Experimental identification of high order Lamb waves and estimation of the mechanical properties of a dry human skull

A comparative study of experimental and simulated ultrasound beam propagation through cranial bones

Objective.Transcranial ultrasound is used in a variety of treatments, including neuromodulation, opening the blood-brain barrier, and high intensity focused ultrasound therapies. To ensure safety and efficacy of these treatments, numerical simulations of the ultrasound field within the brain are used for treatment planning and evaluation. This study investigates the accuracy of numerical modelling of the propagation of focused ultrasound through cranial bones.Approach.Holograms of acoustic fields after propagation through four human skull specimens were measured for frequencies ranging from 270 kHz to 1 MHz, using both quasi-continuous and pulsed modes. The open-source k-Wave toolbox was employed for simulations, using an equivalent-source hologram and a uniform bowl source with parameters that best matched the measured free-field pressure distribution.Main results.The average absolute error in k-Wave simulations with sound speed and density derived from CT scans compared to measurements was 15% for the spatial-peak acoustic pressure amplitude, 2.7 mm for the position of the focus, and 35% for the focal volume. Optimised uniform bowl sources achieved calculation accuracy comparable to that of the hologram sources.Significance.This method is demonstrated as a suitable tool for prediction of focal position, size and overall distribution of transcranial ultrasound fields. The accuracy of the shape and position of the focal region demonstrate the suitability of the sound speed and density mapping used here. However, large errors in pressure amplitude and transmission loss in some individual cases show that alternative methods for mapping individual skull attenuation are needed and the possibility of considerable errors in pressure amplitude should be taken into account when planning focused ultrasound studies or interventions in the human brain, and appropriate safety margins should be used.

Study of Ultrasonic Guided Wave Propagation in Bone Composite Structures for Revealing Osteoporosis Diagnostic Indicators

Tubular bones are layered waveguide structures composed of soft tissue, cortical and porous bone tissue, and bone marrow. Ultrasound diagnostics of such biocomposites are based on the guided wave excitation and registration by piezoelectric transducers applied to the waveguide surface. Meanwhile, the upper sublayers shield the diseased interior, creating difficulties in extracting information about its weakening from the surface signals. To overcome these difficulties, we exploit the advantages of the Green's matrix-based approach and adopt the methods and algorithms developed for the guided wave structural health monitoring of industrial composites. Based on the computer models implementing this approach and experimental measurements performed on bone phantoms, we analyze the feasibility of using different wave characteristics to detect hidden diagnostic signs of developing osteoporosis. It is shown that, despite the poor excitability of the most useful modes associated with the diseased inner layers, the use of the improved matrix pencil method combined with objective functions based on the Green's matrix allows for effective monitoring of changes in the elastic moduli of the deeper sublayers. We also note the sensitivity and monotonic dependence of the resonance response frequencies on the degradation of elastic properties, making them a promising indicator for osteoporosis diagnostics.

Multiscale static and dynamic mechanical study of the Turritella terebra and Turritellinella tricarinata seashells

Marine shells are designed by nature to ensure mechanical protection from predators and shelter for molluscs living inside them. A large amount of work has been done to study the multiscale mechanical properties of their complex microstructure and to draw inspiration for the design of impact-resistant biomimetic materials. Less is known regarding the dynamic behaviour related to their structure at multiple scales. Here, we present a combined experimental and numerical study of the shells of two different species of gastropod sea snail belonging to the Turritellidae family, featuring a peculiar helicoconic shape with hierarchical spiral elements. The proposed procedure involves the use of micro-computed tomography scans for the accurate determination of geometry, atomic force microscopy and nanoindentation to evaluate local mechanical properties, surface morphology and heterogeneity, as well as resonant ultrasound spectroscopy coupled with finite element analysis simulations to determine global modal behaviour. Results indicate that the specific features of the considered shells, in particular their helicoconic and hierarchical structure, can also be linked to their vibration attenuation behaviour. Moreover, the proposed investigation method can be extended to the study of other natural systems, to determine their structure-related dynamic properties, ultimately aiding the design of bioinspired metamaterials and of structures with advanced vibration control.

