Quantification of Whole-Brain Oxygenation Extraction Fraction and Cerebral Metabolic Rate of Oxygen Consumption in Adults with Sickle Cell Anemia using Individual T₂-based Oxygenation Calibrations

Abstract

Purpose:

To evaluate different T₂-oxygenation calibrations for estimating venous oxygenation in people with sickle cell anemia (SCA).

Methods:

Blood T₂ values were measured at 3T in the internal jugular veins of 12 healthy volunteers and 11 SCA participants with no history of stroke, recent transfusion, or renal impairment. T₂-oxygenation relationships of both sickled and normal blood samples were calibrated individually and compared with values generated from published models. After converting venous T₂ values to venous oxygenation, whole-brain oxygen extraction fraction (OEF) and cerebral metabolic rate of oxygen (CMRO₂) were calculated.

Results:

Sickle blood samples’ oxygenation values (Y) calculated from our individual calibrations agreed well with measurements using a blood analyzer, while previous T₂ calibrations based on normal blood samples showed 13–19% underestimation. Meanwhile, Y values calculated from previous grouped T₂ calibration for sickle blood agreed well with experimental measurement on averaged values, but showed up to 20% variation for several individual samples. Using individual T₂ calibrations, the whole-brain OEF and CMRO₂ of SCA participants were 0.38+/−0.08 and 172+/−42μmol/min/100g, respectively, which were comparable to those values measured on normal volunteers.

Conclusion:

Our results confirm that sickle blood T₂ values not only depend on Hct and Y, but also on other hematological factors. The individual T₂ calibrations minimized the effect of heterogeneity of sickle blood between different SCA populations and improved the accuracy of T₂-based oximetry. The measured OEF and CMRO₂ of this group of SCA participants were found to not differ significantly from those of healthy people.

INTRODUCTION

Sickle cell anemia (SCA) is an inherited blood disorder that is characterized by the presence of two genes for hemoglobin S (HbS). It not only causes the abnormal shape (sickled) of erythrocytes, but also significant hemolysis. This decreases the hematocrit (Hct, the volume fraction of erythrocytes in blood), and thus the arterial oxygen content. In response to this low arterial oxygen content, autoregulation causes elevated cerebral blood flow (CBF) to normalize oxygen delivery in SCA^1–9. When oxygen delivery can no longer be maintained, the oxygen extraction fraction (OEF) increases to preserve oxygen delivery, very similar to acute ischemia in non-SCA populations^10–15. As such, OEF may be a marker of inadequate cerebrovascular reserve in SCA and an indicator of increased risk of cerebral dysfunction and ischemia induced due to the lack of tissue oxygen^8,16. Positron emission tomography (PET) is able to measure CBF, oxygen extraction fraction (OEF) and cerebral oxygen metabolic rate (CMRO₂)¹⁷, but is invasive, expensive and not widely available. Oxygen-15 PET has been applied to study the cerebral oxygen utilization of SCA patients and no significant differences of OEF and CMRO₂ were found when comparing a small group of patients with SCA and normal adults².

MRI oximetry using either T₂*^18–23 or T₂^24–33 provides an alternative to measure OEF non-invasively. This approach is based on the principle that hemoglobin changes its magnetic property from paramagnetic to diamagnetic when binding oxygen, thereby altering water T₂ and T₂*. A T₂* oximetry method based on asymmetric spin echo (ASE) acquisition³⁴ has been used to measure the OEF in children with SCA^7,35,36, however, increased iron deposition in tissue of SCA patients would reduce tissue T₂*³⁷ and this could lead to bias and limit its application in SCA.

The T₂ oximetry method could alleviate this problem, as it is independent of the tissue environment. The blood T₂ value measured from a large vein can be converted to oxygenation (Y) through a predefined calibration based on the dependence of T₂ on both Y and Hct^24–32. Therefore, a proper calibration is crucial to obtain a reliable oxygenation measurement. Previously, sickle blood was assumed to have blood T₂ calibration similar to normal blood³⁸. Using an existing T₂ calibration developed from normal blood³⁹, elevated OEF values were reported for the SCA volunteers, both with blood transfusion and without blood transfusion^38,40,41, however, another study⁴² measured T₂ values of sickle blood samples, showing a ~20% shorter T₂ value of sickle blood than T₂ value of normal blood at the same Hct and Y. Based on these in vitro data, they developed a group-based T₂ calibration specific for sickle blood and observed reduced OEF and CMRO₂ of SCA patients⁴².

The discordant findings of OEF among SCA patients from the few MRI studies^38,40–42 is perplexing. One possibility explaining the discrepancy could be the heterogeneity of sickled blood composition between different SCA participants. Sickled blood contains erythrocytes with normal shape (biconcave disk) in addition to those reversibly and irreversibly sickled. The percentage of these sickled erythrocytes highly varies depending on multiple factors, such as the concentration of HbS and fetal hemoglobin (HbF) in erythrocytes, which differs among individual erythrocytes in the same SCA patient^43,44. It has been shown that blood T₂ values also depend on the shape of erythrocyte⁴⁵. Meanwhile, aggregation of HbS under deoxygenated conditions also shortens blood T₂ values⁴⁶. This dependence of T₂ values of blood on factors other than Y and Hct should be taken into account when studying sickled blood and indicate that calibrations from normal blood may not be correct.

To take into account the heterogeneity of sickle blood T₂-Y relationships between different SCA participants, we measured the Y dependence of sickle blood T₂ for each subject and used the individual T₂-Y calibration to convert the venous T₂ value to Y_v for each SCA participant. Using this method, we determined whole-brain OEF and CMRO₂ for 11 SCA participants and compared the results with those obtained from 12 healthy participants.

Methods

In Vivo Experiments

Experiments were performed on a 3T Philips Achieva scanner (Philips Medical Systems, Best, Netherlands) using a 32-channel head coil for signal reception and the body coil for radiofrequency transmission. Twelve healthy volunteers (35 ± 7 yrs; 6M / 6F; Hct: 0.42 ± 0.04) and eleven subjects with SCA with no history of stroke, recent transfusion, or renal impairment (25 ± 7 yrs; 4M / 7F; Hct: 0.27 ± 0.04; sickle hemoglobin (HbS): 82.7% ± 6.4%; fetal hemoglobin (HbF): 8.7% ± 4.3%) participated in this study after providing informed written consent in accordance with local Institutional Review Board guidelines.

For the scan planning, phase-contrast magnetic resonance angiogram (PC-MRA) survey images were acquired in both sagittal and coronal planes to visualize the location and orientation of internal jugular veins (IJVs), using the acquisition parameters: slab thickness = 50 mm, TR/TE = 20/6.3 ms, FOV = 250 × 250 mm², and scan matrix of 256 × 128 (acquisition time: 20 s × 2).

Venous blood T₂ was measured in the right IJV using a 5 mm axial slice perpendicular to it for localization, using an MRI protocol with a T2prep module that played out with five different echo times (TEprep = [20, 40, 80, 120, 160] ms) and a constant inter-echo spacing of 10 ms as described previously²⁶. Composite refocusing pulses, 90°_x180°_y90°_x, and MLEV-16 phase cycling were used in the T2prep module for reliable refocusing in vivo and the corrected echo times (TE_corr = [18.3, 36.5, 73.0, 109.6, 146.1] ms) were used to take into account of the pulse length of the refocusing composite pulse^26,47. Following the acquisition, a tailored hard-pulse train⁴⁸ for global saturation (65°, 83°, 143°, 162°) resets the remaining magnetization to zero, with a fixed delay of 2 sec to ensure a constant initial longitudinal magnetization before T2prep module. The acquisition parameters were: FOV = 169 ×169 mm², in-plane resolution = 0.8 × 0.8 mm², TR/TE/FA = 13 ms/ 7.6 ms/ 50°, sensitivity encoding (SENSE) factor = 2, multi-shot turbo field echo (TFE) acquisition with 7 shots and TFE factor = 15, the acquisition window for each shot was about 195 ms. The total acquisition time was 1 min.

Although the SCA participants have faster flow than normal participants we studied previously²⁶, the T₂ preparation (CPMG) module in this protocol used global refocusing pulses, which means all venous blood in the brain experienced the same T₂ decay during the T₂ preparation module. This T₂ preparation module was short, varying from 20ms to 160ms. During this short time, all the blood in the imaging plane experienced the same T₂ preparation; therefore, there should be not significant flow effect on our T₂ measurement.

To evaluate the reliability of this T₂ protocol ²⁶ on SCA participants, we recruited three SCA participants, and repeatedly measured T₂ values at IJV three times consecutively during the same session.

In order to obtain the baseline whole-brain CBF, phase-contrast MRI (PC-MRI) was used to measure the blood flow rates at the bilateral internal carotid arteries (ICA) and vertebral arteries (VA). Four runs of 2D PC MRI were planned perpendicular to the corresponding arteries as described previously ⁴⁹ with the acquisition parameters: slice thickness = 5 mm, FOV = 200 × 200 mm², in-plane resolution = 0.5 × 0.5 mm², TR/TE/FA = 19 ms / 9 ms / 15°. The encoding velocities were 60 cm/s (ICA) and 40 cm/s (VA) for healthy volunteers and 100 cm/s (ICA) and 60 cm/s (VA) for SCA participants, respectively. In addition, a T₁-weighted magnetization prepared rapid gradient-echo (MPRAGE) scan was added for brain gray matter volume estimation to obtain a unit volume CBF value, using the acquisition parameters: TR/TE/FA = 12 ms / 3.2 ms / 9°, shot interval = 1720ms, inversion time (TI) = 1100 ms, FOV = 220 × 220 × 180 mm³, nominal voxel size of 1.1 mm isotropic, SENSE factor = 2 × 2, duration of 5 min.

In Vitro Experiments

Four 4 mL-tubes of blood were collected from the antecubital vein of all participants right before their MRI scans. Two tubes of blood anticoagulated using EDTA were sent to the hospital’s pathology laboratory to have a complete blood count (CBC) for all subjects and a hemoglobin variant quantification for SCA subjects only. The other tubes of blood were anticoagulated with lithium heparin and stored at room temperature. They were used for in vitro experiments on the same day as the in vivo measurements. Following a previous protocol⁵⁰, the oxygenation of the blood samples was first adjusted using air or N₂ gas moisturized by PBS buffer. Then the blood samples (2~3mL) were sealed in a tube with a diameter of 1 cm and equilibrated at 37.8 °C water bath for 5 min before the MRI measurement. During the MRI experiment, the blood tube was placed in a 1L water bath (37.8 °C) to maintain the temperature. After MRI experiments, the oxygenations of blood samples were immediately measured using a blood analyzer equipped with co-oximetry (ABL800, Radiometer). For each sickle blood sample, 5–7 oxygenations were prepared to cover the oxygenation range from ~50% to ~100%.

It is worthy to note that because the erythrocytes’ volume changes at different oxygenations, the Hct definition used in the blood analyzer (i.e. Hct is equal to the total hemoglobin concentration divided by 33.2g/dL), was used in this study.

A two-channel shoulder coil was used for signal reception in the in vitro experiments. The T₂ of blood samples were measured using a pulse sequence with a T2prep module similar to the in vivo experiments. Two-shot TFE (TR/TE/FA = 15 ms/2.5 ms/8°, TFE factor = 20) was used to acquire a 2D image of 3 mm thick with FOV of 64 × 120 mm² and a resolution of 1 × 2 mm². A sagittal slice was acquired, which was used to check whether there was erythrocyte settlement by evaluating the blood T₂ values vertically (Supporting Information Fig. S1)⁵⁰. The scan time was 27 s for each oxygenation level. The complete MRI measurement, including placing the sample into MRI scanner, survey scan and T₂ scan, was controlled to be under 2 min to prevent the settling of erythrocytes.

Data Analysis

Matlab (MathWorks, Natick, Massachusetts, USA) was used for data processing. T₂ values were obtained from mono-exponential fitting of the MRI signal as a function of effective TE at both in vivo and in vitro experiments.

To establish an analytical relationship between Y and T₂ for each individual, the in vitro T₂ data for the blood samples from the same volunteer with different oxygenation levels were fitted to an empirical model²⁸:

$$R_2=1/T_2=A_1\times {\left(1-Y\right)}^2+A_2$$ Eq. 1

where R₂ was the measured T₂ relaxation rate (1/T₂) and A₁ and A₂ were the fitting parameters which are characteristic for each volunteer.

In addition to the individual T₂ calibration, previously reported T₂ calibrations for normal blood ^39,51 and sickle blood⁴² were used to calculate Y, and the values (Y_Cal) from different calibration approaches were compared with the observed Y (Y_Observe) obtained from the blood analyzer.

Note that the previous T₂ calibrations^39,42,51 were built from apparent T₂ (T_2,app) without correcting the pulse width (pw) of refocusing pulses in a CPMG sequence⁴⁷. To compare different T₂ calibrations, our measured corrected T₂ (T_2,corr) values that take into account the refocusing pulse lengths should be converted to the T_2,app values that were used in the previous T₂ calibrations. Since the inter-echo spacing between refocusing pulses (τ_cp) and pw of refocusing pulses used in the previous experiments^39,50,51 were the same (τ_cp: 10 ms; pw: ~1.74 ms), the relationship between T_2,app and T_2,corr can be calculated as

$$T_{2,app}=T_{2,corr}/k$$ Eq. 2

where k = 1 - pw/(2×τ_cp) = 1 – 1.74/(2×10) = 0.913 ^26,47. Using Eq.2, the T_2,corr can be simply scaled to T_2,app that is suitable to calculate Y using the previous T₂ calibrations^39,42,51.

The venous oxygenation (Y_v) of SCA participants was calculated by substituting the in vivo measured T₂ value in the IJV into their own T₂–Y calibration. OEF was calculated using

$$OEF=\left(Y_a-Y_v\right)/Y_a$$ Eq. 3

assuming an arterial blood oxygenation Y_a of 0.98.

In order to obtain baseline whole-brain CBF, the fluxes of ICAs and VAs were extracted from PC-MRI data following the method used in a previous study ⁴⁹. An ROI was drawn on each of these four main feeding arteries based on magnitude image and used to create an ROI mask. The velocity values within this ROI mask were integrated to yield the flux (mL/min) for each artery. To calculate CBF value, the image from the MPRAGE experiment was segmented using the software FSL (FMRIB software Library, Oxford University) and the brain’s total parenchymal volume was estimated by the sum of gray and white matter volumes and converted to the weight of the brain using a parenchymal density of 1.06g/mL⁵². The CBF (mL/min/100g) was then calculated by normalizing the main arterial blood flux to the brain parenchymal mass.

CMRO₂ (μmol/min/100g) was then calculated using the equation introduced by Kety and Schmidt ⁵³ based on the Fick principle of arteriovenous oxygen difference:

$$CMR{O}_2=Ca{O}_2\times CBF\times OEF$$ Eq. 4

where CaO₂ (μmol/mL) is the arterial oxygen content which represents the amount of oxygen that a unit volume of arterial blood can carry. Considering one tetramer of hemoglobin can carry four oxygen molecules, CaO₂ is calculated based on the hemoglobin concentration in the blood (ctHb, g/L) as

$$Ca{O}_2\left(\text{μmol}/\text{mL}\right)=4\times \frac{ctHb\left(g/L\right)\times {10}^{-3}L/mL}{64.5\times {10}^{3}g/mol\times {10}^{-6}mol/\text{μmol}}\times Y_a$$ Eq. 5

where 64.5×10³g/mol is the molecular weight of hemoglobin tetramer, which is the same for normal and sickle hemoglobin.

The oxygen delivering rate DO₂ (μmol/min/100g) can be calculated as

$$D{O}_2=CBF\times Ca{O}_2$$ Eq. 6

An F-test was used to test the homogeneity of group variance for differences between in vitro measured Y and calculated Y based on different T₂ calibrations. The intraclass correlation coefficient (ICC) was calculated for three repeated T₂ measurements on each SCA participants to evaluate the reliability. The Wilcoxon rank-sum test was used to evaluate the group difference on OEF, CBF and CMRO₂ between healthy volunteers and SCA participants.

Results

Figs. 1a and b show representative images acquired at the shortest TE_corr for the in vivo and in vitro experiments from one SCA participant, respectively. The T₂ values were obtained from fitting the signal intensities in the IJV (Fig. 1c) or the blood tube (Fig. 1d) as a function of corrected TE. For in vitro scan of Fig. 1b, three smaller ROIs were chosen from the top to the bottom of the tube, and their T₂ values were fitted separately (Supporting Information Fig. S1) and found to be similar, from which we concluded that there was minimal erythrocyte settlement during our measurements.

Figure 1.

In vivo and in vitro experiments to determine blood T₂ for one SCA participant. A representative image at the shortest TE_corr (a) in a slice through the IJV and (b) on a blood sample drawn from the same participant. The average intensities of each ROI (red) were fitted as a function of TE_corr using a single exponential decay function, I = A×exp(−TE_corr/T₂), for the in vivo (c) and in vitro (d) experiments.

The fittings (black lines) of R₂ of blood samples (black dots) from each individual SCA participant are displayed in Fig. 2 and show a quadratic dependence on the deoxygenation fraction (1-Y) (Eq. 1), similar to plots for normal blood (Supporting Information Fig. S2). When comparing these curves with previous generalized calibrations (Fig. 2), the individually measured R₂ values from sickled blood are in better agreement with the calculated values based on grouped T₂ calibration for sickle blood⁴² (blue line) than with those for normal blood^39,51 (red and magenta lines), with volunteer 3 being an exception. In contrast, the individually measured R₂ calibrations from normal blood do not show such large deviations from grouped T₂ calibrations (Supporting Information Fig. S2).

Figure 2.

The individual fittings (black lines) of sickle blood R₂ (black dots) as a function of oxygenations in samples from different SCA volunteers. The R₂-(1-Y) curves calculated using Bush-Wood’s grouped calibration model from sickle blood (blue lines), Bush Wood’s grouped calibration from normal blood (red lines) and Lu’s grouped calibration from normal blood (magenta lines) are also shown.

In Fig. 3, the calculated and measured Y for sickle blood samples were compared quantitatively. In terms of average performance over all of the blood samples, the calculated Y based on both the individual calibration and Bush-Wood’s grouped calibration for sickle blood⁴² correlated best with the measured Y (Figs. 3a and b), while the general T₂ calibrations for normal blood^39,51 underestimated Y by 13% (Fig. 3c) or 19% (Fig. 3d), respectively. In terms of individual measurements, the standard deviation (σ_Δ) of the difference between the measured and calculated Y based on the individual calibration was 0.030, which was half of the one between the measured and calculated Y based on the group calibration for sickle blood (σ_Δ : 0.062). Moreover, in the range of venous oxygenations (Y<0.8), σ_Δ of the individual T₂ calibrations was even smaller (0.015), compared to the 0.056 of the grouped calibration, showing a better agreement between measured and calculated Y values (Figs. 3a, b). This is very different from normal blood samples, in which the calculated Y values based on previous group calibrations for normal blood^39,51 showed good agreement and correlation with the measured individual Y values (Supporting Information Fig. S4).

Figure 3.

The correlation and agreement (Bland-Altman) plots between the measured Y_Observe of sickled blood samples from the blood analyzer and predicted Y_cal from four T₂-Y calibrations: (a) the individual calibration developed in this study; (b) Bush-Wood’s group calibration for sickle blood c) Bush-Wood’s group calibration for normal blood; (d) Lu’s group calibration for normal blood; The average $\overline{\text{Δ}}$ and standard deviation (σ_Δ) of the difference between predicted and measured Y are labeled in the plots. The dashed lines in the agreement plot represent two times the standard deviation from the mean difference.

To further explore the relationship between sickle blood T₂ and other hematological parameters, the two coefficients describing the Y dependence of sickle blood T₂ in Eq. 1 were fitted relative to Hct and the percentage of sickle hemoglobin in the total hemoglobin (HbS%) in Fig. 4. Coefficient A₁ of sickle blood (Fig. 4a), had a positive Hct-correlation similar to normal blood (r: 0.71 vs 0.61, respectively), but with a very different slope, namely 3–4 fold larger than that of normal blood (278 vs 79.9, respectively). Coefficient A₂ of sickle blood (Fig. 4b), had a very weak correlation with Hct (r = −0.34), while A₂ of normal blood had a strong positive correlation with Hct (r = 0.93). Meanwhile, although sickle blood samples had lower Hct, their A₂ values were generally higher than ones of normal blood. We also investigated the dependence of A₁ and A₂ on the HbS% for sickle blood. To remove the interference of the A₁ dependence on Hct, A₂ was first scaled by Hct, then correlated with HbS%. Figs. 4c and d showed that neither A₁ nor Hct-scaled A₂ had any strong correlation with HbS%.

Figure 4.

The correlation of the coefficients A₁ (a,c) and A₂ (b,d) in the individual calculation (Eq. 1) with Hct and the percentage of sickle hemoglobin relative to the total hemoglobin (HbS%). The black dots represent A₁ and A₂ of each individual calibration from healthy volunteers, while the red dots represent A₁ and A₂ of each individual calibration from participants with SCA. The solid lines represent the linear fitting of the data and the correlation coefficients (r) are also given in the plot.

When determining ICC to assess reliability of our in vivo protocol²⁶ for measuring blood T₂ of SCA participants, we found a value of 0.986 (p-value < 0.00001), showing a high reliability. Using this protocol, T₂ values in the IJV were measured and converted to Y_v using several different T₂ calibrations for SCA participants (Table 1) and healthy participants (Supporting Information Table S1). As shown in Table 1, SCA participants’ Y_v values obtained from the two T₂ calibrations for normal blood (0.504+/−0.071 and 0.447+/−0.105) were 18% and 26% lower than Y_v values obtained from individual calibrations (0.612+/−0.077). Bush-Wood’s group calibration for sickle blood obtained an averaged Y_v value comparable to individual calibrations (0.625+/−0.053 vs 0.612+/−0.077), but Y_v values derived from these two calibrations sometimes still showed about 20% difference for some participants (#1 and #3). As a comparison, in healthy volunteers, Y_v values obtained from previous T₂ calibrations (0.603+/−0.058 and 0.637+/−0.062) were very close to Y_v values obtained from individual calibrations for every volunteer (0.610+/−0.062) (Supporting Information Table S1). Therefore, individual calibrations were used to calculate Y_v for SCA participants, and Bush-Wood normal blood calibrations were used for healthy volunteers.

Table 1.

The calculated Y_v at IJV of each participant with SCA based on different T₂ calibrations. The numbers in the brackets show the normalized differences between the grouped calibrations and the individual calibrations.

		individual calibration	Bush-Wood’s group calibration for sickle blood*	Bush-Wood’s group calibration for normal blood*	Lu’s group calibration for normal blood
	1	0.43	0.51 (21%)	0.33 (−22%)	0.19 (−56%)
	2	0.66	0.60 (−8.9%)	0.52 (−21%)	0.54 (−19%)
	3	0.54	0.64 (20%)	0.53 (−0.7%)	0.50 (−6.2%)
	4	0.66	0.70 (6.5%)	0.59 (−10%)	0.53 (−19 %)
Participants	5	0.59	0.55 (−6.3%)	0.43 (−28%)	0.38 (−36%)
with SCA	6	0.59	0.61 (3.9%)	0.50 (−15%)	0.46 (−22%)
	7	0.63	0.63 (−0.5%)	0.53 (−17%)	0.51 (−20%)
	8	0.70	0.65 (−7.5%)	0.55 (−22 %)	0.52 (−25%)
	9	0.66	0.68 (2.3%)	0.55 (−16%)	0.48 (−28%)
	10	0.63	0.64 (1.0%)	0.48 (−23%)	0.35 (−44 %)
	11	0.65	0.66 (1.6%)	0.53 (−18%)	0.45 (−30%)
Average+/−STD		0.61+/−0.08	0.63+/−0.05	0.50+/−0.07	0.45+/−0.10

^* Our measured T_2,corr values were converted based on Eq. 2 to T_2,app that is suitable for Bush-Wood’s and Lu’s cablibrations for normal blood.

Using the Y_v values determined for the IJV and the CBF values measured by PC-MRI, the whole-brain DO₂, OEF and CMRO₂ were calculated for SCA participants and healthy volunteers (Table 2). The Wilcoxon rank rum test showed that CBF of SCA participants (93.6+/−23.9 mL/min/100g) was significantly higher (p-value = 1.04×10⁻⁴) than CBF of healthy volunteers (53.5+/−9.1 mL/min/100g), but DO₂ for SCA participants and healthy volunteers (457+/−57 vs 453+/−52 μmol/min/100g, p-value = 0.78) did not show a significant difference, and neither did OEF (0.375+/−0.075 vs 0.389+/−0.051, p-value = 0.31) and CMRO₂ (172+/−42 vs 174+/−17 μmol/min/100g, p-value = 0.73). Except for CBF (p-value < 0.01), correlations with Hct were not significant (p-values > 0.10) for any of the physiological parameters (DO₂, OEF or CMRO₂) either for SCA or healthy groups (Fig. 5).

Table 2.

The calculated whole-brain CaO₂, CBF, DO₂, OEF, and CMRO₂ of SCA participants and normal volunteers.

		T2.corr*	Hct	HbS(%)	HbF(%)	MetHb(%)	OEF***	CaO2*	CBF*	DO2*	CMRO2*
	1	41	0.18	91.0	2.7	1.8	0.57	3.71	131	485	275
	2	54	0.34	79.0	14.2	1.8	0.33	6.87	74.9	514	168
	3	62	0.27	84.8	6.5	1.8	0.45	5.41	74.5	403	182
	4	77	0.25	86.5	6.5	1.5	0.33	4.98	105.3	525	172
Participants	5	47	0.25	68.4	4.8	1.9	0.40	5.04	92.6	467	185
with SCA	6	57	0.26	78.2	16.4	2.0	0.40	5.17	95.7	494	197
	7	60	0.28	**	**	1.9	0.35	5.71	65.1	372	131
	8	64	0.28	85.2	9.1	1.9	0.28	5.65	60.4	341	96.5
	9	71	0.23	80.4	11.9	2.1	0.33	4.68	100.2	469	152
	10	61	0.19	86.8	7.8	2.2	0.36	3.83	132.2	506	180
	11	65	0.23	86.4	7.5	2.7	0.34	4.56	98.1	447	153
Average ±STD		60 ±10	0.27 ±0.04	82.7 ±6.4	8.7 ±4.3	2.0 ±0.3	0.38 ±0.08	5.06 ±0.85	93.6 ±23.9	457 ±57	172 ±42
	1	58	0.40	**	**	**	0.41	8.31	58.2	474	196
	2	89	0.41	**	**	**	0.29	8.37	61.8	507	145
	3	84	0.35	**	**	**	0.32	7.26	74.8	532	170
	4	55	0.45	**	**	**	0.41	9.18	52.3	471	194
	5	51	0.39	**	**	**	0.46	8	44.4	348	161
Healthy	6	63	0.47	**	**	**	0.36	9.67	50.4	478	172
Volunteers	7	59	0.44	**	**	**	0.40	9.05	51.5	457	181
	8	57	0.39	**	**	**	0.43	7.94	57.2	445	192
	9	49	0.49	**	**	**	0.45	10.1	38.3	380	169
	10	67	0.4	**	**	**	0.37	8.31	49.9	407	148
	11	59	0.47	**	**	**	0.39	9.74	50.2	479	185
	12	60	0.43	**	**	**	0.39	8.93	52.4	458	178
Average +/−STD		63 ±12	0.42 ±0.04	**	**	**	0.39 ±0.05	8.74 ±0.85	53.5 ±9.1	453 ±52	174 ±17

^*The unit of T_2,corr, CaO₂, CBF, DO₂ and CMRO₂ are ms, μmol/mL, mL/min/100g, μmol/min/100g, and μmol/min/100g, respectively.

^**The HbF and HbS data for SCA Participant 7 and all healthy volunteers were not obtained

^***OEF of SCA participants is calculated based on Y_v obtained from individual calibration

Figure 5:

Hct dependence of a) CBF, b) DO₂, c) OEF, and d) CMRO₂ for SCA participants (red) and healthy volunteers (black). In contrast to inverse correlations between Hct and CBF (a), no significant correlation between Hct and DO₂ (b), OEF (c), CMRO₂ (d) were observed. Linear fitting results were shown as solid lines for SCA participants (red) and healthy volunteers (black) in (a) while mean values of DO₂ (b), OEF (c) and CMRO₂ (d) were shown as solid lines with 95% confidence intervals (+/−1.96 standard deviation) as dash lines.

Discussion

In this study, we evaluated both individual and group-based calibrations for the T₂-oxygenation relationships of sickled and normal blood. Our in vitro experiments demonstrated that for sickle blood Y calculation, T₂ calibrations built from sickle blood had better accuracy than those built from normal blood and that calibrating on sickle blood individually yielded higher precision than calibrating as a group (Figs. 2 and 3). When applying the individual calibrations to estimate the venous oxygenation of volunteers, no significant differences of OEF and CMRO₂ were observed between this group of SCA participants and healthy subjects.

Our in vitro measurement showed that T₂ values of sickle blood were mostly shorter than the ones based on normal blood’s T₂ calibration at the same Hct (Fig. 2), confirming the findings of Bush et al.⁴². This phenomenon that HbS could induce shorter T₂ for the HbS solution and sickle blood were also observed previously at lower magnetic field^46,54. One reason for this could be that deoxygenated HbS tends to aggregate, and the aggregation of protein has been proven to induce a shorter water T₂ ⁵⁵. Meanwhile, the irregular shape of sickled erythrocyte may induce a stronger magnetic field gradient around the erythrocyte, which will further dephase the transverse magnetization of water diffusing around the erythrocyte and induce stronger T₂ relaxation; however, we did observe one subject (SCA volunteer 3 in Fig. 2) whose sickle blood T₂ values were close to the calculations based on the normal blood calibration. Such an occasional observation, similar to one measurement in a previous study³⁸, illustrates the diversity of T₂-Y relationships, but is insufficient evidence that T₂ calibration of normal blood is suitable for the Y calculation of sickle blood.

Our in vitro data also showed that Bush-Wood’s group T₂ calibration specific for sickle blood⁴², which only considered the effect of Y, could not accurately obtain Y values for some of the sickle blood samples (Fig. 3b). This relatively large difference between the measured and calculated Y in some individuals thus hampers its general application for in vivo measurements. To test whether this difference could result from the different SCA populations between our and their study, we applied the model used in Bush-Wood’s sickle blood calibration (1/T₂ = A₁+A₂×(1-Y)² where A₁ and A₂ were constant for all the samples) to fit our data, and we still found relatively large differences for some blood samples (Supporting Information Fig S3), which is similar to the original Bush-Wood’s sickle blood calibration (Fig. 3b). We also evaluated Bush-Wood’s normal blood calibration⁵¹ on our normal blood samples (Fig. 4Sb). The high agreement between the calculated and measured Y on all normal blood samples indicates that the large difference between the calculated and measured Y for some sickle blood samples most likely results from a high variation in the composition of sickle blood, especially the erythrocyte size^56–58 and hemoglobin aggregation⁵⁴. Current molecular studies have shown that many factors such as HbF could retard the HbS aggregation and erythrocyte sickling, and thus prevent the extra T₂ relaxation from HbS. All these factors make it difficult to universally characterize the sickle blood T₂ with a dependence only on Hct and Y.

To mitigate the heterogeneity effect of sickled blood, we investigated the T₂-Y relationship in blood samples from each SCA participant separately (Fig. 2). Compared with the group calibration⁴², the individual calibration more accurately converted measured T₂ values into Y values for each subject (Fig. 3). Especially for the venous oxygenation range (Y<0.8), individual calibration provided superior accuracy and precision for in vivo measurements. Note that sickle blood T₂ values of different subjects all displayed a very good quadratic dependence on deoxygenation (1-Y) (Eq. 1) as shown in Fig. 2. This roots in two facts: 1). The two main contributions of T₂ relaxation, exchange⁵⁹ and diffusion^56–58,60 mechanisms have a (1-Y)² dependence; 2). The extra T₂ relaxation induced by the HbS aggregation process was observed to have a dependence of (1-Y), with the power of 2–2.4 ⁵⁴.

The individual calibration (1/T₂ = A₁×(1-Y)² + A₂) can further decompose sickle blood T₂ into a proportionality constant for oxygenation dependence (term A₁) and oxygenation independence (A₂), which provides the opportunity to investigate the relationship between sickle blood T₂ and blood physiology. As shown in Fig. 4a, A₁ highly correlated with Hct both for sickle and normal blood, in line with the fact that Hct determines the amount of hemoglobin that can be deoxygenated. The slope of the A₁ dependence on Hct was larger for sickle blood than for normal blood, indicating that HbS aggregation during deoxygenating increased T₂ relaxation of sickle blood^46,54; however, A₁ of sickle blood did not depend on the percentage of HbS, even if we scaled A₁ by Hct and so removed its effect (Fig. 4c). HbS aggregation and variability in erythrocyte shape are complicated processes that may be affected by other factors, such as the percentage of HbF.

Fig. 4b shows the Hct dependence of the oxygenation independent term A₂, which represents the arterial blood R₂ (i.e. 1/T₂). Unlike normal blood, A₂ of sickle blood showed an weak and negative correlation with Hct, which was similar to previous observation by Bush et al.⁴². This was unexpected, because the hemoglobin was the main source of T₂ relaxation of arterial blood and blood T₂ should be shorter with increasing Hct, as shown in normal blood. One possibility is that sickle blood contains a relatively high concentration of young erythrocytes (reticulocytes) which contain high molecular weight micro-organelles such as ribosomes, and these could shorten T₂ values⁶¹ and thus affect the Hct dependence of arterial blood R₂ (A₂). This could also explain why sickle blood with low Hct had similar or even higher A₂ values than normal blood. Another possibility results from the byproducts of hemolysis releasing to the plasma. These byproducts, especially methemoglobin, could shorten plasma T₁^62–64 and, to a lesser extent, T₂ and induce this abnormal Hct dependence of A₂. However, as listed in Table 2, the methemoglobin levels of our SCA volunteers were low and thus should have relatively small effect on the blood T₂ values. Certainly, concentration changes of other serum proteins, such as higher level of methemalbumin and lower levels of haptoglobin and hemopexin in SCA patients^65,66, could also affect A₂. However, these serum proteins’ concentrations are relatively low compared to albumin^65,67, so they may not have a significant effect on A₂ values.

Using our individual calibration, we found that OEF and CMRO₂ of these SCA participants without a history of stroke or recent transfusion were similar to the values of healthy people. This is consistent with a previous PET study², but different from the MR results from Jordan et al.³⁸, Juttukonda et al.⁴¹ and Guilliams et al.⁷, which found people with SCA to have higher OEF, and the results from Bush et al.⁴² which found people with SCA to have lower OEF. Besides the choice of T₂ calibrations used in these studies, another reason could be the different SCA populations that these studies focused on. One of the hypotheses in this latter studies^38,41 was that OEF was compensating CaO₂ and CBF. The total CMRO₂ is a multiplication product of CaO₂, CBF and OEF (Eq. 4). The population with SCA generally had lower Hct, which limits the amount of oxygen that a unit volume of arterial blood can carry (CaO₂); however, OEF has to be elevated only if CBF cannot be further increased to maintain the oxygen metabolism in the brain. However, in our (Fig. 5a) and many other studies^2,4,7–9,68, cerebral autoregulation of the arteriolar radius was able to sufficiently increase CBF to compensate for the reduced CaO₂ and maintain the cerebral oxygen delivery (DO₂ in Table 1). This was very similar to other studies of non-SCA hypoxia, such as hemodilution^69,70 and hypoxic hypoxia⁷¹. When CBF can no longer compensate for the deficiency in oxygen delivery, OEF will increase as shown in stroke patients⁷². Meanwhile, possible arterial-venous shunting in SCA participants⁷³ may decrease OEF⁷⁴.

The most important result from our study is that T₂-based OEF and CMRO₂ can be determined correctly only from proper individual calibration for each patient. With the availability of our approach, these more accurate values can now be used to further investigate the relationship between changes in OEF and CMRO₂ values and the risk of cerebral dysfunction and ischemia. Based on the stroke risk studies of non-SCA patients^75,76, OEF should be increased in response to reduced oxygen delivery secondary to anemia or stenosis and the CMRO₂ level should be maintained. However, the value of OEF as a potential indicator of increased risk of cerebral ischemia in SCA patients still need to be evaluated, due to different types of ischemia in SCA (chronic vs acute complications). Our work brings a non-invasive and convenient method to measure both OEF and CMRO₂, which supplies a powerful noninvasive approach to study the meaning of OEF and CMRO₂ changes in the evolution of ischemia in SCA patients.

The findings from present work should be considered in view of several limitations. First, in the comparison of whole brain OEF and CMRO₂ between healthy and SCA participants, the two groups were not well matched in age and sex; however, based on previous studies^77–80, these age or sex-related changes have a small effect considering the limited age difference between our two groups (35 ± 7 yrs vs. 25 ± 7 yrs). Second, in the calculation of OEF, we assumed the arterial oxygenation fraction (Y_a) in the arterial blood as 0.98 for SCA participants. This was because our SCA participants did not have significant cardiopulmonary disease, and thus arterial oxygenation fraction should be normal, which was also observed by previous study⁸¹ Third, the sample size of our study was modest, and because of the complexity of sickle cell disease, we observed slightly larger variation of OEF and CMRO₂ among SCA participants (Table 2). Fourth, our study did not record some important physiological parameters, such as the reticulocyte concentration to help us extrapolate a universal T₂ calibration for sickle blood. Fifth, our study mainly focused on the global OEF and CMRO₂, which may miss possible changes in local oxygen stress, especially in the white matter,³⁵ for which the blood volume to ratio is small^82,83. However, our study, which establishes a more correct relationship between blood T₂ and oxygenation in SCA patients and demonstrates the applicability of T₂-oxymetry in SCA patients, can in the future be combined with T₂-based oximetry mapping techniques^29,30,32 to further investigate the local oxygen stress in SCA patients. Last, we did not track the morphologic change of the erythrocyte. It is well known that the erythrocyte shape affects the blood T₂ value,^56,84 and that the shape of the erythrocyte depends on pO₂ (i.e. low pO₂ leads to increased sickling, while exposure to atmospheric oxygen can cause some sickled cells to regain the biconcave shape). Therefore, tracking the shape is ideal to thoroughly study the T₂ property of sickle blood. However, missing the morphologic information may not affect the accuracy of our T₂-Y calibration curve. This is because the degree of sickling mainly depends on the blood contents and oxygenation. For our individual calibration method, the blood samples in the in vitro calibration experiment were the same as the in vivo experiment for each SCA volunteer. Therefore, these blood samples had the same erythrocyte shape dependence on the pO₂, i.e. the in vitro blood T₂ measured at each blood oxygenation (or pO₂) included the effect of erythrocyte sickling. In other words, the T₂-Y calibration curve from these in vitro experiments contained the information of erythrocyte sickling and could faithfully transfer blood T₂ to Y for each SCA participant as possible. Certainly, many other factors such as temperature, pH and the concentration of 2,3-DPG could affect the sickling of the erythrocyte^85,86 and some of these parameters may change during the blood storage⁸⁷. However, our storage protocol, which kept the blood sample at room temperature and finished the experiment the same day, and our in vitro experimental protocol, which measures blood T₂ at 37°C minimized the possibility of this occurring.

Conclusion

Our in vitro validation showed that sickle blood T₂ values not only depend on Hct and Y as normal blood, but also on other hematological factors. The use of individual (patient-based) calibrations minimized the effect of heterogeneity of sickle blood between different SCA patients and improved the accuracy of T₂-based oximetry to study the cerebral oxygen utilization of SCA patients. Using the individual calibration, the measured OEF and CMRO₂ of SCA participants without a history of stroke were found to be not significantly different from the values of healthy people, despite their largely elevated CBF. Thus, individual T₂-Y calibrations are likely to be needed, if these non-invasively determined physiological parameters are to be studied and ultimately used to indicate the danger of ischemia in SCA patients and the need for treatment.