2.1.

Magnetomotive Optical Coherence Tomography Setup

All experiments were carried out with a self-developed spectral-domain OCT system operating at 880 nm, which is described in more detail elsewhere.¹⁹ In brief, the system is equipped with a superluminescent diode (Exalos EXS8810-2411, Switzerland) with a center wavelength of 876 nm and a bandwidth of 64 nm full width at half maximum. Interference spectra are generated in a separate fiber-coupled OCT scanning unit containing a Michelson interferometer and are subsequently detected using a linear-in-wavenumber spectrometer and a charge-coupled device (CCD) line scan sensor (Teledyne DALSA IL–C6–2048C, Canada) with a high dynamic range of 80 dB. The CCD line acquisition rate has a fixed value of 11.9 kHz, which is defined by the custom-made readout electronics. Each acquired line scan, i.e., interference spectrum, is converted into an axial depth scan (A-scan) giving the reflectance profile of the sample. Typically, a series of 480 adjacent A-scans are then laterally combined to create a cross-sectional tomographic image (B-scan). The OCT system provides an axial resolution of $6\mu \mathrm{m}$ in air, an optical imaging depth of 3 mm, and a sensitivity of $-102\mathrm{dB}$.

In order to generate a magnetic field for magnetomotive imaging, an electromagnet (Intertec Components ITS-MS 5030 12 VDC, Germany) was integrated into the OCT scanning unit. The optics of the scanning unit was partially incorporated into a center bore of the solenoid’s ferromagnetic core in order to optimize working distance. To maximize the amount of core material and thus the magnetic field, a small bore size was chosen suitable to bear 0.25-in. optics. In summary, this MM-OCT probe has a working distance of 6 mm measured from the solenoid surface, an imaging numerical aperture (NA) of 0.1, and a field of view of 1.5 mm in diameter in the focal plane.

The solenoid coil (18.5 Ω) is driven in a pulsed operation mode as proposed by Koo et al.¹¹ by a self-developed capacitive-discharge pulse generator that is synchronized to the OCT system. To that, a power capacitor (Vishay BCcomponents MAL210222472E3) of 4.2 mF is charged by a dc power supply with up to 120 V. Once the charging is completed, the capacitor is grounded using an insulated-gate bipolar transistor switch (IXYS Corporation IXGH48N60C3), and the resulting high discharge current is conducted through the coil. As shown in Figs. 1(a) and 1(b), a peak current of 5.7 A was obtained with this setup, which resulted in a maximum magnetic flux density of 0.2 T (measured with Magnetometer KOSHAVA 5, Wuntronic GmbH, Germany) and an axial field gradient of $18\mathrm{T}/\mathrm{m}$ at a working distance of 6 mm. The magnetic pulse length related to the 90% level of the pulse maximum was measured to be 33 ms, which is in the range of the B-scan period (40 ms) of the OCT system. Typically, the magnetic field is switched on for 80 ms, (two B-scans), as depicted in Fig. 1(a), with a repetition rate of 1 Hz. During the pulse, the magnetic flux density peaks within 10 ms after current onset and falls off to approximately 71% of its maximum value at current shut-down. The corresponding time period of 0.92 s between adjacent pulses is thereby used to recharge the capacitor. Due to this relatively small duty cycle of 8%, no additional cooling of the solenoid is required.

Fig. 1

Pulsed magnetic field and magnetic nanoparticles: (a) Current pulse using a capacitor charging voltage of 120 V and resulting magnetic flux density measured 10 mm above the solenoid’s surface. (b) Peak magnetic flux density versus axial distance from solenoid. (c) Electron microscopy image and (d) magnetization curve of the applied magnetic nanoparticles.

2.2.

Magnetic Nanoparticles and Magnetic Forces

For the magnetic labeling of cells, commercially available nanoparticles (nano-screenMAG/R-DXS, chemicell, Germany) were used. These particles exhibit a distinct core-shell structure, where the core is formed through the agglomeration of magnetite (${\mathrm{Fe}}_3{\mathrm{O}}_4$) primary particles with sizes in the range of 8 to 12 nm. Each core is surrounded by a fluorescent shell and a coating of dextran sulfate for biomolecule coupling. The hydrodynamic diameter of the particles amounts to 200 nm, while the core size is roughly 170 nm (personal communication with manufacturer). The fluorescence excitation and emission maximum of the selected nanoparticles were in the green and red visible spectral ranges ($578\mathrm{nm}/613\mathrm{nm}$), respectively.

