Establishing finite element model credibility of a pedicle screw system under compression-bending: An end-to-end example of the ASME V&V 40 standard.

Computational modeling and simulation (CM&S) is a key tool in medical device design, development, and regulatory approval. For example, finite element analysis (FEA) is widely used to understand the mechanical integrity and durability of orthopaedic implants. The ASME V&V 40 standard and supporting FDA guidance provide a framework for establishing model credibility, enabling deeper reliance on CM&S throughout the total product lifecycle. Examples of how to apply the principles outlined in the ASME V&V 40 standard are important to facilitating greater adoption by the medical device community, but few published examples are available that demonstrate best practices. Therefore, this paper outlines an end-to-end (E2E) example of the ASME V&V 40 standard applied to an orthopaedic implant. The objective of this study was to illustrate how to establish the credibility of a computational model intended for use as part of regulatory evaluation. In particular, this study focused on whether a design change to a spinal pedicle screw construct (specifically, the addition of a cannulation to an existing non-cannulated pedicle screw) would compromise the rod-screw construct mechanical performance. This question of interest (?OI) was addressed by establishing model credibility requirements according to the ASME V&V 40 standard. Experimental testing to support model validation was performed using spinal rods and non-cannulated pedicle screw constructs made with medical grade titanium (Ti-6Al-4V ELI). FEA replicating the experimental tests was performed by three independent modelers and validated through comparisons of common mechanical properties such as stiffness and yield force. The validated model was then used to simulate F1717 compression-bending testing on the new cannulated pedicle screw design to answer the ?OI, without performing any additional experimental testing. This E2E example provides a realistic scenario for the application of the ASME V&V 40 standard to orthopedic medical device applications.

Genome-wide identification and integrated analysis of the FAR1/FHY3 gene family and genes expression analysis under methyl jasmonate treatment in Panax ginseng C. A. Mey.

Ginseng (Panax ginseng C. A. Mey.) is an important and valuable medicinal plant species used in traditional Chinese medicine, and its metabolite ginsenoside is the primary active ingredient. The FAR1/FHY3 gene family members play critical roles in plant growth and development as well as participate in a variety of physiological processes, including plant development and signaling of hormones. Studies have indicated that methyl jasmonate treatment of ginseng adventitious roots resulted in a significant increase in the content of protopanaxadiol ginsenosides. Therefore, it is highly significant to screen the FAR1/FHY3 gene family members in ginseng and preliminarily investigate their expression patterns in response to methyl jasmonic acid signaling. In this study, we screened and identified the FAR1/FHY3 family genes in the ginseng transcriptome databases. And then, we analyzed their gene structure and phylogeny, chromosomal localization and expression patterns, and promoter cis-acting elements, and made GO functional annotations on the members of this family. After that, we treated the ginseng adventitious roots with 200 mM methyl jasmonate and investigated the trend of the expression of four genes containing the largest number of methyl jasmonate cis-acting elements at different treatment times. All four genes were able to respond to methyl jasmonate, the most significant change was in the PgFAR40 gene. This study provides data support for subsequent studies of this family member in ginseng and provides experimental reference for subsequent validation of the function of this family member under methyl jasmonic acid signaling.

Space-Confined Growth for Thickness-Controlled Cs3Bi2I9 Perovskite Single Crystal Wafers for X-Ray Detectors.

The Cs3Bi2I9 single crystal, as an all-inorganic non-lead perovskite, offers advantages such as stability and environmental friendliness. Its superior photoelectric properties, attributed to the absence of grain boundary influence, make it an outstanding X-ray detection material compared to polycrystals. In addition to material properties, X-ray detector performance is affected by the thickness of the absorption layer. Addressing this, a space-confined method is proposed. The temperature field is determined through finite element simulation, effectively guiding the design of the space-confined method. Through this innovative method, a series of thickness-controlled perovskite single crystal wafers (PSCWs) are successfully prepared. Corresponding X-ray detectors are then prepared, and the impact of single crystal thickness on device performance is investigated. With an increase in single crystal thickness, a rise followed by a decline in device sensitivity is observed, reaching an optimal value at 0.7 mm thickness at 40V mm-1 with a device performance of 11313.6µC Gy-1 cm-2. This space-confined method enables the direct growth of high-quality perovskite single crystals with specified thickness, eliminating the need for slicing or etching.

Functional adaptation of the infant craniofacial system to mechanical loadings arising from masticatory forces.

