THC Science

Introduction

Confocal time-of-flight diffuse optical tomography (CToF-DOT) represents a significant advancement in the realm of diffuse optical tomography, tailored specifically to enhance both resolution and imaging speed. By harnessing the depth resolution capabilities of time-of-flight alongside the spatial precision afforded by confocal optical techniques and multiplexing, researchers have successfully engineered a novel DOT system capable of achieving remarkable spatial resolution down to 1mm, coupled with an impressive >50 mean free paths^[1].

Motivation

Diffuse optical tomography (DOT) serves as a valuable tool in biomedical imaging, offering a non-invasive means to probe tissue composition and function. Its ability to exploit the scattering and absorption properties of biological tissues to reconstruct spatial maps of parameters like hemoglobin concentration and oxygen saturation has found widespread use in fields ranging from cancer detection to brain imaging. However, despite its versatility, DOT faces inherent challenges, primarily stemming from the scattering of light as it traverses through tissue. This scattering leads to blurred images with limited spatial resolution and depth penetration, hindering its efficacy, particularly in applications requiring precise localization of structures or accurate characterization of deeper regions within the tissue.

To overcome these limitations, researchers have been actively exploring novel variants and enhancements to traditional DOT methodologies. One promising avenue involves integrating principles from confocal microscopy and time-of-flight measurements into DOT systems. The integration of the confocal time-of-flight variant into diffuse optical tomography (DOT) serves a dual purpose. On one hand, confocal principles tackle the pressing need for improved spatial resolution, crucial for delineating small anatomical structures. On the other hand, time-of-flight measurements specifically address depth penetration, particularly from deeper tissue layers. This combined approach enhances the fidelity and accuracy of DOT reconstructions, making it more effective for clinical diagnosis and monitoring while opening up new avenues for biomedical research.

Methods

Time-of-Flight

Time of flight (ToF) in the context of optical imaging refers to the measurement of the time it takes for light to travel from a source to a detector. It's a fundamental principle used in various imaging techniques, including diffuse optical tomography (DOT). In ToF imaging, a short pulse of light is emitted from a source, and its time of arrival at a detector is recorded. By analyzing these time-of-flight measurements, valuable information about the properties of the imaged medium or objects within it can be obtained.

In the case of diffuse optical tomography, ToF is particularly useful for imaging through strongly diffusive media like biological tissue^[2]. When light propagates through such media, it follows a random path due to multiple scattering events. This leads to a broadening of the light pulse and a delay in its arrival time at the detector compared to a direct, unobstructed path. By measuring these time delays, ToF imaging can provide insights into the scattering and absorption properties of the medium, as well as the presence and characteristics of embedded objects.

ToF imaging offers several advantages. Firstly, it enables depth-resolved imaging, allowing researchers to distinguish between signals originating from different depths within the medium. This depth localization is crucial for applications such as medical imaging, where precise information about the location of anomalies or structures within tissue is required. Secondly, ToF measurements can help mitigate the effects of scattering, as direct photons that travel without scattering will arrive earlier than those undergoing multiple scattering events^[2]. By focusing on these early-arriving photons, ToF imaging can improve image contrast and resolution, particularly in highly scattering environments.

Confocal Optics

Multiplexing

Illumination multiplexing has historically been used to increase the irradiance during imaging, thus improving the signal-to-noise ratio while not increasing exposure time.^[3] With DOT, however, multiplexing can be used to speed up the data capture time. When sources are separated by sufficient distance, there is nearly no cross-talk between the measurements, as the signal is attenuated exponentially with distance as according to Beer's Law. Thus, sources that are separated sufficiently can be on and taking measurements simultaneously. Given the source-detector pairs from to the confocal setup, the measurements at each detector are attributed to the nearest source. The speed-up in capture time is directly proportional to the number of sources multiplexed together ^[1].

Even given small amounts of cross-talk, multiplexing is still useful in this system. The SNR of the image is improved, and the multiplexed signals with cross-talk can be demultiplexed computationally ^[3]. The gains from multiplexing sources with and without cross-talk can also be decoupled during reconstruction ^[1].