Effect of skull porosity on ultrasound transmission and wave mode conversion at large incidence angles

BACKGROUND

Transcranial ultrasound imaging and therapy depend on the efficient transmission of acoustic energy through the skull. Multiple previous studies have concluded that a large incidence angle should be avoided during transcranial-focused ultrasound therapy to ensure transmission through the skull. Alternatively, some other studies have shown that longitudinal-to-shear wave mode conversion might improve transmission through the skull when the incidence angle is increased above the critical angle (i.e., 25° to 30°).

PURPOSE

The effect of skull porosity on the transmission of ultrasound through the skull at varying incidence angles was investigated for the first time to elucidate why transmission through the skull at large angles of incidence is decreased in some cases but improved in other cases.

METHODS

Transcranial ultrasound transmission at varying incidence angles (0°-50°) was investigated in phantoms and ex vivo skull samples with varying bone porosity (0% to 28.54% ± 3.36%) using both numerical and experimental methods. First, the elastic acoustic wave transmission through the skull was simulated using micro-computed tomography data of ex vivo skull samples. The trans-skull pressure was compared between skull segments having three levels of porosity, that is, low porosity (2.65% ± 0.03%), medium porosity (13.41% ± 0.12%), and high porosity (26.9%). Next, transmission through two 3D-printed resin skull phantoms (compact vs. porous phantoms) was experimentally measured to test the effect of porous microstructure alone on ultrasound transmission through flat plates. Finally, the effect of skull porosity on ultrasound transmission was investigated experimentally by comparing transmission through two ex vivo human skull segments having similar thicknesses but different porosities (13.78% ± 2.05% vs. 28.54% ± 3.36%).

RESULTS

Numerical simulations indicated that an increase in transmission pressure occurs at large incidence angles for skull segments having low porosities but not for those with high porosity. In experimental studies, a similar phenomenon was observed. Specifically, for the low porosity skull sample (13.78% ± 2.05%), the normalized pressure was 0.25 when the incidence angle increased to 35°. However, for the high porosity sample (28.54% ± 3.36%), the pressure was no more than 0.1 at large incidence angles.

CONCLUSIONS

These results indicate that the skull porosity has an evident effect on the transmission of ultrasound at large incidence angles. The wave mode conversion at large, oblique incidence angles could enhance the transmission of ultrasound through parts of the skull having lower porosity in the trabecular layer. However, for transcranial ultrasound therapy in the presence of highly porous trabecular bone, transmission at a normal incidence angle is preferable relative to oblique incidence angles due to the higher transmission efficiency.

Optimizing transcranial ultrasound delivery at large incident angles by leveraging cranial leaky guided wave dispersion

We investigate the role of leaky guided waves in transcranial ultrasound transmission in temporal and parietal bones at large incidence angles. Our numerical and experimental results show that the dispersion characteristics of the fundamental leaky guided wave mode with longitudinal polarization can be leveraged to estimate the critical angle above which efficient shear mode conversion takes place, and below which major transmission drops can be expected. Simulations that employ a numerical propagator matrix and a Semi-Analytical approach establish the transcranial dispersion characteristics and transmission coefficients at different incident angles. Experimental transmission tests conducted at 500 kHz and radiation tests performed in the 200-800 kHz range confirm the numerical findings in terms of transmitted peak pressure and frequency-radiation angle spectra, based on which the connection between critical angles, dispersion and transmission is demonstrated. Our results support the identification of transcranial ultrasound strategies that leverage shear mode conversion, which is less sensitive to phase aberrations compared to normal incidence ultrasound. These findings can also enable higher transmission rates in cranial bones with low porosity by leveraging dispersion information extracted through signal processing, without requiring measurement of geometric and mechanical properties of the cranial bone.

Error analysis and reliability of zero-order Lamb mode inversion for waveguide characterization

In recent years, several fitting techniques have been presented to reconstruct the parameters of a plate from its Lamb wave dispersion curves. Published studies show that these techniques can yield high accuracy results and have the potential of reconstructing several parameters at once. The precision with which parameters can be reconstructed by inverting Lamb wave dispersion curves, however, remains an open question of fundamental importance to many applications. In this work, we introduce a method of analyzing dispersion curves that yields quantitative information on the precision with which the parameters can be extracted. In our method, rather than employing error minimization algorithms, we compare a target dispersion curve to a database of theoretical ones that covers a given parameter space. By calculating a measure of dissimilarity (error) for every point in the parameter space, we reconstruct the distribution of the error in that space, beside the location of its minimum. We then introduce dimensionless quantities that describe the distribution of this error, thus yielding information about the spread of similar curves in the parameter space. We demonstrate our approach by considering both idealized and realistic scenarios, analyzing the dispersion curves obtained numerically for a plate and experimentally for a pipe. Our results show that the precision with which each parameter is reconstructed depends on the mode used, as well as the frequency range in which it is considered.

