Quantification of Whole-Organ Individual and Bilateral Renal Metabolic Rate of Oxygen

Abstract

Purpose:

Renal metabolic rate of oxygen (rMRO₂) is a potentially important biomarker of kidney function. The key parameters for rMRO₂ quantification include blood flow rate (BFR) and venous oxygen saturation (SvO₂) in a draining vessel. Previous approaches to quantify renal metabolism have focused on the single organ. Here, both kidneys are considered as one unit to quantify bilateral rMRO₂. A pulse sequence to facilitate bilateral rMRO₂ quantification is introduced.

Methods:

To quantify bilateral rMRO₂, measurements of BFR and SvO₂ are made along the inferior vena cava (IVC) at suprarenal and infrarenal locations. From the continuity equation, these four parameters can be related to derive an expression for bilateral rMRO₂. The recently reported K-MOTIVE pulse sequence was implemented at four locations: left kidney, right kidney, suprarenal IVC, and infrarenal IVC. A dual-band variant of K-MOTIVE (db-K-MOTIVE) was developed by incorporating simultaneous-multi-slice imaging principles. The sequence simultaneously measures BFR and SvO₂ at suprarenal and infrarenal locations in a single pass of 21 seconds, yielding bilateral rMRO₂.

Results:

SvO₂ and BFR are higher in suprarenal vs. infrarenal IVC, and the renal veins are highly oxygenated (SvO₂>90%). Bilateral rMRO₂ quantified in 10 healthy subjects (8M, 30±8y.o.) was found to be 291±247 and 349±300(μmolO₂/min)/100g, derived from K-MOTIVE and db-K-MOTIVE, respectively. In comparison, total rMRO₂ from combining left and right was 329±273(μmolO₂/min)/100g.

Conclusion:

The present work demonstrates that bilateral rMRO₂ quantification is feasible with fair reproducibility and physiological plausibility. The indirect method is a promising approach to compute bilateral rMRO₂ when individual rMRO₂ quantification is difficult.

1. INTRODUCTION

Renal oxygen utilization is a potentially valuable physiological biomarker that indicates kidney health and function(1). Prior studies using invasive measurements in an animal model of diabetes have reported that renal metabolic rate of oxygen (rMRO₂) increases by 40–65%, at the whole-organ level(2–4) during early-stage kidney disease. Since increased oxygen utilization contributes to hypoxia of the kidney tissue(5), quantification of rMRO₂ is of interest.

rMRO₂ is expressed in units of oxygen consumed per unit time per unit tissue mass: (μmol O₂/min)/100g. Quantification of rMRO₂ follows from Fick’s Principle: $rMR{O}_2=k\cdot RBF\cdot \left(Sa{O}_2-Sv{O}_2\right)$, where $k=C_a/mass$, and C_a (μmol/mL) is the oxygen carrying capacity of arterial blood. RBF (mL/min) is the renal blood flow rate. SaO₂ and SvO₂ (decimals) represent the arterial and venous oxygen saturation levels. MRI can be used to noninvasively determine blood flow rate and venous oxygen saturation (the key parameters of Fick’s Principle) with phase-contrast imaging(6) and T₂-based oximetry(7,8), respectively. T₂ is converted to SvO₂ via a calibration model(9).

We have previously reported the MOTIVE(10) (Metabolism of Oxygen via T₂ and Interleaved Velocity Encoding) and K-MOTIVE(11) (Kidney MOTIVE) pulse sequences, which interleave a phase-contrast module before a background-suppressed T₂-prepared EPI or bSSFP readout, for simultaneous measurements of blood flow rate and T₂ (and SvO₂).

Initially, K-MOTIVE quantified rMRO₂ of only the left kidney with measurements of flow and SvO₂ in the left renal vessels(11). Here, however, quantification of rMRO₂ of the left and right kidneys is demonstrated. Furthermore, a method is proposed to quantify “bilateral” rMRO₂, i.e., rMRO₂ of both kidneys considered as a single unit. This approach relies on measurements made along the inferior vena cava at two locations (above and below the branching the renal vessels) and then applies a difference to quantify bilateral rMRO₂. The bilateral approach may be advantageous because kidney disease often depends on the function of both kidneys, not just one. Further, slice prescription along the inferior vena cava is relatively more straightforward than individual renal vessels, and the expected (lower) SvO₂ of the inferior vena cava is in a more sensitive region of the T₂-SvO₂ calibration model. Given that measurements at two locations are necessary for the “difference approach,” K-MOTIVE was applied separately at both locations. In addition, a dual-band implementation of K-MOTIVE (db-K-MOTIVE) was developed to enable simultaneous quantification of blood flow rate and SvO₂ at the two locations during a single acquisition.

2. METHODS

2.1. Bilateral rMRO₂ equation

Quantification of rMRO₂ of an individual kidney is based on measurements of renal blood flow rate (RBF) and SvO₂ in the renal vessels. These are the key parameters of Fick’s Principle: $rMR{O}_2=k\cdot RBF\cdot \left(Sa{O}_2-Sv{O}_2\right)$. Here, however, an alternate method is proposed by considering both kidneys as a single unit and measuring blood flow and venous oxygenation in the inferior vena cava (IVC) above and below the branching of the renal vessels (Figure 1)(12,13). Bilateral rMRO₂ can then be expressed as

$$Bilateral rMR{O}_2=k\left(Q_A^s-Q_A^i\right)\left(Sa{O}_2-\left(\frac{\left(Q_V^s\cdot Sv{O}_2^s\right)-\left(Q_V^i\cdot Sv{O}_2^i\right)}{Q_V^s-Q_V^i}\right)\right)$$ [1]

Figure 1:

The kidneys, inferior vena cava (IVC), and aorta are presented in standard radiologic coordinates. Blood flow rates (Q) and venous oxygen saturation levels (SvO₂) are defined in the aorta (A) and IVC (V) at suprarenal (s) and infrarenal (i) locations, marked in dashed lines. Quantification of bilateral renal metabolic rate oxygen (rMRO₂) follows from enforcing conservation of mass and flow. In the present study, the simplified equation was selected for quantification of bilateral rMRO₂. The slice prescription locations are marked as suprarenal IVC (s), infrarenal IVC (i), left renal vein (L), and right renal vein (R). Figure is not to scale.

In Eq. (1), “k” represents the combined constant terms. Superscripts “s” and “i” indicate the parameter at suprarenal and infrarenal locations, i.e., above and below the branching of the renal vessels, respectively. Q represents flow rate in mL/min with subscripts “A” and “V” corresponding to flow rate in the aorta and IVC, respectively. SvO₂ represents venous oxygen saturation at suprarenal and infrarenal locations of the IVC. SaO₂ is oxygen saturation of arterial blood. The derivation of this equation is provided in Supporting Information (Figure S1).

