13 July 2016 Overview of diffuse optical tomography and its clinical applications
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Near-infrared diffuse optical tomography (DOT), one of the most sophisticated optical imaging techniques for observations through biological tissue, allows 3-D quantitative imaging of optical properties, which include functional and anatomical information. With DOT, it is expected to be possible to overcome the limitations of conventional near-infrared spectroscopy (NIRS) as well as offering the potential for diagnostic optical imaging. However, DOT has been under development for more than 30 years, and the difficulties in development are attributed to the fact that light is strongly scattered and that diffusive photons are used for the image reconstruction. The DOT algorithm is based on the techniques of inverse problems. The radiative transfer equation accurately describes photon propagation in biological tissue, while, because of its high computation load, the diffusion equation (DE) is often used as the forward model. However, the DE is invalid in low-scattering and/or highly absorbing regions and in the vicinity of light sources. The inverse problem is inherently ill-posed and highly undetermined. Here, we first summarize NIRS and then describe various approaches in the efforts to develop accurate and efficient DOT algorithms and present some examples of clinical applications. Finally, we discuss the future prospects of DOT.



Jöbsis1 first reported biomedical applications of near-infrared spectroscopy (NIRS); NIRS was originally designed for clinical monitoring, and it has also become a useful tool for neuroimaging studies with the so-called functional NIRS (fNIRS).23.4.5 (In this context, the term “NIRS” is sometimes used to express the optical method for studying brain functions apart from the original meaning of NIRS, causing some confusions in the community. In this article, the authors keep the original meaning of NIRS.) In parallel to these developments, optical computed tomography (CT) using near-infrared (NIR) light has been and is still being developed. Optical CT is a technique to reconstruct images of optical properties, including the absorption (μa) and reduced scattering coefficients (μs), within highly scattering media from measurements of the light propagation at the tissue boundary.67.8.9

The photons emerging from a thin turbid medium consists of ballistic (coherent), snake (quasicoherent), and diffusive (incoherent) components. The ballistic, snake, and diffusive components refer to photons traveling along the straight-line path without being scattered, photons traveling along quasistraight-line paths with experiencing only a few scattering events, and photons traveling along zig-zag paths with being scattered many times in all directions, respectively.10,11 When the thickness of biological tissue is sufficiently thin (less than a few millimeters) so that ballistic and/or snake photons can reach a detector,10,11 a conventional image reconstruction algorithm for x-ray CT can be applied to optical CT.1213.14 However, in the case of thicker tissue, the ballistic and snake components of the transmitted light are extremely rare due to the strong light scattering, and here, the diffusive component is exclusively detected at the tissue boundary. Because of this image reconstruction algorithms utilizing diffusive photons were proposed in the early 1990s,1516.17 and a variety of algorithms for diffuse optical tomography (DOT) based on the technique of the inverse problem has been proposed.1819.20 However, DOT is still a technique that is under development and not fully ready for full-scale application.

Today, DOT is often confused with optical topography based on the spatial interpolation method (see below) with multichannel NIRS instruments, in general, continuous wave (CW) instruments (see Sec. 2.3). Optical topography, which is typically applied in functional brain mapping, is roughly divided into two categories on the basis of the selected image reconstruction approach. The first is to generate topographic images using a spatial interpolation method for the changes in NIRS signals at all measurement points without depth discrimination.21,22 This approach is commonly used in fNIRS studies, although the lateral spatial resolution is limited to the source-detector distance.23,24 Since the depth resolution is not considered, i.e., it is assumed that all changes are occurring in a single layer, these topographic images are inherently influenced by variations in the depth direction, such as the presence of the cerebrospinal fluid (CSF)25 and changes in the optical properties of the extracerebral tissue including skin blood flow changes.26,27 These problems could be solved by DOT.

The other category of optical topography is to reconstruct images based on the techniques of inverse problems using data acquired at multiple source-detector distances.28,29 This approach improves the spatial resolution and provides some depth discrimination. A research group at the University College London (UCL) argued that topography of this type be distinguished from optical tomography based on the aims of the experiments involved.30 When a three-dimensional (3-D) volume is intended to be reconstructed from light detected at the surface opposite to the source position in the transmittance mode, they propose to term it optical tomography. If the intention is to measure activity in a small portion of the head with limited depth discrimination and high temporal resolution, the term they propose is optical topography. In the report here, we will consider the topography of this type as being DOT, based on the classification of the image reconstruction algorithms involved, which has since been also adopted by the UCL group.

In this paper, we first describe the basic theory of NIRS and then review the image reconstruction algorithms and the clinical applications. Finally, future prospects for DOT will be discussed.


Basic Principles of Near-Infrared Spectroscopy


Near-Infrared Spectroscopy

NIRS, utilizing light in the NIR region, wavelength range approximately from 700 to 2500 nm, is a noninvasive technique for analysis of various substances including agricultural products and food. Biological tissue is relatively transparent for light in the wavelength range from 650 to 950 nm,31 the so-called optical window, where absorption spectra vary with the oxygenation–deoxygenation states of hemoglobin (Hb) and myoglobin and the redox state of cytochrome c oxidase. These spectroscopic characteristics were the background for the biomedical applications of NIRS: light sources emit NIR light on the body surface, and the light propagates through biological tissue and the reflected light emerging a few centimeters from the incident position is detected. This kind of NIRS has typically been applied to measure concentration changes in cerebral Hb qualitatively, although organs and tissue other than the brain, such as muscle tissue,32,33 and the redox state of cytochrome c oxidase34,35 have also been measured with NIRS.

Presently, NIRS has become widely applied in a variety of neuroimaging studies as well as in clinical monitoring of tissue oxygenation.36 The introduction of multichannel NIRS instruments, which are mainly used for optical topography, is facilitating neuroimaging studies using light, while difficulties in the selective and quantitative measurements of cerebral Hb, a central issue in the NIRS field, remain to be overcome.


Modeling Light Propagation in Biological Tissue

The main interaction between light and biological tissue is absorption and scattering when the wave nature of light is neglected. Biological tissue, in which scattering is generally dominant over absorption, exhibits a highly anisotropic forward scattering,37,38 and light propagation in biological tissue is characterized by the optical properties of absorption, scattering, scattering anisotropy, and refractive indexes. Understanding light propagation is crucial for developing therapeutic and diagnostic optical techniques and for the quantitative analysis of measurements.39,40 The radiative transfer equation (RTE) and diffusion equation (DE) are the most commonly used as light propagation models.


Radiative transfer equation

It is widely accepted that the RTE, which is based on the law of conservation of energy for light propagation through a volume element of a medium with absorbers and scatterers, correctly describes light propagation in biological tissue.4142.43.44 The time-domain (TD) RTE is expressed as


where I(r,Ω,t) is the energy radiance (the light intensity) as a function of the position r=(x,y,z), angular direction Ω=(sinθcosφ,sinθsinφ,cosθ) with the zenith angle θ and azimuth angle φ, and time t. The μa(r) and μs(r) terms are the absorption and scattering coefficients, respectively, v is the velocity of light in a turbid medium, and q(r,Ω,t) is the light source. Further, P(r,Ω·Ω) is the scattering phase function that describes the probability that a photon with the direction Ω is scattered to the direction Ω during a scattering event. The phase function P is normalized with



The Henyey–Greenstein function [Eq. (3)] is commonly employed as the scattering phase function45


P(r,Ω·Ω)  =  14π  1g(r)2[1+g(r)22gΩ·Ω]32,
where g(r) is the anisotropic factor ranging from 1 (complete backscattering) via 0 (isotropic scattering) to +1 (complete forward scattering).


Diffusion equation

The RTE is an integro-differential equation, and it is difficult to solve it analytically; also, the computation load for numerical solutions is extremely heavy. Alternatively, light propagation in biological tissue is commonly modeled by the DE based on the assumption that the radiance in an optically thick medium, in which multiple scattering occurs, is almost isotropic. The DE is derived from a diffusion approximation to the RTE in which the intensity I(r,Ω,t) is approximated by the first two terms of a series expansion in spherical harmonics (P1 approximation), the temporal variation in the flux vector [J(r,t)=  4πΩI(r,Ω,t)dΩ] is assumed to be negligible, and the light source is isotropic.7 The time domain DE is expressed as


where Φ(r,t) is the fluence rate given by 4πdΩI(r,Ω,t), D is the diffusion coefficient given by [3(1g)μs(r)]1 for the time domain,46,47 and q(r,t) is the isotropic source given by 4πdΩq(r,Ω,t). The term (1g)μs=μs is the reduced scattering coefficient.


