The Luz-Meiboom model defines the physical basis for the relationship between the relaxation of the MRI signal and the proportion of hemoglobin in blood that is bound to oxygen [25]. Wright et al. derived a term that relates T2 to oxygen saturation (SaO₂) [58]:
where T2o is the T2 of fully oxygenated blood for a given hematocrit and K is a constant that is dependent on the magnetic field strength and the refocusing interval of the T2 preparation sequence used to measure T2. We have shown good agreement between MR oximetry and conventional blood gas measurements made in the large mediastinal vessels of children undergoing cardiac catheterization [33]. Since this work, modern sequences have been developed for performing MR relaxometry that produce maps allowing ready placement of a region of interest (ROI) within the vessel lumen for measuring the T2 of blood. Stainsby et al. have provided guidance on the requisite conditions for avoiding contamination of the signal from structures surrounding the vessel, which include a minimum of six voxels across the diameter and a slice thickness no greater than the vessel diameter [51]. This poses a challenge to imaging fetal vessels because shorter scan times are required to avoid excessive motion artifact, resulting in the usual trade-off between signal-to-noise ratio and spatial resolution. However, innovations in sequence design have helped to make the technique feasible in the larger vessels of late gestation fetuses. One such innovation is a sequence designed for myocardial relaxometry that employs a rapid SSFP readout following the T2 preparation and a nonrigid registration motion correction algorithm [12, 13]. The fast readout provides individual T2 preparation images that are free from motion artifact. However, it is only with motion correction, which adjusts for small fetal and maternal movements occurring during the several second intervals required for magnetization recovery between the acquisition of individual T2 preparation images, that the straightforward determination of T2 from the T2 map becomes feasible. Without motion correction, accurate T2 values could presumably still be obtained by placing individual ROIs over the vessel lumen on each individual T2 preparation image, although this would be more time consuming. One aspect of using the imaging sequence devised by Giri et al. is that the magnetization recovery intervals and triggers for acquiring the readout are based on an ECG signal. For fetal imaging, it is therefore necessary to produce an artificial ECG signal to run the acquisition. Most modern MRI systems have the facility to produce such a signal, and the R-R interval can be programmed according to the estimated fetal heart rate, a process we have termed pseudo-gating. We generally measure the fetal heart rate with a cardiotocograph for several minutes prior to MRI in order to determine the average fetal heart rate for each case and use this for the sequences requiring pseudo-gating. A second longer R-R interval is chosen for the sequences using MOG, to ensure that the k-space data used to reconstruct these images is oversampled.

Once the T2 of each vessel of interest is measured, a conversion to SaO₂ can be undertaken. We are currently attempting to calibrate in vitro measurements of T2 to the SaO₂ of human umbilical cord blood, in order to provide accurate human fetal MR oximetry. In the meantime, we have used the sequence developed by Giri et al. with the parameters shown in Table 10.1 to measure T2 in adult blood samples with a hematocrit matching late gestation fetal blood in order to convert T2 to SaO₂. The samples were prepared by exposure to nitrogen gas to have a range of SaO₂ to simulate blood in various fetal vessels. The calibration curve and a term fitting T2 to SaO₂ are shown in Fig. 10.2. This conversion assumes that the magnetic properties of fetal and adult hemoglobin are the same, an assumption that is likely to be flawed, and until a calibration using fetal blood is obtained, it may be more appropriate to report MR oximetry in terms of vessel T2 rather than SaO₂.

A potential source of error in the oximetry method described above is the requirement for an estimation of fetal hemoglobin concentration. While reference data indicates a fairly narrow range of hemoglobin concentration is present in utero [32], we are currently lacking sufficient data for reliable reference ranges in late gestation fetuses. Furthermore, fetal anemia resulting from allo-immunization and viral infection is not uncommon, and chronic hypoxia induces fetal polycythemia [42]. We recognize therefore that the use of an estimated fetal hemoglobin concentration represents a potentially important source of error in fetal MR oximetry based purely on the quantification of T2. However, there may be an elegant solution to this problem that takes advantage of the strong relationship that exists between the T1 relaxation of blood and its hematocrit with higher hematocrits resulting in shorter T1s [15]. Therefore, while the T2 of blood is primarily affected by SaO₂, but weakly impacted by hematocrit, its T1 is primarily influenced by hematocrit, but weakly affected by SaO₂. We have recently shown that these two relationships can be rearranged in a cubic polynomial equation whereby, with the exception of samples with very high SaO₂, there is a single solution for SaO₂ and hematocrit for any pair of T1 and T2 values that might coexist in an individual blood sample [38]. A computer simulation showing contour lines for oxygen saturation and hematocrit based on this solution is shown in Fig. 10.3. This work includes a validation of the technique, whereby good agreement is shown between conventional blood gas analysis of adult blood samples manipulated to have a range of oxygen saturations and hematocrits with values predicted for those samples based on their T1 and T2 values measured by MRI in vitro (Fig. 10.4). We anticipate further calibration using umbilical cord blood will confirm that the combination of T1 and T2 mapping will then form the basis of an accurate noninvasive technique for determining the oxygen content of fetal blood in vivo.

