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(Circulation. 1996;94:792-807.)
© 1996 American Heart Association, Inc.

Articles

Noninvasive Quantification of Regional Myocardial Metabolic Rate for Oxygen by Use of ¹⁵O₂ Inhalation and Positron Emission Tomography

Theory, Error Analysis, and Application in Humans

Hidehiro Iida, DSc; Christopher G. Rhodes, MSc; Luis I. Araujo, MD; Yusuke Yamamoto, MD; Ranil de Silva, PhD; Attilio Maseri, MD, FRCP; Terry Jones, DSc

MRC Cyclotron and Cardiovascular Research Units, Hammersmith Hospital, London, UK.

Correspondence to Hidehiro Iida, DSc, Department of Radiology and Nuclear Medicine, Research Institute for Brain and Blood Vessels, 6-10 Senshu-Kubota-Machi, Akita City, Akita 010, Japan.

	Abstract

Top Abstract Introduction Methods Results Discussion Appendix 1 Appendix 2 References

 
Background A method has been developed to measure the regional myocardial metabolic rate of oxygen consumption (rMMRO₂) and oxygen extraction fraction (rOEF) quantitatively and noninvasively in humans by use of ¹⁵O₂ inhalation and positron emission tomography. This article describes the theory, an error analysis of the technique, and procedures of the method used in a human feasibility study.

Methods and Results Inhaled ¹⁵O₂ is transported to peripheral tissues, where it is converted to ¹⁵O-labeled water of metabolism, which exchanges with the relatively large extravascular tissue space. Quantification of this buildup of radioactivity allows the calculation of rMMRO₂ and rOEF. However, a correction for the spillover of the pulmonary gas radioactivity signal into myocardial regions is required and has been made by use of a gas volume distribution estimated from the transmission scan. This was validated by comparative measurements using the inert gas [¹¹C]CH₄ in four greyhounds. Spillover of the cardiac chamber radioactivity has been corrected for with an inhaled [¹⁵O]CO (blood volume) scan. The underestimation of myocardial radioactivity due to wall motion and thickness has been corrected for by use of values of tissue fraction obtained from the flow measurement [¹⁵O](CO₂ scan). Values of rOEF were similar (within 4%) whether obtained from gas volume measurements determined from the transmission or [¹¹C]CH₄ scan data. ¹⁵O₂ scan information from six healthy volunteers showed a clear distribution of myocardial radioactivity after the vascular and pulmonary gas ¹⁵O background was subtracted. Subsequent compartmental analysis resulted in values for rOEF and rMMRO₂ of 0.60±0.11 and 0.10±0.03 mL·min^-1·g^-1 in the human myocardium at rest.

Conclusions The results of this study are in good agreement with established values. This is the first known approach to allow the direct quantitative determination of rOEF and oxygen metabolism to be made noninvasively on a regional basis.

Key Words: myocardium • oxygen • blood flow • tomography

	Introduction

Top Abstract Introduction Methods Results Discussion Appendix 1 Appendix 2 References

 
Under normal physiological conditions, the changing oxygen demand of myocardial tissue is well supported by variation of the oxygen supply via the control of blood flow. However, severe perturbations in this relationship can occur in disease that may result in the need to obtain information on the rMMRO₂. This uncoupling of the blood flow–to–oxygen consumption relationship is uniquely and quantitatively defined by the value of the OEF, which therefore represents a parameter of significant importance in the investigation of myocardial function.

PET is a noninvasive imaging technique that allows the in vivo investigation of regional myocardial metabolism. After initial studies by Pike et al,¹ it has been shown that [1-¹¹C]acetate is a marker of tricarboxylic acid cycle flux and that it may be a useful tracer for the assessment of rMMRO₂.^{2 3 4 5 6 7 8} Although it has been demonstrated that the rate constant describing the clearance of [1-¹¹C]acetate from the myocardium is linearly related to indexes of rMMRO₂, in both humans and experimental animals,^{2 3 4 5 6 7 8} absolute quantification of rMMRO₂ using this tracer has yet to be achieved because of the lack of a suitable model with which to describe the precise tissue kinetics of this tracer.

A method has therefore been developed for the noninvasive quantification of both rMMRO₂ and rOEF in humans by use of inhalation of ¹⁵O₂ gas and PET imaging. The tracer kinetic model used is based on that originally proposed to describe the behavior of ¹⁵O₂ in brain tissue.^{9 10 11 12 13 14 15 16} However, the direct translation of the compartmental model for the brain to the heart requires the resolution of a number of methodological issues. During the inhalation of ¹⁵O₂ gas, there are relatively high levels of radioactivity in the pulmonary alveolar space, in the heart chambers (because of hemoglobin-bound ¹⁵O₂), and in the myocardium. The measured radioactivity signal from myocardial tissue is contaminated by those originating from the lungs and from the heart chambers. Such spillover effects represent image reconstruction artifacts that result from both cardiac wall motion and the small transmural thickness of the heart wall relative to the spatial resolution of PET cameras. In addition, underestimation of the myocardial signal arises for the same reasons.^{17 18 19} These phenomena are known collectively as the partial volume effect.²⁰

The aims of this paper were (1) to describe the theory and methods of data analysis for rMMRO₂ and rOEF measurements by ¹⁵O₂ gas inhalation and PET imaging, including the development and implementation of solutions to the methodological considerations described above; (2) to validate the lung gas-volume measurement derived from the transmission scan; (3) to perform simulation studies to assess error propagation; and (4) to assess the clinical applicability of this technique with measurements in humans.

A full experimental validation of this technique is provided in the companion article,^19a in which values of rOEF and rMMRO₂ measured with the ¹⁵O₂-PET method are compared with those obtained from AV sampling and -labeled microsphere blood flow measurements in an animal model.