Types of Near-Infrared Spectroscopy Measurements

A wide range of NIRS instruments, which are able to perform various types of measurement, have been developed. Figures 1Fig. 23 show three representative types of measurements: (1) CW measurement (steady-state domain measurement), (2) TD measurement, and (3) frequency-domain (FD) measurement.

Fig. 1

CW measurement in a brain model and the MBLL.


Fig. 2

TD measurement. Photons traveling through each path (1 to 3) shown in the inserted figure are detected at corresponding time (1 to 3). tm, mean time of flight.


Fig. 3

FD measurement.



Continuous wave measurements

In CW measurement, the light source emits light at a constant intensity into the tissue and the transmitted and back scattered light intensities are measured (Fig. 1). In general, commonly available CW instruments analyze the transmitted light based on the modified Beer–Lambert law (MBLL).48 The MBLL is expressed as


where A is the attenuation measured in optical density, I and I0 are the intensities of the detected and incident light, ϵ is the molar absorption coefficient, C is the concentration of chromophore (e.g., Hb), and L is the mean length of the optical path, also known as the “mean total pathlength” (t-PL), and S denotes the optical attenuation mainly due to scattering. However, CW instruments cannot measure the optical pathlength, with the result that instruments of this type do not provide absolute values of concentration changes, and the NIRS signal is expressed as the product of concentration change and optical pathlength. To overcome the problem with quantification, TD (time-resolved spectroscopy, TRS)48,49 and FD measurements (frequency-domain spectroscopy),50,51 which can determine the t-PL have been developed. However, functional brain activation is accompanied by localized Hb concentration changes within the cerebral tissue, which requires the determination of mean partial optical path lengths (p-PL) in the cerebral tissue for the quantification, something that is not feasible at present. Since both the t-PL and p-PL vary with the region of measurement, the amplitudes of NIRS signals for different regions reflect both concentration changes in the cerebral Hb and also other phenomena in the tissue involved.


Time-domain measurements

In TD measurements, the tissue is irradiated by ultrashort (picosecond order) laser pulses, and the intensity of the emerging light is recorded over time to show a temporal point spread function (TPSF) with picosecond resolution (Fig. 2). The mean t-PL is determined by multiplying the light speed in the media by the mean transit time of the scattered photons, which is calculated with the TPSF. The TRS data carry information about depth-dependent attenuation based on the correlation of the detection time to the penetration depth of photons. Changes in cerebral Hb concentrations can be more selectively and quantitatively determined by analyzing the TPSF, as the TPSF contains information about the optical properties of the media, i.e., the absorption (μa) and reduced scattering (μs) coefficients.

Several different methods for analyzing the TPSF have been proposed.5253.54.55 One method is a curve-fitting method based on the diffusion equation (the DE, DE-fit method) (see Sec. 2.2). In this method, optical properties are determined by fitting the TPSF, the temporal probability function for all detected photons, obtained from the analytical solution to the DE to the measured TPSF with the assumption that the human head is a semi-infinite homogeneous medium. Here it has been reported that the estimated μa by the DE-fit method is very similar to the deeper-layer μa under conditions where the μa of the upper layer is larger than that of the lower layer in two-layered slab models.56 We have also confirmed that the DE-fit method is more sensitive to μa changes in cerebral tissue by measuring adult heads with TRS during carotid endoarterectomy.57 This is explained by the fact that the later (falling) part of the TPSF, which includes more photons traveling through the cerebral tissue, is critical for the determination of the μa in the fitting process.58 Overall, this allows changes in cerebral Hb concentrations to be more selectively measured by TRS than with CW measurements, although the selective and quantitative accuracies are not perfect.


Frequency-domain measurements

In FD measurements shown in Fig. 3, the light source is sinusoidally intensity-modulated at radio frequencies, in general, between 100 and 1000 MHz,59 and the light intensity (I, the DC component), its phase shift (Φ), and modulation depth (M), the ratio of AC (the amplitude of the intensity oscillations, the AC component) to DC with respect to the incident light are measured. The information obtained with TPSF through TD measurements can be obtained by FD measurements, the relation between the time and frequency information being the Fourier transform; however, measuring I, Φ, and M for all frequencies (from DC to 10 GHz, when TD measurements are made with a resolution of 10 ps) are required to obtain the TD data.60 It has been demonstrated that for typical tissue, and at frequencies below 200 MHz, Φ is linearly related to the mean t-PL.60 Based on analytical solutions of the frequency domain DE for a homogeneous infinite medium,61,62 numerical expressions including μa and μs in the FD measurement parameters have been derived, enabling experimentally based estimates of optical properties.63,64


Diffuse Optical Tomography Algorithms


General Concept of Diffuse Optical Tomography

DOT recovers 3-D distributions of the optical properties from multiple boundary measurements. With μa=2.303ϵC (molar absorption coefficient x concentration), and unlike conventional NIRS, DOT could enable a quantitative determination of regional cerebral Hb without contamination of signals arising from extracerebral tissue (Fig. 4). The DOT algorithm essentially consists of two parts: one is a forward model to calculate the light propagation and the resultant outward re-emissions at the boundary of the tissue, typically based on the DE or the RTE. The other is an inverse model searching for the distribution of optical properties.

Fig. 4

DOT image of total Hb concentrations of the brain in an extremely low birth weight infant under hypocapnic conditions. (a) Sixteen coaxial optical fibers, consisting of a single fiber for illumination in the center and outer bundle fibers for detection, were placed on the scalp of the infant. (b) Image reconstruction was performed by using the DE-based algorithm. The axial image shows the total Hb concentration changes cause by hypocapnia in comparison with normocapnic conditions. (From Ref. 123, with permission.)


The DOT image reconstruction can be approximately divided into two kinds: one is a linearization approach and another is a nonlinear iterative approach. The linearization approaches use Born or Rytov approximations, and the linearization is developed from an analytical (Green’s function) solution to the DE for a homogeneous semi-infinite background54,65 with assumed known optical properties. Linearization approaches were employed to earlier DOT algorithms,66,67 but as they cannot correctly predict large changes in the optical properties because of the limitations of the Born or Rytov approximations,68 nonlinear iterative approaches have also been investigated. Recently, however, DOT based on linearization approaches has attracted attention in neuroimaging studies. Here, brain activity-related μa changes are very small, the Born and Rytov approximations hold, and high-quality images are provided by high-density DOT systems (CW instruments with spatially overlapping multidistance source-detector arrangements).69,70 This approach reconstructs only qualitative images of measured changes, which is, however, sufficient for functional neuroimaging studies. In clinical use, quantitative images of steady-state Hb are further useful with diagnostic optical imaging, and DOT based on the nonlinear approaches have been developed to enable this. Implementation of DOT with both approaches is possible with CW, TD, and FD measurements, where the TD measurements provide more of the information required for image reconstruction.


Linearization Approaches

In linearization approaches, the relationship between the optical properties and measurements of the diffusive light is linearized; here, the forward problem is expressed as


The vectors y and x are a set of measurements and perturbed optical properties (μa and μs) in discrete volume elements (voxels), respectively. The matrix A is the Jacobian or sensitivity matrix. The vector x can be obtained from the vector y through inversion of matrix A. Since, however, the number of unknowns is larger than the number of measurements, regularization methods are usually used to solve inverse problems. While various inverse solutions have been developed, a widely used approach is the single step solution with Tikhonov regularization and a Moore–Penrose generalized inverse.28,6970.71

The main issues of single step algorithms are the difficulty in depth localization and low-image quality.72 To solve these issues, spatial variant regularization73,74 and high-density source-detector arrangements68 have been used. Further, recent studies have proposed a variety of advanced methods, such as methods using sparse regularization75,76 and a Bayesian approach,72,7778.79 which require iterative processes. To reduce calculation times and avoid Born and Rytov approximation errors, a noniterative linear approach based on compressed sensing theory has also been developed.80,81


Nonlinear Iterative Approaches


Model-based iterative image reconstruction

In general, the DE is used as the forward model and it is typically solved numerically by the use of the finite element method. A number of image reconstruction methods have been reported, but the most widely used is based on the iterative optimization scheme, in which the distribution of optical properties is searched for by minimizing the differences between the calculated and the measured data (model-based iterative image reconstruction,82,83 Fig. 5).

