# ChiSCAT: unsupervised learning of recurrent cellular micro-motion patterns
from a chaotic speckle pattern

Andrii Trelin  Institute of Physics, University of Rostock, 18059 Rostock,
Germany  Sophie Kussauer  Department of Cardiac Surgery, Rostock University
Medical Centre, 18057 Rostock, Germany  Paul Weinbrenner  Institute of
Physics, University of Rostock, 18059 Rostock, Germany  Anja Clasen  Institute
of Physics, University of Rostock, 18059 Rostock, Germany  Robert David
Department of Cardiac Surgery, Rostock University Medical Centre, 18057
Rostock, Germany  Christian Rimmbach  Department of Cardiac Surgery, Rostock
University Medical Centre, 18057 Rostock, Germany  Friedemann Reinhard
Institute of Physics, University of Rostock, 18059 Rostock, Germany
<EMAIL_ADDRESS>
###### Abstract

There is considerable evidence that action potentials are accompanied by
”intrinsic optical signals”, such as a nanometer-scale motion of the cell
membrane. Here we present ChiSCAT, a technically simple imaging scheme that
detects such signals with interferometric sensitivity. ChiSCAT combines
illumination by a chaotic speckle pattern and interferometric scattering
microscopy (iSCAT) to sensitively detect motion in any point and any
direction. The technique features reflective high-NA illumination, common-path
suppression of vibrations and a large field of view. This approach maximizes
sensitivity to motion, but does not produce a visually interpretable image. We
show that unsupervised learning based on matched filtering and motif discovery
can recover underlying motion patterns and detect action potentials. We
demonstrate these claims in an experiment on blebbistatin-paralyzed
cardiomyocytes. ChiSCAT promises to even work in scattering tissue, including
a living brain.

###### keywords:

Action potential, label-free imaging, microscopy

Department of Life, Light, and Matter of the Interdisciplinary Faculty at
Rostock University, 18059 Rostock, Germany Department of Life, Light, and
Matter of the Interdisciplinary Faculty at Rostock University, 18059 Rostock,
Germany Department of Life, Light, and Matter of the Interdisciplinary Faculty
at Rostock University, 18059 Rostock, Germany Department of Life, Light, and
Matter of the Interdisciplinary Faculty at Rostock University, 18059 Rostock,
Germany Department of Life, Light, and Matter of the Interdisciplinary Faculty
at Rostock University, 18059 Rostock, Germany Department of Life, Light, and
Matter of the Interdisciplinary Faculty at Rostock University, 18059 Rostock,
Germany These authors contributed equally Department of Life, Light, and
Matter of the Interdisciplinary Faculty at Rostock University, 18059 Rostock,
Germany These authors contributed equally

##  1 Introduction

Literature data suggests that action potentials are accompanied by ”intrinsic
optical signals”, tiny changes in the optical properties of a cell that can be
detected by label-free optical imaging 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
The most accepted mechanism is a nanometer-scale motion of the cell membrane
7, occurring due to various factors, including the flexoelectric effect or
voltage-induced changes in membrane tension 13. Detecting action potentials by
direct label-free observation of nanoscale cell motions in interferometric
microscopy is highly promising, since it provides several unique advantages
over dye-based voltage or calcium imaging: it does not suffer from
photobleaching, which enables prolonged observation. Moreover, the
illumination wavelength can be freely chosen and can be optimized to minimize
cellular damage or to minimize optical scattering and hence allow chronical
imaging through multiple tissue layers, e.g. the cortex of the brain.

Intrinsic signals are a small fluctuation on a large background. Past studies
have established that the average scale of membrane movement is $\Delta
z\approx 1$ nm 14, 7, 15, 11, 12. In a suitable phase sensitive
interferometric microscopy technique, this translates into an intensity change
of

$\frac{\Delta I_{\text{signal}}}{I}\approx\Delta\phi\approx\frac{\Delta
n}{n}\frac{\Delta z}{\lambda}\approx 10^{-5}$

assuming a relative refractive index change between cell and medium ${\Delta
n/n}\approx 10^{-2}$ (according to 16) and a relative phase change of $\Delta
z/\lambda\approx$1\text{\times}{10}^{-3}$$. Intriguingly, such a signal should
be easily detectable in a single shot. The quantum shot noise limit of
interferometry is

$\frac{\Delta I_{\text{shot noise}}}{I}=\sqrt{\frac{1}{N}}$

where $N=P\Delta t/(\hbar\omega)$ denotes the number of photons employed.
Assuming $P=1$ mW of illumination power and an integration time of $\Delta
t=1$ ms, matching the timescale of an action potential (AP), the quantum shot
noise limit is on the order of $\Delta I_{\text{shot noise}}/{I}\approx
10^{-7}$, and the expected signal-to-noise ratio (SNR) is around 100.

