Optimal Stiffness Research Articles

Development of innovative system of universal stent graft for endovascular treatment of aneurysm and aortic displacement in various locations

This study presents the technology of developing a universal stent graft for endovascular treatment of aneurysms and aortic dissection of various localizations, without considering the vessel diameter. A self-expanding nitinol stent was used as the frame of the main trunk of the stent graft. During the study, several variants of the aortic linear graft were manufactured and tested. The optimal stiffness and diameter of the nitinol wire were selected based on the results. When creating a bifurcation module, special attention was paid to simplifying the positioning and intravascular assembly of the structure. Implantable modules have been developed for the prosthetics of the main branches of the aorta. Dacron, optimal in terms of fiber structure, was chosen as the material of the woven shell of the graft. Linear extensibility, compactness of the pile, and tensile strength during fenestration were evaluated. To determine the heparin-controlled surgical porosity, experimental samples of stent grafts were tested on a stand simulating arterial blood flow. The wall material of the developed device had a heparin-controlled surgical porosity of 50150 mL/min/cm2 at 120 mm Hg with the possibility of maintaining a controlled endolic. The graft wall created a pressure gradient of no more than 3 mm Hg, and the flow velocity indicators were quite sufficient for adequate perfusion of vital organs. After the inactivation of heparin, blood permeability became zero. The implantation technique of the developed product was implemented on a silicone aortic phantom simulating aneurysm expansion with and without dissection. The phantom contour was filled with a solution simulating the rheological properties of native blood. Pulsating blood flow was simulated using a perfusion pump. Under X-ray control, a stent graft was installed on five large biological samples (sheep). Implantation was performed in the aortic arch with prosthetics of the brachiocephalic trunk and the suprarenal aorta with prosthetics of the visceral branches. With the experiment, we hope that the result will allow us to minimally invasively help patients suffering from aneurysms of any localization.

Analytically optimal parameters of supplemental brace-damper system in single-degree-of-freedom structure based on stability maximization criterion

In this study, optimal parameters (i.e., optimal additional stiffness ratio α and damping ratio λ) for supplemental brace-damper system in a single-degree-of-freedom (SDOF) structure are analytically derived. Different from the design formulations for supplemental brace-damper system proposed by Londoño, which are essentially fitting formulae through extensive parametric study, analytically optimal parameters for supplemental brace-damper system are derived by combining the research work by Londoño and the stability maximization criterion (SMC). Similar to Optimum Brace Stiffness (OBS) criterion and Optimum Damper Size (ODS) criterion proposed by Londoño, SMC-based OBS criterion and SMC-based ODS criterion are respectively proposed to assure a desired structural performance represented by the targeted overall damping ratio of the considered system. Through numerical study, it is demonstrated that the seismic response of the proposed SMC-based OBS criterion and SMC-based ODS criterion excellently agree with those of the existing OBS criterion and ODS criterion, respectively.

Fatigue reliability assessment method for wind power gear system based on multidimensional finite element method

As a core strategic technology industry, the wind power plays an important role in protecting national energy reserves. The large gear component is one of the core foundation parts in wind turbines, and its quality indexes greatly affect the service performance of the wind turbine drive chain and even the wind turbine as a whole. This paper calculates the fatigue load history of the wind power large gear system under the coupling mechanism of elastic behavior based on a multidimensional finite element method, and obtains the probabilistic fatigue strength of gear teeth through the gear low circumference fatigue test and life distribution transformation method, and deeply explores the inherent characteristics of the wind power gear system in functional implementation and then establishes a system fatigue reliability evaluation model. Finally, a mapping path from the global structural elements of the wind power gearbox to the reliability indexes of the gear system is constructed with significant simulation and test cost advantages. It can provide structural optimization guidance in the development and design of large wind power gear systems, and significantly reduce the cost of achieving reliability indexes in the design iterations of such large high-end equipment. At the same time, it can provide cost-effective training data for intelligent optimization algorithms such as the deep reinforcement learning, which will eventually achieve multi-objective optimal stiffness matching for wind power gearboxes under reliability index constraints.

