CMR-based blood oximetry via multi-parametric estimation using multiple T2 measurements

In the model described in Eq. 1, T _2b can be measured using CMR, and Hct (Pa) can be measured from a small blood sample. The parameters ω ₀ and τ ₁₈₀ can be controlled based on the choice of magnetic field strength and T2-preparation pulse design, respectively. This leaves the desired blood oxygen saturation, %SbO ₂, and three other nuisance parameters (T _2O , τ _ex , and α) as unknowns.

While a single measurement of the apparent blood T2 would not be sufficient to estimate all of the unknown patient-specific parameters in the L-M model, we propose here a method that allows these unknown parameters to be estimated, within a range, on a patient-specific basis. Noting that τ ₁₈₀ is a controllable parameter, acquiring multiple T2 measurements, each at a different τ ₁₈₀, provides the diversity of data that is needed to characterize the patient-specific relationship between blood T2 and O2 saturation. Once a sufficient number of T2 values have been acquired, each using a different τ ₁₈₀, the four unknown model parameters (%SbO ₂, T _2O , τ _ex , and α) can be estimated using a NLLS curve fit. Under high signal-to-noise (SNR) conditions, the solution remains viable when the nuisance parameters are unknown a priori. However, in order to discourage convergence to local minima and to combat loss of estimation sensitivity in the presence of noise, we opted to constrain the nuisance parameters. This approach provides a framework for patient-specific T2 oximetry (shown in Fig. 1), and eliminates reliance on generic and potentially inaccurate calibration factors [25, 26].

Our lab has previously developed a technique to perform rapid, quantitative characterization of the myocardial T2 to identify inflammation and edema [27, 28]. The T2 mapping sequence consists of the acquisition of several single-shot T2 weighted images at specific T2 preparation times. Each of these images are acquired using a non-selective T2 preparation module, consisting of a 90⁰ tip-down RF pulse, a train of Malcolm Levitt (MLEV) phase cycled composite 180⁰ (90⁰–180⁰–90⁰) refocusing RF pulses, ending with a composite 90⁰ (270⁰–360⁰) tip-up RF pulse. The T2 preparation is immediately followed by a balanced steady-state free precession (bSSFP) readout, with linear traversal across k-space data. The T2 mapping sequence also employs a non-rigid registration motion correction algorithm to correct for motion occurring between the different T2-prepared images. The signal in each of the motion corrected T2 prepared images are fit pixel-wise to a mono-exponential decay curve as a function of T2p, resulting in a quantitative T2 map of the region being imaged.

In this technique, which was primarily designed for myocardial T2 measurement, τ ₁₈₀ was adjusted among a fixed number of refocusing pulses in the T2 preparation train in order to vary the echo times, T2p, which is defined as T2p = number of refocusing pulses x τ ₁₈₀. For the estimation of blood O2 saturation, we extend T2p by increasing the number of refocusing pulses based on a segmented Malcolm Levitt phase cycling pattern (0, 2, 4, 8, and 12 refocusing pulses) [29]. Thus, we generate four T2 maps for a given blood pool, using τ ₁₈₀ values of 12, 15, 20, and 25 ms. The T2p times corresponding to each T2 map used in the study were therefore 0, 24, 48, 96, and 144 ms (for τ ₁₈₀ = 12 ms); 0, 30, 60, 90, and 180 ms (for τ ₁₈₀ = 15 ms); 0, 40, 80, and 160 ms (for τ ₁₈₀ = 20 ms); and 0, 50, 100, and 200 ms (for τ ₁₈₀ = 25 ms), respectively. The number of T2p images used to generate each map was chosen such that the latest T2p for each T2 map remained within a close range, around the expected T2 values of arterial and venous blood. An illustration of the T2 mapping scheme is shown in Fig. 2.

As the CMR imaging planes of the heart usually include both arterial and venous blood pools, each T2 map can provide a T2 measurement of both arterial and venous blood. It is also possible to measure the O2 saturation of arterial blood by non-invasive pulse oximetry. Therefore, joint processing of venous and arterial blood T2 measurements, together with a known value of arterial O2 saturation, can provide additional information that aids in accurate parameter estimation.