Fig. 5

Model-based iterative image reconstruction scheme.


There are two approaches to this optimization problem: one is based on a perturbation method that requires repeated construction and inversion of a large full Jacobian matrix (Newton-like methods).84,85 The other is an approach using gradient-based reconstruction techniques, such as the conjugated gradient method.86,87 In this approach, an objective function describes the difference between the calculated and measured data; the gradient of the objective function in a line minimization is used for the updating. This approach does not require inversion of the Jacobian matrix, offering a reduction in computation load, while the convergence is slow. The Newton-like methods, in which the convergence is faster, were the most commonly applied image reconstruction method in the 1990s, while they are computationally expensive and need to meet the assumption that changes in optical properties are small. As an alternative, a gradient-based iterative image reconstruction scheme has been proposed. However, these optimization problems are inherently ill-posed, and regularization terms generally have to be added.


Data types

As detailed in Sec. 3.1, TD measurements provide more data that can be used for image reconstruction than CW and FD measurements. With the TD data, the temporal profile of the detected light (Fig. 2), the (1) integral intensity, (2) n’th temporal moment, (3) n’th central moment, (4) normalized Laplace transform, and (5) Mellin–Laplace are derived.88 It has been demonstrated that image reconstruction using all of the time-resolved data improves image quality over that reconstructed with a single or combined moments,89 but it is still not conclusively established which data should be used to obtain high quality images.90,91


Hybrid Model Based on the Radiative Transfer Equation and the Diffusion Equation

The DE is widely used as the forward model, but it becomes invalid in low-scattering regions (e.g., CSF space and trachea), highly absorbing regions (e.g., hematoma), and in the vicinity of light sources, where the diffusion approximation does not hold,92,93 and under such disadvantageous conditions, RTE-based DOT algorithms94,95 are required. Several studies on the RTE-based forward model have been reported.9697.98 Typically, the RTE is solved numerically, with only a few analytical solutions reported.99,100 One of the most common methods for solving the RTE is the discrete-ordinate method, which is compatible with finite difference, finite volume, or finite element schemes.97,101

Even with current advanced computer technology, however, the heavy computational load is still the biggest drawback with the RTE. A variety of fast solvers of the RTE have been proposed,102103.104.105 and among these a hybrid model-based the RTE and DE is one of the most promising approaches. The hybrid model is based on the idea that the DE is an accurate model for measurements far from a light source. This model has been proposed in frequency domains102,106,107 where a medium is divided into RTE and DE regions by a crossover interface that is determined by the crossover length beyond which the DA is valid. The concept of the hybrid model in the steady state has recently been extended into the time domain.93,108 Here, light propagation in homogeneous two-dimensional rectangular media (3.2  cm×4.0  cm), like with the optical properties shown in Table 1, is estimated by using three numerical models, the DE, the RTE with g=0.8, and the RTE with g=0. Figure 6(a)93 shows the spatial distributions of the fluence rates at early times (t=20  ps) after a light pulse has been irradiated, and here, the spatial distributions are dependent on the numerical models and conditions. At late times (t=500  ps), the spatial distributions calculated from the DE and RTE are quite similar [Fig. 6(b)] suggesting that a spatially and temporally hybrid is possible in TD.

Table 1

Optical properties of the numerical models.

μa (cm−1)μs (cm−1)μs′ (cm−1)gn

Fig. 6

Spatial distributions of fluence rate (Φ) normalized by its maximum value (Φpeak) at a given time (a) t=20  ps and (b) 500 ps based on the RTE with g=0.8 and the anisotropic source, the RTE with g=0.0 and anisotropic source, and the DE. (From Ref. 91, with permission).



Improvement of Diffuse Optical Tomography Image Quality

The quality of DOT images depends on several factors, including the spatial resolution, image contrast, and artifacts that may be present. These factors are affected by the DOT algorithms as well as the quality of the instruments. As the inverse problem is ill-posed, a regularization term is generally incorporated, and various regularization methods have been tried. Finding an appropriate regularization parameter is crucial to the reconstruction of high-quality images.109,110 A recent cerebral DOT study has reported that the appropriate regularization parameter varies with the number of activation spots; the linearly constrained minimum variance beamforming is the best for single spot activation, while the minimum l1-norm estimate resolves two activation spots best.110

Unlike magnetic resonance imaging (MRI) and x-ray CT, DOT itself does not provide anatomical (structural) information, which makes it difficult to solve the forward model correctly. Combining DOT and MRI is a useful approach to get around this issue. Tissue geometry obtained from segmented MR images is used to constrain the optical model, leading to improvements in the quality of reconstructed images.111112.113 However, it is not always possible to obtain MRI data. When DOT is applied to neuroimaging studies, a general head atlas (the Montréal Neurological Institute template114)-guided DOT has also been proposed.115,116 For measurements of organs/tissue other than the brain, x-ray-guided (e.g., bone)117 and ultrasound-guided DOT118,119 (e.g., the breast and prostate) have also been reported to improve the accuracy of image reconstruction.


Clinical Applications

Linearization approaches applying DOT are exclusively used in neuroimaging studies,28,29,70,120 while various other organs and tissue including breast cancer, are measured by DOT based on the nonlinear iterative approaches. The following presents examples of clinical applications of DOT.


Brain Imaging

The DOT studies based on linearization approaches are typically performed by CW instruments, with fast sampling rates preferable to neuroimaging studies. Zeff et al.28 first succeeded in retinotopic mapping of adult human visual cortex using DOT, and then the DOT has found a wide variety of applications in brain science, such as somatosensory processing29 and speech processing.121 DOT has also been applied to investigation of infants (cerebral hemodynamic changes during face perception)122 and neonates (cortical hemodynamics during seizures).123 However, using TD instruments is also possible. A study with a TD system has clearly demonstrated that DOT enables detection of brain activity-related changes in the cerebral Hb with little contamination from hemodynamic changes in the extracerebral tissue.124 Currently, resting-state fMRI (functional MRI) is a focus of research interest, and NIRS has also been employed in investigating functional connectivity. However, the scalp blood flow fluctuates during resting, as it is also the case with the cerebral blood flow, making it necessary to distinguish NIRS signals originating in cerebral tissue from those coming from the scalp. With DOT, this issue would be solved and such investigations should be performed by DOT.125,126 Very recently, resting-state functional connectivity in infants has been investigated at the bedside by using high-density DOT. The results have indicated that this technique is a powerful approach to understand functional cerebral development.127

The DOT based on nonlinear iterative approaches was developed mainly aiming to reconstruct 3-D images of tissue oxygenation and blood volume in the neonatal brain at bedside,128,129 and multichannel TD systems were developed to be able to do this.130,131 Iterative approaches were also applied to functional brain mapping in neonates.132 Except with extremely low birth weight infants, where the head circumference is very small as in Fig. 4(b), light re-emitting from the human head is hardly detected at the head surface opposite to the source position. It may be concluded that DOT based on either linear or nonlinear iterative approaches rarely provides information of subcortical structures, and this is a limitation for DOT when it is applied to brain imaging.


