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IntroductionDevelopment of novel neural interfaces faces buckling challenges and heavily relies on trial-and-error tests viain vivoanimal brain insertions for design optimizations toward the minimal-damaging version for enhanced recording and stimulation outcome. MethodsTo enable low-cost and fast-turnaround neural interface development and to enable previously impossible insertions via new understanding of the cutting process, this study developed a reproducible, multi-layer brain-mimicking phantom designed to replicate the rodent pia and dura mater dimpling and rupture force performance observed duringin vivotests. The phantom was composed of a 0.5% (w/v) agarose cortex layer, a 1.01% (w/v) agarose pia mater layer, and a pre-stretched polyvinyl chloride (PVC) dura mater layer, assembled via easily duplicable benchtop protocols. Using a cantilever-beam force measurement system, rupture force and dimpling depth were quantified across microwires of varying diameters (12–100 μm), materials (tungsten, stainless steel), and tip geometries, as well as segmented silicon probe shanks. ResultsThe developed multi-layer phantom test results fell within thein vivoSprague–Dawley rat data range. At the same time, phantom insertion trial variability was substantially lower thanin vivotests. DiscussionThe developed multi-layer phantom enabled a repeatable, low-cost, early-stage screening platform of novel electrode designs. The phantom’s modular design also allowed tuning of layer thickness and stiffness of each layer for different species or devices, offering a customizable testing platform to accelerate novel neural implant development and reduce animal use. 

Large-scale chronic recording across the brain with minimal disruption will be critical for understanding the multi-region neural dynamics. But the possibility of such experiments is limited by buckling of the electrodes upon insertion. The least-damaging microelectrode arrays (MEAs) would be preferred for broad chronic recording but buckle against brain membranes during insertion, so larger more damaging electrodes/shuttles are usually used. To address this challenge, in this study, a piezoelectric inchworm insertion robot was developed to enable currently impractical brain implantation of miniaturized flexible MEAs through the dura and pia mater without buckling in a fast and extensible machine-controlled manner. The inchworm inserter robot conducts iterative grip-feed-release inchworm motion holding the electrode body. This reduces buckling by increasing lateral extracranial support along the electrode during implantation and minimizing unsupported length (maximizing the critical buckling load). The prototyped inchworm inserter was composed of three custom piezoelectric unimorph “re-curve” actuators: two horizontal grippers alternatingly gripping the implant and an extender that moves the grippers vertically. The assembly is of miniaturized size of 14 × 5.8 × 3.6 mm and 250 mg in weight. Custom designed piezoelectric ‘re-curve’ actuators together with adjustable gripping plates were used to produce up to 80 µm of purely linear motion with minimal bending, up to 950 mN of gripping/insertion force, and up to 200 Hz of bandwidth, enabling up to 14 mm/s precisely controlled insertion speed and iterative increments as little as 10 µm. These specs were all further tunable by varying the actuator design and power input. Benchtop tests were conducted against a multi-layer (dura-pia-brain tissue) rodent brain-mimicking phantom. The tests with the inchworm insertion robot demonstrated successful buckling-free penetration of dura and pia membrane phantoms with 12 and 25 µm diameter tungsten microwires and 15 µm-thick single-, dual-, and four-shank silicon probes. In comparison, under conventional stereotaxic insertions, these devices were limited to pia-only insertion and would buckle against the dura mater. The inchworm insertion motion also reduced the membrane rupture force and dimpling depth compared to static stereotaxic insertion methods, with optimal performance observed around medium 75 Hz operation frequency for 25 µm diameter tungsten microwires. These results highlighted the great potential of the piezo inchworm insertion robot to achieve broadly applicable improvements in brain surgery methodology by enabling thick membrane penetration by miniaturized MEAs and machine-controlled automatic buckling-free insertion with precise control of the speed and depth. 

Large-scale chronic recording across the brain with minimal disruption will be critical for understanding the multi-region neural dynamics. But the possibility of such experiments is limited by buckling of the electrodes upon insertion. The least-damaging microelectrode arrays (MEAs) would be preferred for broad chronic recording but buckle against brain membranes during insertion, so larger more damaging electrodes/shuttles are usually used. To address this challenge, in this study, a piezoelectric inchworm insertion robot was developed to enable currently impractical brain implantation of miniaturized flexible MEAs through the dura and pia mater without buckling in a fast and extensible machine-controlled manner. The inchworm inserter robot conducts iterative grip-feed-release inchworm motion holding the electrode body. This reduces buckling by increasing lateral extracranial support along the electrode during implantation and minimizing unsupported length (maximizing the critical buckling load). The prototyped inchworm inserter was composed of three custom piezoelectric unimorph “re-curve” actuators: two horizontal grippers alternatingly gripping the implant and an extender that moves the grippers vertically. The assembly is of miniaturized size of 14 × 5.8 × 3.6 mm and 250 mg in weight. Custom designed piezoelectric ‘re-curve’ actuators together with adjustable gripping plates were used to produce up to 80 µm of purely linear motion with minimal bending, up to 950 mN of gripping/insertion force, and up to 200 Hz of bandwidth, enabling up to 14 mm/s precisely controlled insertion speed and iterative increments as little as 10 µm. These specs were all further tunable by varying the actuator design and power input. Benchtop tests were conducted against a multi-layer (dura-pia-brain tissue) rodent brain-mimicking phantom. The tests with the inchworm insertion robot demonstrated successful buckling-free penetration of dura and pia membrane phantoms with 12 and 25 µm diameter tungsten microwires and 15 µm-thick single-, dual-, and four-shank silicon probes. In comparison, under conventional stereotaxic insertions, these devices were limited to pia-only insertion and would buckle against the dura mater. The inchworm insertion motion also reduced the membrane rupture force and dimpling depth compared to static stereotaxic insertion methods, with optimal performance observed around medium 75 Hz operation frequency for 25 µm diameter tungsten microwires. These results highlighted the great potential of the piezo inchworm insertion robot to achieve broadly applicable improvements in brain surgery methodology by enabling thick membrane penetration by miniaturized MEAs and machine-controlled automatic buckling-free insertion with precise control of the speed and depth. 