The second term in Eq. (1) can be considered a flow-weighted average venous oxygenation from both renal veins:

$$Bilateral Sv{O}_2=\frac{\left(Q_V^s\cdot Sv{O}_2^s\right)-\left(Q_V^i\cdot Sv{O}_2^i\right)}{Q_V^s-Q_V^i}$$ [2]

Based on the assumption that total renal arterial inflow is equal to total renal venous outflow, $Q_A^R+Q_A^L=Q_V^R+Q_V^L$, where “R” and “L” indicate right and left kidney, conservation of flow then implies

$$Q_A^s-Q_A^i=Q_V^s-Q_V^i$$ [3]

Thus, the renal arterial inflow, as measured by a difference in suprarenal and infrarenal blood flow rates in the aorta, equals renal venous outflow from a difference in suprarenal and infrarenal blood flow rates in the IVC. Substituting Eq. (3) into Eq. (1), yields the following equation, where all parameters are measured in the IVC:

$$Bilateral rMR{O}_2=k\left(Q_V^s-Q_V^i\right)\left(Sa{O}_2-\left(\frac{\left(Q_V^s\cdot Sv{O}_2^s\right)-\left(Q_V^i\cdot Sv{O}_2^i\right)}{Q_V^s-Q_V^i}\right)\right)$$ [4]

Evaluating the product in Eq. (4) and consolidating terms yields the following equation:

$$Bilateral rMR{O}_2=k\left(Q_V^s\left(Sa{O}_2-Sv{O}_2^s\right)-Q_V^i\left(Sa{O}_2-Sv{O}_2^i\right)\right)$$ [5]

Recasting the difference in oxygen saturation as $AVD{O}_2=Sa{O}_2-Sv{O}_2$ results the following equation:

$$Bilateral rMR{O}_2=k\left(\left(Q_V^s\cdot AVD{O}_2^s\right)-\left(Q_V^i\cdot AVD{O}_2^i\right)\right)$$ [6]

The simplified equation, Eq. (6), was adopted for bilateral rMRO₂ computation. Justification for this choice is provided in the Discussion section. Furthermore, given that bilateral rMRO₂ in Eq. (6) depends on parameters in the venous circulation, computation of whole-organ rMRO₂ of the individual kidneys in the present study was based on flow rates in the respective renal veins.

2.2. Pulse sequences

The previously reported K-MOTIVE sequence simultaneously measures blood flow rate in the renal artery and blood water T₂ in the renal vein. K-MOTIVE comprises a global saturation, golden-angle radial velocity-encoded phase-contrast module, background-suppression by means of adiabatic inversion pulses, global T₂-preparation, and a balanced steady-state free precession (bSSFP) readout(14,15). This scheme represents one interleaf and is repeated for all TEs corresponding to T₂-preparation. The global saturation serves to reset the magnetization at the start of each interleaf followed by the same saturation recovery time to ensure that T₂-preparation is applied to same magnitude of longitudinal-magnetization across all interleaves. Radial velocity-encoded spokes are acquired and shared across all interleaves to generate an average measurement of velocity. This same sequence was implemented in the present study when imaging (separately) at four locations: suprarenal, infrarenal, left and right kidneys. However, the pulse sequence parameters were optimized for the venous circulation (e.g., lower VENC). The parameters are listed in Table 1.

Table 1:

Pulse sequence parameters. Abbreviations: TR = repetition time, TE = echo time, VENC = velocity encoding parameter, FOV = field of view, Tsat = time gap between global saturation and start of background suppression, MLEV-4 = Malcolm-Levitt T₂-preparation scheme, bSSFP = balanced steady-state free precession, and BW = bandwidth.

Module	K-MOTIVE & db-K-MOTIVE
Phase contrast: radial acquisition	TR = 7.50 ms TE = 4.63 ms Flip angle = 12°; in dual-band, flip angles: α = β = 12° The polarity of the β-RF pulse alternates Slice separation ~ 100 mm VENC = 50 cm/s Golden angle = 111.25° FOV = 300 × 300 mm2 Number of readout samples = 300 Voxel size = 1 × 1 × 5 mm3 BW/pixel = 833 Hz/pixel Tsat = 2500 ms
	Spokes per interleaf = 144 Interleaves = 5 Total spokes = 720
Background suppression	Slice-selective saturation followed by 4 adiabatic inversion pulses 90°SS-180°SS-180°SS-180°NS-180°NS SS: slice-selective; NS: non-selective Ratio of inversion slab thickness to T2-prepared bSSFP imaging slice thickness = 1.5 SS inversion slab thickness = 18 mm Total duration = 1000ms Pulse times (ms): 0, 140, 450, 750, 940 In dual-band implementation, the first two SS adiabatic inversions are composed of the sum of two adiabatic inversion pulses, partially shifted in time.
T2-preparation	90°x…(90°x180°y90°x)4n…270°x360°-x MLEV-4 pattern: +y, +y, -y, -y All non-selective RECT pulses Five interleaves: n = 0, 1, 2, 3, sat* τ180 = 12 ms T2-preparation times = 0, 48, 96, 144, and ∞ ms * Saturated magnetization for a three-parameter fit of bSSFP signal
bSSFP Readout	Flip angle = 60°; in dual-band, flip angles: α = β = 60° The phase increments of the α- and β-RF pulses are +π/2 and –π/2, respectively, to modulate every other line of k-space by π Slice separation ~ 100 mm 10 catalyzation TRs Phase partial-Fourier factor = 50% 14 reference lines TR = 4.50 ms, TE = 2.25 ms FOV = 300 × 300 mm2 Reconstruction matrix = 200 × 200 Voxel size = 1.5 × 1.5 × 12 mm3 BW/pixel = 1250 Hz/pixel

Quantification of bilateral rMRO₂ by imaging at suprarenal and infrarenal locations is suitable for a multiplexed acquisition because information from two different locations is required. Compared to an interleaved acquisition where K-MOTIVE is implemented twice (necessitating two breath holds), applying simultaneous multi-slice(16) (SMS) principles to the K-MOTIVE sequence will improve the efficiency of data acquisition to quantify the four parameters (per Eq. [6]): $Q_V^s$, $Q_V^i$, $AVD{O}_2^s$, and $AVD{O}_2^i$, in a single breath hold. Here, a dual-band-K-MOTIVE sequence (db-K-MOTIVE) was developed by incorporating SMS strategies into the golden-angle radial velocity-encoded phase-contrast and bSSFP modules. A timing diagram is illustrated in Figure 2. Each component is described in more detail in the subsequent sections.

