodes, thickness determines the volume of tissue displaced during insertion and influences both acute mechanical trauma and chronic inflammatory response. Thinner devices have been associated with reduced glial encapsulation and better long-term signal stability (Seymour et al. 2007). A study from Spencer et al. 2017 showed that at 8 weeks post-implantation, larger diameter implants (GC400) induced significantly greater GFAP reactivity (inflammatory response) than smaller ones (GC150). This means that increased diameter alone can exacerbate chronic glial scarring, even when implant stiffness is constant.

Glial Fibrillary Acidic Protein (GFAP) is a filament protein expressed by astrocytes. It is commonly used as a biomarker for astrocyte activation and glial scar formation in response to neural implants.

Neuralink’s 5 µm-thick polyimide threads is another notable example, where it appeares to provoke limited gliosis in early histological samples compared to needles (needles are conically shaped with a ~80 µm diameter basis).

However, as we will see in the next section, thickness is not the only parameter that can influence tissue response. Young’s modulus can also impact it. In this example, the Utah array is made of Silicon (Young’s modulus of ~150 GPa), whereas the Neuralink thread is made mostly of polyimide (Young’s modulus of ~3 GPa), which is 50 times lower. So it is hard to do comparison when two parameters are changed (here we have both a different geometry and a different Young’s modulus).

Surface electrodes

Subdural (surface) electrodes must conform to the tight anatomical space between dura and the cortex. Historically, commercial arrays from Ad-Tech and PMT have had total thicknesses in the 1 mm range. These devices are still relatively thick, potentially leading to foreign body reaction, cortical compression, subdural hematomas or disruption of cerebrospinal fluid dynamics. This is why modern thin-film ECoG arrays typically target <1 mm total thickness, offering better anatomical compatibility.

Scalability and handling trade-offs

As we saw, thinner devices naturally occupy a smaller physical footprint, which is generally advantageous when interfacing with the brain—particularly in the case of penetrating electrodes, where minimizing insertion damage and chronic displacement is critical. A smaller cross-sectional area reduces disruption to neural structures, lowers insertion force, and facilitates tighter integration with the surrounding tissue.

However, this geometric advantage comes with practical drawbacks. As devices become thinner, surgical handling becomes increasingly challenging. Ultra-thin structures tend to bend, fold, or adhere to unintended surfaces during implantation. They are more fragile and less predictable in behavior, especially in wet, dynamic environments like the brain. As a result, new surgical tools are often required, ranging from temporary stiffeners to suction-based applicators, whose complexity increases as devices become thinner. This introduces additional surgical overhead, potentially limiting clinical scalability or requiring specialized training for clinicians.

An illustrative example of these trade-offs is Neuralink’s design approach: to minimize glial encapsulation, they use ultra-thin (5 μm) and narrow (80 μm) threads. Because each thread only yields a limited number of recording units due to its small footprint, Neuralink compensates by deploying 64 threads per device, a form of architectural redundancy. This design necessitates a custom surgical robot to insert each thread individually. In contrast, soft electrode, can tolerate larger geometries (e.g., Axoft’s 10 × 700 μm FLEURON) without triggering the same foreign body response, thus avoiding this constraint and potentially simplifying deployment.

Although we have seen that reducing thickness can improve the tissue response (by decreasing glial scarring) and will later explore how it also enhances conformability, it is important to recognize that thickness is not the only mechanical parameter that matters. Other factors, especially Young’s modulus, play a key role in how a device interacts with brain tissue. For example, recent work by Lee et al., 2025 demonstrated that moderately thicker devices (≥10 µm) made from very soft materials can still achieve excellent biocompatibility. This highlights the possibility of optimizing devices for mechanical compliance without relying exclusively on ultra-thin geometries.

Thickness also influences electrical performance and design flexibility. Thicker substrates allow for multi-layer routing, enabling higher channel counts without expanding the lateral footprint, an essential consideration for high-density arrays. They also help reduce capacitive coupling between signal traces and the surrounding environment, improving signal integrity by minimizing parasitic leakage, particularly for small-amplitude or high-impedance recordings.

