Optical tomographic imaging of dynamic features of dense-scattering media.

Methods used in optical tomography have thus far proven to produce images of complex target media (e.g., tissue) having, at best, relatively modest spatial resolution. This presents a challenge in differentiating artifact from true features. Further complicating such efforts is the expectation that the optical properties of tissue for any individual are largely unknown and are likely to be quite variable due to the occurrence of natural vascular rhythms whose amplitudes are sensitive to a host of autonomic stimuli that are easily induced. We recognize, however, that rather than frustrating efforts to validate the accuracy of image features, the time-varying properties of the vasculature can be exploited to aid in such efforts, owing to the known structure-dependent frequency response of the vasculature and to the fact that hemoglobin is a principal contrast feature of the vasculature at near-infrared wavelengths. To accomplish this, it is necessary to generate a time series of image data. In this report we have tested the hypothesis that through analysis of time-series data, independent contrast features can be derived that serve to validate, at least qualitatively, the accuracy of imaging data, in effect establishing a self-referencing scheme. A significant finding is the observation that analysis of such data can produce high-contrast images that reveal features that are mainly obscured in individual image frames or in time-averaged image data. Given the central role of hemoglobin in tissue function, this finding suggests that a wealth of new features associated with vascular dynamics can be identified from the analysis of time-series image data.

Influence of Systematic Errors in Reference States on Image Quality and on Stability of Derived Information for dc Optical Imaging.

Optical measurements of tissue can be performed in discrete, time-averaged, and time-varying data collection modes. This information can be evaluated to yield estimates of either absolute optical coefficient values or some relative change in these values compared with a defined state. In the case of time-varying data, additional analysis can be applied to define various dynamic features. Here we have explored the accuracy with which such information can be recovered from dense scattering media using linear perturbation theory, as a function of the accuracy of the reference medium that serves as the initial guess. Within the framework of diffusion theory and a first-order solution, we have observed the following inequality regarding the sensitivity of computed measures to inaccuracy in the reference medium: Absolute measures ? relative measures > dynamic measures. In fact, the fidelity of derived dynamic measures was striking; we observed that accurate measures of dynamic behavior could be defined even if the quality of the image data from which these measures were derived was comparatively modest. In other studies we identified inaccuracy in the estimates of the reference detector values, and not to corresponding errors in the image operators, as the primary factor responsible for instability of absolute measures. The significance of these findings for practical imaging studies of tissue is discussed.

Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography.

Instrumentation is described that is suitable for acquiring multisource, multidetector, time-series optical data at high sampling rates (up to 150 Hz) from tissues having arbitrary geometries. The design rationale, calibration protocol, and measured performance features are given for both a currently used, CCD-camera-based instrument and a new silicon-photodiode-based system under construction. Also shown are representative images that we reconstructed from data acquired in laboratory studies using the described CCD-based instrument.

Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues.

We analyse the limits of the diffusion approximation to the time-independent equation of radiative transfer for homogeneous and heterogeneous biological media. Analytical calculations and finite-difference simulations based on diffusion theory are compared with discrete-ordinate, finite-difference transport calculations. The influence of the ratio of absorption and transport scattering coefficient (mu(a)/mu'(s)) on the accuracy of the diffusion approximation are quantified and different definitions for the diffusion coefficient, D, are discussed. We also address effects caused by void-like heterogeneities in which absorption and scattering are very small compared with the surrounding medium. Based on results for simple homogeneous and heterogeneous systems, we analyse diffusion and transport calculation of light propagation in the human brain. For these simulations we convert density maps obtained from magnetic resonance imaging (MRI) to optical-parameter maps (mu(a) and mu'(s)) of the brain. We show that diffusion theory fails to describe accurately light propagation in highly absorbing regions, such as haematoma, and void-like spaces, such as the ventricles and the subarachnoid space.

Nonlinear effects of localized absorption perturbations on the light distribution in a turbid medium.