	Methods

Top Abstract Introduction Methods Results Discussion Appendix 1 Appendix 2 References

 
The measurement of rMMRO₂ and rOEF relies on the inhalation of ¹⁵O₂ gas, which is carried as ¹⁵O-hemoglobin by blood to peripheral tissues, where it is converted to water of metabolism ([¹⁵O]H₂O_met). The increased distribution volume of [¹⁵O]H₂O_met, represented by the exchangeable water space of tissue, results in the delayed removal of radioactivity. This allows the definition of an appropriate model and equations to be derived for the calculation of rMMRO₂ and rOEF. These calculations, which are based on models similar to those previously used to determine cerebral blood flow and oxygen metabolism,^{9 10 11 12 13 14 15 16} require the measurement of rMBF, which was done by the [¹⁵O]CO₂ inhalation technique.^{21 22} A glossary of terms, the mathematical model, and the derivation of equations for both autoradiographic and steady-state methods are presented in Table 1 and the "Appendixes."

View this table: [in this window] [in a new window]   Table 1. Glossary

A necessary requirement of this model is a correction for spillover of activity from the vascular pools of the heart chambers and the lung, evaluated with a conventional measurement of blood volume using [¹⁵O]CO, and the spillover of activity from the pulmonary airways, corrected for with an unconventional and indirect measurement of gas volume obtained from the transmission scan. Furthermore, one must take account of recirculating [¹⁵O]H₂O_met in blood that freely enters the myocardium. The time course of the whole-body production of this metabolite of ¹⁵O₂ has been modeled by a novel approach previously described.²³

Validation of Gas Volume Measurement
To correct for the spillover of the ¹⁵O₂ signal from the alveolar space into myocardial regions, measurements of lung gas volume are required. In theory, these can be made from the transmission scan data,^{24 25} thus obviating the need to perform an additional emission PET scan during the administration of a radiolabeled gas of low solubility to measure lung gas volume directly. Thus, comparative studies were performed in four greyhounds (weight, 28 to 33 kg) to validate the accuracy of pulmonary gas volume measurements obtained from the transmission data against direct measurements made after the inhalation of ¹¹C-labeled methane gas ([¹¹C]CH₄).

After an overnight fast, the animals were sedated with 4 mg acetapromazine IM, and anesthesia was induced with thiopental sodium (25 mg/kg IV). Animals were intubated and mechanically ventilated with a mixture of oxygen, nitrous oxide, and air (FiO₂, 25% to 30%). Anesthesia was maintained by inhalation of 0.5% to 1% halothane. Catheters were placed in the femoral artery and vein to measure the radioactivity concentration in the arterial blood continuously with an external ß-probe and for sampling by syringe. The ß-probe curves were corrected for delay and dispersion, as reported previously.^{22 26} Arterial blood pressure, an ECG, and arterial blood gases were monitored throughout the procedure.

The PET imaging protocol included the full set of flow and metabolic measurements and was identical to that described for the human volunteers (see below), except that at the end of the dog studies, an additional 10-minute emission scan was performed during the continuous inhalation of [¹¹C]CH₄, a metabolically inert gas of low solubility (solubility=0.00575 mL·100 mL^-1·mm Hg^-1), to assess the distribution of pulmonary gas radioactivity directly. Although rMMRO₂ and rOEF were measured by PET, no comparison with AV sampling was made because of the lack of fluoroscopic facilities for animals in our unit at the time this study was performed.

Feasibility Studies in Humans
Six healthy male volunteers, 22 to 35 years old (mean±SD, 29±5 years), were included in this study. All subjects had neither signs nor symptoms of cardiac disease and had normal ECGs. All volunteers were studied after a minimum period of 8 hours of fasting. Blood glucose and free fatty acid concentrations were measured from sampling of blood from an antecubital vein at the beginning and end of the study to confirm the dietary state. Hemoglobin concentration and hematocrit in venous blood were measured before and after the ¹⁵O₂ scan. Blood pressure (by arm-cuff sphygmomanometry) and an ECG for measurement of heart rate were monitored throughout the study.

All subjects gave written informed consent to a protocol approved by the Hammersmith Hospital Research Ethics Committee and the United Kingdom Administration of Radioactive Substances Advisory Committee.

Scanning Procedures
All PET studies were performed with an ECAT 931-08/12 tomograph (CTI Inc), which allowed 15 planes of data acquisition in an axial FOV of 10.5 cm.^{27 28} All emission and transmission data were reconstructed with a Hanning filter with a cut-off frequency of 0.5 in units of the reciprocal of the sampling interval of the projection data (3.07 mm). This reconstruction resulted in an in-plane spatial resolution of 8.4 mm FWHM for emission data²⁷ and 9.4 mm FWHM for transmission data²⁸ at the center of the FOV. The axial resolution was 6.6 mm FWHM at the center of the FOV.

All subjects lay supine on the scanner bed with their arms out of the FOV. The optimal imaging position was determined by a 5-minute rectilinear scan after exposure to an external ⁶⁸Ge/⁶⁸Ga ring source. A 20-minute transmission scan was then performed by exposure to the same external ring source. These data were used to correct subsequent emission scans for tissue attenuation of the 511-keV annihilation -photons and for generating the gas volume images (see below). At the end of the transmission scan, the blood pool was imaged by inhalation of [¹⁵O]CO, which labels erythrocytes by the formation of carboxyhemoglobin. The [¹⁵O]CO inhalation lasted for 4 minutes (total subject dose, 6 GBq), and a 6-minute single-frame emission acquisition was initiated 1 minute after the end of [¹⁵O]CO inhalation. Venous blood samples were taken every minute during the scan, and the [¹⁵O]CO concentration in whole blood was measured with a sodium iodide well counter cross-calibrated with the scanner.

After a 15-minute period to allow for the decay of ¹⁵O radioactivity to background levels, a dynamic scan was performed to measure rMBF according to a previously validated protocol.²¹ Briefly, [¹⁵O]CO₂ gas was inhaled for a period of 3.5 minutes (3 to 5 MBq/mL at a flow rate of 500 mL/min). A 25-frame dynamic PET scan was started 28 seconds before the start of [¹⁵O]CO₂ delivery and lasted for a total of 7 minutes.