Stiffness optimization based on muscle fatigue and muscle synergy for passive waist assistive exoskeleton

PurposeThis paper aims to optimize the stiffness coefficient of the elastic element for a passive waist assistive exoskeleton (WAE). There is a tradeoff between stiffness coefficient of elastic element of the exoskeleton and work efficiency of the wearer, because elastic element affects original bending motion of the wearer and the force requirement of erector spinae is compensated by the other muscles. However, there is no accepted conclusion on how to determine the proper stiffness coefficient, especially with respected to the effort of groups of muscles, not only erector spinae.Design/methodology/approachIn this study, a consumption indicator based on muscle fatigue of seven muscles is proposed and a Bayesian-based human-in-the-loop optimization approach is adopted to optimize the stiffness coefficient. Pneumatic artificial muscles are used to replace the mechanical elastic part to adjust the assistive force automatically. The proposed optimization method is verified by the way of load-lifting experiments with three different conditions: without exoskeleton, with fixed air pressure and with optimized air pressure. Six subjects participated in the experiment and each experiment is performed in different day.FindingsCompared with No-Exo condition and static assistance condition, the parameter-optimized waist exoskeleton averagely reduces muscle fatigue of the six subjects by 45.30 ± 29.14% and 30.94 ± 30.29%, respectively. The experimental results indicate that the proposed method is effective to reduce muscle fatigue during stoop lifting task.Originality/valueThis paper provides a novel cost function construction method based on muscle fatigue and muscle synergy for passive WAE stiffness optimization.

Abstract 4132: Effect of mechanical cues on T cell killing of cancer cells

Abstract Cancer immunotherapies have focused on strategies to strengthen immune cell activation and effector function. These treatment strategies enhance the effector function of immune cells, particularly cytotoxic T cells (CTL), driving tumor eradication. Methods to improve the killing mechanisms of CTLs are not well studied and largely focused on assessing/strengthening the antigenic responses of T cells. We hypothesize that the mechanical landscape of CTL-tumor interactions can also drastically impact CTL cytotoxicity. By altering the physical context for T cell recognition of tumors, we measured cytotoxicity changes and subsequently used these changes in killing capacities to train and generate a quantitative parametrization of T cell killing. CTLs utilize cytokine expression to kill and shape the inflammatory milieu. Taking advantage of a robotic platform that enables the automatic collection of cytokines, we assembled datasets of T cell attacks of tumor cells grown on substrates with varying stiffness levels. The stiffness levels were altered using polyacrylamide (PAA) gels and ranged from 0.2kPa to approximately 113 kPa. Preliminary results from two different models (i.e., mouse and human TCR-transgenic T cells) suggest that there exists an optimal stiffness value for maximal response by T cells. These results suggest that CTLs utilize biophysical cues in addition to molecular cues (antigen) to properly elicit an immune response—modeling and fine-tuning these mechanical cues can be a novel and effective approach to improving cancer immunotherapies. Citation Format: Hannah Dada, Kun Do, Alexander Cartagena-Rivera, Grégoire Altan-Bonnet. Effect of mechanical cues on T cell killing of cancer cells. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 4132.

Buckling of externally pressurised ellipsoidal domes with variable wall thicknesses

ABSTRACT This paper focuses on the buckling of nontypical ellipsoidal domes under uniform external pressure. According to the strength and stiffness optimisation theory, the structure of the ellipsoidal dome was optimised respectively, and two meridional profiling curves of the ellipsoidal dome were obtained. Two mass-equivalent ellipsoidal domes with variable wall thickness and one mass-equivalent ellipsoidal dome with constant wall thickness were fabricated using CNC machining, with a nominal long-axis and short-axis radius of 100 and 75 mm, respectively. The geometry, wall thickness, and buckling load of each ellipsoidal dome were measured. The agreement between numerical predictions and experimental results is good. The results indicate that the ellipsoidal dome with variable wall thickness has a relatively large load-carrying capacity.