A theoretical model of photon propagation in a scattering medium is presented, from which algebraic formulas for the detector-reading perturbations (delta R) produced by one or two localized perturbations in the macroscopic absorption cross section (delta mu a) are derived. Examination of these shows that when delta mu a is titrated from very small to large magnitudes in one voxel, the curve traced by the corresponding delta R values is a rectangular hyperbola. Furthermore, while delta Rinfinity identical to lim delta mu a-->infinity delta R is dependent on the location of the detector with respect to the source and the voxel, the ratio delta R/ delta Rinfinity is independent of the detector location. We also find that when delta mu a is varied in two voxels simultaneously, the quantity delta R (delta mu a,1 [symbol: see text] delta mu a,2) is a bilinear rational function of the delta mu aS. These results apply not only in the case of steady-state illumination and detection but to time-harmonic measurements as well. The validity of the theoretical formulas is demonstrated by applying them to the results of selected numerical diffusion computations. Potential applications of the derived expressions to image-reconstruction problems are discussed.

Dependence of image quality on image operator and noise for optical diffusion tomography.

By applying linear perturbation theory to the radiation transport equation, the inverse problem of optical diffusion tomography can be reduced to a set of linear equations, Wµ=R, where W is the weight function, µ are the cross-section perturbations to be imaged, and R is the detector readings perturbations. We have studied the dependence of image quality on added systematic error and/or random noise in W and R. Tomographic data were collected from cylindrical phantoms, with and without added inclusions, using Monte Carlo methods. Image reconstruction was accomplished using a constrained conjugate gradient descent method. Results show that accurate images containing few artifacts are obtained when W is derived from a reference state whose optical thickness matches that of the unknown test medium. Comparable image quality was also obtained for unmatched W, but the location of the target becomes more inaccurate as the mismatch increases. Results of the noise study show that image quality is much more sensitive to noise in W than in R, and the impact of noise increases with the number of iterations. Images reconstructed after pure noise was substituted for R consistently contain large peaks clustered about the cylinder axis, which was an initially unexpected structure. In other words, random input produces a nonrandom output. This finding suggests that algorithms sensitive to the evolution of this feature could be developed to suppress noise effects. © 1998 Society of Photo-Optical Instrumentation Engineers.

Improved Reconstruction Algorithm for Luminescence Optical Tomography when Background Lumiphore is Present.

We examine the impact of background lumiphore on image quality in luminescence optical tomography. A modification of a previously described algorithm [J. Chang, H. L. Graber, and R. L. Barbour, J. Opt. Soc. Am. A 14, 288-299 (1997); J. Chang, H. L. Graber, and R. L. Barbour, IEEE Trans. Biomed. Eng. 44, 810-822 (1997)] that estimates the background luminescence directly from the detector readings is developed. Numerical simulations were performed to calculate the diffusion-regime limiting form of forward-problem solutions for a specific test medium. We performed image reconstructions with and without white noise added to the detector readings, using both the original and the improved versions of the algorithm. The results indicate that the original version produces unsatisfactory reconstructions when background lumiphore is present, whereas the improved algorithm yields qualitatively better images, especially for small target-to-background luminescence yield ratios.

Imaging of fluorescence in highly scattering media.

Two one-speed radiation transport equations coupled by a dynamic equation for the distribution of fluorophore electronic states are used to model the migration of excitation photons and emitted fluorescence photons. The conditions for producing appreciable levels of fluorophore in the excited state are studied, with the conclusion that minimal saturation occurs under the conditions applicable to tissue imaging. This simplifies the derivation of the frequency response and of the imaging operator for a time-harmonic excitation source. Several factors known to influence the fluorescence response-the concentration, mean lifetime and quantum yield of the fluorophore, and the modulation frequency of the excitatory source-are examined. Optimal sensitivity conditions are obtained by analyzing the fluorescence source strength as a function of the mean lifetime and modulation frequency. The dependence of demodulation of the fluorescent signal on the above factors is also examined. In complementary studies, transport-theory-based operators for imaging fluorophore distributions in a highly scattering medium are derived. Experimental data were collected by irradiating a cylindrical phantom containing one or two fluorophore-filled balloons with continuous wave laser light. The reconstruction results show that qualitatively and quantitatively good images can be obtained, with embedded objects accurately located and the fluorophore concentration correctly determined.

