NOTE

Investigating the Magnetic Susceptibility Properties ofFresh Human Blood for Noninvasive Oxygen SaturationQuantification

Varsha Jain,1 Osheiza Abdulmalik,2 Kathleen Joy Propert,3 and Felix W. Wehrli1*

Quantification of blood oxygen saturation on the basis of ameasurement of its magnetic susceptibility demands knowl-edge of the difference in volume susceptibility between fullyoxygenated and fully deoxygenated blood (Dxdo). However,two very different values of Dxdo are currently in use. In thiswork we measured Dxdo as well as the susceptibility of oxy-genated blood relative to water, Dxoxy, by MR susceptometryin samples of freshly drawn human blood oxygenated to vari-ous levels, from 6 to 98% as determined by blood gas analy-sis. Regression analysis yielded 0.273 6 0.006 and 20.008 6

0.003 ppm (cgs) respectively, for Dxdo and Dxoxy, in excellentagreement with previous work by Spees et al. (Magn ResonMed 2001;45:533–542). Magn Reson Med 000:000–000, 2011.VC 2011 Wiley Periodicals, Inc.

Key words: MR oximetry; MR susceptometry; susceptibilityimaging; blood oxygen saturation

Hemoglobin is derived from the words ‘heme’ meaningiron and ‘‘globin’’ referring to its globular shape. Theheme iron transitions from a low-spin state in oxyhemo-globin to a high-spin state in deoxyhemoglobin account-ing for the former being diamagnetic and the latter para-magnetic. This oxidation state dependence ofhemoglobin’s magnetic properties is the basis of contrastfor various MRI methods such as blood oxygenation leveldependent MRI (1), susceptibility-weighted imaging (2),detection of acute hemorrhage (3), etc. Although theabove methods exploit qualitative differences in bulkmagnetic susceptibility between oxy- and deoxy-hemo-globin, their quantification enables determination ofintravascular oxygen saturation.

In recent years several articles have appeared in whichvenous oxygen saturation was quantified by magneticresonance techniques (2,4–8). These approaches can bebroadly classified as T2 (7,8) and T0

2 (6) based intravas-

cular and extravascular methods, and susceptibility-based phase methods (4,9). The former rely on an empir-ical relationship to derive oxygen saturation from relaxa-tion rates while the latter are essentially calibration-free.Phase methods are based on an exact solution of Lapla-ce’s equation for the scalar magnetic potential, yielding asimple equation of the fractional induced field inside,relative to the field outside the vessel. The induced fieldcan be translated to oxygen saturation values by approxi-mating the vessel as a long cylinder combined with theknowledge of the volume susceptibility differencebetween fully oxygenated and deoxygenated blood (Dxdo)and hematocrit (Hct). Haacke et al. used the aboveapproach to estimate oxygen saturation in cerebral pialveins (4). Since then, several groups have applied themethod for various in vivo applications (5,10–12). How-ever, much of the prior work has relied on two very dif-ferent values of Dxdo, 0.18 ppm (13) and 0.27 ppm (14;cgs units), yielding substantially different oxygen satura-tions. Although several prior studies have evaluated thisconstant in various ways, no consensus appears to existon its actual value (13–16).

Phase-based oxygen saturation measurements haverecently been used to evaluate global and regional cere-bral oxygen extraction fractions and cerebral metabolicrate of oxygen consumption at rest as well as during met-abolic and motor tasks (10,12,17,18). The soundness andreliability of the results of these experiments is incum-bent on the accuracy of the derived venous oxygen satu-ration. Thus, knowledge of the correct value of Dxdo is ofparamount importance.

In this work, we aimed to measure Dxdo using a frame-work similar to that used by Weisskoff et al. (13). Theexperiments were planned to simulate in vivo conditionsand to overcome some of the limitations of previousstudies. The methodology used in the present work haspreviously been shown to yield accurate and reliablesusceptibility values (19). Additionally, we examinedpotential sources of error in oxygen saturation derivedby MR susceptometry and compared these to valuesobtained by blood gas analysis, widely regarded as theclinical gold standard.

MATERIALS AND METHODS

Blood Preparation

Fresh whole-blood was collected from the antecubitalvein of seven healthy human volunteers via venipunctureunder an Institutional Review Board approved protocol.