However, existing experiments on label-free AP detection still fall short of
this limit. Published results either have been obtained on non-mammalian large
axons and nerves 4, had to resort to invasive techniques like atomic force
microscopy 17 or plasmon imaging 18, or to spike-triggered averaging of
multiple APs to reveal the signal with SNR $\geq 1$ 11, 12, 10.

Presumably, a major reason is that increasing the SNR is more challenging than
merely raising the excitation power. In transmission microscopy, the full-well
capacity of the imaging camera sets a limit for excitation power at the level
of nanowatts. This can be overcome by a reflective illumination scheme,
promising a great gain in sensitivity 12. However, existing reflective schemes
either restrict acquisition to a single diffraction-limited plane 19, 20,
reducing the signal, or merely produce an unspecific speckle pattern, which
cannot be easily interpreted 21: the reflected beam contains interfering
signals from all depth levels inside the cell, which leads to chaotic speckle-
like appearance.

Here, we break this limitation. We present an unsupervised learning scheme to
recover AP signals from a speckle pattern, without a priori knowledge of the
timing of the action potentials or the spatial pattern of motion triggered
during an AP. Moreover, we intentionally maximize the chaotic nature of the
image by illuminating the specimen with a speckle pattern. This creates a
random 3D light field in the cell, making the technique sensitive not just to
the motion in height, but also to motion in X-Y plane, achieving
interferometric sensitivity to motion in any illuminated voxel. In other
words, the observed image is a ”fingerprint” of the cell geometry and exact
volume distribution of intracellular scatterers.

Since ChiSCAT is not based on a visually interpretably image, it paves the way
to detecting action potentials even in scattering tissue, including the living
brain: signal passing through multiple layers of scatterers will change, but
it’s nature of a cell shape ”fingerprint” will be conserved.

##  2 Setup

Figure 1: Experimental setup and exemplary data. (A) Optical setup, combining
iSCAT microscopy with speckle illumination (ChiSCAT) and a fluorescence
voltage imaging path for reference. Both cameras are synchronized. (B) Raw
ChiSCAT image (C) raw fluorescence image (D) model of the ChiSCAT signal. A
static speckle pattern background (”Static speckle”) is superimposed with a
periodically modulated speckle pattern (”AP speckle”) which repeats every
action potential and arises from cellular micromotion.

Our setup (Fig. 1 A) is based on widefield interferometric scattering
microscopy (iSCAT). We illuminate the cell with coherent light. The resulting
image is an interference of light scattered by the cell and light scattered at
the cover slide-immersion medium (water) interface, providing common-path
suppression of vibrations in the setup. Light scattered in random parts of the
cell interferes, forming a speckle signal. In iSCAT, this speckle background
is usually carefully suppressed, e.g. to highlight motion of a single
nanoparticle 22. ChiSCAT takes an opposite approach. In order to generate a
motion fingerprint of the entire cell, we maximize the speckle background by
employing speckle illumination (Fig. 1A+B). This is achieved by a holographic
diffusor in the excitation path. Importantly, speckle illumination uses the
full numerical aperture of the microscope. Both illumination and detection
have a high numerical aperture, yielding a higher resolution than classical
widefield iSCAT or quantitative phase imaging, which employ a parallel, i.e.
low-NA, excitation beam. The setup features a correlative path for
fluorescence voltage imaging (Fig. 1A+C), which is only needed as a ground-
truth reference to benchmark the processing algorithms. We employ this setup
to perform experiments on human induced pluripotent stem cells derived
cardiomyocytes, with mechanical contraction has been disabled by the myosin-
inhibitor blebbistatin. Since this inhibition might not be perfect, these
cells can potentially exhibit larger micromotion in response to an AP than
neurons. Most likely, the motion is larger than few nanometers, but still
significantly below the optical diffraction limit ($\approx$ 240 nm).

