1.

Introduction

The nondestructive characterization of engineered tissues has generated enormous interest recently. Frequently, tissue engineers are interested in monitoring the local microenvironment in an engineered tissue and assessing parameters, such as cell number, cell function, protein expression, and mechanical properties. Most current techniques that characterize these parameters are either destructive, require adding (often expensive) labels to the sample, or making macroscopic measurements with no possibility of assessing local variations.^{1, 2, 3, 4} On the microscopic level, engineered tissue constructs often have local heterogeneities, and the patency of implanted constructs can depend on assessing these local variations.

In general, optical methods have shown great promise for nondestructively characterizing engineered tissues. One particularly promising method is optical coherence tomography (OCT), which offers several unique technological advantages for characterizing engineered tissues⁵. Commercial OCT systems can achieve an axial spatial resolution of $<10\mu \mathrm{m}$ and penetrate up to $1\mathrm{mm}$ in highly scattering media, imaging at video-rate speeds. As a fiber-based technology, OCT can be coupled into flexible handheld probes, allowing them to be easily incorporated into incubators.

Several recent studies have used OCT to characterize engineered tissues. Initially, Tan used OCT to visualize how fibroblasts change the architecture of a 3D chitosan scaffold,⁶ and then to monitor cell migration, proliferation, and detachment off a calcium phosphate scaffold by trypsinization.⁷ Rey visualized chemotaxis-induced cell migration in 3-D agarose substrates.⁸ OCT has also been used to visualize how cells change the porosity in poly(l-lactic acid) scaffolds⁹ and chitosan scaffolds.¹⁰

These papers clearly demonstrate the ability of OCT to characterize features such as cells (or a cluster of cells) on a weakly scattering background of an imaged tissue construct. However, as the tissue construct develops, gel compaction, cell proliferation, and matrix remodeling change the size and density of scatterers in the sample. At this stage, the construct becomes a highly scattering medium, in which the cells can no longer be resolved. Properly characterizing mature tissue constructs just prior to implantation will be important for ensuring successful outcomes, but given the highly scattering nature of mature constructs, making such assessments is quite challenging.

Moreover, the bulk of the work in characterizing engineered tissue constructs using OCT has been qualitative image analysis, based primarily on identifying features of interest (i.e., a cell) by a subjective operator. Given the qualitative nature of these methods, systematically surveying large volumes of data ( $\sim 1{\text{cm}}^3$ ) imaged at micron resolution is both cumbersome and impractical. However, OCT data contain quantitative information on the optical scattering properties of the imaged sample. The optical properties of interest here are the scattering coefficient ${\mu }_{\mathrm{s}}$ [ ${\text{cm}}^{-1}$ ] and anisotropy factor $g$ [dimensionless],¹¹ which provide a measure of the density and size of scattering particles in the medium, respectively. With proper theoretical modeling, it is possible to describe the depth-dependent OCT signal as a function of ${\mu }_{\mathrm{s}}$ and $g$ , as well as the system parameters.¹² By fitting a depth-dependent OCT signal that is representative of local nanoliter volumes in the sample to a theoretical model, it is possible to determine the local scattering properties of the sample. This approach was used to evaluate the optical properties of one of the most common types of engineered tissues, collagen gels, and characterize their development when seeded with cells.

Collagen gels are one of the simplest types of engineered tissues, in which cells are suspended in a 3-D collagen I matrix. Over time, the cells pull on the collagen fibrils causing gel compaction, wherein the gel becomes smaller, with decreased water content, and visibly more opaque. Some mesenchymal cells, such as fibroblasts and smooth muscle cells (SMCs), also contract and remodel the collagen matrix.¹³ An example of SMC-seeded collagen gels at $24\mathrm{h}$ and five days is shown in Fig. 1 . Note that the $24\text{-}\mathrm{h}$ gels are large and nearly transparent, while the five-day gels have contracted and have a cloudy appearance.

Fig. 1

Photographs of triplicate SMC collagen gels at $24\mathrm{h}$ and five days. Well $\text{diameter}=2.26\mathrm{cm}$ .

In this paper, collagen gels are imaged with different cell-seeding densities over a five-day period and the data are used to measure their optical properties. Over time, the reflectivity of the gels increased while the attenuation did not change, which degraded the ability to visualize structures such as cells. This reflectivity increase was due to a decrease in anisotropy $g$ , which caused increased backscatter of light. No such changes were observed in acellular gels. In each set of gels imaged at five days, reflectivity values followed a bimodal distribution, with the major population of gel sites showing a doubling of reflectivity and a sizeable subpopulation showing a roughly tenfold increase in reflectivity relative to the first $24\mathrm{h}$ . Time dynamics of the gels showed that these changes in optical properties were gradual. A careful analysis of the optical properties measured during the earliest time point showed that a correlation existed between cell density and ${\mu }_{\mathrm{s}}$ , but that cell density and $g$ were uncorrelated. Finally, mechanisms that could be responsible for the observed changes in optical properties are discussed.