While fetal color and pulsed Doppler techniques provide a wealth of hemodynamic information about the fetal circulation and have been used to calculate combined ventricular output (CVO) and umbilical blood flow [19, 29, 50, 55], ultrasound measurements of vessel flow are prone to inaccuracy [11]. Although inferior spatial resolution and motion artifact degrade flow measurements made with cine PC CMR and currently limit the technique to late gestation fetuses, this approach avoids some of the difficulties encountered with ultrasound flow measurements. These include problems with obtaining an adequate angle of insonation and inaccuracies resulting from difficulties in measuring vessel area and with accounting for the faster velocities of blood flow in the center of the vessel and slower flow adjacent to the vessel wall. Under ideal conditions, PC CMR is more accurate than ultrasound for blood flow quantification, and criteria for acquiring adequate temporal and spatial resolution to achieve accurate flow measurements in small vessels have been reported [17, 24]. We attempted to assess the accuracy of PC CMR with MOG using flow phantoms and by comparing measurements made in the neck vessels of exercising adult volunteers using conventionally gated PC CMR measurements with those made using MOG [18, 48]. The results of this comparison are shown in Fig. 10.5 and indicate that flow measurements made in the larger fetal vessels of a human fetus close to term are likely to be accurate. Further reassurance regarding the accuracy of fetal PC MRI is to be found in the good correlation between direct and indirect measurements of pulmonary blood flow made using PC CMR [40]. Figure 10.6 shows good agreement between pulmonary blood flows calculated as the difference between main pulmonary artery and ductus arteriosus flow versus the sum of the right and left pulmonary arteries in normal late gestation human fetuses.

One approach to measuring the distribution of the fetal circulation is to use PC CMR flow measurements made in the ascending aorta (AAo), main pulmonary artery (MPA), ductus arteriosus (DA), right and left branch pulmonary arteries (RPA & LPA), superior vena cava (SVC), descending aorta (DAo), and umbilical vein (UV). The CVO can be derived from the sum of AAo and MPA flows, although we have always added 3 % to this figure to account for coronary blood flow, based on the reports of previous fetal lamb experiments [44]. Foramen ovale (FO) flow can be estimated as the difference between the left ventricular output and pulmonary blood flow, as FO flow and pulmonary blood flow are the two alternative sources of filling of the left heart. In order to measure umbilical flow, we target the UV in the liver, several centimeters beyond the umbilicus, but also well proximal to the porta hepatis. The UV takes a relatively straight course in its intrahepatic segment, and this permits PC CMR measurements that avoid the more complex flow patterns that occur in its free loops. Our approach has been to copy the PC CMR slice prescriptions to perform consecutive T2 maps in each of the larger branches (AAo, MPA, DA, SVC, DAo, UV) [46]. One approach to obtaining these flow measurements is shown in Fig. 10.7, and the imaging parameters for each of the sequences we use are shown in Table 10.1. An important principle to follow when acquiring the flow and oximetry measurements is to use two perpendicular long-axis views of each vessel in order to prescribe the slice position. This will ensure the imaging plane is acquired in a true short-axis orientation to the vessel, thus minimizing the chance of partial volume artifacts in the resulting images. We acquire surveys of the fetal thorax in three orthogonal planes using stacks of static SSFP slices with the sequence parameters shown in Table 10.1 in order to guide the subsequent PC and T2 prescriptions. These surveys may need to be repeated several times during the study to relocate the vessels accurately following fetal or maternal movement.

Metric optimization of the PC CMR measurements is currently performed using a purpose designed MATLAB program, which is available as an open-source internet resource [27]. Following MOG, the individual PC files are transferred back to the magnet computer, which converts them to DICOM files that can be processed using conventional CMR software for flow quantification. We use Q-Flow (Medis, Netherlands) to place regions of interest around the target vessel in order to determine vessel flow in ml/min. Vessel flows can be indexed to fetal weight by measuring fetal volume. One such approach involves the acquisition of a three-dimensional SSFP acquisition of the whole fetus. The stark contrast between the high signal of amniotic fluid and dark signal of the fetal skin on this sequence makes automatic segmentation of the fetal envelope reasonably straightforward using a threshold approach. We use Mimics by Materialize (Leuven) for this and have traditionally applied the following previously reported conversion of fetal volume to fetal weight [3]:

The combination of vessel flow and oximetry that is made possible using PC CMR and MR oximetry can be used to quantify placental function and fetal metabolism by allowing the measurement of fetal oxygen delivery (DO₂) and consumption (VO₂). Fetal DO₂ is the product of UV flow and UV oxygen content. The oxygen bound to hemoglobin and oxygen dissolved in plasma comprises the oxygen content of blood. In adult blood, the contribution to blood oxygen content from oxygen dissolved in plasma is in the 2–3 % range, while in fetal blood, this proportion is even lower, so that fetal blood oxygen content can be assumed to be the amount of oxygen combined with hemoglobin [44]. For adult blood, the amount of oxygen bound to hemoglobin can be calculated from the oxygen saturation (SaO₂) and hemoglobin concentration [Hb]:
where 1.36 is the amount of oxygen in ml that can be bound to 1 g of hemoglobin at 1 atm [44]. This figure is likely to be similar for fetal blood, as the total oxygen-carrying capacity of fetal hemoglobin is the same as adult hemoglobin despite the higher affinity of fetal hemoglobin for oxygen.

Fetal VO₂ is given by the product of UV flow (Q _UV) and the difference between the oxygen contents (ΔC) of the UV and the umbilical artery (UA):
Because of the small size of the UA, the T2 in the descending aorta (DAo) is used for this calculation.

If it is assumed that the majority of the flow in the superior vena cava (SVC) is venous return from the brain, then fetal cerebral VO₂ can also be approximated: