Introduction

All of us are exposed to optical (i.e. visible and near-infrared) radiation from the sun and other sources throughout our lives. Assuming our eyes are shielded from excessive intensity, and our skin is protected from the ultraviolet content of sunlight, we accept this exposure in the knowledge that it is perfectly safe. Unlike x-rays, optical photons are insufficiently energetic to produce ionisation, and unless light is concentrated to such a high degree that it causes burning to the skin, optical radiation offers no significant hazard. The diagnostic potential of optical methods has been widely known since Jöbsis [1] first demonstrated that transmittance measurements of near-infrared (NIR) radiation could be used to monitor the degree of oxygenation of certain metabolites. This led to the development and increasingly widespread use of clinical near-infrared spectroscopy (NIRS), which offers a safe, non-invasive means of monitoring cerebral function at the bedside without the use of radioisotopes or other contrast agents [2].

Human tissues contain a variety of substances whose absorption spectra at NIR wavelengths are well defined, and which are present in sufficient quantities to contribute significant attenuation to measurements of transmitted light. The concentration of some absorbers, such as water, melanin, and bilirubin, remain virtually constant with time. However, some absorbing compounds, such as oxygenated haemoglobin (HbO₂), deoxyhaemoglobin (Hb), and oxidised cytochrome oxidase (CtOx), have concentrations in tissue which are strongly linked to tissue oxygenation and metabolism. Increasingly dominant absorption by water at longer wavelengths limits spectroscopic studies to less than about 1000 nm. The lower limit on wavelength is dictated by the overwhelming absorption of Hb below about 650 nm. However, within the 650-1000 nm window, it is possible with sensitive instrumentation to detect light which has traversed up to 8 cm of tissue.

Absorption

The absorption of light intensity in a non-scattering medium is described by the Beer-Lambert Law. This law states that for an absorbing compound dissolved in a non-absorbing medium, the attenuation (A) is proportional to the concentration of the compound in the solution (c) and the optical pathlength (d):

     A  = log₁₀ [I_o/I]  = a.c.d   ,

where A is the attenuation measured in optical densities, I_o is the light intensity incident on the medium, I is the light intensity transmitted through the medium, a is the specific extinction coefficient of the absorbing compound measured in micromolar per cm, c is the concentration of the absorbing compound in the solution measured in micromolar, and d is the distance between the points where the light enters and leaves the medium. The product ac is known as the absorption coefficient of the medium µ_a. In a medium containing several different absorbing compounds (except at very high concentrations not usually met in biological media) the overall extinction coefficient is simply the linear sum of the contributions of each compound:

     A  = log₁₀ [I_o/I]  = [ a₁.c₁ + a₂.c₂+ a₃.c₃ + ... + a_n.c_n ] d   .

A compound which absorbs light in the spectral region of interest is known as a chromophore. Each chromophore has its own particular absorption spectrum which describes the level of absorption at each wavelength. The principle chromophores in tissue are as follows:

i) Water

As shown above in figure 1, the absorption of light by water is relatively low between 200 - 900 nm. Beyond 900 nm absorption starts to rise with increasing wavelength, a spectral peak being visible at 970 nm. The high concentration of water in living tissue, typically 80% in adult brain tissue [3], (equivalent to 56 molar) determines the wavelength region in which spectroscopic interrogation of tissue is possible by strongly limiting the tissue thickness through which light can penetrate. For this reason, the water spectrum is said to demonstrate a "window" of transparency between 200 and 900 nm within which spectroscopic measurements can be made. For the purposes of most clinical measurements the water concentration in tissue can be thought of as constant, and as such water acts as a fixed constant absorber.

ii) Lipids

Although the distribution of lipid in tissue is dependent upon tissue type, it can also be thought of as a constant absorber with changes in its concentration throughout the course of a clinical measurement being unlikely. The absorption spectrum of lipid is approximately the same as that of water and it can comprise 10 - 40 % (i.e. several molar) of tissue.

iii) Melanin

Melanin, found in the epidermis layer of skin, is a highly effective absorber of light, especially in the ultraviolet region of the spectrum. Although this absorption can be considered to be constant and oxygen independent, the concentration of melanin in tissue will directly effect the reflectance of light from the skin and therefore the transmission of light into the tissue below.