2.

Theory

The theory of light propagation in low-coherence imaging systems used to process the data in this paper was derived from the inverse Monte Carlo method.¹² For a homogeneous turbid medium characterized by a scattering coefficient ${\mu }_{\mathrm{s}}$ , an anisotropy factor $g$ , an absorption coefficient ${\mu }_{\mathrm{a}}$ , and a refractive index $n$ , the depth-dependent OCT reflectance signal $R\left(z\right)$ can be described as an exponential decay

In our analysis, a Henyey–Greenstein phase function¹⁴ is assumed. One of the terms in Eq. 3 is $a\left(g\right)$ , $0<a<1$ , that decreases the effectiveness of scattering when the scattering is forward directed such that photons, despite multiple scattering, still manage to reach the focus and cannot be distinguished from the unscattered light. For highly anisotropic media, $a\left(g\right)$ has the effect of reducing the observed attenuation in the OCT signal. The function $a\left(g\right)$ can be approximated by a numerical expression determined from Monte Carlo simulations

For this model to be valid, it is necessary to convert the interferometric OCT envelope (in arbitrary units) into dimensionless units of reflectance $R\left(z\right)$ , i.e., the fraction of delivered light that is collected and detected by the microscope. To do this, the signal is calibrated against the peak signal from a known interface, such as an oil-glass interface, or against the reflectivity of an optical scattering phantom with known optical properties. This calibration is crucial in order to map the observations $\mu$ and $\rho$ into the optical properties ${\mu }_{\mathrm{s}}$ and $g$ .

3.

Materials and Methods

4.

Results

4.1.

Ability to Visualize Cells in OCT Images of Collagen Gels Decreases with Time

Representative images of collagen gels with different cell seeding densities (acellular, $3.8\times {10}^5$ , $1\times {10}^6$ , and $2.1\times {10}^6\text{cells}∕\mathrm{ml}$ ) at $6\mathrm{h}$ , $24\mathrm{h}$ , and five days are shown in Figs. 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 , with corresponding histology for the SMC gels in Figs. 2, 2, 2, 2, 2, 2, 2, 2, 2. The bright line on the top of some of the OCT images represents the air-MEM interface. Overall, the OCT images appeared rather spatially uniform at any given time point, with the only visualized structures being bright spots that presumably represent individual cells or clusters of cells. Such bright spots on a weakly scattering background can be seen in the $6\text{-}\mathrm{h}$ images of SMC gels [Figs. 2, 2, 2]. The density of these small “bright” spots increases with increasing cell seeding density. The bright spots were $\sim 20\mu \mathrm{m}$ in size, comparable to SMCs. At $24\mathrm{h}$ [Figs. 2, 2, 2, 2] a few more of these bright spots can be seen in the $2.1\times {10}^6$ gels [Fig. 2], and to a lesser extent in the $1\times {10}^6$ and $3.8\times {10}^5$ gels [Figs. 2 and 2–2(G)]. At $5\mathrm{d}$ [Figs. 2, 2, 2, 2], the images look different. In the $3.8\times {10}^5$ gels [Fig. 2], there are a few bright spots that are difficult to resolve. The $1\times {10}^6$ and $2.1\times {10}^6$ gels [Figs. 2 and 2] show a superficial high signal region that decays. For both gel conditions, it is not possible to resolve any cells in the foreground, as the bright spots have blended into the signal rich background. Note that because of the high superficial signal and the attenuation, the images appeared featureless and uniform. These gels have entered a scattering regime in which qualitative image visualization does not yield much useful information and in which quantitative image processing techniques are needed. In all the acellular samples [Figs. 2, 2, 2], there were larger, modestly brighter, and darker regions in the background of all the images caused by heterogeneity in scattering from the collagen, which did not appear to change much over time. Histologically, the H&E sections in Figs. 2, 2, 2, 2, 2, 2, 2, 2, 2 show an increase in cell density over time for each of the three different seeding densities.