Finally, it is worth noting that thinner devices often require more advanced and complex manufacturing techniques. Achieving reliable performance at sub-micron or low-micron thickness scales demands tighter fabrication tolerances, more delicate handling during assembly, and greater attention to yield and reproducibility.

In summary, while thinner devices provide clear benefits in terms of tissue integration, footprint, and mechanical softness, they introduce non-trivial challenges in surgical handling, manufacturing, electrical design and overall scalability. Fortunately, other material properties, such as Young’s modulus, can be tuned independently to mitigate these issues. Optimizing brain interfaces thus requires a balanced design approach, where thickness is considered alongside mechanical, surgical, and electrical factors to ensure both performance and scalability.

Young’s Modulus

Definition

Young’s modulus, sometimes referred to as elastic modulus, is a fundamental mechanical property that quantifies how stiff a material is. It is defined as the ratio of stress (force per unit area) to strain (relative deformation) within the linear, elastic region of a material’s deformation:

$E= \frac{\sigma}{\varepsilon}$

The best way to understand Young’s modulus (denoted as $E$) is to see how it is measured. Imagine a rectangular piece of rubber with length $L$, width w$,$ and thickness $t$. For simplicity, let’s assume this rubber is a perfectly elastic material, meaning it deforms linearly with applied force and returns to its original shape when unloaded.

To measure its Young’s modulus, you would fix the sample between two clamps in a tensile testing machine, and slowly pull it along its length while measuring the force applied.

As you stretch the sample, you apply an elongation $\Delta L$. For example, if the sample is initially 10 mm long and you stretch it by 1 mm, the strain $\varepsilon$ is:

$\varepsilon = \frac{\Delta L}{L} =\frac{1 mm}{10 mm}=0.1$ ($= 10\%$)

To maintain this elongation, a certain force $F$ is required. We normalize this force by the cross-sectional area of the material, $A = w \cdot t$, to obtain the stress $\sigma$, expressed in Pascals (Pa):

$\sigma=\cfrac{F}{w \cdot t}$

Let’s say the required force is 0.1 N, and the cross-section is 1 mm × 0.1 mm. Then:

$\sigma=\cfrac{F}{w \cdot t}=\cfrac{0.1 N}{1 mm \cdot 0.1 mm} = 1 \cdot 10^{6} Pa = 1 MPa$

This normalization removes the effect of geometry: a small sample requires less force, a larger one more, but the stress accounts for this and gives a property intrinsic to the material, independently of the geometric form factor of the sample being measured.

Finally, the Young’s modulus is:

$E= \frac{\sigma}{\varepsilon}=\frac{1 MPa}{0.1}=10 MPa$

In this example, 10 MPa is read as 10 mega Pascals or ten million Pascals.

You can also think of Young’s modulus as the slope of the linear region in a stress–strain curve.

The higher the modulus, the stiffer the material. Steel, for example, has a very high Young’s modulus, over 100 GPa ($10^{11}$ Pa), while soft silicone might be in the range of 100 kPa to a few MPa ($10^{5} - 10^{6}$ Pa). It is also important to note that Young’s modulus is an intrinsic material property: a 10 μm thick layer of silicone and a 1 cm thick block of silicone have the same Young’s modulus, even though their bending behavior differs greatly due to geometry.

⚠️ The Young’s modulus describes an idealized elastic regime, which real materials rarely follow perfectly. Most materials exhibit both elastic and plastic behavior and will eventually fail or fracture under large strain. But understanding Young’s modulus gives us a first-order approximation of how much a material resists deformation, and it’s one of the most widely used mechanical parameters in engineering.

Compression vs. Tension

One important nuance, especially relevant for the next section on stretchability, is that Young’s modulus can be measured in compression or tension, and materials can behave quite differently in each mode.

In our previous example, we measured the Young’s modulus in tension (i.e. we pulled on the rubber), but we could do the same in compression.

This is important, because a material, for example a hydrogel, may appear very soft and compliant under compression (easy to squish), but it may tear or rupture under tensile stress, making it unsuitable for stretching applications.

