Diffuse Optics for Tissue Monitoring and Tomography

Abstract

This review describes the diffusion model for light transport in tissues and the medical applications of diffuse light. Diffuse optics is particularly useful for measurement of tissue hemodynamics, wherein quantitative assessment of oxy- and deoxy-hemoglobin concentrations and blood flow are desired. The theoretical basis for near-infrared or diffuse optical spectroscopy (NIRS or DOS, respectively) is developed, and the basic elements of diffuse optical tomography (DOT) are outlined. We also discuss diffuse correlation spectroscopy (DCS), a technique whereby temporal correlation functions of diffusing light are transported through tissue and are used to measure blood flow. Essential instrumentation is described, and representative brain and breast functional imaging and monitoring results illustrate the workings of these new tissue diagnostics.

Figure 1

Absorption (μ_a) spectra of main tissue chromophores over a large wavelength range. The inset shows the so-called “physiological window” in the near-infrared where water and hemoglobin absorption are relatively low. In this part of the spectrum, light can penetrate several centimeters into tissue. Furthermore, there are clear features in the spectra which enable estimation of chromophore concentration from diffuse optical measurements at several wavelengths.

Figure 2

Three common types of sources are employed. On the far left are schematic “banana patterns” showing the sampled volumes in the reflection and transmission geometries. As a rough rule of thumb, the mean light penetration depth in the reflection geometry is ρ/2 (for a more precise relation, see [498]). For continuous wave (CW), intensity modulated (FD) and time-resolved (TR) sources, the detected light intensity over time resembles (1), (2), and (3) respectively.

Figure 3

Constant phase contours shown as a function of position for homogeneous, 0.5% Intralipid solution filling a large aquarium (30 × 30 × 60 cm). At the origin (roughly the middle of the aquarium) is the source (3-mW laser diode operating at 816 nm and modulated at 200 MHz), resulting in a geometry that very well approximates a homogeneous infinite medium. The contours are shown in 20° intervals. Inset: The measured phase shift (squares) and ln |rU(r)| (circles) are plotted as a function of radial distance from the source. The slopes reveal −k_i and k_r, from which μ_a and D can be calculated using Equation (15) and Equation (14). Figure taken from O’Leary et al. [13, Fig. 2].

Figure 4

Common geometry used to model tissue. In the semi-infinite geometry, w, h, and d all go to infinity, while in the infinite slab geometry, w and h are infinite but d is finite. Both geometries have azimuthal symmetry about the z-axis, meaning the photon fluence rate only depends on the radial and axial cylindrical coordinates ρ and z. The unit vector n̂ points from inside the tissue to outside. On the left, a single source-detector pair (with separation ρ) in the reflection geometry is shown. Note that for the slab geometry, detectors can also be used for transmission measurements by being placed on the z = d plane. On the right is a cross-section showing that the radiance moving into the turbid medium at the boundary is due to the Fresnel reflection of the radiance incident on the boundary.

Figure 5

The fluence rate curve is approximated by its tangent line at z = 0, and the Φ = 0 intercept of this curve is found to occur z = −z_b (z_b is defined exactly in Table 1).

Figure 6

Illustration of a single scattering DLS experiment (Top) and of multiple scattering (Bottom) along a single photon path in turbid media. k_j and k_j+1 are the wavevectors before and after the j^th scattering event, respectively. q_j = k_j+1 − k_j is the momentum transfer and θ_j is the scattering angle of the j^th scattering event. The solid line represents the photon path at time t, while the dotted line represents the photon path at time t + τ. During the delay time τ, the j^th scatterer moves Δr_j(τ). Courtesy of C Zhou [499].

Figure 7

The measured intensity auto-correlation curves from two experiments on isolated limb preparations on rats; (Left) Shows the electric field correlation functions during healthy circulation and under artificial perfusion with a pump. (Right) Shows the electric field auto-correlation functions from a rat before/after death.

Figure 8

Data from a mouse tumor, a piglet brain, a human calf muscle and adult human brain. Dots show the experimental data, the dashed line is a fit with 〈Δr²〉 ~ τ² (random flow), and the solid line is a fit with 〈Δr²〉 ~ τ² (Brownian motion). Note how the accuracy of the fits vary depending on the delay time (τ) and the longer delays tend to deviate further from the fits for brain measurements. This is mainly because later delays correspond to photons that probe more superficial tissues and presence of the skull alters this part of the curves. Note, r in the figure titles is the source-detector separation on the tissue surface.

