Cardiac Myometer 

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Chapter 3. Volume Imaging Using OCT

Introduction

Optical Coherence Tomography (OCT) is a light-based imaging technique that provides depth-resolved, cross-sectional images of translucent materials. Images can be gathered at a relatively high spatial resolution (~10 µm) non-invasively and without any sample preparation. This makes OCT well-suited for imaging biological tissues, which both transmit and scatter light, without any modification to, or destruction of, the tissue.
This imaging technique was first introduced by Huang et.al. in 1991 where it was applied to imaging the subsurface layers of the retina [70]. Since then, OCT has become an essential tool for clinical ophthalmologists to diagnose the structure and integrity of the retina non-invasively. Over the past few years, there have been significant advances in the technology, improving the speed, resolution and sensitivity of OCT [71], [72]. New applications for the technique have also been demonstrated, such as volumetric imaging gastrointestinal tissue, arteries, and embryonic hearts [45]–[47].
This chapter reports the first application of OCT to image the static volume of cardiac trabeculae. First, the general principles behind OCT are discussed, along with the challenges and limitations in using this method to image cardiac trabeculae. Then, the chapter reports on the implementation and integration of OCT hardware and software into the Cardiac Myometer, and the development of an image processing pipeline for extracting cross-sectional area and volume from the images. Finally, results are presented from image data gathered from a trabecula undergoing passive stretch.

Background
Basic Principles

During OCT imaging, a low coherence light source is focused on a volume just beneath the surface of a translucent sample, and the photons scattered by the internal microstructures of the sample are collected (Figure 16). The reflected signal is combined with a reference signal that has an optical path length equivalent to the focal position within the volume, creating an interference pattern. This interference pattern encodes the depth from which the photons were reflected, which can be extracted to reconstruct a profile of depth intensity (A-Scan). Steering the focal volume transversely along the surface forms a cross-sectional image (B-Scan). Repeating this along a second axis produces a series of B-Scans, which can then be combined to reconstruct a complete 3D volume of the sample. The terminology for OCT images is summarised in Figure 17.

OCT Types
Time domain OCT

The simplest type of OCT imaging method is time domain OCT (TD-OCT), shown in Figure This method uses a light source with a very low coherence length, allowing interference only to occur when the optical path lengths of two signals from the same source are similar to each other (low coherence tomography). The light is split into two paths, one which travels towards the sample (sample path) and one which travels towards a reference mirror (reference path). Light reflected from both the sample and the mirror are recombined in a Michelson interferometer, and the resulting signal is captured with a photodiode. The power of the signal is correlated to the intensity of the reflection from a certain depth, since only two signals which have travelled similar optical distances will interfere. The reference mirror is translated so that signals reflected from a different layer interfere with the reference, resulting in the intensity of tissue at a different depth. Repeating this across a range of reference-path lengths allows a depth intensity profile along the beam, or A-Scan, to be created.

Spectral domain OCT

More recently, the spectral-domain OCT (SD-OCT) has become popular in commercially available OCT systems due to its high resolution, speed and mechanical stability [73], [74]. The setup, shown in Figure 18, is very similar to TD-OCT. However, instead of a moving reference mirror, a stationary mirror is used. The photodetector is replaced with a spectrometer, to measure the spectral variation of the interference signal. The period of the spectral oscillation is proportional to the path difference: − , where is the optical path length of the reference signal and is that of the sample signal. Therefore taking the Fourier transform of this spectral variation will produce a line scan profile similar to that constructed by the TD-OCT [75]. An obvious advantage offered by this technique is that the reference mirror does not have to move to produce the line scan, allowing for much higher scanning speeds.

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Swept-source OCT

Related to the spectral-domain OCT is swept-source OCT (SS-OCT). In this technique, Instead of illuminating the sample with a broadband light source, a tunable narrowband laser is used. A range of optical frequencies are rapidly swept, and the power of the signal at each frequency is captured by a photodetector (instead of a spectrometer). Once the intensity at each frequency is captured, a Fourier transform is performed, as in the case of SD-OCT. Both the SD-OCT and SS-OCT fall under the class of Fourier domain OCTs [75]. The main advantage of SS-OCT over the SD-OCT approach is that a photodiode is used as the optical detector, which has a much higher dynamic range than a spectrometer, and is therefore less prone to saturation. It is also generally faster as it avoids the serial read-out time of a photodetector array. Its main disadvantage, however, is that it typically offers a lower axial resolution, as discussed in the next section.

Accuracy and Performance
Axial resolution

The axial resolution is defined by the smallest resolvable change in intensity in the optical axis and is a function of the wavelengths emitted by the light source. The axial resolution ( ) can be calculated using the centre wavelength ( ) and full width at half maximum of the light source (FWHM, ∆  ) using Equation (1) [76].
Thus, the shorter the centre wavelength, and the wider the spectral bandwidth, the better the resolution.
Each OCT technology has a typical range of resolutions, due to the type of light sources they use. SS-OCT use tunable lasers which are typically centered at 1000 nm and 1300 nm. A centre wavelength of 800 nm, which would provide higher resolution, is uncommon due to the lack of robust swept sources with a wide spectral bandwidth around this wavelength [77], [78]. SD-OCT, on the other hand, has a centre wavelength of ~800 nm due to the relatively broad availability of superluminescent light diodes (SLD) with that centre wavelength and a wide bandwidth [74], [75], [79]. Additionally, most spectrometers use CCD and CMOS sensors, which are sensitive to wavelengths from approximately 350 nm to 1050 nm [80]. The typically achievable resolutions are summarised in Table 1.