Image Reconstruction

The reconstruction goal, otherwise known as the inverse problem, in DOT is to produce a spatial distribution of the tissue optical parameters (given as μ) from a measured dataset ^[4]. The equation for the forward model is a linearization of the radiative transfer equation:

$f(\mu )=J\mu$

Where J is the Jacobian or sensitivity matrix that represents contribution of each voxel in the imaging volume for a given source-detector measurement. The forward model thus returns the predicted measurement given a set of optical parameters. Given collected measurements, m, the inverse model can then be represented as:

$\mu =J^{-1}m$

With μ being solved via a matrix inversion of the sensitivity matrix. However, for anything beyond simple geometries, the weighing matrix condition number becomes very large and the problem is both ill-defined and ill-conditioned. Thus, an iterative approach is necessary. The inverse problem is formulated as an optimization instead, given as:

$\mu ={\underset {\mu }{argmin}}||m-f(\mu )||+\Lambda (\mu )$

Where Λ(μ) is a regularization term to ensure the variation in μ is small. The above equation is convex and can be solved with a variety of optimization algorithms, such as the fast iterative shrinkage thresholding algorithm (FISTA) ^[5].

Runtime Analysis

Reconstruction for DOT can take on the order of an hour if many iterations are necessary. The iterative optimization involves repeated forward model computations, which requires matrix multiplication using the sensitivity matrix, which can have hundreds of billions of elements. The Big-O runtime for the standard forward model is given by $O(N_{s}N_{d}N_{t}N_{voxels})$ , where $N_{s}$ is the number of sources, $N_{d}$ is the number of detectors, $N_{t}$ is the number of time bins, and $N_{voxels}$ is the number of voxels.

The convolutional approach due to the confocal setup both decreases the number of measurements from $N_{s}N_{d}N_{t}$ to $N_{s}N_{t}$ allows for the use of the Fast Fourier Transform. Using a blur kernel of size $K\times K$ , the runtime complexity is given by $O(N_{t}K^{2}\log(K))$ , which is significantly smaller than the standard runtime. Using this, the reconstruction time can be reduced to the order of milliseconds.

References

^ ^a ^b ^c Zhao, Yongyi; Raghuram, Ankit; Kim, Hyun K.; Hielscher, Andreas H.; Robsinson, Jacob T.; Veeraraghavan, Ashok (2021 June 9). "High Resolution, Deep Imaging Using Confocal Time-of-flight Diffuse Optical Tomography". IEEE Transactions on Pattern Analysis and Machine Intelligence. 43 (7): 2206–2219. doi:10.1109/TPAMI.2021.3075366. PMC 8270678. PMID 33891548. {{cite journal}}: Check date values in: |date= (help)
^ ^a ^b Lyons, Ashley; Tonolini, Francesco; Boccolini, Alessandro; Repetti, Audrey; Henderson, Robert; Wiaux, Yves; Faccio, Daniele (2019-08). "Computational time-of-flight diffuse optical tomography". Nature Photonics. 13 (8): 575–579. doi:10.1038/s41566-019-0439-x. ISSN 1749-4893. {{cite journal}}: Check date values in: |date= (help)
^ ^a ^b Schechner; Nayar; Belhumeur (2003). "A theory of multiplexed illumination". Proceedings Ninth IEEE International Conference on Computer Vision. IEEE. pp. 808-815 vol.2. doi:10.1109/iccv.2003.1238431. ISBN 0-7695-1950-4.
^ Wang, Lihong; Wu, Hsin-i (July 15, 2009). Biomedical Optics: Principles and Imaging. John Wiley & Sons, Inc. ISBN 9780471743040.
^ Beck, Amir; Teboulle, Marc (January 2009). "A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems". SIAM Journal on Imaging Sciences. 2 (1): 183–202. doi:10.1137/080716542. ISSN 1936-4954.

