2.1.

Experimental Autoimmune Encephalomyelitis Rat Model

Flexor digitorum longus (FDL) muscle samples were isolated from 8- to 10-week-old residual female Dark Agouti rats. Rats were purchased from Harlan Netherlands B.V. (Horst, The Netherlands). Experiments were conducted in accordance with institutional guidelines and approved by the Ethical Committee for Animal Experiments of Hasselt University.

EAE was induced by a subcutaneous injection at the base of the tail with a $200\mu \mathrm{l}$ solution composed of $140\mu \mathrm{g}$ of recombinant human myelin oligodendrocyte glycoproteinin complete Freunds adjuvant (F5506, Sigma-Aldrich, St. Louis, Missouri) supplemented with $2.5\mathrm{mg}/\mathrm{ml}$ H37RA heat-inactivated Mycobacterium tuberculosis (Difco, BD Diagnostics, Maryland). Healthy control animals did not receive any injection. Immunized rats were weighed and received a pain score (PS) on a daily basis according to the following neurological scale: $0.5=\text{partial loss of tail tonus}$, $1=\text{complete loss of tail tonus}$, $2=\text{hind limb paresis}$, $3=\text{hind limb paralysis}$, $4=\text{moribund}$, $5=\text{death}$.²⁶ EAE rats were sacrificed 30 days after immunization.

2.2.

Tissue Preparation

All animals were sacrificed by heart perfusion with Ringer solution after Nembutal injection ($100\mathrm{mg}/\mathrm{kg}$). FDL muscles were immediately removed from both hind limbs, incubated overnight in 4% para-formaldehyde at 4°C, followed by cryoprotection in 30% sucrose in phosphate buffered saline (PBS) at 4°C until the tissue had sunk. Muscles were frozen in optimal cutting temperature compound (Tissue-Tek, Sakura Finetek Europe, The Netherlands) using liquid nitrogen cooled isopentane and stored at $-80°\mathrm{C}$. Sections of thickness $14\mu \mathrm{m}$ were cut on a cryostat (CL 1990 UV, Leica, Wetzlar, Germany) along the length of the myocytes, mounted onto Superfrost Plus glasses (Menzel-Gläser, Thermo Fisher Scientific, Waltham, Massachusetts), and stored at $-20°\mathrm{C}$. Before imaging, sections were washed thrice for 5 min in PBS, dipped into milli-Q, and a coverslip was placed using Immu-Mount™ (Thermo Fisher Scientific). Coverslipped sections were stored at 4°C until imaging.

2.3.

Microscopy

SHG imaging was performed using a Zeiss LSM510 META (Carl Zeiss, Jena, Germany) mounted on an Axiovert 200M and a $20\times /0.75$ air objective (Plan-Apochromat $20\times /0.75$, Carl Zeiss). The excitation was provided by a femtosecond pulsed laser (MaiTai DeepSee, Spectra-Physics, California) tuned at a central wavelength of 810 nm. The SHG signal was collected in forward mode by a condenser with a numerical aperture (NA) of 0.55, which we have verified to be sufficient to collect the complete SHG emission profile using the supramolecular sarcomere model.⁸ After passing through a 400 to 410 nm bandpass filter, the signal was detected by an analogue photomultiplier tube, delivered by Zeiss.

2.4.

Sarcomere Profile Analysis

Sarcomere analysis based on manually selected profiles was done as previously described.¹⁴ In short, 2728 intensity profiles were manually selected from 68 SHG images, taken from both healthy ($n=5$) and EAE ($n=8$) animals. Each profile was analyzed using the supramolecular model developed by Rouède et al.,⁸ yielding the sarcomere length $L$ and the disorder-related M-band size $M$. Based on our previous observations, the analysis was done using an A-band length of $A=1.40\mu \mathrm{m}$, a refractive index (RI) at the illumination wavelength $n_{\omega }=1.39$, and an RI at the SHG wavelength $n_{2\omega }=1.41$.¹⁴ For the selected objective, the Gaussian point spread function (PSF) has a lateral size of $w_{xy}=0.59\mu \mathrm{m}$ and an axial size of $w_z=3.45\mu \mathrm{m}$ (half width at $e^{-2}$).¹⁴

2.5.

Gabor Analysis

In general, a Gabor analysis is used to obtain local frequency components in a signal, either in time or in space. In this work, we consider the SHG images of striated muscle as a spatial signal. The main spatial frequency $f$ present in these SHG images of regular sarcomeres is related to the sarcomere length $L$, such that $f=L^{-1}$. The purpose of the algorithm is to locate and quantify sarcomere anomalies at the pixel level. Since SHG images of sarcomere anomalies are typically characterized by spatial frequency components $f^{\prime }$ other than $f$, our algorithm was designed to obtain a local quantifier indicating the relative contribution of $f$ to the signal, which we refer to as the local Gabor value. Regions consisting of regular sarcomeres will then receive the highest possible Gabor value.

Instead of a relative contribution, a standard Gabor analysis returns the absolute contribution of the considered frequency. Hence, regions containing similarly appearing sarcomeres will have undesired differing Gabor values if the signal intensity differs. These intensity variations are likely to occur not only across samples but also within a sample due to variations in a real sample’s thickness or changes in opacity of features above and below the focal plane. To obtain a relative quantifier, we implemented a new normalization procedure, which yields a normalized Gabor value $\overline{G}(x,y)$.

In Appendix A, we give the theory on which our approach is based. In short, the normalized Gabor value is defined as

2.6.

Computing System

The Gabor analysis was performed on a standard 64-bit PC with a 3.6 GHz quad core processor, extended with an Nvidia GeForce GTX 680 graphical processing unit (GPU). The analysis code was written in MATLAB^® (Version R2013a, The Mathworks, Natick, Massachusetts), and the parallel processing toolbox was used for its built-in GPU capabilities.

2.7.

Simulations

Theoretical SHG intensity profiles were simulated using the supramolecular model developed as described before.¹⁴ The one-dimensional profiles were calculated along the $x$-direction by the supramolecular model and copied laterally ($y$-direction) to obtain two-dimensional images. Gaussian noise resembling that of the used imaging modality was superimposed onto the theoretical profiles. The PSF, refractive indexes, and A-band length were fixed to the previously mentioned values. The sarcomere length was fixed to $L=2.2\mu \mathrm{m}$.

2.8.

Statistics

Data comparison over different conditions was done using the one-way analysis of variance algorithm of MATLAB^®’s statistical toolbox. Differences were considered significant for $p<0.001$. Data correlation was tested by MATLAB^®’s corrcoef function, which, besides correlation, returns the probability $p$ of incidental correlation. Correlation was taken to be significant for $p<0.05$.

3.1.

Typical Patterns and Their Gabor Values

To correctly interpret the resulting Gabor values, the Gabor histograms of representative sarcomere structures and anomalies are given in Fig. 1. In Figs. 1(a) and 1(b), the difference between the original and normalized Gabor values, respectively, is shown for the same regular sarcomeres. Without normalization, the Gabor distribution contains two distinct peaks with a central value of $\sim 69$ and $\sim 55$, which is a 20% difference. The distinct peaks suggest the image contains structures with different frequencies. However, a one-dimensional fast Fourier transform (FFT) analysis along the sarcomeres indicates that the frequency mismatch is only apparent (data not shown). The FFT reveals a peak having a width representing a 2.5% frequency spread, corresponding to a 1% normalized Gabor value decrease according to Eq. (9). After normalization [Fig. 1(b)], the Gabor histogram contains only one peak at an average value of 0.932. The standard deviation of 0.018 matches a 2% spread and resembles the mismatch deduced from the FFT analysis. This typical example shows the explicit need for the normalization procedure. From here on, only the normalized Gabor values ($\overline{G}$) are considered.

Fig. 1

Typical results of the suggested Gabor filter. The color map represents the Gabor value, as specified in the histogram above each image. Each panel shows a cropped region of a larger image containing background regions. (a) Typical proper sarcomere pattern without normalization [$G(x,y)$] and (b) the same data as (a) with normalization [$\overline{G}(x,y)$]. In panels (c) to (f), the normalized Gabor coefficient is shown. Typical irregularities such as (c) pitchforks and (d) thinned regions show a slight decreased normalized Gabor value. Other typical structures contributing to the Gabor histogram of an image are: (e) double-band regions and (f) edge effects and dark regions (no mask applied for illustrative purposes). Scale bar $5\mu \mathrm{m}$. All images have the same field of view.

A first type of anomaly that can be detected using the normalized Gabor analysis is a pattern where the signal appears to come from one half of the thick filament [Figs. 1(c)–1(d)]. In these structures, often referred to as pitchforks,⁹ the A-band splits into two smaller myosin regions. One of these two regions typically has a higher SHG intensity. Pitchforks can occur on both short [Fig. 1(c)] or longer transversal length scales [Fig. 1(d)]. However, the Gabor values are independent of this length scale and consistently range from $\sim 0.6$ in the center of the pattern to $>0.85$ near the fully formed sarcomeres.

A second type of anomaly is the double band pattern, which was suggested in previous studies as a typical feature for proteolytic muscle tissue.^8,9 The double-band features result in lower Gabor values, down to a normalized Gabor value of 0.08 when the pattern contains only this doubled frequency. In most cases, the double-band pattern contains a combination of the reference frequency $f$ and the doubled frequency, resulting in Gabor values ranging from 0 to 0.6 [Fig. 1(e)].

The last representative pattern is a technical artifact rather than a sarcomere anomaly. SHG images of sarcomeres will contain myocyte boundaries and background (dark) regions that are also analyzed by the protocol [Fig. 1(f)]. However, these image regions do not contain valuable information on the sarcomere regularity. Therefore, the boundary and background regions are excluded from the Gabor histogram by the mask defined in Appendix B, eliminating the additional histogram peaks near $\overline{G}=0$.

In general, all aforementioned patterns contribute to the final Gabor histogram, which represents the sarcomere regularity in the entire SHG image. It appears that a Gabor value below 0.6 always maps disordered sarcomeres. Values between 0.6 and 0.85 indicate myocyte alterations related to an increasing or decreasing number of sarcomeres, indicated by the presence of pitchforks.⁹ Finally, values above 0.85 will always represent regular sarcomere patterns and are considered as good and healthy regions.

3.2.

Gabor Value Correlates with Myosin Disorder

In order to link the obtained $\overline{G}$ to sarcomere disorder, the correlation between the normalized Gabor value and the M-band size was studied. This was done on a set of samples taken from healthy animals and EAE induced animals for which sarcomere degradation was expected. A broad range of values for $M$ was obtained by analyzing manually selected intensity profiles from samples of both animal groups. The automatically determined normalized Gabor value corresponding to each profile was taken from the pixel at the profile center. For each intensity profile, $\overline{G}$ is plotted against the corresponding $M$ in Fig. 2.

Fig. 2

Sarcomere disorder quantified by $M$ versus normalized Gabor value $\overline{G}$ correlation. The maximum possible normalized Gabor value is indicated by the solid line (simulated). The simulated profiles of the given M-band size are shown on the right.

For $M<0.3\mu \mathrm{m}$, the normalized Gabor value is essentially constant, indicating no detectable change in the SHG profile. Above this threshold value, a transition from single to double band occurs, resulting in a rapid decrease of $\overline{G}$. A correlation between $M$ and $\overline{G}$ exists, validating the applicability of our Gabor approach to automatically estimate sarcomere (ir)regularity from entire SHG images. The observed $M-\overline{G}$ correlation was additionally verified by means of simulations. For each M-band size, images containing only one type of sarcomere were simulated in accordance with experimental conditions and analyzed with the normalized Gabor approach. The resulting maximum possible $\overline{G}$ for each $M$, shown by the solid line in Fig. 2, clearly indicates the upper limit of the experimental data. The simulations show that the Gabor approach is less sensitive to small M-band sizes, while for $0.3<M<0.75$, the method is highly sensitive.

3.3.

Experimental Autoimmune Encephalomyelitis Affects Sarcomere Integrity

Using the Gabor histograms, the effect of EAE on sarcomere integrity was studied. For this, the global EAE severity of each animal is measured by the pain score averaged from the day of EAE induction to the day of sample collection ($⟨\mathrm{PS}⟩$). The data used in Sec. 3.2 were divided into three groups: a healthy control group ($n=5$), animals with a time-averaged pain score below 1 ($⟨PS⟩<1$, $n=5$), referred to as mild EAE, and animals with a time-averaged pain score above 1 ($⟨PS⟩>1$, $n=3$), referred to as severe EAE. For each animal, the Gabor histograms of four to six SHG images from different slices were combined, resulting in one Gabor histogram per animal. These histograms, combined per animal group, are shown in Fig. 3 (histograms per animal are shown in Appendix C).

Fig. 3

Gabor histograms of healthy control group ($n=5$), the mild EAE group ($n=5$), and the severe EAE group ($n=3$). As indicated on the upper horizontal axis, a significantly lower median Gabor value (${\overline{G}}_{1/2}$) for the severe EAE group is observed (*, $p<0.001$). The inset shows the correlation between ${\overline{G}}_{1/2}$ and the time average pain score ($⟨\mathrm{PS}⟩$). The solid line is a linear fit serving as a guideline to emphasize this correlation.

Relative to the control group, the Gabor histogram shifts toward lower values only for the severe EAE group. According to previous observations (Fig. 1), this shift is mainly due to transformation from regular single-band SHG patterns into double-band patterns. The control, mild EAE, and severe EAE histogram cross at values representative for pitchfork structures (see Fig. 1), indicating little or no change in their prevalence. The mild EAE group shows no clear difference with respect to the control group. Only small differences are observed at $\overline{G}>0.85$, for which no sarcomere alterations were assumed. Moreover, statistical comparison of the median normalized Gabor values (${\overline{G}}_{1/2}$, see upper axis in Fig. 3) shows no significant difference between both groups. Only the severe EAE group has a significantly lower ${\overline{G}}_{1/2}$ ($p<0.001$) relative to both the control and mild EAE group.

The fact that severe EAE results in lower median normalized Gabor values than mild EAE suggests that a correlation exists between the EAE pain score on which data grouping was based and the muscle quality assessed by the Gabor analysis. To emphasize this correlation, the time-averaged EAE pain score ($⟨\mathrm{PS}⟩$) is compared to the median Gabor value of each animal. The result is shown in the inset in Fig. 3. A correlation analysis reveals a correlation coefficient of $-0.81$ ($p<0.05$), indicating a strong relation between the average pain score and the median Gabor value.