Figure 2:

Timing diagram of the “dual-band-Kidney Metabolism of Oxygen via T₂ and Interleaved Velocity Encoding” (db-K-MOTIVE) pulse sequence. db-K-MOTIVE builds on the K-MOTIVE sequence and measures T₂ and blood flow velocity at two locations simultaneously (i.e., a total of four parameters). T₂ is converted to venous oxygenation (SvO₂) by calibration model. Following an initial global saturation, an ungated dual-band golden-angle radial phase-contrast module is applied (A) with a zero and nonzero first moment to achieve flow compensation and velocity-encoding, respectively. Dual-band RF-pulse was designed as a combination of two single-band RF-pulses, where the polarity of the second (β) pulse alternates throughout the acquisition (“n” represents pulse index). Dual-band background suppression (B) consists of selective and non-selective adiabatic inversion pulses. The selective adiabatic inversion pulses are in turn a summation of two single-band slice-selective adiabatic inversion pulses that are partially shifted in time to minimize peak RF power. T₂-preparation is based on Malcolm-Levitt (MLEV-4) pattern (C). Lastly, a dual-band bSSFP module sampled the magnetization with a partial-Fourier Cartesian readout (D). In this module, the dual-band RF-pulse also comprises two single-band RF-pulses. However, the phase increments of the (α) and (β) pulses are +π/2 and –π/2, respectively, to shift one slice by half of the FOV. The entire scheme is then repeated N times (N = number of TEs) to result in additional velocity-encoded spokes and T₂-weighted images. With an inter-refocusing pulse time (τ₁₈₀) of 12ms, each additional interleaf extends the MLEV preparation by another four composite pulses to increase the effective TE by 4*τ₁₈₀ ms. In the present study, five TEs were included corresponding to a pulse sequence duration of 21 seconds. Figure is not to scale.

In db-K-MOTIVE, an ungated golden-angle radial phase-contrast module is applied during the saturation time (Tsat). A radial acquisition provides robustness to motion, where artifacts would be distributed throughout the image. Incrementing by the golden-angle (111.25˚) with a Fibonacci number of views ensures that k-space will be sampled uniformly by each additional spoke(17). The RF-pulse was designed to simultaneously excite slices at both suprarenal and infrarenal locations by summing two single-band RF-pulses: $R{F}_{db}=R{F}_{{\varphi }_n}\left(t\right)+R{F}_{{\varphi }_n}\left(t\right)\cdot e^{i\text{Δ}\omega t}\cdot {\left(-1\right)}^n$. In the equation, “n” represents pulse index, ${\varphi }_n$ represents RF-phase, and $\text{Δ}\omega$ represents the modulation frequency to excite the second slice ($\text{Δ}\omega =\gamma G_z\text{Δ}z$, ${\text{G}}_{\text{z}}$ is the slice-select gradient amplitude and $\Delta \text{z}$ is the spacing between the two slices). The polarity of the second RF-pulse alternates throughout the acquisition (Figure 2A). As a result of this phase-cycling scheme in a dual-band radial acquisition, one of the two slices will appear incoherent due to destructive interference (Figure 1 in Yutzy et al.(18)). Slice-separation during reconstruction follows from multiplying the dual-slice k-space data by the phase-conjugate pattern(18). The separation distance between the two locations was approximately 100mm.

The background-suppression module comprises four adiabatic inversion pulses. The timings follow from Maleki et al.’s work, which found that four pulses provided good SNR and suppression of static tissue for a broad range of T₁ (250-4300ms)(19). The module begins with three slice-selective 90˚ excitation pulses with orthogonal gradient spoilers. The three saturation pulses and orthogonal gradient spoilers address B₁ inhomogeneity and suppress RF- and stimulated echoes. Then, two slice-selective (SS) and two non-selective (NS) adiabatic inversion pulses are applied. An even number of NS pulses ensures that the magnetization of inflowing blood will point in +z-direction, so that longitudinal relaxation will increase the magnitude of magnetization during the gap before T₂-preparation. The SS and NS adiabatic inversion pulses are separated by approximately 300 ms. Background-suppression will reduce partial-volume effect and eliminate the need to acquire control and label images, as in TRUST(20). Inflow of venous blood will then provide signal from which T₂ is determined. To implement dual-band background-suppression, the SS adiabatic inversion pulses were modified by summing two single-band adiabatic inversion pulses selective for the two locations (Figure 2B). Peak RF-power was minimized by applying a partial shift in time, as proposed by Goelman(21). Lastly, a gradient spoiler is applied to reduce residual transverse-magnetization.

T₂-preparation imparts T₂-weighting(22) with a series of non-selective excitation and composite refocusing pulses. The module includes a 90°_x excitation pulse (subscript indicates direction of B₁), a set of composite (90°_x180°_y90°_x) refocusing pulses that is repeated in sets of four to achieve longer TEs for greater T₂-weighting, and a composite (270°_x360°_-x) tip-up pulse. Composite pulses reduce the effects of B₀ and B₁-inhomogeneities. Phases of the composite refocusing pulses followed an MLEV-4 pattern (+y, +y, −y, −y)(23). The inter-refocusing time (τ₁₈₀) was 12ms. Five total interleaves, four of which were T₂-preparation times and one was an image with saturated magnetization, corresponded to TEs=0/48/96/144/∞ms. The TE=∞ms permits a three-parameter fit(24) to the exponential decay with a non-zero steady-state signal.

After T₂-preparation, a partial-Fourier Cartesian bSSFP sampling scheme was used to collect k-space data. As in the phase contrast module, dual-band implementation of bSSFP also summed two single-band RF-pulses to simultaneously excite two locations. However, the RF-phase cycling pattern followed from Stab et al.(25), where the phase of one RF-pulse increments by π/2 and the phase of the other increments by –π/2 throughout the acquisition (Figure 2D). This cycling pattern ensures that every other line of k-space will experience a phase-modulation of π between the two RF-pulses while also fulfilling the steady state condition(26). The objective of imparting such a modulation is to shift one of the slices by half of the FOV such that variations in coil sensitivities between the two locations can be maximized to disentangle the simultaneously-excited slices(27).

The single-band implementation of K-MOTIVE entails excitation of a single slice in both the radial phase-contrast and bSSFP modules. Specifically, the RF-pulses in Figure 2A and 2D would comprise single-band excitations, thereby requiring separate acquisitions at suprarenal and infrarenal locations. In turn, the phase-cycling schemes to enable dual-band imaging would not be necessary. The pulse sequence duration of both the K-MOTIVE and db-K-MOTIVE sequences is 21 seconds, permitting a breath-held acquisition during the imaging protocol.

2.3. MRI Experiments

Ten healthy subjects (8M, 30±8y.o.) participated in the study after obtaining informed consent (demographics in Table 2). Human subjects research was conducted in accordance with institutional review board regulations at the University of Pennsylvania. MRI experiments to quantify renal metabolism were conducted at 3T (Siemens Prisma, Erlangen, Germany) with a body-flex array and spine coils (30 total channels). The pulse sequences presented here were developed using SequenceTree(28). Before conducting experiments in human subjects, the dual-band background suppression module was tested in vendor-provided phantoms to verify suppression of signal in a static object. The results of these experiments are in Figure S2.

Table 2:

Subject demographics. Parameters are expressed as mean ± S.D., and range (if applicable) is provided in parentheses.

