2.1.

Polarimetry Systems

Point and imaging polarimetry systems were employed in this study. The former provides a high signal-to-noise ratio (SNR) polarimetric signal, while the imaging system, although having a lower SNR, allows spatial mapping of polarization values. Both systems measure the polarization of the light that has interacted with a sample, yielding results in the form of a Stokes vector, a description of the polarization state of the light. In addition, the polarization properties of the sample, described by its polarization transfer function in the form of a Mueller matrix, can also be measured by varying the input polarizations and measuring the respective outputs.²⁴ Specifically, a Stokes vector $\mathbf{S}={\left(IQUV\right)}^T$ is a four-element vector describing the polarization of a beam of light. Its element $I$ represents the overall intensity of the beam, $Q$ gives the intensity of linear polarization along horizontal and vertical axes (with respect to an arbitrary reference frame), $U$ gives the intensity of linear polarization at $\pm 45\mathrm{deg}$ , and $V$ gives the intensity of light that is circularly polarized. Analogously, a Mueller matrix $\mathbf{M}$ is a $4\times 4$ matrix describing the effects a particular optical element has on the polarization of the input light. The two descriptors are linked in the so-called Mueller calculus: given a beam with a Stokes vector ${\mathbf{S}}_i$ impinging on an optical element with a Mueller matrix $\mathbf{M}$ , the light output from that element will have its polarization described by a Stokes vector as ${\mathbf{S}}_o=\mathbf{M}{\mathbf{S}}_i$ .

A schematic of the point measurement system is shown in Fig. 1 . The beam from a HeNe laser at $632.8\mathrm{nm}$ passes through a mechanical chopper operating at $f_c=300\mathrm{Hz}$ for intensity modulation, then through a linear polarizer and quarter wave plate to control the polarization of the light incident on the sample by adjustment of their orientations. After interacting with the sample, light in the forward ( $20\text{-}\mathrm{deg}$ solid angle) direction is collected with a lens and passes through a removable quarter waveplate oriented at $-45\mathrm{deg}$ . The collected beam then passes through a photoelastic modulator (PEM, IS-90, Hinds Instruments, Hillsboro, Oregon), a linearly birefringent resonant device operating at $f_p=50\mathrm{kHz}$ . The optical axis of the PEM is oriented at $0\mathrm{deg}$ and its magnitude of retardation is modulated according to the sinusoidal function ${\delta }_{\mathrm{PEM}}={\delta }_o\sin {\omega }_{p}t$ , where ${\omega }_p=2\pi f_p$ , and ${\delta }_o$ is the user-specified amplitude of maximum retardation. When the removable quarter wave plate is in place, the Stokes vector parameters $Q$ and $U$ (linear polarization) are modulated; when removed, the Stokes vector parameter $V$ (circular polarization) is modulated. Finally, the beam passes through a linear analyzer oriented at $+45\mathrm{deg}$ , converting the polarization-modulated light into intensity modulated light at $50\mathrm{kHz}$ (and its harmonic at $100\mathrm{kHz}$ ), and is detected with an avalanche photodiode (APD C5460, Hamamatsu, Hamamatsu City, Japan). The resulting photocurrent is then sent to a lock-in amplifier for high SNR synchronous detection, with the reference signal toggled between $300\mathrm{Hz}$ , $50\mathrm{kHz}$ , and $100\mathrm{kHz}$ .

Fig. 1

Schematic of point measurement polarimetry system. C, mechanical chopper; ${\mathrm{P}}_1$ , ${\mathrm{P}}_2$ , polarizers; ${\mathrm{W}}_{\mathrm{p}1}$ , ${\mathrm{W}}_{\mathrm{p}2}$ , quarter wave plates ( ${\mathrm{W}}_{\mathrm{p}2}$ is removable); A, aperture; ${\mathrm{L}}_1$ , ${\mathrm{L}}_2$ , lenses; PEM, photoelastic modulator; D, avalanche photodiode; and $f\mathrm{c}$ , $f\mathrm{p}$ , modulation frequencies of mechanical chopper and PEM, respectively.