Breast Cancer Imaging

Breast cancer is one of the most common cancers and screening is recommended for early detection of these cancers. Currently, the most common and effective screening technique is x-ray mammography combined with a physical examination of the breast. Although the overall specificity of x-ray mammography in breast cancer detection is high, it presents a number of drawbacks such as radiation exposure and a relatively high probability of both false-positives and false-negatives. Here DOT has been considered a promising alternative approach, and it has been extensively studied for diagnosis and evaluation of treatment responses.118,133134.135.136.137 However, the minimum reliably resolved feature size is still insufficient for clinical application (7 to 10 mm),138,139 and new methods to improve the image quality, such as structural-prior guided approaches are needed for further progress here.139


Muscle, Peripheral Circulation, and Joint Imaging

In the field of exercise physiology, electromyography is a principal noninvasive assessment of skeletal muscle functions. Here NIRS has also been employed to examine oxygenation in muscles during the performance of exercises,140,141 but a quantitative evaluation and distinguishing between muscle and adipose tissue are difficult.142 Although only some research groups have reported DOT images of exercising muscles, the findings have suggested the possibility that DOT may be a useful method to examine the physiological functions of muscles.143144.145.146

Peripheral artery disease (PAD) is a disease with narrowing of arteries caused by buildup of plaque in the vascular wall. This reduces the blood supply to the extremities and causes intermittent claudication, and finally critical ischemia. The ankle brachial index, the ratio of the maximum systolic blood pressure at the ankle to the systolic blood pressure in the brachial artery in the upper arm, is used for diagnosis and assessment of the severity of PAD. Unlike this indirect method, DOT has been employed to assess the peripheral circulation at the foot directly, in visualization of the circulation.147

A unique DOT application is imaging of rheumatoid arthritis (RA). Low-field (0.2T) MRI and ultrasound imaging can be used to establish a diagnosis of RA, while MRI is expensive and ultrasound imaging needs contact measurements, which may cause pain. DOT is a potentially attractive alternative diagnostic method. Since, however, the diffusion approximation is not valid in fingers, where the source detector distance is small, the RTE-based algorithm is required. Here frequency-domain DOT (FD DOT) imaging has demonstrated clear differences between healthy subjects and patients with RA.148,149


Thyroid Imaging

There are no reports of DOT imaging of the thyroid gland. This is probably because ultrasound is the primary modality in assessments of thyroid lesions. However, a differential diagnosis distinguishing between thyroid follicular cancer and follicular adenomas is extremely difficult even with fine needle aspiration, and here it is expected that DOT will be able to get around this problem. In addition, the human neck anatomy is optically interesting and challenging, with the presence of void space (the trachea).150 Here, the RTE will need to be used as the forward model, and reflection and refraction at the trachea boundary have to be considered. A recent numerical experiment by our group will be presented next (unpublished data). In this experiment, first, a realistic 3-D human neck model was developed with MRI data [Fig. 7(a)], and 23 sources and 22 detectors were placed alternately on the front surface of the neck with the arrangement of light from each source to be detected by seven detectors [Fig. 7(b)]. The model has two thyroid cancers with different μa values from the μa of the thyroid. Our algorithm is based on the time domain RTE and the Gauss–Newton method, and MRI data are used as the priori anatomical information. Figure 7(c) demonstrates reconstructed images of the absorption coefficient of the human neck, and the thyroid is more clearly imaged than with MRI. Two cancers are also reconstructed.

Fig. 7

RTE-based image reconstruction of the thyroid model. (a) MR images of the human neck. (b) Realistic human neck model based on the MR images. Red and blue spots denote source and detector positions, respectively. Red spots also detect light when they are not a source position. (c) Reconstructed images of μa of the thyroid (white arrow). The yellow triangles denote cancers. (Reported in ISEM 2015 by K. Hashimoto et al.)



Future Prospects

Real-time image recovery, which is possible with conventional NIRS, is the aim of the development of high-density DOT based on linearization approaches.151 Very different from this, developing DOT-based nonlinear iterative approaches is far more challenging and complex. There is still room for improvements; however, several advantages in DOT over other imaging techniques stress the need for DOT applications in clinical medicine. It is able to detect lesions without exogenous probes or contrast agents, it can be employed to measure neonates, and it is useful for planning of photodynamic therapy. Furthermore, DOT can be extended to fluorescence tomography (FDOT).152153.154.155 With FDOT, molecular imaging in living human subjects is possible. Thus, combining DOT and FDOT will make dynamic multilevel, from molecular to whole organism level, bio-optical imaging possible.


This research was supported in part by Japan Agency for Medical Research and Development and JSPS KAKENHI Grant No. 25287028.


1. F. F. Jöbsis, “Noninvasive infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).SCIEAS0036-8075 http://dx.doi.org/10.1126/science.929199 Google Scholar

2. B. Chance et al., “Cognition-activated low frequency modulation of light absorption in human brain,” Proc. Natl. Acad. Sci. U. S. A. 90, 3770–3774 (1993). http://dx.doi.org/10.1073/pnas.90.8.3770 Google Scholar

3. Y. Hoshi and M. Tamura, “Detection of dynamic changes in cerebral oxygenation coupled to neuronal function during mental work in man,” Neurosci. Lett. 150, 5–8 (1993).NELED50304-3940 http://dx.doi.org/10.1016/0304-3940(93)90094-2 Google Scholar

4. T. Kato et al., “Human visual cortical function during photic stimulate on monitoring by means of near-infrared spectroscopy,” J. Cereb. Blood Flow Metab. 13, 516–520 (1993). http://dx.doi.org/10.1038/jcbfm.1993.66 Google Scholar

5. A. Villringer et al., “Near-infrared spectroscopy (NIRS): a new tool to study hemodynamic changes during activation of brain function in human adults,” Neurosci. Lett. 154, 101–104 (1993).NELED50304-3940 http://dx.doi.org/10.1016/0304-3940(93)90181-J Google Scholar

6. J. C. Hebden and K. S. Wing, “Time-resolved optical tomography,” Appl. Opt. 32, 372–380 (1993).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.32.000372 Google Scholar

7. S. R. Arridge, “Optical tomography in medical imaging,” Inv. Prob. 15, R41–R93 (1999). http://dx.doi.org/10.1088/0266-5611/15/2/022 Google Scholar

8. A. H. Hielscher et al., “Near-infrared diffuse optical tomography,” Dis. Markers. 18, 313–337 (2002).DMARD30278-0240 http://dx.doi.org/10.1155/2002/164252 Google Scholar

9. K. Ren, “Recent developments in numerical techniques for transport-based medical imaging methods,” Commun. Comput. Phys. 8, 1–50 (2010).1815-2406 http://dx.doi.org/10.4208/cicp.220509.200110a Google Scholar

10. B. B. Das, K. M. Yoo and R. R. Alfano, “Ultrafast time-gated imaging in thick tissues: a step toward optical mammography,” Opt. Lett. 18, 1092–1094 (1993).OPLEDP0146-9592 http://dx.doi.org/10.1364/OL.18.001092 Google Scholar

11. L. Wang et al., “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).SCIEAS0036-8075 http://dx.doi.org/10.1126/science.253.5021.769 Google Scholar

12. G. Jarry et al., “Imaging mammalian tissues and organs using laser collimated transillumination,” J. Biomed. Eng. 6, 70–74 (1984).JBIEDR0141-5425 http://dx.doi.org/10.1016/0141-5425(84)90013-X Google Scholar

13. P. C. Jackson et al., “The development of a system for transillumination computed tomography,” Br. J. Radiol. 60, 375–380 (1987).BJRAAP0007-1285 http://dx.doi.org/10.1259/0007-1285-60-712-375 Google Scholar

14. R. Abumi et al., “Imaging of rat head under ischemic conditions by near-infrared computed tomography,” J. Clin. Biochem. Nutr. 11, 211–222 (1991).JCBNER0912-0009 http://dx.doi.org/10.3164/jcbn.11.211 Google Scholar

15. I. R. Singer et al., “Image reconstruction of the interior of bodies that diffusion radiation,” Science 248, 990–993 (1990).SCIEAS0036-8075 http://dx.doi.org/10.1126/science.248.4958.990 Google Scholar

16. S. R. Arridge, M. Schweiger and D. T. Delpy, “Iterative reconstruction of near infra-red absorption images,” Proc. SPIE 1767, 372–383 (1992).PSISDG0277-786X http://dx.doi.org/10.1117/12.139033 Google Scholar

17. R. L. Barbour et al., “Imaging of diffusing media by a progressive iterative backprojection method using time-domain data,” Proc. SPIE 1641, 21–34 (1992).PSISDG0277-786X http://dx.doi.org/10.1117/12.59370 Google Scholar

18. B. W. Pogue et al., “Initial assessment of s simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/40/10/011 Google Scholar

19. J. C. Hebden, S. R. Arridge and D. T. Delpy, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841 (1997).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/42/5/008 Google Scholar

20. S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inv. Prob. 25, 123010 (2009). http://dx.doi.org/10.1088/0266-5611/25/12/123010 Google Scholar

