The neurovascular and cortical damages caused by the implantation of a neural probe constitutes the initial trigger of FBR.

The disruption of the BBB allows the recruitment of serum protein, blood borne macrophages, erythrocytes, activated platelets and clotting factors to the site of the injury. In addition, the BBB breach leads to the infiltration of neurotoxic factors, proinflammatory myeloid cells and ROS, consequently leading to oxidative stress and excitotoxicity in the local tissue around the implant. Moreover, ROS directly downregulate proteins responsible for tight junctions, establishing a positive feedback loop with the BBB disruption (Abdul-Muneer et al., 2015). The accumulation of fluid and necrotic nervous tissue around the implanted device also causes edema and an increased local pressure (Polikov et al., 2005; Bennett et al., 2018). Following BBB disruption, components of the complement cascade have been found at enhanced concentrations in the injured brain region, potentially contributing to the generation of a local innate immune response (Bennett et al., 2021).

In the acute phase of implantation, plasma proteins that extravasate due to BBB rupture/leakiness are adsorbed on the surface of the probe, forming a provisional matrix. The Vroman effect describes the continuous process of plasma protein adsorption and desorption from the surface of the probe which leads to the formation of this provisional matrix (Hirsh et al., 2013). High mobility proteins, such as albumin, are adsorbed at first and are gradually replaced by less motile proteins with a higher specific affinity for the probe's surface, such as fibrinogen, fibronectin, and vitronectin (as schematized in Figure 3A) (Klopfleisch and Jung, 2017). Surface physicochemical properties of the probe, such as wettability, topography, chemical composition, and charge are important properties at this stage, because they determine the thermodynamic equilibrium of protein/probe interactions. The provisional matrix formed on the surface of the implant is considered to have a critical impact on the outcome of FBR, by influencing the severity of long-term inflammation and of the immune response.

In addition to the initial physical disruption of the BBB caused by the probe implantation, several studies have shown that the presence of an external body alone elicits chronic (up to 4 weeks) homogeneous leakage of macromolecules with a size up to 10 nm, which is not observed following stab wound insults where the foreign object is not left inserted. Such studies were based on the immunohistochemical detection of plasma proteins, such as Mouse Serum Albumin (Tian et al., 2011) and Mouse IgG (Winslow and Tresco, 2010; Potter et al., 2012).

Fluorescent polymer nanoparticles with a larger size (20 nm to 1 μm diameter) were also used to assess long-term BBB permeability in the presence of an implant (Sawyer and Kyriakides, 2013). Nanoparticles with diameters of 20, 200, and 500 nm were found in the brain parenchyma next to the implant up to 4 weeks post implantation (study duration), while 1 μm diameter particles were excluded. This indicates that the presence of a foreign body elicits large gaps in the BBB in a chronic setting.

Microglia and astrocytes are widely considered the two major cell types involved in the brain wound healing response and in FBR (Biran et al., 2005; Polikov et al., 2005; Seymour and Kipke, 2007).

Microglia primarily act as cytotoxic cells killing pathogenic organisms or as phagocytes secreting proteolytic enzymes to degrade cellular debris and damaged matrix. When blood vessels are severed or in the presence of a leaky BBB, microglia are indistinguishable from blood borne, monocyte-derived macrophages (Ajami et al., 2011).

Microglia exist in a highly branched state until they are activated via injury-mediated mechanisms. Upon activation, they begin to proliferate, assume a more compact morphology and upregulate the production of lytic enzymes to aid foreign body degradation. Following probe insertion, during the first 30–45 min, nearby microglia immediately extend processes toward the probe, ensheath the device (Sharon et al., 2021) and 6 h following probe insertion, microglia (<130 μm distance from probe surface) exhibit morphological characteristics of a transitional stage to a reactive state (Kozai et al., 2012a; Wellman and Kozai, 2017). Recently, innate immunity activation pathways of microglia/macrophages have been investigated in the context of FBR. In particular, multiple studies have looked into the role of the innate immune receptor cluster of differentiation 14 (CD14), a molecule primarily expressed on microglia and circulating monocytes and associated with the recognition of pathogen associated and damage associated molecular patterns. The complete inhibition of CD14 resulted in an acute (2 weeks) but not chronic (16 weeks) improvement of histological endpoints (Bedell et al., 2018b), while a more selective suppression of CD14 only in blood derived cells yielded a longer lasting improvement of device electrical interfacing performances (Bedell et al., 2018a; Hermann et al., 2018b). These results, although not conclusive, may indicate that complete removal of CD14 is beneficial at acute time ranges, whereas limited CD14 signaling (from brain resident microglia) is beneficial at chronic time ranges. The impact of two additional receptors tightly associated with CD14 activation, Toll-like receptors 2 and 4, has also been investigated by Hermann et al. (2018a), but in this case the authors did not observe any beneficial effect from the partial or complete inhibition of these molecules. Recently, Franklin et al. (2023) have assessed the role of inflammasomes in the innate immune response to implanted neural devices.