Figure 9

Slices from three dimensional image reconstructions of the relative absorption coefficient $(\delta {\mu }_a/{\mu }_a^{(0)})$ for targets suspended in a 6 cm thick slab filled with highly scattering fluid. The Rytov linearized analytic inversion was used for this reconstruction. The three slices shown for each reconstruction correspond to depths of 1 cm (left), 3 cm (middle), and 5 cm (right) from the source plane. (a) Schematics of the positions of the letters during the experiments. Left: The target consists of letters “DOT” and “PENN” suspended 1 cm and 5 cm from the source plane, respectively. Right: The target consists only of the letters “DOT” suspended 3 cm from the source plane. (b) Reconstructed image of the letters “DOT” and “PENN” (c) Reconstructed image of the letters “DOT”. This figure is reproduced from Konecky et al. [250, Figure 1].

Figure 10

Flow chart of Born and Distorted Born iterative methods. A linear inverse problem of the form Jδx = y is solved for each iteration. Both the fluence rate and Green’s function are updated in the Distorted Born method, but only the fluence rate is updated in the Born iterative method (see text for details). The iterations continue until χ² has reached the desired tolerance.

Figure 11

(a)Tumor-to-normal ratio of total hemoglobin concentration (rTHC) of 10 benign and 41 malignant lesions. (b) Receiver-operating-characteristic curve for rTHC showing true positive rate for malignant lesions versus false positive rate for benign lesions.(Reprinted with permission from Ref. [122].)

Figure 12

A case of 3D optical tomography of breast with maligant cancer is shown with both endogenous (relative total hemoglobin, relative blood oxygen saturation and relative tissue scattering) and exogeneous contrast images (relative Indocyanine Green concentration measured from fluorescence) (left). On the top right, a parallel-plane DOT instrument and measurement geometry is illustrated. The isosurface diagram on the bottom right shows the volumetric extent of the observed tumor for each optically derived parameter. (Reprinted with permission from Ref. [26].)

Figure 13

(a) Schematic showing placement of probes used for hypercapnia (frontal) and sensorimotor (side) studies. For the frontal probe, a laser Doppler flowmetry (LDF) probe was placed mid-way the source and detector fibers to record scalp blood flow. (b) Increased CO₂ breathing (hypercapnia) results in significant increases in end-tidal CO₂ (EtCO₂) and blood-flow in brain (rCBF(DCS)) but only a negligible amount in scalp blood-flow (rCBF(LDF)). (c–d) Hemodynamic response to finger-tapping when the probe is placed (c) away from the contralateral sensorimotor cortex and (d) when its placed on the contralateral sensorimotor cortex.

Figure 14

(a–b) Morphological MRI scans showing location of fiducial markers indicating the location of NIRS/DOS probe which is then overlaid onto BOLD and ASL scans to define ROIs. As shown in (c), an MRI compatible NIRS/DOS probe was used for simultaneous data acquisition. (d) Group averaged responses from simultaneous ASL, BOLD and NIRS/DOS studies. Temporal evolution of NIRS/DOS measures of ΔTHC and ΔHbO₂ agree with ASL and ΔHb agrees with BOLD. Notice how ASL, ΔTHC and ΔHbO₂ maxima are earlier than BOLD and ΔHb maxima. ΔHb curve is shown inverted. Figure courtesy of D. A. Boas [474]).

Figure 15

(Top) Cerebral autoregulation implies a range of cerebral perfusion pressure (CPP) values where CBF is kept constant. As shown in the inset, impairment causes CBF to depend passively on CPP. Head-of-bed positioning was used to induce orthostatic changes in CPP. Schematic showing placement of probes where one is placed on the infarcted hemisphere and the other on contralateral, ‘healthy’ hemisphere. (Bottom) Changes in ΔTHC and rCBF are significantly larger on the infarcted hemisphere (right) which is presumably due to impaired cerebral autoregulation.

Figure 16

(Left) Placement of probes on an infant. (Right) Coronal sections showing (a) blood volume, (b) blood oxygen saturation and (c) the corresponding ultrasound image. Figure courtesy of J. C. Hebden [480].