Numerical investigation of knee prosthesis stresses in daily activities: Insight into knee rehabilitation and Creation of a new optimal model.

Total knee arthroplasty (TKA) is a cornerstone in addressing knee joint disorders, significantly enhancing patients' quality of life. However, despite technological advancements, a comprehensive understanding of the dynamic stresses experienced by knee prostheses during daily activities, particularly under rehabilitation interventions, remains elusive. This study aims to bridge this gap by employing numerical simulations and finite element analysis to elucidate these dynamic stresses and their interaction with rehabilitation protocols. A real-life knee replacement prosthesis model was meticulously constructed through coordinate measuring and 3D scanning, facilitating detailed finite element analysis in ANSYS Workbench version 17.1. Two distinct boundary conditions and loading scenarios were applied, with comparisons made between linear and nonlinear material assumptions. The simulation results using these different boundary condition methods revealed minimal differences. Specifically, at a knee angle of 0°, the relative stress error rate between the two boundary condition types was approximately 1 % (1.11 MPa and 1.099 MPa, respectively). At 15° and 90°, the error rates were 1.9 % and 0.56 %, respectively (10.275 MPa and 10.078 MPa at 15°; 10.275 MPa and 10.078 MPa at 90°). Given these minimal differences, the first type of boundary condition was adopted for the subsequent scenarios to enhance convergence efficiency in the analysis. Moreover, comparative analyses between linear and nonlinear material behaviors demonstrated acceptable agreement, offering insights into potential efficiency gains in simulation methodologies. Building on this foundation, an optimized tibial model was proposed, incorporating geometric alterations to the tray. Quantitative assessments revealed significant reductions, with von Mises stress decreasing by 23.35 % and equivalent strain by 17 % at a knee angle of 140°. Further evaluations at varying angles, including 60°, consistently showed positive influences on stress and strain. These quantitative findings not only contribute valuable insights into the mechanical behavior of knee prostheses but also provide tangible evidence for the efficacy of linear material behavior assumptions. The proposed optimized model exhibits promising potential for enhancing the design and performance of knee prostheses, particularly under critical loading conditions. In conclusion, these results underscore the importance of a nuanced understanding of knee prosthesis behavior during rehabilitation, offering a quantitative foundation for refining existing designs and informing the development of next-generation prostheses.

CutFEM-based MEG forward modeling improves source separability and sensitivity to quasi-radial sources: A somatosensory group study.

Source analysis of magnetoencephalography (MEG) data requires the computation of the magnetic fields induced by current sources in the brain. This so-called MEG forward problem includes an accurate estimation of the volume conduction effects in the human head. Here, we introduce the Cut finite element method (CutFEM) for the MEG forward problem. CutFEM's meshing process imposes fewer restrictions on tissue anatomy than tetrahedral meshes while being able to mesh curved geometries contrary to hexahedral meshing. To evaluate the new approach, we compare CutFEM with a boundary element method (BEM) that distinguishes three tissue compartments and a 6-compartment hexahedral FEM in an n = 19 group study of somatosensory evoked fields (SEF). The neural generators of the 20 ms post-stimulus SEF components (M20) are reconstructed using both an unregularized and a regularized inversion approach. Changing the forward model resulted in reconstruction differences of about 1 centimeter in location and considerable differences in orientation. The tested 6-compartment FEM approaches significantly increase the goodness of fit to the measured data compared with the 3-compartment BEM. They also demonstrate higher quasi-radial contributions for sources below the gyral crowns. Furthermore, CutFEM improves source separability compared with both other approaches. We conclude that head models with 6 compartments rather than 3 and the new CutFEM approach are valuable additions to MEG source reconstruction, in particular for sources that are predominantly radial.

Numerical simulation study on opening blood-brain barrier by ultrasonic cavitation.

Experimental studies have shown that ultrasonic cavitation can reversibly open the blood-brain barrier (BBB) to assist drug delivery. Nevertheless, the majority of the present study focused on experimental aspects of BBB opening. In this study, we developed a three-bubble-liquid-solid model to investigate the dynamic behavior of multiple bubbles within the blood vessels, and elucidate the physical mechanism of drug molecules through endothelial cells under ultrasonic cavitation excitation. The results showed that the large bubbles have a significant inhibitory effect on the movement of small bubbles, and the vibration morphology of intravascular microbubbles was affected by the acoustic parameters, microbubble size, and the distance between the microbubbles. The ultrasonic cavitation can significantly enhance the unidirectional flux of drug molecules, and the unidirectional flux growth rate of the wall can reach more than 5 %. Microjets and shock waves emitted from microbubbles generate different stress distribution patterns on the vascular wall, which in turn affects the pore size of the vessel wall and the permeability of drug molecules. The vibration morphology of microbubbles is related to the concentration, arrangement and scale of microbubbles, and the drug permeation impact can be enhanced by optimizing bubble size and acoustic parameters. The results offer an extensive depiction of the factors influencing the blood-brain barrier opening through ultrasonic cavitation, and the model may provide a potential technique to actively regulate the penetration capacity of drugs through endothelial layer of the neurovascular system by regulating BBB opening.