Astrocytes constitute another key cellular component of FBR. While they were initially assumed to serve as little more than passive physical support elements for neurons, it is now clear that they play a key role in healthy physiology, in brain development and in the pathology of the nervous system (Kimelberg and Norenberg, 1989; Sofroniew and Vinters, 2010).

In the presence of various types of brain insults, and potentially through different activation pathways, astrocytes undergo numerous cytological, histochemical and biochemical changes, including increases in nuclear diameter, elevated DNA levels, accumulation of intermediate filaments, elevated oxidoreductive enzyme activity and increased synthesis of GFAP (Bovolenta et al., 1992). Astroglial swelling is also reported among the first responses in the presence of brain injury. It is likely that chemical factors released by injured neurons such as potassium, glutamate and lactate are responsible for astrocytic swelling. BBB disruption may also induce astrocytes to swell by taking up excess protein and water released in the extracellular environment (Michael, 1994).

Astrocytes and microglia initially form a layered sheet that insulates the foreign body from surrounding healthy brain tissue. By approximately 4–6 weeks, they begin to form a dense scar around the device that can last for years (Salatino et al., 2017).

Besides insulating the probe and physically displacing neurons from the electrode's proximity, activated astrocytes and microglia release proinflammatory cytokines, that induce excitotoxicity and neurodegeneration.

Interestingly, a recent ultra structural study reported a remarkable tissue re-generation around and in contact with a flexible polyimide implant was found after 8 weeks, which led to a recovery of neuronal cell body densities at a distance of ~ 1 μm from the microelectrodes surfaces (Sharon et al., 2021).

In addition to microglia and astrocytes, oligodendrocyte precursor cells, also referred to as NG2-Glia, have been shown to become activated and migrate toward the injury site (Wellman and Kozai, 2018). The delayed time-course of their activation (days) may indicate that they play a role in the formation of the outer layers of the glial scar.

Post-mortem immunohistochemistry/immunofluorescence are still the most commonly used methods to assess the extent of FBR in the presence of intracortical neural probes. These strategies generally employ primary antibodies to assess the distribution of relevant antigens in the proximity of an implanted device and secondary antibodies, with specific affinity for the primary ones, to visualize it.

Table 1 shows the biomarker antigens that are most frequently targeted with these techniques, based on the category of FBR component that they represent. Despite being relatively easy to implement and allowing the determination of biomarker distribution with an extremely high spatial resolution, these strategies provide a relatively narrow view of the complex biological phenomena involved in FBR. In fact, their application requires an a priori selection of a relatively small subset of biomarkers of interest, typically selected among the ones presented in Table 1. To overcome this limitation and to identify novel FBR biomarkers and potential druggable targets, the application of transcriptomics to FBR assessment has recently emerged, as reviewed in the following paragraph.

In recent years, molecular biology methods have been employed to achieve a broader understanding of the complex biological phenomena underlying FBR. In this context, transcriptomics emerges as a key tool to allow to simultaneous assessment of the expression of hundreds to thousands of genes, obviating the need to pre-select a limited number of biomarkers of interest, which is a requirement for immunohistochemical/immunofluorescence and qPCR-based strategies. Table 2 summarizes the strategies and outcomes of studies investigating FBR through transcriptomics.