The morphology and biomechanics of infant crania undergo significant changes between the pre- and post-weaning phases due to increasing loading of the masticatory system. The aims of this study were to characterize the changes in muscle forces, bite forces and the pattern of mechanical strain and stress arising from the aforementioned forces across crania in the first 48 months of life using imaging and finite element methods. A total of 51 head computed tomography scans of normal individuals were collected and analysed from a larger database of 217 individuals. The estimated mean muscle forces of temporalis, masseter and medial pterygoid increase from 30.9 to 87.0 N, 25.6 to 69.6 N and 23.1 to 58.9 N, respectively (0-48 months). Maximum bite force increases from 90.5 to 184.2 N (3-48 months). There is a change in the pattern of strain and stress from the calvaria to the face during postnatal development. Overall, this study highlights the changes in the mechanics of the craniofacial system during normal development. It further raises questions as to how and what level of changes in the mechanical forces during the development can alter the morphology of the craniofacial system.

Association of dorsal malunion in distal radius fractures with wrist osteoarthritis: Alterations of bone density and stress-distribution patterns in relation to deformation angles.

OBJECTIVE: Distal radius fractures (DRFs) with dorsal malunion increase the risk of osteoarthritis (OA), although the cause of post-DRF OA is yet to be elucidated. To clarify the abnormal effects of a post-DRF dorsal radius deformity, we evaluated the bone density (BD) and stress-distribution patterns of the articular surface in dorsally malunited DRFs. DESIGN: In 36 cases of dorsally malunited DRFs following extra-articular fractures, we generated three-dimensional computerized models of the malunited distal radius from computed tomography data and extracted the subchondral bones of the radiocarpal joint (RCJ) and distal radioulnar joint (DRUJ). Both BD and stress distribution in the subchondral bones were quantitatively evaluated by comparing the affected and normal sides. Correlations of alterations in high-BD distribution and deformation angles were analyzed. RESULTS: The center of high-BD distribution from the center of the RCJ in the volar(-)-dorsal(+) direction was dorsal (0.56 ± 0.72 mm) on the affected side compared with the normal side (-0.15 ± 0.63 mm) [95% CI: 0.43, 1.00, P < 0.0001]. The maximum stress distribution was also dorsal on the affected side (2.34 ± 3.52 mm) compared with the normal side (-2.49 ± 1.62 mm) [95% CI: 0.89, 1.79, P < 0.0001]. The alterations in BD and stress distribution correlated with the dorsiflexion and radial deviation angles. In the DRUJ, there was no significant difference in BD between the affected and normal sides. CONCLUSIONS: In dorsally malunited DRFs, the alignment change of the RCJ resulted in high BD-concentration areas and stress distribution on the dorsal side of the radius, which may constitute a precursor for OA.

A new hip fracture risk index derived from FEA-computed proximal femur fracture loads and energies-to-failure.

Hip fracture risk assessment is an important but challenging task. Quantitative CT-based patient-specific finite element (FE) analysis (FEA) incorporates bone geometry and bone density in the proximal femur. We developed a global FEA-computed fracture risk index to increase the prediction accuracy of hip fracture incidence. PURPOSE: Quantitative CT-based patient-specific finite element (FE) analysis (FEA) incorporates bone geometry and bone density in the proximal femur to compute the force (fracture load) and energy necessary to break the proximal femur in a particular loading condition. The fracture loads and energies-to-failure are individually associated with incident hip fracture, and provide different structural information about the proximal femur. METHODS: We used principal component analysis (PCA) to develop a global FEA-computed fracture risk index that incorporates the FEA-computed yield and ultimate failure loads and energies-to-failure in four loading conditions of 110 hip fracture subjects and 235 age- and sex-matched control subjects from the AGES-Reykjavik study. Using a logistic regression model, we compared the prediction performance for hip fracture based on the stratified resampling. RESULTS: We referred the first principal component (PC1) of the FE parameters as the global FEA-computed fracture risk index, which was the significant predictor of hip fracture (p-value < 0.001). The area under the receiver operating characteristic curve (AUC) using PC1 (0.776) was higher than that using all FE parameters combined (0.737) in the males (p-value < 0.001). CONCLUSIONS: The global FEA-computed fracture risk index increased hip fracture risk prediction accuracy in males.

CT image-based biomarkers for opportunistic screening of osteoporotic fractures: a systematic review and meta-analysis.

