2.1.

Algorithms to Quantify Changes in [HbO ₂ ] and [Hb]

NIR spectroscopy can be used to measure hemoglobin concentrations and oxygen saturation since light absorptions of HbO ₂ and Hb are different at the wavelengths selected (758 and 785 nm). In common with our previous work,¹¹ we assumed that HbO ₂ and Hb are the only significant absorbing materials in tumors within the selected NIR range of 700 to 900 nm. Based on Beer-Lambert’s law, the absorption coefficients μ_a comprise the extinction coefficients for deoxyhemoglobin (ɛ _Hb ) and oxyhemoglobin (ɛ _HbO2) multiplied by their respective concentrations:

We have not yet completed a suitable algorithm to compute μ_a of rat tumors due to their finite size and high heterogeneity. Instead of diffusion theory, we modified Beer-Lambert’s law, i.e., μ_a=2.3ɛC=(2.3/L)log(I₀/I), to analyze the data using only amplitude values to quantify changes in [HbO ₂] and [Hb]. In this case, I₀ is the detected light intensity when no absorption is present. Specifically, changes in absorption coefficient of the tumor, Δμ_a, between baseline and transient conditions under respiratory intervention can be expressed as

By manipulating Eqs. (1) to (3), changes of [HbO ₂] and [Hb] due to an intervention can be expressed using the transmitted amplitudes of the light through the tumor as:

In principle, L⁷⁵⁸ and L⁷⁸⁵ given in Eqs. (4) and (5) are not constants, depending on both the source-detector separation and the optical properties of the measured medium. Optical path length in a scattering medium L has been expressed¹³ as the source-detector separation d multiplied by a differential pathlength factor (DPF), i.e., L=d^*DPF. DPF values of blood-perfused tissues should be wavelength- and oxygenation-dependent, and they have been studied intensively for muscles¹⁴ and brains¹⁵ with approximate values of 4 to 6 and 5 to 6, respectively. Little is known about DPF for tumors although a DPF value of 2.5 has been used by others.¹⁶ In our approach, we define two parameters, β _HbO2 and β _Hb , as ratios between DPF⁷⁵⁸ and DPF⁷⁸⁵ for oxygenated blood and deoxygenated blood, respectively, as given below:

To further quantify β _HbO2 and β _Hb , we associate L to μ_a by $$L=\left(\sqrt{3}/2\right)d{\left({\mu }_s^{\text{'}}/{\mu }_a^{\text{'}}\right)}^{1/2}$$ where μ_s ^′ is the reduced scattering coefficient, according to Sevick et al.;¹⁰ and Liu.¹⁷ Equation (6) becomes

The units for Δ[HbO ₂], Δ[Hb], and Δ[Hb _total ] in Eqs. (13) to (15) are mM/DPF ₀, which is still a variable, depending on the optical properties of the tumor at a particular wavelength. Since our study involves changes in [HbO ₂] due to respiratory challenges, we can obtain a normalized Δ[HbO ₂] at its maximal value, i.e., Δ[HbO ₂]/Δ[HbO ₂] _max , to eliminate the unit so as to minimize the effect of DPF on our results. Next, we will show that a normalized Δ[HbO ₂] has a close relationship with hemoglobin oxygen saturation sO ₂.

2.2.

Relationship Among Normalized Δ[HbO ₂ ], sO ₂ and Blood pO ₂

We define sO ₂ values of the measured sample at the baseline, transient state, and maximal state, i.e., (sO ₂) _base , (sO ₂)_t, and (sO ₂) _max , respectively:

During a cycle of oxygenation and deoxygenation in a blood-perfused tissue, if the total concentration of hemoglobin remains constant, we have the following condition: [Hb _total ] _max =[Hb _total ]_t=[Hb _total ] _base . In the case of tumors under gas intervention, total hemoglobin concentration does not always remain constant, but the changes in [Hb] _total appeared relatively small in comparison to the changes in [HbO ₂]. ^{11 18} It is reasonable to assume that Δ[Hb _total ]≪[Hb _total ], i.e., the condition of [Hb _total ] _max =[Hb _total ]_t=[Hb _total ] _base still holds for the tumor under oxygen/carbogen interventions. Then, Eq. (19) becomes

To further make correlation between the normalized Δ[HbO ₂] and blood pO ₂, Hill’s equation¹⁹ can be combined with Eq. (20) to characterize oxygen transport in the tissue vasculature:

In our phantom studies, the measured pO ₂ values are considered as blood pO ₂ in tissue vasculature since blood is well mixed in the solution (see details in Sec. 3.4). Therefore, values of P ₅₀ ^B, n, a, and b in Eq. (21) can be fitted to the experimental data, allowing us to determine the initial, transient, and maximal values of sO ₂ of the simulating tissue due to oxygen/nitrogen interventions.