iv) Haemoglobin

Figure 2 above shows the specific extinction coefficients of oxygenated haemoglobin (HbO₂) and deoxyhaemoglobin (Hb) in the wavelength range 450 - 1000 nm [4]. The difference in the absorption spectra explains the well recognised phenomena of arterial blood (containing approximately 98% HbO₂) having a bright red appearance while venous or deoxygenated blood appears more blue. In the NIR region of the spectrum the absorption of both chromophores decreases significantly compared to that observed in the visible region. However the absorption spectra of Hb and HbO₂ remain significantly different in this region allowing spectroscopic separation of the compounds to be possible using only a few sample wavelengths. An isobestic point where the specific extinction coefficients of the two compounds are equal can be seen at around 800 nm, which can be used to calculate haemoglobin concentration independent of oxygen saturation. The typical value for haemoglobin concentration in, for example, adult brain tissue is 84 micromolar.

There are other haemoglobin compounds which have a characteristic absorption in the near infrared, although their concentrations in tissue are low and in many cases almost non existent in normal blood. These compounds include carboxyhaemoglobin, (HbCO), which may be present in significant quantities in the tissue in some subjects, but has a low specific extinction coefficient in the NIR rendering its effect on most in-vivo measurements negligible. Haemiglobin (Hi) is present in very low concentrations and sulfhaemoglobin (SHb) is not present at all in normal blood. The combined error in ignoring these compounds in the measurement of the total haemoglobin signal is probably less than 1% in normal blood and in the majority of clinical conditions encountered. However it is worth remembering that some of these forms of haemoglobin, especially Hi, may become significantly raised in some diseases of the liver or in malaria.

v) Cytochrome c oxidase

Cytochrome oxidase (CtOx) is the terminal enzyme in the cellular respiratory chain, and is located in the mitochondrial membrane. The enzyme contains four redox active groups, two haem iron (a and a₃) and two copper (Cu_A and Cu_B) centres. These four metal centres change their redox state (i.e. accept or donate electrons) during electron turnover of the enzyme. The oxygen binding site of the enzyme is the binuclear unit which is formed of the Cu_B and haem a₃. It is the donation of electrons from this unit to oxygen which accounts for the great majority of oxygen consumption in biological tissue. The Cu_A and haem a centres donate electrons to this binuclear unit and are therefore not directly involved in reduction of oxygen. However absorption of NIR radiation by cytochrome oxidase occurs primarily at the Cu_A centre, the oxidised spectrum having a characteristic shape, with a broad peak centred around 830 nm which is missing in the reduced enzyme. In the short term the total tissue CtOx concentration does not vary and NIRS measurements of changes in CtOx thus measure alterations in the redox state concentration of Cu_A within cytochrome oxidase.

     Figure 3: The difference absorption spectrum between the oxidised and reduced forms of CtOx.

Since the total CtOx concentration does not alter, NIRS measurements need only be made of the change in redox state, so it is only necessary to know the difference spectrum between the oxidised and reduced forms of the enzyme. This difference spectrum is shown in figure 3. It can be seen that the magnitude of the specific extinction coefficients are similar to those of haemoglobin, but since the concentration of cytochrome oxidase in living tissue is usually at least an order of magnitude below that of haemoglobin [5], the measurement of cytochrome oxidase with optical techniques is by no means as easy as that of haemoglobin. When oxygen limits the rate of oxygen consumption by cytochrome oxidase, the Cu_A centre becomes more reduced. Therefore the absorbance of NIR light by cytochrome oxidase may be used as an indicator of oxygen availability at a cellular level and ultimately of cell metabolism.

Scattering

Scatter of light in tissue is due to the chaotic variation in refractive index at a microscopic and macroscopic scale. This occurs at membrane boundaries of the cells themselves as well as at boundaries between various organelles inside the cell. Index mismatching will occur between intra and extracelluar fluid, or intracellular fluid and fluid inside the nucleus of the cell or other enclosed particles such as mitochondria, ribosomes, fat globules, glycogen and secretory globules. As with absorption, the volume of a particular scatterer within the tissue is as important as its scattering ability. Evidence suggests that cell membranes are the most important source of scattering in brain tissue since they account for a large proportion of the solid content of the tissue.