1Department of Radiology, Laboratory of Structural NMR Imaging, Universityof Pennsylvania Perelman School of Medicine, Philadelphia, PA.2Department of Pediatrics (Hematology), The Children’s Hospital ofPhiladelphia, University of Pennsylvania Perelman School of Medicine,Philadelphia, PA.3Department of Biostatistics and Epidemiology, University of PennsylvaniaPerelman School of Medicine, Philadelphia, PA.

Grant sponsor: National Heart, Lung, and Blood Institute; Grant number:K01HL103186 (OA); Grant sponsor: NIH; Grant numbers: RC1-HL099861,R21-HD069390 (FW).

*Correspondence to: Felix W. Wehrli, Ph.D., Laboratory for Structural NMRImaging, Department of Radiology, 1 Founders Pavilion, 3400 SpruceStreet, Philadelphia, PA 19104. E-mail: wehrli@mail.med.upenn.edu

Received 19 July 2011; revised 15 September 2011; accepted 12 October2011.

DOI 10.1002/mrm.23282Published online in Wiley Online Library (wileyonlinelibrary.com).

Magnetic Resonance in Medicine 000:000–000 (2011)

VC 2011 Wiley Periodicals, Inc. 1

The samples were drawn in 7 mL K2 ethylenediaminete-traacetic acid (EDTA) (1.7 mg/mL of blood) Vacutainertubes (Becton, Dickinson and Company, NJ). Followingcollection the blood was stored over ice and immediatelytransferred to the hematology lab for preparation. Allblood specimens were used within 6 h after collection.

The samples were pipetted into 2-mL large-surface-areacylindrical tubes (diameter ¼ 20 mm and height ¼ 6 mm)to ensure maximal exposure to the diffusing gases andplaced into an Eppendorf Thermomixer (New Brunswick,NJ) via a custom-designed mount. This mount had anair-tight seal with inlet/outlet nozzles for adding gases.Subsequently, the blood was oxygenated to varying levels(range: 6–98%) by either exposure to room air or a contin-uous stream of N2 gas, while being maintained at 37�C. Toprevent the red blood cells (RBCs) from settling or foamingand to ensure maximal surface area for gas diffusion, thesamples were continuously agitated. The samples hadvariable incubation periods to achieve their desired levelof oxygenation (verified by blood gas analysis).

Blood samples from multiple large surface-area 2-mLtubes were transferred into 6-mL glass cylindrical tubes(diameter: 10 mm and height: 75 mm) and sealed with arubber stopper in preparation for MR scanning. Subse-quently, the blood was injected into the MR sample tubevia an inflow needle and another needle was placed forair outflow. The above procedure ensured that the tubeswere filled completely with no remaining air spaces. Thesample tubes were gently tumbled to prevent the bloodfrom settling and maintained at a temperature of 37�C.

Four to five air-tight blood samples of different oxy-genation were prepared per subject in the above manner(total of 30 samples with variable oxygenation levels forthe entire study). The samples for each subject wereplaced in a cylindrical container filled with distilledwater at 37�C and brought to the MRI suite for scanning.The setup in MR scanner included a heating pad toensure a constant temperature of 37�C throughout theexperiment. Care was taken to scan the samples quickly(less than 1.5 min after they were placed in the scanner)to prevent RBC settling. Prior work had shown that set-tling of RBCs can substantially affect the NMR lineshape; with settling occurring within 2–3 min (14). AfterMRI, oxygen saturation level and Hct in each tube wereremeasured in the hematology lab using the RadiometerBlood Gas Analyzer (Model: ABL 725, Radiometer Medi-cal ApS, and Denmark). To examine the precision of thephase-based MRI method, samples from the last threesubjects were scanned five times each. Between measure-ments, the sample tube assembly was removed from thescanner and gently tumbled to prevent RBC settling.

MR Protocol

All MRI measurements were performed on a 3 T SiemensTim Trio system (Siemens Medical Solutions, Erlangen,Germany) using a 12-channel head coil. The cylindricalcontainer was placed in the scanner with its long axis par-allel to the B0 field. A two-dimensional gradient-recalledecho sequence was used to obtain axial phase maps withthe following imaging parameters, voxel size: (voxel size¼ 1 � 1 � 5 mm3, field of view ¼ 76 � 76 mm2, flip angle

¼ 25�, echo time ¼ 7.2 ms, pulse repetition time ¼ 70 ms,number of echoes ¼ 2, echo spacing (DTE) ¼ 2.5 ms, totalscan time �11 s). Phase difference (Df) was computed bytaking the difference of the phase images from the twoechoes.

