Determination of Fatty Acid Metabolism with Dynamic [ 11 C]Palmitate Positron Emission Tomography of Mouse Heart In Vivo

Abstract

The goal of this study was to establish a quantitative method for measuring fatty acid (FA) metabolism with partial volume (PV) and spill-over (SP) corrections using dynamic [¹¹C]palmitate positron emission tomographic (PET) images of mouse heart in vivo. Twenty-minute dynamic [¹¹C]palmitate PET scans of four 18- to 20-week-old male C57BL/6 mice under isoflurane anesthesia were performed using a Focus F-120 PET scanner. A model-corrected blood input function, by which the input function with SP and PV corrections and the metabolic rate constants (k₁–k₅) are simultaneously estimated from the dynamic [¹¹C]palmitate PET images of mouse hearts in a four-compartment tracer kinetic model, was used to determine rates of myocardial fatty acid oxidation (MFAO), myocardial FA esterification, myocardial FA use, and myocardial FA uptake. The MFAO thus measured in C57BL/6 mice was 375.03 ± 43.83 nmol/min/g. This compares well to the MFAO measured in perfused working C57BL/6 mouse hearts ex vivo of about 350 nmol/g/min and 400 nmol/min/g. FA metabolism was measured for the first time in mouse heart in vivo using dynamic [¹¹C]palmitate PET in a four-compartment tracer kinetic model. MFAO obtained with this model was validated by results previously obtained with mouse hearts ex vivo.

HEART FAILURE (HF) affects nearly 6 million people in the United States. Coronary heart disease, high blood pressure, and diabetes are common causes of HF. The estimated cost for HF management in the United States is about 34 billion dollars per year.¹ Current medical therapies are ineffective, with a 5-year survival rate of only 25%.² It is well established that cardiac metabolism is inextricably linked to cardiac function, and modulation of substrate energy metabolism may be an attractive strategy for treatment of HF.^3

5 However, the molecular mechanisms connecting cardiac function and metabolism are not well understood, and our current understanding of metabolic alterations in the heart is largely based on ex vivo studies in animal models.^6

9

Transgenic and knockout mouse models offer opportunities to address this issue in vivo and in parallel at the molecular level. However, a severe limitation to this approach is that there are no suitable methods that allow noninvasive assessment of cardiac energy metabolism and correlation to cardiac function in an intact mouse.

Imaging myocardial metabolism in mouse heart is challenging due to the limited intrinsic resolution of small animal scanners and the small size of the mouse heart, resulting in image blur. Recently, we optimized a model-corrected blood input function (MCBIF) from time-resolved gated 2-[¹⁸F]fluoro-2-deoxy-D-glucose (FDG) positron emission tomographic (PET) images of mouse heart to measure myocardial glucose metabolism in vivo.^10,11 Measuring fatty acid (FA) metabolism using [¹¹C]palmitate in mouse heart is even more challenging than measuring glucose metabolism due to the long range of positrons emitted by ¹¹C. Poor quality of images results in severe partial volume (PV) averaging, and spill-over (SP) contamination is further confounded by the rapid heart rate. Previous studies using [¹¹C] palmitate PET have only been performed in dog and rat hearts.^12

15 In this study, we developed a method to measure FA metabolism from dynamic [¹¹C]palmitate PET images of mouse heart using a four-compartment tracer kinetic model, for the first time, in vivo. Our computed rate of myocardial fatty acid oxidation (MFAO) in mouse heart in vivo was in agreement with the measured palmitate oxidation in the working mouse heart ex vivo.¹⁶

Materials and Methods

Animal Model

Four adult C57BL/6N male mice (18–20 weeks of age) were imaged using the Focus-F120 PET scanner (Siemens Medical Solutions USA, Inc., Malvern, PA) under isoflurane anesthesia.¹⁷ The mice were kept on a normal chow diet (7912 Teklad LM-485 from Harlan Laboratories, Indianapolis, IN) and had free access to food and water before the study. All experiments were performed in compliance with the Guide for the Care and Use of Laboratory Animals, published by the National Institutes of Health, and were conducted under protocols approved by the Institutional Animal Care and Use Committee at the University of Virginia.