2.3.

Relationship Between Normalized Δ[HbO ₂ ] and Tissue/Tumor pO ₂

In principle, blood pO ₂ and tissue pO ₂ are different, depending on the relative distance between a capillary vessel, oxygen consumption, and the location where pO ₂ is measured.¹⁹ It is shown that there exists a constant pressure drop between blood pO ₂ and tissue pO ₂ as the blood passes through a capillary vessel. Therefore, it is reasonable to assume

Ideally, when both Δ[HbO ₂] and tissue pO ₂ are measured at the same physical location, the maximal and initial oxygen saturations, i.e., a and b in Eq. (23), of the measured tissue vasculature can be obtained by fitting Eq. (23) to the measured data. In our tumor study, we then can estimate the maximal and initial hemoglobin oxygen saturations of the tumor by fitting the measured values of global normalized Δ[HbO ₂] and global tissue pO ₂, which result from adding up all local pO ₂ values obtained from ¹⁹ F MR pO ₂ mapping.

3.1.

Tumor Model

Dunning prostate rat tumors (eight R3327-HI and four R3327-AT1)²⁰ were implanted in pedicles on the foreback of adult male Copenhagen rats, as described in detail previously.²¹ Once the tumors reached approximately 1 cm in diameter, the rats were anesthetized with 0.2 ml ketamine hydrochloride (100 mg/mL; Aveco, Fort Dodge, IA) and maintained under general gaseous anesthesia with isoflurane in air (1.3 isoflurane at 1 dm³/min air) through a mask placed over the mouth and nose. Tumors were shaved to improve optical contact for transmitting light. Body temperature was maintained by a warm water blanket and was monitored by a rectally inserted thermal probe connected to a digital thermometer (Digi-Sense, model 91100-50, Cole-Parmer Instrument Company, Vernon Hills, IL). A pulse oximeter (model 8600, Nonin, Inc., Plymouth, MN) was placed on the hind foot to monitor arterial oxygenation (S _a O ₂). Tumor volume V (in cubic centimeters) was estimated as V=(4π/3) [(L+W+H)/6]³, where L, W, and H are the three respective orthogonal dimensions.

In general, the source-detector fiber separation was about 1 to 1.5 cm in transmittance geometry, and thus the maximal tumor volume interrogated by NIR light can be estimated as follows. By the diffusion approximation, the optical penetration depth from the central line between the source and detector is about one half of the separation (source-detector separation=d) . The total tumor volume interrogated by NIR light can be estimated as the spherical volume with a radius of one half of d, i.e., (π/6)d³. In this way, the estimated tumor volume interrogated by NIR light is in the range of 0.5 to 2.0 cm³, depending on the actual source-detector separation.

3.2.

NIRS and pO ₂ Needle Electrode Measurements

Figure 1 shows the schematic setup for animal experiments using both NIRS and a pO ₂ needle electrode. A needle type oxygen electrode was placed in the tumor, and the reference electrode was placed rectally. The electrodes were connected to a picoammeter (Chemical Microsensor, Diamond Electro-Tech Inc., Ann Arbor, MI) and polarized at −0.75 V. Linear two-point calibrations were performed with air (21 O ₂) and pure nitrogen (0 O ₂) saturated saline buffer solutions before the electrode was inserted into the tumor, and we estimated an instrumental precision of 2 to 3 mm Hg. Measurement points of pO ₂ were manually recorded, while the NIRS data were acquired automatically. Measurements of pO ₂ and NIRS were initiated, while the rats breathed air for ∼10 min to demonstrate a stable baseline. The inhaled gas was then switched to carbogen for 15 min and switched back to air.

Figure 1

Schematic experimental setup of one-channel, near-infrared, frequency-domain IQ instrument for tumor investigation in vivo. The 5-mm-diameter fiber bundles deliver the laser light, comprising two wavelengths (758 and 785 nm), and detect the laser light transmitted through the implanted tumor. The pO ₂ needle electrode measures tumor tissue pO ₂.

Our NIR system as shown in Figure 1 (Refs. 11 and 22) is a homodyne frequency-domain photon migration system (NIM, Inc., Philadelphia, PA) and uses commercially available in-phase and quadrature (IQ) demodulator chips to demodulate the detected, amplitude-modulated optical signal.

3.3.

Experimental Validation for β _HbO2 and β _Hb Values

In order to validate β _HbO2 and β _Hb values, we conducted phantom calibration measurements. We used 2 l of 0.01 M phosphate buffered saline (P-3813, Sigma, St Louis, MO) and 1 Intralipid (Intralipid^® 20, Baxter Healthcare Corp., Deerfield, IL) with pH=7.4 at 25 °C. To deoxygenate the solution, 14 g of baking yeast was dissolved in the phantom solution, and pure oxygen gas was used to oxygenate the solution. After the yeast was well mixed in the solution, 3 ml of human blood was added twice. When the blood was fully deoxygenated, pure oxygen was introduced in the solution to oxygenate the blood. After the blood was fully oxygenated, oxygen blowing was stopped in order to deoxygenate the solution with yeast again.

Equations (4) and (5) were applied to the raw amplitude data to calculate Δ[HbO ₂] and Δ[Hb]. Large unexpected and erroneous fluctuation of Δ[Hb _total ] (=Δ[HbO ₂]+Δ[Hb]) were seen during the oxygenation and deoxygenation cycles (Figure 2). However, when we applied Eqs. (13) to (15) to calculate Δ[HbO ₂], Δ[Hb], and Δ[Hb _total ], Δ[Hb _total ] remained constant during the oxygenation and deoxygenation cycles as expected. This demonstrates that the values of β _HbO2=1.103 and β _Hb =0.9035 are correct and necessary to compensate the differences in DPFs caused by the two different wavelengths.

Figure 2

Simultaneous dynamic changes of Δ[HbO ₂], Δ[Hb], and Δ[Hb] _total in the phantom solution measured using NIRS. The gray solid curve is for Δ[Hb] _total without using β _{HbO 2} and β _Hb values. Oxygen consumption by yeast produced deoxygenated blood and blowing oxygen restored oxygenation. During the oxy- and deoxygenation process, Δ[Hb] _total is supposed to be a constant. However, as we can see here, Δ[Hb] _total calculated without β _HbO2 and β _Hb values shows the fluctuation during the oxy- and deoxygenation while Δ[Hb] _total calculated using β _HbO2 and β _Hb values shows the veracity of these modified algorithms.

3.4.

Tissue Phantom Solution Model

In order to study the relationship between pO ₂ and Δ[HbO ₂] in regular tissues, we conducted a tissue-simulating phantom study by using the liquid solution similar to that mentioned above. In normal tissues, there are several steps of oxygen transport from the blood to tissue cells.²³ In the tissue-simulating phantom, blowing oxygen gas represents oxygenation process of blood in the lungs, and blowing nitrogen gas simulates deoxygenation process of blood in the tissues. The differences between the tissue-simulating phantom and real tissues are that there is no capillary membrane in the phantom, and that the phantom is more homogeneous than real tissues. Capillary membranes have high permeability of oxygen, so oxygen transport from blood to tissues crossing the capillary membranes occurs straightforwardly. Furthermore, normal tissues are well vascularized, and the NIR techniques are more sensitive toward measuring small vessels and vascular bed of the tissue.²⁴ Therefore, vasculature of normal tissues has been simulated by a turbid solution mixed with blood as a simplified laboratory model in NIRS measurements for oxygen transport from blood to normal tissues.^{10 18 22}

The experimental setup shown in Figure 3 was made to simulate tumor oxygenation/deoxygenation. Oxygen needle electrodes, a pH electrode, and a thermocouple probe (model 2001, Sentron, Inc., Gig Harbor, WA) were placed in the solution, and the gas tube for delivery of N ₂ or air was placed opposite the NIRS probes to minimize any liquid movement effects. Source and detector probes for the NIRS were placed in reflection geometry with a direct separation of 3 cm. The solution was stirred constantly to maintain homogeneity by a magnetic stirrer at ∼37 °C. Fresh whole rabbit blood (2 mL) was added to the 200 mL solution before baseline measurement. Nitrogen gas and air were used to deoxygenate and oxygenate the solution, respectively.

Figure 3

Experimental setup for phantom study using 1 Intralipid in saline buffer. NIRS probes were placed in reflectance mode, while the gas bubbler was placed opposite to minimize liquid movement effects. After adding 2 ml of rabbit blood to a 200 ml solution, nitrogen gas and air were introduced to deoxygenate and oxygenate the solution, respectively.

3.5.

MRI Instrumentation and Procedure

To support the findings obtained from the pO ₂ electrode measurements and NIRS, we conducted MRI experiments using an Omega CSI 4.7 T 40 cm system with actively shielded gradients. A homebuilt tunable ¹ H/¹⁹ F single turn solenoid coil was placed around the tumor. 45 μL hexafluorobenzene (HFB; Lancaster, Gainesville, FL) was administered directly into the tumor using a Hamilton syringe (Reno, NV) with a custom-made fine sharp (32 gauge) needle and HFB was deliberated dispersal along several tracks to interrogate both central and peripheral tumor regions, as described in detail previously.⁵ HFB is ideal for imaging pO ₂ because it has a single resonance and its relaxation rate varies linearly with oxygen concentration. ¹ H images were acquired for anatomical reference using a traditional 3-D spin-echo pulse sequence. Conventional ¹⁹ F MR images were taken to show the 3-D distribution of the HFB in the tumor. ¹⁹ F MR images were directly overlaid over ¹ H images to show the position of the HFB in that slice.

Tumor oxygenation was assessed using fluorocarbon relaxometry using echo planar imaging for dynamic oxygen mapping (FREDOM) based on ¹⁹ F pulse burst saturation recovery (PBSR) echo planar imaging (EPI) of HFB.²⁵ The PBSR preparation pulse sequence consists of a series of 20 nonspatially selective saturating 90 deg pulses with 20 ms spacing to saturate the ¹⁹ F nuclei. Following a variable delay time τ, a single spin-echo EPI sequence with blipped phase encoding was applied.²⁶ Fourteen 32×32 PBSR-EPI images, with τ ranging from 200 ms to 90 sec and a field of view (FOV) of 40×40 mm, were acquired in 8 min using the alternated relaxation delays with variable acquisitions to reduce clearance effects (ARDVARC) acquisition protocol.²⁵ An R1(=1/T1) map was obtained by fitting the signal intensity of each voxel of the 14 images to a three-parameter relaxation model by the Levenberg-Marquardt least-squares algorithmml:

4.1.

Tumor Study Results

We have measured relative changes of [HbO ₂], [Hb], [Hb _total ], and tumor tissue pO ₂ (electrode) from eight Dunning prostate R3327-HI tumors, and Figure 4 shows three representative data sets. Figure 4(a) shows the temporal profiles of Δ[HbO ₂] and pO ₂ in a small Dunning prostate R3327-HI tumor (1.5 cm³) measured simultaneously with NIRS and the pO ₂ needle electrode during respiratory challenge. After a switch from air to carbogen, Δ[HbO ₂] increased rapidly, along with tumor tissue pO ₂. Figure 4(b) was obtained from a large tumor (3.1 cm³): the electrode readings showed a slower pO ₂ response, whereas the NIRS response was biphasic, which has been a commonly observed dynamic feature.¹¹ In a third tumor (1.6 cm³), NIRS behaved as before, but pO ₂ did not change [Figure 4(c)].

Figure 4

Simultaneous dynamic changes of Δ[HbO ₂] and pO ₂ in R3327-HI rat prostate tumors using NIRS and pO ₂ needle electrode. (a) A small tumor (1.5 cm³) showed a rapid pO ₂ response (case 1), whereas (b) a bigger tumor (3.1 cm³) showed a slower pO ₂ response (case 2). (c) In a third tumor (1.6 cm³) where regional baseline pO ₂ was <5 mm Hg, there was no pO ₂ response (case 3). The unit of Δ[HbO ₂] is mM/DPF, where DPF is equal to the optical path length divided by the source-detector separation. Dotted vertical line marks the time when the gas was changed.

In four tumors from a separate subline (Dunning prostate R3327-AT1), NIRS and ¹⁹ F MRI were taken sequentially with carbogen challenge, and two representative data sets are shown in Figure 5. NIRS response showed vascular oxygenation changes as before, and FREDOM revealed the distinct heterogeneity of the tumor tissue response. Initial pO ₂ was in the range of 1 to 75 mm Hg, and carbogen challenge produced pO ₂ values in the range of 6 to 350 mm Hg. Representative voxels are shown in each figure by dashed lines with open symbols. In addition, mean pO ₂ values were calculated by averaging all available pO ₂ readings over 21 and 45 voxels for the two respective tumors. We usually obtain pO ₂ temporal profiles from individual voxels among 200 to 400 voxels in a tumor during the entire intervention period. The pO ₂ readings presented here were picked to show heterogeneity of the tumor. In Figure 5(a), the closest distance between the two voxels is 1.25 mm (between ⋄ and □), and the furthest distance is 7.6 mm (between × and ▵). In Figure 5(b), the closest distance is 3.6 mm (between × and ▵) and the furthest distance is 16 mm (between × and □). These indeed showed that tumor pO ₂ responses to carbogen intervention could be quite different at different locations. Notice that Figure 5(a) showed spikes of Δ[HbO ₂] during the measurement. We expect this to be caused by sudden changes in rat respiratory circulation or motion, rather than resulting from simple instrumental noise. It is also seen that mean pO ₂ values have displayed a consistent increase when Δ[HbO ₂] showed spikes, suggesting that such spikes may result from changes in rat physiological conditions.

Figure 5

Dynamic changes of Δ[HbO ₂] and pO ₂ in two R3327-AT1 rat prostate tumors measured sequentially using NIRS and ¹⁹ F MR pO ₂ mapping. The solid curves represent Δ[HbO ₂], and the solid lines with solid circles represent mean pO ₂±SE (standard error) of 21 (a) and 45 (b) voxels of the respective tumor. Dashed lines with open symbols are 4 representative voxels for each case. After a gas switched from air to carbogen, the mean pO ₂ values of both tumors increased, but individual voxels showed quite different responses, indicating high heterogeneity in the tumors. The tumor sizes were 3.2 cm³ and 2.7 cm³ for (a) and (b), respectively.

4.2.

Tissue Phantom Study Results

Figure 6 shows a temporal profile for Δ[HbO ₂] and pO ₂ measured from the tissue phantom during a cycle of gas change from air to nitrogen and back. The first three minutes were measured as a baseline after adding 2 ml blood. Bubbling nitrogen deoxygenated the solution and caused the pO ₂ values to fall; Δ[HbO ₂] declined accordingly with a small time lag. After the bubbling gas was switched from nitrogen to air, both Δ[HbO ₂] and pO ₂ started to increase simultaneously, but the recovery time of Δ[HbO ₂] to the baseline was faster than that of pO ₂. The small time lag between the changes of Δ[HbO ₂] and pO ₂ is probably due to the allosteric interactions between hemoglobin and oxygen molecules. According to the hemoglobin oxygen-dissociation curve,^{19 27} oxyhemoglobin starts to lose oxygen significantly when pO ₂ falls below 70 mm Hg at standard conditions (pH=7.4, pCO ₂=40 mm Hg, and temperature=37 °C) . The same principle can explain why Δ[HbO ₂] has a faster recovery than that of pO ₂. Figure 6 shows that Δ[HbO ₂] is already saturated when pO ₂ is at 50 mm Hg, while the solution was still being oxygenated. This may be due to low pCO ₂ in the solution where this can shift the oxyhemoglobin dissociation curve to the left, causing oxyhemoglobin to be saturated at lower pO ₂. Importantly, Δ[Hb] _total remained unchanged, as expected, during a cycle of deoxygenation and oxygenation.

Figure 6

Simultaneous dynamic changes of Δ[HbO ₂], Δ[Hb] _total , and pO ₂ in the phantom solution measured using NIRS and pO ₂ needle electrode. The dark solid curve is for Δ[HbO ₂], the lighter solid line is for Δ[Hb] _total , and the solid circles show pO ₂ values in the phantom solution. After ∼3 min baseline, the bubbling gas was changed from air to nitrogen to deoxygenate the solution and then switched back to air to reoxygenate the solution. The unit of Δ[HbO ₂] is mM/DPF.

4.3.

Correlation between pO ₂ and Normalized Δ[HbO ₂ ]

For Tissue Phantoms. Figure 7(a) replots the data given in Figure 6, showing the relationship between normalized Δ[HbO ₂] and pO ₂ measured from the tissue phantom during the oxygenation (air blowing) period after the nitrogen blowing. Open circles are the measured data, and the solid line is the fitted curve using Eq. (23). The error bars for the data were not shown here since they are smaller than the symbols of the data points. For the curve fitting procedure, we used a nonlinear curve-fitting routine provided through KaleidaGraph (Synergy software, Reading, PA). The fitted parameters are n=1.9, P ₅₀=15.2 mm Hg, [sO ₂] _base =0, and [sO ₂] _max =99 with R=0.997 and minimized chi-square. The fitted values of [sO ₂] _base and [sO ₂] _max are in good agreement with the expected values, since the corresponding pO ₂ values are 0 and 160 mm Hg, respectively. This agreement validates Eq. (23) and further indicates that we can measure approximate sO ₂ values during the gas interventions in a homogeneous system by fitting the experimental data using Eq. (23) even though we do not measure absolute [HbO ₂]. The Hill coefficient (n) and pO ₂ value at 50 of sO ₂ (P ₅₀) are smaller than the values from a standard oxyhemoglobin saturation curve, probably due to the shift of the oxyhemoglobin dissociation curve. For Tumor Study. Figure 7(b) replots the data given in Figures 4 and 5, showing a direct relationship between the normalized Δ[HbO ₂] and tissue pO ₂ in the tumors. NIRS results tended to be similar for several tumors, and pO ₂ electrode measurements showed considerable variation even in the same tumor type, suggesting distinct tumor heterogeneity. This was substantiated by the ¹⁹ F MR pO ₂ mappings (Figure 5): indeed, in some cases, pO ₂ values did not change with respiratory challenge, especially when baseline pO ₂ values were lower than 10 mm Hg.

Figure 7

Changes of tissue pO ₂ with normalized changes of oxygenated hemoglobin (a) in the phantom solution using the NIRS and pO ₂ needle electrode and (b) in tumors measured with NIRS, pO ₂ needle electrode, and ¹⁹ F MR pO ₂ mapping. In (a), the open circles are measured data and the solid line is the fitted curve using Eq. (21). This shows that Eq. (21) works well in a homogeneous system. In (b), all the tumor data are shown indicating that tumors are highly heterogeneous for pO ₂ response to carbogen inhalation. Open symbols show local pO ₂ changes (from Figure 4) and solid symbols show the mean pO ₂ changes (from Figure 5) during gas intervention. To estimate global sO ₂ in tumors during respiratory challenges, we applied Eq. (23) to Figure 5(a), indicating sO ₂ changes during carbogen inhalation when compared via tumor pO ₂.

Equation (23) can be used to estimate values of [sO ₂] _base and [sO ₂] _max for the tissue-simulating phantom (a homogeneous system). However, the relationship fails for heterogeneous systems such as tumors. The NIRS measurements interrogate a large volume of tumor tissue, giving a global value of normalized Δ[HbO ₂], whereas the pO ₂ readings are local near the tip of the needle electrode. However, to estimate mean values of [sO ₂] _base and [sO ₂] _max , it is reasonable to compare the global normalized Δ[HbO ₂] with global tissue pO ₂, which can be obtained by summing up all local pO ₂ readings at different pixels measured from the ¹⁹ F MRI mapping, as done in Sec. 4.1 and shown by solid lines in Figure 5. The data shown in Figure 7(b) with solid symbols are the global mean pO ₂ values calculated from the corresponding MRI data. The solid fitting curve shown in Figure 7(a) is obtained from the mean pO ₂ data given in Figure 5(a). In this case, the fitting parameters are P ₅₀, [sO ₂] _base , and [sO ₂] _max with a fixed Hill coefficient n to be the same as that under standard conditions. The best fitting curve of Eq. (23) is shown in Figure 7(b), having P ₅₀=20.6±4.1 mm Hg, [sO ₂] _base =37±13, and [sO ₂] _max =100 with R=0.985 and goodness-of-fit χ²=0.031. Estimated errors for P ₅₀ and [sO ₂] _base are not insignificant and a better fit could be found by measuring pO ₂ with better temporal resolution.