A wavelet-based multiresolution regularized least squares reconstruction approach for optical tomography.

In this paper, we present a wavelet-based multigrid approach to solve the perturbation equation encountered in optical tomography. With this scheme, the unknown image, the data, as well as the weight matrix are all represented by wavelet expansions, thus yielding a multiresolution representation of the original perturbation equation in the wavelet domain. This transformed equation is then solved using a multigrid scheme, by which an increasing portion of wavelet coefficients of the unknown image are solved in successive approximations. One can also quickly identify regions of interest (ROI's) from a coarse level reconstruction and restrict the reconstruction in the following fine resolutions to those regions. At each resolution level a regularized least squares solution is obtained using the conjugate gradient descent method. This approach has been applied to continuous wave data calculated based on the diffusion approximation of several two-dimensional (2-D) test media. Compared to a previously reported one grid algorithm, the multigrid method requires substantially shorter computation time under the same reconstruction quality criterion.

Iterative total least-squares image reconstruction algorithm for optical tomography by the conjugate gradient method.

We present an iterative total least-squares algorithm for computing images of the interior structure of highly scattering media by using the conjugate gradient method. For imaging the dense scattering media in optical tomography, a perturbation approach has been described previously [Y. Wang et al., Proc. SPIE 1641, 58 (1992); R. L. Barbour et al., in Medical Optical Tomography: Functional Imaging and Monitoring (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 87-120], which solves a perturbation equation of the form W delta x = delta I. In order to solve this equation, least-squares or regularized least-squares solvers have been used in the past to determine best fits to the measurement data delta I while assuming that the operator matrix W is accurate. In practice, errors also occur in the operator matrix. Here we propose an iterative total least-squares (ITLS) method that minimizes the errors in both weights and detector readings. Theoretically, the total least-squares (TLS) solution is given by the singular vector of the matrix [W/ delta I] associated with the smallest singular value. The proposed ITLS method obtains this solution by using a conjugate gradient method that is particularly suitable for very large matrices. Simulation results have shown that the TLS method can yield a significantly more accurate result than the least-squares method.

Optical imaging of anatomical maps derived from magnetic resonance images using time-independent optical sources.

We present a model suitable for computing images of absorption cross sections of thick tissue structures illuminated at near infrared (NIR) wavelengths from tomographic projection data. Image reconstruction is accomplished by solving a system of linear equations derived from transport theory. Reconstruction results using different algebraic solvers are shown for anatomical maps of the breast, derived from magnetic resonance imaging data, containing two simulated pathologies, in which case qualitatively good reconstructions were obtained. Evaluation of magnetic resonance (MR) data to optimize NIR optical tomographic imaging methods and to assess the feasibility of a combined MR-optical measurement scheme is discussed.

Luminescence optical tomography of dense scattering media.

Using a set of coupled radiation transport equations, we derive image operators for luminescence optical tomography with which it is possible to reconstruct concentration and mean lifetime distribution from information obtained from dc and time-harmonic optical sources. Weight functions and detector readings were computed from analytic solutions of the diffusion equation and from numerical solutions of the transport equation by Monte Carlo methods. Detector readings were also obtained from experiments on vessels containing a balloon filled with dye embedded in an Intralipid suspension with dye in the background. Image reconstructions were performed by the conjugate gradient descent method and the simultaneous algebraic reconstruction technique with a positivity constraint. A concentration correction was developed in which the reconstructed concentration information is used in the mean-lifetime reconstruction. The results show that the target can be accurately located in both the simulated and the experimental cases, but quantitative inaccuracies are present. Observed errors include a shadowing effect in regions that have the lowest weight within the inclusion. Application of the concentration correction can significantly improve computational efficiency and reduce error in the mean-lifetime reconstructions.

