David T. Delpy

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.

System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infra-red transillumination

The technique of near-infra-red spectroscopy allows safe continuous monitoring of changes in blood and tissue oxygenation on an intact organ. This is made possible by observing spectral changes in the tissues caused by oxygenated haemoglobin [HbO2], deoxygenated haemoglobin [Hb] and cytochrome aa3 [Cyt aa3]. The paper describes the design and performance of an instrument that has been developed to apply this technique to the monitoring of the brain in newborn infants. The instrument monitors optical transmission changes across a newborn infants brain at four wavelengths. A standard deviation in error of 1 per cent (0·01 optical density OD) is achieved on measurements of transmission changes at 20s intervals. This performance is obtained at a mean attenuation of 10 OD, the approximate attenuation across a term infants head. Long-term monitoring is possible as instrumental drift is less than 0·004 OD per hour.

OPTICAL PATHLENGTH MEASUREMENTS ON ADULT HEAD, CALF AND FOREARM AND THE HEAD OF THE NEWBORN-INFANT USING PHASE-RESOLVED OPTICAL SPECTROSCOPY

We have used an intensity modulated optical spectrometer, which measures the phase shift across tissue experienced by intensity modulated near-infrared light, to determine the absolute optical pathlength through tissue. The instrument is portable and takes only 5 s to record pathlength at four wavelengths (690 nm, 744 nm, 807 nm and 832 nm). The absolute pathlength divided by the known spacing between the light source and detector on the skin is the differential pathlength factor (DPF) which previous studies have shown is approximately constant for spacings greater than 2.5 cm. DPF results are presented for measurements on 100 adults and 35 newborn infants to determine the statistical variation on the DPF. All measurements were made at a frequency of 200 MHz with source-detector spacings of > 4 cm. Results at 807 nm show a DPF of 4.16(+/- 18.8%) for adult arm, 5.51(+/- 18%) for adult leg, 6.26(+/- 14.1%) for adult head and 4.99(+/- 9%) for the head of a newborn infant. A wavelength dependence was obtained for DPF on all tissues and a difference in DPF between male and female was observed for both the adult arm and leg. The results can be used to improve the quantitation of chromophore concentration changes in adults and newborn infants.

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.

Delayed ("secondary") cerebral energy failure after acute hypoxia-ischemia in the newborn piglet: continuous 48-hour studies by phosphorus magnetic resonance spectroscopy

ABSTRACT: Phosphorus (31P) spectra from the brains of severely birth-asphyxiated human infants are commonly normal on the first day of life. Later, cerebral energy failure develops, which carries a serious prognosis. The main purpose of this study was to test the hypothesis that this delayed (“secondary”) energy failure could be reproduced in the newborn piglet after a severe acute reversed cerebral hypoxicischemic insult. Twelve piglets were subjected to temporary occlusion of the common carotid arteries and hypoxemia [mean arterial Po2 3.1 (SD 0.6) kPa]. Mean cerebral phosphocreatine concentration [PCr]/inorganic orthophosphate concentration [Pi] decreased from 1.40 (SD 0.29) to 0.01 (SD 0.02), and nucleotide triphosphate concentration [NTP]/exchangeable phosphate pool concentration [EPP] decreased from 0.19 (SD 0.02) to 0.06 (SD 0.04) (p<0.001 for each decrease). On reperfusion and reoxygenation of the brain, mean [PCr]/[Pi] and [NTP]/[EPP] returned to baseline. Observations continuing for the next 48 h showed that [PCr]/[Pi] again decreased, in spite of normal arterial Po2, mean arterial blood pressure, and blood glucose, to 0.62 (SD 0.61) at 24 h (p<0.01) and 0.49 (SD 0.37) at 48 h (p<0.001). [NTP]/[EPP] also decreased, but to a lesser degree. Intracellular pH remained unchanged. These findings appeared identical with those seen in birth-asphyxiated human infants. No changes in cerebral metabolite concentrations took place in six control piglets. The severity of secondary energy failure, as judged by the lowest [PCr]/[Pi] recorded at 24-48 h, was directly related to the extent of acute energy depletion, obtained as the time integral of reduction in [NTP]/[EPP] (p<0.0001). This animal model of secondary energy failure may prove useful for testing cerebroprotective strategies.

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.

Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head

Near-infrared light propagation in various models of the adult head is analyzed by both time-of-flight measurements and mathematical prediction. The models consist of three- or four-layered slabs, the latter incorporating a clear cerebrospinal fluid (CSF) layer. The most sophisticated model also incorporates slots that imitate sulci on the brain surface. For each model, the experimentally measured mean optical path length as a function of source-detector spacing agrees well with predictions from either a Monte Carlo model or a finite-element method based on diffusion theory or a hybrid radiosity-diffusion theory. Light propagation in the adult head is shown to be highly affected by the presence of the clear CSF layer, and both the optical path length and the spatial sensitivity profile of the models with a CSF layer are quite different from those without the CSF layer. However, the geometry of the sulci and the boundary between the gray and the white matter have little effect on the detected light distribution.

Optical imaging in medicine: I. Experimental techniques

The overwhelming scatter which occurs when optical radiation propagates through tissue severely limits the ability to image internal structure using measurements of transmitted intensity. A broad range of methods has been proposed during the past decade or so in order to improve imaging performance. Direct methods involve isolating an unscattered or least-scattered component of transmitted scattered light. Indirect methods generally involve measuring some characteristic of the temporal distribution of transmitted light, or an equivalent in the frequency domain, and obtaining a computational solution to the inverse problem. In this paper, we review the experimental techniques which have been proposed in order to explore both direct and indirect imaging. The relative merits and limitations of the various experimental methods are discussed, and we consider the future directions and likelihood of success of optical imaging in medicine.