Approximately 20 minutes after this scan, another dynamic scan was performed during the continuous inhalation of ¹⁵O₂ (2.5 MBq/mL at a flow rate of 500 mL/min). The scan sequence consisted of a 30-second background scan, four 30-second scans, and six 1-minute scans, corresponding to the 8-minute buildup phase, and a single 10-minute scan during the steady-state phase. After the end of radioactive gas delivery, an additional six 30-second scans were performed to record the washout of the radioactivity from the myocardium. At the end of the study, a second transmission scan was performed. The two transmission data sets obtained at the beginning and at the end of the study were reconstructed and visually compared with each other to confirm that the subject had not moved during the study. The absorbed radiation doses to the subjects for the [¹⁵O]CO, [¹⁵O]CO₂, and ¹⁵O₂ scans were 2.3, 3.4, and 4.8 mSv, respectively.

Calculation of Functional Images
All images were reconstructed on a Micro Vax II computer (Digital Equipment Corp) with dedicated array processors and standard reconstruction algorithms. Images were transferred to SUN 3/60 workstations for further analysis. Image manipulations were performed with the Analyze software package.²⁹ Previously reported approaches were used to create images of blood volume,^{21 30} extravascular tissue density,^{30 31} and myocardial [¹⁵O]H₂O distribution.²¹ The image processing required to create images of lung gas volume and myocardial ¹⁵O₂ uptake at steady state were as follows.

Gas Volume
Images of the gas volume (fractional alveolar gas volume in each pixel) were calculated according to the method previously reported by Brudin et al²⁴ and Valind et al.²⁵ Briefly, the reconstructed transmission images, which had effectively the same spatial resolution as the emission data, were normalized to have units of tissue volume (milliliters of gas-free tissue per milliliter of image volume element) by use of the counts in an LV ROI. This image was then subtracted from unity. The resultant image of gas volume has units of milliliters of gas per milliliter of image volume element. In the animal studies, images of the relative distribution of gas volume were also obtained directly from the [¹¹C]CH₄ emission data sets.

¹⁵O₂ Steady State
The steady-state image of myocardial ¹⁵O₂ uptake was determined from normalized subtractions of blood volume and lung gas volume from the 10-minute data acquisition obtained during steady-state conditions. ROI counts in the left ventricle and the lung were used to provide A_t(t) and R^lung(t), respectively, and to scale the subtraction by use of relationships similar to those in Equation 12 of "Appendix 1."

ROI Definition
ROIs were drawn in five anatomic locations: anterior, lateral, and septal myocardial segments, the left ventricular chamber, and the lung. The myocardial regions were positioned on the extravascular density images; large and small LV chamber ROIs for calculation of rMBF and rOEF, respectively, were positioned on the blood volume images, and the lung ROIs were positioned in midventral and middorsal regions as identified on the gas volume images.

All ROIs were projected onto the blood and gas volume images and the dynamic ¹⁵O₂ and [¹⁵O]CO₂ data sets to generate arterial and myocardial tissue time-activity curves. These data were used in subsequent modeling procedures to calculate rMBF, rOEF, and rMMRO₂.

Data Analysis
Myocardial Blood Flow
rMBF was calculated from the inhalation of [¹⁵O]CO₂ by fitting of myocardial and arterial time-activity curve data to a previously validated single-tissue-compartment model that implemented corrections for partial-volume effects by introducing the tissue fraction () and for spillover from the LV chamber into the myocardial ROI by introducing the arterial blood volume (V_a).^{21 22} In these investigations, the time-activity curves generated from the large LV chamber ROIs were used as the input function for the rMBF modeling procedures. These curves were corrected for the spillover from the myocardium by a method that has been shown to correspond well to the directly measured arterial input function.²²

rOEF: Steady-State Method
rOEF was calculated according to Equation 17, as derived in "Appendix 1," for all myocardial ROIs by use of the radioactivity concentration data measured during steady-state conditions. In this formulation, the following parameters were fixed: the microscopic venous blood volume (F_vein) was assumed to be 0.10 mL/g tissue, according to previous studies of the coronary circulation,^{32 33} and the myocardium/blood partition coefficient of water (p) was fixed at 0.91 mL/g,¹⁹ on the assumption that [¹⁵O]H₂O was freely exchangeable with all the tissue water.^{34 35} The blood volume image obtained from the [¹⁵O]CO scan²² was used for the determination of V_B^myo and V_B^lung. The ratio of the lung gas volume in the myocardial region to that in the lung region, V_G^myo/V_G^lung, was calculated from the image of the lung gas volume obtained from the transmission data. For comparison, in the four animal studies, this ratio was also measured by use of the [¹¹C]CH₄ scan data.

The total ¹⁵O radioactivity concentration in arterial whole blood (A_t) was obtained from the LV radioactivity concentration measured from the PET data set with the smaller LV ROIs to minimize the spillover from the myocardium. The calculations for the estimation of recirculating [¹⁵O]H₂O (A_w) are described in "Appendix 2."

rOEF: Autoradiographic (Build-Up) Method
Time-activity curves obtained for all myocardial ROIs were integrated over both the first 5 and the first 8 minutes of the ¹⁵O₂ inhalation, and rOEF values were calculated according to Equation 16 in "Appendix 1." The same values of f, , V_B^myo, V_B^lung, V_G^myo, V_G^lung, F_vein, and p used in the steady-state analysis were used in this analytical approach. For the human study, A_t(t) was determined from the LV time-activity curve. The arterial [¹⁵O]H₂O component, A_w(t), was then generated from A_t(t) in a novel way by a previously validated model²³ that assumed a constant production rate of [¹⁵O]H₂O by the whole body (see "Appendix 2").