Optimization of the Position and Stiffness of Passive Walking Assistance Devices

Walking is a fundamental movement in daily life; however, many factors affect walking that may reduce the mobility of the people. Walking assistance devices can help with gaining mobility back for people who suffer from walking problems. In the present study, a computational method to determine the location and stiffness of the assistive walking systems was developed. The human walking model was created by using nine rigid bodies and eight revolute joints connecting them in the sagittal plane. The walking assistance system was considered as a tension spring with both ends attached to the human walking model. A coordinate system was defined along the distal–proximal direction of the human body. The position of the walking assistance system was determined by using four design variables, and the optimal position of the assistive walking system to reduce the total positive joint energy was found around the hip joint at a walking speed of 1.3 m/s. Hip joint moment and power were significantly affected by the walking assistance system, and the total positive joint energy was reduced by 8.8%. Because walking speed significantly affects walking kinematics and kinetics, the effect of walking speed on the optimal walking assistance device was investigated. The position of the device was kept the same, and the optimal stiffness and free length of the spring were found at different walking speeds. Two different cases were considered: a speed-specific design in which stiffness characteristics were separately optimized for each speed and a general design in which stiffness characteristics were optimized by considering all walking speeds. It was found that, in both cases, hip joint moment and power significantly reduced, and the speed-specific design produced a slightly larger reduction in total joint energy. The performance of the walking assistance systems in both cases were found to be higher at faster walking speeds.

Diatom-inspired stiffness optimization for plates and cellular solids

Diatoms, a class of aquatic autotrophic microorganisms, are characterized by silicified exoskeletons with highly complex architectures. These morphologies have been shaped by the selection pressure that the organisms have been subjected to during their evolutionary history. Two properties which are highly likely to have contributed to the evolutionary success of current diatom species are lightweightness and structural strength. Thousands of diatom species are present in water bodies today, and although each has its unique shell architecture, a strategy that is common across species is the uneven and gradient solid material distribution across their shells. The aim of this study is to present and evaluate two novel structural optimization workflows inspired by material grading strategies in diatoms. The first workflow mimics the Auliscus intermidus diatoms’ surface thickening strategy and generates continuous sheet structures with optimal boundaries and local sheet thickness distributions when applied to plate models subjected to in-plane boundary conditions. The second workflow mimics the Triceratium sp. diatoms’ cellular solid grading strategy, and produces 3D cellular solids with optimal boundaries and local parameter distributions. Both methods are evaluated through sample load cases, and prove to be highly efficient in transforming optimization solutions with non-binary relative density distributions into highly performing 3D models.

Seismic isolation effect of a new type of friction pendulum bearing in high-speed railway girder bridge

Residual displacement exists in the traditional friction pendulum bearings (FPB) under the action of earthquakes, which makes them fail to self-reset. In view of this, a new type of FPB called double concave friction pendulum with spring (DCFPS) is proposed. Firstly, the restoring force model and hysteresis characteristics of the theoretical DCFPS are derived. Then, the seismic isolation effect of the high-speed railway simply supported girder bridges (HRSB) equipped with the DCFPS is evaluated. Finally, the optimal spring parameters of the DCFPS are determined in terms of the efficiency coefficient and the optimal order method. The results show that the DCFPS has superior self-reset performance, and the hysteresis curve is “S” shaped. The stiffness of the DCFPS gradually increases with the swing displacement, which heightens the overall stiffness of the structure equipped with DCFPS. After HRSB is installed DCFPS, the displacement of the girder and the residual displacement of the DCFPS itself are reduced. The optimal stiffness and the initial tension of spring for the bridges exemplified in the paper are suggested as 3000 kN/m and 9 kN, respectively, through the efficiency coefficient method and the optimal order method. This research proposes a feasible solution for reducing the maximum displacement and residual displacement of bearings under an earthquake.

A fast calculation method for the optimal clearance and stiffness of the aerostatic guideway considering fluid-structure interaction

The static performances of the aerostatic spindles/guideways are significantly affected by the fluid-structure interaction (FSI) effect. However, the existing two-way FSI calculation method for the aerostatic spindles and guideways is inefficient. It takes much time to calculate the optimal parameters and static performance in the design and study process. This paper proposes a fast calculation method for the optimal clearance and stiffness of the aerostatic guideway considering FSI, and the calculation process of a cruciform-layout aerostatic guideway was detailed as a case study. Moreover, the accuracy of the proposed fast calculation method is verified numerically and experimentally, which proves that the computational efficiency can be improved dozens or even hundreds of times under the premise of minor calculation errors.