21. G. Gratton et al., “Shades of gray matter: noninvasive optical images of human brain responses during visual stimulation,” Psychophysiology 32, 505–509 (1995).PSPHAF0048-5772 http://dx.doi.org/10.1111/psyp.1995.32.issue-5 Google Scholar

22. A. Maki et al., “Spatial and temporal analysis of human motor activity using noninvasive NIR topography,” Med. Phys. 22, 1997–2005 (1995).MPHYA60094-2405 http://dx.doi.org/10.1118/1.597496 Google Scholar

23. T. Yamamoto et al., “Arranging optical fibres for the spatial resolution improvement of topographical images,” Phys. Med. Biol. 47, 3429–3440 (2002).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/47/18/311 Google Scholar

24. H. Kawaguchi et al., “Theoretical evaluation of accuracy in position and size of brain activity obtained by near-infrared topography,” Phys. Med. Biol. 49, 2753–2765 (2004).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/49/12/019 Google Scholar

25. S. Wang et al., “Effects of spatial variation of skull and cerebrospinal fluid layers on optical mapping of brain activities,” Opt. Rev. 17, 410–420 (2010).1340-6000 http://dx.doi.org/10.1007/s10043-010-0076-6 Google Scholar

26. T. Takahashi et al., “Influence of skin blood flow on near-infrared spectroscopy signals measured on the forehead during a verbal fluency task,” NeuroImage 57, 991–1002 (2011).NEIMEF1053-8119 http://dx.doi.org/10.1016/j.neuroimage.2011.05.012 Google Scholar

27. E. Kirillina et al., “The physiological origin of task-evoked systemic artefacts in functional near infrared spectroscopy,” NeuroImage 61, 70–81 (2012).NEIMEF1053-8119 http://dx.doi.org/10.1016/j.neuroimage.2012.02.074 Google Scholar

28. B. W. Zeff et al., “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. U. S. A. 104, 12169–12174 (2007). http://dx.doi.org/10.1073/pnas.0611266104 Google Scholar

29. C. Habermehl et al., “Somatosensory activation of two fingers can be discriminated with ultrahigh-density diffuse optical tomography,” NeuroImage 59, 3201–3211 (2012).NEIMEF1053-8119 http://dx.doi.org/10.1016/j.neuroimage.2011.11.062 Google Scholar

30. T. Correia et al., “Three-dimensional optical topography of brain activity in infants watching videos of human movement,” Phys. Med. Biol. 57, 1135–1146 (2012).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/57/5/1135 Google Scholar

31. A. M. Smith, M. C. Mancini and S. Nie, “Second window for in vivo imaging,” Nat. Nanotechnol. 4, 710–711 (2009).NNAABX1748-3387 http://dx.doi.org/10.1038/nnano.2009.326 Google Scholar

32. T. Hamaoka et al., “The use of muscle near-infrared spectroscopy in sports, health and medical sciences: recent developments,” Philos. Trans. R. Soc. A 369, 4591–4604 (2011).PTRMAD1364-503X http://dx.doi.org/10.1098/rsta.2011.0298 Google Scholar

33. M. Ferrari, M. Muthalib and V. Quaresima, “The use of muscle near-infrared spectroscopy in understanding skeletal muscle physiology: recent developments,” Philos. Trans. R. Soc. A 369, 4577–4590 (2011).PTRMAD1364-503X http://dx.doi.org/10.1098/rsta.2011.0230 Google Scholar

34. Y. Hoshi et al., “Redox behavior of cytochrome oxidase in the rat brain measured by near-infrared spectroscopy,” J. Appl. Physiol. 83, 1842–1848 (1997). Google Scholar

35. G. Bale et al., “A new broadband near-infrared spectroscopy system for in-vivo measurements of cerebral cytochrome-c-oxidase changes in neonatal brain injury,” Biomed. Opt. Express 5(10), 3450–3466 (2014).BOEICL2156-7085 http://dx.doi.org/10.1364/BOE.5.003450 Google Scholar

36. M. Ferrari and V. Quaresima, “A brief review on the history of human functional near-infrared spectroscopy (fNIRS) development and fields of application,” NeuroImage 63(2), 921–935 (2012).NEIMEF1053-8119 http://dx.doi.org/10.1016/j.neuroimage.2012.03.049 Google Scholar

37. S. L. Jacques, C. A. Alter and S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1(4), 309–334 (1987). Google Scholar

38. S. T. Flock, B. C. Wilson and M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14(5), 835–843 (1987).MPHYA60094-2405 http://dx.doi.org/10.1118/1.596010 Google Scholar

39. M. S. Patterson, B. C. Wilson and D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155–168 (1991). http://dx.doi.org/10.1007/BF02032543 Google Scholar

40. A. Kienle et al., “Spatially resolved absolute diffuse reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35(13), 2304–2314 (1996).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.35.002304 Google Scholar

41. J. J. Duderstadt and W. R. Martin, Transport Theory, John Wiley & Sons, New York (1979). Google Scholar

42. A. Ishimaru, Wave Propagation and Scattering in Random Media, IEEE Press, New York (1997). Google Scholar

43. P. Wang, S. R. Arridge and M. Jiang, “Radiative transfer equation for media with spatially varying refractive index,” Phys. Rev. A 90, 023803 (2014). http://dx.doi.org/10.1103/PhysRevA.90.023803 Google Scholar

44. A. D. Klose, “The forward and inverse problem in tissue optics based on the radiative transfer equation: a brief review,” J. Quant. Spectrosc. Radiat. Transfer 111, 1852–1853 (2010).JQSRAE0022-4073 http://dx.doi.org/10.1016/j.jqsrt.2010.01.020 Google Scholar

45. L. G. Henyey and L. J. Greenstein, “Diffuse radiation in the galaxy,” J. Astrophys. 93, 70–83 (1941).JASRD70250-6335 http://dx.doi.org/10.1086/144246 Google Scholar

46. K. Furutsu and Y. Yamada, “Diffusion approximation for a dissipative random medium and the applications,” Phys. Rev. E 50(5), 3634–3640 (1994). http://dx.doi.org/10.1103/PhysRevE.50.3634 Google Scholar

47. R. Pierrat, J.-J. Greffet and R. Carminati, “Photon diffusion coefficient in scattering and absorbing media,” J. Opt. Soc. Am. A Opt. Imag. Sci. Vis. 23, 1106–1110 (2006). http://dx.doi.org/10.1364/JOSAA.23.001106 Google Scholar

48. D. T. Delpy et al., “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/33/12/008 Google Scholar

49. B. Chance et al., “Comparison of time-resolved and -unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. U. S. A. 85, 4971–4975 (1988). http://dx.doi.org/10.1073/pnas.85.14.4971 Google Scholar

50. J. R. Lakowicz and K. Berndt, “Frequency domain measurement of photon migration in tissues,” Chem. Phys. Lett. 166, 246–252 (1990).CHPLBC0009-2614 http://dx.doi.org/10.1016/0009-2614(90)80024-8 Google Scholar

51. A. Duncan et al., “A multiwavelength, wideband, intensity modulated optical spectrometer for near infrared spectroscopy and imaging,” Proc. SPIE 1888, 248–257 (1993).PSISDG0277-786X http://dx.doi.org/10.1117/12.154641 Google Scholar

52. J. Steinbrink et al., “Determining changes in NIR absorption using a layered model of the human head,” Phys. Med. Biol. 46, 879–896 (2001).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/46/3/320 Google Scholar

53. A. Liebert et al., “Time-resolved multidistance near-infrared spectroscopy of the adult head: intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons,” Appl. Opt. 43, 3037–3047 (2004).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.43.003037 Google Scholar

54. M. S. Patterson, B. Chance and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28(12), 2331–2336 (1989).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.28.002331 Google Scholar

55. A. Torricelli et al., “Time domain functional NIRS imaging for human brain mapping,” NeuroImage 85, 28–50 (2014).NEIMEF1053-8119 http://dx.doi.org/10.1016/j.neuroimage.2013.05.106 Google Scholar

56. C. Sato et al., “Extraction of depth-dependent signals from time-resolved reflectance in layered turbid media,” J. Biomed. Opt. 10, 064008 (2005).JBOPFO1083-3668 http://dx.doi.org/10.1117/1.2136312 Google Scholar

