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1.
Figure 2

Figure 2. From: Resonant acoustic spectroscopy of soft tissues using embedded magnetomotive nanotransducers and optical coherence tomography.

Displacement waveform for an agarose cylinder at varying depths z inside the cylinder demonstrating global vibrations in response to a swept driving frequency. z positions were chosen within equally spaced intervals by selecting the position with the highest OCT signal amplitude, in order to minimize noise.

Amy L Oldenburg, et al. Phys Med Biol. ;55(4):1189-1201.
2.
Figure 6

Figure 6. From: Resonant acoustic spectroscopy of soft tissues using embedded magnetomotive nanotransducers and optical coherence tomography.

Young’s modulus is measured over 2 decades using MRAS in agarose cylinders of varying concentration. Moduli are plotted on a log–log plot and are fit to a phenomenological model (solid line, R2 = 0.9965). Error bars are derived from the half maxima of the resonant frequencies.

Amy L Oldenburg, et al. Phys Med Biol. ;55(4):1189-1201.
3.
Figure 4

Figure 4. From: Resonant acoustic spectroscopy of soft tissues using embedded magnetomotive nanotransducers and optical coherence tomography.

Complex resonance mode data from figure 3 are fit to Lorentzian curves (solid lines) according to equation (3) to determine the resonant frequencies ωn and damping factors γn. Data are shown for n = 1 and 2 (left and right columns, respectively).

Amy L Oldenburg, et al. Phys Med Biol. ;55(4):1189-1201.
4.
Figure 5

Figure 5. From: Resonant acoustic spectroscopy of soft tissues using embedded magnetomotive nanotransducers and optical coherence tomography.

Resonant frequencies in agarose cylinders as a function of their aspect ratio are consistent with the solution for longitudinal modes. Resonant frequency data for modes n = 1, …, 5 (where detectible) are plotted with theoretical curves by solving equation (2) using the best-fit Young’s modulus E = 57.1 kPa.

Amy L Oldenburg, et al. Phys Med Biol. ;55(4):1189-1201.
5.
Figure 3

Figure 3. From: Resonant acoustic spectroscopy of soft tissues using embedded magnetomotive nanotransducers and optical coherence tomography.

Resonance modes are observed in an agarose cylinder during swept-frequency excitation. Top: raw displacement data versus instantaneous driving frequency. Middle and bottom: computed amplitude and phase, respectively, of the mechanical spectral response Ĩ(ω). Four longitudinal resonance modes are indicated as n = 1, …, 4. As expected, the phase of Ĩ(ω) shifts from 0 (stress and strain in phase) below each resonance to π (stress and strain opposed) above each resonance.

Amy L Oldenburg, et al. Phys Med Biol. ;55(4):1189-1201.
6.
Figure 7

Figure 7. From: Resonant acoustic spectroscopy of soft tissues using embedded magnetomotive nanotransducers and optical coherence tomography.

Mechanical resonances with Q ≈ 3 are observed in a rat liver, and are used to measure its relative stiffening during formaldehyde fixation. The mechanical spectra of control liver (top panel) and fixing liver (middle and bottom panels) are plotted from 0 to 147 min after exposure to formaldehyde. Results indicate increasing resonant frequency in the fixing liver only, consistent with an increasing Young’s modulus.

Amy L Oldenburg, et al. Phys Med Biol. ;55(4):1189-1201.
7.
Figure 1

Figure 1. From: Resonant acoustic spectroscopy of soft tissues using embedded magnetomotive nanotransducers and optical coherence tomography.

Diagram of the OCE system and longitudinal modes in tissues. A high axial magnetic field gradient below the electromagnet induces a force on embedded magnetic nanoparticles (TEM shown in the inset) that is parallel with the OCT imaging beam. The resulting tissue displacement is detected as an optical phase shift with OCT. Mechanical resonant frequencies observed in cylindrical tissue phantoms correspond to longitudinal modes where the bottom surface is fixed under its own weight and the top surface is free.

Amy L Oldenburg, et al. Phys Med Biol. ;55(4):1189-1201.

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