Structural analysis of the frontal and parietal bones of the human skull

Simultaneous High-Frame-Rate Acoustic Plane-Wave and Optical Imaging of Intracranial Cavitation in Polyacrylamide Brain Phantoms during Blunt Force Impact

Blunt and blast impacts occur in civilian and military personnel, resulting in traumatic brain injuries necessitating a complete understanding of damage mechanisms and protective equipment design. However, the inability to monitor in vivo brain deformation and potential harmful cavitation events during collisions limits the investigation of injury mechanisms. To study the cavitation potential, we developed a full-scale human head phantom with features that allow a direct optical and acoustic observation at high frame rates during blunt impacts. The phantom consists of a transparent polyacrylamide material sealed with fluid in a 3D-printed skull where windows are integrated for data acquisition. The model has similar mechanical properties to brain tissue and includes simplified yet key anatomical features. Optical imaging indicated reproducible cavitation events above a threshold impact energy and localized cavitation to the fluid of the central sulcus, which appeared as high-intensity regions in acoustic images. An acoustic spectral analysis detected cavitation as harmonic and broadband signals that were mapped onto a reconstructed acoustic frame. Small bubbles trapped during phantom fabrication resulted in cavitation artifacts, which remain the largest challenge of the study. Ultimately, acoustic imaging demonstrated the potential to be a stand-alone tool, allowing observations at depth, where optical techniques are limited.

The influence of bone model geometries on the determination of skull acoustic properties

In this study, we investigated the impact of various simulated skull bone geometries on the determination of skull speed of sound and acoustic attenuation values via optimization using transmitted pressure amplitudes beyond the bone. Using the hybrid angular spectrum method (HAS), we simulated ultrasound transmission through four model sets of different geometries involving sandwiched layers of diploë and cortical bone in addition to three models generated from CT images of ex-vivo human skull-bones. We characterized cost-function solution spaces for each model and, using optimization, found that when a model possessed appreciable variations in resolvable layer thickness, the predefined attenuation coefficients could be found with low error (RMSE < 0.01 Np/cm). However, we identified a spatial frequency cutoff in the models' geometry beyond which the accuracy of the property determination begins to fail, depending on the frequency of the ultrasound source. There was a large increase in error of the attenuation coefficients determined by the optimization when the variations in layer thickness were above the identified spatial frequency cutoffs, or when the lateral variations across the model were relatively low in amplitude. For our limited sample of three CT-image derived bone models, the attenuation coefficients were determined successfully. The speed of sound values were determined with low error for all models (including the CT-image derived models) that were tested (RMSE < 0.4 m/s). These results illustrate that it is possible to determine the acoustic properties of two-component models when the internal bone structure is taken into account and the structure satisfies the spatial frequency constraints discussed.

The effect of morphometric and geometric indices of the human calvarium on mechanical response

BACKGROUND

When developing a surrogate model of the human skull, there is a multitude of morphometric and geometric properties to consider when constructing the model. To simplify this approach, it is important to identify only the properties that have a significant influence on the mechanical response of the skull. The objective of this study was to identify which morphometric and geometric properties of the calvarium were significant predictors of mechanical response.

METHODS

Calvarium specimens (N = 24) were micro-computed tomography scanned to determine morphometric and geometric properties. The specimens were assumed to be Euler-Bernoulli beams and were subject to 4-point quasi-static bending to determine mechanical response. Univariate linear regressions were performed whereby the morphometric and geometric properties were independent or predictor variables and the mechanical responses were dependent or outcome variables.

FINDINGS

Nine significant linear regression models were established (p < 0.05). In the diploë, trabecular bone pattern factor was a significant predictor of force and bending moment at fracture. The inner cortical table had more significant predictors (thickness, tissue mineral density, and porosity) of mechanical response compared to the outer cortical table and diploë.

INTERPRETATION

Morphometric and geometric properties had a key influence on the calvarium's biomechanics. Trabecular bone pattern factor and the morphometry and geometry of the cortical tables must be considered when evaluating the mechanical response of the calvarium. These properties can aid the design of surrogate models of the skull that seek to mimic its mechanical response for head impact simulation.