H∞ Optimization of a Novel Maxwell Dynamic Vibration Absorber with Lever, Inerter, and Grounded Stiffness

In this paper, we propose a novel Maxwell dynamic vibration absorber (DVA) with lever, inerter, and grounded stiffness. Firstly, the governing equation of the coupled system is established. The analytical formula of the amplitude amplification factor of the primary system and the natural frequencies of the coupled system are derived. There are three fixed points in the amplitude–frequency response curve of the primary system, which are independent of damping. Then, based on H∞ optimization criterion, two possible optimal parameter designs of the proposed model are obtained. Considering the practical engineering application and ensuring the stability of the system, the optimal grounded stiffness ratio is selected, and six working ranges of inerter–mass ratio are calculated. Furthermore, the performance of the vibration reduction is compared for six cases. It is found that when the values of the mass ratio, lever amplification ratio, and inerter–mass ratio change in different intervals, and the optimal grounded stiffness ratio has different cases of negative, zero, and positive results. Especially when the stiffness coefficient of the viscoelastic Maxwell model and another grounded stiffness are positive at the same time, the vibration absorption effect is better theoretically. Finally, comparing with the traditional DVAs, the performance of the novel DVA is better under harmonic excitation and random excitation. The results could provide theoretical guidance for the design of inerter-based Maxwell-type DVA with a lever component.

Vibration Control of Steel Wind Turbine Tower Using a Novel Tuned Mass Damper Refitted via Inner Platform

Steel large-megawatts wind turbines have the light-damping and long-period properties, resulting in the adverse vibrations under the wind loads. In this paper, a novel tuned mass damper refitted via inner platform (IP-TMD) is proposed to control the excessive vibration of steel wind turbine tower (WTT). Firstly, the dynamic equation of steel WTT controlled by the IP-TMD system is established according to the principle of virtual work, and its dynamic coefficient and frequency ratio at corresponding fixed points are deduced. Then, the optimal frequency ratio and optimal stiffness and damping coefficients are obtained by the system optimization. Furthermore, a numerical simulation research is employed to analyze the frequency-response curves and resonance mitigation effect of IP-TMD under harmonic excitation. Finally, the vibration control efficiency of IP-TMD is calculated using the Wilson-θ method under the wind loadings; the results indicated that IP-TMD is able to reduce the dynamic response of steel WTT over 45% compared with the uncontrolled WTT cases.

Analytical H∞ and H2 optimization for negative-stiffness inerter-based systems

Two novel dynamic vibration absorbers containing inerter and negative stiffness (NI-DVA) are presented to reduce the vibration of a primary system which is subjected to the acceleration excitation from the base. The NI-DVAs which are called N-TID and N-TVMD, are composed of a parallel inerter and negative stiffness spring that connected with a spring and a dashpot in different layouts. The analytical expressions of optimal stiffness ratio, damping ratio and negative stiffness ratio for both H∞ and H2 optimization design are derived based on the fixed-points theory and extreme value theory under the Routh-Hurwitz stability condition. These analytically optimal design parameters of NI-DVAs are expressed as functions of the inertance mass ratio. The effectiveness of the analytical solutions of optimal parameters for two NI-DVAs is verified by comparing them with the results obtained from the numerical searching optimization method. The vibration reduction performance of the negative stiffness element in the N-TID and N-TVMD is evaluated by comparing it with TID and TVMD harmonic excitation, white noise, and non-stationary earthquake waves. The numerical studies suggest that the presence of the negative stiffness element in NI-DVAs possesses superior vibration reduction performance compared with their original counterparts. Though higher improvement in vibration reduction performance is observed from N-TID due to the existence of a negative stiffness element, N-TVMD outperforms N-TID in terms of vibration reduction under both harmonic and random acceleration excitation.

The effect of upper panel stiffness on biomechanical performance in athletic footwear

Athletic footwear can improve performance through targeted design features to improve biomechanical mechanisms of performance. The alteration of athletic shoe uppers can impact athletic performance and biomechanics in both males and females; moreover, the impact may differ between males and females due to anatomical differences between sexes. Therefore, assessment of sex-specific impacts of footwear modification on athletic performance is essential when determining how to modify footwear. The purpose of this research was to determine the impact of upper panel stiffness on biomechanical performance during agility tasks and determine if the optimal upper stiffness depends on the sex of the athlete. It was hypothesized that stiffening the upper panel, quantified through uniaxial tension testing, would result in decreased contact time and increased force production during jumping and change of direction tasks. Forty participants (20 males, 20 females) were recruited and completed eight lateral skater jumps, eight counter movement jumps, three triangle drop step drills and six anterior-posterior drills in three footwear conditions that varied in upper panel stiffness. 3D motion capture and embedded force plates were used to measure biomechanical outcomes that were compared between stiffness conditions using a linear mixed effect model. Upper panel stiffness significantly affected contact time during the lateral skater jump with the stiffest shoe resulting in the shortest contact time compared to the two other conditions (p = .02–.046, η2 = 0.18). No sex-related interactions were found for any outcome variable. Taken together, upper panel stiffness is important to consider when developing both male and female footwear.