In the ChiSCAT channel we expect a signal as sketched in Figure 1 D. It
consists of three components: a static speckle background created mainly by
light scattered from the coverslide, a speckle pattern which is modulated by
the time-dependent and repeating AP signal, and noise which for sufficiently
strong illumination is dominated by photon shot noise.

Mathematically, the superposition of two of these three components in the
camera plane can be modeled as a complex (phasor) electric fields

$E_{\text{all}}=E_{\text{static}}+E_{\text{AP}}$

Here, $E_{\text{static}}$ refers to light reflected from the cover slide and
static parts of the cell, and $E_{\text{AP}}$ to light scattered from cellular
components varying along the AP, e.g. a vibrating plasma membrane. All fields
$E_{\text{all$|$static$|$AP}}(x,y,t)$ are random speckle fields in the spatial
coordinates $x$ and $y$, and can depend on time ($t$). The intensity recorded
by the camera is then given by

$I_{\text{all}}=E_{\text{all}}^{*}E_{\text{all}}\approx
I_{\text{static}}+I_{\text{AP}}+I_{\text{noise}}$

Here, a noise term $I_{\text{noise}}$ has been added. Crucially, the AP signal
can be factorized as follows

$\displaystyle E_{\text{AP}}(x,y,t)=E_{\text{AP}}(x,y)\otimes a(t);\qquad$
$\displaystyle
I_{\text{AP}}(x,y,t)=\text{Re}\left[E_{\text{static}}(x,y)^{*}\cdot
E_{\text{AP}}(x,y)\right]\otimes a(t)=:I_{\text{AP}}(x,y)\otimes a(t);$

where $a(t)$ denotes action potential amplitude, likely following a similar
time trace as the trans-membrane voltage. In a simplified picture, whenever
$a(t)$ spikes, a characteristic pattern $I_{\text{AP}}(x,y)$ appears in the
ChiSCAT recording.

The ChiSCAT recording is interferometrically sensitive to motion, and
meaningful images can be reconstructed from the chaotic speckle pattern by
data processing. As a simple example, temporal band-pass filtering of the
video stream reveals an easily recognizable image of individual cells.
Fluctuations at high ($>300$ Hz) frequencies are markedly reduced in or around
the nucleus, possibly due to restricted diffusion in the nucleus and
reticulum, confirming recent observations by refractive index tomography 23.
ChiSCAT is depth-selective. The signal observed in a region of interest arises
mainly from a range of depths comparable to the size to the region, because
ChiSCAT, in contrast to existing schemes 24, 21 employs high-NA illumination.
We demonstrate this by measuring the suppression of light scattered from a
movable out-of-focus plane (Fig. 2, F + G).

##  3 Data processing

###  3.1 Preliminary analysis

Figure 2: Frequency-resolved cellular dynamics imaging by ChiSCAT imaging.
A-D: rms activity in a band-pass-filtered ChiSCAT recording. E: visualisation
as an RGB image (red channel = B, green channel = C, blue channel = D), a
region with reduced high-frequency fluctuations is visible in the center of
the cell, presumably the nucleus and/or reticulum. F: Measurement of depth-
selectivity. The data presented are camera images of a coverslide moving out
of focus for iSCAT and ChiSCAT illumination. The number in the corner denotes
the distance from the focal plane in $\mu$m. G: observed signal intensity as a
function of distance from focus, obtained by integrating across a region of
interest in F. We compare a smooth sample (cover slide, traces ”iSCAT smooth”,
”ChiSCAT smooth”) and a rough sample (polymer microspheres, ”iSCAT rough”,
”ChiSCAT rough”). In all cases, the ChiSCAT signal intensity drops
significantly faster then iSCAT.  Figure 3: Supervised match filtering
approach. Ground truth AP is extracted from the training subset of the
fluorescence movie to calculate average spike-triggered speckle movie. The
latter is then used as convolution filter on the rest of the speckle signal,
allowing to extract AP from the validation part of the movie.