Regularized progressive expansion algorithm for recovery of scattering media from time-resolved data.

Reconstructions of the absorption cross sections of dense scattering media from time-resolved data are presented. A progressive expansion (PE) algorithm, similar to a layer-stripping, is developed to circumvent the underdeterminedness of the inverse problem. An overlapping scheme, which used detector readings from several consecutive time intervals, is introduced to reduce the propagation of reconstruction errors that occur at shallower depths. To reduce the sensitivity of the PE algorithm to noise a regularized progressive expansion (RPE) algorithm is proposed, which incorporates regularization techniques into the PE algorithm. The PE and the RPE algorithms are applied to the problem of image reconstruction from time-resolved data. The test media were isotropically scattering slabs containing one or two compact absorbers at different depths below the surface. The data were corrupted by additive white Gaussian noise with various strengths. The reconstruction results show that the PE and the RPE algorithms, when they are combined by proper overlapping, can effectively overcome the underdeterminedness of the inverse problem. The RPE algorithm yields reconstructions that are more accurate and more stable under the same noise level.

Frequency-domain optical imaging of absorption and scattering distributions by a Born iterative method.

We presents a Born; iterative method, for reconstructing optical properties of turbid media by means of frequency-domain data. The approach is based on iterative solution of a linear perturbation equation, which is derived from the integral from of the Helmholtz wave equation for photon-density waves in each iteration the total field and the associated weight matrix are recalculated based on the previous reconstructed image. We then obtain a new estimate by solving the updated perturbation equation. The forward solution, also based on a Helmholtz equation, is obtained by a multigrid finite difference method. The inversion is carried out through a Tikhonov regularized optimization process by the conjugate gradient descent method. Using this method, we first reconstruct the distribution of the complex wave numbers in a test medium, from which the absorption and the scattering distributions are then derived. Simulation results with two-dimensional test media have shown that this method can yield quantitatively (in terms of coefficient valued) as well as qualitatively (in terms of object location and shape) accurate reconstructions of absorption and scattering distributions in cases in which the first-order Born approximation cannot work well. Both full-angle and limited-angle measurement schemes have been simulated to examine the effect of the location of detectors and sources. The robustness of the algorithm to noise has also been evaluated.

Sensitivity studies for imaging a spherical object embedded in a spherically symmetric, two-layer turbid medium with photon-density waves.

We present analytic expressions for the amplitude and phase of photon-density waves in strongly scattering, spherically symmetric, two-layer media containing a spherical object. This layered structure is a crude model of multilayered tissues whose absorption and scattering coefficients lie within a range reported in the literature for most tissue types. The embedded object simulates a pathology, such as a tumor. The normal-mode-series method is employed to solve the inhomogeneous Helmholtz equation in spherical coordinates, with suitable boundary conditions. By comparing the total field at points in the outer layer at a fixed distance from the origin when the object is present and when it is absent, we evaluate the potential sensitivity of an optical imaging system to inhomogeneities in absorption and scattering. For four types of background media with different absorption and scattering properties, we determine the modulation frequency that achieves an optimal compromise between signal-detection reliability and sensitivity to the presence of an object, the minimum detectable object radius, and the smallest detectable change in the absorption and scattering coefficients for a fixed object size. Our results indicate that (l) enhanced sensitivity to the object is achieved when the outer layer is more absorbing or scattering than the inner layer; (2) sensitivity to the object increases with the modulation frequency, except when the outer layer is the more absorbing; (3) amplitude measurements are proportionally more sensitive to a change in absorption, phase measurements are proportionally more sensitive to a change in scattering, and phase measurements exhibit a much greater capacity for distinguishing an absorption perturbation from a scattering perturbation.

Recovery of optical cross-section perturbations in dense-scattering media by transport-theory-based imaging operators and steady-state simulated data.

We present a useful strategy for imaging perturbations of the macroscopic absorption cross section of dense-scattering media using steady-state light sources. A perturbation model based on transport theory is derived, and the inverse problem is simplified to a system of linear equations, WΔµ = ΔR, where W is the weight matrix, Δµ is a vector of the unknown perturbations, and ΔR is the vector of detector readings. Monte Carlo simulations compute the photon flux across the surfaces of phantoms containing simple or complex inhomogeneities. Calculation of the weight matrix is also based on the results of Monte Carlo simulations. Three reconstruction algorithms-conjugate gradient descent, projection onto convex sets, and the simultaneous algebraic reconstruction technique, with or without imposed positivity constraints-are used for image reconstruction. A rescaling technique that improves the conditioning of the weight matrix is also developed. Results show that the analysis of time-independent data by a perturbation model is capable of resolving the internal structure of a dense-scattering medium. Imposition of positivity constraints improves image quality at the cost of a reduced convergence rate. Use of the rescaling technique increases the initial rate of convergence, resulting in accurate images in a smaller number of iterations.

Ferrylmyoglobin formation induced by acute magnesium deficiency in perfused rat heart causes cardiac failure.

The oxidation states of intracellular myoglobin and cytochrome oxidase aa3 were monitored by reflectance spectrophotometry in isolated perfused rat hearts subjected to an acutely magnesium deficient environment. After exposure to low extracellular [Mg2+]o (i.e., 0.3 mM) for 30 min, more than 80% of the oxymyoglobin converted to its deoxygenated form. The level of reduced cytochrome oxidase aa3 also increased about 80% in low [Mg2+]o. The deoxymyoglobin was converted further to a species identified as ferrylmyoglobin by its reaction with Na2S to form ferrous sulfmyoglobin which was optically visible. This process, set into motion by acute Mg deficiency, resulted from a direct accessibility of the exogenous peroxide to the cytosolic protein. The results suggest that a pathway leading to cardiac tissue damage, induced by magnesium deficiency, is probably involved in the generation of a ferrylmyoglobin radical which could be prevented by addition of ascorbate, which is known to be a one-electron reductant of this hypervalent form of myoglobin. In further studies, we also investigated whether addition of different concentrations of ascorbic acid (AA) to the perfusate could enhance myocardial function after exposure to low [Mg2+]o perfusion. Four concentrations of AA (0.5, 1, 5, 10 mM) were tested, and the results indicate that they exert their effects in a concentration-dependent manner; 1 mM AA was the most effective dose in improving aortic output in a Mg-deficient heart. Ferrylmyoglobin formation was found to be formed considerably before intracellular release of either creatine phosphokinase or lactic dehydrogenase. These studies may have wide implications as a new mechanism by which low extracellular Mg2+ can induce myocardial injury and subsequent cardiac failure.

Characterization of a new ion selective electrode for ionized magnesium in whole blood, plasma, serum, and aqueous samples.