A useful mental image is that of a panna cotta or flan: it easily deforms when compressed, but if you tried to pick it up and pull it apart, it would disintegrate. Many hydrogels behave similarly, they feel soft, but that doesn’t mean they’re stretchable. This distinction will become central in the upcoming chapters.

Young’s modulus for neurotech

The human central nervous system is among the softest tissues in the body. Brain tissue typically exhibits a Young’s modulus in the range of 100 Pa to 10 kPa, depending on measurement methods, brain region, and species. The dura mater, a tougher membrane that envelopes the brain and spinal cord, has values ranging from 0.5 to 2 MPa. The table below summarizes key biological tissues:

In contrast, neural implants are typically made from one of four material classes:

• Semiconductors (e.g., silicon)
• Plastics (e.g., polyimide, parylene)
• Elastomers (e.g., PDMS or fluorinated silicones)
• Hydrogels, which are currently under research but not yet used clinically

The chart below compares the Young’s moduli of these materials with relevant biological tissues:

*PDMS refers to polydimethylsiloxane, a standard silicone used in soft bioelectronic interfaces.

The next figure highlights the materials used by companies developing neural interfaces, showing how their elastic moduli compare. However, it is important to note:

• This is not a direct comparison of companies or technologies: there are too many parameters involved, as we mentioned in the previous structure.
• Some companies, like Axoft, can tune the modulus of their material, so their position on this scale may vary.
• A lower Young’s modulus does not guarantee a softer device in practice: a thicker device can still be mechanically stiff due to increased bending stiffness.

As we will see below, this mechanical mismatch is not just a curiosity: it has real biological consequences. Implants that are orders of magnitude stiffer than brain tissue can induce persistent mechanical stress at the tissue–device interface, especially during micromotions from breathing, heartbeat, or postural shifts. This stress can trigger a cascade of adverse biological responses:

• Glial scarring
• Chronic inflammation
• Blood-brain barrier disruption
• Electrode failure over time

Some people, including myself, have been referring to materials with a Young’s modulus around 1 MPa or below as soft. This is not a strict definition, but rather a practical threshold that captures the range of biological tissues we aim to interface with (e.g., brain, dura) and the class of polymeric materials (e.g., hydrogels, elastomers) that mimic their compliance (as we will see below). Most conventional electronic materials, like silicon or polyimide, are orders of magnitude stiffer. However, even a material that is technically soft, can still end up feeling very “rigid” if it is too thick.

Clinical implications of Young’s modulus

The foreign body response (FBR) to neural implants is strongly influenced by the implant’s mechanical and geometrical properties, especially its Young’s modulus. This has been demonstrated in both in vitro and in vivo studies. Neuronal cells are highly sensitive to the stiffness of their environment, and even small deviations can significantly affect biological outcomes.

A landmark in vitro study by Saha et al., 2008 showed that the stiffness of the substrate on which adult neural stem cells were cultured strongly influenced their differentiation. On soft substrates (~100–500 Pa), mimicking the mechanical properties of brain tissue, cells predominantly became β-tubulin III⁺ neurons (a marker for mature neurons). On stiffer substrates (>1 kPa), the same stem cells tended to become GFAP⁺ glial cells, marked by glial fibrillary acidic protein. Critically, this shift occurred despite an identical chemical environment, highlighting the powerful role of mechanics in neural cell fate.

One of the first clear in vivo demonstrations came from the e-dura neural interface, developed by Minev et al., 2015. Designed to match the mechanical properties of the dura (~1 MPa), this soft, stretchable implant was placed subdurally on the spinal cord. Compared to a “flexible” but rigid polyimide implant (~3 GPa), the e-dura device caused minimal immune response, enabling chronic stimulation and recording.

For penetrating electrodes, which are implanted directly into the brain’s gray or white matter, mechanical mismatch becomes even more critical. These devices experience relative motion with surrounding tissue due to breathing, heartbeat, or movement. This motion induces strain at the interface, triggering chronic inflammation, glial scarring, and eventual device failure.