###  3.2 Supervised learning

We now turn to the main goal of this work: label-free detection of action
potentials from a visually non-interpretable ChiSCAT recording. In
mathematical terms, the goal is finding $a(t)$, the time-varying amplitude of
AP activity with maximum signal-to-noise ratio.

It is known that the optimal linear solution to this problem is matched
filtering 25. This scheme provides an estimate $a_{\text{MF}}(t)$ of $a(t)$ by
convolving the signal (in our case a ChiSCAT movie $I_{\text{all}}$) with a
time-reversed elementary template $a_{\text{el}}$

$a_{\text{MF}}=I_{\text{all}}\circledast_{t}a_{\text{el}}=\sum_{x,y,t}I_{\text{all}}(x,y,t)I_{\text{el}}(x,y,-t)$

In our case, $I_{\text{el}}=I_{\text{AP}}\otimes a_{\text{el}}(t)$ can be
thought of as a noise-free ChiSCAT movie of a perfect single action potential.
Crucially, neither $I_{\text{AP}}$ nor $a_{\text{el}}$ is known in advance.

One way to obtain $I_{\text{AP}}$ is supervised learning by spike-triggered
averaging of the ChiSCAT signal, which we demonstrate in Figure 3. We first
extract a fluorescence trace by spatially averaging the fluorescence movie.
Fluorescence peaks, corresponding to individual APs, are detected and used to
extract slices from the ChiSCAT movie (only training subset), which are then
averaged to produce an estimation of $I_{\text{AP}}$. The original speckle
movie is then convolved with this extracted matched filter to produce the
recovered signal $a_{\text{MF}}(t)$.

As visible from Figure 3, this approach is indeed able to recover individual
APs, however it suffers from two problems: firstly, it requires a known ground
truth signal for training (fluorescence in our case), which undermines the
concept of label-free microscopy. Secondly, this approach is only optimal
under assumption of static background (static speckle $I_{\text{static}}$ in
the Figure 1, D) and a perfectly repeating dynamic pattern $I_{\text{AP}}$,
while in reality both slowly drift on a scale of 2-3 seconds due to slow
motion of the cell. This makes the spike-triggered average incoherent and
reduces the signal. In an experiment on 64 regions of cells, supervised
learning was successful in 36% of the regions.

###  3.3 Unsupervised learning

The most central discovery of this work is an unsupervised learning scheme
that can efficiently recover repeating patterns of motion without requiring
ground truth information. It instead exploits the a priori information that
APs are recurring events and that the approximate temporal amplitude pattern
$a_{\text{el}}$ of an AP is known.

The full algorithm is visualized in the Figure 4 (A). It is based on a
combination of temporal matched filtering and motif discovery. The algorithm
begins by convolving the raw ChiSCAT movie along the time axis with a 1D model
of the signal $a_{\text{el}}$. For simplicity, a zero-mean Gaussian function
was chosen, the width $\sigma$ of which was adapted to the typical timescale
of an AP.

Figure 4: Unsupervised reconstruction of action potentials. (A) Signal
processing pipeline. The ChiSCAT movie is matched-filtered by convolution with
a temporal template of the action potential. Recurring events are identified
by computing the Gramian matrix $G_{ij}=f_{i}\dot{f}_{j}$ for each pair of
frames $f_{i},f_{j}$. Recurring events appear as off-diagonal peaks in this
matrix, and a column or row crossing one of the peaks (”Cross-correlation
trace”) is a time trace of the AP activity. A full-length AP trace (”largest
eigenvector”) is obtained by eigendecomposition of $G$. (B) reconstructed AP
activity for different samples of cells. (C) Distribution of correlation
coefficient between extracted signal and ground truth for different samples of
cells. ChiSCAT restores the AP signal in the majority of cases. (D) Simulated
SNR of the extracted signal for different algorithms as a function of SNR in a
single pixel ($N_{\text{px}}=100^{2}$, 9 APs in the simulated data). The full
ChiSCAT algorithm demonstrates an intermediate performance between matched
filtering with a perfect template and simple extraction of off-diagonal peaks
in the Gramian.

The resulting convolved movie was subsequently cropped to a region of interest
(ROI), identified from pixels with high temporal variability. This is
accomplished by computing the standard deviation along the time axis, followed
by Gaussian smoothing and thresholding.

