1. Introduction

In compression optical coherence elastography (OCE), a quasi-static compressive mechanical load is applied to the sample surface and the resulting deformation is measured using optical coherence tomography (OCT) [1,2]. Local axial strain is then estimated as the axial gradient of displacement over a finite depth in the sample at each pixel in the imaging field-of-view [3], enabling the formation of two-dimensional (2-D) or three-dimensional (3-D) images, referred to as strain elastograms [4,5]. Under the assumption of uniform stress throughout the sample, strain is inversely related to elasticity [3]. However, strain is a qualitative measure of elasticity, which makes it challenging to track elasticity over time and, also, to compare elasticity between different samples [6–8]. Therefore, it is advantageous to perform quantitative elasticity imaging, which further requires the estimation of sample stress.

A range of techniques have been proposed to quantify the stress induced from mechanical loading in compression OCE [9,10]. For example, Quince et al. evaluated the mechanical properties of soft contact lens materials by employing OCT to measure the bulk strain of the contact lens and a load cell to estimate the applied bulk stress [11]. Cabeza-Gil et al. also characterized the mechanical properties of ex vivo porcine lenses using compression OCE implemented with a load cell to measure the applied force and solving the inverse problem using finite element analysis [12]. In other studies, Qiu et al. incorporated a Fabry-Perot force sensor at the tip of an OCE probe and simultaneously measured both the probe and sample deformation using spatial division multiplexing for in situ elasticity measurements [9,13]. Separately, Wang et al. mounted a circular glass window connected to a metal ring through elastic spokes at the tip of a handheld quantitative compression OCE probe [14]. Then, the applied force was measured as a function of window displacement using OCT. In another study, Yao et al. designed a loading apparatus that used a water sink to preload the sample, and estimated the applied force by controlling the volume of each water droplet on the sample [15].

Preceding each of these studies, Kennedy et al. used a pre-characterized compliant silicone layer placed between the sample and the imaging window to quantify the axial compressive stress at the sample surface in a technique referred to as optical palpation [16]. The local axial stress corresponding to the layer axial strain was estimated from the stress-strain curve of the layer material, which was characterized using an independent uniaxial compression testing system [16]. Unlike the other proposed techniques that measure a single value of stress and assume that stress is laterally uniform [13–15], optical palpation provides a 2-D map of surface stress by estimating the local axial stress at each lateral position [17]. Kennedy et al. further combined optical palpation with 3-D axial strain in the sample, in a technique referred to as quantitative micro-elastography (QME) [18]. Assuming that stress is uniaxial in depth, 3-D local elasticity can be estimated from the ratio of local axial stress to local axial strain [18]. To maximize the imaging depth in the sample, a thinner compliant layer between 0.25 mm to 0.5 mm is normally used, with a diameter matching that of the sample. It is also recommended to match the mechanical properties of the compliant layer and the sample as closely as possible, at least within an order of magnitude, to obtain measurable deformation in both the layer and the sample using OCT [18]. QME has shown promise in many applications, most notably in breast tumor margin assessment [19,20] and mechanobiology [21–23]. Separately, a related technique that performs 2-D elasticity imaging at a series of pre-strains has also been proposed [24–26].

A challenge in QME, and related techniques, is that the stress-strain relationship of the compliant layer is not characterized under QME experimental conditions, rather, it is characterized independently using uniaxial compression testing [18], in which a phantom comprising the material of the compliant layer, is placed between two rigid metal plates that are adjusted to deform the phantom. Strain is then measured by recording the position of the plates, and the corresponding stress is estimated using a load cell and the phantom cross-sectional area, allowing the bulk elasticity of the phantom to be determined [18,27]. Axial deformation in incompressible materials, such as silicone, is accompanied by lateral expansion to conserve volume. However, friction at the contact boundaries restricts the lateral expansion of the phantom. Therefore, to minimize friction at the boundaries, and its resulting impact on the measured stress-strain relationship, a cylindrical phantom with equal diameter and height (i.e., an aspect ratio of 1:1) is typically used [28,29]. The interfaces between the phantom and the rigid plates are also lubricated with silicone oil to further reduce the impact of friction. To address the discrepancy in the stress-strain characterization between uniaxial compression testing and the QME setup, the dimensions of the characterized phantom using uniaxial compression testing can be matched with the dimensions of the compliant layer in the QME experiment. However, the friction imposed by two metal plates in uniaxial compression testing is very different to that imposed by tissue and a glass imaging window in QME [3]. Whilst it has been demonstrated that accurate elasticity estimation can be achieved using lubrication, the efficacy of lubrication is dependent on several variables, including the lubricant viscosity, the mechanical contrast between the compliant layer and the sample, and both the magnitude of the pre-strain and the time following its application [30]. Another possibility is to use a more sophisticated computational model based on finite element methods (FEM) [31]. Whilst this approach holds promise, the friction coefficients must be known, which is challenging in practice, particularly for the spatially and temporally varying friction commonly found in experiment [30]. Our group has also previously implemented iterative solutions to the inverse problem of elasticity using a compliant layer with known elasticity to provide a reference elasticity used to scale elasticity measured in the sample [32,33]. In another approach, by employing inverse methods, elasticity can be directly measured without using a compliant layer [34,35]. Importantly, in all cases, iterative solutions to the inverse problem require substantial computational resources, which limit the potential for eventual translation of OCE to clinical applications. This can be restrictive in time-sensitive applications of QME such as breast conserving surgery where live screening or immediate response is required [36].