Intraosseous administration into the skull: Potential blood-brain barrier bypassing route for brain drug delivery

Progress in treating central nervous system (CNS) disorders is retarded owing to a limited understanding of brain disease pathology. Additionally, the blood-brain barrier (BBB) limits molecular entry into the brain. Many approaches for brain drug delivery to overcome the BBB, such as BBB permeability enhancement, transient BBB disruption, and direct surgical administration have been explored with limited success. Recent research has shown that direct vascular channels exist between the skull bone marrow and the meninges, allowing myeloid and lymphoid cells to migrate. We hypothesized that these direct channels may also allow brain drug delivery from the skull bone marrow to the brain. In this study, for the first time we propose intraosseous administration of drugs into the skull (intracalvariosseous [ICO]) as a novel approach for brain drug delivery via BBB bypassing routes. We tested the feasibility of the approach by applying nine representative compounds over thinned mouse skulls to simulate ICO and measuring the compound entry level in the brain compared to that after systemic administration. Surprisingly, we found that the skull is not completely impermeable to drug penetration into the brain and the tested compounds reached the brain tissue several tens-to-hundred times higher by ICO than systemic application. These findings suggest a role for the BBB bypassing route from skull to brain, apart from the systemic route, in the drug entry into the brain after ICO. This approach should be applicable to other CNS drugs and even BBB impermeable drugs. Overall ICO provides an innovative and advantageous pathway for effective treatment of brain diseases.

Development of a Coherent Model for Radiometric Core Body Temperature Sensing

This paper examines the utility of a wideband, physics-based model to determine human core body or brain temperature via microwave radiometry. Pennes's bioheat equation is applied to a six-layer human head model to generate the expected layered temperature profile during the development of a fever. The resulting temperature profile is fed into the forward electromagnetic (EM) model to determine the emitted brightness temperature at various points in time. To accurately retrieve physical temperature via radiometry, the utilized model must incorporate population variation statistics and cover a wide frequency band. The effect of human population variation on emitted brightness temperature is studied by varying the relevant thermal and EM parameters, and brightness temperature emissions are simulated from 0.1 MHz to 10 GHz. A Monte Carlo simulation combined with literature-derived statistical distributions for the thermal and EM parameters is performed to analyze population-level variation in resulting brightness temperature. Variation in thermal parameters affects the offset of the resulting brightness temperature signature, while EM parameter variation shifts the key maxima and minima of the signature. The layering of high and low permittivity layers creates these key maxima and minima via wave interference. This study is one of the first to apply a coherent model to and the first to examine the effect of population-representative variable distributions on radiometry for core temperature measurement. These results better inform the development of an on-body radiometer useful for core body temperature measurement across the human population.

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

Computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston operating at 500 kHz), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross-comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons.

Deep Learning-Based Photoacoustic Imaging of Vascular Network Through Thick Porous Media

Photoacoustic imaging is a promising approach used to realize in vivo transcranial cerebral vascular imaging. However, the strong attenuation and distortion of the photoacoustic wave caused by the thick porous skull greatly affect the imaging quality. In this study, we developed a convolutional neural network based on U-Net to extract the effective photoacoustic information hidden in the speckle patterns obtained from vascular network images datasets under porous media. Our simulation and experimental results show that the proposed neural network can learn the mapping relationship between the speckle pattern and the target, and extract the photoacoustic signals of the vessels submerged in noise to reconstruct high-quality images of the vessels with a sharp outline and a clean background. Compared with the traditional photoacoustic reconstruction methods, the proposed deep learning-based reconstruction algorithm has a better performance with a lower mean absolute error, higher structural similarity, and higher peak signal-to-noise ratio of reconstructed images. In conclusion, the proposed neural network can effectively extract valid information from highly blurred speckle patterns for the rapid reconstruction of target images, which offers promising applications in transcranial photoacoustic imaging.

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

Computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston operating at 500 kHz), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross-comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons.

Similarities and Differences in Bone Mineral Density between Multiple Sites in the Same Individual: An Elderly Cadaveric Study

Bone mineral density (BMD) is known to vary based on various factors, and the degree of variation is site-specific. However, few studies have investigated the relationship between bone density at trabecular bone-rich and cortical bone-rich sites in the same individual. In this study, we attempted to measure BMD at multiple sites using whole-body computed tomography images taken immediately after death and to clarify the similarities and differences between skeletal sites. Additionally, we aimed to examine the factors that influence changes in BMD, such as the loading environment, bone microstructure, and the ossification process of each skeletal region. A 3D model containing BMD data of the skull, clavicle, lumbar vertebrae, and femur (neck and diaphysis) was created using computed tomography images taken immediately after the death of 60 individuals (28 men and 32 women, average age: 84.0 years) who consented to participate in the study before death. Arbitrary measurement sites were defined, and bone density was measured at each site. We found that the BMDs of all regions were negatively correlated with age, but this correlation was weaker in the skull than in other regions. The negative correlation was especially pronounced in areas with more trabecular bones in men and in areas with more cortical bones in women. Furthermore, these findings suggest that factors, such as the loading environment, bone microstructure, and the ossification process of the skeletal sites, affect the BMD. Furthermore, our results suggest that it is important to assess the BMD of cortical bone in older women.