57. C. Sato et al., “Intraoperative monitoring of depth-dependent hemoglobin concentration changes during carotid endarterectomy by time-resolved spectroscopy,” Appl. Opt. 46, 2785–2792 (2007).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.46.002785 Google Scholar

58. B. Chance et al., “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).ANBCA20003-2697 http://dx.doi.org/10.1016/0003-2697(88)90076-0 Google Scholar

59. A. H. Hielscher et al., “Near-infrared diffuse optical tomography,” Dis. Markers 18(5-6), 313–337 (2002).DMARD30278-0240 http://dx.doi.org/10.1155/2002/164252 Google Scholar

60. S. R. Arridge, M. Cope and D.T. Delpy, “Theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/37/7/005 Google Scholar

61. J. B. Fishkin and E. Graton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J. Opt. Soc. Am. A. 10(1), 127–140 (1993).JOAOD60740-3232 http://dx.doi.org/10.1364/JOSAA.10.000127 Google Scholar

62. S. Fantini, M. A. Franceschini and E. Graton, “Semi-infinite geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation,” J. Opt. Soc. Am. B 11, 2128–2138 (1994).JOBPDE0740-3224 http://dx.doi.org/10.1364/JOSAB.11.002128 Google Scholar

63. S. Fantini et al., “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: a light-emitting-diode based technique,” Appl. Opt. 33(22), 5204–5213 (1994).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.33.005204 Google Scholar

64. V. Toronov et al., “Study of local cerebral hemodynamics by frequency-domain near-infrared spectroscopy and correlation with simultaneously acquired functional magnetic resonance imaging,” Opt. Express 9(8), 417–427 (2001).OPEXFF1094-4087 http://dx.doi.org/10.1364/OE.9.000417 Google Scholar

65. A. Kienle and M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14(1), 246–254 (1997).JOAOD60740-3232 http://dx.doi.org/10.1364/JOSAA.14.000246 Google Scholar

66. M. A. O’Leary et al., “Experimental images of heterogenous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20, 426–428 (1995).OPLEDP0146-9592 http://dx.doi.org/10.1364/OL.20.000426 Google Scholar

67. R. L. Barbour et al., “Perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” Medical Optical Tomography: Functional Imaging and Monitoring, and G. Muller et al., Eds., Vol. IS11, pp. 87–120, SPIE Press, Bellingham (1993). Google Scholar

68. D. A. Boas, “A fundamental limitation of linearized algorithms for diffuse optical tomography,” Opt. Express 1(13), 404–413 (1997).OPEXFF1094-4087 http://dx.doi.org/10.1364/OE.1.000404 Google Scholar

69. N. M. Gregg et al., “Brain specificity of diffuse optical imaging: improvements from superficial signal regression and tomography,” Front. Neuroenerg. 2, 14 (2010). http://dx.doi.org/10.3389/fnene.2010.00014 Google Scholar

70. A. T. Eggebrecht et al., “Mapping distributed brain function and networks with diffuse optical tomography,” Nat. Photonics 8(6), 448–454 (2014). http://dx.doi.org/10.1038/nphoton.2014.107 Google Scholar

71. D. A. Boas, A. M. Dale and M. A. Franceshini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” NeuroImage 23, S275–S288 (2004).NEIMEF1053-8119 http://dx.doi.org/10.1016/j.neuroimage.2004.07.011 Google Scholar

72. T. Shimokawa et al., “Hierarchical Bayesian estimation improved depth accuracy and spatial resolution of diffuse optical tomography,” Opt. Express 20(18), 20427–20446 (2012).OPEXFF1094-4087 http://dx.doi.org/10.1364/OE.20.020427 Google Scholar

73. B. W. Pogue et al., “Spatially variant regularization improve diffuse optical tomography,” Appl. Opt. 38, 2950–2961 (1999).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.38.002950 Google Scholar

74. J. P. Culver et al., “Diffuse optical tomography of cerebral blood flow, oxygenation, and metabolism in rat during focal ischemia,” J. Cereb. Blood Flow Metab. 23, 911–924 (2003). http://dx.doi.org/10.1097/01.WCB.0000076703.71231.BB Google Scholar

75. N. Cao, A. Nehorai and M. Jacob, “Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm,” Opt. Express 15(21), 13695–13708 (2007).OPEXFF1094-4087 http://dx.doi.org/10.1364/OE.15.013695 Google Scholar

76. M. Jacob et al., “Level-set algorithm for the reconstruction of functional activation in near-infrared spectroscopic imaging,” J. Biomed. Opt. 11(6), 064029 (2006).JBOPFO1083-3668 http://dx.doi.org/10.1117/1.2400595 Google Scholar

77. M. Guven et al., “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Boil. 50, 2837 (2005). http://dx.doi.org/10.1088/0031-9155/50/12/008 Google Scholar

78. F. Abdelnour, C. Genovese and T. Huppert, “Hierarchical Bayesian regularization of reconstructions for diffuse optical tomography using multiple priors,” Biomed. Opt. Express 1(4), 1084–1103 (2010).BOEICL2156-7085 http://dx.doi.org/10.1364/BOE.1.001084 Google Scholar

79. T. Shimokawa et al., “Extended hierarchical Bayesian diffuse optical tomography for removing scalp artifact,” Biomed. Opt. Express 4(11), 2411–2432 (2013).BOEICL2156-7085 http://dx.doi.org/10.1364/BOE.4.002411 Google Scholar

80. O. Lee et al., “Compressive diffuse optical tomography: noniterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imaging 30(5), 1129–1142 (2011).ITMID40278-0062 http://dx.doi.org/10.1109/TMI.2011.2125983 Google Scholar

81. O. Lee and J. C. Ye, “Joint sparsity-driven non-iterative simultaneous reconstruction of absorption and scattering in diffuse optical tomography,” Opt. Express 21(22), 26589–26604 (2013).OPEXFF1094-4087 http://dx.doi.org/10.1364/OE.21.026589 Google Scholar

82. S. Saquib, K. M. Hanson and G. S. Cunningham, “Model-based image reconstruction from time-resolved diffusion data,” Proc. SPIE 3034, 369–380 (1997).PSISDG0277-786X http://dx.doi.org/10.1117/12.274123 Google Scholar

83. A. H. Hielscher, “Model-based iterative image reconstruction for photon migration tomography,” Proc. SPIE 3171, 106–117 (1997).PSISDG0277-786X http://dx.doi.org/10.1117/12.294239 Google Scholar

84. S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part 2: finite-element-method calculation,” Appl. Opt. 34(34), 8026–8037 (1995).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.34.008026 Google Scholar

85. K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22(6), 691–701 (1995).MPHYA60094-2405 http://dx.doi.org/10.1118/1.597488 Google Scholar

86. S. A. Arridge and M. Schweiger, “A gradient-based optimization scheme for optical tomography,” Opt. Express 2(6), 213–226 (1998).OPEXFF1094-4087 http://dx.doi.org/10.1364/OE.2.000213 Google Scholar

87. A. H. Hielscher, A.D. Klose and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).ITMID40278-0062 http://dx.doi.org/10.1109/42.764902 Google Scholar

88. M. Schweiger and S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699 (1999).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/44/7/310 Google Scholar

89. F. Gao, H. Zhao and Y. Yamada, “Improvement of image quality in diffuse optical tomography by use of full time-resolved data,” Appl. Opt. 41(4), 778–791 (2002).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.41.000778 Google Scholar

90. F. A. Grünbaum, “A nonlinear inverse problem inspired by three-dimensional diffuse tomography,” Inverse Probl. 17, 1907–1922 (2001).INPEEY0266-5611 http://dx.doi.org/10.1088/0266-5611/17/6/322 Google Scholar

91. H. Dehghani et al., “Numerical modeling and image reconstruction in diffuse optical tomography,” Philos. Trans. R. Soc. A 367, 3073–3093 (2009).PTRMAD1364-503X http://dx.doi.org/10.1098/rsta.2009.0090 Google Scholar

92. A. H. Hielscher, R. E. Alcouff and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculation for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/43/5/017 Google Scholar

93. H. Fujii et al., “Hybrid model of light propagation in random media based on the time-dependent radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 147, 145–154 (2014). http://dx.doi.org/10.1016/j.jqsrt.2014.05.026 Google Scholar

