P. van der Zee

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.

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.

Methods of Quantitating Cerebral Near Infrared Spectroscopy Data

Non invasive infrared spectroscopy is a well established technique for monitoring changes in the oxygenation status of tissues (1). The technique has in particular been successfully employed to monitor changes in cerebral blood and tissue oxygenation by observing the absorption of haemoglobin and cytochrome aa3 respectively. Because of the highly light scattering nature of the tissues studied, it has normally not been possible to quantitate the observed changes.

A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy

In order to quantify near-infrared spectroscopic (NIRS) data on an inhomogeneous medium, knowledge of the contribution of the various parts of the medium to the total NIRS signal is required. This is particularly true in the monitoring of cerebral oxygenation by NIRS, where the contribution of the overlying tissues must be known. The concept of the time point spread function (TPSF), which is used extensively in NIRS to determine the effective optical pathlength, is expanded to the more general inhomogeneous case. This is achieved through the introduction of the partial differential pathlength, which is the effective optical pathlength in the inhomogeneous medium, and an analytical proof of the applicability of the modified Beer-Lambert law in an inhomogeneous medium is shown. To demonstrate the use of partial differential pathlength, a Monte Carlo simulation of a two-concentric-sphere medium representing a simplified structure of the head is presented, and the possible contribution of the overlying medium to the total NIRS signal is discussed.

Spectral dependence of temporal point spread functions in human tissues

We have determined the spectral dependence of the temporal point spread functions of human tissues experimentally between 740 and 840 nm in transmittance measurements on the adult head, forearm, and calf (in vivo) and the infant head (post mortem) by using picosecond laser pulses and a streak camera detector. Two parameters are extracted from the temporal point spread function; the differential path-length factor (DPF), calculated from the mean time, and the slope of the logarithmic intensity decay. In all tissues the DPF and the logarithmic slope show a reciprocal relationship and exhibit characteristics of the absorption spectra of hemoglobin. The DPF falls with increasing wavelength, the variation being typically 12%, while the logarithmic slope increases with wavelength. A quantitative analysis of the logarithmic slope spectrum significantly underestimated expected tissue chromophore concentrations. The absolute magnitudes of the DPF showed considerable intersubject variation, but the variation with wavelength was consistent and thus may be used in the correction of tissue attenuation spectra.

Wavelength Dependence of the Differential Pathlength Factor and the Log Slope in Time-Resolved Tissue Spectroscopy

The monitoring of tissue oxygenation by the technique of near infrared spectroscopy (NIRS) was first described by Jobsis in 1977 (Jobsis, 1977). The technique relies upon the relative transparency of tissue to near infrared (NIR) light to enable measurements of changes in optical attenuation across many centimetres of tissue. Early NIRS measurements could only derive qualitative changes in tissue and blood oxygenation from the observed variations in tissue attenuation (Brazy et al., 1985). However, data on the optical pathlength of light in tissue, measured by time resolved techniques employing picosecond laser pulses, have now permitted a quantitative analysis of attenuation measurements to be made (Delpy et al., 1988; Wyatt et al., 1990a). By incorporating information on the optical pathlength into a modified Beer-Lambert law it is possible to quantify changes in chromophore concentration from the measured changes in tissue attenuation. The optical pathlength needed in this calculation, the Differential Pathlength (DP) is defined as the local gradient in a plot of the attenuation measured in a scattering medium versus the absorption coefficient of the medium (Cope et al., 1991a; Cope, 1991b). It has been shown in previous studies (Delpy et al., 1988) that the DP can be approximated by measuring the mean distance that a picosecond light pulse travels across the tissue. Furthermore, a dimensionless multiplying factor, the Differential Pathlength Factor (DPF), can be obtained when the DP is divided by the geometric distance between light source and detector on the tissue surface. This factor has been shown, both theoretically and experimentally, to be approximately constant for any tissue once the optode spacing is larger than about 25 mm (van der Zee et al., 1990; van der Zee et al, in press), enabling clinical NIRS measurements to be made with varying optode geometries.

The Effect of Optode Positioning on Optical Pathlength in Near Infrared Spectroscopy of Brain

The use of optical spectroscopy for the non-invasive monitoring of tissue oxygenation and metabolism is well established (Chance et al., 1975). Historically because of the high absorption by tissue of light in the visible range, optical monitoring was often restricted to measurements of reflected light (Jobsis et al., 1977). Subsequently Jobsis showed that by using near infrared light (NIR), tissue absorption became sufficiently low to make transillumination of the cat head possible (Jobsis, 1977). In the near infrared region (700–1300 nm) there is sufficient spectral information available to permit changes in the concentration of haemoglobin and cytochrome aa3 to be calculated, and hence changes in the oxygenation state of the brain (Brazy et al., 1985, 1986; Ferrari et al., 1986; Fox et al., 1985). This technique is now used routinely to monitor cerebral oxygenation and haemodynamics in the human newborn infant (Wyatt et al., 1986; Edwards et al., 1988), using an instrument designed to transilluminate the heads of most newborn infants (Cope and Delpy, 1988). This instrument allows for measurements through heads up to 8–9 cm in diameter.

Quantitation of Pathlength in Optical Spectroscopy

The relative transparency of tissues to near infrared light means that it is possible to transilluminate intact organs. In the infrared region, oxygen dependent absorptions due to haemoglobin and cytochrome aa3 can be observed, and it is therefore possible to monitor changes in both the blood and tissue oxygenation of the organ.1 This monitoring technique is particularly applicable to the study of the brain since there is no interfering absorption from myoglobin, and recent technical developments of the instrumentation have made it possible to transilluminate 8–9 cm of brain tissue.2 However, once measurements of absorption change at several wavelengths are available, there are still considerable problems in converting this data into quantitative changes in the concentration of oxy and deoxy haemoglobin and of oxidised cytochrome aa3.

Computed point spread functions for light in tissue using a measured volume scattering function.

Optical techniques are increasingly being used in the field of medicine in areas as diverse as surgery (for cutting and coagulation), cancer treatment (through photoradiation therapy) and blood flow monitoring (by laser doppler measurements). At University College, we are using the technique of near infrared spectroscopy (nirs) to monitor changes in cerebral blood and tissue oxygenation in newborn infants (1), and are investigating methods of optical imaging across the head (2). In all these applications, a detailed knowledge of light transport in tissue is required. For spectroscopy studies, in order to quantitate data, one needs to know the effective photon pathlength through the tissue, and a knowledge of the path also allows one to calculate the volume of tissue from which results are being obtained. In the case of imaging through tissue, data is required on the point spread function (PSF) for the tissue, both for the prediction of the image quality that could be obtained using various imaging schemes, and for use in image enhancement and reconstruction computations.

Particle sizing in the Mie scattering region: singular-value analysis

A method for finding the singular system of the Mie scattering kernel for continuous data over all angles is given, based on a result for the spherical harmonic expansion of the kernel. This technique provides a limit to the system obtained using discrete data. Results are given for continuous data and finite support. A comparison is made with the Fraunhofer kernel as the large-particle limit of the Mie case. The use of weighted spaces for the inversion is discussed.