Acoustic properties across the human skull

Transcranial ultrasound is emerging as a noninvasive tool for targeted treatments of brain disorders. Transcranial ultrasound has been used for remotely mediated surgeries, transient opening of the blood-brain barrier, local drug delivery, and neuromodulation. However, all applications have been limited by the severe attenuation and phase distortion of ultrasound by the skull. Here, we characterized the dependence of the aberrations on specific anatomical segments of the skull. In particular, we measured ultrasound propagation properties throughout the perimeter of intact human skulls at 500 kHz. We found that the parietal bone provides substantially higher transmission (average pressure transmission 31 ± 7%) and smaller phase distortion (242 ± 44 degrees) than frontal (13 ± 2%, 425 ± 47 degrees) and occipital bone regions (16 ± 4%, 416 ± 35 degrees). In addition, we found that across skull regions, transmission strongly anti-correlated (R=-0.79) and phase distortion correlated (R=0.85) with skull thickness. This information guides the design, positioning, and skull correction functionality of next-generation devices for effective, safe, and reproducible transcranial focused ultrasound therapies.

Factors Associated with Energy Efficiency of Focused Ultrasound Through the Skull: A Study of 3D-Printed Skull Phantoms and Its Comparison with Clinical Experiences

While focused ultrasound (FUS) is non-invasive, the ultrasound energy is attenuated by the skull which results in differences in energy efficiency among patients. In this study, we investigated the effect of skull variables on the energy efficiency of FUS. The thickness and density of the skull and proportion of the trabecular bone were selected as factors that could affect ultrasound energy transmittance. Sixteen 3D-printed skull models were designed and fabricated to reflect the three factors. The energy of each phantom was measured using an ultrasonic sound field energy measurement system. The thickness and proportion of trabecular bone affected the attenuation of transmitted energy. There was no difference in the density of the trabecular bone. In clinical data, the trabecular bone ratio showed a significantly greater correlation with dose/delivered energy than that of thickness and the skull density ratio. Currently, for clinical non-thermal FUS, the data are not sufficient, but we believe that the results of this study will be helpful in selecting patients and appropriate parameters for FUS treatment.

Computational modeling investigation of pulsed high peak power microwaves and the potential for traumatic brain injury

When considering safety standards for human exposure to radiofrequency (RF) and microwave energy, the dominant concerns pertain to a thermal effect. However, in the case of high-power pulsed RF/microwave energy, a rapid thermal expansion can lead to stress waves within the body. In this study, a computational model is used to estimate the temperature profile in the human brain resulting from exposure to various RF/microwave incident field parameters. The temperatures are subsequently used to simulate the resulting mechanical response of the brain. Our simulations show that, for certain extremely high-power microwave exposures (permissible by current safety standards), very high stresses may occur within the brain that may have implications for neuropathological effects. Although the required power densities are orders of magnitude larger than most real-world exposure conditions, they can be achieved with devices meant to emit high-power electromagnetic pulses in military and research applications.

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.

Cortical and trabecular morphometric properties of the human calvarium

There is currently a gap in the literature that quantitatively describes the complex bone microarchitecture within the diploë (trabecular bone) and cortical layers of the human calvarium. The purpose of this study was to determine the morphometric properties of the diploë and cortical tables of the human calvarium in which key interacting factors of sex, location on the calvarium, and layers of the sandwich structure were considered. Micro-computed tomography (micro-CT) was utilized to capture images at 18 μm resolution of male (n = 26) and female (n = 24) embalmed calvarium specimens in the frontal and parietal regions (N = 50). All images were post-processed and analyzed using vendor bundled CT-Analyzer software to determine the morphometric properties of the diploë and cortical layers. A two-way mixed (repeated measures) analysis of variance (ANOVA) was used to determine diploë morphometric properties accounting for factors of sex and location. A three-way mixed ANOVA was performed to determine cortical morphometric properties accounting for factors of cortical layer (inner and outer table), sex, and location. The study revealed no two-way interaction effects between sex and location on the diploë morphometry except for fractal dimension. Trabecular thickness and separation in the diploë were significantly greater in the male specimens; however, females showed a greater number of trabeculae and fractal dimension on average. Parietal specimens revealed a greater porosity, trabecular separation, and deviation from an ideal plate structure, but a lesser number of trabeculae and connectivity compared to the frontal location. Additionally, the study observed a lower density and greater porosity in the inner cortical layer than the outer which may be due to clear distinctions between each layer's physiological environment. The study provides valuable insight into the quantitative morphometry of the calvarium in which finite element modelers of the skull can refer to when designing detailed heterogenous or subject-specific skull models to effectively predict injury. Furthermore, this study contributes towards the recent developments on physical surrogate models of the skull which require approximate measures of calvarium bone architecture in order to effectively fabricate a model and then accurately simulate a traumatic head impact event.