Ideally, the stress-strain relationship of the compliant layer would be characterized on the same layer, and in conditions identical to those present in the QME experiment. This is currently not practical, as uniaxial compression testing characterizes either the bulk behavior of the compliant layer, or the combined behavior of the compliant layer and the sample. As a result, the characterized stress-strain relationship of the material often does not correspond to the layer behavior in QME, leading to inaccurate elasticity estimation [30].

In this study, we propose in situ stress estimation by characterizing the layer stress-strain response in the QME experiment itself. To achieve this, we integrate OCT-based compression testing into the existing QME setup to measure in situ stress in the QME experiments, to develop a distinct technique that we term in situ QME. By combining the OCT-measured axial strain with the axial stress measured using a load cell, for the first time, we generate in situ stress-strain curves of the compliant layer during a QME experiment. Importantly, this approach reduces the need to apply lubrication between the contact interfaces (i.e., window-layer, layer-sample, and sample-rigid plate), simplifying the experimental procedure and increasing its robustness. Using in situ stress estimation, we demonstrate improved elasticity accuracy with <10% error compared to uniaxial compression testing in both lubricated and unlubricated conditions, an improvement by as much as 78% compared to existing QME with no lubrication. We then demonstrated our novel in situ QME method in the context of cell mechanobiology by imaging cells and spheroids embedded in gelatin methacryloyl (GelMA) hydrogels, demonstrating improved accuracy in the elasticity estimation of cancer spheroids and GelMA hydrogels.

2. Methods

2.1 OCT-based compression testing setup

Figure 1 shows a schematic diagram of OCT-based compression testing in which the upper stationary rigid plate in the uniaxial compression testing setup comprises an imaging window through which an optical beam illuminates the sample for OCT imaging. We used a fiber-based spectral-domain OCT system (Telesto III, Thorlabs Inc., USA). The light source is a superluminescent diode with a central wavelength of 1300 nm and a spectral bandwidth of 170 nm. The measured OCT axial resolution in air is 4.8 µm (full width at half maximum (FWHM)). The OCT system was set up in a common-path configuration, where the interface between the imaging window and the layer acted as the reference reflector [37]. The objective scan lens (LMS03, Thorlabs Inc., USA) has a numerical aperture of 0.06, and a working distance of 25.1 mm, with a measured FWHM lateral resolution of 7.2 µm.

 

Fig. 1. Schematic diagram of OCT-based compression testing system integrated with QME setup. SLD: superluminescent diode, Amp: amplifier, WG: waveform generator, SL: scan lens, RA: ring actuator, IW: imaging window, CL: compliant layer, S: sample, RP: rigid plate, TS: translation stage, LC: load cell.

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OCT-based compression testing was used to characterize the stress-strain relationship of the compliant layer in two scenarios. Firstly, the compliant layer was placed between the imaging window and the rigid plate to understand how the stress-strain relationship of the compliant layer is affected by friction. Secondly, the compliant layer was placed between the imaging window and a phantom, replicating the conditions present in QME experiments (such as in Fig. 1). For the results presented in Sections 3.1 and 3.2, OCT volumes comprising 1,000 A-scans per B-scan and 1,000 B-scans per volume were acquired over a 4 mm × 4 mm lateral area at intervals of 2% strain from 0 to 20%. Note that 0% strain corresponds to the position where the sample is determined to be under minimal loading, i.e., at the point where contact is made across the sample surface. Importantly, the change in compliant layer thickness in OCT-based compression testing is measured from OCT images rather than from the position of the translation stage in uniaxial compression testing. Stress at each loading position was recorded using a load cell, similar to that used in uniaxial compression testing.

2.2 QME system setup

QME measurements were performed using the same OCT system as used for OCT-based compression testing. To generate an elastogram, the sample with the compliant layer on top is placed between a rigid plate and an imaging window through which the beam illuminates the sample. The imaging window is connected to a piezoelectric actuator that applies quasi-static micro-scale compression to the layer and sample operating at a frequency of 10 Hz. The rigid plate is attached to a translation stage, providing a means to control the deformation introduced to the layer-sample system. In all the experiments a consistent loading speed of 0.1 mm/s was implemented to minimize the effect of strain rate on elasticity measurement. The axial displacement in the layer and the sample resulting from micro-scale compression is measured using phase-sensitive detection [38]. The local axial strain is estimated as the gradient of axial displacement with depth using weighted least squares linear regression, over a fitting range of 100 µm [39,40].

Using the axial strain in the compliant layer at each lateral position and the pre-characterized stress-strain curve of the layer, we are able to estimate the axial stress applied at the sample surface. Further, the compliant layer and the sample can be considered as a one-dimensional (1-D) spring system connected in series [41]. Thereby, the axial stress applied at the sample surface can be assumed to be uniaxial and uniform throughout the sample. In this work, consistent with most other compression elastography techniques, several assumptions are made to simplify the mechanical model to measure the elasticity of the sample. For instance, it is assumed that the sample is incompressible and exhibits isocsetropic, homogeneous, and linear elastic mechanical properties. Using these assumptions, the elasticity, or equivalently, Young’s modulus under the assumption of linear elasticity, can be determined at each position in the sample from the ratio of the axial stress to the axial strain within the sample [18].