Fig. 2

(a–l) Representative OCT images at (a–d) $6\mathrm{h}$ , (e–h) $24\mathrm{h}$ , and (i–l) five days for acellular gels and three different cell seeding densities. Acellular gels are shown in (a, e, i); gels seeded with $3.8\times {10}^5\text{cells}∕\mathrm{mL}$ are shown in (b, f, j); $1\times {10}^6\text{cell}∕\mathrm{mL}$ gels are shown in (c, g, k); and $2.1\times {10}^6\text{cell}∕\mathrm{mL}$ gels are shown in (d, h, l). Note that other than a few bright spots, the images (particularly at five days) are rather featureless, making visual characterization difficult. The bright spots are presumed to be cells or clusters of cells. Gray scale represents ${\log }_{10}\left(\rho \right)$ . (m–u) Corresponding histology for the three seeding densities of SMC gels: (m–o) $6\mathrm{h}$ , (p–r) $24\mathrm{h}$ , and (s–u) $5\mathrm{d}$ . Gels seeded with $3.8\times {10}^5\text{cells}∕\mathrm{mL}$ are shown in (m, p, s); $1\times {10}^6\text{cell}∕\mathrm{mL}$ gels are shown in (n, q, t); and $2.1\times {10}^6\text{cell}∕\mathrm{mL}$ gels are shown in (o, r, u). The histology images show an increase in cell density took place for the three sets of gels over time. $\text{Bar}=100\mu \mathrm{m}$ .

4.2.

Collagen Gels Exhibit an Increase in Reflectivity/Decrease in Anisotropy over Time

The optical properties of the developing collagen gels from a single representative set are shown on a scatter plot in Fig. 3 . Also plotted on the scatter plot is a grid that maps theoretical $({\mu }_{\mathrm{s}},g)$ values to the observed $(\mu ,\rho )$ pairs. Here, the initial collagen density was $2.43\mathrm{mg}∕\mathrm{mL}$ and the initial cell density was $1\times {10}^6\text{cells}∕\mathrm{mL}$ . Figure 3 compares SMC and acellular gels at two key time points of one and five days, with each datum point representing a $(\mu ,\rho )$ pair from a single ROI. In assessing the SMC and acellular gels at $24\mathrm{h}$ , the relative proximity of these two groups suggests that the scattering is dominated by the collagen fibrils, not the cells, which make sense given the small volume fraction the cells occupy. Also, note that the reflectivity in the SMC gels more than doubled from one to five days, whereas the corresponding acellular gels had only a modest increase in reflectivity. There was a large variance in attenuation values in all the samples. This feature has been observed consistently over multiple sets of collagen gels and results in poorer ability to resolve $\mu$ in collagen gels, in contrast to sphere phantoms (Table 1). Moreover, neither the SMC nor acellular gels experienced a major shift in attenuation over five days.

Fig. 3

Representative scatter plot showing the overall trends in $(\mu ,\rho )$ data from both SMC and acellular gels at one and five days. Each point represents the fit results from an individual ROI. Note that at $1\mathrm{d}$ there was overlap between the SMC and acellular gel data, but at five days the $(\mu ,\rho )$ data from SMC and acellular gels have drifted apart. The data displayed here correspond to sets 2 and 4 in Table 1, with an initial collagen density was $2.43\mathrm{mg}∕\mathrm{mL}$ and an initial cell density (passage 9) of $1\times {10}^6\text{cell}∕\mathrm{mL}$ .

A summary of the optical property results from multiple sets of collagen gels is detailed in Table 2 , which lists the peak values and range ( $\pm 1∕e$ or $\pm 0.37$ of peak value) for each $\mu$ and $\rho$ of the joint PDFs. These ranges provide an estimate of how $\mu$ and $\rho$ values were distributed around the joint PDF peaks. In comparing multiple sets of gels, the optical properties follow a general trend of starting out at low reflectivity and low attenuation at times $<24\mathrm{h}$ , and gradually increasing reflectivity over five days, approximately twofold, while attenuation remained relatively constant. These observed ( $\mu$ , $\rho$ ) pairs corresponded to ${\mu }_{\mathrm{s}}$ values that varied greatly, from $7\text{to}93{\mathrm{cm}}^{-1}$ , while $g$ values were consistently closely centered around 0.90 in the first $24\mathrm{h}$ . At five days, ${\mu }_{\mathrm{s}}$ values of SMC gels consistently decreased 30–50%, while $g$ decreased to $\sim 0.75$ . Moreover, at five days, there was also a consistent subpopulation of data with higher reflectivity values, which were approximately tenfold the reflectivity observed in the first $24\mathrm{h}$ . Thus, at five days the reflectivity of collagen gels followed a bimodal distribution as can be seen in the reported peak ranges in Table 2. Note that the peak $\rho$ value is consistently closer to the lower boundary than the upper boundary, which suggests that although most of the data were centered around the peak, there was always a sizeable subpopulation with even higher $\rho$ values. In contrast to the SMC gels, acellular gels from set 4 and set 6 had very minor shifts toward either higher or lower reflectivity, respectively. Nonetheless, despite a large variance in $\mu$ , the increase in $\rho$ of collagen gels over time was both consistent and reproducible. Thus, although the spatial heterogeneity of collagen structures in the acellular gels remained constant over time, the subpopulation of higher $\rho$ values across the various sets of five-day SMC gels suggests that some spatial heterogeneity developed in the SMC gels over time.

Table 2

Summary of optical properties from multiple sets of collagen gels, from the earliest time point ( 6h in sets 1–3, 24h in sets 4 and 5) to the final time point ( 5d for all sets). For both μ and ρ , we report both the peak of the joint PDF and the range over which the joint PDF > 1∕e* maximum. Square brackets denote concentration. Collagen density units are mg/ml; cell density units are cells/ml; μ and μs units are cm−1 ; ρ and g units are dimensionless.

Set	No. gels	[collagen]t=0	[cell]t=0	Cell passage no.	μearly	μfinal	μearly pk. range	μfinal pk. range
1	24	2.43	$3.8\times {10}^5$	9	16.22	15.31	4.37–35.48	6.38–36.31
2	24	2.43	$1\times {10}^6$	9	30.90	30.55	16.79–49.55	6.68–80.35
3	24	2.43	$2.1\times {10}^6$	9	43.15	53.09	17.99–76.86	24.55–84.14
4	32	2.43	0	NA	10.47	15.14	4.57–29.51	4.37–32.36
51	6	2	$1\times {10}^6$	5	59.57	48.98	14.62–117.49	17.99–108.39
61	6	2 or 53	0	NA	38.46	60.26	9.12–92.26	26.00–89.13
Set	${\rho }_{\text{early}}$	${\rho }_{\text{final}}$	${\rho }_{\text{early}}$ pk. range	${\rho }_{\text{final}}$ pk. range	${\mu }_{\mathrm{s}\text{-early}}$	${\mu }_{\mathrm{s}\text{-final}}$	${\mathrm{g}}_{\text{early}}$	${\mathrm{g}}_{\text{final}}$
1	$1.38\times {10}^{-6}$	$2.95\times {10}^{-6}$	$5.19–29.2\times {10}^{-7}$	$2.16–3.94\times {10}^{-6}$	10.50	8.19	0.896	0.756
2	$2.16\times {10}^{-6}$	$5.37\times {10}^{-6}$	$1.01–3.51\times {10}^{-6}$	$2.60–21.1\times {10}^{-6}$	21.69	16.55	0.919	0.775
3	$3.27\times {10}^{-6}$	$4.79\times {10}^{-6}$	$7.16–73.3\times {10}^{-7}$	$2.40–29.5\times {10}^{-6}$	29.23	33.66	0.910	0.889
4	$7.76\times {10}^{-7}$	$1.80\times {10}^{-6}$	$4.37–11.78\times {10}^{-7}$	$1.11–3.09\times {10}^{-6}$	7.16	8.85	0.913	0.847
51	$1.15\times {10}^{-6}$	$2.48\times {10}^{-6}$	$7.16–21.4\times {10}^{-7}$	$1.30–5.01\times {10}^{-6}$	37.30	25.75	0.878	0.690
61	$4.95\times {10}^{-7}$	$3.05\times {10}^{-7}$	$1.93–12.6\times {10}^{-7}$	$1.35–5.62\times {10}^{-7}$	28.32	93.47	0.927	0.985

^aNote that sets 5 and 6 were imaged with a different OCT system.

^bNote 3 samples were imaged at eight different time points.

^cThe initial collagen concentration in the gels imaged at 1d and 5d were 2 and 5mg∕mL , respectively.

4.3.

Time Dynamics of Collagen Gels

Although Fig. 3 shows the overall shift in the local optical properties of the collagen gels, it is also worthwhile to visualize the time dynamics of the optical properties. However, because the shift in the $(\mu ,\rho )$ data over time is slow and many data points lie on top of one another, the actual 2-D distribution of $\mu$ and $\rho$ values is presented as the joint PDF. A representative set of the calculated joint PDFs at $6\mathrm{h}$ , $24\mathrm{h}$ , three days, and five days are plotted superimposed on a grid in Figs. 4, 4, 4, 4 , showing the gradual increase in reflectivity over five days. Figures 4 and 4 shows that there are not many changes in the optical properties over the first $24\mathrm{h}$ . However, from one to five days [Figs. 4, 4, 4] the center of the PDF shifted to the right toward higher reflectivity, without changing much in attenuation. There was also a substantial subpopulation in the five-day time point that had an even higher reflectivity (lower anisotropy), similar to the other data sets (Table 2).

Fig. 4

Log-log plots showing 2-D PDFs of collagen gels at (a–d) $6\mathrm{h}$ , $24\mathrm{h}$ , $3\text{days}$ , and $5\text{days}$ . Also on each plot is a grid that shows how theoretical optical properties $({\mu }_{\mathrm{s}},g)$ map to $(\mu ,\rho )$ in our OCT system. Over time, the center of the PDF moves to the right, showing an increase in reflectivity. Moreover, the $5\text{-}\mathrm{d}$ PDF also has a subpopulation at higher $\rho$ values, indicating that a subpopulation of the ROIs had a higher reflectivity. (e, f) Plots of peaks in $(\mu ,\rho )$ space that were mapped back to $({\mu }_{\mathrm{s}},g)$ , plotted versus time. The displayed data in (a–f) correspond to set 2 in Table 1, in which the initial collagen density was $2.43\mathrm{mg}∕\mathrm{mL}$ , and the initial cell density (passage 9) was $1\times {10}^6\text{cells}∕\mathrm{mL}$ . (g) Gel compaction curve for the gels versus time. These data correspond to sets 1–4 in Table 1; the first four legend entries represent initial cell concentrations in units of cells/ml. Cummings’ gels had a $1\times {10}^6\text{cell}∕\mathrm{mL}$ seeding density, and an initial collagen density of either 4 or $2\mathrm{mg}∕\mathrm{mL}$ .¹⁷

Additionally, the peaks of the joint PDFs shown in Figs. 4, 4, 4, 4 were mapped from $(\mu ,\rho )$ space back to $({\mu }_{\mathrm{s}},g)$ space. Plots of ${\mu }_{\mathrm{s}}$ and $g$ versus time for eight time points spanning five days are displayed in Figs. 4 and 4. Error bars represent the $1∕e$ width of the joint PDF at the iso- ${\mu }_{\mathrm{s}}$ and iso- $g$ lines of the PDF peak. The $g$ versus time curve [Fig. 4] shows that over one to five days, there was a moderate but steady decrease in anisotropy. A similar moderate but steady decrease is also seen in the ${\mu }_{\mathrm{s}}$ versus time plot [Fig. 4]. Note the nonlinear mapping of $({\mu }_{\mathrm{s}},g)$ to $(\mu ,\rho )$ that occurs at $g$ values $>0.9$ , such that reflectivity can increase and attenuation can show no change while $g$ and ${\mu }_{\mathrm{s}}$ both decrease.

Macroscopically, the SMC collagen gels showed a moderate but consistent rate of gel compaction, i.e., the rate of decrease in collagen gel volume as the cells pull on the fibrils was steady [Fig. 4]. Gel compaction was assessed at the eight imaging time points by quantifying the volume of media in the gel well just before imaging. The volume of gels from each of the three SMC groups shrunk to about 20–30% of their original volume. These data agreed with end point measurements by Cummings ¹⁷

4.4.

Cell Density Correlates with Scattering Coefficient of Collagen Gels

When analyzing the optical property results, the $6\text{-}\mathrm{h}$ data were closest to the zero time point and thus had minimal change in both the cells and the collagen. In plotting the peaks of the joint PDFs on a grid [Fig. 5 ], these $(\mu ,\rho )$ pairs were colocated on an iso- $g$ line, and that their ${\mu }_{\mathrm{s}}$ value increased with cell concentration. The corresponding ${\mu }_{\mathrm{s}}$ and $g$ values for the four points were backtracked, as in Figs. 4 and 4, and plotted against the cell seeding density [Figs. 5 and 5]. Included in Figs. 5 and 5 are linear fits of both ${\mu }_{\mathrm{s}}$ and $g$ against cell seeding density. The fit results showed that ${\mu }_{\mathrm{s}}$ was highly correlated with cell concentration $(R^2=0.998)$ and increased linearly with cell density at a rate of $10.8{\mathrm{cm}}^{-1}∕({10}^6\text{cells}∕\mathrm{mL})$ plus a $7.0\text{-}{\mathrm{cm}}^{-1}$ offset that represents scattering from collagen alone [Fig. 5]. Moreover, the $7.0{\mathrm{cm}}^{-1}$ measured from $2.43\mathrm{mg}∕\mathrm{mL}$ acellular collagen corresponds to a ${\mu }_{\mathrm{s}}$ increase of $2.88{\mathrm{cm}}^{-1}∕(\mathrm{mg}∕\mathrm{mL})$ of collagen density. A similarly high correlation $(R^2=0.985)$ between cell density and ${\mu }_{\mathrm{s}}$ was obtained by correlating cell-like structures (i.e., “bright spots”) counted manually in the $6\text{-}\mathrm{h}$ gel images (data not shown). In contrast to ${\mu }_{\mathrm{s}}$ , $g$ remained flat relative to the concentration [Fig. 5] and was uncorrelated $(R^2=0.035)$ . Such an increase in ${\mu }_{\mathrm{s}}$ without a change in $g$ is expected for a static system with an increasing scattering particle (i.e., cell) density. However, the imaged collagen gels are dynamic over five days, and no such clear cut correlations existed between either ${\mu }_{\mathrm{s}}$ or $g$ and cell concentration at any of the later time points. This suggests that, over five days, the contraction process involved a fundamental change in the overall collagen gel architecture.

Fig. 5

(a) Peak of $\mu$ and $\rho$ PDFs from $6\mathrm{h}$ gels plotted on grid. Note how all the points line up on the same iso- $g$ line, with increasing ${\mu }_{\mathrm{s}}$ values. These data correspond to sets 1–4 in Table 1; the units on the legend are in cells per milliliter. Plots of (b) ${\mu }_{\mathrm{s}}$ and (c) $g$ data calculated from the $(\mu ,\rho )$ PDFs for the four cell densities, along with corresponding linear fits. Note that ${\mu }_{\mathrm{s}}$ increases linearly with cell density, while $g$ does not change.

5.

Discussion

In this paper, OCT was used to image developing collagen gels at different time points and to measure the optical properties from the images by fitting the OCT signal to a theoretical model. The results showed that over time, there was a consistent twofold increase in reflectivity with little change in the attenuation in four separate sets of experiments with various cell seeding densities (Table 2, Figs. 3 and 4). Also, consistently present in each set of gels imaged at five days was a sizeable subpopulation of sites on the gel with a higher reflectivity, roughly tenfold greater than the first $24\mathrm{h}$ . These trends in attenuation $\mu$ and reflectivity $\rho$ correspond to a decrease in anisotropy $g$ and a moderate decrease in scattering coefficient ${\mu }_{\mathrm{s}}$ , suggesting an overall decrease in the size of the scattering particles.

Several models have been proposed for measuring optical properties from OCT signals. The first model is the single-scattering (SS) model, in which the signal is assumed to follow an exponential decay $R\left(z\right)\propto \exp [-2({\mu }_{\mathrm{s}}+{\mu }_{\mathrm{a}})z]$ $\approx \exp (-2{\mu }_{\mathrm{s}}z)$ , since ${\mu }_{\mathrm{s}}⪢{\mu }_{\mathrm{a}}$ for most tissues at near-infrared wavelengths. Despite similarities between the SS and $\mu \text{-}\rho$ models used here, our results illustrate several flaws in using the SS model for measuring optical properties. First, the $\mu \text{-}\rho$ model fits two parameters that map back to two unknowns, ${\mu }_{\mathrm{s}}$ and $g$ , whereas the SS model only fits one parameter $\left({\mu }_{\mathrm{s}}\right)$ . However, our results repeatedly showed that the shift with time in optical properties of the collagen gels was more clearly observed in $g$ , not ${\mu }_{\mathrm{s}}$ . Second, the main difference in the attenuation term of the two models is the factor $a\left(g\right)$ , which describes how scattered light can still reach the focus despite multiple scattering. It is $a\left(g\right)$ that makes the mapping from ${\mu }_{\mathrm{s}}$ to $\mu$ nonlinear (and hence nontrivial) at high $g$ values, to which the $6–24\mathrm{h}$ collagen gel $(\mu ,\rho )$ data mapped.

Most of the work on fitting optical properties from OCT imaging has focused on differentiating different types of atherosclerotic plaques.^{18, 19, 20} Each of these studies used a different theoretical model. Van der Meer ¹⁹ used the SS model and showed differences in ${\mu }_{\mathrm{s}}$ between normal arteries and atherosclerotic plaques. Levitz ¹⁸ used the extended Huygens–Fresnel (EHF) model²¹ and showed differences in anisotropy between normal arteries and atherosclerotic plaques. The EHF model has the added advantage of accounting for multiple scattering and defocusing; that is, it is capable of evaluating both ${\mu }_{\mathrm{s}}$ and a measure of anisotropy similar to $g$ without the need for the (time consuming) quasi-focus tracking scheme implemented in our study. However, the EHF model is highly nonlinear and thus requires a computationally burdensome algorithm that does not always converge to a solution. Alternatively, there are other models that have been used to measure optical properties from highly scattering samples. The model used by Xu ²⁰ is very similar to the $\mu \text{-}\rho$ model used here, but with key differences. First, the $a\left(g\right)$ is missing from this model, and second, $\rho$ is represented as the backscattering coefficient ${\mu }_{\mathrm{b}}$ , with no nonlinear mapping back to $g$ .

Similar to our work, Xu ²² characterized cytochrome oxidase activity in astrocytes suspended in agarose gels by measuring changes in ${\mu }_{\mathrm{a}}$ via the fitted attenuation, but using the SS model with its inherent limitations. Nonetheless, it is also worth noting that in their cell-agarose samples, a negligible amount of scattering and absorption from the agarose contributed to the signal; thus, all the scattering and absorption measured could be attributed to the cells. Figure 5 shows that cells are mild scatterers and that a very high density is needed to obtain a measureable change in attenuation. The attenuation values measured by Xu ²² required very high cell seeding densities $(\sim {10}^7–{10}^8\text{cells}∕\mathrm{mL})$ , which is in general agreement with our results.

The experiments presented here highlight several advantages to measuring local optical properties of samples using OCT. The method is nondestructive, which makes continuous and time-lapse monitoring of the tissue gels feasible. Because this OCT method depends on endogenous contrast, no labels are needed, which has the added benefits of both preserving the sample unperturbed in its native environment and reducing the costs associated with fluorescent labels. Moreover, the visual information contained in the OCT images complements the quantitative optical property data. And although these experiments were destructive in nature—samples were prepared, removed from the sterile incubator and imaged, and then fixed for histological analysis—one of OCT’s primary advantages is that it is a fiber-based technology that can be sterilized and integrated into the incubator for continuous, time-lapse monitoring.⁶ The adaptation of confocal mosaicing technology²³ to OCT will enable rapid surveying of large sample volumes. These features, if successfully implemented, could enable automated nondestructive evaluation of large volumes of engineered tissues.

In this study, samples were imaged and images were further divided into volume regions of about $90\times 10\times 450\mu \mathrm{m}$ $\left(xyz\right)$ , or $0.4\mathrm{nL}$ . This resulted in a rather large number of ROIs with volumes on the nanoliter scale, which partly affected the analyses. Implicit in the definition of ${\mu }_{\mathrm{s}}$ and $g$ is the assumption of averaging over some volume. The nanoliter volumes assessed here approach the size limit over which these properties are defined, but nonetheless, it is still possible to define optical properties within these volumes. These small volumes, from which optical properties are measured, are a direct consequence of the spatial resolution and field of view of OCT images. Indeed, ROI volumes on the nanoliter scale have been used by others when measuring optical properties from OCT data.^{18, 19, 20, 22}

One consequence of these small sampling volumes is an increase in the variance of the optical properties, which may simply reflect the intrinsic heterogeneity of the samples on this size scale. The variance in optical properties of acellular gels was much larger than those in SMC gels (Figs. 3 and 4, Table 2), paradoxically suggesting that acellular gels were less homogeneous than SMC gels. However, this is not the complete picture. A careful examination of the acellular gels with the naked eye showed that some regions are cloudier than others, confirming millimeter-scale heterogeneity, seen in the OCT images and observed in the optical property data. Moreover, the histological sections [Figs. 2, 2, 2, 2, 2, 2, 2, 2, 2] showed that within the field of view of an OCT or histology image, the cells were generally uniformly distributed. Noting that cells are mild scatterers but with a higher reflectivity than the background collagen, the scattering in the SMC gels from the “uniformly” distributed cells contrasted with the collagen background and shifted the optical properties accordingly. However, in the acellular gels, all the scattering was due to the slowly varying background, which explains the increased variance observed in the acellular gels. Indeed, perhaps the large spatial variability in collagen distribution may offer clues as to why some regions in tissue-engineered implants are at increased risk of mechanical failure.²⁴

The optical properties at five days showed a consistent increase in $\rho$ with little change in $\mu$ , which correspond to a decrease in anisotropy $g$ with a modest decrease in ${\mu }_{\mathrm{s}}$ . Such changes in optical properties suggest a decrease in the overall size of the scattering particles, not an increase in particle density, which would increase ${\mu }_{\mathrm{s}}$ , and hence increase both $\mu$ and $\rho$ . In attempting to identify which microstructural changes caused this shift in optical properties, we (initially) proposed four potential reasons: increased collagen density, increased cell density, SMC contraction (i.e., a change in cell morphology), and collagen remodeling. Further analyses of some of the data presented here rules out increases in collagen and cell density, and preliminary results (not shown) suggest that collagen remodeling is responsible for the changes in optical properties.

To test if increased collagen density (i.e., gel compaction) caused the twofold increase in reflectivity, the collagen density was plotted against both $\mu$ and $\rho$ for the different collagen gel samples and the correlation coefficient was calculated. There was little to no correlation between collagen density and optical properties: for $\rho$ versus collagen density, $R^2<0.2$ ; for $\mu$ versus collagen density, $R^2<0.06$ (data not shown). These poor correlations suggest that collagen density was not the primary cause of the measured shifts in optical properties. Furthermore, the changes in optical properties caused by changes in collagen density were very subtle $[{\mu }_{\mathrm{s}}=2.88{\mathrm{cm}}^{-1}∕{(\mathrm{mg}∕\mathrm{mL})}_{\text{collagen}}]$ , and are well below the $14\text{-}{\mathrm{cm}}^{-1}$ algorithm resolution for ${\mu }_{\mathrm{s}}$ at $g=0.9$ . Such an increase in ${\mu }_{\mathrm{s}}$ with little change in $g$ does not explain the shift in optical properties over time observed in our data, namely, a decrease in $g$ a modest decrease in ${\mu }_{\mathrm{s}}$ . Also, data from set 6 (Table 2), in which higher density $(5\mathrm{mg}∕\mathrm{mL})$ acellular gels were imaged at five days, suggests that gel compaction did not cause the change in optical properties, because the characteristic increase in reflectivity (with no change in attenuation) that was consistently observed in the SMC gels was absent. Of note, we do not expect that extracellular matrix laid down by SMCs over the five-day incubation period contributed significantly to the change in optical properties, because previous work has shown the matrix synthesized by SMCs embedded in both collagen and fibrin gels to make up $<1\mathrm{\%}$ of the total collagen content.^{25, 26}

Additionally, the correlation between the optical properties and cell density was checked. An increase in cell density may be caused either by cell proliferation and/or compounded by gel compaction. However, an alamar blue assay on three extra sets of gels did not show an increase in cell metabolism over five days, suggesting no proliferation took place (data not shown). The result is in agreement with previously published results.²⁷ Nonetheless, to confirm whether cell density correlates with optical properties, cells were manually counted in 15 histological H&E sections for each gel (three analogous sites in five sections separated by $50\mu \mathrm{m}$ ), which were normalized by the area of the collagen in that section. These cell density counts were compared to both the $\mu$ and $\rho$ values for that gel, and the correlation coefficient $R^2$ was calculated. The correlations between the cell density and both $\mu$ and $\rho$ were rather weak. For $\mu$ versus cell density, $R^2=0.25$ , whereas for $\rho$ versus cell density $R^2=0.34$ (data not shown). These weak correlations, together with the $6\text{-}\mathrm{h}$ data showing how cell density correlates with ${\mu }_{\mathrm{s}}$ but not $g$ (Fig. 5) suggest that although an increase in cell density contributed partly to an increase in $\rho$ , it was not the primary reason for the twofold increase in $\rho$ shown in the data.

The data showed that over time, there was an overall decrease in anisotropy factor $g$ of the collagen gels, as well as a moderate decrease in scattering coefficient ${\mu }_{\mathrm{s}}$ . The decrease in ${\mu }_{\mathrm{s}}$ seems a bit counterintuitive because it is expected for there to be an overall increase in the density of scattering particles. However, treating the scattering particles in the gels as discretely sized microspheres, Mie theory provides some additional insight.¹¹ Mie theory states that the relationship between the particle size and scattering cross section is highly nonlinear. Thus, consider two scattering solutions, one made with small microspheres and the other with large microspheres, but where in both cases the spheres occupy the same volume fraction. It is obvious that the small sphere solution will have a smaller $g$ value than the large sphere solution. However, these two scattering media will also have different ${\mu }_{\mathrm{s}}$ values, with the small sphere solution having a smaller ${\mu }_{\mathrm{s}}$ than the large sphere solution. Thus, if the increase in the number of small scattering particles (as indicated by the higher reflectivity) was caused by a breakdown of larger particles, one would expect a moderate decrease in the ${\mu }_{\mathrm{s}}$ along with a decrease in $g$ . Such a scenario supports the hypothesis that remodeling of the collagen matrix into small fibril fragments caused the observed changes in optical properties.

6.

Conclusion

In this study, OCT was used to image development in several sets of collagen gels with different cell seeding densities, as well as acellular gels, over a five-day period. After the first $24\mathrm{h}$ , changes in the collagen gels made structures (i.e., cells) impossible to resolve. To characterize the samples quantitatively, the optical properties of the gels were determined using an image-processing algorithm that fit the OCT signal from a region of interest to a theoretical model. In doing so, the observed fit results (attenuation $\mu$ and reflectivity $\rho$ ) were mapped back to the optical properties, the scattering coefficient ${\mu }_{\mathrm{s}}$ and the scattering anisotropy factor $g$ . Within the first $24\mathrm{h}$ , the optical properties of the SMC and acellular gels were similar (Figs. 3 and 4), suggesting that the optical properties were dominated by scattering from collagen fibrils. Over time, collagen gels with SMCs consistently exhibited a twofold increase in reflectivity, while acellular gels did not (Figs. 3 and 4, Table 2). The shift in optical properties toward higher reflectivity was gradual. A sizeable subpopulation of the SMC gels at five days had reflectivity values roughly tenfold higher than those in the first $24\mathrm{h}$ were consistently observed in five sets of gels. Such a shift corresponded to a decrease in $g$ and an overall decrease in the size of the scattering particles. Additionally, at the earliest imaging time point ( $6\mathrm{h}$ , Fig. 5), cell seeding density was strongly correlated to ${\mu }_{\mathrm{s}}$ $(R^2>0.99)$ , but not to $g$ $(R^2=0.02)$ . All in all, the data suggest that SMCs change the architecture of the collagen gel and that OCT can visualize and quantify these changes.