Highly Sensitive Plasmon Refractive Index Sensor Based on MIM Waveguide.

This paper introduces a novel plasmon refractive index nanosensor structure based on Fano resonance. The structure comprises a metal-insulator-metal (MIM) waveguide with an inverted rectangular cavity and a circle minus a small internal circle plus a rectangular cavity (CMSICPRC). This study employs the finite element method (FEM) to analyze the sensing characteristics of the structure. The results demonstrate that the geometrical parameters of specific structures exert a considerable influence on the sensing characteristics. Simulated experimental data show that the maximum sensitivity of this structure is 3240 nm/RIU, with a figure of merit (FOM) of 52.25. Additionally, the sensor can be used in biology, for example, to detect the concentration of hemoglobin in blood. The sensitivity of the sensor in this application, according to our calculations, can be 0.82 nm∙g/L.

Towards Design Optimization of Compliant Mechanisms: A Hybrid Pseudo-Rigid-Body Model-Finite Element Method Approach and an Accurate Empirical Compliance Equation for Circular Flexure Hinges.

Innovative designs such as morphing wings and terrain adaptive landing systems are examples of biomimicry and innovations inspired by nature, which are actively being investigated by aerospace designers. Morphing wing designs based on Variable Geometry Truss Manipulators (VGTMs) and articulated helicopter robotic landing gear (RLG) have drawn a great deal of attention from industry. Compliant mechanisms have become increasingly popular due to their advantages over conventional rigid-body systems, and the research team led by the second author at Toronto Metropolitan University (TMU) has set their long-term goal to be exploiting these systems in the above aerospace applications. To gain a deeper insight into the design and optimization of compliant mechanisms and their potential application as alternatives to VGTM and RLG systems, this study conducted a thorough analysis of the design of flexible hinges, and single-, four-, and multi-bar configurations as a part of more complex, flexible mechanisms. The investigation highlighted the flexibility and compliance of mechanisms incorporating circular flexure hinges (CFHs), showcasing their capacity to withstand forces and moments. Despite a discrepancy between the results obtained from previously published Pseudo-Rigid-Body Model (PRBM) equations and FEM-based analyses, the mechanisms exhibited predictable linear behavior and acceptable fatigue testing results, affirming their suitability for diverse applications. While including additional linkages perpendicular to the applied force direction in a compliant mechanism with N vertical linkages led to improved factors of safety, the associated increase in system weight necessitates careful consideration. It is shown herein that, in this case, adding one vertical bar increased the safety factor by 100N percent. The present study also addressed solutions for the precise modeling of CFHs through the derivation of an empirical polynomial torsional stiffness/compliance equation related to geometric dimensions and material properties. The effectiveness of the presented empirical polynomial compliance equation was validated against FEA results, revealing a generally accurate prediction with an average error of 1.74%. It is expected that the present investigation will open new avenues to higher precision in the design of CFHs, ensuring reliability and efficiency in various practical applications, and enhancing the optimization design of compliant mechanisms comprised of such hinges. A specific focus was put on ABS plastic and aluminum alloy 7075, as they are the materials of choice for non-load-bearing and load-bearing structural components, respectively.

Effect of condylar rotation on the stress environment of the temporomandibular joint in patients with mandibular protrusion.

