2.1.

Sarcomere Length Measurement by Polarization-Gated Laser Diffraction

To perform sarcomere length measurement by LD, a $633\text{-}\mu \mathrm{m}$ wavelength He–Ne laser transilluminated tissue samples (Fig. 1). The resultant diffraction pattern and diffuse-transmitted light illuminated a measurement screen and spacing between diffracted peaks (if present) was measured by digital calipers and used to solve for sarcomere length using the grating equation⁹

Fig. 1

Sarcomere length measured by polarization-gated laser diffraction (PGLD). Polarizing filters extract diffraction signal from superimposed noise.

Polarization gating was performed by inserting linear polarizers in rotary optic mounts (#52-574, Edmund Optics Inc., Barrington, New Jersey) above and below the sample stage (Fig. 1). The linear polarization angle for each polarizer could be adjusted manually with 0.5-deg accuracy. Polarization angles for both polarizers were manually adjusted to visually maximize diffraction patterns.

Though sarcomere length measurements were made manually, a stationary camera was used to image the diffraction screen as an example of PGLD signal extraction. Images were processed using MATLAB (The MathWorks, Inc., Natick, Massachusetts) to obtain an average signal intensity plotted against the long axis of the muscle fibers.

2.2.

Hindlimb Immobilization to Generate Highly Scattering Muscle

One hindlimb each of four 8-week old wild-type (C57BL/6) mice were immobilized in paris casts for 14 days such that the ankle was in dorsiflexion ($42.4\pm 12.5\mathrm{deg}$) stretching the soleus muscle, following the protocol of Williams and Goldspink.²³ The contralateral uncasted hindlimbs served as controls. The casts were repaired as needed to ensure that the integrity of the casts was maintained throughout two weeks.

2.3.

Tissue Preparation

Hindlimbs from the euthanized immobilized mice were disarticulated at the hip, skinned, pinned to a cork board at a fixed angle of 90 deg at the knee and ankle and chemically fixed in 10% formalin for two days. Whole tibialis anterior (TA) and soleus muscles were surgically removed then rinsed and stored in $1\times$ phosphate-buffered saline. To facilitate fiber bundle dissection, muscles were partially digested in 15% ${\mathrm{H}}_2{\mathrm{SO}}_4$ for 30 min, similar to the protocol of Shah et al.²⁴ Fiber bundles containing 1-10 myofibers were microdissected under a microscope and mounted on a glass slide for sarcomere length measurements. Ten to fifteen fiber bundles were dissected from each muscle.

2.4.

Light Microscopy

A microscope (Model DM6000, Leica Microsystems Inc., Buffalo Grove, Illinois) was used to take BF images of soleus and TA muscle fiber bundles using a $40\times$ objective. ImageJ software²⁵ was used to average 10 to 30 sarcomere lengths in series within an image. Measured regions were chosen based on the ability to clearly see the sarcomeres-in-series, unimpaired by the increased connective tissue.

Confocal BF microscopy (Model SP5, Leica Microsystems Inc., Buffalo Grove, Illinois) was used to sample sarcomere length through a muscle fiber bundle with a $63\times$ objective. Focal depth was adjusted to image at least 50 focal planes through each fiber bundle (0.5 to $1.5\text{-}\mu \mathrm{m}$ Sol, 2.5 to $3.5\text{-}\mu \mathrm{m}$ TA). In each focal plane, the sarcomere length was averaged across 10 in-focus sarcomeres in series. Measured regions of muscle fiber bundles were marked on the slide, and the same volume of muscle was measured by PGLD.

2.5.

Data Analysis

Statistical tests were made using Prism (GraphPad Software, Inc., La Jolla, California) using a significance level ($\alpha$) of 0.05. The average sarcomere length measured by PGLD and BF were compared in four immobilized soleus muscles in a two-way ANOVA with the main effects of measurement technique and muscle sample. We did not use a paired $t$-test because the exact sampled location was not the same between tests. However, we did measure the same volume of muscle with PGLD and confocal microscopy and used a paired $t$-test for this comparison.

3.1.

Polarization Gating Rescue Diffracted Signals

Sarcomere lengths from murine soleus muscles harvested from hindlimbs treated with prolonged immobilization could not be measured by traditional LD, due to increased connective tissue content that erodes the diffracted signal with scattering events and buries the signal in diffuse-transmitted light and laser speckle (Fig. 2). However, the diffraction pattern was readily visualized using PGLD, which enabled comparison between sarcomere lengths in fibrotic muscles without sampling bias, as described in Secs. 3.2 and 3.3.

Fig. 2

PGLD extracts diffraction patterns from superimposed diffuse noise.

For our proof-of-principle study, we used simple linear polarizing filters for two reasons: they are simple to use and Li et al.²⁶ showed that the diffuse propagation of circular polarization and linear polarization are similar in muscle. However, it is possible that the signal-to-noise ratio and, more importantly, sensitivity can be further improved by fully characterizing the scattering process in diseased muscle tissue. Different muscular diseases may have different polarization combinations that best extinguish scattered noise.

3.2.

Sarcomere Lengths Measured by PGLD and Bright Field Microscopy

We compared sarcomere lengths from muscle fiber bundles of four immobilized soleus muscles measured by PGLD and BF (Fig. 3). The sarcomere length measured in a normal TA muscle with traditional LD was included for reference. Note that the polarization gating does not shift the location of the diffracted peaks. Statistical analysis by two-way ANOVA shows a significant effect of measurement technique ($p<0.001$), a significant effect of muscle sample ($p<0.001$), and no significant interaction term ($p=0.385$). Surprisingly, these data suggest a systematic measurement bias between sarcomere lengths measured by PGLD and BF ($0.19\text{-}\mu \mathrm{m}$ average difference). BF under estimated the sarcomere length in every sample measured, including both healthy and diseased tissue, despite the varied sarcomere lengths in each muscle sample. This disagreement was surprising because diffraction and microscopy techniques are considered standard methods to measure sarcomere length. However, BF samples a volume of sarcomeres from the muscle fiber bundle that is in focus, whereas PGLD samples throughout the bundle thickness. Therefore, BF may under sample or have a regional sampling bias that results in the sarcomere length disagreement. As an additional positive control, we thus compared PGLD to confocal microscopy images taken throughout the muscle fiber bundle thickness, which we believed would provide a more accurate comparison.

Fig. 3

Sarcomere length ($\text{mean}\pm \text{standard deviation}$, $n=5$ to 15 measurements per muscle) measured by laser diffraction (LD), PGLD, and bright field microscopy (BF). In immobilized muscles, sarcomere length measurement by traditional LD method was not possible. Two-way ANOVA revealed a significant effect of measurement technique ($p<0.001$), a significant effect of muscle sample ($p<0.001$), and no significant interaction term ($p>0.3$).

3.3.

Sarcomere Lengths Measured by PGLD and Confocal Microscopy

Data presented above suggested a systematic bias leading to different sarcomere length measurements between PGLD and BF. We hypothesize that relatively small numbers of sarcomeres measured by BF at specific depths of focus in the fiber bundles produced this measurement bias. We thus performed a rigorous comparison of sarcomere lengths measured by PGLD and confocal microscopy, because confocal microscopy is able to image throughout the muscle fiber bundle volume (Fig. 4).

Fig. 4

PGLD enables sarcomere length measurements in highly scattering muscle tissue. No significant differences were found between the two methods ($p=0.14$). Data shown are $\text{mean}\pm \text{standard deviation}$ ($n=10$ muscles).

Paired $t$-test comparing sarcomere length measured by PGLD and confocal microscopy in 10 fiber bundles (5 from normal TA, 5 from immobilized soleus) showed no significant difference ($p=0.14$) with 80% power to detect a $0.08\text{-}\mu \mathrm{m}$ difference. This serves as a positive control for the new PGLD sarcomere length method, and highlights the need to obtain appropriate samples to accurately perform such comparisons.

3.4.

Trade-offs of Several Sarcomere Length Measurement Methods

There are several important differences among these measurement methods (Table 1). LD was only successful in 7 of 115 fiber bundles obtained from immobilized muscles. Using PGLD drastically improved the sensitivity to 92 of 115, a 1333% improvement in measurement ability. We did not perform BF and confocal microscopy on all 115 fiber bundles, but our experience suggests that 100% sensitivity can be achieved with these techniques if enough time is spent. High sensitivity, however, is balanced by measurement time and sampling bias. BF has high sensitivity, but we yielded a significant bias of $0.19\mu \mathrm{m}$ for shorter sarcomere lengths. Confocal microscopy also has high sensitivity, but it takes significantly longer to perform than PGLD. The sample size was estimated using the following parameters: $1\text{-}\mu \mathrm{m}$ diameter and $2.5\text{-}\mu \mathrm{m}$ length sarcomeres, 1-mm laser beam width, and $50\text{-}\mu \mathrm{m}$ depth of field.

Table 1

Polarization-gated laser diffraction (PGLD) enables sarcomere length measurements in highly scattering muscle tissue.