[11C]Palmitate Labeling

[¹¹C]Palmitate radiolabeling was performed in the Radiochemistry Core Laboratory at the University of Virginia Molecular Imaging Center using the Modular-Lab Pharm-Tracer system (Eckert & Ziegler, E&Z, Hopkinton, MA). We modified the E&Z cassette and software designed for the production of [¹¹C]acetate to make [¹¹C]palmitate following the method of Mock and colleagues.¹⁸ Briefly, [¹¹C]CO₂ from the cyclotron was trapped by carbospheres at −20^oC to remove excess helium carrier gas. The carbospheres were heated to 60^oC, at which point, helium was passed over the carbospheres to force the [¹¹C]CO₂ through the precursor solutions, which consisted of 0.143 M pentadecylmagnesium bromide in diethyl ether (NOVEL Chemical Solutions, Crete, NE). The reaction vessel was then sealed and heated to 30°C for 3 minutes to complete the reaction. The reaction was quenched with 1 normal HCl diethyl ether. The quenched solution was passed through a dry Alumina-N Sep-Pak Plus cartridge that trapped the polar [¹¹C]palmitic acid. Nonpolar chemicals were removed from the Sep-Pak by rinsing with three 1 mL diethyl ether washes. The Sep-Pak was rinsed with two 1 mL portions of 0.5 M NaH₂PO₄ solution to disrupt the carboxylic acid binding to the alumina surface, followed by two 1 mL water washes to remove soluble Mg²⁺ salts from the Sep-Pak. The [¹¹C]palmitic acid was eluted from the Sep-Pak with three portions of absolute ethanol (2 mL total volume), and the solution was then passed through a sterile 0.2 mm Millex-FG filter (EMD Millipore, Darmstadt, Germany) into a sterile intermediate product vial. The non-decay-corrected radiochemical yield of the [¹¹C]palmitic acid product averaged ~ 30% (250 mCi of [¹¹C]CO₂ yielded 75 mCi of [¹¹C]palmitate). The [¹¹C]palmitate ethanol solution was formulated with bovine serum albumin. The synthesis was completed within about 30 minutes.

PET Imaging

Using the [¹¹C]palmitate label described above, we imaged FA metabolism in mouse heart in vivo as follows. Briefly, a mouse with electrocardiographic surface electrodes and a respiratory pillow attached to its limbs and chest, respectively, and under 1 to 1.5% isoflurane anesthesia was positioned in the bore of the PET scanner.¹⁹ A 10-minute ⁵⁷Co transmission scan was performed for attenuation correction. A 20-minute dynamic PET acquisition was then initiated prior to the administration of 300 to 350 μCi in about 200 to 300 μL of [¹¹C]palmitate via the tail vein over 30 seconds. The list-mode dynamic PET data were reconstructed using ordered subset expectation maximization maximum a posteriori (OSEM-MAP) algorithm²⁰ with attenuation correction into the following dynamic frames (frames, time [s]: 12, 5; 8, 30; 4, 150; 1, 300). The reconstructed images were composed of 95 transverse slices with a thickness of 0.79 mm and an in-plane voxel resolution of 0.4 × 0.4 mm (128 × 128 pixels) corresponding to a zoom factor of 2.13. Regions of interest (ROI) in the region corresponding to the left ventricular blood pool (LVBP) and the myocardium were drawn in the last time frame of the dynamic image data in the transverse plane and time-activity curves (TACs) generated for the LVBP and the myocardium for the 20-minute scan. The blood and myocardium TACs were used in a four-compartment tracer kinetic model (described below), written in MATLAB (The Mathworks, Natick, MA) using nonlinear regression with SP and PV corrections, to compute myocardial FA metabolism, including FA oxidation, esterification, use, and uptake in mouse heart in vivo.

Four-Compartment Tracer Kinetic Model

Following Bergmann and colleagues,¹⁵ the differential equations for [¹¹C]palmitate kinetics can be written as follows:

\frac{\partial q_{1}}{\partial t} = F [C_{a} (t) - \frac{q_{1}}{V}] + k_{2} q_{2} - k_{1} q_{1}

(Equation 1)

\frac{\partial q_{2}}{\partial t} = k_{1} q_{1} + k_{4} q_{3} - (k_{2} + k_{3} + k_{5}) q_{2}

(Equation 2)

\frac{\partial q_{3}}{\partial t} = k_{3} q_{2} - k_{4} q_{3}

(Equation 3)

\frac{\partial q_{4}}{\partial t} = k_{5} q_{2} - \frac{F}{V} q_{4}

(Equation 4)

where q₁–q₄ are the concentrations in the four compartments as shown in Figure 1, kn represents the turnover rate constants between the compartments, F is myocardial blood flow, V is the vascular volume, and Ca(t) is the arterial concentration of tracer over time.