PURPOSE: The study aims to analyse the effects of condylar rotation on the biomechanical environment of the TMJ after bilateral sagittal split ramus osteotomy (BSSRO) through the finite element method (FEM). METHODS: Thirteen patients with mandibular prognathism and twenty-three normal subjects were recruited. The three-dimensional (3D) models were reconstructed. 13 representative morphological parameters were measured for comparison. A patient was selected to perform virtual BSSRO surgery by rotating the condyles in MIMICS. The preoperative and postoperative 3D models of the patient were subsequently imported into ABAQUS for finite element analysis. The preoperative and postoperative stresses and joint spaces in the TMJs were investigated. RESULTS: The maxillofacial morphologies of the patients with mandibular protrusion was significantly different from those of the asymptomatic subjects (P<.05). Stresses in the postoperative group were lower than those in the preoperative group. The rotation of the condyle could cause the variations in stress levels and joint spaces within the TMJs. Inward and upward rotation of the condyle was associated with higher stress in the TMJ, whereas the lowest stress was observed when the condyle remained stationary following surgical intervention. SIGNIFICANCE: Lateral, medial and superior joint spaces were more related to the stresses in the TMJs. The condyle should be kept in place as much as possible to avoid disrupting the balance of the TMJ in patients with mandibular protrusion.

Nanomechanical inhomogeneities in CVA-deposited titanium nitride thin films: Nanoindentation and finite element method investigations.

Refractory metals that can withstand at high temperatures and harsh conditions are of utmost importance for solar-thermal and energy storage applications. Thin films of TiN have been deposited using cathodic vacuum arc deposition at relatively low temperatures ∼300 °C using the substrate bias âˆ¼ -60 V. The nanomechanical properties of these films were investigated using nanoindentation and the spatial fluctuations were observed. The nanoindentation results were simulated using finite element method through Johnson-Cook model. A parametric study was conducted, and 16 different models were simulated to predict the hardening modulus, hardening exponent, and yield stress of the deposited film. The predicted values of elastic modulus, yield stress, hardening modulus and hardening exponent as 246 GPa, 2500 MPa, 25000 MPa and 0.1 respectively are found to satisfactorily explain the experimental load-indentation curves. We have found the local nitridation plays an important role on nanomechanical properties of TiN thin films and confirms that the nitrogen deficient regions are ductile with low yield stress and hardening modulus. This study further opens the opportunities of modelling the nanoscale system using FEM analysis.

Biomechanical study of effect of tibial posteromedial defect depth and area on primary TKA implant stability.

BACKGROUND: Medial tibial defects are common in patients who underwent primary total knee arthroplasty for varus deformity. Previous clinical studies have categorized tibial defects according to the depth of the defects and recommended different ways of addressing them. This study aimed to perform a biomechanical FE analysis to investigate the role of depth and surface area of the medial tibial plateau defects in the stability of the tibial component in primary TKA implants. METHOD: Forty posteromedial tibial defect models with eight different depths (including 2, 4, 6, 8, 11, 13, 16, and 18 mm) and five different surface areas (including 10, 20, 30, 40, and 50% medial surface involvement) were used to create the FE models. Loads were applied to ellipses on tibial tray with 70-30% mediolateral distribution. The resulting relative motion of the bone and implant was measured to evaluate the tibial tray instability. RESULTS: For defects with less than 20% surface involvement, the amount of relative motion had a moderately increasing fashion; however, in more significant percentages of surface involvement of the medial tibial plateau, especially in 50%, the graphs revealed a nonlinear increasing pattern which means that the depth would affect the amount of relative motion only when defect area is large. CONCLUSION: In defects with less than 20% surface involvement approaches like graft and cement augmentation would suffice whereas it would be essential to consider a more appropriate method like stem or metal augments for defects with more than 20% of medial surface involvement as the instability increased nonlinearly.

The mechanical characteristics of an aluminum foam winding CFRP composite structure under axial compression.

To enhance the energy absorption properties of the energy-absorbing structure, carbon fiber-reinforced polymer (CFRPs) with higher specific energy absorption and porous material aluminum foam with better compressive characteristics were organically combined, and a lighter aluminum foam winding carbon fiber-reinforced polymer structure (CFRP-FA-FW) was designed. Through quasi-static compression testing, the deformation mode and energy absorption properties of CFRP-FA-FW under axial load were examined. The energy absorption and specific energy absorption of CFRP-FA-FW are both increased by 113.55 % and 60.73 %, respectively, compared to the simple composite structure CFRP-FA. Finite element simulation was used for the parametric analysis of the CFRP-FA-FW structure to assess the effects of the relative density of the aluminum foam, the fiber lay-up angle, and the thickness. The results reveal that the change in the relative density of aluminum foam has little impact on the failure deformation mode of CFRP-FA-FW under axial load; the structure has a higher energy absorption capacity and a smoother energy absorption process when the fiber lay-up angle is [0°/90°]ns and [45°]ns; the energy absorption capacity of CFRP-FA-FW is significantly improved by increasing the thickness of the carbon fiber lay-up, and the procedure is also more efficient.