94. A. D. Klose and A. H. Hielscher, “Optical tomography with the equation of radiative transfer,” Int. J. Numer. Methods Heat Fluid Flow 18(3/4), 443–464 (2008). http://dx.doi.org/10.1108/09615530810853673 Google Scholar

95. A. Charette, J. Boulanger and H. K. Kim, “An overview on recent radiation transport algorithm development for optical tomography imaging,” J. Quant. Spectrosc. Radiat. Transfer 109, 2743–2766 (2008). http://dx.doi.org/10.1016/j.jqsrt.2008.06.007 Google Scholar

96. A. D. Klose and A. H. Hielscher, “Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26(8), 1698–1707 (1999).MPHYA60094-2405 http://dx.doi.org/10.1118/1.598661 Google Scholar

97. C. Das et al., “Experimental and numerical analysis of short-pulse laser interaction with tissue phantoms containing inhomogeneities,” Appl. Opt. 42(25), 5173–5180 (2003).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.42.005173 Google Scholar

98. J. Boulanger and A. Charette, “Numerical developments for short-pulsed near infra-red laser spectroscopy. Part I: direct treatment,” J. Quant. Spectrosc. Radiat. Transfer 91, 189–209 (2005). http://dx.doi.org/10.1016/j.jqsrt.2004.05.057 Google Scholar

99. M. Machida et al., “The Green’s function for the radiative transport equation in the slab geometry,” J. Phys. A: Math. Theor. 43, 065402 (2010).JPAMB51751-8113 http://dx.doi.org/10.1088/1751-8113/43/6/065402 Google Scholar

100. A. Liemert and A. Kienle, “Exact and efficient solution of the radiative transport equation for the semi-infinite medium,” Sci. Rep. 3, 2018 (2013).SRCEC32045-2322 http://dx.doi.org/10.1038/srep02018 Google Scholar

101. Z. Guo and K. Kim, “Ultrafast-laser-radiation transfer in heterogeneous tissues with the discrete-ordinate method,” Appl. Opt. 42(16), 2897–2905 (2003).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.42.002897 Google Scholar

102. T. Tarvainen et al., “Hybrid radiative-transfer-diffusion model for optical tomography,” Appl. Opt. 44(6), 876–886 (2005).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.44.000876 Google Scholar

103. H. Gao and H. Zhao, “A fast-forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38(3), 149–192 (2009).TTSPB40041-1450 http://dx.doi.org/10.1080/00411450903187722 Google Scholar

104. P. González-Rodríguez and A. D. Kim, “Comparison of light scattering models for diffuse optical tomography,” Opt. Express 17(11), 8756–8774 (2009).OPEXFF1094-4087 http://dx.doi.org/10.1364/OE.17.008756 Google Scholar

105. J. Jia, H. K. Kim and A. H. Hielscher, “Fast linear solver for radiative transport equation with multiple right hand sides in diffuse optical tomography,” J. Quant. Spectrosc. Radiat. Transfer 167, 10–22 (2015). http://dx.doi.org/10.1016/j.jqsrt.2015.07.015 Google Scholar

106. T. Tarvainen et al., “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol. 50, 4913–4930 (2005).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/50/20/011 Google Scholar

107. T. Tarvainen et al., “Image reconstruction in diffuse optical tomography using the coupled radiative transport-diffusion model,” J. Quant. Spectrosc. Radiat. Transfer 112, 2600–2608 (2011). http://dx.doi.org/10.1016/j.jqsrt.2011.07.008 Google Scholar

108. H. Fujii et al., “A coupling model of the radiative transport equation for calculating photon migration in biological tissue,” Proc. SPIE 9792, 979214 (2015).PSISDG0277-786X http://dx.doi.org/10.1117/12.2203638 Google Scholar

109. T. Correria et al., “Selection of regularization parameter for optical topography,” J. Biomed. Opt. 14(3), 034044 (2009).JBOPFO1083-3668 http://dx.doi.org/10.1117/1.3156839 Google Scholar

110. C. Habermehl et al., “Optimizing the regularization for imaginf reconstruction of cerebral diffuse optical tomography,” J. Biomed. Opt. 19(9), 096006 (2014).JBOPFO1083-3668 http://dx.doi.org/10.1117/1.JBO.19.9.096006 Google Scholar

111. A. H. Barnett et al., “Robust inference of baseline optical properties of the human head with three-dimensional segmentation from magnetic resonance imaging,” Appl. Opt. 42(16), 3095–3108 (2003).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.42.003095 Google Scholar

112. P. K. Yalavarthy et al., “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15(13), 8043–8058 (2007).OPEXFF1094-4087 http://dx.doi.org/10.1364/OE.15.008043 Google Scholar

113. L. Zhang et al., “Direct regularization from co-registered anatomical images for MRI-guided near-infrared spectral tomographic image reconstruction,” Biomed. Opt. Express 6(9), 3618–3630 (2015).BOEICL2156-7085 http://dx.doi.org/10.1364/BOE.6.003618 Google Scholar

114. D. L. Collins et al., “Design and construction of a realistic digital brain phantom,” IEEE Trans. Med. Imaging 17(3), 463–468 (1998).ITMID40278-0062 http://dx.doi.org/10.1109/42.712135 Google Scholar

115. A. Custo et al., “Anatomical atlas-guided diffuse optical tomography of brain activation,” NeuroImage 49(1), 561–567 (2010).NEIMEF1053-8119 http://dx.doi.org/10.1016/j.neuroimage.2009.07.033 Google Scholar

116. Z. Lin et al., “Atlas-guided volumetric diffuse optical tomography enhanced by generalized linear model analysis to image risk decision-making responses in young adults,” Hum. Brain Mapp. 35, 4249–4266 (2014).HBRME71065-9471 http://dx.doi.org/10.1002/hbm.v35.8 Google Scholar

117. Z. Yuan et al., “Tomographic x-ray-guided three-dimensional diffuse optical tomography of osteoarthritis in the finger joints,” J. Biomed. Opt. 13(4), 044006 (2008).JBOPFO1083-3668 http://dx.doi.org/10.1117/1.2965547 Google Scholar

118. C. Xu et al., “Ultrasound-guided diffuse optical tomography for predicting and monitoring neoadjuvant chemotherapy of breast cancers: recent progress,” Ultrason. Imaging 38(1), 5–18 (2015).ULIMD40161-7346 http://dx.doi.org/10.1177/0161734615580280 Google Scholar

119. V. C. Kavuri and H. Liu, “Hierarchical clustering method to improve transrectal ultrasound-guided diffuse optical tomography for prostate cancer imaging,” Acad. Radiol. 21(2), 250–262 (2014). http://dx.doi.org/10.1016/j.acra.2013.11.003 Google Scholar

120. T. Correia et al., “Three-dimensional optical topography of brain activity in infants watching videos of human movement,” Phys. Med. Biol. 57, 1135–1146 (2012).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/57/5/1135 Google Scholar

121. M. S. Hassanpour et al., “Mapping cortical responses to speech using high-density diffuse optical tomography,” NeuroImage 117, 319–326 (2015).NEIMEF1053-8119 http://dx.doi.org/10.1016/j.neuroimage.2015.05.058 Google Scholar

122. A. Blasi et al., “Investigation of depth dependent changes in cerebral haemodynamics during face perception in infants,” Phys. Med. Biol. 52, 6849–6864 (2007).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/52/23/005 Google Scholar

123. H. Singh et al., “Mapping cortical haemodynamics during neonatal seizures using diffuse optical tomography: a case study,” NeuroImage: Clin. 5, 256–265 (2014). http://dx.doi.org/10.1016/j.nicl.2014.06.012 Google Scholar

124. Y. Ueda et al., “Reflectance diffuse optical tomography; its application to human brain mapping,” Jpn. J. Appl. Phys. 44(38), L1203–L1206 (2005). http://dx.doi.org/10.1143/JJAP.44.L1203 Google Scholar

125. B. R. White et al., “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47, 148–156 (2009).NEIMEF1053-8119 http://dx.doi.org/10.1016/j.neuroimage.2009.03.058 Google Scholar

126. B. R. White et al., “Bedside optical imaging of occipital resting-state functional connectivity in neonates,” NeuroImage 59, 2529–2538 (2012).NEIMEF1053-8119 http://dx.doi.org/10.1016/j.neuroimage.2011.08.094 Google Scholar

