Calibration of T₂ oximetry MRI for subjects with sickle cell disease

Abstract

Purpose:

Cerebral T₂ oximetry is a non-invasive imaging method to measure blood T₂ and cerebral venous oxygenation. Measured T₂ values are converted to oximetry estimates using carefully validated and potentially disease-specific calibrations. In sickle cell disease, red blood cells have abnormal cell shape and membrane properties that alter T₂ oximetry calibration relationships in clinically meaningful ways. Previous in vitro works by two independent groups established potentially competing calibration models.

Methods:

This study analyzed pooled datasets from these two studies to establish a unified and more robust sickle-specific calibration to serve as a reference standard in the field.

Results:

Even though the combined calibration did not demonstrate statistical superiority compared to previous models, the calibration was unbiased compared to blood-gas co-oximetry and yielded limits of agreement of (−10.1%, 11.6%) in non-transfused subjects with sickle cell disease. In transfused patients, this study proposed a simple correction method based on individual hemoglobin S percentage that demonstrated reduced bias in saturation measurement compared to previous uncorrected sickle calibrations.

Conclusion:

The combined calibration is based on a larger range of hematocrit, providing greater confidence in the hematocrit-dependent model parameters, and yielded unbiased estimates to blood-gas co-oximetry measurements from both sites. Additionally, this work also demonstrated the need to correct for transfusion in T₂ oximetry measurements for hyper-transfused sickle cell disease patients and proposes a correction method based on patient-specific hemoglobin S concentration.

Introduction:

Cerebral MRI oximetry is an approach to measure venous oxygenation based on the principle that oxyhemoglobin experiences a shift in magnetic susceptibility when transitioning to deoxyhemoglobin. Amongst different MRI oximetry techniques, T₂-relaxation-under-spin-tagging (TRUST) uses arterial spin labeling to isolate venous blood, applies T₂ preparation and measures blood T₂ signal in a large cerebral vein.¹ This technique has recently been applied by different groups to estimate oxygen extraction fraction and cerebral metabolic rate of oxygen in sickle cell disease (SCD) subjects.^2–6 However, since T₂ oximetry relies on a calibration model to convert blood T₂ into oxygen saturation, the estimates are heavily dependent on the choice of empirical calibration model, whether derived from bovine blood,¹ healthy human blood⁷ or human blood from patients with SCD.^2,3 In particular, the non-sickle calibration curves yield much higher estimates of oxygen extraction fraction and cerebral metabolic rate than calibration curves derived from patients with SCD.

Compared to calibrations derived from bovine and sickle blood, Li et al. demonstrated better accuracy in measuring cerebral oxygenation in SCD patients using each subject’s individual calibration.³ While performing individual calibrations would be ideal, such an approach is impractical for clinical use or even many research applications. Since the calibration methodologies are challenging and time-consuming, prior sickle cell blood calibration studies suffered from small sample size and limited power. The current work combines raw calibration data from two independent reports by Bush et al.² and Li et al.³ to establish a unified, robust T₂ calibration for SCD patients. It also presents a method to compensate for the admixture of normal and sickle hemoglobin observed in transfused patients with SCD, who make up approximately 10-20% of the SCD population.

Methods:

The Committee on Clinical Investigation at Children’s Hospital Los Angeles (CHLA) approved the protocol; written informed consent and/or assent were obtained from all subjects (CCI#2011-0083). This study was performed in accordance with the Declaration of Helsinki.

1. T₂ oximetry calibration model:

The sequence to measure venous T₂ has been explained in prior publications.^2,7,8 Briefly, a transverse, single-slice T₂ preparation sequence that uses Carr-Purcell-Meiboom-Gill (CPMG) T₂ weighting was used to measured blood T₂ in the sagittal sinus. The number of refocusing pulses was varied across four acquisitions (0, 4, 8 and 16 pulses) to acquire images at effective echo times (eTE) of 0ms, 40ms, 80ms and 160ms. Unlike in vivo TRUST acquisitions, since ex vivo imaging did not involve flowing blood, the magnetic tagging module is turned off. The signal at four eTE were fit to the mono-exponential decay equation:

$$\text{S}\left(\text{eTE}\right)={\text{S}}_0\times {\text{e}}^{-\frac{\text{eTE}}{{\text{T}}_2}}$$ [1]

where S is the signal measured, S₀ is a constant across echo times and T₂ is the transverse relaxation times of blood. Equation 1 did not include the blood longitudinal relaxation time T₁ since the magnetic spin labeling is off. The relationship between venous blood relaxation and oxygenation is illustrated with the empirical model:

$$R_2=\frac{1}{T_2}=A\times {\left(1-Y\right)}^2+B$$ [2]

where R₂ is the measured T₂ relaxation rate, Y is saturation, A and B are empirically determined coefficients from least-square fitting. We previously observed that both A and B coefficients varied linearly with hematocrit:

$$A=a_1\times Hct+a_2$$ [3]

$$B=b_1\times Hct+b_2$$ [4]

where a₁, a₂, b₁ and b₂ are coefficients for linear dependence on hematocrit. Equations 2–4 are consistent with our prior calibration studies.^2,3,7 When formulating this model, care was taken to convert apparent T₂ (T_2,app) from the Bush study² to T₂ corrected for pulse width (T_2,corr) with T_2,corr = T_2,app × k, where k = 1 − pulse_width/(2 × interecho_spacing) = 0.913 with pulse width of 1.74ms and CPMG interecho spacing of 10ms.^3,9,10

2. Raw calibration data:

Raw T₂ oximetry calibration data and individual hematologic measurements were extracted from Bush et al.² (N=11) and Li et al.³ (N=11). Each individual dataset consisted of the subject’s hematocrit, percentage of hemoglobin S (HbS), a set of venous saturation measurements by blood gas co-oximetry and corresponding measured venous R₂.

Briefly, this set of saturation values and venous R₂ was determined from a blood sample drawn from the antecubital vein from each participant and was used to construct individual T₂ oximetry calibration at the native hematocrit. For each point on the R₂–Y empirical model in Equation 2, the blood sample underwent oxygenation adjustment by exposure to room air or nitrogen gas and was equilibrated at 37˚C; each sample’s saturation was measured with co-oximeter and corresponding blood R₂ was measured with TRUST MRI acquisition. This process was repeated 5-7 times in each sample to provide the R₂–Y relationship, and least squares fitting of this relationship with Equation 2 yielded A and B coefficients for each subject.

3. Sickle calibration for non-transfused blood:

To have the most robust SCD calibration, only non-transfused patients with hemoglobin SS disease were extracted from the Bush study (N=5) and pooled with similar patients from the Li study (N=11), resulting in a cohort with high HbS (80±12%, N=16, Table 1). Patients with hemoglobin SC and Sβ₊ were eliminated from analysis. A population calibration model based on Equation 2 was derived for this non-transfused SCD group.

Table 1.

Subject demographics and hematologic parameters.

	Subject	Hematocrit (%)	HbS (%)	A	B
Non-transfused	Li #1	18.0	91.0	51.7	7.8
	Li #2	34.0	79.0	98.1	7.2
	Li #3	27.0	84.8	54.4	4.7
	Li #4	25.0	86.5	46.2	7.6
	Li #5	25.0	68.4	72.7	9.2
	Li #6	26.0	78.2	63.9	6.9
	Li #7	28.0	N/A	68.0	6.4
	Li #8	28.0	85.2	102.7	6.8
	Li #9	23.0	80.4	78.5	6.2
	Li #10	19.0	86.8	64.7	7.7
	Li #11	23.0	86.4	67.7	7.0
	Bush #1	35.2	64.1	84.2	5.7
	Bush #2	33.4	69.3	80.2	5.4
	Bush #3	36.0	95.3	76.2	7.0
	Bush #4	24.0	85.0	69.4	5.8
	Bush #5	24.0	93.2	70.1	5.8
Transfused	Bush #6	30.3	24.5	73.7	6.6
	Bush #7	28.9	39.4	68.7	5.5
	Bush #8	37.0	45.9	75.5	5.4

4. Sickle calibration for transfused blood:

In the case of hyper-transfused patients with lower HbS, we hypothesized that a different HbS-based mixture calibration model, representing a linear mixture of HbA and HbS calibrations, would be more appropriate for SCD patients who receive chronic transfusion. The accuracy of this transfusion-specific calibration was assessed on three SCD patients (N=3, including 2 hemoglobin SS and 1 hemoglobin Sβ₀) from Bush et al.² who were undergoing chronic transfusion to maintain HbS less than 30%.