Mathematical modeling of flexible printed circuit configuration: a study in deformation and optimization.

This manuscript offers an exhaustive analysis of Flexible Printed Circuits (FPCs), concentrating on enhancing their design to surmount two primary challenges. Firstly, it seeks to obviate contact with proximate components. Secondly, it aspires to adhere to pre-established curvature constraints. Predicated on the curvature properties of FPCs, we have developed a model adept at accurately forecasting FPC deformation under diverse conditions. Our inquiry entails a thorough examination of various FPC configurations, including bell, 'U', and 'S' shapes. Central to our methodology is the strategic optimization of FPC spatial arrangements, aiming to avert mechanical interference and control curvature, thus mitigating mechanical strain. This dual-faceted strategy is pivotal in enhancing the durability and operational reliability of FPCs, particularly in contexts demanding elevated flexibility and precision. Our research offers essential insights into the refinement of FPC design, skillfully addressing the complexities associated with curvature and physical interaction. Collectively, this study advocates a comprehensive framework for the design and implementation of FPCs, significantly advancing the field of contemporary electronics by ensuring these components meet the evolving demands of the industry.

Microstructural Evolution and Failure in Fibrous Network Materials: Failure Mode Transition from the Competition between Bond and Fiber.

For the complex structure of fibrous network materials, it is a challenge to analyze the network strength and deformation mechanism. Here, we identify a failure mode transition within the network material comprising brittle fibers and bonds, which is related to the strength ratio of the bond to the fiber. A failure criterion for this type of fibrous network is proposed to quantitatively characterize this transition between bond damage and fiber damage. Additionally, tensile experiments on carbon and ceramic fibrous network materials were conducted, and the experimental results show that the failure modes of these network materials satisfy the theoretical prediction. The relationship between the failure mode, the relative density of network and strength of the components is established based on finite element analysis of the 3D network model. The failure mode transforms from bond damage to fiber damage as increasing of bond strength. According to the transition of the failure modes in the brittle fibrous network, it is possible to tailor the mechanical properties of fibrous network material by balancing the competition between bond and fiber properties, which is significant for optimizing material design and engineering applications.

AI-based predictive approach via FFB propagation in a driven-cavity of Ostwald de-Waele fluid using CFD-ANN and Levenberg-Marquardt.

The integration of Artificial Intelligence (AI) and Machine Learning (ML) techniques into computational science has ushered in a new era of innovation and efficiency in various fields, with particular significance in computational fluid dynamics (CFD). Several methods based on AI and Machine Learning (ML) have been standardized in many fields of computational science, including computational fluid dynamics (CFD). This study aims to couple CFD with artificial neural networks (ANNs) to predict the fluid forces that arise when a flowing fluid interacts with obstacles installed in the flow domain. The momentum equation elucidating the flow has been simulated by adopting the finite element method (FEM) for a range of rheological and kinematic conditions. Hydrodynamic forces, including pressure drop between the back and front of the obstacle, surface drag, and lift variations, are measured on the outer surface of the cylinder via CFD simulations. This data has subsequently been fed into a Feed-Forward Back (FFB) propagation neural network for the prediction of such forces with completely unknown data. For all cases, higher predictivity is achieved for the drag coefficient (CD) and lift coefficient (CL) since the mean square error (MSE) is within ± 2% and the coefficient of determination (R) is approximately 99% for all the cases. The influence of pertinent parameters like the power law index (n) and Reynolds number (Re) on velocity, pressure, and drag and lift coefficients is also presented for limited cases. Moreover, a significant reduction in computing time has been noticed while applying hybrid CFD-ANN approach as compared with CFD simulations only.

Simulation-Informed Power Budget Estimate of a Fully-Implantable Brain-Computer Interface.

This study aims to estimate the maximum power consumption that guarantees a thermally safe operation for a titanium-enclosed chest wall unit (CWU) subcutaneously implanted in the pre-pectoral area. This unit is a central piece of an envisioned fully-implantable bi-directional brain-computer interface (BD-BCI). To this end, we created a thermal simulation model using the finite element method implemented in COMSOL. We also performed a sensitivity analysis to ensure that our predictions were robust against the natural variation of physiological and environmental parameters. Based on this analysis, we predict that the CWU can consume between 378 and 538 mW of power without raising the surrounding tissue's temperature above the thermal safety threshold of 2  ∘ C. This power budget should be sufficient to power all of the CWU's basic functionalities, which include training the decoder, online decoding, wireless data transmission, and cortical stimulation. This power budget assessment provides an important specification for the design of a CWU-an integral part of a fully-implantable BD-BCI system.

A semi-automated pipeline for finite element modeling of electric field induced in nonhuman primates by transcranial magnetic stimulation.

BACKGROUND: Transcranial magnetic stimulation (TMS) is used to treat a range of brain disorders by inducing an electric field (E-field) in the brain. However, the precise neural effects of TMS are not well understood. Nonhuman primates (NHPs) are used to model the impact of TMS on neural activity, but a systematic method of quantifying the induced E-field in the cortex of NHPs has not been developed. NEW METHOD: The pipeline uses statistical parametric mapping (SPM) to automatically segment a structural MRI image of a rhesus macaque into five tissue compartments. Manual corrections are necessary around implants. The segmented tissues are tessellated into 3D meshes used in finite element method (FEM) software to compute the TMS induced E-field in the brain. The gray matter can be further segmented into cortical laminae using a volume preserving method for defining layers. RESULTS: Models of three NHPs were generated with TMS coils placed over the precentral gyrus. Two coil configurations, active and sham, were simulated and compared. The results demonstrated a large difference in E-fields at the target. Additionally, the simulations were calculated using two different E-field solvers and were found to not significantly differ. COMPARISON WITH EXISTING METHODS: Current methods segment NHP tissues manually or use automated methods for only the brain tissue. Existing methods also do not stratify the gray matter into layers. CONCLUSION: The pipeline calculates the induced E-field in NHP models by TMS and can be used to plan implant surgeries and determine approximate E-field values around neuron recording sites.

Surrogate metamodels from digital image correlation for testing high-performance composite vessels.

In this work, a workflow has been developed for the generation of surrogate metamodels to predict and evaluate failure with a confidence above 95 % in initial service conditions of high-performance cylindrical vessels manufactured in composites by Roll Wrapping technology. Currently, there is no specific testing standardization for this type of vessel and to fill this gap probabilistic numerical models were developed, performed by the Finite Element Method, fed with the material characteristics obtained experimentally by 2D digital image correlation from flat specimens. From the initial numerical model, a surrogate metamodel was generated by stochastic approximations. Once the metamodels were obtained by robust engineering, an experimental ring-ring tensile test was developed under service conditions and deformations were measured by high-precision 3D digital image correlation. Parametric and robust tests showed that the results of the metamodel did not show statistically significant differences, with errors in the rupture part of less than 2 % with respect to the results obtained in the test, being proposed as a basis for new test procedures.

A Self-Temperature Compensation Barometer Based on All-Quartz Resonant Pressure Sensor.

This paper reports a self-temperature compensation barometer based on a quartz resonant pressure sensor. A novel sensor chip that contains a double-ended tuning fork (DETF) resonator and a single-ended tuning fork (SETF) resonator is designed and fabricated. The two resonators are designed on the same diaphragm. The DETF resonator works as a pressure sensor. To reduce the influence of the temperature drift, the SETF resonator works as a temperature compensation sensor, which senses the instantaneous temperature of the DETF resonator. The temperature compensation method based on polynomial fitting is studied. The experimental results show that the accuracy is 0.019% F.S. in a pressure range of 200~1200 hPa over a temperature range of -20 °C~+60 °C. The absolute errors of the barometer are within ±23 Pa. To verify its actual performance, a drone flight test was conducted. The test results are consistent with the actual flight trajectory.

Evaluating the effect of functionally graded materials on bone remodeling around dental implants.

OBJECTIVES: This study evaluates the potential for osseointegration and remodeling of customized dental implants made from Titanium-Hydroxyapatite Functionally Graded Material (Ti-HAP FGM) with optimized geometry, using the finite element method (FEM). METHODS: The study utilized CT scan images to model and assemble various geometrical designs of dental implants in a mandibular slice. The mechanical properties of Ti-HAP FGMs were computed by varying volume fractions (VF) of hydroxyapatite (0-20%), and a bone remodeling algorithm was used to evaluate the biomechanical characteristics of the ultimate bone configuration in the peri-implant tissue. RESULTS: The findings of the FEA reveal that osseointegration improves with changes in the density and mechanical properties of the bone surrounding Ti-HAP implants, which are influenced by the varying VF of hydroxyapatite in the FGM. SIGNIFICANCE: Increasing the hydroxyapatite fraction improves osseointegration, and appropriate length and diameter selection of Ti-HAP dental implants contribute to their stability and longevity.