Measurement of rMMRO₂
The relationship between rOEF ("Appendix 1") and rMMRO₂ is as follows:

(E1)

where [O₂]_a is the total oxygen content of the arterial blood [mL O₂/mL blood]. The determination of [O₂]_a is performed as

(E2)

where Hb is the hemoglobin concentration of the blood (g hemoglobin/mL blood), %Sat represents the percentage saturation of oxygen in arterial blood, and 1.39 denotes the maximum binding capacity of oxygen per unit mass of hemoglobin (mL O₂/g hemoglobin). Since arterial blood was not sampled in humans, Hb was determined from venous blood samples and a value of 94% was assigned to %Sat.

Statistics
Values are expressed as mean±SD throughout this article. The unpaired Student's t test was used to compare parametric values between heart regions. A value of P<.05 was considered statistically significant.

Simulation Studies
The method described involves a number of assumptions and the direct measurement of several parameters. To assess the sensitivity of the final values of rOEF and rMMRO₂ to errors in these assumptions and measurements, the following simulation studies were performed for the steady-state and the 5-minute and 8-minute autoradiographic methods.

Effect of Errors in Measurements of V_B^myo, rMBF, , V_G^myo, and Assumed Value of F_vein
Simulation studies have been performed to assess the effects of errors in the measurement of V_B^myo, rMBF, , V_G^myo, and the value assigned to F_vein on the final values of rOEF and rMMRO₂.

First, the radioactivity concentration in a myocardial ROI was calculated and integrated according to Equations 14 and 15, corresponding to the buildup and steady-state conditions, respectively. In these simulations, the values of the following parameters were fixed: rOEF=0.70, rMBF=1.0 mL·min^-1·g^-1, V_B^myo=0.26 mL/mL, V_B^lung=0.16 mL/mL, V_G^myo=0.20 mL/mL, V_G^lung=0.64 mL/mL, =0.60 g/mL, and F_vein=0.10 mL/mL.

The LV chamber and lung time-activity curves, obtained from a typical study during ¹⁵O₂ inhalation, were used as A_t(t) and R^lung(t), respectively. For the autoradiographic method, Equations 20 and 21 were used to generate the arterial [¹⁵O]H₂O and ¹⁵O₂ concentration curves, respectively, and Equations 18 and 19 were used for the steady-state calculations (see "Appendix 2").

Subsequently, rOEF values were calculated from Equations 16 and 17. In each case, the values of V_B^myo, rMBF, , V_G^myo, and F_vein were varied to determine the error propagated to the calculated rOEF values.

Effects of Spillover of Tissue Radioactivity Into the LV ROI
A simulation study was also performed to investigate the effect on the calculated rOEF values of tissue radioactivity contaminating the LV ROI, caused by the limited recovery coefficient of this region. The radioactivity concentration in the LV ROI, LV(t), can be expressed as

(E3)

where ß corresponds to the recovery coefficient of the LV ROI.²² The calculated LV radioactivity concentration was used as A_t(t), and the errors in the resulting rOEF values were obtained for changes in the recovery coefficient.

Effects of Errors in Estimation of Recirculating [¹⁵O]H₂O
The effects of errors in the estimation of the arterial ¹⁵O₂ and [¹⁵O]H₂O concentrations from the total radioactivity (Equations 18 through 21) have been determined. rOEF values were calculated for various ratios of the arterial ¹⁵O₂ to [¹⁵O]H₂O concentrations, and the percentage change in rOEF was calculated as a function of the percentage change in the A_w/A_t ratio, for both the autoradiographic and the steady-state methods.

	Results

Top Abstract Introduction Methods Results Discussion Appendix 1 Appendix 2 References

 
Validation of Gas Volume Measurement
In all the studies performed on the greyhounds, heart rate, blood pressure, and other hemodynamic parameters were stable throughout the whole experimental period. Fig 1 shows gas volume images obtained from the transmission data and those directly measured by the [¹¹C]CH₄ emission scan. Visual inspection of the two image sets indicated no obvious regional differences. Thus, the images of myocardial ¹⁵O₂ uptake obtained by subtracting the radioactive spillover arising from both the blood pool and the pulmonary gas volume with either [¹¹C]CH₄ or transmission scanning were comparable (Fig 2). A quantitative comparison was made using the whole-heart OEF values, as summarized in Table 2. These results demonstrate that measurements of V_G^myo by the two independent methods provide similar values of rOEF within the heart regions defined.

View larger version (36K): [in this window] [in a new window]   Figure 1. Comparison of gas volume images obtained from transmission scan (top) with those obtained directly from the inhalation of [11C]CH4 (bottom). Data were obtained from an animal study.

View larger version (23K): [in this window] [in a new window]   Figure 2. Procedure to calculate image of 15O2 uptake in the myocardium (data from a typical animal study). Subtraction of blood and gas volume radioactivity contributions from original 15O2 steady-state image provides 15O2 uptake in the myocardium. Gas volume images obtained by use of transmission and [11C]CH4 emission data were consistent with each other and hence resulted in similar myocardial images after subtraction from the steady-state image.

View this table: [in this window] [in a new window]   Table 2. Comparison of Two Methods to Correct for Spillover of Activity From Pulmonary Gas Volume

Human Studies
Hemodynamics and Metabolic Parameters
All subjects tolerated the scanning procedures well. Table 3 summarizes the hemodynamic and metabolic parameters of the six human subjects studied. The heart rate and systolic blood pressure were 63±5 bpm (mean±SD) and 119±9 mm Hg, respectively. Free fatty acid concentration in venous blood was 1.60±0.88 mmol/L, glucose concentration 5.5±0.5 mmol/L, and hemoglobin concentration 14.7±0.6 g/dL.

View this table: [in this window] [in a new window]   Table 3. Hemodynamics and Metabolic Parameters of the Subjects

PET Images
Typical images acquired during a normal volunteer study are shown in Fig 3. We confirmed in all six studies that the last set of transmission images was visually consistent with the first set, suggesting that the subject did not move during the PET study.

View larger version (137K): [in this window] [in a new window]   Figure 3. Primary tomographic images obtained from a typical volunteer study, including the 20-minute transmission scan recorded at the beginning of the study, the 6-minute static [15O]CO inhalation scan, the time frames of a [15O]CO2 scan integrated for the first 3.5 minutes during the continuous inhalation, the 15O2 steady-state images, and the second 20-minute transmission scan recorded at the end of the study, are shown from top to bottom.

