Andreas H. Hielscher

Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics

We have studied the optical properties of mammalian cell suspensions to provide a mechanistic basis for interpreting the optical properties of tissues in vivo. Measurements of the wavelength dependence of the reduced scattering coefficient and measurements of the phase function demonstrated that there is a distribution of scatterer sizes. The volumes of the scatterers are equivalent to those of spheres with diameters in the range between ~0.4 and 2.0 mum. Measurements of isolated organelles indicate that mitochondria and other similarly sized organelles are responsible for scattering at large angles, whereas nuclei are responsible for small-angle scattering. Therefore optical diagnostics are expected to be sensitive to organelle morphology but not directly to the size and shape of the cells.

Three-dimensional optical tomography of hemodynamics in the human head

We report on the first three-dimensional, volumetric, tomographic localization of vascular reactivity in the brain. To this end we developed a model-based iterative image reconstruction scheme that employs adjoint differentiation methods to minimize the difference between measured and predicted data. The necessary human-head geometry and optode locations were determined with a photogrammetric method. To illustrate the performance of the technique, the three-dimensional distribution of changes in the concentration of oxyhemoglobin, deoxyhemoglobin, and total hemoglobin during a Valsalva maneuver were visualized. The observed results are consistent with previously reported effects concerning optical responses to hemodynamic perturbations.

Gradient-based iterative image reconstruction scheme for time-resolved optical tomography

Currently available tomographic image reconstruction schemes for optical tomography (OT) are mostly based on the limiting assumptions of small perturbations and a priori knowledge of the optical properties of a reference medium. Furthermore, these algorithms usually require the inversion of large, full, ill-conditioned Jacobian matrixes. In this work a gradient-based iterative image reconstruction (GIIR) method is presented that promises to overcome current limitations. The code consists of three major parts: (1) A finite-difference, time-resolved, diffusion forward model is used to predict detector readings based on the spatial distribution of optical properties; (2) An objective function that describes the difference between predicted and measured data; (3) An updating method that uses the gradient of the objective function in a line minimization scheme to provide subsequent guesses of the spatial distribution of the optical properties for the forward model. The reconstruction of these properties is completed, once a minimum of this objective function is found. After a presentation of the mathematical background, two- and three-dimensional reconstruction of simple heterogeneous media as well as the clinically relevant example of ventricular bleeding in the brain are discussed. Numerical studies suggest that intraventricular hemorrhages can be detected using the GIIR technique, even in the presence of a heterogeneous background.

Instrumentation for fast functional optical tomography

In this article, we describe the design rationale and performance features of an integrated multichannel continuous wave (cw) near-infrared (NIR) optical tomographic imager capable of collecting fast tomographic measurements over a large dynamic range. Fast data collection (∼70 Hz/channel/wavelength) is achieved using time multiplexed source illumination (up to 25 illumination sites) combined with frequency encoded wavelength discrimination (up to four-wavelength capability) and parallel detection (32 detectors). The described system features a computerized user interface that allows for automated system operation and is compatible with various previously described measuring heads. The results presented show that the system exhibits a linear response over the full dynamic measuring range (180 dB), and has excellent noise (∼10 pW noise equivalent power) and stability performance (<1% over 30 min). Recovered images of laboratory vessels show that dynamic behavior can be accurately defined and spatially loca...

Influence of particle size and concentration on the diffuse backscattering of polarized light from tissue phantoms and biological cell suspensions

We present experimental results that show the spatial variations of the diffuse-backscattered intensity when linearly polarized light is incident upon highly scattering media. Experiments on polystyrene-sphere and Intralipid suspensions demonstrate that the radial and azimuthal variations of the observed pattern depend on the concentration, size, and anisotropy factor g of the particles that constitute the scattering medium. Measurements performed on biological-cell suspensions show the potential of this method for cell characterization.

Influence of blood vessels on the measurement of hemoglobin oxygenation as determined by time-resolved reflectance spectroscopy

We report the development of a heterogeneous resin-tube model to study the influence of blood vessels on the apparent absorption of the system, mu a(sys), using a time-resolved technique. The experimental results show that mu a(sys) depends on the absorption inside the tubes, mu a(tube), tube diameters, and tube-to-sample volume ratios. A mathematical expression relating mu a(sys) and mu a(tube) is derived based on the experimental results and is verified by time-resolved Monte Carlo simulations for heterogeneous models. This analytical formula predicts that the apparent absorption coefficient measured on a biological organ is a volume-weighted sum of the absorption coefficients of different absorbing components. We present some apparent absorption coefficients measured in vivo in animals and humans and discuss improved algorithms that calculate the hemoglobin saturation by including background-tissue absorption and blood vessel distribution.

Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer.

We report on the development of an iterative image reconstruction scheme for optical tomography that is based on the equation of radiative transfer. Unlike the commonly applied diffusion approximation, the equation of radiative transfer accurately describes the photon propagation in turbid media without any limiting assumptions regarding the optical properties. The reconstruction scheme consists of three major parts: (1) a forward model that predicts the detector readings based on solutions of the time-independent radiative transfer equation, (2) an objective function that provides a measure of the differences between the detected and the predicted data, and (3) an updating scheme that uses the gradient of the objective function to perform a line minimization to get new guesses of the optical properties. The gradient is obtained by employing an adjoint differentiation scheme, which makes use of the structure of the finite-difference discrete-ordinate formulation of the transport forward model. Based on the new guess of the optical properties a new forward calculation is performed to get new detector predictions. The reconstruction process is completed when the minimum of the objective function is found within a defined error. To illustrate the performance of the code we present initial reconstruction results based on simulated data.

Diffuse backscattering Mueller matrices of highly scattering media

We report on the development of a method that records spatially dependent intensity patterns of polarized light that is diffusely backscattered from highly scattering media. It is demonstrated that these intensity patterns can be used to differentiate turbid media, such as polystyrene-sphere and biological-cell suspensions. Our technique employs polarized light from a He-Ne laser (l=543nm), which is focused onto the surface of the scattering medium. A surface area of approximately 4x4 cm centered on the light input point is imaged through polarization-analysis optics onto a CCD camera. One can observe a large variety of intensity patterns by varying the polarization state of the incident laser light and changing the analyzer configuration to detect different polarization components of the backscattered light. Introducing the Mueller-matrix concept for diffusely backscattered light, a framework is provided to select a subset of measurements that comprehensively describe the optical properties of backscattering media.

Monte Carlo simulations of the diffuse backscattering Mueller matrix for highly scattering media

We have developed a Monte Carlo algorithm that computes all two-dimensional elements of the diffuse backscattering Mueller matrix for highly scattering media. Using the Stokes-Mueller formalism and scattering amplitudes calculated with Mie theory, we are able to consider polarization-dependent photon propagation in highly scattering media, including linearly and circularly polarized light. The numerically determined matrix elements are compared with experimental data for different particle sizes and show good agreement in both azimuthal and radial direction.

Sagittal laser optical tomography for imaging of rheumatoid finger joints.

We present a novel optical tomographic imaging system that was designed to determine two-dimensional spatial distribution of optical properties in a sagittal plane through finger joints. The system incorporates a single laser diode and a single silicon photodetector into a scanning device that records spatially resolved light intensities as they are transmitted through a finger. These data are input to a model-based iterative image reconstruction (MOBIIR) scheme, which uses the equation of radiative transfer (ERT) as a forward model for light propagation through tissue. We have used this system to obtain tomographic images of six proximal interphalangeal finger joints from two patients with rheumatoid arthritis. The optical images were compared to clinical symptoms and ultrasound images.