2.1.

Physiologic Model

It is useful to first outline a model in which changes in the optical signal can be evaluated in terms of the physiologic changes in oxygen extraction and blood volume. Since the near-infrared signal interrogates a large portion of tissue (several mm ² in the rat brain) it is necessary to determine the oxygen concentration in arterial, capillary, and venous compartments of the microvasculature. Using the model of van Zijl et al.;²² we first assume that the fraction of deoxyhemoglobin in arterioles ( x _deoxy,a ) and venules ( x _deoxy,v) are given by

Assuming a linear oxygen gradient between arterioles and venules²² the capillary deoxyhemoglobin fraction is, therefore,

The fractions of oxyhemoglobin are likewise given by

The concentration of oxy-( c _oxy ) , deoxy- (c _deoxy ) , and total (c _tot ) hemoglobin in tissue is then given by

Substituting Eqs. (4), (6), and (8 9 10 11) into Eq. (12) yields

2.2.

Experiment

2.2.1.

Spectroscopy System

Measurement of transcranial tissue oxygenation changes was performed using a dual wavelength near-infrared spectrometer (NIRS), shown in Figure 1. This system is based on the design in Ref. 10. Laser diodes at 700 and 799 nm (1–3 mW) were coupled into a single 1 mm optical fiber which was placed on the scalp of the animal (excess hair was shaved for better optical contact). The resultant reflectance signal was obtained from a similar fiber placed 5–8 mm from the transmission fiber. This signal was sent to an avalance photodiode system (Hamamatsu Photonics). The laser diodes were frequency modulated in order to resolve the signal into each wavelength component. The signal detected was then demodulated through single phase lock-in amplifiers (Boston Electronics). The data were then recorded on a computer for analysis. The pathlength-dependent changes in oxy-, deoxy-, and total hemoglobin were evaluated via matrix inversion of Eq. (2).

Figure 1

Schematic of the dual frequency animal NIRS system.

2.2.3.

Phantom Evaluation of Path Length Dependence on Optical Absorption

An important hypothesis in this discussion is that the pathlength of light remains constant during mild hypoxia and the activation challenge. To validate this, measurements were performed on a layered tissue like phantom system, illustrated in Figure 2. The phantom consisted of a 1.5 cm inner diameter (i.d.) clear plastic centrifuge tube which contained a light scattering medium of 7 intralipid (Sigma Chemicals). In order to change the optical absorption, human hemoglobin was dissolved in the intralipid at concentrations ranging from 0 to 0.22 mM. This range is roughly equivalent to a whole blood volume fraction of 0–10 at a normal hematocrit of 0.4. The centrifuge tube was placed inside an opaque Teflonshell to simulate skin and bone. Optical fibers were then mounted on the surface of the shell at a fiber spacing of approximately 5 mm. The effective path length is defined in terms of the optically measured change in total hemoglobin and the known change in total hemoglobin which is added to the intralipid solution, i.e.,

Eq. (29)

$$d_{\text{eff}}=\Delta C_{\text{tot}}^{\text{meas}}(\text{mM mm})/\Delta C_{\text{Hb}}^{\text{true}}(\text{mM}).$$

Figure 2

Schematic of the layered phantom system.

3.1.

Mild Hypoxia

Figure 3 shows a typical time course for oxy-, deoxy-, and total hemoglobin as oxygen is cycled from 100 to 19 and back. Figure 3(a) shows results for a fiber spacing of 8 mm while Figure 3(b) shows the result with a spacing of 5 mm. This data illustrate the clear dependence of these parameters on the optical pathlength. Figure 4 shows an example of the change in transcranial oxygenation as a function of arterial oxygen saturation during mild hypoxia/hyperoxia. Over the range of arterial oxygenation studied and the fiber spacings used the changes in brain oxyhemoglobin concentration were approximately linear. Furthermore, it is apparent that for larger optode spacings the slope of the oxygen response curve becomes correspondingly larger. This is consistent with the light following a longer pathlength and thus the increase net absorption from chromophores should enhance the changes. If the oxygenation changes are homogeneous then Eq. (21) shows that the ratio of the slopes at each spacing corresponds to the pathlength ratio for this system. When averaged over all animals we found the oxyhemoglobin response slope to be 2.6±0.1 (mM mm /ΔY_a ) for a spacing of 5 mm and 4.9±0.6 (mM mm/ ΔY_a ) for a spacing of 8 mm. No significant changes in total hemoglobin concentration were observed for either optode spacing during mild hypoxia/hyperoxia, i.e., ΔC _tot (5 mm)=0.01±0.03 (mM mm) and ΔC _tot (8 mm)=−0.03±0.04 (mM mm).

Figure 3

Typical time course for pathlength-dependent oxy- and deoxy-hemoglobin responses during mild hypoxia as a function of fiber spacing. Fiber separation= (a) 8 and (b) 5 mm.

Figure 4

Pathlength-dependent oxyhemoglobin changes, ΔC _oxy (mM mm) as a funciton of arterial saturation, Y_a, for optode spacings of 8 and 5 mm.

3.2.

Hypercarbia

Figure 5 shows a typical time course for blood oxygenation, which shows the contrast in changes during hypoxia and hypercarbia. The data shown are as breathing gas is cycled from hyperoxia ( Y_a=1.0 ) to mild hypoxia ( Y_a=0.9 ) and then through mild hypercarbia. ( Y_a=1.0 , PCO ₂ increase by 11 mm.) The total hemoglobin is shown to change much more during hypercarbia which is consistent with the expected vasodilatory effects of increased carbon dioxide concentration in the blood. It is also interesting to note that the temporal response during hypercarbia was much slower than that of hypoxia which is probably indicative of the slower vasoactive responses of flow and volume in hypercarbia compared to the response time for hemoglobin desaturation in mild hypoxia.

Figure 5

Time course of oxy- deoxy- and total hemoglobin changes during mild hypoxia and hypercarbia. The gas concentrations are (A) 90 oxygen/10 nitrogen, (B) 19 oxygen/81 nitrogen, (C) 90 oxygen/10 carbon dioxide.

Figure 6 shows the results averaged over all experiments for the mean oxy- and deoxyhemoglobin changes during mild hypercarbia, in which the mean PCO ₂ was raised from 30±4 to 44±8 mm as the optode spacing was increased from 5 to 8 mm. It is clear that for large spacing significantly larger concentration changes are observed which are associated with the increase in optical pathlength.

Figure 6

Mean changes in oxygenation as a function of fiber spacing for all animals ( N=5) .

Figure 7 shows a comparison of the changes in signal at different pathlengths by calculating the ratio of each oxygenation parameter and the normalized TOI with spacings of 8 and 5 mm. For oxy- and deoxy- and total hemoglobin, the paired ratio of signal changes, Δ_8 mm /Δ_5 mm , were 1.7±0.2, 1.9±0.15, and 1.7±0.4, respectively. It is apparent that when the data are normalized via the hyperoxia response the corresponding tissue oxygenation parameters show little dependence on the pathlength. The normalized paired ratios of oxy- deoxy- and total hemoglobin signal changes were 0.96±0.07, 1.07±0.15, and 0.97±0.2, respectively. The calculated volume changes during hypercarbia were ΔV/V _rest =0.06±0.02 at 5 mm and 0.05±0.01 at 8 mm. The corresponding estimated changes in the tissue oxygenation index, ΔTOI/TOI, were 0.082±0.02 at 5 mm and 0.086±0.04 at 8 mm. This confirms that by normalizing the signal changes it is possible to obtain pathlength-independent information which can be compared across experiments.

Figure 7

Paired comparison of signal changes as a function of optode spacing during mild hypercarbia. Columns 1–3 denote the ratios of changes in signals at 8 and 5 mm without normalization, while columns 4–7 show the same results with oxygenation normalization. The normalized signals demonstrate little pathlength dependence as the fiber spacing is varied.

3.3.

Phantom Results

Figure 8(a) shows the optical absorption measured as a function of the hemoglobin concentration in the intralipid phantom. The range of hemoglobin concentrations is equivalent to blood volumes ranging from 2.5 to 10. For comparison, the typical resting cortical blood volume in the rat brain ranges from 2 to 5.³¹ Figure 8(b) shows the relative pathlength as a function of the hemoglobin concentration. The effective pathlength is normalized to the lowest hemoglobin concentration for presentation purposes. When averaged over all concentrations the effective pathlength was 27±2 mm. The data show that as optical absorption increases there is a systematic decrease in the relative pathlength. However, as the optical absorption is varied by more than fourfold there is less than a 15 change in the optical pathlength. During normal brain activation, venous blood oxygenation may change by as much as 50^{32 33} whereas the blood volume can be expected to change by a maximum of 10–20.^{34 35} For example, one can assume a relatively extreme case in which during activation the blood volume increases as ΔCBV/CBV=0.20. From a linear fit to the phantom data of Figure 8(b), the effective pathlength would change by less than 2. This would lead to an estimate of ΔCBV/CBV=0.18. It is probable that in most in vivo applications to the rat brain, the change in optical pathlength will be small compared to the change in absorption. While this layered is clearly a very rough approximation of tissue it illustrates the important point that as absorption is varied over a wide physiologic range the optical pathlength remains relatively invariant, although systematic errors can be introduced.

Figure 8

Results from phantom experiments. (a) Optical absorption as a function of the hemoglobin concentration. (b) Relative optical pathlength given by Eq. (29) as a function of the hemoglobin concentration in the phantom system. The pathlength data are normalized to the lowest Hb concentration to illustrate fractional changes.

4.1.

Diffusion Equation Methods for TOI Evaluation

Light diffusion theory allows the evaluation of the tissue oxygenation index by measuring the dependence of change in light absorption on the optode spacing. For example, if one measures the local gradient of light attenuation, A=log(S) , with respect to source/detector spacing, ρ, one can determine the pathlength-independent product of the absorption and scattering via²⁵

Assuming that changes in scattering are weak compared to changes in absorption during activation, as is also assumed in the normalization approach, Eq. (30) can be fit at various wavelengths and the tissue oxygenation index may be determined.^{25 38 39} Alternatively, using phase modulation or time of flight techniques it is also possible to obtain pathlength information. For diffusion theory to be valid, the optode spacing must be much greater than the optical scattering thus typically requiring fiber separations of 2–3 cm. While this is often employed in transcranial spectroscopy across the adult human head this cannot be achieved in small animal models where the separations are on the order of several millimeters. The hypoxia normalization method allows the changes in volume oxygenation to be determined without relying on explicit models of light diffusion. Therefore, under any conditions in which the pathlength is short relative to the scattering length it would be useful to perform physiologic normalization such as mild hypoxia. The primary assumptions in the normalization model are the validity of the Beer–Lambert approximation, as in Eqs. (1) and (2), and that the optical pathlength is not changed by the functional activation. The phantom study has shown that care must be taken in this assumption, however, for the range of absorption changes expected in the brain, the changes in pathlength are relatively small. This may not be valid in regions of higher blood volume, such as myocardial tissue, in which absorption changes will be more significant.

4.2.

Partial Volume Effects

It is important to note that the hypoxia method outlined above is only directly interpretable as changes relative to the entire area of tissue interrogated by the light. For example, if the area of activation were a small focal region with spatial extent smaller than the fiber spacings then it would be expected that upon charging the fiber spacing the relative volume and oxygenation changes for this region would be affected. This was clearly not the case for the hypercarbic challenge illustrated above although this would need to be confirmed for other conditions by performing similar pathlength alteration experiments. However, there are many cases where the methods outlined above should be useful to study less focal hemodynamic effects such as pharmaceutical drug dose responses and autoregulatory and systematic responses. The technique should still prove useful in comparing focal responses across subjects, in which case the normalized signal changes will represent a combination of the magnitude and spatial extent of the response.

4.3.

Application to Multi Optode Mapping

The use of recording from multiple optode arrays simultaneously allows one to map changes in blood oxygenation over the entire cortex.^{10 11 40 41} These methods have been exploited in the development of a variety of optical imaging systems. An implicit assumption in any continuous-wave mapping system is than when the spacing of optodes is constant the differential pathlength factor for all optodes is approximately equivalent and thus maps of relative hemoglobin changes truly reflect the degree of vascular activity. It is possible however that some optodes could be placed over regions with greater blood content than others, and thus responses would be weighted unequally. The hypoxia normalization technique could again provide a useful means by which to spatially normalize the response. Furthermore, if the assumption of equivalent pathlength is correct then maps of the oxygenation gradient, m_Y, response will provide a map of relative blood volume without the use of exogenous agents. In either case the implementation of this technique will improve the accuracy of the response maps and provide valuable quantitative data for cross-subject comparisons.