2.1.

Optical Mapping

A number of techniques have been applied to investigate the propagation of action potential within cardiac tissues. Techniques such as using patch clamps provide meticulous information regarding the ionic currents across the membranes, but do not offer information regarding the interaction between cells. Multielectrode recordings provide reasonable spatial resolution but not the time course of action potential propagations. Optical mapping techniques, although relatively new, have the ability to provide both high spatial resolution and temporal resolution.^{6 7 8 9}

Optical mapping systems are generally composed of specialized illumination and detection instruments with a variety of characteristics depending on the application. In this paper, stained cardiac tissue preparations are illuminated with a chosen light source. The light source is filtered to select the optimal excitation wavelengths for the specific dye chosen to convert transmembrane potentials into optical signals. Fluorescent light from the preparation, due to the excitation by the illumination, is filtered to remove the background-reflected light before reaching the CCD detector. The CCD detector is placed in the objective image plane and acquires the final optical signals. The signal is then processed and stored by a frame grabber.^{10 11 12 13 14 15 16 17 18 19}

3.1.

Optical Mapping System

A digital imaging system setup was designed to map the action potential propagation within a piece of cardiac tissue with dimensions of 20×20 mm. A detailed representation of the setup is shown in Fig. 1. The system consists of a 150-W quartz halogen light source, a fiber optic light guide, an emission filter, an excitation filter, a dichroic filter, and a custom CCD imager.

Figure 1

Optical mapping system. Light from the halogen light source is filtered by the excitation filter and reflected by the dichroic mirror onto the tissue sample. The induced fluorescence from the di-4-anepps molecules, bonded to the tissue sample, is then filtered twice through the dichroic filter and then through the emission filter before reaching the CCD detector.

3.2.

CCD Imager

The spatial complexity of the propagating wavefront dictates the spatial resolution requirements for the CCD detector. However, it is often difficult to know, before hand, the spatial complexity of wavefronts, thus making it difficult to decide on a minimum spatial resolution. Independent of wavefront complexity, with a spatial resolution of 1 mm or lower, many cells will contribute to the light signals acquired by an individual detector element and to the optical action potential. This can result in blurring of the action potential. Therefore, a photodetector with a spatial resolution significantly higher than 1 mm is required. However, without adequate temporal resolution, it is impossible for any detector, no matter how high the spatial resolution, to accurately acquire an action potential wavefront propagation.

The temporal resolution requirement of the detector is dictated mainly by the propagation velocity of the action potential within the tissue preparation. The wavefront propagation in cardiac tissues has an average velocity around 0.5 m/s, with individual velocities ranging from 0.1 to 1 m/s. With a 20×20-mm tissue preparation, an action potential starting at one corner of the tissue with a velocity of 0.5 m/s will take approximately 28 ms to traverse to the opposite corner. It will take a photodetector with a minimum frame rate of 36 frames/s (1/28 ms) to capture the propagation. The detailed information of action potential propagation requires higher temporal resolution.

Another factor involved in setting a standard for temporal resolution is the temporal characteristic of the individual action potential. Experiments using floating microelectrode recordings from the epicardial surface of guinea pig ventricle showed²⁰ that approximately 90% of action potential signal was below 150 Hz. Since sampling theory requires a rate of at least twice the highest frequency component of a given signal for its correct reconstruction, a CCD detector with a sampling rate at least greater than 300 frames/s is necessary.

The dynamic range of the photodetector is also a crucial factor. A low dynamic range makes it difficult to capture large background fluorescence while providing adequate voltage resolution for the action potential. This is important because the total fluorescence measured consists mostly, around 90%, of background fluorescence. A system with high temporal and spatial resolutions but low dynamic range will not be able to distinguish between noise and changes in signal intensity due to the propagation of the action potential wave front.

Taking account of the preceding considerations, a CCD chip with 128×128 pixels, each pixel having a dimension of 0.016×0.016 mm (Dalsa, Ontario, Canada), was selected. With dedicated readout electronics, the CCD detector system provides a frame rate of 490 frames/s and 12-bit digitization. The lens system was designed to image an area of approximately 20×20 mm at its minimum object distance. A 25-mm/ f-0.95 lens was chosen. It utilizes a C-mount connection. The resulting lens setup has a demagnification ratio of 9.2:1, and a spatial resolution of 3.2 line pairs/mm with an image area of 20×20 mm at its minimum object-image conjugate.