Nguyen et al., 2014 compared two penetrating devices: a rigid silicon electrode (~50–80 GPa) and a mechanically adaptive nanocomposite that softened in situ to ~12 MPa. Despite being geometrically thicker, the compliant implant induced far less tissue reaction. After 16 weeks, it maintained stable blood-brain barrier integrity, preserved neuronal density, and significantly reduced astrocyte and microglia activation—clear evidence that compliance matters more than thinness alone.

This pattern has been reinforced by other intracortical studies. Notably, recent data from the Axoft platform shows that even thicker but softer intracortical probes elicit significantly lower FBR after chronic implantation Lee et al., 2025, preprint.

In short, brain interfaces that match the mechanical environment of the tissue they target—whether dura for subdural or brain parenchyma for intracortical—achieve better biological integration.

An added benefit of softer materials is their lack of sharp mechanical edges, reducing the risk of physically damaging delicate brain structures. Moreover, as discussed in the next section, lowering the Young’s modulus can also enhance flexibility, providing another design axis without necessarily reducing thickness.

Design implications and trade-offs

While lowering the elastic modulus offers clear biological advantages, it introduces manufacturing challenges. Soft materials like silicones or hydrogels are harder to process, particularly when high-resolution photolithography or precise patterning is required. This is one reason why many groups still rely on stiffer platforms, such as polyimide or parylene, which are easier to fabricate, even if they do not mechanically match brain tissue.

Bending stiffness

Definition

If Young’s modulus captures how much a material resists tension or compression, bending stiffness describes how much it resists bending. This is particularly important in thin-film neural interfaces, where devices are expected to conform to curved brain surfaces.

Bending stiffness is not a purely material property—it depends both on the intrinsic stiffness of the material (i.e. its Young’s modulus, $E$) and on its geometry, particularly the thickness, $t$. For a rectangular beam (or thin film), the bending stiffness $D$ is given by:

$D = \frac{E \cdot t^3}{12(1 - \nu^2)}$

where $\nu$ is the Poisson’s ratio of the material (typically ~0.5 for elastomers, ~0.3 for plastics).

In most cases, we simplify this to focus on the dominant term:

$D \propto E \cdot t^3$

This cubic dependence on thickness is a critical insight: doubling the thickness increases bending stiffness by a factor of eight, even if the material remains the same. Conversely, even a stiff material can feel flexible if it's thin enough.

This means that any material can eventually become “flexible”, if it’s made thin enough. A good mental image is to think of a piece of aluminum foil. Even if aluminum is intrinsically very stiff (high Young’s modulus), if it is made thin enough (like in a foil), it will end up being flexible.

This also means that softer materials can be made thicker (and potentially easier to handle) while achieving the same flexibility as a thin device made of stiff material. For example, a silicone-based device (1 MPa) that is 320 µm thick has the same bending stiffness as a 22 µm polyimide device (3 GPa).

In summary, bending stiffness can be reduced by either:

• Lowering the Young’s modulus (softer material), or
• Reducing the thickness (thinner device)

Practical considerations

A practical use of this concept is assessing whether a flat neural interface can conform, by capillarity, to a curved surface like a wet cylinder. Mathematically, the balance between bending energy $(E_{bend} = \frac{Eh^{3}L}{12(1-\nu^{2})2R^{2}})$and surface energy $(E_{surface}=\gamma L)$ determines whether the film wraps. $\gamma$ represents the surface tension at the surface of the cylinder, which is equal to roughly 62 $[mJ/m^{2}]$ for water.

The critical thickness $t_{c}$for which the film conforms to the cylinder is therefore given when $E_{surface}=E_{bend}$:

$t_{c}=\sqrt[3]{\frac{R^{2} \cdot 24(1-\nu^{2}\gamma)}{E}}$

This defines the critical thickness below which a film will conform to a wet cylinder of radius $R$.