The susceptibility differences between various compart-ments (such as air, tissue, etc.) cause field inhomogene-ities and result in low spatial-frequency modulations ofthe phase signal. To minimize this interfering effect a ret-rospective correction method was implemented, whichapproximates the field inhomogeneity by a second-orderpolynomial. The compartments where oxygen saturationwas to be determined were masked out and the Df imagewas weighted with the corresponding masked magnitudeimage. The robustness and accuracy of the method forquantifying susceptibility has been previously validatedby some of the present authors (19). The experimental setup, duplicated in the current work, consisted of an arrayof sample tubes filled with Gd-doped water of variousconcentrations and known volume susceptibilities.

The susceptibility difference (Dx) between blood andwater was computed from the Df between an region ofinterest (ROI) placed inside the cross sectional area ofeach tube and the surrounding water as

Dx ¼ 3Df

gB0DTE½1�

Dxdo was obtained from the slope of Dx/Hct, where Hctare the individual Hct levels, and the concentration ofdeoxyhemoglobin (1 � HbO2) obtained from blood gasanalysis (Eq. 2):

Dx

Hct¼ Dxdoð1�Hbo2Þ þ Dxoxy ½2�

where Dxoxy is the susceptibility difference between fullyoxygenated blood and water. In this model, it is assumedthat the xplasma � xwater (14).

Statistical Analysis

Regression lines were calculated using standard linearregression. Bland–Altman method was used to evaluateagreement between blood gas and phase based oxygensaturation measurements. The Bland–Altman test is astatistical method to compare two different methods ofmeasurement and test if one can be replaced by another.The mean difference between the two methods for meas-uring oxygen saturation (‘‘bias’’) and 95% limits of agree-ment (1.96 � standard deviation) are then calculated. Tobe equivalent, 95% limits must include 95% of differen-ces between the two measurement methods (20). Allanalyses were performed using JMP (Version 7, SASInstitute Inc., Cary, NC).

RESULTS

Representative Df maps for calculating blood susceptibil-ity are shown in Fig. 1. The slope of the regression line ofDx/Hct versus deoxygenation yielded a value of 0.273 60.006 ppm (cgs units) for Dxdo and a y-intercept of �0.0086 0.003 ppm corresponding to Dxoxy, the susceptibility of

2 Jain et al.

fully oxygenated blood relative to water (Fig. 2). Hct anddeoxygenation (1 � HbO2) ranges for the measurementswere 36–49% and 2–94%, respectively. Repeated meas-urements of blood susceptibility at a given oxygen satura-tion and Hct level yielded a coefficient of variation of<5%. Figure 3 shows Bland–Altman plots for assessingthe agreement between phase and blood gas analyzerderived oxygen saturation measurements. The mean biasand limits of agreement were �0.7% and 66.4 % HbO2,respectively. A 95% confidence interval for the meanyielded a lower and upper limit of �2.0 and 0.6% HbO2,respectively, suggesting that the two measurements arenot significantly different from one another. Figure 4illustrates the sensitivity of the derived oxygen saturationto Hct, Dxdo and Df. A fractional error of sHct, sDxdo

, andDxdo in Hct, Dxdo and phase (Df), respectively, introducesan absolute error eHbO2

,

eHbO2¼ ð1�HbO2Þ � s ½3�

in the derived oxygen saturation estimates; where

s ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2Hct þ s2

Dxdoþ s2

Df

q(see Appendix for derivation of

Eq. 3). Thus, errors in the above parameters affect lower

oxygen saturation values more severely. Additionally, for

a given phase value the sensitivity of HbO2 measure-

ments to uncertainties in Hct and Dvdo is greatest at low

values of Hct and Dvdo as is evident from the increased

slope of the surface plot in Fig. 4a at low values of these

parameters. Figure 4b illustrates that phase errors lead to

greater absolute errors in HbO2 at low Hct values.

DISCUSSION AND CONCLUSIONS

In this work, we determined the bulk volume susceptibil-ity difference between fully oxygenated and deoxygenatedhuman blood by varying blood oxygen saturation ex vivoin a controlled environment. The ability of the proposedphase difference method and processing technique to

FIG. 1. Representative Df images of cylindrical sample tubesfilled with blood oxygenated to various HbO2 levels, oriented par-

allel to the B0 field and immersed in distilled water. Note thechange in contrast at different oxygenation levels.