2.3 In situ QME system setup

Combining OCT-based compression testing with the QME system setup enables in situ stress estimation of the compliant layer during the experiment. The compression procedure in in situ QME is conducted using the same method employed in existing QME experiments where the imaging window, connected to the piezoelectric actuator, applies a micro-scale compression to the layer and sample following the pre-strain. However, unlike existing QME, which estimates the applied stress using the pre-characterized stress-strain curve of the layer, in situ QME characterizes only the part of stress-strain curve of the layer at the applied pre-strain, providing more precise bulk elasticity of the compliant layer in the experiment. The applied bulk stress is measured using the integrated load cell, accounting for the compliant layer’s boundary conditions. The layer bulk strain resulting from the compression applied by the translation stage is measured using OCT. The bulk elasticity of the compliant layer is calculated by dividing the bulk stress by the bulk strain. The estimated layer elasticity is then employed to compute the local stress within the compliant layer, achieved by multiplying it by the corresponding local strain [18]. As mentioned above, by assuming a uniaxial stress throughout the sample, the elasticity of the sample is estimated by dividing the local stress in the layer by the local strain in the sample.

For the data presented in Sections 3.3, 3.4 and 3.5, OCT volumes comprising 1,000 A-scans per B-scan and 100 B-scans per volume were acquired over a lateral area of 2 mm × 0.2 mm in the center of the sample for strains ranging from 3–25%. Similarly, for the results shown in Section 3.5, for GelMA samples with cells and spheroids, OCT data were acquired in a similar manner, with the exception that 1,000 B-scans were acquired per volume over a lateral distance of 2 mm.

2.4 Phantom and compliant layer fabrication

To demonstrate the impact of aspect ratio on the measured stress-strain curve of the material (Section 3.1; Fig. 2(a)), two cylindrical phantoms were fabricated from a two-part, vulcanizing silicone elastomer, Elastosil P7676 (Wacker, Germany). The first had a diameter of 10 mm and a height of 10 mm (aspect ratio of 1:1) and the second had a diameter of 10 mm and a height of 500 µm (aspect ratio of 20:1). The elasticity measured using uniaxial compression testing of the phantom with an aspect ratio of 1:1 at 10% strain was 19 kPa. Two different silicone phantoms (Phantom 1 and 2, respectively) were also fabricated with thicknesses of ∼3 mm and diameters of 6 mm (Section 3.1; Fig. 2(b)). The elasticity of Phantom 1 was 19 kPa, and Phantom 2 was ∼970 kPa at 10% strain.

To investigate the effect of sample elasticity on the stress-strain curve of the compliant layer using uniaxial compression testing (Section 3.2; Fig. 3(b)), three cylindrical phantoms with different elasticity were fabricated. Each phantom was fabricated by varying the mixing ratio between the liquid cross-linker, catalyst, and the amount of polydimethylsiloxane (PDMS) silicone oil (AK50, Wacker, Germany), and each phantom had a thickness of 3 mm and diameter of 6 mm. The elasticity of Phantoms 1, 2, and 3 measured from uniaxial compression tests on cylindrical phantoms with an aspect ratio of 1:1 at 10% strain were 970 kPa, 204 kPa, and 78 kPa, respectively. To increase optical scattering and, therefore, OCT signal-to-noise ratio (SNR), titanium dioxide particles were evenly mixed into the silicone at a concentration of 2 mg/ml. A transparent cylindrical compliant layer of thickness 500 µm was fabricated from Elastosil P7676 with a diameter of 6 mm.

To perform in situ QME measurements (Sections 3.2 and 3.3), four cylindrical phantoms of different elasticity were fabricated using various combinations of Silpuran 2400 (Wacker, Germany) and AK50 silicone oil. These phantoms had measured elasticities of 47.6 kPa, 84.2 kPa, 139.6 kPa, and 181.2 kPa at 10% strain. Each phantom was ∼3 mm thick and had a diameter of 6 mm.

2.5 Cell-laden GelMA hydrogel fabrication

GelMA hydrogels used to encapsulate cells were synthesized by the methacrylation of gelatin, as previously described [42]. Precursor GelMA solution with 6% weight-to-volume ratio was prepared 24 hours in advance by dissolving lyophilized GelMA in phosphate-buffered saline (PBS; pH7.4, Gibco) at 37°C and adding 0.1% weight-to-volume Irgacure-2959 (Sigma-Aldrich) dissolved in ethanol. The GelMA solution was then stored at 4°C overnight and was reheated at 37°C for an hour before use. A concentration of 3% volume poly-methyl methacrylate (PMMA) beads were also added to the GelMA to increase optical scattering. To fabricate blank circular GelMA hydrogels of 500 µm height and 6 mm diameter, 3-D printed acrylic molds attached to a coverslip were lubricated with dichlorodimethylsilane (DCDMS; Sigma-Aldrich). Coverslips were functionalized with 3-(trimethoxysilyl) propyl methacrylate (0.5% v/v) for 5 minutes, then were transferred to 20 ml of 100% ethanol for 5 minutes and then left to air dry in a fume hood at room temperature. The previously prepared 6% w/v GelMA solution was then pipetted into the mold and covered with a methacrylated coverslip. The blank hydrogels were then polymerized using UV light (365 nm, 3.51 mW.cm^-2) for 195 seconds.

For cell encapsulation, MCF7 cells were resuspended in GelMA solution (10,000 MCF7 cells per hydrogel). The cell-laden GelMA was pipetted on a DCDMS glass slide and covered with a methacrylated coverslip. Cell-laden GelMA was exposed to ultra-violet (UV) light for 90 seconds. After polymerization, the molds were removed, and the hydrogels were immersed in culture media containing high glucose Dulbecco’s Modified Eagle Medium (hg-DMEM; Gibco), 10% fetal bovine serum (FBS) and 1% antibiotics/antimycotics and incubated at 37°C and 5% CO₂ until QME scanning was conducted. For uniaxial compression testing, 3 mm thick blank GelMA hydrogels with a 3 mm diameter were fabricated by casting in a negative mold made of a flexible silicone. A certain volume (24 µl) of GelMA solution was added to mold cavities and photo-crosslinked using a UV transilluminator for 225 seconds (3.27 mW.cm^-2). Following photo-crosslinking, the mold was removed from around the hydrogels, then the hydrogels were detached from the coverslip and immersed in culture media. The hydrogels were incubated at 37°C and 5% CO₂ until compression testing was performed.

3. Results

3.1 Impact of aspect ratio on the measured stress-strain curve

To demonstrate the effect of aspect ratio on the measured stress-strain curve using uniaxial compression testing, experiments were performed on two silicone phantoms, made from the same material comprising the compliant layer (Elastosil P7676), with a diameter of 10 mm and thickness of 500 µm and 10 mm, respectively. In each setup, the interfaces between the phantoms and rigid plates were lubricated with AK50 silicone oil. Figure 2(a) shows the characterized stress-strain curves of both phantoms. Since the effect of friction on the stress-strain response varies, despite being fabricated from the same material, the phantoms clearly exhibit different stress-strain relationships. The lateral expansion of the thin phantom was restricted by friction to a greater degree, resulting in a larger stress being required to compress the phantom to an equivalent axial strain, corresponding to a steeper gradient in the stress-strain curve when compared to the thicker phantom.

 

Fig. 2. (a) Characterized stress-strain curves of the material comprising the compliant layer with aspect ratios (diameter: height) of 1:1 (Blue) and 20:1 (Green), respectively. (b) Corresponding elasticity estimated using QME versus expected elasticity from uniaxial compression testing. Diamonds represent Phantom 1, and the circles represent Phantom 2. Error bars indicate the standard deviation of elasticity in the specific ROIs.

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To assess the effect of these different stress-strain curves on QME accuracy, experiments were performed on identical compliant layers placed on top of two different silicone phantoms (Phantoms 1 and 2, respectively). Phantom 1 had a similar elasticity to the compliant layer (19 kPa at 10% strain), whilst Phantom 2 had a higher elasticity of ∼970 kPa at 10% strain. Each curve from Fig. 2(a) was then used separately in QME processing to generate 3-D elasticity maps of both phantoms. Figure 2(b) shows the measured elasticity using QME (generated using both compliant layers) versus expected elasticity measured using uniaxial compression testing. In each case, the elasticity was measured in a 600 µm (lateral) × 150 µm (axial) region of interest (ROI). The solid line represents the ideal case, where the measured elasticity is equal to the expected value. Diamonds and circles represent the elasticity measurements for Phantom 1 and Phantom 2, respectively. An elasticity of 21.3 kPa was estimated for Phantom 1 at 10% pre-strain using the thick phantom curve (blue diamond), which is close to the expected value (19 kPa), corresponding to an error of ∼12%. In comparison, when the same data for Phantom 1 was processed with the thin phantom curve, there was a larger error of ∼240% between the expected elasticity (19 kPa) and the measured elasticity (64.6 kPa) (green diamond).

This analysis was repeated for Phantom 2, shown in Fig. 2(b) by circles. The percentage error for measured elasticity at 2% pre-strain using the thick phantom curve (blue circle) was 87% when compared to the uniaxial compression testing (59.7 kPa compared to 460.9 kPa), while the calculated error for elasticity using the thin phantom curve (green circle) was 18.2% (544.8 kPa compared to 460.9 kPa).

As the elasticity of the compliant layer and the softer phantom (Phantom 1) are similar, they behave as a uniform thick phantom between two rigid plates, therefore, more accurately representing the boundary conditions present in the thick layer stress-strain curve. Consequently, using the thick characterization curve leads to more accurate QME measurements for Phantom 1. On the other hand, the frictional conditions when the compliant layer was placed between the rigid imaging window and the stiffer phantom (Phantom 2) were similar to the friction conditions of the thin layer characterized between two rigid plates, as the elasticity of the phantom is sufficiently high that its deformation under compression is negligible. The similarity of these conditions resulted in higher QME accuracy for Phantom 2 when using the thin layer characterization curve. These results indicate that using a single stress-strain curve for the compliant layer when performing QME on phantoms with varying elasticity, is likely to cause errors in elasticity estimation. Moreover, we anticipate different behavior of the compliant layer when placed on top of samples with varying elasticities. Therefore, characterizing in situ stress-strain curves in conditions that match those found in QME experiments, i.e., when the compliant layer is placed on top of the phantom, may help to alleviate this problem.