The particle structure and morphology were characterized by means of transmission electron microscopy (TEM) using a FEI Tecnai 20 microscope with a thermal ${\mathrm{LaB}}_6$ emitter at an accelerating voltage of 200 kV. Our structural investigations confirmed the information provided by the manufacturer. As an example, a TEM overview image of the particles dispersed on an amorphous carbon support film is shown in Fig. 1(c).

The magnetic properties of the particles were measured by vibrating sample magnetometry using a physical property measurement system (PPMS, Quantum Design). The magnetization curve shown in Fig. 1(d) was obtained from a macroscopic ensemble of particles at room temperature in a magnetic field of up to 3 T. The magnetization loop is hysteretic with coercive fields of roughly 20 mT and a slow approach to saturation below 1 T. This reveals that the particles are ferromagnetically blocked, which is consistent with the size of the magnetic core. While individual magnetite particles are expected to be superparamagnetic at sizes below 26 nm, the agglomeration of primary particles to a larger magnetic entity (with a diameter of 170 nm) leads to an increase of the superparamagnetic blocking temperature to beyond their Curie temperature. Hence, the particles respond as “normal” blocked ferromagnets.

In order to obtain a large magnetomotive effect that can be detected with sufficient signal-to-noise ratio, a high magnetic force is desired. To illustrate the fundamental relation between the magnetic field and the force, we approximate the slightly ferromagnetic particles (small hysteresis and low remanent magnetization) by paramagnets. Hence, the magnetic force $F_z$ that attracts the particles at location $r$ in the axial direction ($z$-direction) toward the solenoid can be expressed by Eq. (1):

Hence, in this nonsaturation regime, $F_z$ can be enhanced relatively easily, since a twofold increase of the solenoid current, i.e., magnetic flux density, would result in a fourfold magnetic force.

In saturation, however, the particle magnetization ${\chi }_p$ $B/{\mu }_0$ in Eq. (1) becomes a constant value, which cannot be further increased by the magnetic field. Hence, neglecting the small magnetization of the diamagnetic medium, the magnetic force increases only with $\partial B/\partial z$, i.e., $F_z$ scales with $B$ to the power of 1:

As it can be seen in the magnetization curve in Fig. 1(d), saturation of the particles is already beginning at approximately 0.1 T, whereas the maximum flux density delivered by the solenoid was measured to be 0.2 T in the sample region. Therefore, we assume that further increase of the flux density would have only a reduced effect on the magnetic force due to operation in the saturation regime. Moreover, the generation of stronger magnetic fields is technically challenging since the solenoid’s efficiency significantly degrades at higher currents due to the limited permeability (saturation) of the ferromagnetic core. Considering these facts and taking into account that the present field parameters ($B=0.2\mathrm{T}$ and $\partial B/\partial z=18\mathrm{T}/\mathrm{m}$) are slightly above the values reported for in vivo MM-OCT studies,²⁰ no additional efforts were made to further increase the magnetic field.

2.3.

Light Microscopy and Laser Speckle Reflectometry

In order to investigate the MM-OCT signal in dependency of the cellular magnetic particle content, combined OCT and light microscopy imaging of identical cells are necessary. Therefore, we integrated the MM-OCT probe into a conventional epi-fluorescence microscope (Leica DMRB, Germany) by replacing the microscope’s condenser unit. As shown in Fig. 2, the OCT scanning unit was positioned upside-down in a way that the distal end of the probe with the solenoid and the OCT objective lens is placed directly underneath the object stage of the microscope. With this setup, it is possible to image the same cells with both two-dimensional (2-D) light microscopy (bright-field/multicolor fluorescence) and 3-D OCT in an upright and an inverted configuration, respectively.