Results from a novel ion selective electrode (ISE) for ionized magnesium (Mg2+) correlate well with atomic absorption spectroscopy on aqueous solutions containing from 0.1-3.0 mmol MgCl2/L. Day to day precision (coefficient of variation) of the electrode on protein-based controls is < 4%; aqueous-based controls < 6%. The new ISE is selective for Mg2+ with a selectivity constant for Ca2+ (KMgCa) of 8 x 10(-2). Adding pathophysiologic concentrations of Cd2+, Ca2+, Cu2+, Fe3+, K+, Na+, or Zn2+ to serum and aqueous solutions gave negligible to minimal changes in measured Mg2+. Ligand binding studies in aqueous solution indicate that pathophysiologic concentrations of different anions (e.g. heparin, lactate, bicarbonate, phosphate, acetate and sulfate) bind to Mg2+, effectively reducing its concentration in solution. Likewise, silicon (as either found in Vacuutainer tubes or as chlorosilane) failed to exert any significant effect on measured Mg2+. Addition of Intralipid (up to 500 mg/dL) gave negligible to minimal changes in Mg2+. Mg2+ measurements on whole blood, plasma, and serum for a given human subject's samples are virtually identical, at least within the reference range for Mg2+. Typically, Mg2+ is 71% of TMg, but varies from subject to subject; i.e. Mg2+ cannot be predicted from TMg. Clinical studies revealed that the Mg2+/TMg ratio could be remarkably consistent in sequential samples (e.g., throughout the course of coronary bypass surgery) taken from one patient, but that this ratio could differ dramatically from the ratio in sequential samples taken from another. Mg2+ is held within a narrow range (0.53-0.67 mmol/L) in normal, healthy subjects when compared to TMg (0.70-0.96 mmol/L).

Optical spectroscopy and cerebral vascular effects of alcohol in the intact brain: effects on tissue deoxyhemoglobin, blood content, and reduced cytochrome oxidase.

Dose-response effects of acute ethanol infusions were studied, noninvasively, in the unopened brain to examine the hypothesis that ethanol can induce stroke-like events as a consequence of cerebral vasospasm and tissue ischemia. By using a single sending and receiving fiber, an optical backscatter measurement (500-800 nm) was used to monitor the levels of deoxyhemoglobin (DH), reduced cytochrome oxidase (rCO), and relative tissue blood content in a closed cranium preparation. Anesthetized rats were prepared by cannulating a branch of the internal carotid artery and subjected to either bolus infusions (1.25 or 2.5 microM ethanol in Ringers/g tissue) or to constant infusions of 5 or 10% ethanol at various rates (0.30-2.92 microM/g/min). To facilitate optical penetration, a portion of the left parietal cranium was shaved to a translucent appearance. Results showed that low, bolus doses of ethanol typically produced a slight increase (5-10%) in the oxyhemoglobin signal, indicating that vasodilation had probably occurred. Higher doses, however, produced a prompt and significant reduction in the hemoglobin signal, increased levels of DH, and a rise in rCO suggesting a vasoconstrictor response leading to ischemia had occurred, followed by recovery within 3-5 min. Constant infusions of ethanol produced a similar cerebral vascular response, in a dose-related manner, but of a more sustained nature. At levels of 50-60% of the maximum bolus dose, the effect was more pronounced, accompanied by an increase in the levels of rCO (by 50-90%). Control experiments using identical volumes/flow rates of Ringers solution produced no significant alterations in the optical spectrum.(ABSTRACT TRUNCATED AT 250 WORDS)

Low extracellular magnesium induces intracellular free Mg deficits, ischemia, depletion of high-energy phosphates and cardiac failure in intact working rat hearts: a 31P-NMR study.

Hemodynamic and 31P-NMR spectroscopic studies were performed on intact, perfused working rat hearts exposed to low (0.3 mM) extracellular Mg([Mg2+]o). Low [Mg2+]o perfusion resulted in rapid and significant falls in cardiac output, coronary flow, stroke volume, developed pressure and the rate-pressure product. Concomitant with this O2 consumption decreased and lactate production increased. Hearts perfused with 0.3 mM, instead of 1.2 mM, [Mg2+]o exhibited significant reductions in [ATP], [PCr], intracellular free Mg ([Mg2+]i), and pHi; a marked rise in intracellular Pi corresponding to a precipitous fall in the cytosolic phosphorylation potential was seen. Reintroduction of 1.2 mM [Mg2+]o failed to reestablish either normal hemodynamics, or high-energy phosphates and intracellular Pi, suggesting irreversible myocyte injury. These observations are consistent with the tenet that low [Mg2+]o can result in marked reduction in oxygen and substrate delivery to the cardiac myocytes, probably as a result of coronary vasoconstriction.