The use of opportunistic computed tomography (CT) image-based biomarkers may be a low-cost strategy for screening older individuals at high risk for osteoporotic fractures and populations that are not sufficiently targeted. This review aimed to assess the discriminative ability of image-based biomarkers derived from existing clinical routine CT scans for hip, vertebral, and major osteoporotic fracture prediction. A systematic search in PubMed MEDLINE, Embase, Cochrane, and Web of Science was conducted from the earliest indexing date until July 2023. The evaluation of study quality was carried out using a modified Quality Assessment Tool for Diagnostic Accuracy Studies (QUADAS-2) checklist. The primary outcome of interest was the area under the curve (AUC) and its corresponding 95% confidence intervals (CIs) obtained for four main categories of biomarkers: areal bone mineral density (BMD), image attenuation, volumetric BMD, and finite element (FE)-derived biomarkers. The meta-analyses were performed using random effects models. Sixty-one studies were included in this review, among which 35 were synthesized in a meta-analysis and the remaining articles were qualitatively synthesized. In comparison to the pooled AUC of areal BMD (0.73 [95% CI 0.71-0.75]), the pooled AUC values for predicting osteoporotic fractures for FE-derived parameters (0.77 [95% CI 0.72-0.81]; p < 0.01) and volumetric BMD (0.76 [95% CI 0.71-0.81]; p < 0.01) were significantly higher, but there was no significant difference with the pooled AUC for image attenuation (0.73 [95% CI 0.66-0.79]; p = 0.93). Compared to areal BMD, volumetric BMD and FE-derived parameters may provide a significant improvement in the discrimination of osteoporotic fractures using opportunistic CT assessments.

A new biomechanical model of the mammal jaw based on load path analysis.

The primary function of the tetrapod jaw is to transmit jaw muscle forces to bite points. The routes of force transfer in the jaw have never been studied, but can be quantified using load paths--the shortest, stiffest routes from regions of force application to support constraints. Here we use load path analysis to map force transfer from muscle attachments to bite point and jaw joint, and to evaluate how different configurations of trabecular and cortical bone affect load paths. We created three models of the mandible of the Virginia opossum, Didelphis virginiana, each with a cortical bone shell, but with different material properties for the internal spaces: a cortical-trabecular model, in which the interior space is modeled with bulk properties of trabecular bone; a cortical-hollow model, in which trabeculae and mandibular canal are modeled as hollow; and a solid-cortical model, in which the interior is modeled as cortical bone. The models were compared with published in vivo bite force and bone strain data, and the load paths calculated for each model. The cortical-trabecular model, which most closely approximates the actual morphology, was best validated by in vivo data. In all three models the load path was confined to cortical bone, although its route within the cortex varied depending on the material properties of the inner model. Our analysis shows that most of the force is transferred through the cortical, rather than trabecular bone, and highlights the potential of load path analysis for understanding form-function relationships in the skeleton.

Computational model of the cancer necrotic core formation in a tumor-on-a-chip device.

The mechanisms underlying the formation of necrotic regions within avascular tumors are complex and poorly understood. In this paper, we investigate the formation of a necrotic core in a 3D tumor cell culture within a microfluidic device, considering oxygen, nutrients, and the microenvironment acidification by means of a computational-mathematical model. Our objective is to simulate cell processes, including proliferation and death inside a microfluidic device, according to the microenvironmental conditions. We employed approximation utilizing finite element models taking into account glucose, oxygen, and hydrogen ions diffusion, consumption and production, as well as cell proliferation, migration and death, addressing how tumor cells evolve under different conditions. The resulting mathematical model was examined under different scenarios, being capable of reproducing cell death and proliferation under different cell concentrations, and the formation of a necrotic core, in good agreement with experimental data reported in the literature. This approach not only advances our fundamental understanding of necrotic core formation but also provides a robust computational platform to study personalized therapeutic strategies, offering an important tool in cancer research and treatment design.

Design of the distribution of iron oxide (Fe3O4) nano-particle drug in realistic cholangiocarcinoma model and the simulation of temperature increase during magnetic induction hyperthermia.

The prognosis for Cholangiocarcinoma (CCA) is unfavorable, necessitating the development of new therapeutic approach such as magnetic hyperthermia therapy (MHT) which is induced by magnetic nano-particle (MNPs) drug to bridge the treatment gap. Given the deep location of CCA within the abdominal cavity and proximity to vital organs, accurately predict the individualized treatment effects and safety brought by the distribution of MNPs in tumor will be crucial for the advancement of MHT in CCA. The Mimics software was used in this study to conduct three-dimensional reconstruction of abdominal computed tomography (CT) and magnetic reso-nance imaging images from clinical patients, resulting in the generation of a realistic digital geometric model representing the human biliary tract and its adjacent structures. Subsequently, The COMSOL Multiphysics software was utilized for modeling CCA and calculating the heat transfer law resulting from the multi-regional distribution of MNPs in CCA. The temperature within the central region of irregular CCA measured approximately 46°C, and most areas within the tumor displayed temperatures surpassing 41°C. The temperature of the inner edge of CCA is only 39 ∼ 41℃, however, it can be ameliorated by adjusting the local drug concentration through simulation system. For CCA with diverse morphologies and anatomical locations, the multi-regional distribution patterns of intratumoral MNPs and a slight overlap of drug distribution areas synergistically enhance intratumoral temperature while ensuring treatment safety. The present study highlights the practicality and imperative of incorporating personalized intratumoral MNPs distribution strategy into clinical practice for MHT, which can be achieved through the development of an integrated simulation system which incorporates medical image data and numerical calculations.

All that glitters is not gold: X-ray fluorescence analysis of a fixed dental prosthesis from Colecção de Esqueletos Identificados Século XXI, Portugal (CEI/XXI).

Access to better health care anticipates that more medical devices can be found alongside skeletal remains. Those employed in oral rehabilitation, with available brands or batch/series, can prove useful in the identification process. A previous study in the Colecção de Esqueletos Identificados Século XXI described macroscopically the dental prostheses. An unusual case of a dental device with chromatic alterations demonstrated to require a more detailed analysis. The individual, a 53-year-old male, exhibited, at both arches, a fixed tooth-supported rehabilitation, with gold colouring classified initially as a gold-palladium alloy. Simultaneously, a green pigmentation deposit was observable in bone and prosthesis. This investigation aimed to verify the elemental composition of the dental prosthesis alloy. Elemental analysis was performed by X-ray fluorescence in two regions (labial surface of the prosthetic crown and the root surface of the lower right lateral incisor). Both the spectra and the qualitative results found higher levels of copper and aluminium, followed by nickel, iron, zinc, and manganese. No gold or palladium was detected. The most probable assumption is that a copper-aluminium alloy was used, as its elemental concentration corresponds to those measured in similar devices. Dental prostheses of copper-aluminium alloys have been made popular since the 1980s, particularly in the USA, Japan, and Eastern Europe. Apart from the biographical information, it was also known that the individual's place of birth was an Eastern European country, which highlighted the usefulness of this type of information when dealing with missing people cases.

Subject-specific finite element head models for skull fracture evaluation-a new tool in forensic pathology.

Post-mortem computed tomography (PMCT) enables the creation of subject-specific 3D head models suitable for quantitative analysis such as finite element analysis (FEA). FEA of proposed traumatic events is an objective and repeatable numerical method for assessing whether an event could cause a skull fracture such as seen at autopsy. FEA of blunt force skull fracture in adults with subject-specific 3D models in forensic pathology remains uninvestigated. This study aimed to assess the feasibility of FEA for skull fracture analysis in routine forensic pathology. Five cases with blunt force skull fracture and sufficient information on the kinematics of the traumatic event to enable numerical reconstruction were chosen. Subject-specific finite element (FE) head models were constructed by mesh morphing based on PMCT 3D models and A Detailed and Personalizable Head Model with Axons for Injury Prediction (ADAPT) FE model. Morphing was successful in maintaining subject-specific 3D geometry and quality of the FE mesh in all cases. In three cases, the simulated fracture patterns were comparable in location and pattern to the fractures seen at autopsy/PMCT. In one case, the simulated fracture was in the parietal bone whereas the fracture seen at autopsy/PMCT was in the occipital bone. In another case, the simulated fracture was a spider-web fracture in the frontal bone, whereas a much smaller fracture was seen at autopsy/PMCT; however, the fracture in the early time steps of the simulation was comparable to autopsy/PMCT. FEA might be feasible in forensic pathology in cases with a single blunt force impact and well-described event circumstances.

Analysis of the characteristics of silver nanowires (AgNW) random network for transparent heater applications.

Transparent heaters (THs) find widespread application in various indoor and outdoor settings, such as LCD panels and motorcycle helmet visors. Among the materials used for efficient TH performance, the AgNW network stands out due to its high conductivity, substantial transmittance, and minimal solution requirement. Extensive research has been directed towards enhancing AgNW characteristics, focusing on smaller diameters and longer wires. In TH applications, the primary considerations include a rapid response and elevated temperature. Consequently, this research delves into investigating the impact of parameters like diameter, length, and density on random AgNW networks under varying applied voltages. The finite element method is employed for analyzing temperature changes in response to voltage application, particularly in scenarios involving small-scale setups with high-density and high-percolation AgNW networks. The results reveal a significant increase in the thermal transition rate, ranging from 28% to 36%, with varying densities in the random network. Within the same density, the AgNW network with larger diameters and lengths demonstrates the highest temperatures, aligning with previous calculations. Furthermore, a trade-off exists between optical properties in smaller diameters and electrical properties in larger diameters within a relatively narrow temperature range.

Ultrafast synthesis and luminescence properties of rare earth orthoniobates RENbO4(RE = La, Eu, Gd, Yb, Lu).

Rare earth orthoniobates (RENbO4) are one kind of important functional materials due to its applications in solid-state phosphors, thermal barrier coatings, and microwave dielectric ceramics. The synthesis of rare earth niobates often needs high reaction temperatures (1300 °C-1700 °C) and long processing times (from hours to tens of hours) in solid-state reactions, which can increase the study time of the relationship between structure and properties. In this work, we used ultrafast high-temperature sintering method to synthesize RENbO4(RE = La, Eu, Gd, Yb, Lu), and found specific structure and properties in these materials obtained with specific synthetic techniques. Based on the electronegativity scale, the charge transfer energy of lanthanide ions in the YNbO4crystal was calculated. The rapid synthesis of RENbO4in a vacuum atmosphere generated more oxygen vacancies, and the structures of [REO8] and [NbO6] were distorted. The shortening of the fluorescence lifetime of LaNbO4and EuNbO4was related to the formation of self-trapped excitons facilitated by lattice distortion. The emission peak of LuNbO4at about 530 nm is attributed to the oxygen vacancy in the niobate group. The reported synthetic methods can provide a fast materials screening route for high melting point inorganic materials.

Transparent and Soft Crack-Resistant Bouligand Elastomers Inspired by Fish Scales.

Nature with its abundant source offers numerous inspirations for structural and engineering designs. The oriented membranes stacked with bouligand structures in the fish scales show an outstanding combination of high strength and crack resistance. Although the applications of hard biomimetic composites are reported, the structures are rarely utilized in soft materials. Inspired by the scales of various fishes, electrospun membranes are used and stacked to fabricate bouligand elastomers, including orthogonal-plywood, single-bouligand, and double-bouligand structures. The effects of different structures on the properties of elastomers are systematically investigated and possible mechanism is explained using finite element analysis (FEA). The stiffness and fatigue characteristics of these biomimetic elastomers with the above structures are improved compared with the original membranes, especially the elastomers with a single-bouligand structure, which can undergo 5 000 cycles at a maximum strain of 35% without complete failure. The crack only propagates to half of the width of the elastomer with remaining strength of 50% of its original strength. Moreover, the mechanical performance can be adjusted by regulating the proportion of the components. The excellent crack-resistant properties and transparency promote its various potential applications.

The perpendicular gyroscope: modal analysis of plate, beam and gyroscope multistructures.

This paper presents a study of the perpendicular gyroscope, which is formed of two orthogonal beams, a flexural plate and a gyroscope. Two sets of chiral-torsional boundary conditions are derived to analytically model the dynamic effects of the gyroscope while taking into account the broken symmetries of the system. The perpendicular junction causes the coupling of the compressional, flexural and torsional displacements in the system. This complex behaviour is accounted for with a comprehensive set of kinematic and dynamic junction conditions. Modal analysis demonstrates the fully coupled system and reveals how the spinning gyroscope induces dynamic chiral Chladni patterns in the plate.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

A forecasting model for suitable dental implantation in canine mandibular premolar region based on finite element analysis.

