| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
1Department of Pharmacology, State University of New York, Upstate Medical University, Syracuse, New York; and 2Biomedical Engineering Program, Department of Electrical and Computer Engineering, University of Rhode Island, Kingston, Rhode Island
Submitted 19 September 2005 ; accepted in final form 17 January 2006
 |
ABSTRACT |
|---|
 TOP ABSTRACT METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
voltage-sensitive dyes; spatial spectrum analysis; cardiac electrophysiology; linear low-pass filtering
0.5 m/s), recording optical action potentials (OAPs) remains a significant technological challenge, requiring high acquisition speeds and transducers with a very wide dynamic range. Contemporary CCD cameras, CMOS cameras, and photodiode arrays used in optical mapping of cardiac propagation run up to 10,000 frames/s. At such acquisition rates, it is extremely difficult to achieve high signal-to-noise ratios, which makes spatial and temporal filtering of the acquired signals one of the key elements of optical mapping. Although spatial and temporal filtering is routinely used in optical mapping studies, there is no consensus regarding the design and use of such filters. There is a concern that filtering decreases spatial resolution and induces distortion. Thus some researchers avoid applying any spatial filters (2), whereas others use complicated adaptive filters (14, 21, 22). This indicates a great need for the development of quantitative criteria that would enable a rational design strategy for spatial and temporal filters in a given application.
The goals of this study were to assess the spatial and temporal spectral characteristics of optically recorded action potentials, design an experimental procedure for selecting the optimal linear filter characteristics, and determine the level of distortions produced by the resulting filters. It is well known that aggressive filtering reduces the noise. The main question, however, is how much filtering can be afforded without significantly distorting the signal? The answer to this question can be obtained only by looking at how the given filtering procedure affects the signal itself. To approximate the uncorrupted signal as closely as possible, we select recordings with better signal-to-noise ratios and subsequently use ensemble averaging. After the spectral characteristics of the pure signal are determined and appropriate filter characteristics (as broad as possible, yet not causing significant signal distortion) are chosen, the filters are applied to raw signals, and their effect is evaluated.
We demonstrate that in three-dimensional pig ventricular wall preparations, spatial filters with kernel diameter as large as 3 mm produce <4% distortion. Temporal filters with five-frame kernels can also be safely used in such preparations even at modest acquisition rates (with 800-frames/s movies). We show examples where applying such filters to raw data significantly increased the signal-to-noise ratio in both the space and time domains. Combining both spatial and temporal filters can improve the signal-to-noise ratio by an order of magnitude and is comparable to ensemble averaging of 100 optical action potentials. The application and limitations of our approach for selecting the parameters of spatial and temporal filters in various optical mapping settings are discussed.
|
METHODS |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
Preparations were perfused with a standard oxygenated Tyrode solution (2, 20) at 80 mmHg and superfused with the same solution at a rate of 40 ml/min. Diacetyl monoxime was added to the Tyrode solution (15 mmol/l) to suppress contractions and eliminate motion artifacts. The voltage-sensitive dye di-4-ANEPPS (15 µg/ml) was added to the perfusate as described previously (9). The preparation was paced at a point on the epicardial surface with a basic cycle length of 500 ms at twice diastolic threshold.
Optical mapping.
Movies were acquired using a high frame-rate 12-bit digital CCD camera (Dalsa CA-D1–0128T) in 2 x 2 binning mode for a final resolution of 64 x 64 pixels. The camera was fitted with a Computar lens (relative aperture 1:1.2, 12-mm focal length) that provided an object field of view of 25 x 25 mm. The movies were acquired at 800 frames/s. Ensemble averaging at each pixel was performed over 100 or more propagating wave fronts synchronized with stimuli markers recorded during acquisition. For spatial and temporal filtering the weighting coefficient, w(i,j), was computed using a triangular (Bartlett) window function (17). The weighting coefficient was maximal at the central pixel (Eq. 1) and linearly decreased toward the edge of the kernel
 | (1) |
Spatial filtering was carried out with conical filters using kernels ranging from 3 x 3 to 25 x 25 pixels. Temporal filtering was performed similarly as weighted averages over a sequence of three or five frames with maximal weight on the central frame.
Noise measurement.
In the time domain, the signal-to-noise ratio was calculated as ratio of signal amplitude for each pixel (calculated after ensemble averaging) to the root-mean-square (RMS) of each pixel in the image obtained during a diastolic interval recording. The RMS was calculated as
 | (2) |
i is averaged intensity for nine neighbor (from i – 4 to i + 4) frames, and n is number of frames in the ensemble.