Concurrent multi-material and multi-scale design optimization of fiber-reinforced composite material and structures for minimum structural compliance

With the development of additive manufacturing technology for fiber-reinforced composite materials, topology optimization of fiber-reinforced composite laminates involving multiple materials and variable stiffness is gaining increasing attention. This study proposes an effective methodology for a Multi-scale and Multi-material Composite Anisotropic Penalization (MMCAP) model to investigate multi-scale and multi-material design optimization of a fiber-reinforced variable stiffness (VS) composite structure to minimize structural compliance. In the concurrent MMCAP model, the macroscopic multi-material structural topology and microscopic discrete fiber laying angle selection are introduced as independent design variables and optimized simultaneously. The modified Solid Isotropic Material with Penalization (SIMP) and the Discrete Material Optimization (DMO) approaches are utilized at the macro- and micro-scales, respectively, to realize a clear macroscopic multi-material structural topology and microscopic specific discrete fiber laying angle selection. Multi-material fiber-reinforced plastic (FRP) materials, such as carbon fiber–reinforced plastic (CFRP) and glass fiber–reinforced plastic (GFRP), are considered two types of solid materials in terms of structural volume cost. Sensitivity analysis of the structural compliance concerning the variables of the two geometrical scales is performed using the analytical sensitivity analysis method. The DMO approach is utilized to couple two geometrical scales: macroscopic topology and microscopic material selection. The capabilities of the proposed MMCAP are demonstrated by concurrent multi-material and multi-scale design optimization of composite panels. The influence of the number of discrete fiber laying angles on the structural compliance and optimized topology configuration is also been discussed. Numerical studies showed that the proposed MMCAP scheme can effectively realize multi-material and multi-scale design optimization of fiber-reinforced composite structure with achieving a clear macroscopic multi-material structural topology and microscopic fiber laying angle. The proposed MMCAP scheme provides a new implementation strategy for lightweight, multi-material, and multi-scale design optimization of composite materials, considering the design and manufacturing collaboration through additive manufacturing technology.

Self-learning vibration absorber with negative electromagnetic stiffness for variable vibration

Variable vibration is difficult to control due to the uncertainty and variability of vibration frequency. Vibration absorbers are widely used in engineering, however, the efficiency of mathematical design method decreases significantly once the external vibration changes. In order to suppress the variable frequency vibration, a novel self-learning tuning method for the vibration absorbers is proposed based on a large number of experimental vibration data, which contains the actual information of the optimal absorber parameters. The self-learning tuning method proposed can identify the external excitation frequency and label the optimal stiffness of the absorbers adaptively. In addition, model training can help achieve optimum vibration suppression through reasonable stiffness tuning for different variable low frequency excitation. Two vibration absorbers are designed with negative electromagnetic stiffness, and the effective frequency band can be decreased by applying current into the coil automatically. The vibration absorbers are slightly askew installed on the primary system to achieve bidirectional vibration attenuation. The experimental results indicate that the maximum vibration attenuation ratio is improved from 87.96% to 95.88% along Z-axis and 79.21% to 89.93% along X-axis in the bandwidth of 7–9 Hz.

Stiffness optimization method of locking unit for space manipulator based on plant root adaptive growth theory

Based on plant root adaptive growth theory of monocotyledons, a stiffness optimization method of locking unit for multi-rigid body space manipulator is proposed. The optimization process of locking unit stiffness is transformed into the increase and elimination of spring constraints. The kinematic model of the locking unit is established, and the equivalent method of the locking stiffness of the locking unit is proposed to make the three-dimensional support model of the locking unit correspond to the three-dimensional stiffness of the locking space. According to the proposed optimization method of locking unit and equivalent method of locking stiffness, a parallel optimization method is used to optimize the stiffness of space manipulator locking unit. The stiffness optimized locking system is compared with the conventional locking system, and the higher fundamental frequency of the system is verified by simulation analysis, which proves the effectiveness of the stiffness optimization method of the locking unit.