Fig 4 shows a typical example of temporally sequential ¹⁵O₂ images observed in a second normal volunteer. The data were taken from a midventricular plane (showing the maximum LV chamber size). Sample time-activity curves taken from ROIs positioned in the LV chamber, the lateral wall, and the lung region are illustrated in Fig 5. The LV region had the highest concentration of radioactivity during the scan.

View larger version (114K): [in this window] [in a new window]   Figure 4. Sequential midventricular cross-sectional tomographic images obtained from a 15O2 study. Times above the images represent the scan start and end times of each frame. The dynamic scan includes a 30-second background scan before start of gas delivery. 15O2 gas delivery was started at time zero and continued for 18 minutes. The 10-minute scan initiated 8 minutes after the start of gas delivery corresponds to the steady-state scan. An additional six frames of acquisition, which correspond to the washout phase, were taken after the steady-state scan (these data, which represent additional information for interest, were not used in the analysis).

View larger version (30K): [in this window] [in a new window]   Figure 5. Time-activity curves taken from the LV, the myocardium (lateral wall), and a lung region in the 15O2 human study illustrated in Fig 4. Delivery of the radioactive gas (15O2) was started at time 0.5 minute and stopped at 18.5 minutes. Histogram drawn with bold lines corresponds to net myocardial concentration curve, with spillover from the blood and pulmonary-gas radioactivity subtracted.

The [¹⁵O]H₂O buildup and the ¹⁵O₂ steady-state images are shown in Fig 6. These images, which are very similar, represent qualitative images of the regional distribution of rMBF and rMMRO₂, respectively. The statistical noise in the two sets of images appears to be similar. These images were reconstructed by use of a convolution filter that gave a spatial resolution of 8 to 9 mm FWHM, and no further image manipulation processes, such as filtering or smoothing, were performed. Such statistical noise may be reduced by smoothing of the images, by use of a reconstruction filter with a lower cutoff frequency, or by use of iterative reconstruction techniques.

View larger version (92K): [in this window] [in a new window]   Figure 6. Comparison of tomographic images of myocardium obtained from a further volunteer study. The [15O]H2O buildup images were calculated by subtracting the vascular radioactivity distribution from the sum of the [15O]H2O images acquired during the first 3.5 minutes of continuous inhalation of [15O]CO2 gas. These represent the spatial distribution of rMBF. Lower images were obtained by subtracting the radioactivity contributions of both the blood and pulmonary-gas volumes from the 15O2 steady-state image and represent the spatial distribution of rMMRO2 at rest.

rMBF, rOEF, and rMMRO₂
Table 4 summarizes the calculated values of rMBF, , V_B^myo, rOEF, and rMMRO₂ in three myocardial segments in the normal volunteer studies. rMBF was homogeneously distributed in all parts of the LV myocardium and had an average value of 0.86±0.15 mL·min^-1·g^-1. Values of were consistently higher in the septum than in the anterior and lateral walls. By the steady-state method, the mean rOEF for all myocardial segments was 0.60±0.11. Inspection of the regional data showed that rOEF values were similar in the anterior and lateral walls but were systematically lower in the septum. The mean rMMRO₂ value for all myocardial segments was 0.10±0.02 mL·min^-1·g^-1. The pattern of regional rMMRO₂ was similar to that of rOEF. The rOEF and rMMRO₂ values obtained with both the 5-minute and the 8-minute autoradiographic methods were not significantly different from those obtained from the steady state (Table 4).

View this table: [in this window] [in a new window]   Table 4. Results of Studies Carried Out on Six Normal Volunteers at Rest

Simulation Studies
Fig 7 shows the simulated radioactivity concentrations in a myocardial ROI for various rMBF values as a function of rOEF. It can be seen that the ROI concentration increases as rMMRO₂ (proportional to the product of rMBF and rOEF) increases. The radioactivity existing in the myocardial ROI when rMMRO₂ is equal to zero is a result of the spillover of radioactivity from the blood (mainly the LV chamber) and pulmonary gas into the myocardial ROI. The radioactivity concentration is always less in the myocardial ROI than in the LV chamber. This is because of the limited recovery of counts from the myocardium, as evidenced by being 0.7 and the arterial radioactivity concentration being always higher than the myocardial concentration during the buildup and steady-state phases.

View larger version (20K): [in this window] [in a new window]   Figure 7. Relationship between radioactivity concentration in a myocardial ROI and the rOEF value at steady state. Lines are simulated by use of Equation 15 for various values of rMBF and the parameter values listed in "Methods." Myocardial concentration is denoted as relative concentration to total arterial blood concentration. rMMRO2 is proportional to the product of rMBF and rOEF, and hence, the ROI concentration increases as rMMRO2 increases. The existence of radioactivity in the myocardial ROI for a rMMRO2 value of zero (rOEF=0) is due to the spillover of the radioactivity from the blood (the LV chamber) and the pulmonary gas. The radioactivity concentration in the myocardial ROI is less than that of the arterial blood (LV chamber), even for large values of rMMRO2 (combination of large rOEF and rMBF).

Fig 8 shows the results of the simulation studies, which demonstrate the error propagated to the final rOEF value as a result of potential errors in the measured values of V_B^myo, rMBF, , and V_G^myo, the limited recovery of the LV ROI, and uncertainties in the assumed values of F_vein and the A_w/A_t ratio. The error sensitivity for the rOEF calculation was found to be similar for the steady-state and the 5-minute and 8-minute autoradiographic techniques in all the simulation studies except for (1) the effect of errors in rMBF, for which the 8-minute autoradiographic technique incurred the fewest errors (Fig 8b); (2) the effect of limited recovery of the LV ROI, for which the performance of the 5-minute technique was best and that of the steady-state technique was by far the worst (Fig 8e); and (3) the effect of uncertainties in the recirculating water component, for which the steady-state technique incurred the highest error propagation (Fig 8g).

