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Mozumder M, Tarvainen T. Evaluation of temporal moments and Fourier transformed data in time-domain diffuse optical tomography. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2020; 37:1845-1856. [PMID: 33362126 DOI: 10.1364/josaa.405541] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2020] [Accepted: 10/03/2020] [Indexed: 06/12/2023]
Abstract
Time-domain diffuse optical tomography (TD-DOT) uses near-infrared pulsed lasers as light sources to measure time-varying exitance on the boundary of the target. These are used to estimate optical properties of the imaged target. Several integral-transform-based moments of the time-resolved data have been utilized in TD-DOT, the most common being the mean time of flight and variance. Recently, it has been shown that Fourier transforming the time-domain data to frequency domain enables utilization of these data at one or several frequencies, producing equally as good estimates as the whole time-domain data. In this work, we present a systematic comparison of the usage of the temporal moments and Fourier transformed data in TD-DOT. Both absolute and difference imaging are evaluated using numerical simulations. The simulations show that utilizing temporal moments and Fourier transformed data in TD-DOT provides good quality reconstructions with a good estimation accuracy. These estimates are improved if more than one data type is used. Furthermore, the simulations show that the frequency-domain computations enable computationally cheaper and straightforward implementation of the inverse solver when compared to the temporal moments.
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Mozumder M, Tarvainen T. Time-domain diffuse optical tomography utilizing truncated Fourier series approximation. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2020; 37:182-191. [PMID: 32118896 DOI: 10.1364/josaa.37.000182] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2019] [Accepted: 12/04/2019] [Indexed: 05/25/2023]
Abstract
Diffuse optical tomography (DOT) uses near infrared light for in vivo imaging of spatially varying optical parameters in biological tissues. It is known that time-resolved measurements provide the richest information on soft tissues, among other measurement types in DOT such as steady-state and intensity-modulated measurements. Therefore, several integral-transform-based moments of the time-resolved DOT measurements have been considered to estimate spatially distributed optical parameters. However, the use of such moments can result in low-contrast images and cross-talks between the reconstructed optical parameters, limiting their accuracy. In this work, we propose to utilize a truncated Fourier series approximation in time-resolved DOT. Using this approximation, we obtained optical parameter estimates with accuracy comparable to using whole time-resolved data that uses low computational time and resources. The truncated Fourier series approximation based estimates also displayed good contrast and minimal parameter cross-talk, and the estimates further improved in accuracy when multiple Fourier frequencies were used.
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Jha AK, Zhu Y, Arridge S, Wong DF, Rahmim A. Incorporating reflection boundary conditions in the Neumann series radiative transport equation: application to photon propagation and reconstruction in diffuse optical imaging. BIOMEDICAL OPTICS EXPRESS 2018; 9:1389-1407. [PMID: 29675291 PMCID: PMC5905895 DOI: 10.1364/boe.9.001389] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2017] [Revised: 11/28/2017] [Accepted: 12/26/2017] [Indexed: 05/11/2023]
Abstract
We propose a formalism to incorporate boundary conditions in a Neumann-series-based radiative transport equation. The formalism accurately models the reflection of photons at the tissue-external medium interface using Fresnel's equations. The formalism was used to develop a gradient descent-based image reconstruction technique. The proposed methods were implemented for 3D diffuse optical imaging. In computational studies, it was observed that the average root-mean-square error (RMSE) for the output images and the estimated absorption coefficients reduced by 38% and 84%, respectively, when the reflection boundary conditions were incorporated. These results demonstrate the importance of incorporating boundary conditions that model the reflection of photons at the tissue-external medium interface.
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Affiliation(s)
- Abhinav K. Jha
- Department of Radiology and Radiological Sciences, Johns Hopkins University, Baltimore, MD,
USA
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, MO, USA
- Mallinckrodt Institute of Radiology, Washington University in St. Louis, St. Louis, MO, USA
| | - Yansong Zhu
- Department of Radiology and Radiological Sciences, Johns Hopkins University, Baltimore, MD,
USA
- Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA
| | - Simon Arridge
- Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK
| | - Dean F. Wong
- Department of Radiology and Radiological Sciences, Johns Hopkins University, Baltimore, MD,
USA
- Department of Neuroscience, Johns Hopkins University, Baltimore, MD, USA
- Department of Psychiatry and Behavioral Sciences, Johns Hopkins University, Baltimore, MD, USA
- Department of Neurology, Johns Hopkins University, Baltimore, MD, USA
| | - Arman Rahmim
- Department of Radiology and Radiological Sciences, Johns Hopkins University, Baltimore, MD,
USA
- Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA
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Liu B, Li Q, Wang J, Xiang H, Ge H, Wang H, Xie P. A Highly Similar Mathematical Model for Cerebral Blood Flow Velocity in Geriatric Patients with Suspected Cerebrovascular Disease. Sci Rep 2015; 5:15771. [PMID: 26497612 PMCID: PMC4620558 DOI: 10.1038/srep15771] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2015] [Accepted: 10/01/2015] [Indexed: 11/21/2022] Open
Abstract
Cerebral blood flow velocity(CBFV) is an important parameter for study of cerebral hemodynamics. However, a simple and highly similar mathematical model has not yet been established for analyzing CBFV. To alleviate this issue, through TCD examination in 100 geriatric patients with suspected cerebrovascular disease (46 males and 54 females), we established a representative eighth-order Fourier function Vx(t) that simulates the CBFV. The measured TCD waveforms were compared to those derived from Vx(t), an illustrative Kolmogorov-Smirnov test was employed to determine the validity. The results showed that the TCD waves could been reconstructed for patients with different CBFVs by implementing their variable heart rates and the formulated maximum/minimum of Vx(t). Comparisons between derived and measured TCD waveforms suggest that the two waveforms are very similar. The results confirm that CBFV can be well-modeled through an eighth-order Fourier function. This function Vx(t) can be used extensively for a prospective study of cerebral hemodynamics in geriatric patients with suspected cerebrovascular disease.
