High Temporal Resolution In Vivo Blood Oximetry Via Projection-Based T₂ Measurement

Abstract

Measuring venous oxygen saturation (HbO₂) in large blood vessels can provide important information about oxygen delivery and its consumption in vital organs. Quantification of blood’s T₂ value via MR can be utilized to determine HbO₂ noninvasively. We propose a fast method for in vivo blood T₂ quantification via computing the complex difference of velocity-encoded projections. As blood flows continuously, its signal can be robustly isolated from the surrounding tissue by computing the complex difference of two central k-space lines with different velocity encodings. This resultant signal can then be measured as a function of echo time for rapidly quantifying T₂ of blood. We applied the method to quantify HbO₂ in three cerebral veins at rest and in one of the veins in response to hypercapnia. Average HbO₂ measurements in superior sagittal sinus (SSS), straight sinus and internal jugular vein in the group were 63 ± 3%, 68 ± 4% and 65 ± 4%, respectively. Average HbO₂ values in SSS during baseline, hypercapnia, and recovery were 63 ± 2%, 79 ± 5%, and 61 ± 3%, respectively. When compared with standard T₂ quantification techniques, the proposed method is fast, reliable, and robust against partial volume effects.

INTRODUCTION

Since the first report by Wright et al. (1), there has been an increasing interest in developing faster and more robust methods to quantify the oxygenation level of blood. Such measurements, especially in large venous vessels, can provide valuable information on oxygen delivery to, and its consumption in, vital organs. Recently, several groups have combined this information with blood-flow measurements to obtain additional insights into organ energy metabolism in response to physiologic challenges as well as in a number of pathologic conditions (2–7).

Current intravascular MR-based methods for evaluating oxygen saturation (HbO₂) in large blood vessels can be broadly grouped into phase-based and T₂-based methods. The major strengths of phase-based methods are their robustness, acquisition speed and temporal resolution (8). These methods are based on an exact solution of Laplace’s equation for the scalar magnetic potential for an infinitely long circular cylinder, yielding a simple equation of the differential induced field inside relative to that outside the vessel. The induced field is translated to oxygen saturation values using a whole-blood susceptibility model (9,10). However, knowledge of exact vessel orientation with respect to the main B₀ field and suitable surrounding reference tissue are needed to accurately quantify HbO₂. Additionally, the method is sensitive to static field inhomogeneities caused by tissue interfaces. For example, air-tissue interfaces in the neck make the HbO₂ measurements in jugular vein challenging.

T₂-based methods overcome some of the above restrictions on vessel orientation and the need for reference tissue. These methods aim to quantify intravascular trans-verse relaxation of blood caused by protons diffusing through spatially varying magnetic field gradients. Such field gradients are created as a result of the frequency shifts between intra- and extra-erythrocyte spaces due to the paramagnetism of deoxygenated hemoglobin (11). However, most T₂ based methods are limited in their application by long acquisition times and sensitivity to partial volume effects from surrounding tissues (1,12,13).

Here, we propose a fast method for in vivo blood T₂ quantification via computing the complex difference of velocity-encoded projections. The proposed method is quick, robust, and immune to tissue-induced partial-volume effects.

METHODS

Theory

The oxygenation dependence of T₂ of blood arises due to irreversible dephasing of water protons as they exchange/diffuse through the magnetic field gradients induced by paramagnetic deoxyhemoglobin. The echo generated from a Carr-Purcell-Meiboom-Gill (CPMG) sequence, can be described on the basis of the Luz-Meiboom model that invokes exchange of spins between two sites differing in resonance frequencies as (14):

$$R_{2\mathrm{b}}=R_{20}+P_{\mathrm{A}}(1-P_{\mathrm{A}}){\tau }_{\text{ex}}{\left[\right(1-\%{\mathrm{HbO}}_2∕100\left){\alpha \omega }_0\right]}^2\times \left(1-\frac{2{\tau }_{\text{ex}}}{{\tau }_{180}}\tan h\frac{{\tau }_{180}}{{\tau }_{\text{ex}}}\right)$$ [1]

where R₂₀ is the R₂ = (1/T₂) of fully oxygenated blood, P_A is the fraction of protons resident at one of the sites under exchange, τ_ex is the average exchange time between the two sites, ω₀ is the Larmor frequency, α is a constant dependent on the geometry of erythrocytes and susceptibility of deoxyhemoglobin, and τ₁₈₀ is the interval between consecutive 180° refocusing pulses. Some of the parameters in the above equation such P_A, α, τ_ex, etc. are difficult to determine experimentally. Wright et al. (1) proposed a calibration method to determine oxygen saturation of blood without exact knowledge of all these parameters by combining them into a single constant K as:

$$R_{2\mathrm{b}}=R_{20}+K(1-\%{\mathrm{HbO}}_2∕100)$$ [2]

Using the above model several groups have computed coefficients R₂₀ and K by quantifying R₂ at various known %HbO₂ levels in an ex-vivo experiment and used this calibration curve for in vivo blood oxygenation measurements (1,15,16).

As a modification to the standard method for T₂ quantification, using a CPMG based T₂-preparation sequence to acquire images at different echo times, we propose a quicker single-projection method in this investigation. As blood flows continuously, its signal can be robustly isolated from the surrounding tissue by computing the complex difference of two central k-space lines (k_y = 0) with different velocity encodings (VENC) (17). The resultant signal can then be measured as a function of effective echo time (TE_eff) for quantifying T₂ of blood. The magnitude of complex difference (CD) of the signal with two different velocity encodings can be denoted as:

$$\mathrm{CD}=2Z\mid \mathrm{Sin}(\pi v∕2\mathrm{VENC})\mid$$ [3]

where Z is weighted by spin density, sequence parameters (flip angle, TE, TR) and relaxation times T₁ and T₂ and v represents the blood flow velocity. Assuming flow and other sequence parameters remain constant for successive echoes, complex difference processing can be used to estimate T₂ of the flowing spins. Signal variations due to flow can be minimized by choosing VENC close to the average velocity in the vessel (due to sinusoidal dependence of CD on velocity).

MR Protocol

All experiments were performed on a 3T Siemens TIM Trio scanner. A peristaltic pump (Masterflex L/S Digital Drive, HV-07523-80, Cole Parmer, Vernon Hills, IL) connected to a function generator (Model 4075, B&K Precision, Yorba Linda, CA) was used to generate pulsatile flow and placed outside the scanner room. A sinusoidal wave function of 1 Hz frequency was used to mimic venous flow waveforms. The amplitude of the function was varied to achieve different levels of pulsatility. A 0.12 mM MnCl₂ solution was pumped via silicone tubing (Masterflex, Cole Parmer, Vernon Hills, CA; ID: 6.4 mm) inside the bore of the scanner where the tubing was wrapped in Gd-doped saline bags to mimic the tissue surrounding blood vessels. The various resultant flow waveforms are shown in the Figure 1. Prior to conducting the flow experiment using the proposed projection method, T₂ of the MnCl₂ solution was determined using the standard method for measuring T₂ (T₂ preparation followed by full k-space readout).

FIG. 1.

Average flow waveforms obtained using the peristaltic pump. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Eight healthy human volunteers (age = 27 ± 4 years) participated in the study approved by Institutional Review Board (IRB) of University of Pennsylvania. Resting-state T₂ measurements were performed in each subject in the superior sagittal sinus (SSS), straight sinus (SS), and internal jugular vein (IJV) using the proposed projection method. The measurements in the SSS were repeated three times in each subject to test the reproducibility of T₂ measurements in vivo. A multi-axial localizer scan was used to select slices where the vessel segments were approximately straight and the direction of flow perpendicular to the slice orientation to ensure maximal signal and a laminar flow profile. The subject was asked to rise from the scanner table before being repositioned prior to each repeat scan. A cushioned head stabilizer was used to minimize motion and the subjects were instructed to stay alert during the course of the experiment as cerebral oxygenation is known to vary with the level of consciousness.

Additionally, changes in blood oxygenation in response to a hypercapnia challenge (5% CO₂) were evaluated in the SSS of five subjects. The experimental setup was similar to that used in a previous hypercapnia study in the authors’ laboratory (7). The paradigm consisted of three phases: normocapnia (baseline), hypercapnia, and normocapnia (recovery) for durations of 3, 5, and 4 min, respectively. End-tidal CO₂ (EtCO₂), heart rate and arterial oxygen saturation (S_aO₂) were monitored throughout the experiment using an MR-compatible physiological monitoring system (Precess, Invivo, Orlando, FL). Data acquisition during hypercapnia began ~2–3 min after the subject had started breathing in the gas mixture once the EtCO₂ reading stabilized. This protocol ensured that data collection occurred during a hypercapnic steady-state.

In order to evaluate the accuracy of the projection method with the standard method (T₂ preparation followed by full k-space readout as described by Qin et al. (15), however to ensure exactly the same TE between the two compared methods a single k-space line was acquired for each TR instead of a multi-shot EPI acquisition), two subjects were imaged again in a separate scanning session. T₂ measurements in the SSS were conducted in the same scan session using both methodologies. Also a gated phase-contrast sequence was used to obtain velocity profiles of the three vessels investigated in the study (SSS, SS, IJV).

Sequence Design

The sequence used for preparing T₂ magnetization was similar to that used by Qin et al. (15) (including the timing of various sequence parameters), consisting of a slice-selective saturation pulse with a dephasing gradient followed by a series of non-selective T₂ preparation pulses (τ_CPMG = 10 ms). Following slice-selective excitation, a velocity-encoded projection (e.g., at +VENC) was acquired. Finally, a nonselective global saturation pulse with a dephasing gradient was used to reset the longitudinal magnetization and thus effectively remove any spin history from previous pulse sequence cycles. The above was repeated for −VENC, and so forth, for each TE_eff. The main difference in the present implementation is that instead of full k-space readout, two velocity-encoded projections were obtained for each TE_eff. It is noted that similar to Qin et al. (15), a saturation delay of 200 ms was used. This saturation delay is optimal for all vessels investigated in this study. We have not encountered velocities below 6–7 cm/s in any of the three venous vessels in healthy adults. For a slice thickness of 5 mm, the chosen saturation delay would be adequate for velocities as low 3 cm/s. Additionally, it is noted that the use of a saturation pulse in the current application is not critical as the complex difference subtraction is very effective in suppressing the background tissue signal. However, the saturation pulse was used to enable direct comparison of the present method with that of Qin et al. (15) (for in vivo studies) and to ensure maximum possible tissue suppression.

Sequence parameters: FOV = 176 × 176 mm², number of readout points = 208, TE_eff 20, 40, 80, and 160 ms, VENC = 15 cm/s (flow phantom), 20 cm/s (flow phantom, SSS), 40 cm/s (SS), 15 cm/s (IJV), 45 cm/s (SSS, hypercapnia) cm/s, nominal scan time = 1875 ms (TR) × (velocity encodes) × 4 (TE_eff) s ~15 s, NEX = 3 (SSS), 3 (SS), 6 (IJV). It is noted that the use of composite pulses can lead to overestimation of T₂ due to short periods in refocusing during which the magnetization is transiently stored on the longitudinal axis. During these periods, the magnetization evolves with a time constant T₁ instead of T₂. To correct for these effects, echo times TE_corr = 18.3, 36.6, 73.2, 146.5 ms were used for T₂ fitting (15,18). Additionally, in order to accurately measure T₂ using the proposed method, it is important that the average flow in the vessel be similar for different TEs. Hence a metric that represents the level of pulsatility in flow in the blood vessel was used to determine NEX (number of complex difference averages per TE). NEX was calculated using a standard error formula based on the mean (μ) and standard deviation (σ) of the complex difference of the vessel signal over several cardiac cycles (acquired using a high temporal-resolution velocity mapping method (19) with a temporal resolution of 20 ms) as $\mathrm{NEX}={\left(\frac{0.05\times \mu }{\sigma }\right)}^2$. A standard error of 5% in the T₂ measurement was deemed acceptable. This level of error would correspond to an absolute error of ~4 ms in T₂ and hence 2.2% HbO₂ points in blood oxygenation measurements (for a blood T₂ ~65 ms).

Data Analysis

The pulsatility index (PI) of the flow waveforms obtained using the flow phantom and in vivo was quantified as:

$$\mathrm{PI}=\frac{{\text{velocity}}_{\max }-{\text{velocity}}_{\min }}{{\text{velocity}}_{\mathrm{avg}}}$$ [4]

Complex difference subtraction of velocity-encoded projections taken at four values of TE was logarithmically transformed and T₂ extracted using a weighted least square fit. Finally, T₂ measurements were converted to HbO₂ values using a calibration equation (Eq. [2]) reported previously using similar sequence parameters for a hematocrit (Hct) of 0.46 (15) as:

$${\mathrm{HbO}}_2=\left(1-\sqrt{\frac{(1∕T_2-7.18)}{59}}\right)\times 100$$ [5]

Analysis of Variance (ANOVA) was used to statistically compare the mean HbO₂ values in the three tested cerebral veins; SSS, SS, and IJV. Within subject coefficient of variation (CV) and intra-class correlation coefficient (ICC) were used to test reproducibility in the SSS. Lastly, a three-point moving average algorithm was used to plot changes in HbO₂ in response to hypercapnia.

RESULTS

T₂ of the MnCl₂ doped water (stationary) was determined to be 68.5 ± 1.9 ms. Measured T₂ values in the MnCl₂ doped water circulated through the pulsatile flow phantom using the proposed projection method are listed in Table 1. Comparison of T₂ measurements using standard (full k-space) and projection methods in SSS is tabulated in Table 2.

Table 1.

Measured T₂ Values and Errors in Comparison to the Gold Standard (No Flow Condition) in MnCl₂ Doped Water Flow Phantom with Variable Pulsatility Indices (PI)

	Flow 1	Flow 2	Flow 3	Flow 4
T2 (ms)	69.5 ± 1.4	69.2 ± 4.3	70.6 ± 5.6	71.4 ± 3.8
Error (ms)	1	0.7	2.1	2.9
PI (%)	4.0	38.7	47.0	52.7

Table 2.

T₂ (ms) and HbO₂ (%) Measurements in SSS Using Standard and Projection-Based Readout Methods

		ms	%
Subject 1	Standard	65 (5)	62 (3)
	Projection	62 (7)	61 (4)
Subject 2	Standard	68 (2)	65 (1)
	Projection	71 (5)	66 (3)

The standard error in each measurement is reported in parentheses.

Representative flow profiles obtained in various venous vessels are reported in Figure 2. Steps undertaken to obtain T₂ values are highlighted in Figure 3. Average T₂ and HbO₂ values in SSS, SS, and IJV of eight subjects were 67 ± 7%, 77 ± 9%, and 70 ± 7 ms, and 63 ± 3%, 68 ± 4%, and 65 ± 4%, respectively. The average HbO₂ values in SSS were significantly lower than in the SS (P = 0.038) (Table 3). The mean CV and ICC of repeated HbO₂ measurements in the SSS were 3% and 0.914, respectively. Average HbO₂ values in SSS during baseline, hypercapnia, and recovery were 63 ± 2%, 79 ± 5%, and 61 ± 3%, respectively. A significant undershoot in HbO₂ values during recovery was observed in two subjects (Fig. 4). Average change in EtCO₂ in response to hypercapnia was 13 ± 5 mm of Hg.

FIG. 2.

Average velocity profiles of internal jugular vein (IJV), superior sagittal sinus (SSS) and straight sinus (SS). The pulsatility indices (PI) of the three vessels were 37, 31, and 23%, respectively. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

FIG. 3.

Magnitude images of the slices used for imaging: (a) SSS; (c) SS; (e) IJV. Red arrow indicates the projection direction. Corresponding T₂-weighted projections at TE_eff = 20, 40, 80, and 160 ms (zoomed in top to bottom, panels b, d, and f). (g) The signal in (b) plotted against different TE_corrs.

Table 3.

T₂ (ms) and HbO₂ (%) Measurements in SSS, SS, and IJV with the Standard Error in Each Measurement Reported in Parentheses

	SSS		SS		IJV
	ms	%	ms	%	ms	%
Subject 1	56 (5)	57 (3)	66 (5)	63 (3)	63 (3)	61 (2)
	58 (6)	59 (4)
	60 (5)	60 (3)
Subject 2	75 (9)	68 (4)	80 (4)	70 (2)	74 (8)	67 (4)
	72 (5)	66 (2)
	70 (3)	65 (1)
Subject 3	59 (4)	60 (2)	63 (11)	62 (6)	58 (12)	59 (7)
	56 (4)	58 (3)
	56 (5)	57 (3)
Subject 4	69 (8)	65 (4)	81 (10)	70 (5)	77 (5)	69 (2)
	69 (9)	65 (5)
	69 (9)	65 (4)
Subject 5	67 (4)	64 (2)	87 (6)	73 (2)	75 (4)	68 (2)
	64 (7)	62 (4)
	68 (8)	64 (4)
Subject 6	72 (5)	67 (3)	85 (5)	72 (2)	78 (4)	69 (2)
	73 (6)	67 (3)
	73 (4)	66 (2)
Subject 7	70 (6)	65 (3)	74 (5)	67 (3)	66 (3)	63 (2)
	68 (5)	64 (3)
	68 (8)	64 (4)
Subject 8	70 (5)	65 (2)	76 (3)	68 (1)	71 (4)	66 (2)
	68 (5)	64 (2)
	68 (5)	65 (2)
Average (SE)	67 (7)	63 (3)	77 (9)	68 (4)	70 (7)	65 (4)

Measurements at the SSS were repeated thrice to test measurement precision.

FIG. 4.

Time-course of HbO₂ changes in SSS in response to hypercapnia (5% CO₂) obtained at a temporal resolution of ~15 s. The shaded area represents the hypercapnic episode. It is noted that hypercapnia was preceded (~2–3 min) and followed (<1 min) by periods during which data acquisition was suspended. The error bars represent the standard error in the HbO₂ measurements.

DISCUSSION

In this study, we demonstrated a rapid, robust, noninvasive MR based method for estimating venous oxygen saturation via T₂ mapping in large blood vessels with low flow pulsatility, a condition met for most cerebral veins. The accuracy and robustness of the method was evaluated using a pulsatile flow phantom. Additionally, we illustrated that the method is sensitive to physiologic perturbations in oxygen saturation in response to a hypercapnia challenge. The main advantage of the method when compared with conventional T₂ based methods is its speed and hence ability to obtain physiologically relevant oxygen saturation information with a high temporal resolution at arbitrary anatomic locations. Additionally, the method is robust against partial volume effects as only signal from moving blood is detected (complex difference).

HbO₂ was measured in three veins representing different cerebral drainage territories. The superior sagittal sinus receives venous drainage from superficial cortical veins over both cerebral hemispheres (i.e., the majority of the cerebral hemisphere’s gray matter mantle). In contrast, the straight sinus mostly drains the deep cerebral venous system as well as some areas of the upper brainstem through the confluence of the vein of Galen and the inferior sagittal sinus. The straight sinus then joins the superior sagittal sinus posteriorly at the torcula (confluence of the sinuses). This venous outflow is directed towards the sigmoid sinuses and finally the internal jugular veins (Schaller, 2004).

HbO₂ measurements in the SSS and IJV were found to be in good agreement with previous studies (6,12,15,20). To the best of our knowledge, however, this is the first report of HbO₂ measurements in the SS. It is interesting to note variations in HbO₂ between different cerebral veins. The average HbO₂ values in the SS were higher than those in the SSS (P = 0.038). The IJV, which represents the weighted sum of venous outflow from SSS and SS (in addition to other veins, e.g., superior and inferior petrosal sinuses), was observed to have HbO₂ values in general intermediate between those of the SSS and SS. While we have no literature values to compare our SS measurements with, previous PET based studies (21,22) have shown that deep brain structures such as pontine nuclei, midbrain, parahippocampal gyri, and thalami have significantly lower oxygen extraction fractions than cerebral cortices. While the reasons for such oxygenation differences are not well understood, it is noteworthy that these structures represent more conserved parts of the brain. Since these structures deal with basic activities needed to sustain life such as cardiovascular system control, consciousness, etc., it is plausible that these structures receive higher perfusion and hence have lower oxygen extraction fractions (OEF) when compared with more evolved structures such as cerebral cortices. Significantly higher perfusion in deep brain structures has also been noted in previous PET based studies.

We also investigated the effect of hypercapnia on venous oxygenation. CO₂ is a potent arteriolar vasodilator and thus increase in blood pCO₂ causes a drop in vascular resistance and concomitant increase in cerebral blood flow (23). Assuming that CO₂ does not alter cerebral metabolism, this increase in blood flow is accompanied by an increase in venous oxygenation as well. The observed changes in HbO₂ in response to the hypercapnia challenge are in agreement with known physiological principles and previous results (2,3,7). Interestingly, we observed a distinct undershoot in HbO₂ upon recovery from hypercapnia in two subjects. This phenomenon has been reported previously (7). It is noted that this change in HbO₂ is accompanied by a change in blood flow as well and could potentially yield incorrect T₂ values. However, our previous hypercapnia data indicates that blood flow velocity changes insignificantly during a single T₂ measurement period and hence is not likely to affect the fidelity of our T₂ estimates (increase in mean blood flow velocity in the internal carotid arteries during recovery from hypercapnia was observed to be ~0.05 cm/s², hence the change in velocity during the 15s data acquisition period will be <1 cm/s (7)). Additionally, the gradual change in HbO₂ during recovery and lack of scatter in the calculated HbO₂ values as it rises towards the baseline value reinforces our confidence that the observation is real.

The method has some limitations. The technique relies on a general assumption of constant blood flow velocity during acquisition of consecutive TE_effs (i.e., at least over 15s period). However, some oscillation/pulsatility in flow is always present in blood vessels. Pulsatility is lower in veins than in arteries and as such even lower in cerebral vessels. To decrease the sensitivity of the T₂ measurement to flow variations, we chose a VENC close to the average velocity in the vessel. Under these conditions, fluctuation in computed complex difference signals due to flow variations is minimized (Eq. [3]). Also, signal averaging was used to reduce the effect of pulsatility in flow. Additionally, using a nonsteady flow phantom, we demonstrate that the method is robust to flow fluctuations with a PI values of up to 50%. This PI is higher than that observed in the investigated venous vessels in our healthy young subjects (typically <40%). However, it should be noted that the flow phantom may have underestimated the effect of flow pulsatility especially in situations where the peaks and troughs in flow occur over a short duration of time. This might limit the applicability of the method in certain pathological conditions that are associated with increased venous flow pulsatility such as diseases which result in reduced intracranial compliance. Simulations to model the effect of flow variations on T₂ values (assuming a normal distribution of flow velocities with a worst case scenario of 30% standard deviation about mean) yielded a coefficient of variation ~7% in T₂ estimates (assuming T₂ = 65 ms, NEX = 3). Typical fluctuation in complex difference signal over several cardiac cycles was <10% in the SS and SSS and <30% in IJV using a high temporal resolution phase-contrast velocity mapping sequence (19).

Another pitfall of the method is that since it relies on projections the vessels can be spatially resolved in only one dimension. Hence, one needs to appropriately choose a projection direction to avoid vessel overlap. This constraint might be particularly challenging if trying to determine HbO₂ in thoracic vessels. However, this was less of a concern for the current application. Intracranial vascular anatomy is unique in that major venous and arterial pathways infrequently run parallel to each other. Hence, for most cranial veins one can almost always find a projection direction with no major vessel overlap. The contribution from smaller skull based veins with very low flow can be neglected since a much larger VENC is employed. The situation is more challenging in the case of the IJV as the internal carotid arteries tend to run parallel in most of the neck. However, we observed that higher in the neck, it was easier to find a projection direction (at least for one of the two IJVs) with no vessel overlap.

Lastly, it should be noted that HbO₂ values derived from T₂ measurements rely on empiric calibration curves that are hematocrit level specific. While it is reasonable to use a calibration curve pertaining to mean values in healthy adults, caution must be exercised in populations where variability in Hct from normal values might be expected. Additionally, it is noted that at higher blood oxygenation levels errors in translating T₂ to HbO₂ values due to differences from assumed Hct increase.

In conclusion, we introduced a fast, robust, and reliable method to determine HbO₂ with a high temporal resolution in blood vessels with low flow pulsatility. The method demonstrated sensitivity to detect oxygenation differences between different cerebral drainage territories (cortex vs. deep brain) as well as in response to a hypercapnic stimulus. Potential clinical applications extend to the study of pathologic conditions affecting cerebral metabolism, for example, neurodegenerative conditions such as Alzheimer’s dementia, Parkinson’s disease, multiple sclerosis, etc.