3.3.

Optical Filters

The fast fluorescence dye di-4-ANEPPS as the mapping agent was selected for the experiment. Di-4-ANEPPS is a voltage-sensitive, fast dye used in detecting the action potential across all, or portions of, the membranes of nerve and cardiac muscle cells. It has a high SNR and a relatively high fluorescent change in the presence of a change in voltage^{21 22 23 24 25 26} (∼10% per 100 mV). Di-4-ANEPPS has an absorption maximum around 475 nm and an emission maximum around 617 nm. Designed in accordance with the dye absorption/emission characteristics, the excitation filter is a bandpass filter (480±30 nm), the emission filter is a bandpass filter (635±27.5 nm), and the dichroic filter transmits light only with a wavelength above 550 nm.

3.4.

System Characterization

The performance of the system must be evaluated. Because CCD detectors have different responses to different wavelengths of light, all the illuminations used in the evaluation experiments were filtered to approximate the wavelengths given off by Di-4-ANEPPS dye molecules during fluorescence.

3.4.1.

Linearity

Linearity is one of the most important characteristics of the optical mapping system. To be able to accurately acquire fluorescence signals and to study their behaviors, the optical mapping system must have as close to a linear relationship as possible between the input intensity of the light photons and its digital output. To test the linearity of the optical system, a series of frames of a uniformly illuminated constant field were taken, with variations in integration time for each individual frame. Because the camera under inspection does not have the ability to allow the control of the integration time, different frame rates were used to acquire the frames. The readout time was then subtracted from the acquisition time of each frame to deduce the integration time for each particular frame:

Eq. (1)

$$\frac{1}{\text{frame rate}}(1\text{ frame})-\text{frame transfer time}(133.9\mu s)=\text{integration time}\text{.}$$

A series of frames were acquired at a frame rate ranging from 30 to 490 frames/s in 10-frame/s intervals. Along with the images, dark images were also acquired at each individual frame rate. The dark image was then subtracted from the corresponding image to remove the offset dark current. The mean was then calculated over a 10×10-pixel region in the center of the processed image. The final result is plotted as a function of integration time in Fig. 2.

Figure 2

Linearity curve. The output intensity in digital units is linearly proportional to the integration time.

3.4.2.

Spatial resolution and contrast transfer function

To determine the spatial resolution of the entire optical mapping system, a target U.S. Air Force (USAF) 2×2-in. NEG made by Edmund Industrial Optics was imaged and the contrast transfer function (CTF) was calculated using the following equation:

Eq. (2)

$$\text{CTF}=\frac{I_{\text{max}}-I_{\text{min}}}{I_{\text{max}}+I_{\text{min}}},$$

where I _max and I _min are maximum and minimum signals, respectively. The resulting curve is shown in Fig. 3.

Figure 3

CTF versus the spatial resolution of the system.

3.4.3.

Photon transfer curve

The photon transfer technique has proven to be one of the most valuable CCD transfer curves for calibrating, characterizing, and optimizing system performance. Every component in a CCD camera must work correctly in order to produce a photon transfer curve with the right characteristics. The photon transfer curve is a plot of signal S(DN) versus noise σ_S(DN) for the optical mapping system, where DN is dark noise.

In our experiment, 50 frames were acquired at a frame rate ranging from 30 to 490 frames/s in 10-frame/s intervals. To improve the statistics for the photon transfer data, the 50 frames taken at the same illumination level were averaged. Then, S(DN) was determined by calculating the mean of the resulting image.

