Simon R. Arridge

Optical tomography in medical imaging

We present a review of methods for the forward and inverse problems in optical tomography. We limit ourselves to the highly scattering case found in applications in medical imaging, and to the problem of absorption and scattering reconstruction. We discuss the derivation of the diffusion approximation and other simplifications of the full transport problem. We develop sensitivity relations in both the continuous and discrete case with special concentration on the use of the finite element method. A classification of algorithms is presented, and some suggestions for open problems to be addressed in future research are made.

Estimation of optical pathlength through tissue from direct time of flight measurement.

Quantitation of near infrared spectroscopic data in a scattering medium such as tissue requires knowledge of the optical pathlength in the medium. This can now be estimated directly from the time of flight of picosecond length light pulses. Monte Carlo modelling of light pulses in tissue has shown that the mean value of the time dispersed light pulse correlates with the pathlength used in quantitative spectroscopic calculations. This result has been verified in a phantom material. Time of flight measurements of pathlength across the rat head give a pathlength of 5.3 +/- 0.3 times the head diameter.

Recent advances in diffuse optical imaging

We review the current state-of-the-art of diffuse optical imaging, which is an emerging technique for functional imaging of biological tissue. It involves generating images using measurements of visible or near-infrared light scattered across large (greater than several centimetres) thicknesses of tissue. We discuss recent advances in experimental methods and instrumentation, and examine new theoretical techniques applied to modelling and image reconstruction. We review recent work on in vivo applications including imaging the breast and brain, and examine future challenges.

A finite element approach for modeling photon transport in tissue

The use of optical radiation in medical physics is important in several fields for both treatment and diagnosis. In all cases an analytic and computable model of the propagation of radiation in tissue is essential for a meaningful interpretation of the procedures. A finite element method (FEM) for deriving photon density inside an object, and photon flux at its boundary, assuming that the photon transport model is the diffusion approximation to the radiative transfer equation, is introduced herein. Results from the model for a particular case are given: the calculation of the boundary flux as a function of time resulting from a delta-function input to a two-dimensional circle (equivalent to a line source in an infinite cylinder) with homogeneous scattering and absorption properties. This models the temporal point spread function of interest in near infrared spectroscopy and imaging. The convergence of the FEM results are demonstrated, as the resolution of the mesh is increased, to the analytical expression for the Greens function for this system. The diffusion approximation is very commonly adopted as appropriate for cases which are scattering dominated, i.e., where mu s >> mu a, and results from other workers have compared it to alternative models. In this article a high degree of agreement with a Monte Carlo method is demonstrated. The principle advantage of the FE method is its speed. It is in all ways as flexible as Monte Carlo methods and in addition can produce photon density everywhere, as well as flux on the boundary. One disadvantage is that there is no means of deriving individual photon histories.

THE THEORETICAL BASIS FOR THE DETERMINATION OF OPTICAL PATHLENGTHS IN TISSUE - TEMPORAL AND FREQUENCY-ANALYSIS

A concise theoretical treatment is developed for the calculation of mean time, differential pathlength, phase shift, modulation depth and integrated intensity of measurements of light intensity as a function of time on the surface of tissue, resulting from either the input of picosecond light pulses, or radio frequency-modulated light. The treatment uses the Greens function of the diffusion approximation to the radiative transfer equation, and develops this and its Fourier transform in a variety of geometries. Detailed comparisons are made of several of these parameters in several geometries, and their relation to experimentally measured clinical data. The limitations of the use of phase measurements is discussed.

The finite element method for the propagation of light in scattering media: boundary and source conditions.

This paper extends our work on applying the Finite Element Method (FEM) to the propagation of light in tissue. We address herein the topics of boundary conditions and source specification for this method. We demonstrate that a variety of boundary conditions stipulated on the Radiative Transfer Equation can be implemented in a FEM approach, as well as the specification of a light source by a Neumann condition rather than an isotropic point source. We compare results for a number of different combinations of boundary and source conditions under FEM, as well as the corresponding cases in a Monte Carlo model.

Detection and modeling of non-Gaussian apparent diffusion coefficient profiles in human brain data.

This work details the observation of non‐Gaussian apparent diffusion coefficient (ADC) profiles in multi‐direction, diffusion‐weighted MR data acquired with easily achievable imaging parameters (b ≈ 1000 s/mm2). A technique is described for modeling the profile of the ADC over the sphere, which can capture non‐Gaussian effects that can occur at, for example, intersections of different tissue types or white matter fiber tracts. When these effects are significant, the common diffusion tensor model is inappropriate, since it is based on the assumption of a simple underlying diffusion process, which can be described by a Gaussian probability density function. A sequence of models of increasing complexity is obtained by truncating the spherical harmonic (SH) expansion of the ADC measurements at several orders. Further, a method is described for selection of the most appropriate of these models, in order to describe the data adequately but without overfitting. The combined procedure is used to classify the profile at each voxel as isotropic, anisotropic Gaussian, or non‐Gaussian, each with reference to the underlying probability density function of displacement of water molecules. We use it to show that non‐Gaussian profiles arise consistently in various regions of the human brain where complex tissue structure is known to exist, and can be observed in data typical of clinical scanners. The performance of the procedure developed is characterized using synthetic data in order to demonstrate that the observed effects are genuine. This characterization validates the use of our method as an indicator of pathology that affects tissue structure, which will tend to reduce the complexity of the selected model. Magn Reson Med 48:331–340, 2002.

A survey of hierarchical non-linear medical image registration

In this paper hierarchical non-linear image registration is classified into three main groups, where the registration at successive levels in the hierarchy increases in data complexity, warp complexity, or model complexity. Each method is briefly summarised and analysed in its application to medical images.

Optical imaging in medicine: II. Modelling and reconstruction

The desire for a diagnostic optical imaging modality has motivated the development of image reconstruction procedures involving solution of the inverse problem. This approach is based on the assumption that, given a set of measurements of transmitted light between pairs of points on the surface of an object, there exists a unique three-dimensional distribution of internal scatterers and absorbers which would yield that set. Thus imaging becomes a task of solving an inverse problem using an appropriate model of photon transport. In this paper we examine the models that have been developed for this task, and review current approaches to image reconstruction. Specifically, we consider models based on radiative transfer theory and its derivatives, which are either stochastic in nature (random walk, Monte Carlo, and Markov processes) or deterministic (partial differential equation models and their solutions). Image reconstruction algorithms are discussed which are based on either direct backprojection, perturbation methods, nonlinear optimization, or Jacobian calculation. Finally we discuss some of the fundamental problems that must be addressed before optical tomography can be considered to be an understood problem, and before its full potential can be realized.

Experimentally Measured Optical Pathlengths for the Adult Head, Calf and Forearm and the Head of the Newborn Infant as a Function of Inter Optode Spacing

The Differential Pathlength Factor (DPF) has been measured for several different tissues. The results showed that the DPF varied with the type of tissue studied, and in the case of the adult calf with sex. However, the DPF for all tissues studied was constant once the inter optode spacing exceeded 2.5 cm. Thus, measurements can be made by NIR spectroscopy at a range of inter optode spacings, and a single DPF used in the calculation of chromophore concentration. The results also showed that the major source of error in the DPF lay in the measurement of the inter optode spacing. To improve accuracy, two options are possible. Firstly, some means of continuous measurement of inter optode spacing could be incorporated in the NIR instrumentation. The better alternative would be an instrument incorporating a method of directly measuring the optical pathlength at each wavelength. This could be done either by time of flight measurement, or if it can be validated, by phase shift measurement.