[:0-1] Zhao, Yongyi; Raghuram, Ankit; Kim, Hyun K.; Hielscher, Andreas H.; Robsinson, Jacob T.; Veeraraghavan, Ashok (2021 June 9). "High Resolution, Deep Imaging Using Confocal Time-of-flight Diffuse Optical Tomography". IEEE Transactions on Pattern Analysis and Machine Intelligence. 43 (7): 2206–2219. doi:10.1109/TPAMI.2021.3075366. PMC 8270678. PMID 33891548. {{cite journal}}: Check date values in: |date= (help)

[:2-2] Lyons, Ashley; Tonolini, Francesco; Boccolini, Alessandro; Repetti, Audrey; Henderson, Robert; Wiaux, Yves; Faccio, Daniele (2019-08). "Computational time-of-flight diffuse optical tomography". Nature Photonics. 13 (8): 575–579. doi:10.1038/s41566-019-0439-x. ISSN 1749-4893. {{cite journal}}: Check date values in: |date= (help)

[:1-3] Schechner; Nayar; Belhumeur (2003). "A theory of multiplexed illumination". Proceedings Ninth IEEE International Conference on Computer Vision. IEEE. pp. 808-815 vol.2. doi:10.1109/iccv.2003.1238431. ISBN 0-7695-1950-4.

[4] Wang, Lihong; Wu, Hsin-i (July 15, 2009). Biomedical Optics: Principles and Imaging. John Wiley & Sons, Inc. ISBN 9780471743040.

[5] Beck, Amir; Teboulle, Marc (January 2009). "A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems". SIAM Journal on Imaging Sciences. 2 (1): 183–202. doi:10.1137/080716542. ISSN 1936-4954.

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 == Introduction ==
-'''Confocal time-of-flight diffuse optical tomography (CToF-DOT)''' represents a significant advancement in the realm of diffuse optical tomography, tailored specifically to enhance both resolution and imaging speed. By harnessing the depth resolution capabilities of time-of-flight alongside the spatial precision afforded by confocal optical techniques and multiplexing, researchers have successfully engineered a novel DOT system capable of achieving remarkable spatial resolution down to 1mm, coupled with an impressive >50 mean free paths<ref name=":0">{{Cite journal |last1=Zhao |first1=Yongyi |last2=Raghuram |first2=Ankit |last3=Kim |first3=Hyun K. |last4=Hielscher |first4=Andreas H. |last5=Robsinson |first5=Jacob T. |last6=Veeraraghavan |first6=Ashok |date=2021 June 9 |title=High Resolution, Deep Imaging Using Confocal Time-of-flight Diffuse Optical Tomography |journal=IEEE Transactions on Pattern Analysis and Machine Intelligence |volume=43 |issue=7 |pages=2206–2219 |doi=10.1109/TPAMI.2021.3075366 |pmid=33891548 |pmc=8270678 }}</ref>.
+'''Confocal time-of-flight diffuse optical tomography (CToF-DOT)''' represents a significant advancement in the realm of diffuse [[optical tomography]], tailored specifically to enhance both resolution and imaging speed. By harnessing the depth resolution capabilities of [[Time of flight|time-of-flight]] alongside the spatial precision afforded by confocal optical techniques and [[multiplexing]], researchers have successfully engineered a novel DOT system capable of achieving remarkable spatial resolution down to 1mm, coupled with an impressive >50 [[mean free path]]<nowiki/>s<ref name=":0">{{Cite journal |last1=Zhao |first1=Yongyi |last2=Raghuram |first2=Ankit |last3=Kim |first3=Hyun K. |last4=Hielscher |first4=Andreas H. |last5=Robsinson |first5=Jacob T. |last6=Veeraraghavan |first6=Ashok |date=2021 June 9 |title=High Resolution, Deep Imaging Using Confocal Time-of-flight Diffuse Optical Tomography |journal=IEEE Transactions on Pattern Analysis and Machine Intelligence |volume=43 |issue=7 |pages=2206–2219 |doi=10.1109/TPAMI.2021.3075366 |pmid=33891548 |pmc=8270678 }}</ref>.
 == Motivation ==