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Affiliation(s)
- Bo Liu
- Department of Neurology, The Third Hospital of Mianyang, Mianyang, Sichuan 621000, China.,Department of Neurology, Yongchuan Hospital, Chongqing Medical University, Chongqing 402160, China.,Institute of Neuroscience, Chongqing Medical University, Chongqing 400016, China.,Chongqing Key Laboratory of Neurobiology, Chongqing Medical University, Chongqing 400016, China
| | - Qi Li
- Department of Neurology, The First Affiliated Hospital of Chongqing Medical University, Chongqing 400016, China.,Institute of Neuroscience, Chongqing Medical University, Chongqing 400016, China.,Chongqing Key Laboratory of Neurobiology, Chongqing Medical University, Chongqing 400016, China
| | - Jisheng Wang
- Department of Neurology, The Third Hospital of Mianyang, Mianyang, Sichuan 621000, China
| | - Hu Xiang
- Department of Neurology, The Third Hospital of Mianyang, Mianyang, Sichuan 621000, China
| | - Hong Ge
- Department of Neurology, The Third Hospital of Mianyang, Mianyang, Sichuan 621000, China
| | - Hui Wang
- Department of Neurology, The Third Hospital of Mianyang, Mianyang, Sichuan 621000, China
| | - Peng Xie
- Department of Neurology, The Third Hospital of Mianyang, Mianyang, Sichuan 621000, China.,Department of Neurology, Yongchuan Hospital, Chongqing Medical University, Chongqing 402160, China.,Department of Neurology, The First Affiliated Hospital of Chongqing Medical University, Chongqing 400016, China.,Institute of Neuroscience, Chongqing Medical University, Chongqing 400016, China.,Chongqing Key Laboratory of Neurobiology, Chongqing Medical University, Chongqing 400016, China
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Yi X, Wang B, Wan W, Wang Y, Zhang Y, Zhao H, Gao F. Full time-resolved diffuse fluorescence tomography accelerated with parallelized Fourier-series truncated diffusion approximation. JOURNAL OF BIOMEDICAL OPTICS 2015; 20:56003. [PMID: 25965088 DOI: 10.1117/1.jbo.20.5.056003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2014] [Accepted: 04/17/2015] [Indexed: 06/04/2023]
Abstract
Of the three measurement schemes established for diffuse fluorescence tomography (DFT), the time-domain scheme is well known to provide the richest information about the distribution of the targeting fluorophore in living tissues. However, the explicit use of the full time-resolved data usually leads to a considerably lengthy time for image reconstruction, limiting its applications to three-dimensional or small-volume imaging. To cope with the adversity, we propose herein a computationally efficient scheme for DFT image reconstruction where the time-dependent photon density is expanded to a Fourier-series and calculated by solving the independent frequency-domain diffusion equations at multiple sampling frequencies with the support of a combined multicore CPU-based coarse-grain and multithread GPU-based fine-grain parallelization strategy. With such a parallelized Fourier-series truncated diffusion approximation, both the time- and frequency-domain inversion procedures are developed and validated for their effectiveness and accuracy using simulative and phantom experiments. The results show that the proposed method can generate reconstructions comparable to the explicit time-domain scheme, with significantly reduced computational time.
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Affiliation(s)
- Xi Yi
- Tianjin University, College of Precision Instrument and Optoelectronics Engineering, Weijinlu Avenue #92, Tianjin 300072, China
| | - Bingyuan Wang
- Tianjin University, College of Precision Instrument and Optoelectronics Engineering, Weijinlu Avenue #92, Tianjin 300072, China
| | - Wenbo Wan
- Tianjin University, College of Precision Instrument and Optoelectronics Engineering, Weijinlu Avenue #92, Tianjin 300072, China
| | - Yihan Wang
- Tianjin University, College of Precision Instrument and Optoelectronics Engineering, Weijinlu Avenue #92, Tianjin 300072, China
| | - Yanqi Zhang
- Tianjin University, College of Precision Instrument and Optoelectronics Engineering, Weijinlu Avenue #92, Tianjin 300072, China
| | - Huijuan Zhao
- Tianjin University, College of Precision Instrument and Optoelectronics Engineering, Weijinlu Avenue #92, Tianjin 300072, ChinabTianjin Key Laboratory of Biomedical Detecting Techniques and Instruments, Tianjin 300072, China
| | - Feng Gao
- Tianjin University, College of Precision Instrument and Optoelectronics Engineering, Weijinlu Avenue #92, Tianjin 300072, ChinabTianjin Key Laboratory of Biomedical Detecting Techniques and Instruments, Tianjin 300072, China
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Abstract
Diffuse optical imaging is highly versatile and has a very broad range of applications in biology and medicine. It covers diffuse optical tomography, fluorescence diffuse optical tomography, bioluminescence, and a number of other new imaging methods. These methods of diffuse optical imaging have diversified instrument configurations but share the same core physical principle – light propagation in highly diffusive media, i.e., the biological tissue. In this review, the author summarizes the latest development in instrumentation and methodology available to diffuse optical imaging in terms of system architecture, light source, photo-detection, spectral separation, signal modulation, and lastly imaging contrast.
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