Tensorial Tomographic Fourier Ptychography with Applications to Muscle Tissue Imaging
Advanced Photonics (2024)
1Duke Univ. (United States), 2Friedrich-Alexander-Univ. Erlangen-Nürnberg (Germany), 3Univ. of California, San Diego (United States), 4Yonsei Univ. (Korea, Republic of), 5Univ. of California, Berkeley (United States), 6Duke Univ. Medical Ctr. (United States), 7Yonsei Univ. (Korea, Republic of)

Abstract
We report tensorial tomographic Fourier ptychography (T2oFu), a nonscanning label-free tomographic microscopy method for simultaneous imaging of quantitative phase and anisotropic specimen information in 3D. Built upon Fourier ptychography, a quantitative phase imaging technique, T2oFu additionally highlights the vectorial nature of light. The imaging setup consists of a standard microscope equipped with an LED matrix, a polarization generator, and a polarization-sensitive camera. Permittivity tensors of anisotropic samples are computationally recovered from polarized intensity measurements across three dimensions. We demonstrate T2oFu’s efficiency through volumetric reconstructions of refractive index, birefringence, and orientation for various validation samples, as well as tissue samples from muscle fibers and diseased heart tissue. Our reconstructions of healthy muscle fibers reveal their 3D fine-filament structures with consistent orientations. Additionally, we demonstrate reconstructions of a heart tissue sample that carries important polarization information for detecting cardiac amyloidosis.
Muscle Fiber Assessment
High-contrast and high-resolution structural imaging of intrinsic signals in muscle skeletal fibers is an important task for the rapid detection of changes in myofibrillar organization that can lead to skeletal myopathies. Currently, 3D muscle tissue is typically imaged by complex and expensive systems, such as second-harmonic generation (SHG) microscopy. SHG exploits the contrast of polarization properties from the nonlinear susceptibility in molecules like myosin, by using high-power, ultrashort pulsed lasers in a point scanning configuration. Here we show 3D T2oFu, reconstruction results of an isolated healthy muscle fiber using our inexpensive, LED-based, and scanning-free system, which generally shows similar results as described for SHG imaging in the literature. Figure 2(a) shows an image of a muscle fiber captured with center LED illumination. Figure 2(b) shows a volumetric reconstruction of the muscle fiber. The cross sections of regions highlighted in Fig. 2(a) are depicted. Figure 2(c) shows an image of the same muscle fiber from a different field of view, where a non-muscle fiber with a 90 deg bend is placed below the muscle fiber. Figure 2(d) depicts reconstructed orientation and birefringence at two different depths, showing the regular pattern of a healthy muscle fiber. The zoom-in region highlights the muscle grains with consistent orientations, in agreement with the results reported by Both et al. The reconstruction shows a change in orientation at the bend of the non-muscle fiber [Fig. 2(d1)], while the orientation of the muscle fiber remains constant. Furthermore, the spatial resolution of the reconstruction is sufficient to clearly resolve the muscle filaments [Fig. 2(d3)]. Figure 2(e) shows a histogram of orientation of the reconstruction shown in Fig. 2(d), indicating two different types of cells.

Additionally, we apply our method to image a heart tissue sample that has cardiac amyloidosis. Cardiac amyloidosis is a lethal disease that affects < 12,000 patients in the US alone, with a < 5 % 10-year survival rate. In current practice, the biopsied tissue is first frozen and thinly sliced, then stained with a congo red-colored dye, and inspected under a cross-polarized microscope. Figure 3(a) shows the bright-field image. Figure 6(b) shows the same region, imaged with a cross-polarized color microscope. The vibrant apple green color suggests mostly likely amyloid protein has built up inside the tissue sample. Figures 3(c) and 3(d) depict the reconstructed refractive index and birefringence, while zoom-ins of the boxed region are shown in Figs. 3(e)–6(h). Figures 3(e) and 3(g) show lateral slices at different depths, while Figs. 3(f) and 3(h) show cross sections of the region highlighted with dashed lines in Figs. 3(c) and 3(d). Since the sample is thinly sliced, we do not observe noticeable structural changes in different layers. However, the structure of the birefringence reconstruction is correlated with the color-stained cross-polarized image, which could potentially be useful for rapid on-site inspections in the future.