Scatter is by far the most dominant tissue-photon interaction at NIR wavelengths. The effect of scattering is to substantially increase the pathlength travelled by photons within tissue, and therefore significantly increase the probability of absorption occurring. When NIR radiation is scattered in tissue virtually all the collisions are elastic, and the direction in which the scattered photon travels is dependent upon the size of the scattering particle, the wavelength of the light, and the refractive indices of the scattering media through which it is travelling.

The attenuation (A) due to single scattering is proportional to the number density of the scattering particles (N), the scattering cross section of the particles (s) and the optical pathlength (d):

     A  = log₁₀ [I_o/I]  = N.s.d   .

The product Ns is known as the scattering coefficient of the medium (µ_s), and is the probability per unit length of a photon being scattered. The reciprocal is the mean free path between scattering events. The scattering coefficients of human tissues are generally within the range 10 - 100 mm^-1, roughly one hundred times greater than those for absorption [6]. The most highly scattering tissues include bone, cerebral white matter, and skin dermis.

For multiply scattering media such as tissue, the simple formula given above no longer applies. In order to fully describe scatter of light in tissue, it is necessary to consider the probability of a photon being scattered in a given direction at each interaction. The probability of a photon, incident along a unit vector p being scattered into a direction q is described by the phase function f(p,q). For a random medium it can be assumed that this probability is independent of p and only depends on the angle between the incident and scattered directions, e. Thus the phase function can be conveniently expressed as a function of the scalar product of the unit vectors in the initial and final directions, which is equal to the cosine of the scattering angle cos(e). The anisotropy in the probability distribution is commonly characterised in terms of the mean cosine of the scattering angle g.

In biological tissues, scatter occurs principally in a forward direction, corresponding to an anisotropy in the range 0.69 >g >0.99 [6]. Despite the forward scatter, typical values of scattering coefficient ensure that light travelling through more than a few millimetres of tissue loses all of its original directionality, and can be treated as effectively isotropically distributed. Thus it is convenient to express the characteristic scatter of tissues in terms of a transport scatter coefficient:

     µ_s´  = µ_s (1 - g)   ,

which represents the effective number of isotropic scatters per unit length, and is a fundamental parameter in diffusion theory.

The Modified Beer-Lambert Law

When a highly scattering medium is considered, the Beer-Lambert relationship must be modified to include (i) an additive term, G, due to scattering losses and (ii) a multiplier, to account for the increased optical pathlength due to scattering. The true optical distance is known as the differential pathlength (DP) and the scaling factor as the differential pathlength factor (DPF):

     DP  = DPF . d   ,

where d is the geometrical distance. The modified Beer-Lambert law which incorporates these two additions is then expressed as:

     A  = log₁₀ [I_o/I]  = a.c.d. DPF + G   .

Unfortunately G is unknown and is dependent upon the measurement geometry and the scattering coefficient of the tissue interrogated. Therefore this equation cannot be solved to provide a measure of the absolute concentration of the chromophore in the medium from a measure of absolute attenuation. However if G does not change during the measurement period, it is possible to determine a change in concentration (c₂-c₁) of the chromophore from a measured change in attenuation (A₂-A₁):

     (A₂-A₁)  = (c₂-c₁).a.d. DPF   .

Note that the differential attenuation is actually measured, giving rise to the terminology differential pathlength and differential pathlength factor. The quantification of the change in concentration still depends upon the measurement of the geometrical distance d and the differential pathlength factor, i.e. the true optical pathlength which the scattered light has travelled. Although d is simple enough to measure, as it is purely the geometrical distance between the points where the light enters and leaves the medium, determination of DPF is more difficult. There are a number of different techniques which can be used to measure DPF in tissue, as briefly described in the following section.