In recent years, dental implants have become a trend in the treatment of human patients with missing teeth, which may also be an acceptable method for companion animal dentistry. However, there is a gap challenge in determining appropriate implant sizes for different dog breeds and human. In this study, we utilized skull computed tomography data to create three-dimensional models of the mandibles of dogs in different sizes. Subsequently, implants of various sizes were designed and subjected to biomechanical finite element analysis to determine the optimal implant size. Regression models were developed, exploring the relationship between the average weight of dogs and the size of premolar implants. Our results illustrated that the regression equations for mean body weight (x, kg) and second premolar (PM2), third premolar (PM3), and fourth premolar (PM4) implant length (y, mm) in dogs were: y = 0.2785x + 7.8209, y = 0.2544x + 8.9285, and y = 0.2668x + 10.652, respectively; the premolar implant diameter (mm) y = 0.0454x + 3.3506, which may provide a reference for determine suitable clinical implant sizes for dogs.

Stress analysis of horizontal mid-root fracture managed with different intraradicular fixation protocols: A 3D-finite element study.

The current study evaluated the stress distribution in a maxillary central incisor with mid-root fracture after splinting with different intra-radicular posts using 3D-finite element analysis (FEA). Five 3D-FEA models were constructed. Model 1 was an intact tooth with no fracture, Model 2: A tooth with a horizontal mid-root fracture, with no treatment. Model 3: Same as model 2, and intraradicular splinting using fiber post. Model 4: Same as model 2 and intra-radicular splinting using Protaper Gold file F3. Model 5: Same as model 2, and with intraradicular splinting with Ribbond. The FEA of all models was done to obtain the maximum Von-Mises stress in the root canal space, the dentin, the periodontal ligament, and the bone. The highest Von Mises stresses for the root canal space and the dentin were found in Model 3, followed by models 4, 5, and 2, and least in Model 1. The Von Mises stress of the periodontal ligament was the least in model 1. The Von Mises stress of bone was higher in all experimental models than in the baseline model. The results suggest that in cases where intra-radicular splinting is indicated, fiber posts and Ribbond are better alternatives to endodontic files due to the lower stresses exerted.

Integration of Febio as an Instructional Tool in the Undergraduate Biomechanics Curriculum.

Computer simulations play an important role in a range of biomedical engineering applications. Thus, it is important that biomedical engineering students engage with modeling in their undergraduate education and establish an understanding of its practice. In addition, computational tools enhance active learning and complement standard pedagogical approaches to promote student understanding of course content. Herein, we describe the development and implementation of learning modules for computational modeling and simulation (CM&S) within an undergraduate biomechanics course. We developed four CM&S learning modules that targeted predefined course goals and learning outcomes within the febio studio software. For each module, students were guided through CM&S tutorials and tasked to construct and analyze more advanced models to assess learning and competency and evaluate module effectiveness. Results showed that students demonstrated an increased interest in CM&S through module progression and that modules promoted the understanding of course content. In addition, students exhibited increased understanding and competency in finite element model development and simulation software use. Lastly, it was evident that students recognized the importance of coupling theory, experiments, and modeling and understood the importance of CM&S in biomedical engineering and its broad application. Our findings suggest that integrating well-designed CM&S modules into undergraduate biomedical engineering education holds much promise in supporting student learning experiences and introducing students to modern engineering tools relevant to professional development.

Sensitivity of Phonation Onset Pressure to Vocal Fold Stiffness Distribution.

Phonation onset is characterized by the unstable growth of vocal fold (VF) vibrations that ultimately results in self-sustained oscillation and the production of modal voice. Motivated by histological studies, much research has focused on the role of the layered structure of the vocal folds in influencing phonation onset, wherein the outer "cover" layer is relatively soft and the inner "body" layer is relatively stiff. Recent research, however, suggests that the body-cover (BC) structure over-simplifies actual stiffness distributions by neglecting important spatial variations, such as inferior-superior (IS) and anterior-posterior gradients and smooth transitions in stiffness from one histological layer to another. Herein, we explore sensitivity of phonation onset to stiffness gradients and smoothness. By assuming no a priori stiffness distribution and considering a second-order Taylor series sensitivity analysis of phonation onset pressure with respect to stiffness, we find two general smooth stiffness distributions most strongly influence onset pressure: a smooth stiffness containing aspects of BC differences and IS gradients in the cover, which plays a role in minimizing onset pressure, and uniform increases in stiffness, which raise onset pressure and frequency. While the smooth stiffness change contains aspects qualitatively similar to layered BC distributions used in computational studies, smooth transitions in stiffness result in higher sensitivity of onset pressure than discrete layering. These two general stiffness distributions also provide a simple, low-dimensional, interpretation of how complex variations in VF stiffness affect onset pressure, enabling refined exploration of the effects of stiffness distributions on phonation onset.