Theoretically proposed optimal frequency for ultrasound induced cartilage restoration.

BACKGROUND: Matching the frequency of the driving force to that of the system's natural frequency of vibration results in greater amplitude response. Thus we hypothesize that applying ultrasound at the chondrocyte's resonant frequency will result in greater deformation than applying similar ultrasound power at a frequency outside of the resonant bandwidth. Based on this resonant hypothesis, our group previously confirmed theoretically and experimentally that ultrasound stimulation of suspended chondrocytes at resonance (5 MHz) maximized gene expression of load inducible genes. However, this study was based on suspended chondrocytes. The resonant frequency of a chondrocyte does not only depend on the cell mass and intracellular stiffness, but also on the mechanical properties of the surrounding medium. An in vivo chondrocyte's environment differs whether it be a blood clot (following microfracture), a hydrogel or the pericellular and extracellular matrices of the natural cartilage. All have distinct structures and compositions leading to different resonant frequencies. In this study, we present two theoretical models, the first model to understand the effects of the resonant frequency on the cellular deformation and the second to identify the optimal frequency range for clinical applications of ultrasound to enhance cartilage restoration. RESULTS: We showed that applying low-intensity ultrasound at the resonant frequency induced deformation equivalent to that experimentally calculated in previous studies at higher intensities and a 1 MHz frequency. Additionally, the resonant frequency of an in vivo chondrocyte in healthy conditions, osteoarthritic conditions, embedded in a blood clot and embedded in fibrin ranges from 3.5 - 4.8 MHz. CONCLUSION: The main finding of this study is the theoretically proposed optimal frequency for clinical applications of therapeutic ultrasound induced cartilage restoration is 3.5 - 4.8 MHz (the resonant frequencies of in vivo chondrocytes). Application of ultrasound in this frequency range will maximize desired bioeffects.

Selective Cell-Cell Adhesion Regulation via Cyclic Mechanical Deformation Induced by Ultrafast Nanovibrations.

The adoption of dynamic mechanomodulation to regulate cellular behavior is an alternative to the use of chemical drugs, allowing spatiotemporal control. However, cell-selective targeting of mechanical stimuli is challenging due to the lack of strategies with which to convert macroscopic mechanical movements to different cellular responses. Here, we designed a nanoscale vibrating surface that controls cell behavior via selective repetitive cell deformation based on a poroelastic cell model. The vibrating indentations induce repetitive water redistribution in the cells with water redistribution rates faster than the vibrating rate; however, in the opposite case, cells perceive the vibrations as a one-time stimulus. The selective regulation of cell-cell adhesion through adjusting the frequency of nanovibration was demonstrated by suppression of cadherin expression in smooth muscle cells (fast water redistribution rate) with no change in vascular endothelial cells (slow water redistribution rate). This technique may provide a new strategy for cell-type-specific mechanical stimulation.

Finite element analysis of the influence of cyclic strain on cells anchored to substrates with varying properties.

The response of cytoskeleton to mechanical cues plays a pivotal role in understanding several aspects of cellular growth, migration, and cell-cell and cell-matrix interactions under normal and diseased conditions. Finite element analysis (FEA) has become a powerful computational technique to study the response of cytoskeleton in the maintenance of overall cellular mechanics. With the revelation of role of external mechanical microenvironment on cell mechanics, FEA models have also been developed to simulate the effect of substrate stiffness on the mechanical properties of cancer cells. However, the models developed so far model cellular response under static mode, whereas in physiological condition, cells always experience dynamic loading conditions. To develop a more accurate model of cell-extracellular matrix (ECM) interactions, this paper models the cytoskeleton and other parts of the cell by beam and solid elements respectively, assuming spherical morphology of the cell. The stiffness and roughness of extracellular matrix were varied. Furthermore, static and dynamic sinusoidal loads were applied through a flat plate indenter on the cell along with providing sinusoidal strain at the substrate. It is observed that due to axial loading, cell reaches a plastic region, and when the sinusoidal loading is added to the axial load, the cell experiences permanent deformation. Degradation of the cytoskeleton elements and a physiologically more relevant spherical cap shape of the cell were also considered during the analysis. This study suggests that asperity topology of the substrate and indirect cyclic load can play a significant role in the shape alterations and motion of a cell.

In situ deformation of growth plate chondrocytes in stress-controlled static vs dynamic compression.

Longitudinal bone growth in children/adolescents occurs through endochondral ossification at growth plates and is influenced by mechanical loading, where increased compression decreases growth (i.e., Hueter-Volkmann Law). Past in vivo studies on static vs dynamic compression of growth plates indicate that factors modulating growth rate might lie at the cellular level. Here, in situ viscoelastic deformation of hypertrophic chondrocytes in growth plate explants undergoing stress-controlled static vs dynamic loading conditions was investigated. Growth plate explants from the proximal tibia of pre-pubertal rats were subjected to static vs dynamic stress-controlled mechanical tests. Stained hypertrophic chondrocytes were tracked before and after mechanical testing with a confocal microscope to derive volumetric, axial and lateral cellular strains. Axial strain in hypertrophic chondrocytes was similar for all groups, supporting the mean applied compressive stress's correlation with bone growth rate and hypertrophic chondrocyte height in past studies. However, static conditions resulted in significantly higher lateral (p<0.001) and volumetric cellular strains (p≤0.015) than dynamic conditions, presumably due to the growth plate's viscoelastic nature. Sustained compression in stress-controlled static loading results in continued time-dependent cellular deformation; conversely, dynamic groups have less volumetric strain because the cyclically varying stress limits time-dependent deformation. Furthermore, high frequency dynamic tests showed significantly lower volumetric strain (p=0.002) than low frequency conditions. Mechanical loading protocols could be translated into treatments to correct or halt progression of bone deformities in children/adolescents. Mimicking physiological stress-controlled dynamic conditions may have beneficial effects at the cellular level as dynamic tests are associated with limited lateral and volumetric cellular deformation.