This paper presents a simple analytical circuit-like model to study the transmission of electromagnetic waves through stacked two-dimensional (2-D) conducting meshes. When possible the application of this methodology is very convenient since it provides a straightforward rationale to understand the physical mechanisms behind measured and computed transmission spectra of complex geometries. Also, the disposal of closed-form expressions for the circuit parameters makes the computation effort required by this approach almost negligible. The model is tested by proper comparison with previously obtained numerical and experimental results. The experimental results are explained in terms of the behavior of a finite number of strongly coupled Fabry-Pérot resonators. The number of transmission peaks within a transmission band is equal to the number of resonators. The approximate resonance frequencies of the first and last transmission peaks are obtained from the analysis of an infinite structure of periodically stacked resonators, along with the analytical expressions for the lower and upper limits of the pass-band based on the circuit model.

Decompressive craniectomy is a traditional but controversial surgical procedure that removes part of the skull to allow an injured and swollen brain to expand outward. Recent studies suggest that mechanical strain is associated with its undesired, high failure rates. However, the precise strain fields induced by the craniectomy are unknown. Here we create a personalized craniectomy model from magnetic resonance images to quantify the strains during a decompressive craniectomy using finite element analysis. We swell selected regions of the brain and remove part of the skull to allow the brain to bulge outward and release the intracranical swelling pressure. Our simulations reveal three potential failure mechanisms associated with the procedure: axonal stretch in the center of the bulge, axonal compression at the edge of the craniectomy, and axonal shear around the opening. Strikingly, for a swelling of only 10%, axonal strain, compression, and shear reach local maxima of up to 30%, and exceed the reported functional and morphological damage thresholds of 18% and 21%. Our simulations suggest that a collateral craniectomy with the skull opening at the side of swelling is less invasive than a contralateral craniectomy with the skull opening at the opposite side: It induces less deformation, less rotation, smaller strains, and a markedly smaller midline shift. Our computational craniectomy model can help quantify brain deformation, tissue strain, axonal stretch, and shear with the goal to identify high-risk regions for brain damage on a personalized basis. While computational modeling is beyond clinical practice in neurosurgery today, simulations of neurosurgical procedures have the potential to rationalize surgical process parameters including timing, location, and size, and provide standardized guidelines for clinical decision making and neurosurgical planning.

Effective properties of split-ring resonator metamaterials using measured scattering parameters: Effect of gap orientation J. Appl. Phys. 100, 034910 (2006) A simple structure comprising a metal mesh, symmetrically surrounded by subwavelength thickness dielectric layers, is shown to give near total microwave transmission over a broad frequency range. The mesh may be considered to be a tunnel barrier since it behaves as an ideal plasmonic metamaterial with a negative effective permittivity and no loss. The introduction of the mesh into the dielectric cavity imposes a finite gradient on the electromagnetic fields at the two mesh-dielectric interfaces. This defines a finite wavelength of the zeroth order Fabry-Pérot-type mode, which would otherwise be infinite. Suitable choice of the mesh parameters yields a broad band of near total transmission associated with the overlap of this zeroth order mode with that of the first order half-wavelength Fabry-Pérot-type resonance.

A metamaterial layer comprising of a conducting square mesh surrounding subwavelength holes has a largely pure imaginary effective refractive index. We explore the microwave transmissivity of a stack of such metamaterial layers separated by dielectric spacers. As expected, a family of high transmissivity bands is experimentally observed. It is found that the lowest frequency edge is independent of the number of unit cells making up the structure and is highly tunable by appropriate geometrical design of the metamaterial layers. © 2009 American Institute of Physics. ͓doi:10.1063/1.3253703͔Multilayer metal-dielectric structures have been extensively studied at visible frequencies, and their response utilized in areas such as electromagnetic shielding, nonlinear photonics and perfect lensing.1-3 Geffcken 4 in 1939 fabricated metal-dielectric thin film stacks that exhibited transmission features that were significantly narrower than those previously observed in conventional dielectric-dielectric multilayer arrangements. 5The spectral response of metal-dielectric stacks in the visible regime comprises of a series of photonic band gaps where the reflectivity is high ͑and the transmissivity is low͒, separated by a series of peaks of high transmissivity. These transmission peaks correspond to near-standing-wave resonances within each dielectric cavity, coupled together via exponential fields within the metal film. Near the high frequency band edge of the first transmission band, the electric fields are predominantly confined to the dielectric and pass through zero in the metal. In contrast, at the low frequency band edge a significant proportion of the field enhancement occurs inside the metal regions. [6][7][8] An equivalent study of a metal-dielectric layer stack in the microwave domain ͑10 9 -10 10 Hz͒ is at first sight impractical since the real and imaginary parts of the refractive index of metals are both large ͑Ͼ10 3 ͒ and almost equal ͑i.e., the metal is near-perfectly conducting͒. Even a metal film of thickness 20 nm will almost completely screen the incident field 9 because of the large impedance mismatch. Instead, a metal is structured on the subwavelength scale to create a metamaterial with effective electromagnetic properties which replicates the behavior of Drude-like ͑plasmonic͒ metals in the visible regime ͑Ag, Au, etc.͒. 10 The metamaterial layer consists of a non diffracting square metal mesh surrounding an array of identical square holes. At wavelengths greater than the size of the holes, the electromagnetic fields are exponential within the holes with a decay length that is primarily dictated by the metamaterial geometry. Consequently the metamaterial is equivalent to a thin layer with a pure imaginary refractive index. 12,13The sample shown in Fig. 1͑a͒ comprises of eight printed circuit board ͑PCB͒ layers that are originally clad with 18 m of copper on one face. The copper is removed from three of these substrates the remaining five being etched to leave a copper square mesh ͑Fig. 1͑b͒͒ with period...

Brain swelling is a serious condition associated with an accumulation of fluid inside the brain that can be caused by trauma, stroke, infection, or tumors. It increases the pressure inside the skull and reduces blood and oxygen supply. To relieve the intracranial pressure, neurosurgeons remove part of the skull and allow the swollen brain to bulge outward, a procedure known as decompressive craniectomy. Decompressive craniectomy has been preformed for more than a century; yet, its effects on the swollen brain remain poorly understood. Here we characterize the deformation, strain, and stretch in bulging brains using the nonlinear field theories of mechanics. Our study shows that even small swelling volumes of 28 to 56 ml induce maximum principal strains in excess of 30%. For radially outward-pointing axons, we observe maximal normal stretches of 1.3 deep inside the bulge and maximal tangential stretches of 1.3 around the craniectomy edge. While the stretch magnitude varies with opening site and swelling region, our study suggests that the locations of maximum stretch are universally shared amongst all bulging brains. Our model has the potential to inform neurosurgeons and rationalize the shape and position of the skull opening, with the ultimate goal to reduce brain damage and improve the structural and functional outcomes of decompressive craniectomy in trauma patients.