Figure 1.

Block diagram of the four-compartment model. Compartment 1 represents the vascular space; 2, the interstitial and intracellular spaces; 3, neutral lipids, amino acids, and other slow turnover pools; and 4, mitochondrial β-oxidation. k_n represents the forward and backward rate constants between compartments, F is myocardial blood flow, V is fractional vascular volume, and C_a(t) is arterial tracer concentration over time.

The total tracer concentration in myocardium can be defined by the sum of the tracer in each compartment:

C_{T} (t) = q_{1} (t) + q_{2} (t) + q_{3} (t) + q_{4} (t)

(Equation 5)

Performing Laplace and inverse Laplace transforms (see Supplementary Material, online version only), we get the final form as follows:

C_{T} (t) = q_{1} (t) + q_{2} (t) + q_{3} (t) + q_{4} (t) = F \cdot M \otimes C_{a} (t)

(Equation 6)

where M is composed of the rate constants (k₁–k₅) and F/V.

Dual Output Model

Ideally, when an ROI is drawn within the cavity of the left ventricle, the image-derived input function (IDIF) would equal the whole-blood TAC Ca(t). However, due to SP and PV effects, the model equation for an image-derived TAC from the blood pool can be written as fractions of the tissue concentration in the blood compartment and partial recovery of radio activity concentration from the blood as follows:

M o d e l_{I D I F, i} = \frac{\int_{t_{b}^{i}}^{t_{e}^{i}} [S_{m b} C_{T} (t) + r_{b} C_{a} (t)] d t}{t_{e}^{i} - t_{b}^{i}}

(Equation 7)

Similarly, the myocardium tissue of the model equation is

M o d e l_{m y o, i} = \frac{\int_{t_{k}^{i}}^{t_{e}^{i}} [r_{m} C_{T} (t) + S_{b m} C_{a} (t)] d t}{t_{e}^{i} - t_{b}^{i}}

(Equation 8)

where r_b and r_m are the recovery coefficients (accounting for PV effect) for the myocardium and blood pool, respectively. S_mb and S_bm are the SP coefficients from the blood pool to the myocardium and vice versa, respectively; t_eⁱ and t_bⁱ are the beginning and end times, respectively, for frame in a dynamic PET scan.

The model equation for the blood input function can be written as follows:

\begin{array}{r} C_{a} (t) = & (A_{1} (t - τ) - A_{2} - A_{3}) e^{L_{1} (t - τ)} \\ + A_{2} e^{L_{2} (t - τ)} + A_{3} e^{L_{3} (t - τ)} \end{array}

(Equation 9)

where each term determines the amplitude, shape, and washout of the tracer over time; r indicates the time lag between the initiation of imaging and injection of the tracer. The model equations can be fitted to the blood (PET_IDIF) and myocardial tissue (PET_myo) TACs obtained from OSEM- MAP dynamic PET images with attenuation correction by substituting equations 6 and 9 into equations 7 and 8, as indicated below:

\begin{array}{r} O_{p} = & \sum_{n}^{i = 1} [(M o d e l_{I D I F, i} - P E T_{I D I F, i})^{2} \\ + (M o d e l_{m y o, i} - P E T_{m y o, i})^{2}] \end{array}

(Equation 10)

Interpolation and Simultaneous Estimation

The shorter reconstructed frames at the early time points limited the data resolution, resulting in fluctuations in the blood and tissue TACs at these points. A cubic spline interpolation was used to approximate the peak of curve and improve the accuracy of fitting. The interpolation was used near the peak (PET_IDIF,max, PET_myo,max) of blood (PET_IDIF,i) and tissue (PET_myo,i) concentrations obtained from the dynamic PET data. The interpolated sequences were written as follows:

\begin{array}{l} {P E T}_{I D I F, i} = [{P E T}_{I D I F, 1}, \dots \dots, {P E T}_{I D I F, max - 1}, \\ {P E T}_{I D I F, k_{1}}, \dots \dots, {P E T}_{I D I F, k_{n}}, {P E T}_{I D I F, max}, \\ {P E T}_{I D I F, k_{n + 1}}, \dots \dots, {P E T}_{I D I F, k_{2 n},} \\ {P E T}_{I D I F, max + 1}, \dots \dots]; \\ {P E T}_{m y o, i} = [{P E T}_{m y o, 1}, \dots \dots, {P E T}_{m y o, max - 1}, \\ {P E T}_{m y o, k_{1}}, \dots \dots {P E T}_{m y o, k_{n}}, {P E T}_{m y o, max}, \\ {P E T}_{m y o, k_{n + 1}}, \dots \dots, {P E T}_{m y o, k_{2 n},} \\ {P E T}_{m y o, max + 1}, \dots \dots] . \end{array}

All numeric analyses were done using MATLAB R2013b. Optimization was performed by minimizing the objective function (equation 10) using the MATLAB function “fmincon,” which is based on an interior-reflective Newton method. The initial guesses and bounds for all the parameters used in the optimization routine are shown in Table 1.

The following constraints and previous knowledge were used to set the bounds: (a) rates of palmitate oxidation are greater than esterification, that is, k₅ > k₃ under control conditions¹⁵; (b) in the steady state, the rate of backflow from compartment 3 (neutral lipids and amino acids) to compartment 2 (interstitial and cytosolic) is close to zero, that is, k₄ = 0¹⁵; and (c) the bounds for the recovery coefficients were based on structural measurements using magnetic resonance imaging (MRI) of control mouse heart.²¹ Since the spillover factors, S_bm and S_mb, are changing with time (multiplied by time-dependent image-derived blood and tissue curves; see equations 7 and 8), there is no good way to get a previous estimate of these factors. Hence, we set the bounds for these factors from 0 to 1. We also observed that the computed results have little influence on the changes in the bounds and initial guess values of the seven-parameter blood function (see equation 9).

The minimization of equation 10 results in simultaneous estimation of the parameters of blood input function Ca(t), compartment model parameters k₁–k₅, and the SP and PV coefficients (S_mb, r_b, r_m, S_bm). The optimized rate constants and SP and PV coefficients are listed in Table 2. A myocardial blood flow (F) value of 4.8 mL/min/g²² and vascular blood volume (V) of 0.1 mL/g¹⁵ was used for the calculations.

Free Fatty Acid in Mouse Blood

For the measurement of free fatty acid (FFA) levels in the mouse blood, samples (~ 20 μL) from the tail vein were collected during the dynamic PET scan at 10 and 15 minutes following tracer administration using nonheparinized capillary tubes. The blood was allowed to clot for 30 minutes; serum was then separated from the clot by centrifugation (15 minutes at 1,600g at room temperature in a microcentrifuge) and stored in a −20^oC freezer until analyzed. FFA levels were measured using HR series NEFA-HR2 reagents (Wako Life Sciences Inc., Richmond, VA).

Results

In this study, using dynamic [¹¹C]palmitate PET of mouse heart in vivo, we measured myocardial FA metabolism including rates of oxidation, esterification, use, and uptake.

Table 1.

Biodistribution of [^99mTc]-Met Peptide in MKN-45 Xenografts after 30, 60, 120, and 180 Minutes

	%ID/g (normalized to a 20 g mouse)
	30 min	60 min	120 min	180 min
Blood	3.19 ± 0.18	1.81 ± 0.54	1.00 ± 0.14	0.54 ± 0.01

Heart	1.63 ± 0.18	0.64 ± 0.15	0.24 ± 0.03	0.14 ± 0.01

Lungs	5.18 ± 0.61	1.50 ± 0.27	0.55 ± 0.05	0.32 ± 0.01

Liver	3.49 ± 0.29	1.69 ± 0.17	1.78 ± 0.08	1.18 ± 0.10

Kidneys	26.67 ± 3.40	11.84 ± 1.11	9.64 ± 1.33	6.80 ± 0.80

Spleen	1.61 ± 0.24	0.61 ± 0.07	0.43 ± 0.06	0.30 ± 0.01

MKN-45 tumor	10.13 ± 1.56	9.36 ± 1.92	5.03 ± 0.67	4.19 ± 0.98

Muscle	0.92 ± 0.27	0.27 ± 0.07	0.10 ± 0.01	0.08 ± 0.01

Each value represents (% injected dose per gram [%ID/g]) ± SD of [^99mTc]-Met peptide (n = 4 [60-minute group] or 5 [all other time points]).