We then search for recurring patterns in the resulting movie by calculating
the dot product between every possible pair of frames, forming a Gramian
matrix. A recurring events, i.e. a set of two similar frames occurring some
time apart, will produce an off-diagonal peak in this matrix because the
frames are strongly correlated with each other, whereas each of them is
uncorrelated with the noise. This approach to identifying recurring events is
reminiscent of a recurrence plot 26, only using a dot product rather than a
difference as a metric for similarity. APs can be detected as off-diagonal
peaks of the Gramian matrix, and a column or row crossing one of the peaks is
a time trace of AP activity.

Due to the slow fluctuations of the cell, the cross-correlation between two
frames both containing an AP decreases with increasing temporal distance
between them, and vanishes for timescales larger than few seconds. To
reconstruct a non-decaying AP trace over the ChiSCAT movie, we use a rank-one
approximation, that is we find a vector $a_{\text{rec}}$, such that its outer
product with itself $a_{\text{rec}}a_{\text{rec}}^{\intercal}$ approximates
the Gramian matrix. One can imagine this as finding a checkerboard pattern in
the matrix which best approximates the experimentally observed Gramian.
Technically, this is achieved by finding the largest eigenvector of the
Gramian. Before the eigendecomposition, the diagonal of the Gramian matrix is
zeroed out to reduce the influence of random non-recurrent events.
Importantly, the low-rank approximation aggregates information from multiple
action potentials and hence improves the signal-to-noise ratio over what could
be obtained in a single correlation of one pair of frames.

Applying the algorithm to a set of cell regions (Fig. 4 B), we find that it
indeed recovers action potentials, even for regions where supervised learning
has failed. Overall, detection succeeds in 71% of the regions (Fig. 4 C),
which is a marked improvement over supervised detection.

We can confirm this improvement by a simple numerical model (Fig. 4 D). It
models the frames $\vec{f}_{i}$ of the speckle movie as random Gaussian noise
with an additional fixed zero-mean random pattern $\vec{p}$ periodically
superimposed onto some selected frames to model the signal. This effectively
models action potentials as a train of delta functions in time. From this
synthetic dataset we compute three time traces: 1) The time series
$r_{i}=\vec{f}_{i}\cdot\vec{p}$, effectively modeling spatial matched
filtering with a perfect template $\vec{p}$. 2) The time series
$r_{i}=\vec{f}_{s}\cdot\vec{f}_{i}$, where $\vec{f}_{s}$ is a signal frame
containing both the signal pattern $\vec{p}$ and Gaussian noise, effectively
modeling a single column or row of the Gramian matrix in Fig. 4. 3) The time
series obtained from the full ChiSCAT algorithm, i.e. all steps of Fig. 4 A.
For all series, we compare the height of a signal peak with the rms noise of a
signal-free region. As expected, spatial matched filtering performs best, and
can be fully matched by the other schemes only if a signal-to-noise ratio
larger than one is already obtained in a single-pixel time trace. Unsupervised
detection correlates the movie with a signal frame instead of the perfect
pattern $\vec{p}$. For weaker signals, this signal frame is dominated by
noise, which leads to inferior performance. A simple analytical estimate (SI)
suggests that this overhead is a factor of $\sqrt[4]{N_{\text{px}}}$ in SNR,
where $N_{\text{px}}$ is the number of pixels in a frame. Due to the slow
($\sqrt[4]{\;}$) scaling, this overhead is not excessive, reducing the SNR by
one order of magnitude for a $100\times 100$ pixel movie. The full ChiSCAT
algorithm recovers for part of this loss, because it searches for an extended
pattern of cross-peaks in the Gramian matrix and hence aggregates information
from multiple action potentials. Over a wide range of single-pixel signal-to-
noise ratios, the resulting performance approaches matched filtering.

##  4 Results and discussion

In summary, we have demonstrated an unsupervised learning algorithm that can
recover action potentials from a microscopy movie, even from a chaotic speckle
pattern, without a priori information on the timing and the exact spatial
pattern of an AP. With this tool at hand, we detect action potentials with
interferometric sensitivity in an experimentally simple microscopy scheme.
Combining iSCAT microscopy with speckle illumination, makes it
interferometrically sensitive to motion. It harnesses the higher sensitivity
that can be achieved in reflective schemes and features common-path rejection
of vibrations and a freely tunable illumination wavelength.

Our results also demonstrate that living cells are interferometrically stable
for at least a few seconds and that APs repeating within this time indeed
trigger the same interferometric pattern. This opens a window where algorithms
can be devised to search for repeating signals rather than a known pattern.

The signal to noise ratio of our algorithm is inferior to algorithms searching
for a known spatial pattern, and scales as $\sqrt[4]{N_{\text{px}}}$, i.e. for
a realistic setup having $100\times 100$ pixels ChiSCAT will be 10 times less
sensitive than matched filtering. The theory predicts that lowering the number
of pixels will improve the SNR, achieving optimality in the limiting case of
$N_{\text{px}}=1$. However, this would make distinguishing between an AP
signal and a random fluctuations impossible, since both of them will exhibit
exactly same spatial pattern (consisting of 1 pixel). This trade-off leads to
the existence of an optimal number of pixels for the given experiment, which
will need more investigation in future work.

Recovery of signal with ChiSCAT algorithm depends not only on the number of
pixels, but also on the density of spikes: the low rank approximation
minimizes the sum of squares of residuals, i.e. the algorithm will converge to
a component which dominates the Gramian matrix. Increasing the number of
spikes increases the number of off-diagonal peaks in the Gramian matrix
quadratically, helping the algorithm to recover the real AP signal. Thus, the
theory predicts that the ChiSCAT algorithm can recover even weaker signals if
cells spike more often, e.g. in primary neurons.

While our demonstration is based on a speckle-based variant of iSCAT
microscopy, the algorithm is agnostic against the imaging scheme employed, and
could also operate on visually interpretable imaging datasets obtained by e.g.
quantitative phase microscopy, ROCS, refractive index tomography or coherence
tomography 21, 27, 28, 29. Importantly, it could identify any repeating motion
correlating with action potentials, not only motion of the plasma membrane. It
could thus discover additional intrinsic signals, such as motion of organelles
in response to Ca release, or a lateral motion in the axoplasm which is
predicted by a non-standard theory of action potentials 30. Still, it is
notable that our algorithm can even operate on speckle patterns. This paves
the way to detecting action potentials even in scattering tissue, including
the living brain.

##  5 Methods

All the experiments have been performed with custom-built microscope (see SI
for details). The commercially available iPS cell line SC950A-1 (Biocat) was
cultivated in StemMACS iPS-Brew (Miltenyi Biotech). Once the cells had reached
80% confluence, they were split as aggregates using ReLeSR (Stemcell
technologies) according to the manufacturer’s instructions and seeded at a
cell density of 20,000 cells/cm2. For the selection of cardiomyocytes, clones
with the $\alpha$MHC promoter 31 and for the selection of pacemaker cells,
double transfected clones with TBX3 and $\alpha$MHC promoter 32 were
generated. Four days before the start of differentiation, 20000 cells/cm2 were
seeded into one well of a 6 well plate in StemMACS iPS-Brew. Differentiation
protocol was applied. After end of differentiation, cells were dissociated
using the Multi Tissues Dissociation Kit 3 (Miltenyi Biotech) and seeded as
single cells for further analyses. See SI for detailed information about
methods.

The authors wish to thank Marten Möller for expert technical assistance. This
work has been supported by the Deutsche Forschungsgemeinschaft (DFG) SFB 1477
“LightMatter Interactions at Interfaces,” Project No. 441234705. S.K., C.R.
and R.D. received funding from the EU Structural Fund (ESF/14- BM-A55-0024/18)
and the Federal Ministry for Economic Affairs and Climate Action (16KN083635).
In addition, S.K. is supported by the DFG (VA1797/1-1). Moreover, R.D. is
supported by the DFG (DA1296/6-1 and GRK 2901 Sylobio), the DAMP foundation,
the German Heart Foundation (F/01/12), the BMBF (VIP+00240) and the BMEL (FKZ:
281A819B21).

Optical setup description, details about numerical and analytical estimation
of ChiSCAT algorithm performance.