The mixture model provided a weighted calibration between the sickle calibration (current Li-Bush calibration) and normal hemoglobin calibration,⁷ namely the model coefficients would be weighted by individual HbS percentage:

$$a_1=\left(1-\frac{Hbs\%}{80\%}\right)\times a_{1,HbA}+\left(\frac{Hbs\%}{80\%}\right)\times a_{1,Hbs}$$ [5]

$$a_2=\left(1-\frac{Hbs\%}{80\%}\right)\times a_{2,HbA}+\left(\frac{Hbs\%}{80\%}\right)\times a_{2,Hbs}$$ [6]

$$b_1=\left(1-\frac{Hbs\%}{80\%}\right)\times b_{1,HbA}+\left(\frac{Hbs\%}{80\%}\right)\times b_{1,Hbs}$$ [7]

$$b_2=\left(1-\frac{Hbs\%}{80\%}\right)\times b_{2,HbA}+\left(\frac{Hbs\%}{80\%}\right)\times b_{2,Hbs}$$ [8]

where HbS% of each subject is the model weight, a_1,HbA, a_2,HbA, b_1,HbA and b_2,HbA are coefficients from calibration⁷ for normal blood and a_1,HbS, a_2,HbS, b_1,HbS and b_2,HbS are coefficients from Li-Bush calibration for sickle blood. Since the pure sickle Li-Bush model is derived from non-transfused blood with an average HbS% of 80%, the HbS model weights are normalized by 80% instead of 100%. Summary of calibration models in this manuscript is shown in Supporting Information Table S1.

5. Statistical analysis:

Statistical analysis was performed in JMP (SAS, Cary, NC). Bland-Altman analyses were performed to assess agreement between different calibration models and blood-gas co-oximetry.

Results:

1. Non-transfused population SCD calibration:

Figure 1 demonstrates the linear dependence of the A and B coefficients on hematocrit levels; open circles represent data from the Bush study and closed circles are from the Li study. Hematocrit explains 44% of the variance in A and 10% of the variance in B, whereas neither A nor B demonstrate a significant dependence on hemoglobin S concentrations (p=0.22 and p=0.91 respectively). Confidence limits and standard error of the parameter estimates are illustrated in Supporting Information Figures S1 and S2. The combined data have double the number of points at hematocrits greater than 0.3, stabilizing the linear estimation. From this bilinear dependence of blood R₂ on both saturation and hematocrit, the Li-Bush population calibration model for non-transfused S hemoglobin patients was formulated:

$$R_{2,corr}=\left(196.8\times Hct+16.7\right)\times {\left(1-Y\right)}^2+\left(-6.6\times Hct+8.6\right)$$ [9]

Figure 1.

HbS-specific Li-Bush calibration for non-transfused SCD patients. Linear dependence of (A) A and (B) B coefficients on hematocrit using pooled datasets from Bush et al.² and Li et al.³

A and B coefficients calculated from the individual model and the population model are shown in Table 1 and Supporting Information Table S2. Graphical comparison between sickle-specific calibrations, bovine calibration¹ and HbA calibration⁷ is shown in Figure 2 for a subset of patients and in Supporting Information Figure S3 for the full cohort. Subject-based blood calibrations yielded no significant bias and small variance compared to blood-gas co-oximetry (Figure 3A). Bovine¹ and non-sickle hemoglobin A⁷ models demonstrated systemic underestimation of 16.6% and 12.0% saturation units compared to co-oximetry in SCD patients (Table 2, Figure 3BC). On the other hand, the sickle-specific Bush calibration, Li calibration and Li-Bush combined calibration (Figure 3D–F) were unbiased, had comparable variance to one another and smaller variability compared to bovine and HbA models. Between the Li-Bush and patient-specific blood calibrations, there is no significant bias and 95% limits of agreement of 10%.

Figure 2.

Individual and group sickle calibration models in a subset of 2 subjects from Li et al.³ and 2 non-transfused HbSS subjects from Bush et al.² Individual calibration data (black filled circles) were fitted with individual calibration (dotted line), Li population calibration (red solid line), Bush population calibration (blue), Li-Bush combined calibration (green), bovine calibration (purple) and HbA calibration (orange). In Li Subject 2, Bush Subjects 1 and 2, the blue Bush calibration overlaps and is plotted underneath the red Li-Bush combined calibration.

Figure 3.

Bland-Altman analyses of different calibration models on non-transfused SCD subjects (closed circle, 5 from Bush et al.² and 11 from Li et al.³) and transfused subjects (open circle, 3 from Bush et al.²). Each data point represents a set of in vitro blood saturation measurement by cerebral T₂ oximetry and blood-gas co-oximetry. (A) Subject-specific calibration gave the highest accuracy and lowest bias but is infeasible for routine clinical use. (B) Bovine and (C) healthy human blood HbA models exhibited large bias and variance when used in subjects with sickle cell disease. Sickle-specific population models by (D) Bush et al.² and (E) Li et al.³ displayed comparable results. Therefore, (F) a combined consensus Li-Bush HbS model was reported and recommended for use in non-transfused SCD subjects. (G) In hyper-transfused patients, subject-specific calibration yielded low bias and variance, whereas (H) the Li-Bush consensus sickle calibration displayed a bias in transfused subjects. To correct for this bias, (I) a mixture HbS-weighted model was developed that demonstrated a smaller bias for use in transfused SCD patients.

Table 2.

Bland-Altman analysis for different population calibration models^1–3,7 on transfused and non-transfused sickled blood. Even though Li et al. only reported patient-specific sickle calibration, a population model was derived from individual datasets.³

	Non-transfused subjects			Transfused subjects
Calibration	Bias	Standard Deviation	95% Confidence Interval	Bias	Standard Deviation	95% Confidence Interval
Individual3	0.5	3.0	(−5.5, 6.5)	−0.1	2.3	(−4.7, 4.5)
Bovine1	16.6*	11.5	(−6.4, 39.7)	7.3*	6.2	(−5.1, 19.7)
HbA7	12.0*	6.7	(−1.5, 25.4)	7.0*	3.5	(0.0, 13.9)
HbS Bush2	0.3	5.2	(−10.2, 10.7)	−2.7*	2.9	(−8.4, 3.1)
HbS Li3	−0.6	6.1	(−12.8, 11.7)	−3.9*	2.9	(−9.6, 1.9)
HbS Li-Bush	0.8	5.4	(−10.1, 11.6)	−2.1*	2.5	(−7.0, 2.8)
HbS-weighted Li-Bush	0.6	6.1	(−11.7, 12.8)	1.1	3.6	(−6.1, 8.3)

^*denotes the bias is significantly different from zero.

2. HbS-based SCD calibration for hyper-transfused patients:

Comparisons between individual calibration, Li-Bush calibration uncorrected for transfusion, HbS-based mixture model for transfused blood is demonstrated in Table 2 and Figure 3G–I. When T₂ oximetry measurements in hyper-transfused subjects were assessed with uncorrected sickle calibration, venous saturation showed a slight overestimation compared to blood-gas analysis. However, when the HbS-based mixture model was used to correct for transfusion, the bias between T₂ oximetry and blood-gas co-oximetry was reduced.

Discussion:

In this study, we established a T₂ oximetry calibration for non-transfused sickle blood by combining calibration data from two independent studies.^2,3 The combined Li-Bush calibration was unbiased compared to blood-gas co-oximetry and yielded limits of agreement of (−10.1%, 11.6%). Although the combined calibration did not demonstrate statistical superiority compared to previous Li or Bush models, by increasing the number of patients and broadening the hematocrit range, we strengthened the robustness and generalizability of our calibration. This larger working range of hematocrit also revealed the dependency of blood T₂ on hematocrit, which was not previously observed by the Bush sickle calibration.² Additionally, this work demonstrated the need to correct for transfusion in T₂ oximetry in hyper-transfused SCD patients and explored a correction method based on HbS percentage; this correction demonstrated no bias and lower variance than uncorrected Li-Bush calibration in transfused blood.