IntroductionWide use of miniaturized and flexible microwire electrodes faces challenges of wire buckling against the brain membrane layers. The field lacks quantitative understanding of such buckling phenomena, especially on the effective length factor, which is required to determine the wire’s critical buckling load. MethodsThis study presents an experimental investigation into the buckling behavior of tungsten microwire electrodes during implantation through dura and pia mater layers using a validated multilayer brain-mimicking phantom. Microwires with three diameters (25.4, 50.8, and 76.2 µm) and different tip geometries—including blunt, beveled, and electrochemically (conical) sharpened profiles—were evaluated under controlled axial insertion. Critical buckling length, insertion outcomes (buckled/penetrated), and rupture/buckling force were quantified across the experimental dataset. Buckling behavior was analyzed using the Euler column framework with experimentally estimated effective length factors (Kˆ) to represent each unique membrane-wire tip boundary interaction. ResultsResults indicated that wire diameter strongly influences buckling resistance, with larger diameters yielding quartic (fourth order) higher critical buckling load of the electrode, whereas the corresponding membrane rupture force only increases linearly with the diameter. But smaller microwires tend to anchor better against the brain membrane, generating a more stable wire-membrane interface closer to the ideal pin end condition. Tip geometry also significantly affected rupture force and insertion stability; conical tips dramatically reduced the membrane rupture force with less variance. In general, tip sharpening choice for small microwires should focus on optimizing tips anchoring mechanism and minimizing rupture force uncertainty introduced by tip asymmetry while thick microwires mainly benefit from membrane rupture force reduction. For theoretical prediction of a microwire electrode’s critical buckling load based on Euler’s buckling equation, unlike conventional fixed-pinned assumption (K= 0.7), experimentally measured effective length factors ranged from approximately 0.72 – 0.82. DiscussionDesigning with ≈ 0.8 provides a conservative estimate that may reduce the risk of buckling under membrane penetration conditions compared to the commonly assumed fixed-pinned value of 0.7. These findings provide quantitative design guidance for optimizing microwire geometry and offer a validated benchtop framework for predicting buckling-limited insertion performance in neural interface applications. 

Abstract We prove a suite of results classifying holomorphic maps between configuration spaces of Riemann surfaces; we consider both the ordered and unordered setting as well as the cases of genus zero, one, and at least two. We give a complete classification of all holomorphic maps$$\operatorname {Conf}_n(\mathbb {C})\rightarrow \operatorname {Conf}_m(\mathbb {C})$$ ${Conf}_n\left(C\right)\to {Conf}_m\left(C\right)$provided that$$n\ge 5$$ $n\ge 5$and$$m\le 2n$$ $m\le 2n$extending the Tameness Theorem of Lin, which is the case$$m = n$$ $m=n$. We also give a complete classification of holomorphic maps between ordered configuration spaces of Riemann surfaces of genus at most one (answering a question of Farb), and show that the higher genus setting is closely linked to the still-mysterious “effective de Franchis problem”. The main technical theme of the paper is that holomorphicity allows one to promote group-theoretic rigidity results to the space level. 

For each circle bundleS^{1}\to X\to\Sigma_{g}over a surface with genusg\ge2, there is a natural surjection\pi:\operatorname{Homeo}^{+}(X)\to\operatorname{Mod}(\Sigma_{g}). WhenXis the unit tangent bundleU\Sigma_{g}, it is well known that\pisplits. On the other hand,\pidoes not split when the Euler numbere(X)is not divisible by the Euler characteristic\chi(\Sigma_{g})by Chen and Tshishiku (2023). In this paper, we show that this homomorphism does not split in many cases where\chi(\Sigma_{g})dividese(X). 

The moiré structure of AB-stacked ${\mathrm{MoTe}}_2/{\mathrm{WSe}}_2$represents a natural platform to realize Kondo lattice models due to the discrepancy of the bandwidth between the individual layers. Here, we study this system at the commensurate filling of ${\nu }_{\mathrm{tot}}=2$. Our focus is on the $1+1$filling setting of ${\nu }_{\mathrm{Mo}}={\nu }_{\mathrm{W}}=1$, which enables a Kondo lattice description. We find a Kondo semimetal due to the sizable intraorbital hopping among the electrons in the ${\mathrm{MoTe}}_2$layer. The Kondo-driven (emergent) flat band is naturally pinned to the Fermi energy. When combined with the inherent topology of the electronic structure, a topological Kondo semimetal phase ensues. We calculate the valley Hall response, and due to the breaking of inversion symmetry we also identify a spontaneous Hall effect. There is a Berry curvature dodecapole that leads to a fourth-order spontaneous Hall effect in the perturbative regime of the electric field that is further amplified in the nonperturbative regime. As such, the system provides a tunable setting to simulate topological Kondo semimetals. Finally, we discuss the pathways that connect the physics realized here to the Weyl-Kondo semimetals and their proximate phases,which have been advanced in recent years in topological Kondo lattice models and materials.