Lateral resolution

The lateral resolution is limited by the size of the focal spot. The size of the spot is a function of the wavelength of the light source and the numerical aperture of the focusing lens. For the lens and light source combinations used in most OCT systems, the beam width is typically between 10 µm and 20 µm.

Penetration depth

The maximum theoretical working depth is determined by the depth of focus, which can be parameterised as the Rayleigh length [81]. The Rayleigh length defines the distance from the focal point where the cross-sectional area is double that of the waist. The Rayleigh length is proportional to the square of the beam waist and inversely proportional to wavelength. Therefore longer wavelengths will have a higher penetration limit, at the expense of the axial resolution (which is directly proportional to the resolution size).
The penetration depth also depends on the optical transmission properties of the tissue. Taking into account the main components in tissue which absorb and scatter light, the optimal wavelength range is 700 nm to 1300 nm [77], [82]. Light penetration is greater at the upper end of the spectrum (1300 nm), at the expense of axial resolution. For applications requiring maximum axial resolution, 800 nm is typically used.

Speed

The issue of imaging speed is currently limited by the acquisition and processing steps required to generate one or more depth scans. TD-OCT is typically the slowest because the position of the mirror must be modulated to construct a single depth scan. SD-OCT is typically much faster as an entire depth scan can be captured with one acquisition, although processing (linearization and Fourier transform) is more computationally expensive. Nevertheless, modern advances in computing have enabled speeds that are typically much faster than TD-OCT. The CCD and CMOS cameras used in these systems can currently achieve A-scan rates of 50 kHz, to 300 kHz in reduced resolution mode. SS-OCT requires the source to be swept, but this can be achieved at a very high rate – currently up to 400 kHz [83].
Table 1 summarises the reported typical performances to date of the three main technologies [76], [77].

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Requirements for Scanning Trabecula

The typical diameters of trabeculae used in experiments are between 150 μm and 300 μm. To image these specimens with OCT requires a working penetration of at least 300 μm, which all types of OCT can achieve [45], [84]. Since penetration is not an issue, SD-OCT can be employed, which has the highest resolution of all types as discussed earlier. The imaging speed is sufficient to scan trabecula both during quiescence, and a single cross section during contraction. Assuming a 10 μm lateral spacing, and a cross-sectional (B-Scan) scan width of μm, and a capture rate of 100 Hz, the A-Scan rate would need to be at least 5000 A-Scans/s, which is easily achievable by a standard SD-OCT.

Assumptions and Limitations

Although there are several speed and resolution advantages of Fourier domain OCTs compared to those in the time domain, there are some disadvantages which can affect trabecula imaging. The two main disadvantages are the presence of a mirror image and a decrease in SNR with increasing depth [85], [86]. The following subsections will explain these problems, and provide solutions for their mitigation, in the context of imaging trabeculae.

Mirror image

Performing a Fourier transform on a purely real spectrum produces a Hermitian function, where the complex conjugate and original function are identical. As a result, the A-Scan will contain two symmetrical images, as depicted in the example of Figure 19. This is usually not an issue until the point of zero path difference is below the surface of the tissue. When this occurs, the image of the object will overlap its complex conjugate (mirror terms) (Figure 20). This creates depth ambiguity and makes the image appear as if the image has been folded upon itself [75], [77].
The small diameter of trabeculae (150 μm to 300 μm) means that the entire cross section can lie in half of the total imaging range (~1 mm). By ensuring this condition is maintained, the overlap of conjugates will not affect the ability to image the entire trabecula at once. However, the glass capillary that contains the trabecula is larger (1 mm inner dimension), therefore its mirror term will be present in the image. This can be mitigated by adjusting the focal position of the OCT to ensure that the mirror terms do not overlap the trabecula, and therefore can simply be cropped out of the reconstructed image.

Table of Contents
Chapter 1. Introduction 
1.1. Cardiac Muscle
1.2. Studying Muscle Contraction
1.3. First Problem: Comparing Results
1.4. Second Problem: Non-Uniformity of Contraction
1.5. Third Problem: Synchronising and Integrating Measurements
1.6. Impact of Research
1.7. Thesis Overview .
Chapter 2. Cardiac Myometer 
2.1. Introduction
2.2. Existing Configuration
2.3. Integration Challenges
2.4. Conclusions
Chapter 3. Volume Imaging Using OCT 
3.1. Introduction
3.2. Background
3.3. Image Acquisition
3.4. Integration in the Cardiac Myometer
3.5. Experimental Procedure
3.6. Image Processing
3.7. Results
3.8. Discussion
3.9. Conclusions
Chapter 4. Imaging Actively Contracting Trabeculae 
4.1. Introduction
4.2. Gated Imaging Procedure
4.3. Validation of Gated Imaging
4.4. Characterisation of Volume in Contracting Muscle
4.5. Results
4.6. Discussion
4.7. Conclusions
Chapter 5. Tracking Tissue Movement 
5.1. Introduction
5.2. Background
5.3. Image Acquisition
5.4. Image Processing
5.5. Results
5.6. Discussion
5.7. Conclusions
Chapter 6. Combining Measurement Modalities 
6.1. Introduction
6.2. Hardware Integration
6.3. Interference Among Measurement Modalities
6.4. Heat Sensor Calibration
6.5. Muscle Experiment
6.6. Results
6.7. Discussion
6.8. Conclusions
Chapter 7. Conclusions 
7.1. Thesis Summary
7.2. Summary of Novel Contributions
7.3. Final Thoughts
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Volumetric Characterisation of Contracting Cardiac Trabeculae

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