1. Sickle-specific Li-Bush population model:

A and B coefficients derived from both the individual calibration and the sickle population calibration demonstrated large inter-subject variations; this high variance in measured A and B coefficients can be explained by the variation in hematocrit in the patient cohort. Additional variations in the ex vivo blood calibration procedure such as precise temperature control and minimization of red cell aggregation, as well as inter-subject differences in red cell damage, could potentially contribute to the remaining variation in blood T₂ measurements.

Similar to previous studies,^2,3 our results did not demonstrate a statistically significant dependence between A, B and hemoglobin S percentage. The lack of HbS dependence could be due to its smaller effect size compared to the larger inter-subject variability in subjects with similar HbS.³ Additionally, in subjects with lower hemoglobin S percentage, HbA-containing red blood cells could be damaged by the inflamed vascular endothelium,¹¹ altering the density and membrane permeability and leading to similar magnetic characteristics as sickle red blood cells.

Additionally, since our Li-Bush calibration model was constructed from hemoglobin SS subjects, we could not predict how well the calibration will perform on other sickle genotypes, including SC, Sβ₀, and Sβ₊. Patients with Sβ₀ have very similar clinical and hematological characteristics as SS disease,^12,13 so we anticipate that the SS calibration would translate well to Sβ₀ genotype. Sβ₊ has varying mixtures of hemoglobin A and S within individual red blood cells depending on the type of mutations.¹⁴ Mild forms will behave like sickle cell trait (best described by the normal hemoglobin calibration)² while more severe forms will mimic non-transfused SS disease. Red blood cells in hemoglobin SC disease suffer from significant dehydration and membrane abnormalities,^15,16 similar to cells with SS hemoglobin, but it is possible that the calibration coefficients would be subtly different. In the absence of future disease-specific calibration data, we advocate using the SS calibration for SC patients based upon these a priori considerations.

2. Importance of a unified SCD calibration:

Currently, there is instability in the field of cerebral oxygenation with respect to patients with SCD. Oxygen extraction fraction has been reported as increased,^4,5 decreased,² and unchanged³ in SCD by different, well-regarded groups. The choice of T₂ oximetry calibration is at the center of the controversy, and the recent addition of two, potentially-competing sickle cell calibrations complicates the issue.^2,3 Since calibration experiments are challenging to perform, sample size constraints and intrinsic inter-subject variability limits the accuracy of both prior reports. Furthermore, institutional differences in treatment of SCD and patient compliance with medications limit the generalizability of results from any single center. The combined Li-Bush calibration was derived from wider intrinsic hematocrit range, lowering variability, increasing robustness and increasing the confidence of individual parameter estimates. It also demonstrated favorable Bland-Altman agreement with patient-specific calibrations. Most importantly, it represents a “consensus” calibration between the two groups responsible for the prior SCD calibrations and should serve as the single reference for future T₂ oximetry studies in SCD, even if statistical superiority could not be demonstrated with respect to previous Li and Bush calibrations.

3. Importance of a calibration for transfused SCD patients:

Regular transfusion therapy is the treatment of choice for stroke prophylaxis for SCD patients with abnormal transcranial Doppler, pulmonary hypertension, and acute chest syndrome.¹⁷ Chronically transfused SCD patients typically maintain pre-transfusion HbS of 30%. Roughly 10-20% children and young adults with SCD receive chronic transfusion, so it is important to be able to apply cerebral oximetry in this patient cohort. Both the hemoglobin A model and all of the hemoglobin S models were biased with respect to transfused SCD subjects. We demonstrated that a simple linear admixture model using HbS percentage as weighting coefficient produced unbiased estimate with lower error than any of the individual models. While there is no a priori reason to believe that the calibration coefficients should vary linearly with HbS, this simple approach provides smooth behavior between well-calibrated boundary points, similar to Taylor’s series expansion, and is unlikely to introduce wild deviations from expected behaviors. Although the validation sample was small, additional validation work in this cohort is unlikely, so it is important to establish a practical and logical approximation.