Distortion measurement.
Signal distortion for each pixel was calculated as the ratio of the square root of the mean deviation of the filtered movie from the ensemble-averaged (EA) movie to the signal amplitude calculated from the EA movie:
 | (3) |
and F
are the pixel values in the filtered and EA movie, respectively; N is the number of frames in the movie; and F
and F
are the maximal and minimal values of the pixel, respectively, in the EA movie over the N frames. The distortion d for the entire movie was calculated by averaging the pixel dx,y values. Frequency spectra. To obtain the spatial spectra, we applied a two-dimensional (2-D) fast Fourier transform (FFT) to each frame of the movie. The 2-D Fourier transform was computed by first transforming each row in the image, replacing each row with its transform, and then transforming each column, replacing each column with its transform (19). We rearranged the quadrants of the resulting spectrum to place the zero frequency component at the center of the spectral image. Spectra were normalized to the noise level in the raw signal. Because the range of the power values in the spectra is very wide, for imaging purposes all spectra were limited by a level of 5.0 (arbitrary units).
To analyze the spatial frequencies, we rotationally averaged the spatial spectra (1, 7). The values of the spatial power spectrum were averaged over all pixels at a given radius from the center of the spatial spectrum.
To obtain the averaged temporal spectra, we calculated the individual spectrum for each pixel in every frame of the movie. Finally, the individual pixel spectra were averaged to obtain a single temporal spectrum for the entire movie.
|
RESULTS |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
|
|
To determine the origin of specific spectral components and the significance of the diagonal bands, we selectively eliminated the respective components and evaluated the effect on the image by applying an inverse FFT. Figure 2 A, top, shows a snapshot of the wave front (frame 9 from Fig. 1A), which occupies approximately half the field of view. Figure 2A, bottom, shows the corresponding spatial power spectrum. The spectrum consists of three main components: the dense core at the center, a diffuse cloud of gray pixels around the core, and a diagonal band. The diagonal band in the spectrum was caused by the shadow of the stimulating electrode in the snapshot (arrow in Fig. 2A) because the orientation of the band is orthogonal to the direction of the electrode shadow. This was demonstrated by eliminating the diagonal band with a notch filter (Fig. 2B, bottom) and applying the inverse FFT; the electrode shadow was removed from the time domain image (Fig. 2B, top). Removing the dense spectral core (Fig. 2C) resulted in subtracting the propagating wave front, leaving only small (high frequency) features in the time domain image. Finally, removing the diffuse cloud resulted in a smooth and clear image of the propagating wave front (Fig. 2D). This suggests spectral components pertinent to wave propagation are concentrated in the low-frequency core of the spectrum.
|
To quantify the time evolution of the spatial spectra, we constructed the plot shown in Fig. 3, which is a horizontal stack of 50 sequential rotationally averaged spatial spectra. This plot eliminates the anisotropy of propagation, thus allowing us to identify the major phases in the evolution of the spectrum over time. Columns in the plot represent the averaged spectra for all pixels equidistant from the center, thus having the same spatial frequency. The plot shows that the high-frequency components due to the propagating wave front constitute the early spectra, but these components diminish during the first 16 ms as the wave front expands over the field of view. In later images, the high-frequency components return when the stimulus electrode, boundary effects, and small surface features of the specimen dominate the image.
|
5 pixels, indicating that the image contained substantial high-frequency components. As time increased and the wave front spread across the field of view, the high-frequency content diminished in the images; this is consistent with the individual spectra in the second row of Fig. 1B and the progressive shortening of the nonzero portions of the columns in the plot of Fig. 3. The reduction of high frequencies continued until 16 ms (Fig. 3, second dashed line and inset). After this, the intensity of the high frequencies increased again (see second row of spectra in Fig. 1B) and reaches maximum after 31 ms. At this time, the wave occupies the entire field of view (Fig. 3, right dashed line), and this late image contains only a small portion of the wave front (Fig. 3, right inset). The spectra of these late-phase images contain a very high level of the high frequencies due to boundary effects and small surface features as explained above. Spatial filtering. On the basis of the plot of Fig. 3, we chose two different strategies for spatial filtering. The first was a conservative strategy to maximally preserve the useful signal. The kernel size was determined by the length of the nonzero portion in the earliest spectrum (the horizontal white dotted line in Fig. 3) and equaled 6 pixels. However, because the conical spatial filter used the peripheral pixels with minimal weight and, respectively, should have smaller effective size, we chose a kernel that was one pixel wider, or 7 x 7 pixels (2.8 x 2.8 mm). The second strategy was more aggressive and was based on the narrowest spectrum (horizontal black dotted line). We chose the second filter with a kernel size of 13 x 13 pixels (5.2 x 5.2 mm) to preserve the wave front shape only during the late phases of propagation, with any distortion concentrated in the earlier phases.