3.2 In situ stress-strain curves

Prior to performing QME using in situ stress estimation, OCT-based compression testing was validated against uniaxial compression testing by simultaneously performing both techniques on a 500 µm compliant layer with lubricated interfaces. The layer was subjected to axial compression, and the applied stress was measured for both methods using a load cell. Axial strain in the layer was measured using each method, as described in Section 2.2. Figure 3(a) shows the stress-strain characterization curves measured for a compliant layer of elasticity 19 kPa using each technique. The two curves show close agreement, with a mean percentage error of 2.9%, which is less than the variation of the measurements of each curve at higher strains.

 

Fig. 3. (a) Validation of OCT-based compression testing against uniaxial compression testing. (b) In situ stress-strain curves of a compliant layer placed on top of three silicone phantoms with varying elasticity of 970 kPa (Phantom 1, blue curve), 204 kPa (Phantom 2, green curve), and 78 kPa (Phantom 3, orange curve) at 10% strain. (c) The intra-sample, and (d) inter-sample repeatability of in situ stress-strain measurements.

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OCT-based compression tests were then performed on three silicone phantoms (Phantoms 1, 2, and 3) with elasticity of 970 kPa, 204 kPa, and 78 kPa, respectively, where a compliant layer with thickness of 500 µm, diameter of 6 mm and elasticity of 19 kPa at 10% strain was placed on top of each phantom. The interfaces between the phantom and the layer, the phantom and the rigid bottom plate, and the layer and the upper plate were lubricated using AK50 oil. Figure 3(b) shows that the phantom elasticity significantly changes the stress-strain relationship of the compliant layer in response to compressive loading. Importantly, as silicone is nearly incompressible, for it to deform axially, it must be free to expand laterally. When the phantom has a higher elasticity, for a given compression, mechanical coupling between the layer and the phantom, causes reduced axial deformation, and consequently, reduced lateral expansion of the layer. This causes the compliant layer to exhibit higher elasticity when placed on phantoms of increased elasticity.

For Phantom 1, with the highest elasticity (970 kPa at 10% strain), mechanical coupling between the stiff phantom and the softer layer restricts the lateral expansion of the compliant layer. This makes the compliant layer appear artificially stiffer, with additional force required to axially compress the layer. As Phantom 2 has a lower elasticity compared to Phantom 1 (204 kPa compared to 970 kPa), the limitation imposed by friction is less for Phantom 1. As a result, the compliant layer undergoes relatively more lateral expansion when it is placed on Phantom 2 compared to Phantom 1, meaning that less force is required to axially compress the compliant layer. This phenomenon leads to a different stress-strain behavior of the compliant layer. Similarly, a different stress-strain curve was observed for the compliant layer on top of Phantom 3, which has the lowest elasticity (78 kPa).

In Figs. 3(c) and 3(d), we demonstrate the repeatability of in situ OCT-based compression testing. The intra-sample repeatability of the measurements was assessed by performing three OCT-based compression tests on a compliant layer-sample pair (Fig. 3(c)). Inter-sample repeatability was also evaluated by performing OCT-based compression tests on a compliant layer placed on top of three different phantoms fabricated under identical conditions (Fig. 3(d)). Intra-sample repeatability was assessed using percentage of standard deviation over mean stress at three different strains (5%, 10% and 20%) and was calculated to be 7.7%, 2.9% and 5.7%, respectively. This analysis was repeated to determine the inter-sample repeatability with mean errors of 2.8%, 4.3% and 3.7% at strains of 5%, 10% and 20%, respectively.

3.3 Validation of in situ stress estimation in QME

In situ QME was validated against existing QME using a phantom with elasticity of 47.6 kPa and a compliant layer with elasticity of 19 kPa. The interfaces between the phantom and the layer, the phantom and the rigid bottom plate, and the layer and the glass window were lubricated using AK50 oil before each pre-strain was applied. Elasticity measurements were conducted at 3%, 4%, and 5% total strain on the compliant layer and the phantom for both existing QME and in situ QME (Fig. 4).

 

Fig. 4. Validation of in situ QME against existing QME in the lubricated condition.

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At 3% total strain, the averaged phantom elasticity measurement in a 1 mm × 0.5 mm ROI was 44.3 kPa, while the in situ elasticity measurement was 45.8 kPa. The phantom elasticity characterized using uniaxial compression testing at this strain was 49.0 kPa. The percentage error between existing QME and the reference value was 9.7%, whereas the error for in situ QME was 6.6%.

The elasticity of the phantom at 4% strain was measured as 45.5 kPa and 50.1 kPa using existing QME and in situ QME, respectively, with percentage errors of 8.3% and 0.9%. The reference elasticity for the phantom at this strain is 49.7 kPa. For the phantom elasticity measurement at 5% strain, existing QME and in situ QME demonstrated accurate measurements with errors of 3.5% and 0.2%, respectively. The measured phantom elasticity using existing QME and in situ QME were 48.6 kPa and 50.5 kPa, respectively (the reference value is 50.3 kPa). These results indicate the ability of in situ QME to provide accurate elasticity measurements, demonstrating that in situ QME can outperform existing QME.