127. S. L. Ferradal et al., “Functional imaging of the developing brain at the bedside using diffuse optical tomography,” Cereb. Cortex 26, 1558–1568 (2016). http://dx.doi.org/10.1093/cercor/bhu320 Google Scholar

128. J. C. Hebden et al., “Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography,” Phys. Med. Biol. 49, 1117 (2004).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/49/7/003 Google Scholar

129. R. Fukuzawa, “Diffuse optical tomography for premature neonate head,” Master’s Thesis, The University of Electro-Communications, Tokyo, Japan (2009). Google Scholar

130. H. Eda et al., “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70(9), 3595–3602 (1999).RSINAK0034-6748 http://dx.doi.org/10.1063/1.1149965 Google Scholar

131. F. E. W. Schmidt et al., “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71(1), 256–265 (2000).RSINAK0034-6748 http://dx.doi.org/10.1063/1.1150191 Google Scholar

132. A. P. Gibson et al., “Three-dimensional whole-head optical tomography of passive motor evoked responses in the neonate,” NeuroImage 30, 521–528 (2006).NEIMEF1053-8119 http://dx.doi.org/10.1016/j.neuroimage.2005.08.059 Google Scholar

133. P. Taroni et al., “Time-resolved optical mammography between 637 and 985 nm: clinical study on the detection and identification of breast lesions,” Phys. Med. Biol. 50(11), 2469–2488 (2005).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/50/11/003 Google Scholar

134. L. C. Enfield et al., “Three-dimensional time-resolved optical mammography of the uncompressed breast,” Appl. Opt. 46(17), 3628–3638 (2007).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.46.003628 Google Scholar

135. A. Cerussi et al., “Predicting response to breast cancer neoadjuvant chemotherapy using diffuse optical spectroscopy,” Proc. Natl. Acad. Sci. U. S. A. 104(10), 4014–4019 (2007). http://dx.doi.org/10.1073/pnas.0611058104 Google Scholar

136. R. Choe et al., “Differentiation of benign and malignant breast tumors by in-vivo three-dimensional parallel-plate diffuse optical tomography,” J. Biomed. Opt. 14(2), 024020 (2009).JBOPFO1083-3668 http://dx.doi.org/10.1117/1.3103325 Google Scholar

137. M. L. Flexman et al., “Monitoring early response to drug therapy with diffuse optical tomography,” J. Biomed. Opt. 17(1), 016014 (2012).JBOPFO1083-3668 http://dx.doi.org/10.1117/1.JBO.17.1.016014 Google Scholar

138. S. D. Konecky et al., “Imaging complex structures with diffuse light,” Opt. Express 16(7), 5048–5060 (2008).OPEXFF1094-4087 http://dx.doi.org/10.1364/OE.16.005048 Google Scholar

139. B. Deng et al., “Characterization of structural-prior guide optical tomography using realistic breast models derived from dual-energy x-ray mammography,” Biomed. Opt. Express 6(7), 2366–2379 (2015).BOEICL2156-7085 http://dx.doi.org/10.1364/BOE.6.002366 Google Scholar

140. D. S. DeLorey, J. M. Kowalchuk and D. H. Paterson, “Relationship between pulmonary O2 uptake kinetics and muscle deoxygenation during moderate-intensity exercise,” J. Appl. Physiol. 95(1), 113–120 (2003). http://dx.doi.org/10.1152/japplphysiol.00956.2002 Google Scholar

141. M. Niwayama et al., “A 200-channel imaging system of muscle oxygenation using CW near-infrared spectroscopy,” IEICE Trans. Inf. Syst. E85-D(1), 115–123 (2002). Google Scholar

142. E. Omae et al., “Sensitivity correction for the influence of the fat layer on muscle oxygenation and estimation of fat thickness by time-resolved spectroscopy,” J. Biomed. Opt. 19(6), 067005 (2014).JBOPFO1083-3668 http://dx.doi.org/10.1117/1.JBO.19.6.067005 Google Scholar

143. L. S. L. Arakaki et al., “Optical diffusion tomograpohy of the exercising human forearm,” in Biomedical Optical Spectroscopy and Diagnostics, OSA Trends in Optics and Photonics, Optical Society of America (2000). Google Scholar

144. E. M. C. Hillman et al., “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).PHMBA70031-9155 http://dx.doi.org/10.1088/0031-9155/46/4/315 Google Scholar

145. H. Zhao et al., “Time-resolved diffuse optical tomographic imaging for the provision of both anatomical and functional information about biological tissue,” Appl. Opt. 44(1), 1905–1916 (2005).APOPAI0003-6935 http://dx.doi.org/10.1364/AO.44.001905 Google Scholar

146. Y. Tanikawa et al., “Time-resolved DOT images of human forearm under exercise,” in Proc. APBP 2009, pp. 120–121 (2009). Google Scholar

147. M. A. Khali et al., “Dynamic diffuse optical imaging of peripheral arterial disease,” Biomed. Opt. Express 3(9), 2288–2298 (2012).BOEICL2156-7085 http://dx.doi.org/10.1364/BOE.3.002288 Google Scholar

148. L. D. Montejo et al., “Computer-aided diagnosis of rheumatoid arthritis with optical tomography, Part 1: feature extraction,” J. Biomed. Opt. 18(7), 076001 (2013).JBOPFO1083-3668 http://dx.doi.org/10.1117/1.JBO.18.7.076001 Google Scholar

149. L. D. Montejo et al., “Computer-aided diagnosis of rheumatoid arthritis with optical tomography, Part 2: image classification,” J. Biomed. Opt. 18(7), 076002 (2013).JBOPFO1083-3668 http://dx.doi.org/10.1117/1.JBO.18.7.076002 Google Scholar

150. H. Fujii et al., “Numerical modeling of photon migration in human neck based on the radiative transport equation,” J. Appl. Nonlinear Dyn. 5(1), 117–125 (2016). http://dx.doi.org/10.5890/JAND.2016.03.009 Google Scholar

151. W. Wu et al., “Fast and efficient image reconstruction for high density diffuse optical imaging of the human brain,” Biomed. Opt. Express 6(11), 4567–4584 (2015).BOEICL2156-7085 http://dx.doi.org/10.1364/BOE.6.004567 Google Scholar

152. V. Nitzachristos et al., “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8(7), 757–761 (2002).1078-8956 http://dx.doi.org/10.1038/nm729 Google Scholar

153. A. Corlu et al., “Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,” Opt. Express 15(11), 6696–6716 (2007).OPEXFF1094-4087 http://dx.doi.org/10.1364/OE.15.006696 Google Scholar

154. A. Marjono et al., “Total light approach of time-domain fluorescence diffuse optical tomography,” Opt. Express 16(19), 15268–15285 (2008).OPEXFF1094-4087 http://dx.doi.org/10.1364/OE.16.015268 Google Scholar

155. N. Durcros et al., “Fluorescence diffuse optical tomography: time-resolved versus continuous-wave in the reflectance configuration,” IRBM 32, 243–250 (2011). http://dx.doi.org/10.1016/j.irbm.2011.04.001 Google Scholar


Yoko Hoshi graduated from Akita University School of Medicine (MD) in 1981 and got her PhD from Hokkaido University in 1990. She is a pediatrician (a child neurologist) while she has also been participating in developing NIRS and research in cognitive neuroscience. She has been a professor in the Department of Biomedical Optics at Hamamatsu University School of Medicine since April 2015. Her recent research interest is developing diffuse optical tomography.

Yukio Yamada received his BS, MS, and PhD degrees from Tokyo Institute of Technology, Department of Mechanical Engineering. From 1974 to 2001, he worked in the Mechanical Engineering Laboratory, Agency of Industrial and Science Technology, the Japanese government. From 2001 to 2013, he was a professor in the Department of Mechanical and Intellectual Engineering, University of Electro-Communications, Tokyo, Japan. He has been a professor emeritus at the University of Electro-Communications since 2013. He specializes in biomedical photonics and biomedical thermal engineering

© The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.
Yoko Hoshi, Yoko Hoshi, Yukio Yamada, Yukio Yamada, } "Overview of diffuse optical tomography and its clinical applications," Journal of Biomedical Optics 21(9), 091312 (13 July 2016). https://doi.org/10.1117/1.JBO.21.9.091312 . Submission:

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