The most general approach to assessing the local change in gene expression induced by invasive neural probes, is to perform RNA sequencing (RNA-seq) on tissue samples collected at different distances from the implant site. Thompson et al. (2021) applied this methodology on interfacial (100 μm from implant site) and distal (500 μm from implant site) brain tissue samples and found significant differential expression (DE) both among these samples and in their comparison with naïve brain tissue. Besides identifying genes traditionally associated with FBR, the authors were also able to point out novel potential mechanisms associated with neuronal, oligodendrocytic, microglial, and astroglial function. The following year, the same research group also presented a computational study aimed at extending the impact of their observations (Moore et al., 2022). They performed a differential co-expression analysis on their RNA-Seq dataset to identify coordinated expression of genes, which could implicate the activation of specific regulatory pathways and allow the identification of novel hub gene targets for FBR reduction. Hub genes associated with cellular structure, synaptic plasticity, axonal transport, and metabolism were identified through this approach, although direct validation is still missing.

Other research groups have employed a different approach to analogous transcriptomics studies. Rather than performing RNA-seq to assess DE in the whole genome, mRNA extracted from tissue is hybridized with a pre-set of capture and reporter probes, available through commercial transcriptomic microarrays. Some of these RNA hybridization kits are very broad, such as the one used by Joseph et al. (2021) encompassing more than 20,000 genes, while others focus on a limited number of genes mainly associated with neuroinflammation, such as the nCounter^® Mouse Neuroinflammation Panel by NanoString Technologies, used in the works of Bedell et al. (2020) and Song et al. (2022). Although this kit provides information on the expression of a relatively large number of genes (770), it may limit the chances of spotting alternative regulatory pathways of FBR, not strictly related to neuroinflammation.

Joseph et al. (2021) performed the longest (18 weeks) transcriptomics study to date, assessing long-term brain tissue responses to flexible, minimally tethered probes. The authors observed a transcriptional profile of implanted animals similar to that of non-implanted controls, with an increased expression of genes associated with wound healing and angiogenesis, which is consistent with the probe design and tethering strategy they adopted. However, a significant enrichment of genes related to gliogenesis and glial cell differentiation was reported after 18 weeks, consistent with the results of immuno-fluorescence imaging. The authors also observed an elevated expression of genes belonging to the family of intermediate early genes, which may arisen due to the continuous interfacial stress caused by brain micromotion.

Although the application of transcriptomics to the study of FBR paves the way to a deeper understanding of its underlying mechanisms of action, this strategy also presents drawbacks and potential limitations. The main technical pitfalls are that the generation of datasets is resource intensive and that their interpretation can be difficult. Two conceptual limitations of this strategy are that gene expression does not always align with protein expression and that this method does not elucidate whether DE is driven by altered phenotypes at a cellular level or by changes in the overall cellular population. To address these issues and to validate mRNA as a predictor of protein expression, Thompson et al. (2023) performed an immunohistochemical analysis to evaluate the distribution of a sub-set of proteins identified through a previous RNA-Seq analysis (Thompson et al., 2021). In this work, the authors observed that all the proteins identified through transcriptomics and quantified with immunofluorescence were in some way disrupted, although the expression of some of them did not match the observations from RNA-seq. This result suggests that although protein expression does not always reflect gene expression, it is possible to use RNA-seq to predict broad and cell-type specific changes of proteins involved in FBR.

A further limitation to the use of a standard transcriptomics approach for FBR assessment is that it does not provide spatial resolution. Typically, a relatively large portion of brain tissue around the probe (diameter in the range of hundreds of μm) is extracted from brain tissue slices and pooled to assess DE compared to naïve brain tissue. A strategy to overcome this limitation is the application of recently introduced spatial transcriptomics (Ståhl et al., 2016), which allows a spatial resolution in the range of 10–15 cells per spot (50–100 μm diameter spots). Whitsitt et al. applied this strategy, in combination with immuno fluorescence, both for FBR assessment (Whitsitt et al., 2021) and to understand the impact of electrical stimulation on the genetic expression of surrounding brain tissue (Whitsitt et al., 2022).

Overall, transcriptomics appears to be a promising avenue to achieve a deeper understanding of FBR and to identify novel biomarkers of interest and druggable targets to improve the integration of neural probes within brain tissue, particularly when it provides high resolution spatial information. The recent introduction of high-definition spatial transcriptomics (Vickovic et al., 2019) appears to be a key step toward this direction, although it has thus far never been implemented in the context of FBR assessment. However, to this date, immunofluorescence or immunohistochemistry are still required to validate the results of transcriptomic studies and appears to be a more practical approach for FBR assessment.