Mechanism and microstructure based concept to predict skull fracture using a hybrid-experimental-modeling-computational approach

Cellular and tissue-scale indent/impact thresholds for different mechanisms of functional impairments to the brain would be the preferred method to predict head injuries, but a comprehensive understanding of the dominant possible injury mechanisms under multiaxial stress-states and rates is currently not available. Until then, skull fracture could serve as an indication of head injury. Therefore the ability to predict the initiation of skull fracture through finite element simulation can serve as an in silico tool for assessing the effectiveness of various head protection scenarios. For this objective, skull fracture initiation was represented with a microstructurally-inspired, mechanism-based (MIMB) failure surface assuming three different dominant mechanisms of skull failure: each element, with deformation and failure properties selected based on its microstructure, was allowed to fail either in tension, compression, or shear, corresponding to clinical linear, depressed or penetrating shear-plug failure (fracture), respectively. Microstructure-inspired a priori values for the initiation threshold of each mechanism, obtained previously from uniaxial and simple-shear experiments, were iterated and optimized for the predicted load-displacement to represent that of the corresponding indentation experiment. Element-level failure enabled the visualization of the evolution of fracture by different mechanisms. The final crack pattern at the time of macroscopic (clinically-identifiable) injury was compared between the simulation and experiment obtained through 3D tomography. Even though the timing was slightly different, the simulated prediction represented remarkably well the experimental crack pattern before the appearance of the catastrophic unstable fast crack in the experiment, thus validating the implemented hybrid-experimental-modeling-computational (HEMC) concept as a tool to predict skull fracture initiation.

Topographical mapping of the mechanical characteristics of the human neurocranium considering the role of individual layers

The site-dependent load-deformation behavior of the human neurocranium and the load dissipation within the three-layered composite is not well understood. This study mechanically investigated 257 human frontal, temporal, parietal and occipital neurocranial bone samples at an age range of 2 to 94 years, using three-point bending tests. Samples were tested as full-thickness three-layered composites, as well as separated with both diploë attached and removed. Right temporal samples were the thinnest samples of all tested regions (median < 5 mm; p < 0.001) and withstood lowest failure loads (median < 762 N; p < 0.001). Outer tables were thicker and showed higher failure loads (median 2.4 mm; median 264 N) than inner tables (median 1.7 mm, p < 0.001; median 132 N, p = 0.003). The presence of diploë attached to outer and inner tables led to a significant reduction in bending strength (with diploë: median < 60 MPa; without diploë: median > 90 MPa, p < 0.001). Composites (r = 0.243, p = 0.011) and inner tables with attached diploë (r = 0.214, p = 0.032) revealed positive correlations between sample thickness and age. The three-layered composite is four times more load-resistant compared to the outer table and eight times more compared to the inner table.

Shear behavior of human skull bones

A shear-punch test (SPT) experimental method was developed to address the lack of shear deformation and failure response data for the human skull as a function of local bone microarchitecture. Improved understanding of skull deformation and fracture under varying stress-states helps implement mechanism-based, multi-axial material models for finite element analysis for optimizing protection strategies. Shear-punch coupons (N = 47 specimens) were extracted from right-parietal and frontal bones of three fresh-frozen-thawed human skulls. The specimens were kept as full through-thickness or segmented into the three skull constituent layers: the inner and outer cortical tables and the middle porous diploë. Micro-computed x-ray tomography (μCT) before and after SPT provided the bone volume fraction (BVF) as a function of depth for correlation to shear mechanisms in the punched volumes. Digital image correlation was used to track displacement of the punch above the upper die to minimize compliance error. Five full-thickness specimens were subjected to partial indentation loading to investigate the process of damage development as a function of BVF and depth. It was determined that BVF dominates the shear yield and ultimate strength of human skull bone, but the imposed uniaxial loading rate (0.001 and 0.1 s^-1) did not have as strong a contribution (p = 0.181-0.806 > 0.05) for the shear yield and ultimate strength of the skull bone layer specimens. Shear yield and ultimate strength data were highly correlated to power law relationships of BVF (R² = 0.917-0.949). Full-thickness and partial loaded SPT experiments indicate the diploë primarily dictates the shear strength of the intact structure.