This phenomenon was studied experimentally in Vachicouras et al., 2019, where silicone (PDMS) films of varying thickness were placed on wet cylinders. If the film’s bending stiffness was below the critical threshold, it spontaneously adhered; otherwise, it remained flat. The experiment also showed that integrating a thin-film polyimide-platinum stack (~2-3 µm thick) into the silicone substrate did not drastically affect this behavior, confirming that the substrate mechanics dominate the system’s overall flexibility.

This confirms that lower bending stiffness improves the ability of an interface to conform to cylindrical shapes.

Limitations for complex surfaces

Nevertheless, strictly cylindrical surfaces don’t exist in the central nervous system. Most neural surfaces, especially sulci, have non-zero Gaussian curvature, meaning they curve along multiple axes and cannot be flattened into a 2D sheet without deformation.

Gaussian curvature $K$ is defined as:

$K = \kappa_1 \cdot \kappa_2$

where $\kappa_1$ and $\kappa_2$ are the principal curvatures. Surfaces with $K=0$ such as flat surfaces or cylinders (where $\kappa_1 \ne 0$, but $\kappa_2 = 0$) can be conformed with bending stiffness alone. However, surfaces with $K\ne0$ cannot be conformed to using bending alone: mechanical strain is required (i.e. stretchability).

Materials which cannot stretch (subject we will discuss in the next section) therefore cannot conform to complex surface, and will buckle or crease.

Conclusion: For surfaces with non-zero Gaussian curvature, bending stiffness alone is insufficient. Stretchability becomes essential for true conformability (this will be explored in the next section).

The figure below compares bending stiffness of some neural interfaces with different materials and thicknesses (these are similar devices shown in the two previous chapter).

When people talk about flexibility, they technically mean low bending stiffness. Anything below $10^{-4} [N \cdot m]$ would typically be considered, and feel, flexible.

Clinical implications of bending stiffness

In surgical settings, devices with low bending stiffness are more likely to fold naturally around the brain, improving:

• Conformability to brain surfaces
• Signal-to-noise ratio (SNR) due to better contact
• Stimulation efficiency, with lower thresholds and reduced current spread

However, high flexibility can also create challenges:

• Devices become floppy, harder to place
• Require specialized surgical tools
• Increase surgical complexity and potentially time
• Demand higher surgeon training

Thus, designers must strike a balance: enough flexibility to integrate with tissue, but enough rigidity to allow controlled deployment.

Summary

• Bending stiffness is a key factor in neural interface mechanics and depends on both material and geometry.
• It governs conformability to simple curved surfaces like cylinders.
• For more complex shapes, stretchability is required: bending stiffness alone is not enough.
• While thinner devices offer lower bending stiffness, they introduce challenges in handling, manufacturing, and implantation.
• Material choice (e.g. lower modulus) can allow thicker, more manageable devices to achieve equivalent flexibility.
• Optimal design must weigh mechanical behavior, electrical performance, surgical usability, and clinical scalability together.

Elastic vs. plastic

Definition

The last mechanical concepts we need to understand before moving forward are elastic (reversible) deformation and plastic (irreversible) deformation. These are crucial when discussing the next generation of brain interfaces.

Materials that are elastically stretchable have a fully reversible stress–strain response: after being stretched, folded, or crumpled in multiple directions, they return to their original shape without damage. This behavior is typical of soft elastomers like silicone (PDMS) or rubber.

In contrast, materials like metals or engineering plastics (e.g. polyimide) undergo plastic deformation: when stretched beyond their yield point (typically below 1% strain), they do not recover their original shape. Think of a sheet of paper that retains a crease after being folded.

The table presents key materials used in brain interfaces (that we saw in this article multiple times) and highlights where they fit in terms of flexibility (low bending stiffness) and elastic behavior:

Clinical impact of elastic behavior

The central nervous system (CNS) is not only extremely soft, as we saw in the previous sections,but it is also a very dynamic mechanical system, constantly in motion. The spinal cord experiences large tensile and compressive strains up to 10-20% during back movements, thus causing elongation of the soft spinal cord (Harrison et al. 1999).

Even the brain is subject to micro-motions from blood flow, CSF pulsation, and breathing. These movements cause small but continuous volumetric strains around 0.01-0.03% (Wagshul et al. 2011).