Measurements of DPF

a) Time of Flight Method

The development of picosecond pulse lasers and ultrafast detectors during the past twenty years has made possible the direct measurement of the time of flight of light through tissue [7]. The system currently used at University College London is a Ti:sapphire laser pumped by a diode-pumped CW laser. The system can produce a single pulse with a duration of approximately 2 ps, and with suitable mirrors the laser can be tuned between 740 nm and 920 nm. The laser beam is split and part of the laser output is taken directly to the streak camera as a time reference. The other part of the beam is directed through the tissue sample. The temporal reference and the signal which has traversed the tissue sample are recorded simultaneously on the same streak image. The geometrical distance d between the centre of the transmitting fibre and the centre of the detecting fibre bundle is accurately measured. As with conventional spectroscopy measurements, it is important to minimise movement of the tissue between the fibres and various stereotactic devices have been used to stabilise the tissue under interrogation.

The time difference <t> between the light entering the tissue and the mean time of that which has traversed the tissue is measured from the streak image and is then used in the calculation of the differential pathlength factor in a simple time of flight approximation:

     DPF  = DP / d  = c_v.< t> / d.n   ,

where c_v is the speed of light in a vacuum, and n is the refractive index of the tissue (usually taken as 1.40 [8]). Time of flight systems of the type described above are large, expensive, and confined to dedicated optical laboratories, which precludes routine clinical use on neonates. To date therefore, this method has generally been restricted to measurements on post mortem infants and on adult volunteers [9-11].

b) Intensity Modulated Optical Spectrometer

     Figure 4: Measurement in the time and frequency domains.

When NIRS is applied to measurements of tissue oxygenation in the fetal head during labour and childbirth or in muscles during exercise, large changes in the geometrical distance d may occur during a study. The ultimate goal of a reliable accurate bedside spectrometer can therefore only realistically be achieved when real time measurement of the total light path can be incorporated. By making spectroscopy measurements in the frequency rather than the time domain, it has been possible to develop a new method of continuously monitoring the total path which the NIR light has travelled in the tissue of interest. Figure 4 demonstrates schematically the principles of the time and frequency domain measurements of DPF. A continuous laser source can be easily modulated at all frequencies from DC to a few hundred MHz and the phase shift between the light entering and exiting the tissue can be recorded. It has been shown [12] that if P is the phase shift measured in radians, then for modulation frequencies less than 200 MHz, the total distance travelled through the tissue, DP, is given by:

     DP  = P. c_v / 2.pi. f. n   ,

where f is the modulation frequency. Optical pathlengths at one or two wavelengths have been reported from a measurement of phase shift of light modulated at a single frequency of 220 MHz [13].

An intensity modulated optical spectrometer capable of working at several wavelengths and over a wide range of modulation frequencies has been developed at UCL for use in a number of clinical studies [14-16]. In this spectrometer four intensity modulated laser diode sources produce light in the NIR region enabling the user to measure the optical pathlength at each wavelength and simultaneously perform the conventional spectroscopy measurements for determining the change in concentration of Hb, HbO₂ and CtOx. In this way the change in measured attenuation can be corrected for pathlength variations in real time. Since the distance measured is the total optical pathlength, DP, this instrument negates the need for manual measurement of the geometric distance d, and therefore represents a dramatic improvement in the accuracy of pathlength and spectroscopy measurements. Research with this type of instrument will prove useful not only in studies where the optical fibres are likely to move (e.g. during fetal measurements or exercise studies) but also in improving the accuracy of oxidised cytochrome oxidase measurements which, due to the chromophore's relatively low concentration in tissue are particularly vulnerable to errors in optical pathlength estimation. In addition, since this type of system is capable of measuring DP at four wavelengths, a more accurate correction for the pathlength variations known to occur with absorption coefficient, µ_a, (and hence wavelength) can also be made.

Although this type of system allows a continuous measurement of DP combined with the normal spectroscopic measurements, the first clinical application of the instrument has been to collect data on the absolute values of DP in different groups of subjects. If the geometrical distance d is measured at the time of the study, the DPF can easily be calculated from the DP measurement, and compared with previously recorded values. The portable nature of the instrument has also allowed the measurement of cranial DPF to be made on a large group of live neonates at the cotside [15]. In addition a study has recently been completed to investigate the age dependence of cranial DPF in humans. The intensity modulated spectrometer described above was used to measure cranial DPF in a total of 283 subjects whose age ranged from 1 day to 50 years [16]. The results suggest a slowly varying age dependence of DPF following the relation:

     DPF₇₈₀  = 5.13 + 0.07Y ^0.81   ,

where DPF₇₈₀ is the differential pathlength factor at 780 nm and Y is the age of the subject in years.