An interplay of matrix stiffness, dimensionality and adhesivity on cellular behavior

Cell-based assays are essential in vitro tools for understanding basic cell biology, pathophysiology of diseases and mechanism of drug actions most cancer studies have utilized two-dimensional (2D) cell culture methods, which have their shortcomings including lack of cell- extracellular matrix interactions and three-dimensional (3D) geometry, and inaccurate representation of cell polarity. Hence, 3D matrices are being increasingly used to study the effect of 3D niche on cell behavior. Till date, very few systematic studies have been done to show comparison of cell behavior when seeded on the surface and encapsulated inside the matrix. In this study, we fabricated poly(ethylene glycol) (PEG) and gelatin-based matrices using UV mediated photo-polymerization to establish 2D and 3D cell culture methods using breast cancer MDA-MB-231 cells. We have found that the adhesion and spreading of cells on the gel surface is different from that when embedded in gels. The stiffness of poly (ethylene glycol) diacrylate (PEGDA)-gelatin methacryloyl (GelMA) hydrogels with lower concentration of GelMA is lower than that with higher GelMA; further, those with higher overall concentration of polymers (>5%) retain their mechanical integrity and do not degrade even after 7 d. Physical characterization of these matrices demonstrate their optimal pore size, mechanical stiffness and degradation, which are further tunable for tissue engineering, regenerative medicine, drug delivery and cancer studies. Additionally, these semi-synthetic PEGDA-GelMA matrices are transparent in nature, thereby, allowing easy imaging of cells in 3D. The system developed here can be used for short and long term cell culture and can be potentially explored for cell migration and metastasis studies.

Multi-objective genetic algorithm and Castigliano’s theorem for stiffness optimisation of parallel robots: case study of conventional Stewart platforms

ABSTRACT Study of stiffness characteristics plays a key role in application of parallel robots in precision manufacturing. In this study, stiffness index improvement is utilised as the objective function to obtain optimal configurations and dimensions for parallel robots. The optimisation goal is to maximise the stiffness index throughout workspace of the robots. First, stiffness of the robots is obtained by the strain energy of main components of the robots and Castigliano’s theorem. For a more realistic simulation, compliance of moving platform of the robots is considered. Then a non-dominated sorting genetic algorithm (NSGA-II) is utilised to solve the optimisation problem. A comprehensive case study of stiffness analysis of three conventional SPS (spherical– prismatic–spherical) Stewart platforms to examine such a platform’s optimised design is performed. The relationship between the objective and decision spaces is investigated. A similar approach can be utilised to study optimised design for other parallel robots. Findings of this study provide a general stepwise and conceptual approach to the stiffness analysis of parallel robots that depends on design parameters and configuration of the robots. In case of Stewart platforms, 3SPS configuration was found to be optimised in terms of stiffness performance in their workspace.

Ultrasound-derived mechanical stimulation of cell-laden collagen hydrogels for bone repair.

Cell therapy is emerging as an effective treatment strategy for many diseases. Here we describe a novel approach to bone tissue repair that combines hydrogel-based cell therapy with low intensity pulsed ultrasound (LIPUS), an FDA approved treatment for fracture repair. Bone marrow-derived stromal cells (BMSCs) have been encapsulated in type I collagen hydrogels and mechanically stimulated using LIPUS-derived acoustic radiation force (ARF). We observed the expression and upward trend of load-sensitive, osteoblast-specific markers and determined that the extent of cell response is dependent on an optimal combination of both hydrogel stiffness and ARF intensity. Specifically, cells encapsulated in hydrogels of optimal stiffness respond at the onset of ultrasound by upregulating early bone-sensitive markers such as calcium, cyclooxygenase-2, and prostaglandin E2 , and later by supporting mineralized tissue formation after 21 days of culture. In vivo evaluation of a critical size calvarial defect in NOD scid gamma (NSG) mice indicated that the implantation of BMSC-laden hydrogels of optimal stiffness improved healing of calvarial defects after daily administration of ARF over 4 weeks. Collectively, these findings validate the efficacy of our system of localized cell delivery for treating bone defects where undifferentiated BMSCs are induced to the osteoblastic lineage. Further, in vivo healing may be enhanced via non-invasive transdermal mechanical stimulation of implanted cells using ARF.