4. Is it fair to pool data between Li and Bush studies?

In vitro studies of blood transverse relaxivity are challenging because blood oxygenation must be altered while controlling for temperature, red-cell aggregation, susceptibility artifacts, and pulse sequence differences.^1,2,7 Therefore, it is reasonable to question whether data from the two studies can legitimately be pooled. To address this possibility, Li et al. compared the observed blood R₂ from 9 healthy volunteers against the Bush HbA calibration (Figure S2 in Li et al.)³. Bland Altman analysis between observed and predicted oximetry values were −0.8±2.8% (Figure S4 in Li et al.),³ representing phenomenal concordance between two studies. While this does not guarantee that sickle blood would yield as robust a result between the two centers, it does exclude significant systematic biases from instrumentation and experimental differences. Furthermore, the open and filled symbols in Figure 1 are plausibly from the same distribution, although much larger sample sizes would be needed to prove that point.

5. Importance of a sickle-specific calibration compared to bovine and human blood models

The bovine calibration is used by many studies in subjects with normal hemoglobin.¹ Even though bovine red cells do not form Rouleaux formations and are smaller than human red blood cells, previous work has shown that the bias between bovine model and healthy human blood model was small over the hematocrit range of 35-55% in which this model was originally calibrated.⁷ Outside this range, the bovine model severely underestimated venous oxygenation; this large systematic bias introduced by extrapolating the bovine model outside of its useful calibration range has been reported in anemic subjects.² This bias was further worsened by the failure to account for the presence of sickle hemoglobin. This manuscript demonstrates that whether one uses the Li model, Bush model, the Li-Bush combined model, or individual calibration, the R₂ changes produced by sickle red cells are poorly described by either the bovine or HbA calibrations (Figure 3).

6. Why does sickle blood have different relationship between T₂ and saturation?

Red blood cell R₂ relaxation is primarily determined by their intrinsic magnetic susceptibility, their membrane integrity and degree of hemoglobin S aggregation.¹⁸ Sickle cell trait patients, who have normal red cell membrane characteristics and no hemoglobin polymerization under most physiological conditions despite 40% hemoglobin S concentrations, have identical R₂ characteristics as controls with exclusively hemoglobin A, suggesting that the fundamental magnetic susceptibility of hemoglobin S is not different from hemoglobin A.⁷ However, simple visual inspection of blood smear collected from a patient with SCD highlighted the tremendous spectrum of membrane surface and cytoskeletal damage experienced by these patients.¹⁹ This aberrant shape and increased red cell–red cell interactions potentially magnify the contributions of two relaxation mechanisms to the sickle blood transverse relaxation, with relative importance of each mechanism depending on field strength.²⁰

The first mechanism is simple movement of water protons (by bulk flow and diffusion) in nonhomogeneous magnetic field which causes phase accrual that is incompletely reversed by the CPMG pulses in T₂ preparation.²¹ Since sickle red blood cells are relatively dehydrated compared to normal blood cells (they have a high mean corpuscular hemoglobin concentration, or MCHC),²² it is not surprising that the A and B coefficients might have stronger hematocrit weighting.²³ In addition, the A coefficient depends on the relative length-scale between the magnetic inhomogeneities and the proton mobility,²³ which will be impacted by abnormal cell shape and red cell aggregation in sickle blood.

The second relaxation mechanism involves water exchange across red cell membranes. In the chemical exchange model,^24,25 the coefficient A depends upon susceptibility difference between plasma, deoxygenated red blood cells and exchange time across the membrane. As in the diffusion model, the susceptibility difference between plasma and red cells depends upon hematocrit, MCHC, and saturation. The red cell exchange time varies with cell shape and intrinsic water permeability, both of which are abnormal in SCD. At 3T, diffusion-mediated loss dominate in non-sickle blood²⁶ but the relative contributions of the two mechanisms could differ in SCD blood because red cell membrane shape and membrane properties differ so dramatically.¹⁹ Regardless, both the diffusion and chemical exchange model predict that sickle blood should have a unique calibration compared with non-sickle blood.