Increasing the transmission efficiency of transcranial ultrasound using a dual-mode conversion technique based on Lamb waves

Transcranial focused ultrasound (FUS) is a noninvasive treatment for brain tumors and neuromodulation. Based on normal incidence, conventional FUS techniques use a focused or an array of ultrasonic transducers to overcome the attenuation and absorption of ultrasound in the skull; however, this remains the main limitation of using FUS. A dual-mode conversion technique based on Lamb waves is proposed to achieve high transmission efficiency. This concept was validated using the finite element analysis (FEA) and experiments based on changes in the incident angle. Aluminum, plexiglass, and a human skull were used as materials with different attenuations. The transmission loss was calculated for each material, and the results were compared with the reflectance function of the Lamb waves. Oblique incidence based on dual-mode conversion exhibited a better transmission efficiency than that of a normal incidence for all of the specimens. The total transmission losses for the materials were 13.7, 15.46, and 3.91 dB less than those associated with the normal incidence. A wedge transducer was designed and fabricated to implement the proposed method. The results demonstrated the potential applicability of the dual-mode conversion technique for the human skull.

Modeling lamb wave propagation in visco-elastic composite plates using a fifth-order plate theory

A new extension of the shear deformation theory to fifth order in order to calculate the spectrum of Lamb waves in orthotropic media over a wide frequency range is developed and analyzed. The aspiration of the proposed method is to create an alternative framework to exhaustive 3D elasticity based solutions by increasing computational efficiency without losing accuracy, nor robustness. A new computational framework is introduced which allows to estimate the dispersion curves for the first nine symmetric and nine anti-symmetric Lamb modes. Analytically calculated dispersion curves using 5-SDT for different propagation directions and polar plots for selected frequency of different materials are compared with the results from both the semi analytical finite element method, and lower order shear deformation theories. Careful analysis for individual laminae and for symmetric composite laminates exhibits a good agreement between the new higher order plate theory and the semi analytical finite element method over an extensive frequency range. In addition, attenuation plots show that the proposed method can also be used for visco-elastic materials (or highly damped materials). The advantage of the new higher order plate theory and its numerical implementation is that it is much more computationally efficient compared to comprehensive methods as Lamb wave polar plots of composite plates as function of incidence angle, polar angle and frequency can be calculated in less than a second on a standard laptop. Consequently, the use of this framework in inversion routines opens up the possibility of quasi real-time Structural Health Monitoring for visco-elastic composites covering a sufficiently wide frequency range.

Effect of Skull Porous Trabecular Structure on Transcranial Ultrasound Imaging in the Presence of Elastic Wave Mode Conversion at Varying Incidence Angle

With the advancement of aberration correction techniques, transcranial ultrasound imaging has exhibited great potential in applications such as imaging neurological function and guiding therapeutic ultrasound. However, the feasibility of transcranial imaging varies among individuals because of the differences in skull acoustic properties. To better understand the fundamental mechanisms underlying the variation in imaging performance, the effect of the structure of the porous trabecular bone on transcranial imaging performance (i.e., target localization errors and resolution) was investigated for the first time through the use of elastic wave simulations and experiments. Simulation studies using high-resolution computed tomography data from ex vivo skull samples revealed that imaging at large incidence angles reduced the target localization error for skulls having low porosity; however, as skull porosity increased, large angles of incidence resulted in degradation of resolution and increased target localization errors. Experimental results indicate that imaging at normal incidence introduced a localization error of 1.85 ± 0.10 mm, while imaging at a large incidence angle (40°) resulted in an increased localization error of 6.54 ± 1.33 mm and caused a single point target to no longer appear as a single, coherent target in the resulting image, which is consistent with simulation results. This first investigation of the effects of skull microstructure on transcranial ultrasound imaging indicates that imaging performance is highly dependent on the porosity of the skull, particularly at non-normal angles of incidence.