This biomechanical environment places stringent demands on implanted interfaces: to remain reliable over time, they must not only match tissue softness but also accommodate dynamic deformations. Otherwise, chronic micromotion or mechanical stress during implantation can damage critical features, such as electrode sites, interconnects, or insulation layers, leading to signal degradation or device failure.

Stretchable behavior is clearly important in large moving parts of the body, like the spinal cord, but might be less important for other tissues like the brain that exhibit a lot less deformation.

However, stretchability becomes very important when we look at surgical implantation. As we saw, devices that exhibit elastic behavior are able to be folded in extreme form factors without any damage. That opens up large opportunity for minimally invasive approaches for deploying electrodes in the body with minimal incisions.

A helpful way to think about mechanical compliance is through the lens of degrees of freedom:

• Rigid devices: 0 degrees of freedom

→ Cannot bend or stretch

• Flexible devices: 1 degree of freedom

→ Can bend along one axis (e.g. around a cylinder)

• Stretchable devices: 3 degrees of freedom

→ Can bend, twist, and stretch in all directions

This leap in mechanical freedom opens the door to truly conformable, minimally invasive, and scalable neurotechnologies. For instance, stretchable substrates can be folded and deployed through narrow surgical openings, then unfold and adapt to the complex 3D geometry of sulci, ventricles, or other deep brain structures. At Neurosoft Bioelectronics, we have been actively investigating such strategies in both cortical and intracranial settings.

Engineering and manufacturing challenges of stretchable systems

While the benefits of stretchable electronics are clear, building reliable systems is not trivial. In fact, stretchability is not just about the substrate: it requires a rethinking of the entire system architecture:

• Interconnects must be engineered to deform without breaking
• Electrode sites must maintain low impedance and structural integrity under strain, often requiring composite materials or soft encapsulation layers.
• Connectors and packaging must support compliant integration without introducing rigid failure points.

These challenges are non-trivial from a fabrication standpoint. Unlike rigid or flexible electronics, stretchable devices demand custom processes, materials, and tooling. This specialized expertise creates a high barrier to entry, but also a significant opportunity for teams with deep know-how and long-term commitment.

As one of the few teams to have tackled stretchable bioelectronics across both research and translational domains over multiple years, we believe the field is just beginning to tap into its potential.

Conclusion: from mechanical properties to scalable brain interfaces

In this article, we explored what I believe are the four most critical mechanical parameters for implantable brain interfaces:

• Thickness
• Young’s modulus
• Bending stiffness
• Elasticity vs. plasticity

We saw how bending stiffness governs whether a device conforms to curved surfaces, how modulus mismatch can trigger chronic inflammation, and how plastic deformation can irreversibly damage interconnects or electrode sites. We also uncovered the subtle but important differences between buzzwords like “soft,” “flexible,” and “thin”: terms often used interchangeably but with very different clinical implications.

Among all these factors, one property stands apart in its potential to unlock entirely new capabilities: stretchability.

Stretchability is not just about being soft, it’s about adding mechanical degrees of freedom, enabling devices to bend, twist, and elongate without failure. And that makes all the difference. It’s what enables:

• True 3D conformability to complex brain anatomy like sulci and ventricles
• Minimally invasive deployment, where devices can be folded or rolled through narrow openings
• Mechanical resilience, enduring chronic micromotion without degrading performance

What I am excited about

Overall, this is the key reason why I am personally excited about our work at Neurosoft Bioelectronics. I am proud of the deep expertise we have built in designing, fabricating and translating soft and stretchable electronic technologies for human brain interfaces. I believe stretchability is a unique enabler for scalable BCI systems: devices that can be deployed faster, cover more brain surface, reach brain regions that are otherwise inaccessible, require simpler and less invasive surgeries, and reach wider clinical adoption.

Yes, it’s hard. It requires redesigning every layer of the system: substrate, interconnects, electrodes, packaging (a subject I will be happy to cover in another article), but I believe stretchability is not just a differentiator: it’s a platform shift, and one that will define the next generation of brain interfaces.