In summary, to derive an estimate of blood O2 saturation from its corresponding T2, we acquired four T2 maps resulting in eight equations: four for the venous blood of interest and four for a reference arterial blood pool. We propose that these T2 measurements, together with the hematocrit and non-invasive arterial O2 saturation, collectively support a reliable fit of the L-M model. As shown in Fig. 1, our solution for non-invasive, in vivo estimation of O2 saturation thus involves a two-step procedure: (i) acquire distinct, quantitative blood T2 maps, each at a specific τ ₁₈₀, and (ii) utilize a NLLS fitting approach to jointly estimate venous O2 saturation along with the remaining unknown nuisance parameters of the L-M model.

The study was conducted with the approval of the Institutional Animal Care and Use Committee. Seven pigs were anesthetized with isoflurane and mechanically ventilated on 100% oxygen. Balloon catheters were inserted into the right atrium and proximal aorta for sampling venous and arterial blood, respectively. After placement in the CMR scanner, the animals were subjected to controlled graded hypoxemia by varying the ratio of oxygen to nitrogen gas inhaled [30]. We sought to achieve arterial O2 saturation levels ranging from 100% down to 70% in each animal. The experimental set up is illustrated in Fig. 3.

Each inspired gas mixture was maintained for at least 10 min to allow O2 saturation levels to stabilize before blood sampling and imaging. Arterial and venous blood samples (roughly 0.1 mL) were drawn from aortic and right atrial catheters before and after imaging at each hypoxemic stage; the samples were immediately analyzed with a Vetscan I-stat 1 handheld blood gas analyzer (Abaxis Inc., Union City, California, USA). The arterial and venous O2 saturation for each hypoxemic stage was determined by averaging the saturation levels measured before and after imaging (approximately ten minutes apart). The hematocrit was measured in each blood sample and averaged across all measurements to determine the value for each animal.

After stepping through stages from highest to lowest level of inspired oxygen, the animal was allowed to recover for approximately 15–20 min by breathing 100% oxygen. The animal was then euthanized after a second set of measurements was made at 100% arterial O2 saturation. The two sets of baseline blood gas measurements obtained from each animal before and after CMR imaging were tested to evaluate the reproducibility of O2 saturation measurements by catheterization and blood gas analysis.

All imaging was performed on a 1.5 T magnet (MAGNETOM Avanto, Siemens Healthineers, Erlangen, Germany) with a maximum gradient amplitude of 45 mT/m and slew rate of 200 mT/m/ms. A flexible six-element phased array body coil was placed on the thorax over the heart and combined with elements of a spine array coil for signal reception. CMR at each stage of hypoxemia included the acquisition of four T2 maps, each using a different τ ₁₈₀, in a single short axis view including both right and left ventricles. At each stage of hypoxemia, four T2 maps, each with τ ₁₈₀ of 12, 15, 20, and 25 ms, were acquired in a randomized order to avoid any bias that may be caused by the drifting of the O2 saturation levels. The images were cardiac triggered and acquired free breathing in late systole to avoid rapid, disrupted flow during diastolic filling. The imaging parameters were: TR (time between T2 prepared image acquisitions) 4000 to 5000 ms (seven to fourteen cardiac cycles depending on heart rate, chosen to ensure adequate T1 recovery), two signal averages (NEX), where each NEX is a single shot measurement, flip angle = 70⁰, parallel acceleration = 2, bandwidth = 1182 Hz/pixel, field of view = 400 × 368 mm, matrix size = 128 × 118, spatial resolution = 3.1 × 3.1 × 10 mm. The TE of the SSFP readout was 0.89 ms while TR was 2.2 ms. Parallel acceleration was used in combination with multiple NEX to keep the shot time short while preserving SNR. The acquisition time of each map was approximately 40 to 50 s. Cardiac output was measured at the aortic outflow using a real-time velocity sequence [31] at each hypoxemia stage (TR/TE = 96.4/5.1 ms, TA = 5 s, spatial resolution = 3.8 × 3.1 × 10 mm). Heart rate was monitored using a 3-lead wireless electrocardiogram, and arterial O2 saturation was monitored by placing a pulse oximeter probe on the lower lip of the animal.