Factors influencing the total optical pathlength

It has been shown that DP is dependent upon the following factors:

a) Tissue Type

Measurements of DPF have been made on neonatal head, and adult head, forearm and calf. A marked difference is seen between these four tissue types. This difference is to be expected since the DPF is directly dependent upon the proportion of, for example, soft tissue, muscle and bone in the illuminated tissue.

b) Absorption coefficient (and wavelength)

The time of flight system has been used to demonstrate the relationship between DPF and wavelength (and hence absorption coefficient) in the adult head, forearm and calf (in vivo) and the infant head [17]. The DPF was estimated from mean time of flight measured between 740 nm and 840 nm. In all tissues the DPF generally decreased with increasing wavelength, although also exhibiting the absorption characteristics of haemoglobin, with a variation of typically 12% over the wavelength range. For this reason it is always important when quoting DPF values to also quote the wavelength at which the DPF measurements have been made. The spectral dependence of DPF must also be taken into account in the algorithm used to convert from attenuation (OD) data at a range of wavelengths to changes in chromophore concentration.

c) Geometry of Optodes

It has been demonstrated [18] with the aid of computer simulation, that on a spherical object DPF is dependent upon angular position. DPF may vary significantly between an emitter-detector angle of 180 to 60 degrees, and even more rapidly for lesser angles. In contrast, an experimental study [10] showed that in all tissues DPF initially falls with increasing geometrical distance, d, the value becoming almost constant for source-detector spacings above 2.5 cm. This discrepancy between the theoretical and experimental results can be explained in part by the fact that the theoretical model did not take into account the inhomogeneity of the tissue illuminated. This has been confirmed by modelling of multilayered tissues where the DPF has been shown to vary with angle in the same way as that observed experimentally [19]. Much work is currently being done to further refine the methods used for prediction of DPF, particularly in realistic tissue models [20].

Spectroscopic Measurements of the Brain

     Figure 5: NIRS measurement across the head.

Figure 5 shows a schematic of the experimental set up for the spectroscopic measurement across a head. The optical fibres which carry the NIR light to and from the head are terminated with small prisms which direct the light normally on to the surface of the tissue. The geometrical distance d, known as the interoptode spacing (IOS), is usually measured with a pair of callipers directly over the measurement site. Note this distance is the chord (straight line) distance rather than the length of the arc between the two points. This assumption is based upon the fact that light inside the brain becomes essentially diffuse within a few millimetres of entering the tissue, at which point it becomes an isotropic source [18], even if the angle between the source and detector is less than 180 degrees.

The differential pathlength factor has been measured in the adult head using both the UCL time of flight system and the UCL intensity modulated optical spectrometer, and a value of approximately 6 was obtained. Therefore, for an IOS of 4 cm, the mean distance which the light actually travels in the head is approximately 24 cm.

The chromophores of interest within the tissue, whose concentration vary with oxygenation are HbO₂, Hb and CtOx. The specific extinction coefficients (a) for these chromophores are expressed in units of per micromolar of chromophore per litre of tissue per cm. Once d, a and DP are known the change in chromophore concentration can easily be computed from the measured change in attenuation. However for the simultaneous computation of the changes in concentration of a number of chromophores from the changes in attenuation at a number of wavelengths, a matrix operation must be performed incorporating the relevant extinction coefficients for each wavelength and chromophore. For each wavelength it is assumed that the linear changes in attenuation for each chromophore can be linearly summed. The result of these computations is the value of the absolute change in concentration of each chromophore in the non arbitrary units of micromolar of chromophore per litre of tissue.

Since the absolute concentration of chromophore is unknown (and cannot be determined due to the effects of light scattering within the tissue), all measurements are expressed as absolute concentration changes from an arbitrary zero at the start of the measurement period. Thus using this technique the quantified changes in tissue oxygenation can be non invasively monitored. Furthermore the quantified changes in the concentration of Hb and HbO₂ in the units micromolar can be used to measure absolute haemodynamic parameters such as cerebral blood flow [21] and cerebral blood volume [22].

References

Click here for some useful references on near-infrared spectroscopy and related topics.

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