## References

  * Hill and Keynes 1949 Hill, D. K.; Keynes, R. D. Opacity changes in stimulated nerve. _The Journal of Physiology_ 1949, _108_ , 278–281
  * Cohen et al. 1968 Cohen, L. B.; Keynes, R. D.; Hille, B. Light Scattering and Birefringence Changes during Nerve Activity. _Nature_ 1968, _218_ , 438–441
  * Iwasa et al. 1980 Iwasa, K.; Tasaki, I.; Gibbons, R. C. Swelling of Nerve Fibers Associated with Action Potentials. _Science_ 1980, _210_ , 338–339, Publisher: American Association for the Advancement of Science
  * La Porta et al. 1990 La Porta, A.; Stepnoski, R.; Raccuia-Behling, F.; Kleinfeld, D.; Slusher, R.; Blonder, G. Recording action potential in cultured Aplysia neurons using intrinsic optical signals. OSA Annual Meeting. 1990; p MPP3
  * Stepnoski et al. 1991 Stepnoski, R.; LaPorta, A.; Raccuia-Behling, F.; Blonder, G.; Slusher, R.; Kleinfeld, D. Noninvasive detection of changes in membrane potential in cultured neurons by light scattering. _Proceedings of the National Academy of Sciences_ 1991, _88_ , 9382–9386
  * MacVicar and Hochman 1991 MacVicar, B. A.; Hochman, D. Imaging of synaptically evoked intrinsic optical signals in hippocampal slices. _Journal of Neuroscience_ 1991, _11_ , 1458–1469
  * Kim et al. 2007 Kim, G.; Kosterin, P.; Obaid, A.; Salzberg, B. A mechanical spike accompanies the action potential in mammalian nerve terminals. _Biophysical journal_ 2007, _92_ , 3122–3129
  * LaPorta and Kleinfeld 2012 LaPorta, A.; Kleinfeld, D. Interferometric detection of action potentials. _Cold Spring Harb. Protoc_ 2012, _2012_ , 307–311
  * Badreddine et al. 2016 Badreddine, A. H.; Jordan, T.; Bigio, I. J. Real-time imaging of action potentials in nerves using changes in birefringence. _Biomedical optics express_ 2016, _7_ , 1966–1973
  * Yang et al. 2018 Yang, Y.; Liu, X.-W.; Wang, H.; Yu, H.; Guan, Y.; Wang, S.; Tao, N. Imaging action potential in single mammalian neurons by tracking the accompanying sub-nanometer mechanical motion. _ACS nano_ 2018, _12_ , 4186–4193
  * Ling et al. 2018 Ling, T.; Boyle, K. C.; Goetz, G.; Zhou, P.; Quan, Y.; Alfonso, F. S.; Huang, T. W.; Palanker, D. Full-field interferometric imaging of propagating action potentials. _Light: Science & Applications_ 2018, _7_ , 107
  * Ling et al. 2020 Ling, T.; Boyle, K. C.; Zuckerman, V.; Flores, T.; Ramakrishnan, C.; Deisseroth, K.; Palanker, D. High-speed interferometric imaging reveals dynamics of neuronal deformation during the action potential. _Proceedings of the National Academy of Sciences_ 2020, _117_ , 10278–10285
  * Mueller and Tyler 2014 Mueller, J. K.; Tyler, W. J. A quantitative overview of biophysical forces impinging on neural function. _Physical biology_ 2014, _11_ , 051001
  * Mosbacher et al. 1998 Mosbacher, J.; Langer, M.; Hörber, J.; Sachs, F. Voltage-dependent membrane displacements measured by atomic force microscopy. _The Journal of general physiology_ 1998, _111_ , 65–74
  * González-Pérez et al. 2016 González-Pérez, A.; Mosgaard, L. D.; Budvytyte, R.; Villagrán-Vargas, E.; Jackson, A. D.; Heimburg, T. Solitary electromechanical pulses in lobster neurons. _Biophysical chemistry_ 2016, _216_ , 51–59
  * Choi et al. 2007 Choi, W.; Fang-Yen, C.; Badizadegan, K.; Oh, S.; Lue, N.; Dasari, R. R.; Feld, M. S. Tomographic phase microscopy. _Nature methods_ 2007, _4_ , 717–719