The impact of substrate stiffness on mechanical stress at the biotic-abiotic interface has been estimated through finite element method (FEM) models (Subbaroyan et al., 2005; Polanco et al., 2014, 2016). Based on two of such models (Subbaroyan et al., 2005; Polanco et al., 2014), the stiffness discrepancy between neural probes and brain tissue must be lower than 3 orders of magnitude to significantly reduce the micromotion stress. Therefore, substrates such as Polyimide do not seem to provide a substantial mechanical advantage compared to silicon in applications involving longitudinal loading (Polanco et al., 2014). Figures 5B, C represents the difference in simulated strain distribution for probes with different Young's moduli. The impact of bulk mechanical properties on tissue reaction was also assessed. Nguyen et al. (2014) compared the tissue reaction to mechanically adaptive probes and to stiff silicon probes. Although they observed a similar acute tissue response, they reported an improved neuroinflammatory response at later time-points (of more than 2 weeks).

In another study (Harris et al., 2011), the same probes were compared to stiff metal microwires (160 μm overall diameter). The glial scar response to compliant probes was less vigorous than to stiff wires; however, in this case long-term (8 weeks time point) neuronal survival was comparable between the two types of devices. This outcome might be explained by the different geometry of the two probes, which may lead to different iatrogenic injury and to a different distribution of inflammatory and cytotoxic molecules at the probe-tissue interface.

An important observation made by Lee et al. (2017) is that there may be a limit to the relevance of the probe Young's modulus for FBR reduction. In fact, the authors reported a significant reduction of FBR biomarkers for polymeric probes compared to silicon probes, but no consistent differences among the different “flexible” probes, despite a difference in Young's modulus spanning several orders of magnitude.

Overall, the Young's modulus of materials constituting both the surface and the bulk of neural probes seems to play an important, but not exclusive role in determining the extent of FBR (Stiller et al., 2018).

A meta-analysis performed on the data from nine studies demonstrated that the severity of the immune response is highly correlated with the bending stiffness of the device, as opposed to the bulk Young's modulus or to the cross-sectional area independently (Stiller et al., 2018).

Some research groups aim to achieve a disruptive reduction in device bending stiffness by acting both on the Young's modulus and on cross-sectional dimensions. This approach has been shown to produce favorable results, both based on immunohistochemical analysis and based on the probe's ability to stably track single unit activity for weeks or months.

Luan et al. (2017) fabricated flexible nanoelectronic thread (NET) probes with subcellular cross-sectional dimensions, as small as 10 by 1.5 μm². This allowed to reduce the overall bending stiffness of the device by several orders of magnitude compared to typical neural probes. This approach, which was also recently followed by Zhao et al. (2022) led to a seamless integration of probes within brain tissue and the reliable tracking and detection of single unit activity for months.

Another approach to achieve brain-like ultraflexibility is to generate macroporous mesh structures with feature sizes comparable to neuronal soma (Liu et al., 2015; Xie et al., 2015; Fu et al., 2016; Zhou et al., 2017). While this solution allows to readily scale the number of recording sites, the use of a syringe for implantation induces higher insertion trauma and bleeding, with a potential negative impact on both acute and chronic performances.

A noteworthy effort in the direction of reducing the bending stiffness was reported by Yang et al. (2019). In this case, they designed and fabricated bio-inspired neuron-like electronic devices with a unit building block that is structurally and mechanically similar to a neuron, reaching a cross-sectional dimension of the neurite-like interconnect portion of the device as low as 2 μm wide and 0.9 μm thick. The interpenetration of neuron-like electronics with biological neurons is similar to that of natural brain tissue and the authors were able to track stable single unit activity for the 3 months duration of the study.

The use of neural probes with a ultra low bending stiffness, however, also poses constraints, particularly during the surgical implantation procedure. Recently, a series of methods to aid the implantation of highly compliant neural probes have been reviewed (Thielen and Meng, 2021).

The non-specific adsorption of serum protein on the surface of neural probes (biofouling), particularly fibrinogen, has been shown to drive the activation of microglia/macrophages (Hu et al., 2001).

An approach to target this issue is to coat neural probes with highly hydrophilic polymers (Lu et al., 2009; Kozai et al., 2012b; Rao et al., 2012; Gutowski et al., 2015) or with zwitterionic molecules (Golabchi et al., 2019; Zou et al., 2021).