FIG. 2. Susceptibility difference (Dx) between blood and sur-rounding distilled water normalized to individual Hct level in each

subject plotted against the level of deoxygenation. The slope ofthe regression line represents the susceptibility difference betweenfully oxygenated and deoxygenated blood (Dxdo) and intercept the

susceptibility difference between fully oxygenated blood andwater (Dxoxy).

FIG. 3. Bland–Altman plots showing the agreement between MRsusceptometry and blood gas analyzer derived oxygen saturation

values based on Dxdo ¼ 0.27 ppm and Dxoxy ¼ 0.008 ppm. The redand green lines indicate the mean bias and the limits of agreement

(1.96 � standard deviation), respectively. [Color figure can be viewedin the online issue, which is available at wileyonlinelibrary.com.]

FIG. 4. Surface plot of HbO2 as a function of (a) susceptibility differ-

ence between fully deoxygenated and fully oxygenated blood, Dxdo,and Hct, for a phase value corresponding to 65% HbO2 for Hct ¼0.42 and Dxdo ¼ 0.27 ppm (b) Df and Hct for Dxdo ¼ 0.27 ppm.

The plots illustrate that errors in HbO2 measurement due to uncer-tainties in Dxdo, Hct and Df scale with the level of deoxygenation.

Magnetic Susceptibility Properties of Human Blood 3

determine Dx with high precision and accuracy has beenverified previously (5,19). Further, we evaluated theagreement of MR susceptometry derived oxygen satura-tion measurements with the clinical gold standard, bloodgas measurements.

The value of Dxdo obtained in this study (0.273 60.006 ppm) is in excellent agreement with the work ofSpees et al. based on both NMR and SQUID magnetome-try (14). They obtained Dxdo ¼ 0.27 ppm using bothmethods. Additional support for this value comes fromcalculations based on Cerdonio’s model (14,15) using themagnetic moment of deoxyhemoglobin as initiallydetermined by Pauling et al. (25).

Our measurement of Dxdo is also in good agreementwith earlier magnetic cell capture experiments by Kon-droskii et al. (21) who studied the cellular trajectories ofsingle RBC’s in response to a known magnetic field,from which they deduced a Dxdo value of 0.29 ppm.More recent and technologically improved experimentsby Zborowski et al. (22) on RBC magnetophoretic motil-ities yielded a value of 0.26 ppm for Dxdo.

However, our measured value of Dxdo differs signifi-cantly from Weisskoff and Kiihne’s (13) who examinedthe Df between whole blood oxygenated to various lev-els and distilled water. Based on oxygen saturationdetermined by blood gas analysis, they obtained a Dxdovalue of 0.18 ppm. This value is of the same order as anearly rough estimate by Thulborn et al. (16).

Although our experimental methodology somewhatresembles that used by Weisskoff, who performed fieldmapping with an asymmetric spin-echo sequence usingan echoplanar readout, there are notable issues with thatstudy that could have caused systematic errors. First, theyused expired human blood. Hemorheological and hemato-logical parameters are known to alter significantly withstorage age. For example, erythrocytes swell, deform, lyse,become rigid, and form microaggregates (23). Addition-ally, blood chemistry can change substantially, with pHand 2,3-DPG levels dropping with longer durations exvivo (23,24). These changes significantly alter hemoglo-bin’s oxygen binding affinity. Second, there was no men-tion of any precautions taken to prevent blood from set-tling, which is known to substantially affect the NMR lineshape within 2–3 min (14). Thus, the conditions inWeisskoff and Kiihne’s experiments do differ substan-tially from those of freshly drawn or in vivo blood.

In addition to the value for Dxdo, the intercept of thegraph in Fig. 2 provides an estimate for the value Dxoxy.The observed value for Dxoxy corroborates that fully oxy-genated blood is slightly more diamagnetic than water.This finding was first reported by Pauling and Coryell(25). However, experiments by Cerdonio et al. in the late1970s put this into question. Their measured magneticmoment for oxyhemoglobin suggested a possible paramag-netic contribution (26,27). In line with our measurements,recent work by Savicki et al. and Spees et al. (14,28) hasnot provided evidence for such paramagnetism.