A Dual-Mode Surface Acoustic Wave Delay Line for the Detection of Ice on 64°-Rotated Y-Cut Lithium Niobate.

Ice accumulation on infrastructure poses severe safety risks and economic losses, necessitating effective detection and monitoring solutions. This study introduces a novel approach employing surface acoustic wave (SAW) sensors, known for their small size, wireless operation, energy self-sufficiency, and retrofit capability. Utilizing a SAW dual-mode delay line device on a 64°-rotated Y-cut lithium niobate substrate, we demonstrate a solution for combined ice detection and temperature measurement. In addition to the shear-horizontal polarized leaky SAW, our findings reveal an electrically excitable Rayleigh-type wave in the X+90° direction on the same cut. Experimental results in a temperature chamber confirm capability for reliable differentiation between liquid water and ice loading and simultaneous temperature measurements. This research presents a promising advancement in addressing safety concerns and economic losses associated with ice accretion.

Influence of the Curve of Spee on Tooth Displacement Patterns: A Finite Element Analysis at Varying Implant Heights.

Background Monocortical mini-screw-type temporary anchorage devices (TADs), or mini-screws, have significantly impacted orthodontic treatment strategies, especially in severe crowding and protrusion cases. These devices offer flexibility in placement sites, but the chosen location can considerably influence tooth displacement patterns. Key factors include the 'line of force' and the biomechanical properties of orthodontic tools. By analyzing tension distribution and three-dimensional displacements, the finite element method (FEM) provides a thorough means to comprehend these patterns. The Curve of Spee (COS) is a crucial factor potentially affecting displacement. Objective This study aimed to leverage finite element analysis (FEA) to understand the impact of varying mini-implant heights (10 mm, 13 mm, and 16 mm) on the displacements of different tooth types under a consistent force of 150 gm and compare these displacements both in the presence and absence of the COS. Materials and methods A CAD model of the jaw and teeth was developed using CT scan data and a Rexcan III 3D White Light Scanner. This model was meshed in Altair HyperMesh using tetrahedral elements, resulting in a Finite Element Model. The model incorporated various components, including teeth, the periodontal ligament (PDL), alveolar bone, brackets, a titanium mini-screw, and an archwire measuring 0.019 x 0.025 inches. Unique material properties were assigned to the PDL, and the assembly accurately replicated the clinical alignment of the archwire and brackets. Subsequently, stress and strain analyses were conducted on the model using the FEM. Results The displacement patterns of various teeth at implant heights of 10 mm, 13 mm, and 16 mm under a 150-gm force were analyzed in relation to the COS. Notably, for the central incisor, the COS significantly affected displacements in the Y and Z directions. Similarly, the Lateral Incisor and Canine exhibited marked changes in the Z direction with the presence of the COS. The Second Premolar's apex displacement showed significant variation due to the COS, while the First Molar displayed notable changes in the X direction. Generally, the presence of the COS either maintained or slightly increased Z-directional displacements across teeth, particularly at the apices. Conclusion The presence of COS significantly influences tooth displacement patterns when using mini-screws at different implant heights. Central incisors, lateral incisors, and canines are particularly sensitive to changes in the Z direction with the COS. The biomechanical analysis emphasizes the importance of considering COS in treatment planning for optimal results with mini-implants in orthodontics.

Quasi-Static Modeling Framework for Soft Bellow-Based Biomimetic Actuators.

Soft robots that incorporate elastomeric matrices and flexible materials have gained attention for their unique capabilities, surpassing those of rigid robots, with increased degrees of freedom and movement. Research has highlighted the adaptability, agility, and sensitivity of soft robotic actuators in various applications, including industrial grippers, locomotive robots, wearable assistive devices, and more. It has been demonstrated that bellow-shaped actuators exhibit greater efficiency compared to uniformly shaped fiber-reinforced actuators as they require less input pressure to achieve a comparable range of motion (ROM). Nevertheless, the mathematical quantification of the performance of bellow-based soft fluidic actuators is not well established due to their inherent non-uniform and complex structure, particularly when compared to fiber-reinforced actuators. Furthermore, the design of bellow dimensions is mostly based on intuition without standardized guidance and criteria. This article presents a comprehensive description of the quasi-static analytical modeling process used to analyze bellow-based soft actuators with linear extension. The results of the models are validated through finite element method (FEM) simulations and experimental testing, considering elongation in free space under fluidic pressurization. This study facilitates the determination of optimal geometrical parameters for bellow-based actuators, allowing for effective biomimetic robot design optimization and performance prediction.