Vibration-based elastic parameter identification of the diploë and cortical tables in dry cranial bones

Various human skull models feature a layered cranial structure composed of homogeneous cortical tables and the inner diploë. However, there is a lack of fundamental validation work of such three-layer cranial bone models by combining high-fidelity computational modeling and rigorous experiments. Here, non-contact vibration experiments are conducted on an assortment of dry bone segments from the largest cranial bone regions (parietal, frontal, occipital, and temporal) to estimate the first handful of modal frequencies and damping ratios, as well as mode shapes, in the audio frequency regime. Numerical models that consider the cortical tables and the diploë as domains with separate isotropic material properties are constructed for each bone segment using a routine that identifies the cortical table-diploë boundaries from micro-computed tomography scan images, and reconstructs a three-dimensional geometry layer by layer. The material properties for cortical tables and diploë are obtained using a Hounsfield Unit-based mass density calculation combined with a parameter identification scheme for Young's modulus estimation. With the identified parameters, the average error between experimental and numerical modal frequencies is 1.3% and the modal assurance criterion values for most modes are above 0.90, indicating that the layered model is suitable for predicting the vibrational behavior of cranial bone. The proposed layered modeling and identified elastic parameters are also useful to support computational modeling of cranial guided waves and mode conversion in medical ultrasound. Additionally, the diploë elastic properties are rarely reported in the literature, making this work a fundamental characterization effort that can guide in the selection of material properties for human head models that consider layered cranial bone.

High-resolution Lamb waves dispersion curves estimation and elastic property inversion

Ultrasonic Lamb waves have been widely used for non-destructive evaluation and testing. However, the inversion from the measured guided signals to the material properties is still a challenging task in terms of multimodal dispersive signal processing and parameter estimation. This paper presents a robust strategy including the high-resolution extraction of the multimodal dispersion curves and model-based elastic property estimation. First, the estimation of signal parameters via rotation invariant technique (ESPRIT) is employed to extract the dispersion curves of the Lamb waves in the plates. Then, the particle swarm optimization (PSO) algorithm is used to retrieve the optimal model parameters by maximizing the objective function built from the dispersion equations. The elastic properties (i.e., two independent constants for the isotropic plate and four constants for the transversely isotropic plate) can thus be determined. Results of the steel, aluminum and composite plates demonstrate that the estimates are in agreement with the references. The root mean squared errors (RMSEs) between the estimated and theoretical dispersion curves calculated by the inversed model parameters for simulation, steel, aluminum and composite experiments are 0.027 rad/mm, 0.032 rad/mm, 0.033 rad/mm and 0.102 rad/mm respectively. The estimated error of thickness is less than 1%. The proposed model-based inversion strategy offers several advantages: (1) the high-resolution estimation of dispersion curves allows the objective function built for the parameter inversion without a peak-finding process. (2) The ESPRIT based dispersion curves extraction strategy offers a sharp objective function in the parameter space. (3) The inverse problem for ultrasonic waveguide characterization is solved using the PSO optimizer which can be implemented with ease and few parameters need to be tuned.

Radiation Characteristics of Cranial Leaky Lamb Waves

We numerically and experimentally investigate the dispersion properties of leaky Lamb waves in the cranial bone. Cranial Lamb waves leak energy from the skull into the brain when propagating at speeds higher than the speed of sound in the surrounding fluid. The understanding of their radiation mechanism is significantly complicated by the geometric and mechanical characteristics of the cortical tables and the trabecular bone (diploë). Toward such understanding, we here analyze the sub-1.0 MHz radiation angle dispersion spectrum of porous bone phantoms and parietal bone geometries obtained from μ CT scans. Our numerical results show that, when diploic pores are physically modeled, leakage angles computed from time transient finite-element analyses correspond to those predicted by an equivalent three-layered fluid-loaded waveguide model. For the bone geometries analyzed, two main leaky branches are observed in the near-field dispersion spectrum: a fast wave radiated at small angles, which is related to the fastest fundamental Lamb mode supported by the cranial bone, and a slower wave radiated at larger angles. This observation is also confirmed by experimental tests carried out on an immersed parietal bone.