Results of applying these filters are shown in Fig. 4. Figure 4A shows a snapshot of the raw movie (top image) and its spatial spectrum (bottom image) before application of the filters. Figure 4B shows the same snapshot from the EA movie, and the corresponding spectrum. The spectra of spatially filtered images, shown in Fig. 4, C and D, are similar to the spectrum of the EA image in that all have the same dense core, but the vertical and diagonal bands emanating from the core were markedly weakened by spatial filtering.
|
Spatial filtering not only improved the images by eliminating spatial noise and extrinsic detail but also significantly improved the signal-to-noise ratio in the time domain. The effect of spatial filtering on the OAP signal is shown in Fig. 5. Figure 5A shows OAPs obtained from a single pixel of the raw movie (top trace), of the EA movie (middle trace), and after applying the 13 x 13 pixel kernel to the raw movie (bottom trace). Spatial filtering significantly decreased the noise, and the shape of the filtered OAP closely resembles the shape of the EA OAP. For a more detailed comparison, we superimposed OAP upstrokes from the EA and 13 x 13 kernel filtered movies (Fig. 5B); there was excellent agreement between both OAP traces. Figure 5C shows superimposed OAP upstrokes from the EA movie (black line) and the 13 x 13 pixel filtered movie (gray line). The upstroke from the filtered movie is nearly identical to the one obtained from the EA movie.
|
|
Temporal spectra and filtering. Figure 7A shows normalized power spectra achieved by averaging the individual temporal spectra computed from each pixel in the movie. The dashed line in Fig. 7A shows the temporal spectrum of the raw movie. The temporal spectrum had a flat portion caused by noise at frequencies above 100 Hz. The small peak near 120 Hz is likely a harmonic of 60 Hz power line interference. Spatial filtering with the 7 x 7 pixel kernel (2.8 x 2.8 mm) significantly decreased the noise power (Fig. 7A, dotted line), but none of the spatial filters removed all the noise. The residual noise had low spatial frequency and power above 100 Hz in the temporal spectrum. This residual noise power originated partially from the light source (peak at 120 Hz) because fluctuations in the illumination were synchronous for the entire image and cannot be removed by any spatial filter.
|
Figure 8A shows the effect of varying the additional temporal filter kernel size after applying various spatial filters. Even minimal temporal filtering (3-frame kernel, Fig. 8A, middle trace) significantly increased the signal-to-noise ratio. Figure 8B shows that distortion was not significant relative to the EA movie. Thus additional temporal filtering after spatial filtering significantly decreased noise but did not induce additional distortion (Fig. 7C).
|
|
DISCUSSION |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
Our analysis of temporal spectra revealed that the OAP also lacks high-frequency components above 100 Hz. This should allow the use of small (3-frame) temporal kernels even at modest acquisition rates of 400 frames/s. At 2,000 frames/s, temporal low-pass filters with kernels as large as 15 frames could be used without significantly distorting the optical signal.
Because the filters we used are linear, they can be applied sequentially in either order. Spatial filtering removes asynchronous noise produced by the recording device (i.e., noise uncorrelated with the timing of image acquisition), while temporal filtering removes synchronous noise produced by the light source; this noise is uniform within a single image but varies across images due to fluctuations in the illumination. Applying both types of filters can dramatically improve the signal-to-noise ratio, which is equivalent to ensemble averaging of 130 OAPs. The possibility of using a combination of spatial and temporal filters instead of ensemble averaging is particularly important for optical mapping of wave propagation in the heart during nonstationary cardiac arrhythmias when the latter cannot be applied.
There is a good reason to believe that filter characteristics derived from normal propagation spectra will also be appropriate for processing ventricular fibrillation (VF) data. Indeed, during VF the action potential duration and hence the wavelength shorten significantly (11, 16). However, the highest frequency components related to cardiac propagation in both the spatial and time domains still originate from the excitation front: the steeper the front, the stronger the high-frequency components. It is well known that upstrokes during VF slow down compared with normal propagation (24). Accordingly, a low-pass filter that does not distort the normal fronts will not likely distort fronts during VF. However, the signal-to-noise ratio during VF is in general lower than during normal propagation, and it may be tempting to apply a more aggressive filter; this will likely lead to a more significant distortion of the signal.