The increase in error observed in in situ QME measurements at lower strain values can be attributed to lower strain levels leading to lower stress magnitudes. This noise in the stress data extends into the calculation of elasticity, and ultimately resulting in larger discrepancy between the measured and expected elasticity. In other words, at lower strain levels, the mechanical response of the sample may approach the noise floor of the load cell, making it more challenging to accurately capture subtle changes in stress.

To minimize this issue and enhance the accuracy of in situ QME measurements, several strategies can be employed. One approach is to utilize load cells with higher sensitivities, allowing for more precise and reliable stress measurements across a wider range of strain values. Additionally, optimizing the experimental setup to minimize sources of noise, such as environmental vibrations or electronic interference, can reduce measurement error. By addressing these challenges and implementing appropriate measures to enhance sensitivity and reduce noise, the accuracy and reliability of in situ QME measurements can be significantly improved, particularly at lower strain values.

3.4 In situ QME

In situ QME was conducted separately on four silicone phantoms (Phantoms 1, 2, 3 and 4) with elasticities of 47.6 kPa, 84.2 kPa, 139.6 kPa, and 181.2 kPa, respectively. An identical compliant layer with elasticity of 19 kPa was placed on top of the phantoms in each experiment without lubricating the interfaces to eliminate the previously reported temporal effect of the lubricant on the accuracy of elasticity measurement [30]. Lubrication is often impractical as it depends on different parameters including the layer and sample mechanical properties, the viscosity of lubricant, the magnitude of applied pre-strain, and scanning time [3,30]. Accordingly, it can lead to reduced repeatability in QME measurements. Therefore, the ability to obtain accurate and repeatable elasticity measurements without lubrication represents a key advantage of in situ QME over the existing QME approach.

Figure 5 shows the measured elasticity of each phantom at 4%, 6%, 8%, and 10% total strains. For Phantom 1 elasticities were measured using in situ QME at the aforementioned strains, resulting in values of 43.9 kPa, 46.6 kPa, 50.5 kPa, and 50.8 kPa, respectively with error percentages of 13.8%, 11.3%, 11.7%, and 4.1%. When using existing QME, the elasticities were measured as 9.8 kPa, 9.8 kPa, 9.7 kPa, and 9.7 kPa for the same strains with higher percentage errors of 74.6%, 76.5%, 78.4%, and 79.9%, respectively.

 

Fig. 5. Elasticity measurement for the phantoms with elasticity of (a) 47.6 kPa, (b) 84.2 kPa, (c) 139.6 kPa, and (d) 181.2 kPa in an unlubricated experimental setup. The elasticity was calculated at four different total strains for each phantom. The blue and red bars are the elasticity measured using existing and in situ QME, respectively. The green curve in each diagram shows the characterized elasticity-strain curve of the phantom through uniaxial compression testing as the reference elasticity values. The green shaded areas represent the standard deviation.

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For the other three phantoms, in situ QME was also more accurate than existing QME. The mean percentage error of elasticity using in situ stress estimation was 6.4%, with the highest error being 17.3%, whereas the mean percentage error using existing QME was 85%. This improvement in the accuracy of QME is because in in situ stress estimation, the increased stress required to achieve a given strain under the frictional conditions of the unlubricated setup is accounted for in the stress estimation. Existing QME, on the other hand, uses an independently characterized stress-strain curve of the compliant layer to estimate the layer’s stress and consequently underestimates phantom elasticity.

3.5 Application of in situ QME in mechanobiology

One possible application of in situ QME is studying the elasticity of cells or spheroids embedded in biomaterials. As the boundary conditions of biomaterials in contact with the silicone compliant layer are likely to be different from those between a silicone phantom and a silicone compliant layer, to verify the capability of in situ stress estimation in mechanobiology, we first conducted QME on blank GelMA hydrogels. The elasticity was measured using both in situ QME and existing QME and the results were compared to the reference elasticity generated using uniaxial compression testing. First, uniaxial compression testing was performed on three identical blank GelMA hydrogels, each with a diameter and thickness of 3 mm (aspect ratio of 1:1) to determine a reference elasticity for the samples. The elasticity of the blank hydrogel at 10% strain was measured to be 1.9 kPa. Next, the elasticity of blank hydrogels was estimated for total strain of 10%, 15%, 20%, and 25% using both in situ QME and existing QME. A compliant silicone layer with elasticity of 2 kPa was used in these experiments and no lubrication was applied. Figure 6(a) presents the elasticity estimated using each method. The measured elasticity using in situ QME agreed well with that measured using uniaxial compression testing. For instance, at 15% strain, the estimated elasticity was 3.1 kPa using uniaxial compression testing and 3.3 kPa using in situ QME. The mean percentage error between the two methods was less than 10% for all strains, whilst the error between existing QME and uniaxial compression testing varied between 55% and 85%. Figures 6(b) and 6(c) show the elasticity maps of the blank hydrogel at 25% strain with mean elasticities of 1 kPa and 6.4 kPa, measured using existing QME and in situ QME, respectively, whilst uniaxial compression testing provided an estimated elasticity of 6.2 kPa at 25% strain.