Implementation and validation of finite element model of skull deformation and failure response during uniaxial compression

Numerical studies aimed at evaluating head injury due to externally applied loading can be made more biofidelic by incorporating nonlinear mechanism-based and microstructurally-inspired material models representing the mechanical response and fracture (failure or injury) of the human skull bone. Thus, incorporation of these mechanism-based models would increase the ability of simulations of mechanical impact to identify more realistic fracture-based injuries at clinical relevancy, such as linear (tensile), depressed (compressive), or penetration (shear). One of the challenges for accurate modeling of the mechanical response of the human skull is the intricate location dependent heterogeneous mesostructural arrangement of bone within the structure of the skull. Recently, a power-law relationship between the localized bone volume fraction (BVF) and modulus (E) within the human skull was developed based on quasi-static compression experiments. However, the parameters of the power-law were optimized and obtained using approximations which were not experimentally or computationally validated for the actual heterogeneous 3D bone structure. Here, a hybrid experimental-modeling-computational (HEMC) based concept was used to develop a microstructurally compatible detailed meso-scale finite element (FE) model of the heterogeneous microstructure of one of the human skull bone coupons previously used to derive the E-BVF relationship. Finite elements were mapped to the corresponding regions from microcomputed tomography images, and the BVF of each element was identified. Then, element-specific moduli were calculated from the E-BVF power relationship. The goal of the simulations was twofold: to assess the assumptions used to derive the E-BVF relationship from the linear regime of the experimental response, and also to model the subsequent deviation from linearity. Using the E-BVF relationship, the 3D simulation was able to match the experimentally measured global modulus to within 3%. After validating the E-BVF power law using the initial linear response, to develop and validate failure models, the following steps were completed. The subsequent deviation of the mechanical response from its initial linearity was assumed to be due to failure of elements either by compression or tension. Elemental microstructure-specific compressive and tensile failure thresholds (σ_f) for each element were modeled by BVF (f_BV) power functional relationships of the form: [Formula: see text] MPa. The initial leading coefficients (σ_f,0) for compression and tension were derived from prior reported experimental work. Through incorporating element-level failure and then iterating the leading coefficients, the simulation was able to represent the nonlinearity of the stress-strain curve and its catastrophic failure in the experiment. Evolution of the measured non-uniform full-strain-fields on two surfaces of the coupon, showing the localized regions of failure, was compared between experiment and simulation, and was approximately similar, thus validating the developed HEMC procedure and failure models. The simulation methodology developed here allowed for identification of failure location within the skull coupon specimen, thereby providing a tool to predict the localized failure (fracture or injury) initiation within the human skull in FE simulations at larger length scales.

A computational investigation of strain concentration in the brain in response to a rapid temperature rise

Following the mysterious health attacks on U.S. diplomats in Cuba in 2016, the cause of concussion-like symptoms concurrent with strange noises heard by the diplomats remains undetermined. A wide range of possible causes of the sensations have been proposed: pulsed microwave exposure, infrasound acoustic devices, pesticides/neurotoxins, and even mass hysteria (psychogenic illness). Here, we numerically examine the pulsed microwave exposure hypothesis and the simulated mechanical response of brain tissue. A computational model is used to examine the influence of various spatially varying temperature gradients and pulse durations on the mechanical response of brain tissue. We show that a stress-focusing effect due to a rapid temperature increase may result in brain tissue strains larger than the initially applied thermal strains.