Fig. 2

Setup for combined magnetomotive optical coherence tomography (MM-OCT), laser speckle reflectometry, and light microscopy. The microscope is equipped with a halogen lamp for bright-field transmission imaging and a mercury-vapor lamp (not shown) for epifluorescence imaging. The inset shows a detailed view of the sample region and the OCT scanning unit with attached electromagnet. Abbreviations: BS—beam splitter, C—collimator, CL—condensing lens, DC—dispersion compensation, DM—Vis/NIR dichroic mirror, GS—galvanometer scanners, RL—reference lens, RM—reference mirror, SL—scanning lens, and SMF—single-mode fiber.

In addition to MM-OCT and light microscopy, we use laser speckle reflectometry as a 2-D reference modality to investigate sample motion.²¹ To that, the sample was illuminated in a dark-field manner by a collimated laser beam at 638 nm, which was generated by a fiber-coupled laser diode with 1 mW output power (Lasiris PTL-500-635-1-2.0, Coherent Canada) and a fiber collimator (Fig. 2). The collimator was mounted on a post next to the microscope using tip/tilt kinematics to adjust the laser beam to the microscope’s field of view. The diameter of the collimated beam was approximately 4 mm and the incident angle between the laser beam and the sample surface was approximately 35 deg. Due to the spatial coherence of the illuminating laser, a speckle pattern is created throughout the observed sample, which was detected using the microscope’s video camera (1.3 megapixel monochrome CMOS, Sumix SMX-M71M). The speckle pattern depends on the distribution and distance of single scatterers relative to each other. Hence, local distance changes due to moving scatterers result in an altered speckle pattern in the area around the magnetic nanoparticles. Therefore, motion contrast with subwavelength sensitivity can be achieved by calculating the intensity variance of the raw speckle images over time.

2.4.

Signal Processing

To retrieve magnetomotive contrast from the acquired image data, the following signal processing was applied. In laser speckle reflectometry, raw speckle images were recorded in the presence of the pulsed magnetic field and the laser speckle variance (LSV) ${\sigma }_{\mathrm{LS}}^2$ was calculated in a sliding window manner over five adjacent video frames, as indicated in Eq. (4):

Magnetomotive contrast in OCT was obtained similar to laser speckle reflectometry by OCT speckle variance analysis. To that, the variance ${\sigma }_{\mathrm{OCT}}^2$ of the OCT signal amplitude in linear scale was calculated over five adjacent B-scans, as indicated in Eq. (5):

Moreover, phase-resolved Doppler OCT²² was applied to estimate the magnitude of particle motion. To that, the Doppler phase shift between OCT signals of adjacent B-scans (interframe Doppler OCT) was analyzed to retrieve the axial displacement of the sample in response to the magnetic pulse. The relation between the axial displacement $\mathrm{\Delta }z$ and the measured Doppler phase shift $\mathrm{\Delta }\phi$ is given by Eq. (7):

2.5.

Sample Preparation and Elasticity Estimation

Magnetic cell labeling and sample preparation for cell experiments were performed as follows: MSCs were seeded on a cell culture dish and cocultured with nanoparticle solution ($0.5\mathrm{mg}/\mathrm{ml}$) for 24 h. After rinsing with phosphate-buffered saline (PBS), adherent MSCs were detached from the dish using trypsin and resuspended in fresh cell culture medium. Finally, MSCs were embedded in tissue-mimicking scaffolds made of 1% agar, 49% PBS, and 50% cell culture medium, similar to the protocol proposed by Oldenburg et al.⁶ Molded agar-cell samples with a thickness of 3 to 4 mm were then created in 40-mm cell culture dishes and kept at resting conditions for solidification. Control samples with unlabeled cells were created identically, except that MSCs were not cocultured with magnetic nanoparticles. In terms of cellular particle concentration and its effect on cell function, recent literature indicates that MSCs incubated with 200-nm magnetic particles coated with dextran sulfate take up $\sim 10\mathrm{pg}$ of iron oxide per cell and show a cell viability of $\sim 70\%$ after 24 h.²³

To estimate the elasticity of the agar scaffold, we applied the principles of contact mechanics. To that, a small steel ball (diameter: 3.16 mm and weight: 130 mg) was placed on top of a thick 1% agar sample, which led to an indentation of the elastic surface at the contact point. Following the Hertz model in Eq. (8)