Table 2.

Initial Guess Values and Bounds for Parameters Used in the Optimization

Parameter	k₁	k₂	k₃	k₄	k₅	S_mb	r_b	r_m	S_bm	A₁	A₂	A₃	L₁	L₂	L₃	τ
Initial	5	0.1	0.1	0.001	0.02	0.01	0.9	0.6	0.5	300	0.1	199.97	−5	−0.06	−1	0.1
Upper	6	1.0	1.0	0.005	1.0	1.0	1.0	0.6	1.0	500	2	500	0	0	0	0.5
Lower	0	0.0	0.0	0.0	0.0	0.0	0.9	0.0	0.4	0	0	0	−10	−1	−10	0

Figure 2A shows an example of a [¹¹C]palmitate PET image of mouse heart in vivo. ROI are shown in the blood and the myocardium in the last time frame. The ROI drawn in the last time frame was used to obtain TACs for the blood and the myocardium from the dynamic PET data. In Figure 2B, the model fits (see equations 7 10) to the blood and myocardium TACs are shown without interpolation resulting in poor fit to the blood TAC around the peak region. Cubic spline interpolation with a time interval of 0.5 seconds around the peak resulted in better fits to both the blood and myocardium TACs (Figure 2C). Model fits resulted in simultaneous estimation of blood input function Ca(t), compartment model parameters k₁–k₅, and the SP and PV coefficients (S_mb, r_b, r_m, S_bm). The MCBIF, Ca(t), was compared to the image-derived blood input function (PET blood) in Figure 3. The recovery coefficients for the blood pool and the myocardium are denoted by r_b and r_m, respectively. Since they are a function of structure, the bounds used in the optimization routine were based on structural measurements using MRI of control mouse heart.²¹ As indicated in Figure 3, the model correction results in an ~ 20% increase in the MCBIF at the early time points compared to image-derived input function (PET blood), indicating improved radioactivity recovery. Model correction also eliminated SP contamination from the myocardium into the blood pool at the late time points.

Figure 2.

[¹¹C]Palmitate PET images of mouse heart in vivo. (A) Example of a PET image at the last time frame of the dynamic data set. The image also exhibits regions of interest in the left ventricular blood pool and the myocardium. (B) Model fits to the blood and the myocardial time-activity curves without interpolation. (C) Cubic spline interpolation resulted in improved fits, especially at the peak region for the time-activity curve obtained from the left ventricular blood pool.

Figure 3.

The model-corrected blood input function (MCIF), Ca(t), computed by simultaneous estimation compared to the image-derived blood input function (IDIF: PET blood) obtained from the dynamic [¹¹C]palmitate PET images. MCIF estimation improved radioactivity recovery at the early time points and eliminated SP contamination at the late time points from the myocardium to the left ventricular blood pool.

Using the formulas described in detail in the Supplementary Material (online version only), under steady-state condition, the rates of MFAO, esterification (MFAE), and hence use (MFAU) were computed. Figure 4 shows the computed average MFAO (375.03 ± 43.83 nmol/g/min), MFAE (10.97 ± 7.11 nmol/g/min), and MFAU (385.99 ± 49.51 nmol/g/min) obtained by optimization of the dynamic [¹¹C]palmitate PET data from four 18- to 20-week-old male C57BL/6N mice. The above computed MFAO in vivo agrees with the range of MFAO measured ex vivo in perfused working 12- and 15-week-old strain-matched mouse heart.¹⁶

Figure 4.

Fatty acid metabolic parameters in mouse heart in vivo. Myocardial fatty acid oxidation (MFAO), myocardial fatty acid esterification (MFAE), and myocardial fatty acid use (MFAU) computed from dynamic [¹¹C]palmitate PET images of mouse heart in vivo.

Myocardial fatty acid uptake rate (MFAUp) was also computed by dividing MFAU with measured FFA (849 nM/mL) in mouse blood. The computed MFAUp rate was 0.45 ± 0.06 mL/min/g. When compared to the rate of myocardial FDG uptake, Ki (0.15 ± 0.03 mL/min/g) measured in age- and strain-matched mice in a previously published study from our laboratory,¹⁰ we observed a threefold higher uptake rate of palmitate (MFAUp) compared to FDG uptake rate, Ki.