  * Zhang et al. 2001 Zhang, P.-C.; Keleshian, A. M.; Sachs, F. Voltage-induced membrane movement. _Nature_ 2001, _413_ , 428–432
  * Howe et al. 2019 Howe, C. L.; Webb, K. F.; Abayzeed, S. A.; Anderson, D. J.; Denning, C.; Russell, N. A. Surface plasmon resonance imaging of excitable cells. _Journal of physics D: Applied physics_ 2019, _52_ , 104001
  * Yaqoob et al. 2011 Yaqoob, Z.; Yamauchi, T.; Choi, W.; Fu, D.; Dasari, R. R.; Feld, M. S. Single-shot Full-field reflection phase microscopy. _Opt. Express, OE_ 2011, _19_ , 7587–7595, Publisher: Optica Publishing Group
  * Singh et al. 2019 Singh, V. R.; Yang, Y. A.; Yu, H.; Kamm, R. D.; Yaqoob, Z.; So, P. T. C. Studying nucleic envelope and plasma membrane mechanics of eukaryotic cells using confocal reflectance interferometric microscopy. _Nat Commun_ 2019, _10_ , 3652, Number: 1 Publisher: Nature Publishing Group
  * Hu and Popescu 2019 Hu, C.; Popescu, G. Quantitative phase imaging: principles and applications. _Label-Free Super-Resolution Microscopy_ 2019, 1–24
  * Piliarik and Sandoghdar 2014 Piliarik, M.; Sandoghdar, V. Direct optical sensing of single unlabelled proteins and super-resolution imaging of their binding sites. _Nature communications_ 2014, _5_ , 4495
  * Hugonnet et al. 2023 Hugonnet, H.; Han, H.; Park, W.; Park, Y. Improving Specificity and Axial Spatial Resolution of Refractive Index Imaging by Exploiting Uncorrelated Subcellular Dynamics. _ACS Photonics_ 2023, Publisher: American Chemical Society
  * Kukura et al. 2009 Kukura, P.; Ewers, H.; Müller, C.; Renn, A.; Helenius, A.; Sandoghdar, V. High-speed nanoscopic tracking of the position and orientation of a single virus. _Nature methods_ 2009, _6_ , 923–927
  * North 1963 North, D. O. An analysis of the factors which determine signal/noise discrimination in pulsed-carrier systems. _Proceedings of the IEEE_ 1963, _51_ , 1016–1027
  * Kamphorst et al. 1987 Kamphorst, J.-P.; Ruelle, D.; others Recurrence plots of dynamical systems. _Europhysics Letters_ 1987, _4_ , 17
  * Jünger et al. 2016 Jünger, F.; Olshausen, P. v.; Rohrbach, A. Fast, label-free super-resolution live-cell imaging using rotating coherent scattering (ROCS) microscopy. _Scientific reports_ 2016, _6_ , 30393
  * Charrière et al. 2006 Charrière, F.; Marian, A.; Montfort, F.; Kuehn, J.; Colomb, T.; Cuche, E.; Marquet, P.; Depeursinge, C. Cell refractive index tomography by digital holographic microscopy. _Optics letters_ 2006, _31_ , 178–180
  * Huang et al. 1991 Huang, D.; Swanson, E. A.; Lin, C. P.; Schuman, J. S.; Stinson, W. G.; Chang, W.; Hee, M. R.; Flotte, T.; Gregory, K.; Puliafito, C. A.; Fujimoto, J. G. Optical Coherence Tomography. _Science_ 1991, _254_ , 1178–1181
  * El Hady and Machta 2015 El Hady, A.; Machta, B. B. Mechanical surface waves accompany action potential propagation. _Nature communications_ 2015, _6_ , 6697
  * Klug et al. 1996 Klug, M. G.; Soonpaa, M. H.; Koh, G. Y.; Field, L. J.; others Genetically selected cardiomyocytes from differentiating embronic stem cells form stable intracardiac grafts. _The Journal of clinical investigation_ 1996, _98_ , 216–224
  * Jung et al. 2014 Jung, J. J.; Husse, B.; Rimmbach, C.; Krebs, S.; Stieber, J.; Steinhoff, G.; Dendorfer, A.; Franz, W.-M.; David, R. Programming and isolation of highly pure physiologically and pharmacologically functional sinus-nodal bodies from pluripotent stem cells. _Stem cell reports_ 2014, _2_ , 592–605