Parameter	Value
Number of participants	10 (8 M)
Age (years)	30 ± 8 (24–52)
Height (cm)	174 ± 9 (160–191)
Weight (kg)	68 ± 13 (54–93)
BMI (kg/m2)	23 ± 3 (19–31)
Left kidney mass (g)	180 ± 40 (150–240)
Right kidney mass (g)	180 ± 30 (130–240)
Hematocrit	0.43 ± 0.04 (0.38–0.51)

The K-MOTIVE sequence (parameters optimized for venous flow) was implemented at the following locations: left kidney, right kidney, suprarenal IVC, and infrarenal IVC. In addition, db-K-MOTIVE was run to simultaneously image the suprarenal and infrarenal locations, with a separate calibration scan (gradient-recalled-echo sequence) to obtain coil sensitivity maps. Lastly, ungated standalone Cartesian phase-contrast pulse sequences were developed to measure the blood flow rate in the renal artery (VENC=80cm/s) and vein (VENC=50cm/s) to compare renal arterial inflow to renal venous outflow. Orthogonality to the renal vessels was verified with double-oblique time-of-flight angiography scout images. All acquisitions were performed under a breath-held condition at end-expiration. Reproducibility of the pulse sequences (intrasession and intersession) was evaluated. Intrasession reproducibility refers to an evaluation of the pulse sequence repetitions within the same session. Intersession reproducibility (short term) refers to an evaluation of the pulse sequence repetitions where the subject is taken out of and then placed back into the scanner in the same day. Table 3 details the imaging protocol. In three of the ten subjects, acquisition of the right renal vessels was not possible due to difficulty in identifying an imaging slice. This is not unexpected because the right renal vein is shorter than the left in most humans(29).

Table 3:

Imaging protocol. The pulse sequence order was randomized.

Sequence	Purpose	Sequence Duration (s)	Repetitions	Measurement Locations
				SvO2	Velocity
K-MOTIVE-left *	Interleaved sequence to simultaneously measure flow velocity (optimized for venous flow) with radial phase-contrast and T2 with bSSFP readout.	21	3	Left renal vein
K-MOTIVE-right *				Right renal vein
K-MOTIVE-supra *				Suprarenal inferior vena cava
K-MOTIVE-infra *				Infrarenal inferior vena cava
db-K-MOTIVE *	Dual-band implementation of Interleaved sequence to simultaneously measure flow velocity (optimized for venous flow) with radial phase-contrast and T2 with bSSFP readout.	21	3	Suprarenal & infrarenal inferior vena cava
db-calibration *	Cartesian gradient-recalled-echo sequence to determine coil sensitivity maps for slice separation in db-K-MOTIVE	12	1	Suprarenal & infrarenal inferior vena cava
Cartesian phase-contrast	Reference sequence to separately measure flow velocities in renal artery and vein (via Cartesian readout)	10	3	n.a.	Renal artery & vein

^*Pulse sequences marked by asterisks were repeated at each location in a second scan session on the same day (after repositioning) to evaluate short-term intersession reproducibility. Subjects were requested to perform a post-exhalation breath hold. Abbreviations: supra = suprarenal; infra = infrarenal; db = dual-band; bSSFP = balanced steady-state free precession; and T₂prep = T₂-preparation.

2.4. Data analysis

Quantification of rMRO₂ was performed by invoking Fick’s Principle: $rMR{O}_2=k\cdot BFR\cdot \left(Sa{O}_2-Sv{O}_2\right)$, where $k=C_a/mass$. $C_a=C_{RBC}\cdot hematocrit$. $C_{RBC}$ is the oxygen carrying capacity of red blood cells which is computed with the ideal gas law and an oxygen carrying capacity of 1.34mL O₂ per gram of hemoglobin(30,31), yielding $C_{RBC}=19.93 \mu mol O_2/mL RBC$. Hematocrit was determined via a capillary blood sample (Hb 201+, Hemocue, Angelholm, Sweden). Kidney mass was obtained by determining kidney volume via manual segmentation of multi-slice gradient recalled echo scout images and conversion to mass with a tissue density of 1.06g/mL(32). During bilateral rMRO₂ computation, total kidney mass (left and right combined) was used. SaO₂ was fixed at 98% since all subjects are healthy adults.

For K-MOTIVE (single-band), data analysis was performed as previously described(10). Briefly, the radial spokes across all interleaves were combined before reconstruction. Then, a phase-difference was computed between the two encodings to generate a velocity map. Radial reconstruction was performed with the non-uniform fast Fourier transform by Fessler and Sutton(33). Blood flow rate (BFR) was determined by multiplying the average blood flow velocity with the cross-sectional area of the vessel. The vein of interest (renal vein or inferior vena cava) was manually segmented to determine BFR and Fick’s Principle was derived from venous flow. In images from the reference Cartesian phase-contrast, the renal artery and vein were manually segmented to compare arterial and venous BFR. Partial-Fourier bSSFP acquisition was reconstructed with projection-onto-convex-sets(34). Regions-of-interest were drawn over the vein of interest (vessel boundary identified with Otsu’s method, as described in(35)) on the image corresponding to TE=0ms and then propagated to all TEs. The TEs (0/48/96/144/∞ms) were corrected for the time that magnetization is temporarily stored in the longitudinal direction during refocusing pulses(36) with T₁ and T₂ of 1600 and 110ms(37), respectively. The resulting corrected TEs were as follows: 0/43.7/87.4/131.2/∞ms. A three-parameter exponential(24) was used to fit T₂. TE of ∞ms was set to 10,000ms for the purposes of the exponential fit. Conversion of T₂ to SvO₂ was performed with an integrative calibration model by Li and van Zijl(9).

During db-K-MOTIVE analysis, slice-separation of the radial acquisition was performed with an iterative reconstruction described by Yutzy et al.(18) based on the conjugate gradient SENSE reconstruction proposed by Pruessmann et al.(38) Although the image from one location is dispersed through the image from the other location, multiplication by the conjugate phase pattern will reverse the coherence to facilitate slice-separation(18). Coil sensitivities were determined from a calibration scan of the two locations. Following slice-separation, a velocity map was generated by computing a phase difference, similar to the single-band analysis. Slice-separation of the dual-band bSSFP images was performed using a least-squares minimization algorithm presented by Lee et al.(39), based on work described by Preussmann et al.(38), by exploiting the variations in coil sensitivities at the two locations.

When computing bilateral rMRO₂, measurements of BFR and SvO₂ made in the suprarenal and infrarenal IVC were substituted into Eq. (6). Since K-MOTIVE measured flow rate and oxygenation at suprarenal and infrarenal locations separately, the parameters derived from K-MOTIVE at the two locations were combined in Eq. (6). On the other hand, db-K-MOTIVE acquires flow rate and SvO₂ at both locations in a single pass. In addition, the individual whole-organ rMRO₂ values from each kidney were added together as a reference value to the bilateral experiment. In subjects whose rMRO₂ of the right kidney was unavailable (3/10), rMRO₂ of the left kidney was doubled to obtain total-individual rMRO₂.

The equation for bilateral rMRO₂ depends on several parameters, and there were some instances in which the bilateral rMRO₂ was found to be less than zero. This occurs when the “bilateral SvO₂” (a computed, not measured, parameter that depends on SvO₂ and BFR from two locations: Eq. [2]) exceeds 98%. Since a negative value of metabolic rate of oxygen is not physiologically plausible, any bilateral SvO₂ values higher than 97% were capped at 97% before bilateral rMRO₂ computation. The value of 97% was chosen as a ceiling because the maximum achievable SvO₂ resulting from Li and van Zijl’s calibration model(9) is 97%. Empirical inspection of their model suggests arbitrarily large T₂ values are eventually capped at an SvO₂ of 97% oxygenation. In the single-band K-MOTIVE analysis, 60 measurements were made (10 subjects, 3 repetitions per scan-session, 2 scan-sessions), of which 20 (33%) bilateral SvO₂ values were greater than 97%. Of the 60 measurements from db-K-MOTIVE analysis, there were 16 (27%) such values. On the other hand, in the individual kidney experiments, none of the resultant rMRO₂ values were negative because the calibration model’s maximum achievable SvO₂ is 97%. For arbitrarily longer T₂, there will be a positive AVDO₂ (98%−97%=1%), ensuring a positive rMRO₂.

SNR and CNR values in the veins of interest were calculated for all sequences to evaluate image quality. Reconstruction and analysis were performed in MATLAB (Mathworks, Natick, MA). Statistical tests to evaluate individual and bilateral metabolic parameters were performed in MATLAB and SPSS (IBM, Armonk, NY). Bland-Altman and correlation analyses were performed to assess agreement in the parameters quantified by the pulse sequences at each location. The significance threshold was set to α=0.05. Intraclass correlation coefficients were based on an average-measured two-way mixed-effects model(40).

3. RESULTS

3.1. Renal metabolic parameters

K-MOTIVE and db-K-MOTIVE measure SvO₂ and blood flow rate (BFR) at several locations, including the left renal vein, right renal vein, suprarenal inferior vena cava, and infrarenal inferior vena cava. Representative images with fitted signal-decays are provided in Figure 3. Metabolic parameters quantified across all sequences and locations are listed in Table 4. Boxplots of the parameters are in Figure 4. When examining T₂ and oxygenation at the different locations, the renal veins were found to be highly oxygenated (Figure 4A–4B, pulse sequence indices “1” and “2”), which consequently contributes to the greater SvO₂ in suprarenal than infrarenal IVC (indices “3” to “4” and “5” to “6”). A similar pattern is evident when examining BFR (Figure 4C) since the flow rate in the suprarenal IVC increases after venous outflow from the kidneys drains into the IVC. The relatively high oxygenation level of the renal veins (consequence of long T₂) can also be appreciated from the plot of signal-decays (Figure 3). The suprarenal IVC receives blood from the renal veins and infrarenal IVC, and those T₂ decay curves are thus in between the curves corresponding to the other locations.

Figure 3:

Representative images from K-MOTIVE implemented at (A) left renal vein, (B) right renal vein, (C) suprarenal inferior vena cava (IVC), and (D) infrarenal IVC. Images from db-K-MOTIVE after slice-separation: (E) suprarenal IVC, and (F) infrarenal IVC. A dual-slice bSSFP magnitude image (at TE=0ms) before slice-separation is in (G), illustrating the half-FOV shift. In panels (A)-(F), subpanels (i) background-suppressed bSSFP magnitude image at TE=0ms with renal vein or IVC marked by a blue arrow; (ii) the vein of interest at varying TEs; (iii) magnitude image from radial phase-contrast module; and (iv) corresponding velocity map. The fitted signal-decay curves for each pulse sequence are near the bottom, center.

Table 4:

Summary of metabolic parameters derived from K-MOTIVE and db-K-MOTIVE from 10 subjects. Parameters from right renal vessels were unavailable in three of the subjects. In such instances, the left renal parameters were doubled for subsequent bilateral calculations. Measurements are expressed as mean ± S.D. Abbreviations: SvO₂ = venous oxygen saturation; AVDO₂ = arteriovenous difference in oxygen saturation; blood flow rate = BFR; and rMRO₂ = renal metabolic rate of oxygen.

Pulse Sequence	T2 (ms)	SvO2 (%)	AVDO2 (%)	BFR (mL/min)	rMRO2 ((μmol O2/min)/100g)	Bilateral rMRO2 ((μmol O2/min)/100g)
K-MOTIVE-left	154 ± 20	91 ± 6	7 ± 6	494 ± 101	172 ± 138	n.a.
K-MOTIVE-right	155 ± 26	92 ± 7	6 ± 7	463 ± 186	138 ± 171	n.a.
(K-MOTIVE-left) + (K-MOTIVE-right)	n.a.	n.a.	n.a.	968 ± 230	n.a.	329 ± 273
K-MOTIVE-supra	123 ± 25	81 ± 7	17 ± 7	2091 ± 396	n.a.	291 ± 247
K-MOTIVE-infra	91 ± 18	70 ± 6	28 ± 6	1006 ± 280
(K-MOTIVE-supra) – (K-MOTIVE-infra)	n.a.	n.a.	n.a.	1085 ± 254	n.a.	n.a.
db-K-MOTIVE-supra	123 ± 35	80 ± 8	18 ± 8	2192 ± 442	n.a.	349 ± 300
db-K-MOTIVE-infra	92 ± 22	70 ± 7	28 ± 7	1046 ± 340
(db-K-MOTIVE-supra) – (db-K-MOTIVE-infra)	n.a.	n.a.	n.a.	1146 ± 209	n.a.	n.a.

Figure 4:

Comparison of metabolic parameters from all pulse sequences and locations. (A) T₂, (B) venous oxygen saturation (SvO₂), (C) blood flow rate (BFR), and (D) renal metabolic rate of oxygen (rMRO₂), both individual and bilateral. The box outlines indicate 25^th, 50^th, and 75^th quartiles, and the diamond marks mean value. Significant differences were found in T₂, SvO₂, and BFR and are marked accordingly. Pairwise comparisons are listed above each panel, and p-values significant at α=0.05 are in red. No significant differences were found in rMRO₂. Two RM-ANOVA tests were performed to evaluate rMRO₂ with one comparing individual and bilateral rMRO₂, and the other comparing sum of individual and bilateral rMRO₂. The groupings are in dashed lines. Pulse sequence key: (1) K-MOTIVE-left; (2) K-MOTIVE-right; (3) K-MOTIVE-supra; (4) K-MOTIVE-infra; (5) db-K-MOTIVE-supra; and (6) db-K-MOTIVE-infra. In panel (D), “1+2” represents bilateral rMRO₂ from the sum of left and right kidney rMRO₂. “3 & 4” indicates that measurements from single-band K-MOTIVE at suprarenal and infrarenal locations were combined to determine bilateral rMRO₂. “5 & 6” indicates the same as the latter but from db-K-MOTIVE.