Image analysis was performed on a Leonardo workstation (Siemens Healthineers, Erlangen, Germany). Prior to performing the animal study, the four T2 maps were evaluated on static phantoms prepared to approximate T2 value of arterial and venous blood. The T2 values of the phantoms were measured by placing a region of interest in each of the four maps. These values were compared against a reference T2, measured by a multi-echo turbo spin echo (MESE) sequence. The reference T2 values were calculated by mono-exponential fitting of the signal to the echo times in the MESE sequence. For the animal experiment, the T2 values of arterial and venous blood were measured by manually drawing contours around the lumen of the right ventricular (venous) and left ventricular (arterial) blood pools in each of the four T2 maps acquired at each hypoxemia stage.

For the proposed method, parameter estimation of the L-M model (Eq. 1) was performed using a NLLS curve fit based on an interior point algorithm in Matlab R2016a (Mathworks, Natick, Massachusetts, USA). Blood T2, hematocrit, and arterial O2 saturation (by blood gas analysis) were all measured, and ω ₀ (4 × 10⁸ rad/s at 1.5 T) and τ ₁₈₀ (12, 15, 20, and 25 ms) were known. The eight measurements of blood T2 (four arterial and four venous from the four T2 maps), along with the measured hematocrit and reference arterial O2 saturation at each stage were processed jointly to estimate the O2 saturation in the right ventricular cavity.

For the animal experiment, we tested and compared results from four different approaches. Approach 1: Estimate O2 saturation from the simplified L-M model in Eq. 2 using a single T2 map (τ ₁₈₀ = 12 ms) and a previously defined value of K (25 s⁻¹). There are two unknown parameters, T _2O and %SbO _2, in this simplified model. As previously proposed by Wright et al., T _2O was first calculated for each hypoxemia stage using the reference measurement of arterial O2 saturation (measured in samples drawn by invasive catheterization) for arterial blood T2. The calculated T _2O , predetermined K, and measured venous blood T2 were then used in Eq. 2 to solve for O2 saturation in the right ventricle. Approach 2: Estimate O2 saturation and other nuisance parameters by using the unconstrained optimization of the L-M model described in Eq. 1. The data consisted of multiple T2 maps, each corresponding to a different τ ₁₈₀ value. Approach 3: This approach was similar to Approach 2 with the exception that the values of T _2O , τ _ex , and α were learned from a training dataset. Approach 4 (our proposed approach described above): This approach was similar to Approach 2 with the exception that estimation of nuisance parameters was subjected to constraints (bounds) that were learned from a training dataset.

All variables are reported in mean ± standard deviation. Statistical analysis was performed in MedCalc Statistical Software version 17.8 (MedCalc Software bvba, Ostend, Belgium; http://​www.​medcalc.​org; 2017). The coefficient of variation was calculated to determine the reproducibility of blood gas measurements. Linear regression was performed to compare the relationship between the venous O2 saturation estimated using CMR against the reference venous O2 saturation measured by blood gas analysis. The systematic bias and limits of agreement between the two methods were evaluated by the Bland Altman method. A regression analysis was also performed on the differences of the two methods in the Bland Altman plots to determine any proportional bias [32]. Statistical significance was inferred for P < 0.05.

In the absence of noise or any model mismatch, an unconstrained approach described in this paper should work reliably. In the presence of measurement noise, however, the sensitivity to estimate each of the unknown parameters is limited, which results in parameter estimation with large variance. For such cases, enforcing bounds on parameters acts as a safeguard against assigning unrealistic values to some of the nuisance parameters while still providing some room for the parameters to adapt to the data. Reliance on bounds, however, is one of the limitations of this approach because the results are partially influenced by the selection of the bounds and not entirely by the data. For the in vivo data presented, one or more nuisance parameter bounds became active (for a total of 17 out of 19 tested). Despite this limitation, our preliminary results indicate that the proposed method can outperform existing methods that use a single predetermined calibration constant.

For the hypoxemia experiment, CMR was performed in the left and right ventricles. However, we obtained venous blood samples from the right atrium to avoid any artifacts that may be caused by the catheter being positioned in the imaging plane. The right atrium is known to exhibit greater regional variability of O2 saturation within the blood pool due to blood draining from the superior and inferior vena cavae and the coronary sinus. As the blood from these vessels have different levels of oxygenation, sampling of blood from the right atrium as was done in this experiment could cause greater variability in the catheter based O2 saturation measurement; this may have degraded the correlation with the CMR-based measurement that was made in the right ventricle. In addition, the arterial and venous O2 saturation levels by blood gas analysis varied from the start to the end of imaging at some hypoxemia stages despite waiting for ten minutes for the animal to achieve a steady state. We tried to alleviate any systematic bias in the measurement of T2 by acquiring the T2 maps in a randomized order, and by taking an average O2 saturation of the blood samples obtained at the beginning and end of imaging at each hypoxemia stage as the reference standard. Despite these measures, the resulting variability could account for the small inaccuracy seen between the reference and estimated venous O2 saturation in our study.

Hyperoxia or breathing 100% oxygen can increase the amount of oxygen dissolved in plasma, which is known to increase the relaxation rates. However, a recent study by Ma et al. [41] has shown the changes in R2 to be minimal. In addition, we maintained a sufficiently long interval of five seconds between image acquisitions for all hypoxemia stages to account for any influences of T1 recovery on the T2 estimates.

Although the T2 preparation is non-selective, it is possible that high blood flow rates may result in partial inflow of blood from distal regions that have not experienced the magnetization preparation. Another possibility is that the proximity of the lungs and trachea to the vena cavae may have some influence on the uniformity of T2 preparation of blood. These conditions may have contributed to some of the regional T2 variations in the ventricles, and account for the larger variation in O2 saturation seen in some hypoxemia stages.

Because the non-invasive pulse oximeter readings obtained from the lips of the animals were found to be unreliable, invasive arterial O2 saturation was used as the reference value. With the goal of measuring O2 saturation non-invasively in patients, an invasive arterial O2 saturation measurement would not normally be available; however, in patients a finger pulse oximeter is expected to provide a reasonable reference value for arterial O2 saturation that will support the accurate estimation of venous O2 saturation.

CMR oximetry techniques have been previously described to estimate blood O2 saturation in pediatric and adult populations [5, 18, 23, 26]. However, these methods have not gained clinical acceptance and this may be due to the need for patient-specific in vitro calibration procedures. While other studies have performed T2 measurements across a range of τ ₁₈₀ [12, 13, 35], the goal of those experiments was primarily to derive predetermined calibration parameters for the estimation of O2 saturation from a single T2 measurement. However, this strategy may lead to inaccurate results in the individual patient due to the contributions from multiple patient-specific parameters besides O2 saturation to blood T2. As a simple example, a calibration factor of K = 25 s⁻¹ applied to a venous blood sample having a T2 of 150 ms and T _2O of 300 ms would result in an estimated O2 saturation of 64%, assuming the calibration is performed for the normal hematocrit range. However, if the patient had anemia and the actual Hct was 0.25 instead of a normal value of 0.45, the true O2 saturation would be 58% if one accounted for the contribution of Hct to the L-M model in Eq. 1. We believe that our concept would be universally applicable for any mathematical representation of the exchange/diffusion model that describes the dependence of blood T2 to its corresponding O2 saturation as a function of the inter-echo spacing (τ ₁₈₀). The data could therefore, potentially be acquired with any imaging sequence that achieves T2 weighting with a train of refocusing pulses. By allowing the nuisance parameters to be estimated on a patient-specific basis, we do not have to account for the individual effects of age, gender, etc., on the hemodynamic properties of blood. With regard to applicability at a higher field strength of 3 T, where the effects of B0 and B1 inhomogeneities are greater, our preliminary experiments in a cohort of healthy volunteers [42] indicate that the method is feasible, although the validity of the method at 3 T is yet to be rigorously assessed.

Non-invasive estimation of hematocrit would render the oximetry technique truly non-invasive. As hematocrit factors in as Hct(1 − Hct) in the L-M model, a solution from T2 relaxation alone is difficult due to the possibility of multiple values being estimated. Recent studies have demonstrated the potential to estimate hematocrit and oxygen saturation from T1 measurements [43], and have also proposed a combination of T1 and T2 measurements for joint estimation of hematocrit and O2 saturation [40]. Incorporating these features may lead to a truly non-invasive oximetry technique, but is outside the scope of the current work.

The clinical application of this technique would be especially valuable in heart failure, pulmonary hypertension, and congenital heart disease patients, who may present under different hemodynamic and metabolic states, and altered blood magnetic properties than the normal population. The present study focused on an animal hypoxemia model with normal cardiovascular anatomy. Animal models of intra- and extra-cardiac shunts could also be useful to help establish the performance of the technique under conditions that may be found in a congenital heart disease population.