Noise data for the ordinate were determined by calculating the standard deviation of the region of pixels after pixel-to-pixel nonuniformity was removed. Pixel nonuniformity was eliminated by simply differencing two identical images taken back to back at the same exposure level. The variance, σ_S ²(DN), of this differenced frame was given by

Eq. (3)

$${\sigma }_s^2(\text{DN})=\frac{{\sum }_{{}_{i=1}}^{N_{\text{pix}}}{[S_i(\text{DN})-S(\text{DN})]}^2}{2N_{\text{pix}}},$$

where S_i(DN) is the signal of i’th pixel of the first image, S(DN) is the mean signal of the two images, and N _pix is the number of pixels of one image.

A factor of 2 must be included in the denominator because when two identical frames are either subtracted or added, the random noise component (the standard deviation) of the resultant frame increases by a square root of 2. To improve the statistics for the noise data, the actual noise σ_S(DN) was determined by first differencing frames 1 and 2, then frames 2 and 3, and so on with the last differencing being between the first frame and the very last frame. These values were then averaged to yield the final noise σ_S(DN). The final curve is shown in Fig. 4. The averaged curve, the solid line, is enveloped between two additional dashed curves, which are the maximum and minimum limits derived from all the series of photon transfer curves calculated without averaging.

Figure 4

Photon transfer curve. The curve is initially flat, where DN dominates. The curve then takes on a slope of 1/2 due to shot noise. The final section of the curve has a slope of 1 governed by noises caused by pixel nonuniformities.

The behavior of the optical mapping system’s photon transfer curve is normal, which is an excellent indication that the system works properly. In Fig. 4, the curve is flat when the signal is low (in analog digital units [ADU]). This area is independent of the signal intensity, thus the slope is close to 0. Furthermore, the read noise in this area is very small, less than 10 ADU. In the main body of the curve where shot noise dominates, the slope of the line is close to 1/2. Shot noise represents the noise associated with the random arrival of photons on the CCD, it is proportional to the square root of the number of incident photons, hence the slope of 1/2. The third and final region of the curve is governed by the fixed pattern noise that is the result of variations in sensitivity among detector elements. Noise from pixel nonuniformity is proportional to the signal intensity, and is represented by the slope of 1.

3.5.

Experiments with Tissue Samples

A canine cardiac tissue sample approximately 25×25 mm was harvested from an adult mongrel dog. The tissue was placed within a constant-flow perfusion apparatus immersed with 37 °C Tyrode’s solution (mmol/L: NaCl 123, KCl 5.4, NaHCO ₃ 22, NaH ₂ PO ₄ 0.65, MgCl ₂ 0.5, glucose 5.5, CaCl ₂ 2.0 bubbled with 95% O ₂ and 5% CO ₂ gas mixture). To reduce motion artifacts in the optical recordings, cytochalasin D at concentration of approximately 25 μmol/L was added to the solution, since light scattering caused by mechanical contraction could distort the optical signals of the action potentials. Cytochalasin D has been shown to effectively suppress the cardiac contractile force without significantly altering the action potential characteristics.²⁷

After perfusion with the 37 °C Tyrode’s solution, 5 mg of di-4-ANEPPS dissolved in 4 ml of dimethyl sulfoxide (DMSO) was added to the perfusate to achieve a final concentration of 2 μmol/L. Following the staining with Di-4-ANEPPS, the tissue preparation was again perfused with 37 °C Tyrode’s solution containing 20 μmol/L of cytochalasin D. The final size of the preparation was approximately 20×20 mm. Continued perfusion with warm Tyrode’s solution was used throughout the experiment.

Light coming from a 150-W quartz halogen light source was first filtered through the excitation filter. The remaining light with a wavelength around the absorbance peak of the di-4-ANEPPS dye (∼475 nm) was reflected by the dichroic mirror upon the cardiac tissue preparation. The di-4-ANEPPS dye molecules bonded to the tissue preparation fluoresces under the excitation. The light resulting from the fluorescence (∼617 nm) was double-filtered by the emission filter and the dichroic filter, minimizing the noise from extraneous wavelengths (see Fig. 1). The CCD camera received the optical signal and converted it to digital signal, and then the signal was sent to the computer by the frame grabber. During this process, the tissue preparation was paced by a 2× diastolic threshold current, 1 Hz frequency, using a sheathed plunge bipolar electrode and a programmable stimulator.