In general, T₂, SvO₂, and BFR were significantly different in the renal veins vs. suprarenal IVC; renal veins vs. infrarenal IVC; and suprarenal IVC vs. infrarenal IVC, supporting our hypotheses (p-values are above each panel in Figure 4 and in Tables S1–S3). A boxplot of flow rates including the results from Cartesian phase-contrast sequences is shown in Figure S3. No significant differences were found among the flow rates in individual renal veins from K-MOTIVE and Cartesian phase-contrast (p≥0.98, Table S3). At the suprarenal and infrarenal locations, agreement in T₂, SvO₂, and BFR derived from K-MOTIVE and db-K-MOTIVE was evaluated for each respective parameter and location and overall yielded ICC>0.80. The ICC values and Bland-Altman analyses are presented in Table S4.

The total blood flow rate from the sum of left and right renal veins compared to differences in suprarenal and infrarenal flow in IVC is reported in Figure S4. The objective of this analysis was to evaluate conservation of flow in the venous circulation. These composite flow rate measurements were not found to be significantly different (p≥0.81). Pairwise correlation and Bland-Altman analyses among the composite flow rates are presented in Supporting Information, Figure S5. Comparison of the sum of left and right renal venous flow rate with the difference in suprarenal and infrarenal IVC flow rate from K-MOTIVE yielded a mean bias of −117±216mL/min and ICC=0.80 (p=0.005). The same comparison but to the difference in suprarenal and infrarenal flow rates from db-K-MOTIVE showed a mean bias of −178±158mL/min and ICC=0.77 (p<0.001). Comparing the difference in suprarenal and infrarenal flow between K-MOTIVE and db-K-MOTIVE yielded a mean bias of −61±179mL/min and ICC=0.92 (p<0.001). The total flow rate in both renal veins and the difference flow rate are on the order of 1000mL/min (Table 4); hence, biases of 117, 178, and 61mL/min represent 12%, 18%, and 6%, respectively.

Individual and bilateral rMRO₂ were compared with two RM-ANOVA tests to examine (1) the sum of left and right rMRO₂ vs. bilateral rMRO₂; and (2) individual rMRO₂ vs. bilateral rMRO₂ (dashed boxes in Figure 4D). A single RM-ANOVA examining all five parameters would not be appropriate because the sum of left and right rMRO₂ is not independent from individual rRMO₂. Regardless, no significant differences were found in either case (p≥0.30, Figure 4D). The absence of a significant difference between the sum of the individual rMRO₂ and bilateral rMRO₂ is likely due to the wide standard deviations from error propagation. Given that the equation to quantify bilateral rMRO₂ depends on several parameters, an error propagation analysis (based on Eq. [6]) was performed (Figure S6). The initial analysis assumed that covariances among the parameters were zero. Error propagation will likely worsen when including covariance terms.

3.2. Reproducibility and image quality

Intrasession and intersession reproducibility metrics (coefficients of variation [CoV=σ/μ] and ICC) are listed in Table 5. The 95%-confidence intervals for ICC are in Table S5. CoV was computed for arteriovenous difference in oxygen saturation (98%-SvO₂). Image quality metrics (SNR and CNR) are in Table 6. RM-ANOVA detected no differences in image quality among all sequences.

Table 5:

Reproducibility experiments for all sequences and locations examining intrasession and intersession coefficients of variation (CoV), expressed as mean ± S.D. and intraclass correlation coefficients (ICC). ICC is not affected by addition or subtraction: ICC of SvO₂ and AVDO₂ are equal.

	CoV (%)					ICC
	T2	SvO2	AVDO2	BFR	rMRO2	T2	SvO2	BFR	rMRO2
Intrasession
K-MOTIVE-left	4.9 ± 2.8	3.0 ± 2.2	46 ± 49	6.6 ± 4.2	49 ± 47	0.94	0.88	0.94	0.82
K-MOTIVE-right	7.0 ± 6.3	3.3 ± 4.1	38 ± 46	12 ± 9.2	45 ± 46	0.90	0.82	0.97	0.85
K-MOTIVE-supra	11 ± 8.0	5.3 ± 3.9	33 ± 33	4.2 ± 3.0	65 ± 48	0.81	0.71	0.98	0.70
K-MOTIVE-infra	10 ± 7.2	4.4 ± 3.6	11 ± 9	11 ± 5.4		0.85	0.81	0.94
db-K-MOTIVE-supra	19 ± 8.3	8.2 ± 3.9	44 ± 28	5.6 ± 3.4	72 ± 34	0.65	0.38	0.96	0.41
db-K-MOTIVE-infra	10 ± 7.7	4.6 ± 3.2	12 ± 8	9.5 ± 5.7		0.91	0.89	0.95
Intersession
K-MOTIVE-left	5.7 ± 4.1	2.9 ± 2.8	45 ± 49	8.0 ± 5.1	48 ± 47	0.87	0.88	0.90	0.82
K-MOTIVE-right	7.3 ± 5.8	3.0 ± 4.0	32 ± 47	9.7 ± 7.5	37 ± 42	0.95	0.90	0.98	0.97
K-MOTIVE-supra	14 ± 11	6.5 ± 5.6	39 ± 40	7.3 ± 6.8	68 ± 47	0.77	0.80	0.96	0.11
K-MOTIVE-infra	15 ± 11	6.9 ± 5.1	22 ± 25	13 ± 10		0.66	0.69	0.92
db-K-MOTIVE-supra	16 ± 14	7.4 ± 6.7	46 ± 49	6.7 ± 5.4	69 ± 48	0.79	0.65	0.97	0.61
db-K-MOTIVE-infra	11 ± 10	5.3 ± 5.0	12 ± 10	15 ± 10		0.91	0.87	0.90

Table 6:

Image quality metrics examining SNR and CNR in the renal vein or inferior vena cava for K-MOTIVE and db-K-MOTIVE sequences at various locations. SNR was computed in the image corresponding to TE=0ms, where $SNR={\mu }_{ROI}/{\mu }_{background}$, i.e., the mean signal intensity in ROI (vein or static tissue) divided by the mean signal intensity of background air. Contrast-to-noise ratio (CNR) was calculated as a difference between the SNR of vein and surrounding static tissue. Metrics were not significantly different among all pulse sequences.

Image Quality	$\text{SNR}=\frac{{\text{μ}}_{\text{ROI}}}{{\text{μ}}_{\text{background}}}$		$\text{CNR}={\text{SNR}}_{\text{vein}}–{\text{SNR}}_{\text{tissue}}$
	Vein	Surrounding tissue
K-MOTIVE-left	15 ± 8	2.6 ± 0.9	13 ± 7
K-MOTIVE-right	15 ± 6	2.6 ± 1.1	12 ± 6
K-MOTIVE-supra	18 ± 9	3.0 ± 1.0	15 ± 8
K-MOTIVE-infra	24 ± 10	3.6 ± 1.7	20 ± 9
db-K-MOTIVE-supra	17 ± 9	3.4 ± 1.3	14 ± 9
db-K-MOTIVE-infra	23 ± 14	3.6 ± 1.7	19 ± 14

4. DISCUSSION

An indirect approach is proposed to quantify bilateral rMRO₂ by considering both kidneys as a single unit (Eq. [6]). Rather than measuring SvO₂ and BFR in the individual renal vessels, measurements are made along the inferior vena cava (IVC) above and below the branching of the renal vessels (suprarenal and infrarenal, respectively). A dual-band-K-MOTIVE (db-K-MOTIVE) pulse sequence was designed to simultaneously measure SvO₂ and BFR in two locations (four total parameters from suprarenal and infrarenal IVC) as a means to compute whole-organ bilateral rMRO₂ in a single breath hold. K-MOTIVE(11) (single-band) was separately applied to measure SvO₂ and BFR at the two locations, requiring two breath-holds. For comparison, K-MOTIVE was also implemented to investigate individual left and right whole-organ rMRO₂ based on flow rates and oxygenation in the renal veins.

The renal veins were found to be highly oxygenated (SvO₂>90%, Table 4, Figure 4B), a result consistent with previous findings of SvO₂ in the renal vein(11,41). For instance, de Keijzer et al., reported renal vein SvO₂ of 92.6–93.8%(41) based on blood gas analysis via invasive catheterization in healthy participants. Moreover, we recently implemented K-MOTIVE at the left kidney and reported SvO₂ of 92±6%(11). The present work additionally reports SvO₂ from the right (92±7%) and left renal vein (91±6%), which did not significantly differ. In healthy subjects, both kidneys are expected to share comparable metabolic parameters.

Examining T₂ and SvO₂ values of the IVC in Figures 4A–B indicates that oxygen saturation is greater infrarenally than suprarenally (70% vs. 80%) after the renal veins have entered, an association found for both single-band and dual-band K-MOTIVE. These findings are fundamental to the proposed method. Since the renal veins are highly oxygenated (SvO₂>90%), they result in significantly greater SvO₂ in suprarenal IVC.

As reported in Table 4, K-MOTIVE-derived BFR in the left and right renal veins were 494±101 and 463±186mL/min, which did not significantly differ from arterial and venous BFR measured separately from Cartesian phase-contrast sequences (Figure S3). These values are consistent with prior MRI-based reports(42,43), which altogether suggest that total renal arterial inflow may be comparable to total venous outflow in healthy adults. This supports the simplification of the bilateral rMRO₂ equation to be derived from measurements entirely in the IVC (Eq. [6]).

The present study reported renal SvO₂ and BFR values that are in line to prior work. For example, SvO₂ values of 92–93%(41) or 92%(11) were previously reported. Cox et al.(42) have reported MRI-derived BFR values of 373±105mL/min (renal artery) or 410±134mL/min (renal vein). The literature consensus estimates renal blood flow at approximately 500mL/min(44). The present study’s values compare favorably. Given that SvO₂ and BFR are the key parameters for rMRO₂ quantification via Fick’s Principle, the resultant rMRO₂ values are physiologically plausible. To further evaluate the plausibility of the observed vascular-metabolic values, renal metabolism is grossly compared to cerebral metabolism. Cerebral MRO₂ is a metric that has been extensively reported in the literature using MRI-oximetry(10,45,46) and is on the order of 120–180 (µmol O₂/min)/100g. Bilateral rMRO₂ reported in the present study is 300–350 (µmol O₂/min)/100g. Based on these MRI-derived measurements, the ratio of bilateral rMRO₂ to cerebral MRO₂ is approximately two. Prior studies of resting energy expenditure(47,48) reported organ metabolic rates of brain and kidneys as 240 (kcal/kg)/day and 440 (kcal/kg)/day, respectively. This ratio is also approximately two, suggesting that bilateral rMRO₂ reported here may be physiologically plausible. An additional calculation relating the amount of filtered sodium to the amount ATP and oxygen required is presented in Figure S7, which supports physiological plausibility. Future work may include comparisons to gold standard methods, which are further addressed in a later section of the Discussion.

Each metabolic parameter, T₂, SvO₂, and BFR, quantified by K-MOTIVE and db-K-MOTIVE in the suprarenal and infrarenal IVC was found to agree well between the two methods with ICC>0.80 for each pairwise comparison. Bland-Altman analyses also resulted in biases (Table S4) that were not significant. These findings suggest that db-K-MOTIVE does not introduce a systematic bias compared to single-band K-MOTIVE. Db-K-MOTIVE is more time-efficient because all four parameters from suprarenal and infrarenal IVC are quantified in a single pass.

The average total renal venous blood flow from both kidneys was found to be 986±230mL/min (Table 4), and the flow rate is significantly greater in the suprarenal IVC than in the infrarenal IVC (Figure 4C). To evaluate conservation of flow in the venous circulation, Bland-Altman analysis of total venous blood flow from the kidneys vs. the difference in flow rates between suprarenal and infrarenal IVC resulted in a bias (Figure S5A, S5C) with the sum of renal venous flow underestimating the difference in flow. This may be attributed to the smaller cross-sectional area of the renal veins compared to the IVC. A smaller bias between single-band and dual-band K-MOTIVE was found (Figure S5E), likely because the differences in flow are compared from the IVC only. However, it is important to note that the biases were not significant (Figure S4). The pairwise ICC values among all three comparisons were >0.75, suggesting moderate to good agreement between total renal venous flow and difference flow rate in the IVC (Figure S5). Conservation of flow in the renal circulation had previously been demonstrated on the arterial side(49).

For individual rMRO₂ quantification in the present study, the application of Fick’s Principle was based on venous outflow (vs. renal arterial inflow) of the respective kidney to permit direct comparisons to venous flow rates in the IVC. Using venous flow as a surrogate for arterial inflow has been proposed, for example, in the cerebral circulation where an upscaling factor(50) relates the BFR in the superior sagittal sinus to the BFR in the carotid and vertebral arteries.

In addition to reducing the number of parameters, the simplification to venous-derived measurements entails potential advantages. For instance, Eq. (1) depends on suprarenal and infrarenal measurements of blood flow rate in the pulsatile aorta. This is likely challenging since K-MOTIVE employs an ungated acquisition to quantify velocity. Furthermore, several branches of the abdominal aorta arise in proximity. In particular, the superior mesenteric artery (arterial supply to gastrointestinal tract) typically begins near the origin of the renal arteries. This complicates a suprarenal slice prescription(51) on the aorta that can isolate arterial blood flow directed to the kidneys. On the other hand, venous drainage from most of the gastrointestinal tract is routed to the liver via the portal vein, bypassing the abdominal inferior vena cava. As a result, the IVC is suitable to adequately space the two locations for improved separation of dual-band images. Although vascular anatomy may vary, selection of suprarenal and infrarenal locations along the IVC is relatively more straightforward. Moreover, the dual-band approach to quantify bilateral rMRO₂ synchronizes measurements at suprarenal and infrarenal locations, lowering physiological noise.