Most prior studies in which whole-blood oxygen satu-ration via the long-cylinder approximation and Dfmethod was measured have ignored the contribution ofDxoxy in Eq. 2; assuming its effect to be negligible(4,5,11,29). Our results indicate that neglecting this con-

tribution can introduce a slight bias (on the order of 2–3% HbO2) toward overestimating the oxygen saturationvalues. The effects of ignoring the diamagnetic contribu-tion from fully oxygenated blood can be significant insome hematologic disorders. A case in point is sickle-cell disease. Sakhnini (30), who examined the magneticproperties of hemoglobin in sickle-cell disease patients,found that fully oxygenated HbS is more diamagneticthan normal hemoglobin.

Our results indicate that the mean bias 6 limits ofagreement between MR susceptometry derived and bloodgas analyzer measured HbO2 values were �0.7 6 6.4%.The data thus suggest that HbO2 can be quantified by MRsusceptometry with clinically acceptable levels of agree-ment. The model used to derive whole-blood oxygen satu-ration from susceptibility measurements relies on the ac-curacy of Hct, Dxdo and phase as errors in their values arepropagated into the derived oxygen saturation values. Aspredicted by Eq. 3 and illustrated in Fig. 4, uncertaintiesin these parameters cause the greatest errors at low oxy-gen saturation values as the errors scale according to thelevel of deoxygenation (1 � HbO2). Thus, a populationbased estimate of Hct might suffice when using MR sus-ceptometry to determine oxygen saturation in arterial ves-sels. However, an accurate measurement of Hct is criticalwhen applying this method in vessels where low oxygensaturations are expected. In general, uncertainties inHbO2 estimates are dominated by errors in Hct and Dxdoat low oxygen saturations and by low phase SNR at highoxygenation levels.

It should be noted that our measured value Dxdo mightnot be applicable to all clinical scenarios. Our experi-mental Dxdo was calculated with normal adult hemoglo-bin. Caution must be exercised when using this constantfor oxygen saturation determination in individuals withvariable hemoglobin types (e.g., HbF, HbS, etc.). There issome disagreement in literature on the possible contribu-tion of steric heme–heme interactions on the net dipolemoment of hemoglobin (calculated per heme). Tradition-ally myoglobin has been used to study such interactionsas it consists of a single heme group conjugated to a glo-bin chain. Thus, it is representative of true magneticmoment of heme attached to globin in the absence of anyheme–heme interactions. Although early experiments onthe magnetic moment of myoglobin found values similarto those obtained for hemoglobin (per heme; 31), laterexperiments contradicted this finding (32). Such interac-tions, if present, could have implications on the mag-netic moment of deoxyhemoglobin and hence Dxdo. It isconceivable that in the event of variations in globinchains (e.g., individuals with hemoglobinopathies), theaforementioned steric heme–heme interactions could beaffected, amongst other variables, thereby altering Dxdo.

In conclusion, our results strongly support a Dxdovalue of 0.27 ppm for normal adult human blood. Devia-tions from the present value in prior work are likely dueto experimental inadequacies.

ACKNOWLEDGMENTS

The authors would like to thank Helen Peachey for helpwith collection of blood samples.

4 Jain et al.

APPENDIX

From Eqs. 1 and 2, HbO2 can be calculated as,

HbO2 ¼ 1� 3Df

gHctDxdoB0DTE½A1�

Constants other than Hct, Dxdo, and Df are user speci-fied or empirical and can be replaced by constant k forsimplicity, yielding.

HbO2 ¼ 1� kDf

HctDxdo½A2�

Using basic rules of error propagation, the absoluteerror (e) in HbO2 can be estimated as

e ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi@HbO2

@Df

� �2

dDfð Þ2þ @HbO2

@Hct

� �2

dHctð Þ2þ @HbO2

@Dxdo

� �2

dDxdoð Þ2s

½A3�

Computing partial derivatives and substituting dDf ¼Df � sDf, dHct ¼ Hct � sHct and dDxdo ¼ Dxdo � sDxdo,with s representing the fractional error, yields

e ¼ kDf

HctDxdo

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2Df þ s2

Hct þ s2Dxdo

� �r½A4�

Rearranging and substituting Eq. A2, gives

e ¼ ð1�HbO2Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2Df þ s2

Hct þ s2Dxdo

� �r½A5�

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