The specifics of the signal analysis can be found in previous publications.^{25, 26} Briefly, the normalized Stokes parameters ( $q=Q∕I$ , $u=U∕I$ , and $v=V∕I$ ) of the light that is collected from the sample are calculated from the synchronously detected lock-in amplifier signals at the first harmonic of the chopper frequency $V_{1fc}$ $\left(300\mathrm{Hz}\right)$ , and the first and second harmonics of the signal at the PEM frequency $V_{1fp}$ and $V_{2fp}$ (50 and $100\mathrm{kHz}$ , respectively). When the detection quarter wave plate is in place, the normalized Stokes parameters $q$ and $u$ are calculated from

By cycling through four different input polarization states, specifically linear polarizations at 0, 45, and $90\mathrm{deg}$ , and circularly polarized light (either right or left) denoted as $H$ , $P$ , $V$ , and $R$ , respectively, and measuring the corresponding output polarization states, the Mueller matrix of the sample can be calculated. Specifically, the measured outputs states for the four subscripted input states are combined to calculate the 16 elements of the sample Mueller matrix as

A polarimetry imaging system was also developed for spatial mapping of polarization parameters, as shown in Fig. 2 . The input beam from a diode laser at $635\mathrm{nm}$ (Thorlabs, Newton, New Jersey) first passes through a linear polarizer, removable quarter wave plate, and an aperture to control the beam polarization and width (approximately $1\mathrm{cm}$ diam) before being incident on the sample. A diode laser was employed rather than the HeNe used for point measurements, as additional power was required for a wide beam. After interacting with the sample, the light passes through a pair of lenses to collect and focus the beam, as well as a removable quarter wave plate and a linear analyzer to allow for intensity detection of the output linear polarizations by a charge-coupled camera (CCD) camera (CoolSNAP K4, Photometrics, Tucson, Arizona) with $2048\times 2048\text{pixels}$ , $7.4\times 7.4\text{-}\mu {\mathrm{m}}^2$ pixel size, and field of view approximately $2\times 2{\mathrm{cm}}^2$ . The input beam was angled slightly off axis $\left(7\mathrm{deg}\right)$ to avoid any directly transmitted light saturating the CCD. This imaging system does not employ synchronous lock-in detection, so the SNR of this system is reduced compared to the point measurements. Work is currently underway to incorporate synchronous measurements.

Fig. 2

Schematic of imaging polarimetry system. ${\mathrm{P}}_1$ , ${\mathrm{P}}_2$ , polarizers; ${\mathrm{W}}_{\mathrm{p}1}$ , ${\mathrm{W}}_{\mathrm{p}2}$ , removable quarter waveplates; ${\mathrm{A}}_1$ , ${\mathrm{A}}_2$ , apertures; and ${\mathrm{L}}_1$ , ${\mathrm{L}}_2$ , lenses.

By using this imaging system, full Stokes parameters can be measured. By rotating the analyzing polarizer and inserting the quarter wave plate, the Stokes parameters $Q$ and $U$ can be measured from the detected intensities as,

2.2.

Mueller Matrix Decomposition

The Mueller matrix measured with either system describes the combined effects of all the polarizing properties of the sample. In the case of biological tissues, these effects are depolarization (due to scattering), optical activity, and birefringence. These effects occur simultaneously in tissue, making their unique quantification nontrivial, particularly as tissue is a turbid depolarizing medium. To quantify each of the effects separately (in this case, we are specifically interested in linear birefringence), it is possible to decompose the measured matrix $\mathbf{M}$ into the product of three basis constituent matrices,^{28, 29}

The measurable effect of birefringence, linear retardance $\delta$ , is contained in ${\mathbf{M}}_{\mathrm{R}}$ and can be calculated from its elements as²⁸

2.3.

Multiphoton Microscopy

To determine the underlying microstructural, morphological, and compositional causes for the observed polarization signals, multiphoton microscopy was performed on the cardiac samples. Second harmonic generation (SHG) was used to image the extracellular collagen matrix, while two-photon excited fluorescence (TPEF) was used to image cardiomyocytes. This label-free microscopic and nondestructive approach yields inherently coregistered images of the collagen and the cardiomyocyte compartments, thus giving useful information on cardiac tissue microstructure and composition, including the infarction and regeneration processes.

Images were acquired with a confocal microscope (Zeiss, LSM 510 META NLO, Oberkochen, Germany) using a $20\times$ $0.75\text{-}\mathrm{NA}$ dry objective. The excitation wavelength was set to $840\mathrm{nm}$ using a tunable Ti:sapphire laser (Chameleon, Coherent Incorporated, Santa Clara, California). The SHG signal is emitted at half the excitation wavelength, $420\mathrm{nm}$ , while the TPEF signal is emitted at longer wavelengths above about $440\mathrm{nm}$ . Two wavelength filters were used to spectrally separate the signals: $398\text{to}430\mathrm{nm}$ for SHG, and $430\text{to}463\mathrm{nm}$ for TPEF. While fluorescence is also emitted at wavelengths greater than 463, this narrow wavelength range was chosen so that the TPEF signal would have approximately the same intensity as the SHG signal. Both SHG and TPEF signals were recorded in the back-scattered direction with a spectral detector. In all figures, the SHG signal is shown in green pseudocolor and the TPEF signal is shown in red pseudocolor. The imaging resolution was $0.45\times 0.45\mu \mathrm{m}$ per pixel with a field of view of $460\mu \mathrm{m}\times 460\mu {\mathrm{m}}^2$ . The images were taken at a depth of approximately $50\mu \mathrm{m}$ from the surface of the sample, with the depth of focus being $1\mu \mathrm{m}$ .

2.4.

Myocardial Tissues

To investigate the utility of birefringence measurements for monitoring regenerative treatments, samples from a rat model of myocardial infarction and regeneration were used. All animal studies were carried out under institutional approval (University Health Network, Toronto, Canada).

Myocardial infarctions were induced in adult Lewis rats by coronary artery ligation. One group of animals was used as a control $(n=4)$ , while mesenchymal stem cells were administered to a treatment group $(n=3)$ by intramyocardial injection into the site of infarction, two weeks postligation. Both control and treatment groups were sacrificed four weeks postinfarction ( $2\text{weeks}$ post-stem-cell injection for the treatment group), at which time the hearts were removed, fixed in 10% formalin, and sectioned by a vibratome to $1\text{-}\mathrm{mm}$ -thick axial sections, as shown in Fig. 3 . This sectioning was done to reduce the effects of excessive depolarization by multiple scattering in thick tissues. These $1\text{-}\mathrm{mm}$ sections were also used for multiphoton microscopy. We chose transmission geometry for this initial study for ease of measurement and interpretation; polarization measurements in thick tissues (in reflection geometry) are being initiated. It should also be noted that the tissue fixation process may alter the birefringence properties of tissue through protein cross-linking, so that the absolute values derived in this study can have a systematic offset. However, this should not affect the observed relative changes in birefringence and trends therein. The effects of formalin fixation on tissue birefringence are currently being investigated. To perform the measurements, the sections were mounted on a glass microscope slide and placed horizontally in the beam path. To ensure that the tissues did not dry out, the measurements were performed quickly (less than $5\min$ ). All measurements were performed at room temperature $(25°\mathrm{C})$ . As the field of view for the multiphoton microscopy images is small relative to the size of the samples, whole slice histology was also conducted. One sample from each group was embedded in paraffin, stained with Masson’s trichrome, and sectioned to $5\mu \mathrm{m}$ for histological examination. This enabled whole slice comparison between polarization and histology with regards to myocardial composition.

Fig. 3

Schematic of rat heart showing location of axial section and schematic of a section.

3.1.

Point Retardance Measurements

Results from point retardance measurement on the control and treated tissues are shown in Fig. 4 . For each sample, measurements were performed in the healthy (region distal to the induced infarct), marginal (region adjacent to the induced infarct), and infarcted scar region. Cardiology experts identified these regions based on ventricular wall thinning; the infarction can also be clearly identified by the histology images in Fig. 5 based on collagen content. In each of these regions, five measurements were made at different positions. The results are the mean of all measurements in that region for all samples within each group.

Fig. 4

Results of point measurements; error bars are ± one standard deviation. Results are for control $(n=4)$ and stem-cell-treated $(n=3)$ animals. ${}^{*}$ denotes statistical significance $(\mathrm{p}<0.05)$ with respect to the corresponding control. Note the increase in retardance (birefringence) with stem cell treatment.

Fig. 5

Representative retardance images for (a) control and (b) stem-cell-treated sections with corresponding Masson’s trichrome stained histology images (collagen in blue, muscle in red). Retardance values are given in radians. (Color online only.)

As expected, the myocardium exhibits significant birefringence, particularly in the healthy regions where retardance values of up to $1.4\text{radians}$ were measured. If one assumes the light propagation distance to be at least the tissue thickness $\left(1\mathrm{mm}\right)$ , this corresponds to a birefringence value of $\Delta n⩽1.4\times {10}^{-4}$ , which is comparable to other organized tissues.³⁴ A large reduction in retardance was measured in the infarcted regions compared to the healthy tissue values, indicating a loss of tissue anisotropy and organization most likely due to the loss of cardiomyocyte fibers and their replacement with collagen-rich scar tissue. The normal myocardial tissue is comprised of highly organized cardiomyocytes surrounded with a fibrotic extracellular matrix, which results in a highly anisotropic structure; conversely, the infarction is primarily disorganized scar tissue comprised of randomly oriented, and thus optically isotropic, collagen fibers. The marginal regions represent a mixture of organized myocytes and disorganized collagen scar compartments, resulting in reduced retardance, although not as low as the scar tissue. These tentative interpretations are tested and confirmed by histology in Fig. 5 and the findings of nonlinear microscopy, as discussed in Sec. 3.3.

The tissue response to regenerative treatment is seen as a statistically significant rise ( $\mathrm{p}<0.05$ , calculated using a two-tailed Student’s t-test) in the measured retardance in the infarcted regions, as well as an apparent rise (although not statistically significant) in the marginal region. The addition of stem cells to the infarcted regions results in remodeling of the scar tissue, specifically a reduction in collagen and regrowth of myocytes leading to an improvement in cardiac function. This remodeling results in increased tissue anisoptropy and organization, manifesting as an increase in the retardance but without complete recovery to the normal tissue value. This is consistent with typical myocardial regenerative treatments, as full functional recovery is generally not achieved.⁶ These results are consistent with our previous point measurements where a reduction in birefringence was measured with infarction, and an increase was also measured with regenerative treatment.¹⁰

3.2.

Retardance Imaging

Point polarimetry measurements, sampling approximately $2\text{-}\text{to}4\text{-}{\mathrm{mm}}^3$ volumes of tissues,^{32, 33} likely suffer from sampling bias in the heterogeneous, spatially varying tissues. To better understand how the birefringence values vary spatially in myocardial samples, 2-D retardance images were taken of all samples from the control $(n=4)$ and treatment $(n=3)$ groups. A retardance image from each group is shown in Fig. 5, together with Masson’s trichrome stained histology from the respective sample for comparison. The retardance images show similar trends, as seen in the point measurement results, although some variation was seen as expected (difference in measurement geometry and spatial heterogeneity in tissue optical properties). The retardance is significantly reduced in the region of infarction and increases through the marginal region to higher levels in healthy tissues. In addition, the birefringence in the region of infarct increases with treatment. A reduction in ventricular thickness in the infarct and an increase in thickness with treatment are also visible. The histology images show the healthy myocardium to be nearly entirely composed of muscle (stained red) and little to no collagen (stained blue). This is in sharp contrast to the infarct, which is almost entirely comprised of scar collagen. Some muscle tissue can be seen in the infarct region of the treatment sample, likely as a result of stem-cell-induced regeneration. These imaging results are similar to our previous imaging study,¹¹ where a decrease in retardance with infarction and increase with treatment were also measured.

Considerable spatial variation is seen in the birefringence images; not only do the values change from infarct to normal, but also within each region as well. In general, higher values are measured in the middle of the myocardial wall, with lower values toward the edges. This is likely due to the change in orientation of the myocyte fibers through the wall, which undergo a $180\text{-}\mathrm{deg}$ rotation from the outside of the ventricle to the inside³⁵: on the inside and outside of the ventricle, the fibers are oriented perpendicular to our imaging plane, while in the center of the ventricular wall the fibers are parallel to the imaging plane. Hence, the retardance values are generally lower on the outside and inside walls, since the axis of birefringence (direction of the fibers) is along the direction of light propagation, and greater in the center where the axis of birefringence is perpendicular the direction of propagation. To investigate this further, we are currently examining the effects of birefringence axis orientation, and its spatial variation throughout the samples.

The spatial variations in the samples could be compounded by retardance phase wrap-around. Since retardance is a measure of the phase difference between two orthogonal polarizations states, once these states have gone out of phase by more than $\pi$ radians, the retardance will wrap-around and decrease. However, a wrap-around correction algorithm³⁶ was employed to detect and appropriately modify any retardance values that have undergone wrap-around. Details on the algorithm can be found in the reference. Additional intersample variations can arise from the uncertainty in the angle at which the samples were sectioned. As mentioned previously, higher retardance values are measured when the fibers are oriented parallel to the measurement plane than when the fibers are perpendicular.

Overall statistics from the images are shown in Fig. 6 . Values are the mean and standard deviation of pixel retardance values from the entire healthy, marginal, and infarcted regions of all images for each group. The mean measured retardance values in the images are generally higher than the point measurements, most likely due to the difference in measurement geometry (input imaging beam is $7\text{-}\mathrm{deg}$ off-axis) and the use of wrap-around correction. Reassuringly, the overall trend is similar to that of the point measurements. A statistically significant ( $\mathrm{p}<0.05$ , calculated using a two-tailed Student’s t-test) increase in the retardance was measured in the infarction relative to the control in stem-cell-treated samples, again indicating reorganization of the tissue through remodeling. The margin values remain fairly constant from group to group, while the retardance values in healthy regions increase from the control to the treated samples, although this increase was not found to be significant $(\mathrm{p}>0.05)$ . The difference in retardance values between infarcted and healthy regions is somewhat lower than for the point measurements, likely due to the point measurements from the healthy regions being made in the center of the myocardial wall, where the retardance is the highest, while the image statistics are calculated from pixels averaged across the whole thickness of the myocardium. Also, differences in SNR can contribute to these discrepancies.

Fig. 6

Mean ± one standard deviation retardance pixel values from retardance images from health, marginal, and infracted regions. Results are for control $(n=4)$ and stem-cell-treated $(n=3)$ animals. ${}^{\ast }$ denotes statistical significance $(\mathrm{p}<0.05)$ with respect to the corresponding control.

As considerable spatial variation is seen across the sections in the retardance images, the location of point measurement even within a specific region (i.e., healthy region, marginal zone, or infarcted tissue) can greatly influence the results. Thus, care must be taken when interpreting point measurements, as a single value may not be representative of the region. We are currently conducting further studies of the retardance variations, specifically by measuring the orientation of the birefringent axis and relating this to fiber orientations, as previously mentioned.

3.3.

Nonlinear Microscopy

The underlying morphological, microstructural, and compositional changes responsible for the measured changes in birefringence were investigated using nonlinear microscopy, specifically SHG for collagen and TPEF for cardiomyocyte imaging.²⁰ Representative images from healthy and infarcted regions of a control sample are shown in Figs. 7 and 7 , respectively, while a region of regenerating infarction is shown in Fig. 7.

Fig. 7

Representative nonlinear microscopy images from (a) healthy, (b) infracted, and (c) regenerating regions of myocardial samples. The TPEF signal from cardiomyocytes is shown in red pseudocolor, and the SHG from collagen is shown in green pseudocolor. (Color online only.)

The normal region of the control sample shows primarily highly organized cardiac muscle fibers and occasional collagen fibers, as expected, since collagen comprises less than 2% of healthy myocardial dry weight.³⁷ This correlates well with the histology shown in Fig. 5, where healthy myocardium contains little collagen. Thus, the healthy tissue can be considered to consist primarily of the cardiomyocytes, with interspersed small amounts of collagen, as seen in Fig. 5. This is in sharp contrast to the infarcted region where the opposite is true—the tissue is comprised primarily of scar collagen with decreasing amounts of surviving cardiomyocytes present. This again correlates well with histology shown in Fig. 5, where in contrast to the healthly myocardium, the infarction is nearly entirely composed of collagen. Regions in the infarction image where no signals (neither SHG nor TPEF) were measured likely correspond to regions of myocyte necrosis. The cardiomyocyte compartment has been largely replaced by the collagen compartment due to myocyte death and the resulting collagen scar formation throughout the necrosed tissues. While the collagen fibers in the infarcted region do exhibit some local organization, the overall structure of the tissue is disorganized compared to the healthy tissue. The difference in measured retardance from these two regions is as expected due to the necrosis of the highly organized muscle fibers with high anisotropy, and the partial replacement of these fibers with scar collagen, which overall is relatively isotropic with accordingly low birefringence.

The regenerating infarcted tissue from the treatment sample shows collagenous scar tissue and reorganized collagen fibers, as well as muscle fibers that have likely regrown in the region. As the tissue is more organized than the scar tissue in the control infarction region, the higher retardance measured in these regions correspond to the reorganization of the tissue through remodeling (regrowth of myocytes and reduction in collagen), as reflected in the corresponding trend toward increasing anisotropy. Both cardiomyocyte and collagen compartments are present in the regenerating tissue; this is shown by the histology in Fig. 5 as well, where the regenerating scar tissue does contain some muscle. The cardiomyocyte compartment has infiltrated the scar collagen compartment due to the growth of the injected stem cells into cardiac muscle, and has possibly stimulated regrowth of cardiac muscle cells from the surrounding tissues. While the sampling volumes for the microscopy and polarimetry measurements are quite different, the fact that these morphological changes can be observed through polarimetry measurements demonstrates the potential of this technique to monitor regenerative treatments.