Automated detection of elementary calcium release events using the á trous wavelet transform

Abstract

We developed an algorithm for the automated detection and analysis of elementary Ca2+ release events (ECRE) based on the two-dimensional nondecimated wavelet transform. The transform is computed with the "à trous" algorithm using the cubic B-spline as the basis function and yields a multiresolution analysis of the image. This transform allows for highly efficient noise reduction while preserving signal amplitudes. ECRE detection is performed at the wavelet levels, thus using the whole spectral information contained in the image. The algorithm was tested on synthetic data at different noise levels as well as on experimental data of ECRE. The noise dependence of the statistical properties of the algorithm (detection sensitivity and reliability) was determined from synthetic data and detection parameters were selected to optimize the detection of experimental ECRE. The wavelet-based method shows considerably higher detection sensitivity and less false-positive counts than previously employed methods. It allows a more efficient detection of elementary Ca2+ release events than conventional methods, in particular in the presence of elevated background noise levels. The subsequent analysis of the morphological parameters of ECRE is reliably reproduced by the analysis procedure that is applied to the median filtered raw data. Testing the algorithm more rigorously showed that event parameter histograms (amplitude, rise time, full duration at half-maximum, and full width at half-maximum) were faithfully extracted from synthetic, "in-focus" and "out-of-focus" line scan sparks. Most importantly, ECRE obtained with laser scanning confocal microscopy of chemically skinned mammalian skeletal muscle fibers could be analyzed automatically to reproducibly establish event parameter histograms. In summary, our method provides a new valuable tool for highly reliable automated detection of ECRE in muscle but can also be adapted to other preparations.

FIGURE 1

Noise characteristics. (a) The same simulated ECRE were embedded in Gaussian (left) and Poisson (right) distributed noise at a signal/noise ratio (SNR) of 2.9. Denoising of the images with the wavelet-based denoising method (bottom panels) resulted in identical SNR values (11.7) for both noise types. (b) The histogram of fluorescence intensity background fluctuations of an experimental line scan shows a Poisson distribution that is well approximated by a Gaussian (black solid curve).

FIGURE 2

(a) À trous wavelet transform of different model signals. (Left) A spark-like event; (middle) a square pulse (both synthetic with additive white Gaussian noise); (right) experimental data showing repetitive release events. The lowest trace is the raw data and the underlying smooth trace of F(5) (see text). From bottom to top follow W(5)–W(1). (b) Filter bank structure of the à trous wavelet transform. One iteration consists of one convolution of the signal with a low-pass (LP) and a high-pass (HP) filter (H and G, respectively). The low-pass filtered signal is the input for the next iteration step.

FIGURE 3

Flow-chart diagram of the algorithm. The processing direction starts from the top (input + preprocessing) downwards to the denoising procedure. After convergence of the denoising process, the denoised image is again transformed and ECRE candidates are localized by the detection subroutine. Finally, the morphological analysis (bottom right) of the ECRE is carried out.

FIGURE 4

Sensitivities (left column) and positive predictive values (PPV, right column) at (a) SNR 3.5, (b) 2.5, and (c) 2.0 for the wavelet algorithm (δ = 4.00, τ = 3.25, dashed-dotted lines; δ = 4.00, τ = 5.00, solid lines) and the conventional algorithms (κ = 3.9, dashed lines; κ = 3.5, dotted lines) are shown. The algorithm as in Cheng et al. (15) is labeled conv1 and the algorithm by Izu et al. (11) conv2. Curves shifted to the left denote improved detection properties.

FIGURE 5

Summary of the statistical properties of both algorithms (wavelet, solid lines; conventional, dashed lines) at SNR 2.5. The parameters used were δ = 4.00, τ = 3.75 (wavelet algorithm), and κ = 3.9 (conventional algorithm). Errors are presented as mean ±SE (n = 20, amplitudes 0.2, 0.3 n = 200).

FIGURE 6

Event parameter histograms resulting from the analysis of synthetic images in the line-scan sampling mode. The analysis of the median filtered raw data yields comparable results for both noise levels SNR 3.5 (light gray) and 2.5 (dark gray). RT (8.2 ms), FDHM (16.4 ms), and FWHM (2.39 μm) can reliably be estimated from the distribution modes. All ordinates show relative frequencies.

FIGURE 7

Amplitude distortion introduced by the algorithm. Low event amplitudes are less reliably reproduced because of the additive noise. Events below the detection threshold have to be elevated above this threshold to be detected. Therefore, the curve is flat for small amplitudes. The inset shows the synthetic spark used for the analysis.

FIGURE 8

Direct comparison of denoising and detection properties of the wavelet-based method (c–d), the conventional method 1 (b, e, h, k), and the conventional method 2 (f, l). The analysis was carried out on a simulated event (left column) and raw fluorescence data containing a spontaneous repetitive Ca²⁺ release event (right column). (b, h) The same data after “standard” preprocessing (3 × 3 median and 5 × 5 boxcar filter). (c,i) Wavelet denoised raw data. (d, f, j–l) Output of the detection procedures of the respective algorithms. The single release events appear clearly separated after the wavelet procedure whereas some of them appear clustered after the conventional method. However, they still merge on lower resolution levels as can be seen from the underlying signal elevation in panel i.

FIGURE 9

Simulated line-scan image with high ECRE frequency as it occurs in voltage-clamped amphibian fibers. Events are spark-like and the detection is therefore restricted to wavelet levels W(2) and W(3). The result is almost identical to the conventional(1) algorithm.