7. Limitations:

A limitation to T₂ oximetry imaging is its dependence on hemoglobin-specific calibration curves. The most accurate solution is the use of individual calibrations for each subject.³ Unfortunately, constructing patient-specific calibration curve for each patient may be infeasible for routine clinical or research use because it requires significant time and resources (blood draw, oxygenation adjustments, MRI time). And even though we did not observe bias in oxygenation estimates in the Li-Bush combined calibration compared to co-oximetry, further validation on a separate cohort of hemoglobin SS subjects is important. Additionally, validation against independent methods to measure venous saturation, such as central or peripheral venous catherization, or MRI susceptometry methods^27,28 is required to affirm the clinical utility of this T₂ oximetry model.

We acknowledge that our HbS-weighted mixture model for hyper-transfused subjects is empiric and simplistic. While bias was not observed in our approximation, we were only able to test this model in three transfused patients. Since all three subjects had very similar hemoglobin S (32.1 ± 4.3%), the mixture model could not demonstrate superiority compared to the uncorrected calibration. However, in the clinical setting, transfused SCD subjects can have large variability in hemoglobin S concentrations (range of 0 to 60% after 36 months of continuous transfusion).²⁹ Therefore, the proposed HbS-weighted model that exhibits smooth transition near the HbS extrema is a reasonable correction option. Future work to evaluate the accuracy of this HbS-based correction method on a larger cohort of transfused subjects is desirable, however, it is not a high priority.

8. Conclusion:

In summary, this study established a blood T₂ oximetry calibration derived from pooled data^2,3 to provide a single reference standard in patients with SCD. The revised sickle calibration is unbiased, and the derived oximetry exhibits limits of agreement of (−10.1%, 11.6%), despite residual inter-subject variability. Our results call into question previous MR oximetry studies^4–6 in SCD that used calibration curves derived from bovine blood or human blood with normal hemoglobin. Additionally, this study proposes a correction method for patients undergoing chronic transfusion to correct for the lower HbS percentage in transfusion.

Supplementary Material

SUP

Supporting Information Figure S1. Confidence limits of the hematocrit dependence of (A) A and (B) B coefficients using pooled datasets of sickle cell disease subjects from Bush et al.² and Li et al.³ Individual A and B error bars are calculated from the standard error of parameter estimates. Individual hematocrit error bars are calculated from the hematocrit coefficient-of-variation 3%.

Supporting Information Figure S2. Confidence limits of the hematocrit dependence of (A) A and (B) B coefficients using five healthy control subjects from Bush et al.² Individual A and B error bars are calculated from the standard error of parameter estimates. Individual hematocrit error bars are calculated from the hematocrit coefficient-of-variation 3%.

Supporting Information Figure S3. Individual and group sickle calibration models based on 11 subjects from Li et al.³ and 5 non-transfused HbSS subjects from Bush et al.² Individual calibration data (black filled circles) were fitted with individual calibration (dotted line), Li population calibration (red solid line), Bush population calibration (blue), Li-Bush combined calibration (green), bovine calibration (purple) and HbA calibration (orange).

Supporting Information Table S1. All group calibration formulas used in this manuscript. Note that formulas are shown in similar format to original form found in references. Care was taken to covert R₂ apparent values to R₂ corrected for pulse width (R_2,corr) with 1/R_2,corr = T_2,corr = T_2,app × k = 1/R_2,app × k, where k = 1 − pulse_width/(2 × interecho_spacing) = 0.913 with pulse width of 1.74ms and CPMG module interecho spacing (τ) of 10ms.

Supporting Information Table S2. Subject hematologic and calibration parameters. A and B coefficients were calculated using the individual calibration model and the sickle-specific population calibration model. Li et al. did not measure HbA, pH and pCO₂, but the reader can impute pH and pCO₂ from our data and approximate HbA ≈ 100% − HbS − HbF.