The fact that spatial and temporal filters with relatively large kernels do not distort the optical signal may seem to contradict the widespread belief that the upstroke of the cardiac action potential has a duration of 1 ms (6) and that the response of styryl voltage-sensitive dyes used in this study is fast enough to cause any noticeable delay (6, 15, 18). However, this is not the case. Although the fluorescence closely follows the transmembrane potential, the optically recorded action potential acquired from thick myocardial preparations deviates significantly from electrical recordings acquired from microelectrodes (5, 8, 12, 13). It does so because the light acquired by the sensor originates from a deep volume of muscle underlying the detector, and from the neighboring tissue (outside the field of view) that has scattered light captured by the detector (13). This increases the upstroke duration from 1–2 ms to 13 ms or more (12) and results in removing the high frequencies in the spatial domain.
Rational selection of the kernel size. The kernel sizes that we determined were optimized for a particular experimental setup and will change if the pixel size and the frame rate of the recording device are different. However, characteristic spatial scales determined from our spectral analysis of the signal will be preserved, provided the geometry of the tissue and the spectral characteristics of the dye (the wavelength of the excitation and emission light) remain unchanged. This should allow other investigators using thick ventricular preparations to select an appropriate kernel size based on our findings. Assume, for example, we had mapped propagation over a 1.6 cm x 1.6 cm area on the three-dimensional pig ventricular wall using a 16 x 16 photodiode array (1.0 mm/pixel resolution) acquired at 3,000 frames/s (3). According to the criteria derived in this study, the appropriate kernel size for conservative spatial filtering would be 3 x 3 pixels (3.0 x 3.0 mm); a 19-frame kernel would be equivalent to our 5-frame temporal filter. This would result in a 14 x 14 array of filtered signals (signals on the boundary would be unfiltered because of edge effects) with effectively no temporal components above 158 Hz.
Limitations. The slow optical upstroke is a result of the spatial averaging of the signal emitted by the 3-D tissue preparation and is not a property of the optical signal. Therefore, in some preparations where this depth averaging is not present (in 2-D monolayer tissue culture, for example), the optical signal should have a much faster upstroke, and the best spatial filter will have a very small kernel size; this may significantly reduce the effectiveness of spatial filtering. The optimal kernel sizes should also be different in the hearts of small animals such as mice, guinea pigs, and rabbits where the thickness of the wall and thus the degree of blurring of the optical signal is likely to vary. The derivation of the optimal nondistorting filters for these species will require a dedicated study.
Our selection of filter parameters is based on the analysis of filter-induced distortions relative to the EA signal. While the characteristics of the filter are determined by the signal, the effectiveness of the filtering procedure will depend on the signal-to-noise ratio and the degree of spectral overlap between the noise and the signal. When the signal and noise have little spectral overlap (high-frequency noise), one should expect excellent results even at very low signal-to-noise ratios. When the noise spectrum significantly overlaps with the spectral range of the signal, one should not expect good results even with optimal filter parameters.
This analysis concentrated on classical (linear) filtering operations and has demonstrated that spatial filters or combined spatial-temporal filters can significantly improve the signal-to-noise ratio while inducing negligible distortion in movies of optically recorded action potentials. Future studies are needed to evaluate the effectiveness of nonlinear statistical filters, which may produce better movie enhancement with lower distortion (17).
|
GRANTS |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
|
ACKNOWLEDGMENTS |
|---|
|
FOOTNOTES |
|---|
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
* S. F. Mironov and F. J. Vetter contributed equally to this work. 
|
REFERENCES |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
This article has been cited by other articles:
|
|
 |
|
  O. Ziv, E. Morales, Y.-k. Song, X. Peng, K. E. Odening, A. E. Buxton, A. Karma, G. Koren, and B.-R. Choi Origin of complex behaviour of spatially discordant alternans in a transgenic rabbit model of type 2 long QT syndrome J. Physiol., October 1, 2009; 587(19): 4661 - 4680. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 H. Bien, E. Entcheva, A. Pertsov, S. Mironov, and F. Vetter Spatial Frequency Content in Optical Mapping of Cardiac Cell Monolayers Am J Physiol Heart Circ Physiol, September 1, 2006; 291(3): H1484 - H1485. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |
