Gassan S. Abdoulaev

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.

Near-infrared diffuse optical tomography

Diffuse optical tomography (DOT) is emerging as a viable new biomedical imaging modality. Using near-infrared (NIR) light, this technique probes absorption as well as scattering properties of biological tissues. First commercial instruments are now available that allow users to obtain cross-sectional and volumetric views of various body parts. Currently, the main applications are brain, breast, limb, joint, and fluorescence/bioluminescence imaging. Although the spatial resolution is limited when compared with other imaging modalities, such as magnetic resonance imaging (MRI) or X-ray computerized tomography (CT), DOT provides access to a variety of physiological parameters that otherwise are not accessible, including sub-second imaging of hemodynamics and other fast-changing processes. Furthermore, DOT can be realized in compact, portable instrumentation that allows for bedside monitoring at relatively low cost. In this paper, we present an overview of current state-of-the -art technology, including hardware and image-reconstruction algorithms, and focus on applications in brain and joint imaging. In addition, we present recent results of work on optical tomographic imaging in small animals.

Algorithm for solving the equation of radiative transfer in the frequency domain

We present an algorithm that provides a frequency-domain solution of the equation of radiative transfer (ERT) for heterogeneous media of arbitrary shape. Although an ERT is more accurate than a diffusion equation, no ERT code for the widely employed frequency-domain case has been developed to date. In this work the ERT is discretized by a combination of discrete-ordinate and finite-volume methods. Two numerical simulations are presented.

Three-dimensional optical tomography with the equation of radiative transfer

We report on the derivation and implementation of the first three-dimensional optical tomographic image reconstruction scheme that is based on the time-independent equation of radiative transfer (ERT) and allows for arbitrarily shaped medium boundaries and arbitrary spatial material distributions. The scheme builds on the concept of model-based iterative image reconstruction, in which a forward model provides prediction of detector readings, and a gradient-based updating scheme minimizes an appropriately de- fined objective function. The forward model is solved by using an even-parity formulation of the ERT, which lends itself to a finite- element discretization method. The finite-element technique pro- vides the suitable framework for predicting light propagation in arbi- trarily shaped three-dimensional media. For an efficient way of calculating the gradient of the objective function we have imple- mented an adjoint differentiation scheme. Initial reconstruction re- sults using synthetic data from simple media and a three- dimensional mesh of the human forehead illustrate the performance of the code.

Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia

In this study, we explore the potential of diffuse optical tomography for brain oximetry. While several groups have already reported on the sensitivity of optical measurements to changes in oxyhemoglobin, deoxyhemoglobin, and blood volume, these studies were often limited to single source-detector geometries or topographic maps, where signals obtained from within the brain are projected onto 2-D surface maps. In this two-part study, we report on our efforts toward developing a volumetric optical imaging system that allows one to spatially resolve 3-D hemodynamic effects in rat brains. In part 1, we describe the instrumentation, optical probe design, and the model-based iterative image reconstruction algorithm employed in this work. Consideration of how a priori anatomical knowledge can be incorporated in the reconstruction process is presented. This system is then used to monitor global hemodynamic changes that occur in the brain under various degrees of hypercapnia. The physiologic cerebral response to hypercapnia is well known and therefore allows an initial performance assessment of the imaging system. As expected, we observe global changes in blood volume and oxygenation, which vary linearly as a function of the concentration of the inspired carbon dioxide. Furthermore, experiments are designed to determine the sensitivity of the reconstructions of only 1 mm to inaccurate probe positioning. We determine that shifts can significantly influence the reconstructions. In part 2 we focus on more local hemodynamic changes that occur during unilateral carotid occlusion performed at lower-than-normal systemic blood pressure. In this case, the occlusion leads to a predominantly monohemispherically localized effect, which is well described in the literature. Having explored the system with a well-characterized physiologic effect, we investigate and discuss the complex compensatory cerebrovascular hemodynamics that occur at normotensive blood pressure. Overall, these studies demonstrate the potential and limitations of our diffuse optical imager for visualizing global and focal hemodynamic phenomenon three dimensionally in the brains of small animals.

Three-dimensional optical tomographic brain imaging in small animals, part 2: Unilateral carotid occlusion

This is the second part of a two-part study that explores the feasibility of 3-D, volumetric brain imaging in small animals by optical tomographic techniques. In part 1, we demonstrated the ability to visualize global hemodynamic changes in the rat head in response to elevated levels of CO(2) using a continuous-wave instrument and model-based iterative image reconstruction (MOBIIR) algorithm. Now we focus on lateralized, monohemispherically localized hemodynamic effects generated by unilateral common carotid artery (CCA) occlusion. This illustrates the capability of our optical tomographic system to localize and distinguish hemodynamic responses in different parts of the brain. Unilateral carotid occlusions are performed in ten rodents under two experimental conditions. In the first set of experiments the normal systemic blood pressure is lowered to 50 mmHg, and on unilateral carotid occlusion, we observe an ipsilateral monohemispheric global decrease in blood volume and oxygenation. This finding is consistent with the known physiologic response to cerebral ischemia. In a second set of experiments designed to observe the spatial-temporal dynamics of CCA occlusion at normotensive blood pressure, more complex phenomena are observed. We find three different types of responses, which can be categorized as compensation, overcompensation, and noncompensation.

Combined optical tomographic and magnetic resonance imaging of tumor bearing mice

With the advent of small animal imaging systems, it has become possible to non-invasively monitor the progression of diseases in living small animals and study the efficacy of drugs and treatment protocols. Magnetic resonance imaging (MRI) is an established imaging modality capable of obtaining high resolution anatomical images as well as studying cerebral blood volume (CBV), cerebral blood flow (CBF), and cerebral metabolic rate of oxygen (CMRO2). Optical tomography, on the other hand, is an emerging imaging modality, which, while much lower in spatial resolution and insensitive to CBF, can separate the effects of oxyhemoglobin, deoxyhemoglobin, and CBV with high temporal resolution. In this study we present our first results concerning coregistration of MRI and optical data. By applying both modalities to imaging of kidney tumors in mice that undergo VEGF treatment, we illustrate how these imaging modalities can supplement each other and cross validation can be performed.

Three-Dimensional Optical-Tomographic Localization of Changes in Absorption Coefficients in the Human Brain

We report on the first three dimensional tomographic localization of vascular reactivity in the brain. Using a model-based iterative image reconstruction algorithm we show volumetric spatial changes in the absorption coefficient caused by changes in blood volume. Unlike currently available topographic reconstruction techniques, volumetric reconstruction schemes promise to be capable of spatially distinguishing between signals originating in the cerebral cortex from those originating in the overlying vascular tissues.

Three-dimensional optical tomography based on even-parity finite-element formulation of the equation of radiative transfer

In this work we present the first fully three-dimensional image reconstruction scheme for optical tomography that is based on the equation of radiative transfer. This scheme builds on the previously introduced concept of model-based iterative image reconstruction, in which a forward model provides prediction of detector readings, and a gradient-based updating scheme minimizes an objective function, which is defined as the difference between predicted and measured data. The forward model is solved by using an even-parity approach to reduce the time-independent radiative transfer equation to an elliptic self-adjoint equation of second order. This equation is discretized using a finite element method, in which we apply a preconditioned conjugate gradient method with a multigrid-based preconditioner to solve the arising linear algebraic system. The gradient of the objective function is found by employing an adjoint differentiation method to the forward solver. Initial tests on synthetic data have shown robustness and good convergence of the algorithm.

Optical Tomographic and Magnetic Resonance Imaging of Tumor Growth and Regression in Mice treated with VEGF Blockade

Small animal imaging systems now allow researchers to non-invasively monitor the progression of diseases in living small animals and study the efficacy of drugs and treatment protocols. Magnetic resonance imaging (MRI) is an established imaging modality capable of obtaining high resolution anatomical images which are sensitive to blood volume, blood flow, and metabolic rate of oxygen. Optical tomography, on the other hand, is an emerging imaging modality, which, while much lower in spatial resolution and insensitive to blood flow, can separate the effects of oxyhemoglobin, deoxyhemoglobin, and blood volume with high temporal resolution. We illustrate how these imaging modalities can supplement each other and cross validation can be performed by applying both modalities to imaging of tumors growth and regression in mice that are treated with a vascular endothelial growth factor (VEGF) antagonist