Discussion

The commonly used tracers for measuring myocardial FA metabolism are 14(R,S)-[¹⁸F]fluoro-6-thia-heptadecanoic acid (FTHA)²³ and [¹¹C]palmitate.^12,24 There is a distinct advantage in using [¹¹C]palmitate due to the short half-life of the labeled tracer allowing serial measurements of FA and glucose metabolism in the same animal and monitoring the effect oftherapy in vivo. Imaging the mouse heart using a small animal PET scanner is a challenge due to the limited intrinsic resolution,¹⁹ caused primarily by the finite positron range, which results in image blur. This leads to incomplete radioactivity recovery (PV averaging) and hence SP of radioactivity from the myocardium to the blood pool and vice versa. Cardiac motion results in further image blur, confounding the effects of SP contamination in the image-derived blood input function.²⁵ In a recent study, we optimized an MCBIF from time-resolved gated FDG PET images of mouse heart in vivo.¹⁰ The MCBIF was then used to evaluate glucose metabolism in the pressure overload mouse heart in vivo.¹¹ We observed that under transverse aortic constriction–induced pressure overload stress, the mouse heart exhibited a sixfold increase in FDG uptake at day 1 postconstriction with preserved contractile function, indicating an adaptive metabolic response. At day 7 postconstriction, a further increase in myocardial FDG uptake was found, together with a decrease in cardiac function, indicating maladaptation.¹¹ However, how changes in FA metabolism relate to cardiac dysfunction in the stressed mouse heart is not known.

Clinical data using [¹¹C]palmitate PET in hypertensive left ventricular hypertrophy (LVH) suggested a decrease in myocardial FA oxidation and use as possible causes for a decrease in myocardial efficiency.²⁶ Recent ¹⁸F-FTHA PET imaging studies in vivo in the spontaneously hypertensive rat (SHR) heart over a period of 20 months observed a significant increase in both glucose and fatty acid use, which appeared to precede mechanical changes in LVH progression.²⁷ Studies in a Dahl salt-sensitive rat model ex vivo, however, showed the decrease in FA metabolism to occur late in the progression from LVH to heart failure, whereas glucose uptake was increased at an earlier stage.²⁸ These studies indicate that there is no clear consensus on the abnormalities in FA metabolism in the stressed heart. Improved tools for quantitatively imaging FA metabolism in a compartment model are needed to complement the conventional graphical Patlak analysis.²⁷

In this study, we optimized and implemented a four-compartment tracer kinetic model with SP and PV corrections to quantify FA metabolism from dynamic [¹¹C]palmitate images of mouse heart in vivo. We measured rates of MFAO, MFAE, MFAU, and MFAUp for the first time in mouse heart in vivo. This method can be easily implemented to evaluate the role of FA metabolism in the pressure overload mouse heart in vivo.

Our study, however, is not without limitations. The blood input curves obtained from dynamic PET images were not corrected for the conversion of palmitate to [¹¹C]CO₂. But studies in dog hearts have shown that this correction performed by arterial blood sampling only modestly affects the input curve, especially in the tail region.¹⁵ The factors that may be affected as a result are k₃ (rate of transfer to triglycerides) and the fractional esterification rates because they are represented by the tail of the TAC. Our data in mouse heart, however, suggest that the tail of the input curve may be minimally affected by the correction due to the conversion of palmitate to [¹¹C]CO₂. Thus, this correction may not be necessary when imaging a mouse heart using [¹¹C]palmitate, making the process of obtaining the FA metabolic parameters completely noninvasive.

Conclusions

We have measured FA metabolism, including myocardial FA oxidation, esterification, use, and uptake, for the first time from dynamic [¹¹C]palmitate PET images of mouse heart in vivo. The results for MFAO measured in vivo compared well to the measured range of palmitate oxidation from perfused working mouse heart ex vivo. By comparing rates of FA uptake measured in this study with rates of FDG uptake determined in an earlier study, we corroborated the theory that the normal mouse heart preferentially uses FA over glucose.

Footnotes

Acknowledgments

We thank Gina Wimer and Jeremy Gatesman for performing the tail-vein injections during the course of the study.

Financial disclosure of authors: This work was supported in part by grants R21 HL-102627 (to B.K.K.) and R01 DK-81471 (to S.R.K.) from the National Institutes of Health.

Financial disclosure of reviewers: None reported.

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