In some cases, a covalent binding strategy was used, while in other cases a hydrophilic polymer was passively adsorbed on the surface of the device (Lu et al., 2009; Rao et al., 2012). This second approach generates much thicker layers (μm thickness) which dissolve over time, potentially leading to a loss in antifouling properties.

Antifouling strategies can also be combined with the delivery of bioactive molecules. For example, Gutowski et al. (2015) engineered a protease-degradable PEG antifouling coating which can release IL-Ra in response to tissue inflammation.

Coatings with both an antifouling as well as a bioactive function aiming to improve cell adhesion were also proposed, such as the EK-IKVAV modified electrodes presented by Zou et al. (2021). In this case, an EK zwitterionic peptide sequence head was used to generate a hydration layer with antifouling properties, while an IKVAV tail was used to increase the adhesion of neuronal cells to the microelectrodes. While there is no conclusive evidence that antifouling coatings alone may lead to an improved chronic performance, their combination with bioactive coatings and other strategies for FBR reduction appear promising.

Another strategy to improve biocompatibility of implanted neural probes is to deliver bioactive molecules/drugs at the biotic-abiotic interface or to functionalize their surface with molecules that modulate cellular responses.

The most commonly employed molecules for targeted delivery at the device-tissue interface are anti-inflammatory drugs such as the corticosteroid dexamethasone. Systemic administration of dexamethasone has been shown to affect early and sustained reactive responses to device implantation (Spataro et al., 2005); however, this delivery strategy is inefficient and may cause unintended side effects.

Several strategies can be employed for a more localized and efficient drug delivery:

Besides dexamethasone, a drug that multiple studies have deemed as effective in reducing tissue reaction (Zhong and Bellamkonda, 2007; Mercanzini et al., 2008), other compounds have been proposed. The natural antioxidant curcumin was shown to initially improve neuronal survival and reduce BBB leakage over the first 4 weeks of implantation; however, this benefit was lost over a longer period (12 weeks) (Potter et al., 2014). Nerve growth factor (NGF) (Kato et al., 2006) and α-melanocyte stimulating hormone (α-MSH) (Zhong and Bellamkonda, 2005) have also been successfully loaded in the surface coatings of neural probes; however, their impact on FBR has not yet been assessed in-vivo.

A different strategy for a bioactive functionalization of the device is to bind protein/peptides to its surface, to improve neuronal adhesion and to decrease glial encapsulation. Azemi et al. (2008) covalently bound neuronal adhesion protein L1 to silicon neural probes. The authors observed an increased neuronal density and a decreased activation of astrocytes and macrophages around surface-modified probes. Oakes et al. (2018) implemented a non covalent bioactive surface modification by dip coating neural probes in astrocyte derived extracellular matrix (ECM) and observed a reduction in GFAP immunoreactivity at the 8-weeks timepoint, but no significant changes in neuronal density around ECM coated probes.

Neural implants can be rigidly tethered to the skull or decoupled from the skull using flexible interconnections to approach the conditions of a free-floating implant. Rigidly tethered probes have been reported to lead to oval-shaped cavities, with a cross-sectional area larger than the implant itself (Biran et al., 2007; Thelin et al., 2011) and significantly higher ED1 and GFAP expression, as well as decreased neuronal and axonal density (Biran et al., 2007). Indeed, implants rigidly tethered to the skull were reported to increase FBR compared to free floating implants (Kim et al., 2004; Biran et al., 2007; Thelin et al., 2011; Chauviere et al., 2019), most likely because this fixation modality increases the magnitude of the relative micromotion among the probe and the brain tissue.

Inertial forces resulting from the difference between the density of neural probes and the tissue have also been reported to increase FBR. Lind et al. (2013) tested glial scarring in the presence of untethered probes with similar size, shape, surface structure, and elastic modulus but with densities which differed by an order of magnitude. Under the tested conditions, low-density probes caused significantly smaller scars than high-density probes. This indicates that inertial forces can elicit substantial astrocytic reactions. By extension, this result indicates that forces arising from the micromotion at the tissue/implant interface may also have a significant impact on glial scarring.

A few research groups studied the impact of parameters such as insertion speed (Sharp et al., 2009; Welkenhuysen et al., 2011; Fekete et al., 2015; Hosseini-Farid et al., 2019; Obaid et al., 2020b), probe size (Sharp et al., 2009; Hosseini-Farid et al., 2019; Obaid et al., 2020b), surface properties (Jensen et al., 2006; Sridharan et al., 2015), and tip shape (Fekete et al., 2015; Obaid et al., 2020b) on the magnitude of the insertion force of neural probes measured in-vivo.

Generally, an increase in insertion force with insertion speed is observed (Sharp et al., 2009; Fekete et al., 2015; Hosseini-Farid et al., 2019; Obaid et al., 2020b), which is consistent with the well-known viscoelastic properties of brain tissue. The extent of the reported increase in insertion forces depends both on tested insertion speeds, ranging from 2 μm/s to 1.7 mm/s in different studies, and on the size and layout of the tested probes.

The size of neural probe shanks, i.e., the part of the probe inserted in the tissue, is in fact another important predictor of the insertion force (Sharp et al., 2009; Welkenhuysen et al., 2011; Obaid et al., 2020b). This is due to the larger volume of displaced brain tissue induced by larger probes and to the wider area of the probe in contact with brain tissue, which yields higher frictional forces during insertion.

Interestingly, although only studied in a few works, the surface properties of neural probes have been reported to influence insertion dynamics and a reduced penetration force was reported for probes treated both with hydrophilic and hydrophobic coatings (Jensen et al., 2006).

Finally, the tip geometry has also been shown to influence insertion force. Electro-sharpened tungsten microwires exhibit remarkably different insertion dynamics compared to flat- and angle-polished microwires, particularly in terms of tissue dimpling (Obaid et al., 2020b). In addition, the tip angle of planar silicon probes was also shown to influence insertion force (Fekete et al., 2015).

Despite the information provided from force measurements, these studies rarely report post-implantation immunohistochemical analysis, which would allow to understand if a correlation exists between insertion force and acute tissue damage and chronic FBR. Most likely, this correlation exists and if demonstrated, insertion force measurements would constitute a valuable metric to rapidly validate insertion protocol and probe design, as well as assessing the execution of each probe implantation.

Another key parameter of the implantation procedure is the speed at which the probe is inserted into the tissue. However, no consensus regarding the impact of this parameter on tissue response has been reached so far. While some studies suggest that a slower penetration might result in less tissue damage (Fiáth et al., 2019), especially for smaller probes (Obaid et al., 2020b), others indicate that a faster insertion results in lower mean effective strain (Bjornsson et al., 2006). In this context, however, it is important to recognize that the definition of slow and fast insertions depends on the range of penetration speeds tested in the different studies, which spanned over seven orders of magnitude (from 1 μm/s to 10 m/s).

Mechanical (Rennaker et al., 2005) and pneumatic (Rousche and Normann, 1992) insertion devices have been proposed to implant neural probes with a speed higher than 1 m/s. The insertion of microwire electrode array with a velocity of 1.5 m/s through a mechanical inserter was shown to decrease tissue dimpling compared to a slower insertion (Rennaker et al., 2005). Moreover, the faster insertion procedure resulted in better chronic functional performances when recording neural activity. A potential explanation of the reported improved performance is the prevention of cortical tissue compression (referred to as tissue dimpling), which occurs as the tip of the probe presses on brain tissue, before rupturing its surface and beginning the actual insertion. Reduction of brain tissue dimpling during implantation may prevent traumatic brain injury (TBI) and ischemic damage. Rousche and Normann (1992) reported that a penetration speed of 8.3 m/s, achieved using a pneumatically actuated insertion system, allowed the complete penetration of the Utah Electrode Array. For slower insertion speeds, full penetration of the central electrodes could not be achieved.

In other works, neural probes were inserted at much slower velocities (below 2 mm/s). Bjornsson et al. (2006) observed that a faster insertion (2 mm/s) of sharp devices led to lower mean effective strain in ex vivo tissue compared to lower insertion speeds (125 and 500 μm/s).

However, Fiáth et al. (2019) observed that both the signal-to-noise ratio and the number of separable single units recorded were significantly higher for the slowest insertion speed (2 μm/s) compared to faster speeds (20, 100, and 1,000 μm/s). The different ranges of tested speeds in these two studies may explain their apparent discrepancies. In fact, the improvement in the recording quality reported by Fiath was significantly different only for the slowest insertion speed (2 μm/s), which is far below the experimental range tested by Bjornson.