Spherical depth-sensing nanoindentation of human anterior skull base bones: Establishment of a test protocol

The mechanical properties of anterior skull base (ASB) bones are not well understood due to their complex geometry and deep location. However, it is of particular interest for skull base surgeons to appraise the force range they can apply during procedures and know what kind of haptic feedback a simulation device should produce in order to be realistic for trainees. The aim of this study was to establish a measurement protocol to set the level of hydration state, temperature and curve analysis method for spherical depth sensing nanoindentation of ASB bones. A definitive screening design method was used to test the different possible combinations of these factors. Two samples of ASB bones from the heads of two human body donors (two specimens) were selected according to their microstructure as assessed by micro-CT (microtomography): low-porosity (16.87%, sphenoid bone) and high-porosity (79.85%, ethmoid bone). Depth measurement series of 36 nanoindentations (n = 288) were performed on specimen 1 according to the L8 Taguchi orthogonal array to study the effect of temperature (two levels: 20 or 37 °C), hydration state (dry or immerged in physiological saline sodium chloride), and loading curve analysis according to the Hertzian contact theory (fitting at the start or at the end). The mean values of reduced Young's (E*) modulus varied significantly depending on the hydration status and bone microstructure. In order to obtain the physiological properties of ASB bones, we thus propose performing immersion tests. To simplify the experimentation protocol, future experiments must include a room temperature level and a fit of the curve at the end of the load. A validation series was performed on the second specimen to assess the set of parameters. The E* in dry bone gave mean values of 994.68 MPa, versus 409.79 MPa in immerged bones (p < 0.00001). This is the first time a study has been carried out on ASB bones, defining the experimental parameters related to physiological conditions.

Implicit and explicit finite element models predict the mechanical response of calcium phosphate-titanium cranial implants

The structural integrity of cranial implants is of great clinical importance, as they aim to provide cerebral protection after neurosurgery or trauma. With the increased use of patient-specific implants, the mechanical response of each implant cannot be characterized experimentally in a practical way. However, computational models provide an excellent possibility for efficiently predicting the mechanical response of patient-specific implants. This study developed finite element models (FEMs) of titanium-reinforced calcium phosphate (CaP-Ti) implants. The models were validated with previously obtained experimental data for two different CaP-Ti implant designs (D1 and D2), in which generically shaped implant specimens were loaded in compression at either quasi-static (1 mm/min) or impact (5 kg, 1.52 m/s) loading rates. The FEMs showed agreement with experimental data in the force-displacement response for both implant designs. The implicit FEMs predicted the peak load with an underestimation for D1 (9%) and an overestimation for D2 (11%). Furthermore, the shape of the force-displacement curves were well predicted. In the explicit FEMs, the first part of the force-displacement response showed 5% difference for D1 and 2% difference for D2, with respect to the experimentally derived peak loads. The explicit FEMs efficiently predicted the maximum displacements with 1% and 4% difference for D1 and D2, respectively. Compared to the CaP-Ti implant, an average parietal cranial bone FEM showed a stiffer response, greater energy absorption and less deformation under the same impact conditions. The framework developed for modelling the CaP-Ti implants has a potential for modelling CaP materials in other composite implants in future studies since it only used literature based input and matched boundary conditions. Furthermore, the developed FEMs make an important contribution to future evaluations of patient-specific CaP-Ti cranial implant designs in various loading scenarios.

An Investigation on the Correlation between the Mechanical Properties of Human Skull Bone, Its Geometry, Microarchitectural Properties, and Water Content

With increasingly detailed imaging and mechanical analysis, modalities need arises to update methodology and assessment criteria for skull bone analysis to understand how bone microarchitecture and the presence of attached tissues may affect the response to mechanical load. The main aim was to analyze the effect of macroscopic and microstructural features, as well as periosteal attachment, on the mechanical properties of human skull bone. Fifty-six skull specimens from ethanol-phenoxyethanol-embalmed cadavers were prepared from two human cadavers. Assuming symmetry of the skull, all samples from one-half each were stripped of periosteum and dura mater, while the soft tissues were kept intact on the remaining samples on the contralateral side. The specimens were analyzed using microcomputed tomography to assess trabecular connectivity density, total surface area, and volume ratio. The specimens were loaded under three-point bend tests until fracture with optical co-registration. The bone fragments were then lyophilized to measure their water content. With increasingly detailed imaging and mechanical analysis modalities, there is a need to update methodology and assessment criteria for skull bone analysis to understand how the bone microarchitecture and the presence of attached tissues may affect the response to mechanical load. The mechanical properties were negatively correlated to bone thickness and water content. Conversely, most microarchitectural features did not influence either mechanical parameter. The correlation between mechanical response data and morphologic properties remains similar between the results of embalmed tissues presented here and fresh osseous tissue from literature data. The findings presented here add to the existing methodology to assess human skull for research purposes. The interaction between most microarchitectural features in ethanol-phenoxyethanol-embalmed embalmed skull samples and bending stress appear to be minute.