 

Fig. 6. Blank GelMA elasticity measurements. (a) Validation of in situ QME. The elasticity of a blank GelMA hydrogel was calculated at four different strains. The blue and red bars are the elasticity measured by existing and in situ QME, respectively, and the green curve shows the characterized elasticity-strain curve of the hydrogel through uniaxial compression testing. The green shaded area represents the standard deviation. En face elasticity elastograms using (b) existing QME and (c) in situ QME. Scale bars represent 50 µm.

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Next, in order to evaluate the applicability of employing in situ QME for elasticity measurements of biomaterials with embedded cells, additional experiments were conducted to study surface stress. Importantly, as the load cell in the in situ QME setup only measures the bulk stress and is therefore unable to detect lateral stress variations at the interface between the compliant layer and sample, it is important to ensure the stress at this interface is laterally uniform. Therefore, we performed the existing QME measurements on blank GelMA hydrogels as well as GelMA hydrogels containing MCF7 cell spheroids to demonstrate the feasibility of uniform surface stress for the heterogeneous samples. These experiments were similar to those performed previously by our group [21]. In Fig. 7, the upper and middle panels show the OCT images in the xz (B-scan) and xy (en face) planes, respectively. Figures 7(a) and 7(d) display the OCT images of the blank GelMA hydrogel with corresponding uniform surface stress map indicated in Fig. 7(g). The bright features in the OCT images are the PMMA beads which were added to the GelMA hydrogels to increase optical scattering and improve the OCT SNR. Figures 7(b) and 7(e) show the OCT images of the GelMA hydrogel containing a lower concentration of cell spheroids. As these spheroids are relatively small and far from the sample surface, the corresponding surface stress map of this hydrogel is also uniform (Fig. 7(h)). The spheroid indicated with a red arrow in Figs. 7(c) and 7(f) corresponds to the region indicated with a red arrow in the surface stress map (Fig. 7(i)). Since the indicated spheroid in this sample is larger and closer to the top surface of the hydrogel, it has resulted in a non-uniform surface stress.

 

Fig. 7. Surface stress estimation of GelMA samples using existing QME. The upper and middle panels show OCT in the xz and xy planes for (a) blank GelMA, (b) and (c) GelMA hydrogels with embedded spheroids. Cross-sections in the OCT xy plane are represented by blue dashed squares. The bottom panel shows the uniform surface stress of (g) blank GelMA and (h) GelMA with embedded spheroids, and (i) non-uniform surface stress map of GelMA with embedded spheroids. Green arrows in (b), (e) and (h) demonstrate that the small spheroid does not affect the uniformity of the surface stress. Red arrows in (c), (f) and (i) demonstrate how the large spheroids cause non-uniform stress. Scale bars represent 200 µm.

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The comparison of stress maps in GelMA hydrogels with and without cell spheroids indicates that, in addition to blank GelMA hydrogels, the hydrogels with relatively small spheroids can also generate uniform surface stress maps, suggesting that by controlling the position and the size of the spheroids, the surface stress map can remain uniform and therefore may be suitable for in situ QME.

Following the experiments on the blank GelMA hydrogels presented in Fig. 6, and according to the results shown in Fig. 7, we proceeded to perform in situ QME on the GelMA hydrogels containing individual cells. Figures 8(a) and 8(d) show the OCT and axial strain images in the xy plane obtained using QME. Figures 8(b) and 8(c) show the surface stress maps of the hydrogel corresponding to the region where cells exhibit elevated elasticity, measured through existing QME (Fig. 8(e)) and in situ QME (Fig. 8(f)), respectively. Despite the non-uniform elasticity maps resulting from the presence of the cells, the surface stress maps exhibit uniformity. Indeed, a small variation in the stress map in the region adjacent to the cell is evident as indicated by the yellow arrow in Fig. 8(c), this variation, however, is of an order of magnitude less than the mean stress in the sample and is therefore negligible.

 

Fig. 8. Elasticity measurements of GelMA hydrogel with embedded MCF7 cells. (a) OCT, (b) existing QME and (c) in situ QME measurement of the surface stress of a region with individual cells with elevated elasticity, (d) axial strain, (e) existing QME elasticity measurement, and (f) in situ QME elasticity measurement. The arrows show an example cell embedded within the GelMA. Scale bars represent 50 µm.

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Furthermore, the estimated mean surface stress using in situ QME (2.1 Pa) is larger than the mean surface stress estimation using existing QME (1.4 Pa). As discussed in Section 3.4, existing QME uses the pre-characterized stress-strain curve to estimate the bulk stress in the compliant layer. The lower stress estimation of the existing QME leads to an underestimation of the sample elasticity (Fig. 8(e)) compared to in situ QME elasticity measurement (Fig. 8(f)). These results are consistent with the results in Section 3.4 for silicone samples in the non-lubricated experimental setup.

4. Discussion

We have introduced a novel method for in situ stress estimation in QME by integrating an OCT-based compression testing system with an existing QME setup. In QME, a pre-characterized compliant layer is typically used to estimate the local axial stress at the sample surface, which, together with sample strain, is used to map sample elasticity. However, the different friction conditions present when characterizing the compliant layer, compared to its use during QME experiments leads to inaccuracies in elasticity measurements. In in situ QME, we estimate the stress of the compliant layer and generate stress-strain curves during the QME experiment, allowing for more accurate estimation of elasticity in non-lubricated experimental setup, with 78.6% less error compared to the existing QME method.

In situ QME can potentially improve elasticity measurements in fields, such as mechanobiology and tissue engineering. Validation of in situ QME in mechanobiology showcases the applicability of this technique in studying and characterizing the mechanical properties of biomaterials, including GelMA hydrogels. We have shown that in situ QME can map elevated elasticity of cells within GelMA hydrogels more accurately than existing QME. Further improvements can also be implemented to demonstrate the capability of in situ QME on a subcellular scale. One possible approach is to integrate optical coherence microscopy (OCM) [43] into in situ QME setup to improve the accuracy of elasticity imaging of cell organelles and subcellular structures. OCM is capable of 3-D imaging of cells embedded in hydrogels with elasticity system resolution seven times higher than existing OCE methods. Using this mechano-microscopy system has the potential to provide the elasticity maps of subcellular features such as the nucleus and cytoplasm.

In tissue engineering studies, porous scaffolds are one of the important components which provide structural support for cell growth, where mechanical properties of the scaffolds control their suitability in supporting cell proliferation and tissue integration. Existing methods for assessing of the mechanical properties of porous scaffolds such as uniaxial compression testing, may result in inaccuracies and the failure of engineered tissue. In situ QME potentially can improve the assessment accuracy of mechanical properties of the porous scaffolds. Measuring the deformation of the porous scaffolds using OCT alongside in situ stress estimation during the experiments can determine the elasticity of the scaffolds more accurately. In other words, stress-strain curve of the scaffolds can be determined using OCT-based compression testing. For example, in a study conducted by Meng et al, [44] a digital camera was used to record the deformation of flexible tissue-engineered scaffolds under compression loading. Implementing OCT-based compression testing to measure the deformations instead of camera-based measurements could provide more accurate mechanical properties of the scaffolds to match those of native tissues, enhancing the success and efficacy of the scaffolds. In another study, Lin et al, [45] used tissue engineering scaffold-OCE technique to measure the in situ deformation of tissue engineering scaffolds aiming to visualize the differentiation of the cultured cells on them. While the method measures the deformation and the applied strain to the scaffolds, employing in situ QME can provide quantitative elasticity measurement of the scaffolds, offering a comprehensive understanding of the mechanical environment influencing cells on the scaffolds. The demonstrated accuracy and repeatability of in situ QME make it an improved method for assessing the mechanical properties of scaffolds in the development of engineered tissues.

Another aspect that can substantially improve in situ QME accuracy is using more advanced signal processing algorithms, such as FEM [31]. Implementing FEM in the QME processing could enhance the precision and reliability of our proposed approach, providing additional information about the mechanical behavior of the compliant layer and better describing the interactions between the samples and compliant layer.

Future research could also expand the in situ QME beyond linear elasticity to investigate the hyperelastic properties of soft tissues and biomaterials. Soft tissues and biomaterials typically demonstrate non-linear mechanical behaviors, meaning that their elasticity increases under higher strains [20,46,47]. Hyperelasticity builds upon linear elasticity by incorporating non-linear behavior, enabling accurate modeling of the materials experiencing significant strains [48]. Integrating hyperelastic models into in situ QME can provide an interesting future direction for investigating the non-linear elasticity of biological tissues under varying loading conditions, particularly given the improved temporal stability of in situ QME without lubricant.

One characteristic of in situ QME is that it requires uniform surface stress. Consequently, it may not be suitable for applications beyond cells and spheroids embedded in hydrogels, especially in scenarios where the interface between the compliant layer and the sample is not flat, as observed in heterogeneous tissues or samples with non-uniform surface topography. However, uniform surface stress maps resulting from the non-uniform elevated elasticities demonstrated here suggests that in situ QME could still be employed to provide more accurate in situ stress estimation for homogeneous regions of tissues with boundary conditions similar to those of complex tissues that present non-uniform stress [31]. Further research can also be conducted on incorporating in situ QME with tactile stress sensors [49] or ultrasonic arrays [50] for non-uniform elasticity imaging of the layer to enable the imaging of heterogeneous tissues. Additionally, using more generalized mechanical models can further improve in situ QME accuracy. These approaches may allow for more comprehensive understanding of the non-linear and anisotropic behavior of materials under various stress conditions, including material heterogeneity, viscoelasticity, and non-linear stress-strain relationships [51–53], leading to improved accuracy in estimating surface stress and elasticity.

5. Conclusion

In this paper, we introduced a new method to estimate in situ stress in QME, addressing some of the most prominent challenges regarding the friction conditions of the compliant layer in QME experiments. Considering that the different friction conditions in QME and compliant layer characterization play a crucial role in introducing inaccuracies to elasticity measurements, taking these conditions into account is of high importance. We showed that utilizing OCT-based uniaxial compression testing for in situ stress estimation, improved the accuracy of the elasticity measurements, and reduced errors by 78.6% when compared to existing QME in the non-lubricated experimental setup. Despite the current limitations of the proposed method in characterizing heterogeneous samples, the accuracy and repeatability of in situ QME demonstrated here has the potential to open new avenues and provide valuable insights into the characterization of the mechanical properties of biomaterials and cellular structures.