When examining reproducibility, ICC values of K-MOTIVE at the individual kidneys were >0.80. The bilateral computations also resulted in ICC>0.75; however, there were a few instances of poor reproducibility (Table 5). For example, SvO₂ measurements in the suprarenal IVC exhibited relatively poorer ICC. It is possible that inadequate mixing of blood from the renal veins and infrarenal IVC(52) may be contributing to errors in reproducibility. In addition, acquisition under breath-holds may impact flow in the IVC, as reported by Joseph et al(53). Nonetheless, the ICC values of the parameters derived from K-MOTIVE and db-K-MOTIVE generally suggest fair reproducibility. Future work is needed to study mixing of blood and flow profiles along the IVC under breath-held conditions.

The large coefficients of variation (CoV=σ/μ) in AVDO₂ are a numerical consequence of high oxygenation, and a lower denominator, characteristic of the renal circulation, amplifies the quotient. For comparison, the infrarenal measurements (corresponding to an SvO₂≈70%, or AVDO₂≈18%) resulted in lower CoV of AVDO₂. Since the CoV is numerically sensitive, the precision of the method is best evaluated by examining CoV of the parameters directly measured by the pulse sequences: T₂ and BFR, which were generally <15% for both K-MOTIVE and db-K-MOTIVE (Table 5). Furthermore, recall that during early diabetes, the renal vein oxygenation level is expected to decrease(3,54), which should mitigate the instability in CoV from low arteriovenous differences in oxygenation.

Image quality among all sequences and locations suggests that background-suppression was effective (static tissue SNR<4). Of note, single-band and dual-band background-suppression modules achieved similar SNR values of surrounding tissue at both suprarenal and infrarenal locations. Although SNR of the vein at the infrarenal locations was higher (Table 6), this was not found to be significant. Background-suppression reduces the signal from the surrounding tissue, and inflowing venous blood provides signal to determine T₂. The dual-band implementation may cause blood in the infrarenal IVC that has experienced only one slice-selective adiabatic inversion pulse to flow superiorly and mix with venous outflow from the kidneys. As a result, the signal of blood in the suprarenal IVC may be affected by the infrarenal blood. However, inhomogeneous mixing of blood(52) in the suprarenal IVC and the impact of breath-holding on flow rates in the IVC(53) (addressed later in the Discussion) may further complicate measurements of SvO₂. Future work will investigate background-suppression module design (e.g., different combinations and timing of slice-selective and non-selective inversion pulses). In addition, T₂-preparation consisted of composite refocusing pulses, which should mitigate B₁ inhomogeneities(22,23). Nonetheless, future work may also investigate B₁ mapping in the abdomen.

There are limitations to this work. For instance, MRI-based measurements were not benchmarked to a gold standard (catheterization for SvO₂ and para-aminohippurate clearance for BFR(55)). Nonetheless, internal comparisons were performed to assess the bilateral approach, including venous outflow rate and differences in suprarenal and infrarenal flow. In addition, dual-band and single-band K-MOTIVE were compared. Future work may include validation to a gold standard. Moreover, rMRO₂ and bilateral rMRO₂ capture kidney function at the whole-organ level. Although investigating renal oxygenation and metabolism on a voxel-wise basis may be of interest, prior work in an animal model of diabetes reported an increase in renal metabolism at the whole-organ level during early-stage disease(2–4).

In the present study, SaO₂ was set to 98%. This is a reasonable assumption because all participants were healthy. Future studies in patients may require a peripheral pulse oximeter to measure SaO₂. However, the accuracy of peripheral pulse oximeters that measure SaO₂ depends on the perfusion to the fingers, which is impacted by ambient temperature. As a result, peripheral blood flow may not be representative of central arterial circulation, particularly in scanner room temperatures.

Error propagation is a concern because the equation for bilateral rMRO₂ comprises several parameters (Figure S6). There were instances where the computed bilateral rMRO₂ was negative due to a “bilateral” SvO₂ exceeding 98% (Methods 2.4). This is a consequence of the high oxygenation level of the renal veins. Although the SvO₂ values in the IVC are lower than those in the renal veins, implausible bilateral SvO₂ values may result due to Eq. (2) computation because bilateral SvO₂ is a function of SvO₂ and BFR at suprarenal and infrarenal locations. There were 20 such instances in single-band K-MOTIVE, and 16 in db-K-MOTIVE. These values were capped at 97% oxygenation when computing bilateral rMRO₂.

The indirect approach was, in part, motivated by imaging the IVC, where lower SvO₂ is expected compared to the SvO₂ in renal vein. T₂-SvO₂ calibration models are generally more sensitive in such a range, whereas at high oxygenation levels, the models flatten (e.g., Figure 3 in Wright et al.(7)). Moreover, the IVC is comparatively simpler to localize and has a larger cross-sectional area than the individual renal veins. As a result, more voxels are available for T₂-quantification. However, in the present study, these potential benefits were offset by the additional parameters required to compute bilateral rMRO₂. The resulting error propagation is evident by the wide standard deviations of bilateral rMRO₂ in Table 4. Nonetheless, the indirect method may still be useful to complement data from individual right and left kidneys or when the right renal vein is not available. Future pulse sequence development includes increasing the τ₁₈₀ spacing during T₂-preparation, which may make the calibration model more sensitive to the higher oxygenation range (e.g. Figure 3 in Wright et al.(7): τ₁₈₀=6ms vs. τ₁₈₀=48ms).

Lastly, the kidney experiments were conducted under a breath-hold condition, which may influence BFR in the IVC(53). Future work includes developing a free-breathing protocol, for instance, with a radial-bSSFP readout strategy(11). Further investigation into the effects of breath-holding on BFR and renal metabolism is needed.

In summary, quantification of bilateral rMRO₂ with the indirect approach was found to be feasible and compared well with measurements of individual whole-organ renal metabolism. The methods presented here will need to be evaluated in diabetic patients to address the hypothesis that renal metabolism increases during early-stage diabetes. For the indirect approach, the simplification that total renal arterial inflow and venous outflow are similar must also be assessed in patients.

5. CONCLUSIONS

The present work provides a theoretical framework and pulse sequence, db-K-MOTIVE, to compute bilateral rMRO₂ by exploiting conservation of flow and mass and demonstrates feasibility. Db-K-MOTIVE simultaneously measures SvO₂ and BFR at two locations (four total parameters) along the inferior vena cava to enable bilateral rMRO₂ quantification in a single pass. The indirect approach may be suitable for situations where it is difficult to investigate individual whole-organ renal metabolism, particularly in the right renal vein.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.