View larger version (143K): [in this window] [in a new window]   Figure 8. Simulations demonstrating the effect of errors in the calculated rOEF values. Bold solid lines, dashed lines, and thin solid lines correspond to the steady-state, 5-minute buildup, and 8-minute buildup methods, respectively. a, % error in the calculation of OEF as a function of % error in blood volume; b, % error in the calculation of OEF as a function of % error in rMBF; c, % error in the calculation of OEF as a function of % error in tissue fraction; d, % error in the calculation of OEF as a function of % error in gas volume; e, % error in the calculation of OEF due to the small recovery of the LV ROI; f, % error in the calculation of OEF due to the error in the assumed venous fraction; and g, % error in the calculation of OEF due to the error in the estimation of the arterial [15O]H2O (recirculating water) concentration.

The largest errors in the calculated rOEF values were induced by errors in the blood volume (Fig 8a), the tissue fraction (Fig 8c), and the limited recovery coefficient of the LV ROI (Fig 8e). A 10% overestimation in rOEF resulted from a 9% underestimation in the measured blood volume, a 7% underestimation in the tissue fraction, and a 90% recovery coefficient from the LV ROI (for the steady-state method). The magnitude of errors in rOEF as a result of discrepancies in rMBF and pulmonary gas volume was approximately half of those mentioned above. Errors in the assumed value of F_vein and the A_w/A_t ratio were found to produce only small changes in the calculated rOEF values.

	Discussion

Top Abstract Introduction Methods Results Discussion Appendix 1 Appendix 2 References

 
The quantification of rOEF and rMMRO₂ by ¹⁵O₂ inhalation and PET requires the resolution of a number of methodological difficulties, in particular, the bidirectional spillover of radioactivity from the lung and LV chamber into the myocardial ROI. This article describes the theory and practical implementation of a modeling approach designed to overcome these issues and provides results from a feasibility study performed in humans.

The values of rOEF and rMMRO₂ in both animal and human studies are consistent with those reported previously in the literature from invasive AV sampling.^{36 37 38 39 40} These data suggest that the modeling approach reported in this article successfully resolves the methodological difficulties described above and is suitable for the quantification of rOEF and rMMRO₂ in humans. Furthermore, the validity of this technique has also been confirmed by studies performed by our group^{41 42} and by other investigators.⁴³ The preliminary studies in greyhounds,^{41 42} using various pharmacological interventions with isoprenaline, adenosine, propranolol, and morphine, demonstrated that rOEF and rMMRO₂ values obtained by this technique agreed with those obtained by direct measurement over a wide parameter range with AV sampling (Fick method) and -labeled microspheres. It has also been shown that rMMRO₂ calculated by this method correlated with the clearance of [1-¹¹C]acetate before and after dobutamine infusion in humans.⁴⁴ Although there was a previous attempt to measure rOEF and rMMRO₂ by use of ¹⁵O₂ and PET in an animal model,⁴⁵ the method was invasive (requiring intra-arterial injection) and images were obtained without numerical evaluation. To the best of our knowledge, this is the first article to present noninvasive quantitative measurements of rMMRO₂ and rOEF in humans.

It should be emphasized that the present method provides quantitative regional values of OEF in addition to rMMRO₂. It can be expected that rMBF and rMMRO₂ would be coupled in normal situations to the extent that changes in rMMRO₂ would be accompanied by comparable changes in rMBF, such that rOEF (the parameter describing the balance between O₂ supply and demand in myocardial tissue; see Equation 1) remained constant. Under these circumstances, therefore, measurements of rMBF alone might be expected to provide the necessary information on metabolic demand and rate of oxygen consumption. However, the exception to this should occur when rMBF and rMMRO₂ are uncoupled, eg, conditions of hyperemia (luxury perfusion), when rOEF values would be expected to fall, or conditions of ischemia (critical perfusion), when rOEF values would be expected to increase and approach their maximum value. The usefulness of this parameter has been demonstrated previously in the investigation of acute stroke,⁴⁶ in which the progression from high to low rOEF values has provided insight into the transition of cerebral tissue from a state of critical perfusion, during the early ischemic period, to luxury perfusion as terminal infarction became established. Parallels with the pathophysiology of the myocardium exist, and it should be advantageous to be able to measure rOEF directly in a quantitative manner. It is therefore of benefit that the measurements of rOEF are made with a lower degree of error propagation than the measurement of rMMRO₂.

Measurements in Humans
The present study demonstrated that mean resting values of rOEF were between 0.6 and 0.7 and mean values of rMMRO₂ were between 0.09 and 0.11 mL·min^-1·g^-1 in anterior and lateral myocardial regions. These values are very similar to those reported in the literature that were obtained by measurement of the arterial–coronary sinus differences in oxygen content after cardiac catheterization.^{36 37 38 39 40} It should be emphasized, however, that in these invasive studies, only global measurements of OEF and MMRO₂ were performed, whereas the PET imaging approach allows regional measurements to be made. The similarity between the values obtained by PET and those obtained from previously reported invasive studies strongly supports the feasibility of noninvasively quantifying rMMRO₂ and rOEF by PET in humans.

Use of Transmission Data for the Measurement of Gas Volume
The present method requires the application of two corrections to the measured myocardial radioactivity: one for spillover of the pulmonary gas radioactivity and another for the spillover of vascular radioactivity. Since it is not practical to perform two additional emission scans to implement these corrections [¹¹C]CH₄ and [¹⁵O]CO, the method of using the transmission data to estimate the pulmonary gas volume has been incorporated into this study. This approach proved to be effective for use in human studies.

As shown in Fig 1, similar distributions of pulmonary gas volume were observed and virtually identical rOEF values were obtained by the two methods of determining the pulmonary gas volume (Table 2). The difference in the calculated values of rOEF was only 3% and could be explained by the small amount of [¹¹C]CH₄ radioactivity dissolved in the blood. Thus, the use of the transmission data eliminates the need for an additional lung emission scan.

Simulation Studies
Errors in the Myocardial Blood Volume Measurement, V_B^myo
Simulation studies revealed that V_B^myo is one of the most important sources of error in the determination of rOEF (Fig 8a). The procedure for calculating blood volume from the [¹⁵O]CO data is simple, and therefore, errors in the measurement of this parameter should be minimal, provided that the sodium iodide well counter is accurately cross-calibrated with the PET scanner. To avoid additional sources of error due to poor blood sampling, great care should be used when blood samples are taken manually, especially from venous lines.

The statistical noise in the blood volume images will be an important factor, especially if it is intended either to calculate rOEF for a small myocardial ROI or to generate a functional image of rOEF from the formulations described previously. In both the human and animal studies, the [¹⁵O]CO measurement was one of the largest sources of statistical noise in the myocardial ¹⁵O₂ distribution images illustrated in Fig 6. Further investigation should be aimed at improving the counting statistics in the [¹⁵O]CO scan, either by increasing the inhalation dose or by optimizing the inhalation period and imaging protocol.

Because of the high sensitivity to errors in the blood volume measurement, a large systematic error is expected in the septal region as a result of the difference in the radioactivity concentration of the left and right chambers during the ¹⁵O₂ inhalation (see below).

Nonuniformity of Blood Radioactivity Concentration Throughout the Lung
It was assumed that the concentration of vascular radioactivity was homogeneous throughout the pulmonary vascular bed in the FOV. However, the concentration of radioactivity in the arterial (upstream) portion (A_t^lung-artery) is expected to be less than that in the venous (downstream) portion (A_t^lung-vein) during the inhalation of ¹⁵O₂. Therefore, estimation of C_gas(t) (Equation 11) may be systematically underestimated. In practice, however, this does not constitute a major source of error, since A_t^lung-artery was estimated to be 70% of A_t^lung-vein during steady-state ¹⁵O₂ inhalation from measurements of the RV and LV radioactivity concentrations. If we assume equal contributions from the arterial and venous volumes,⁴⁷ the overestimation of A_t was estimated to be 15%. This resulted in an underestimation of C_gas by 4%, an error that was effectively transferred to V_G^myo. According to the results of the simulation study (Fig 8d), a 4% underestimation in V_G^myo would result in a 2% overestimation in rOEF.

Statistical Fluctuation of Perfusable Tissue Fraction () and rMBF
The simulation studies demonstrated that errors in the measured values of rMBF and propagate to the calculation of rOEF (Fig 8b and 8c), provided that these two parameters are determined independently. In our protocol, however, both parameters are calculated by fitting a single dynamic [¹⁵O]H₂O data set, and thus the statistical noise in each parameter is expected to correlate with the other. Preliminary analysis revealed that the statistical variations in the calculated values of rMBF and take opposite signs (ie, an overestimation in rMBF corresponds to an underestimation in and vice versa) and that the statistical error in rMBF is significantly larger than that in (the factor is 1.6). Furthermore, the simulation study showed that the error sensitivity of rOEF to rMBF is less than that of (the factor is 0.3). It would therefore be expected that the error in the calculated value of rOEF, as a result of statistical fluctuation in rMBF and , would, to a large extent, cancel out. Therefore, kinetic analysis of the [¹⁵O]H₂O dynamic data set is unlikely to be a serious source of error in rOEF.

Limited Recovery of the LV Radioactivity
It has been demonstrated (Fig 8e) that the limited recovery of LV radioactivity causes a systematic overestimation in the calculated rOEF value, which is due to underestimation of the arterial input function and the spillover of the myocardial tissue radioactivity into the LV ROI. Therefore, in the ¹⁵O₂ analysis, we selected small ROIs in the region of the LV to minimize this source of contamination in the noninvasive input function. However, the recovery coefficient was still significantly smaller than 1.0, ranging between 0.85 and 0.95 as evaluated from the [¹⁵O]CO blood volume scan. An overestimation of 6% to 15% in rOEF is expected for the steady-state method.

The smaller error sensitivity in the autoradiographic methods compared with the steady-state method is due to two factors: (1) less spillover of the signal from tissue radioactivity into the LV ROI and (2) better linearity between the PET counts and rOEF values in the autoradiographic method.

The alternative option of taking an ROI in the left atrium might reduce the spillover from the myocardial tissue radioactivity but would probably increase the artifact from the lung gas radioactivity. Thus, further modeling to account for the tissue spillover is required, as has been done for the calculation of rMBF.²²

Heterogeneous Alveolar ¹⁵O₂ Concentration, C_gas(t)
The estimation of C_gas(t) by Equation 11 can be dependent on the ROI selected because of regional changes in the ratio of ventilation to perfusion. The error due to this effect remains unknown but seems not to be important, because the error sensitivity to the gas volume measurement was not as large a source of error as the other factors mentioned above (Fig 8); eg, a 5% error in V_G^myo produced a 3% error in the calculated rOEF value, and the regional variation in the ratio of ventilation to perfusion when the subject is lying supine is not great.⁴⁷ In fact, selection of a lung ROI in a different anatomic area (ie, moving the ROI in a ventral or dorsal direction) typically did not change the rOEF value by more than 5%. This could be entirely explained by the intrinsic error of the gas volume measurement.

Uncertainty in the Assumed Values for Venous Vascular Fraction, F_vein
The validity of assuming a fixed venous fraction (F_vein=0.10 mL/g myocardium)^{32 33} has been discussed in a previous article.³⁰ Briefly, the measurement of V_B^myo from the [¹⁵O]CO scan and V_a from the [¹⁵O]H₂O dynamic analysis gave values of F_vein at rest of 0.103±0.094 and 0.093±0.103 mL/g in the myocardium of dogs and humans, respectively. These values matched our assumed value well. In addition, uncertainty in this value is not important in the calculation of rOEF, as demonstrated in the simulation study (Fig 8f).. Even a 20% error in the assumed F_vein propagated an error of only 4% to the calculated value of rOEF. Thus, fixation of F_vein in the calculation of rOEF and rMMRO₂ should not present a serious source of error, at least in studies performed under resting conditions.

Assumed A_w/A_t Ratio
The contribution of recirculating water was assumed to be 0.176 of A_t in the steady-state analysis. In the autoradiographic analysis, the ratio of A_w(t)/A_t(t) was calculated from Equation 20. According to our previous analysis,²³ these assumptions could vary by up to ±20% in a given individual, with a consequent error in rOEF. In practice, however, it was found from the simulation study (Fig 8g) that an alteration in the A_w/A_t ratio produced only a small change in the calculated rOEF value in both the steady-state and the autoradiographic analyses. The smaller errors predicted for the autoradiographic analyses compared with steady-state analyses are probably due to the small amount of recirculating [¹⁵O]H₂O in blood during the initial phase of gas inhalation.

Movement of the Subject During the Study
Subject movement during data acquisition is probably the most important source of error in all cardiac PET work. Movement causes mismatch between the transmission and the emission data, which can produce serious errors in the reconstructed image because of inappropriate attenuation correction. In one study, an axial movement of 6 mm (equivalent to the thickness of a single slice in our PET scanner) was observed between the two transmission images recorded at the beginning and the end of the study. Use of these two transmission data sets gave markedly differing images of myocardial ¹⁵O₂ distribution, and this case was therefore excluded from the analysis. The image slices that included the top of the liver and the myocardial apex seemed to be those most sensitive to movement, especially in the axial direction. In addition, movement can cause inadequate correction for lung and blood pool radioactivity. Therefore, it is highly desirable to prepare a reliable fixation system for the subject or to develop a sophisticated software algorithm that corrects for such movement. This adjustment should include the attenuation correction process.

Change of Physiological Conditions During the Study
A constant physiological state was assumed in the present study during all imaging procedures. This is an assumption common to all PET studies and is probably valid under resting conditions, but for the application of this technique to various stress studies, such as dipyridamole infusion, the effects of changes in the relevant parameters (such as the attenuation correction factor, F_vein, , V_B^myo, V_B^lung, V_G^myo, and V_G^lung) will require further investigation. However, it should be noted that PET measurements of rMMRO₂ and rOEF made under a variety of pharmacologically induced states, as described in the companion article, agreed well with those obtained from the direct but invasive measurements based on the use of -labeled microspheres and AV blood sampling.

Variation in rOEF
The observed intersubject variation in the calculated values of rOEF was 10% to 15% in the lateral and anterior regions. This variation comprises both methodological uncertainties and the physiological intersubject variability of rOEF. The relative contributions of the various factors contributing to the overall methodological error are ±3% from the blood volume measurement, ±3% error from the lung gas volume measurement, ±20% from the venous fraction, and ±20% from the assumed A_w/A_t ratio, which cause statistical variation in rOEF of ±5%, ±4%, ±4%, and ±5%, respectively. Further variation will be caused by a gradient of blood radioactivity concentration within the lung, variation in the LV recovery for each subject, and a heterogeneous alveolar gas concentration, each of which might produce a variation of ±5% in rOEF. In this situation, the total variation in rOEF calculated according to the error propagation rule would be on the order of ±12%. These estimations indicate that the intersubject variation in rOEF could be accounted for by methodological uncertainties alone, rather than by physiological variability.

Variation in rMMRO₂
The mean intersubject variability was greater for rMMRO₂ (21% to 32%) than for rOEF (10% to 16%), as can be seen from Table 4. This difference was due to the variation of the rMBF values (about 20%), since rMMRO₂ was calculated by the product of rMBF and rOEF, as described in Equation 1. The variation in the measured values of rMBF is probably due to methodological uncertainties, since previous reports in both healthy humans and greyhounds have suggested that transmural rMBF is homogeneously distributed throughout the different regions of the heart, although it may not be uniform within a given region (eg, transmural myocardial differences are known to exist). That the measurement error in rMMRO₂ may be greater than that in rOEF is, however, of reduced importance, since rOEF is a parameter of potentially greater interest in the investigation of myocardial pathophysiology.

Comparison of the Autoradiographic and Steady-State Methods
The present study provided comparable values between the three different analyses (ie, no significant differences were observed between the steady-state, 5-minute, and 8-minute autoradiographic methods). The variation in the calculated rMMRO₂ and rOEF values was also similar between the steady-state and the autoradiographic methods, although the 5-minute autoradiographic technique yielded slightly larger variations than the 8-minute calculation.

The autoradiographic technique has the advantage over the steady-state method in requiring a shorter imaging protocol (with less radiation exposure) and a shorter study duration, since the steady-state method requires a period of gas inhalation before steady-state conditions are reached and scanning can be commenced. However, the steady-state technique has the minor advantage of requiring simpler mathematical methods for the calculation of rOEF and rMMRO₂ and does not require the continuous measurement of the arterial input function. To obtain the arterial time-activity curve, either dynamic scanning to measure the temporal changes in LV activity or the continuous monitoring of arterial blood radioactivity by use of an external radiation detector and cannulation of the radial artery is required, although only a single integration scan is required for measurement of the myocardial signal.

rOEF and rMMRO₂ in the Septum and Posterior Wall
By our method, septal values of rOEF and rMMRO₂ were consistently smaller than those in other regions by 30% (see Table 4). This occurred for the following two reasons.

1. Overestimation of is possible. As shown in Table 4, the values of in the septal regions were larger than in the other regions by 20%. The simulation study (Fig 8c) showed that a 20% increase in caused an underestimation in rOEF of 20%. This overestimation in was caused by the inability of the current modeling procedures to account for the difference in the blood radioactivity concentration between the RV and LV chambers that occurs during [¹⁵O]CO₂ inhalation. This error would be reduced if an [¹⁵O]H₂O infusion protocol were used instead of the [¹⁵O]CO₂ inhalation or if extravascular density were used instead of for the partial-volume correction.³⁰

2. A systematic overestimation of the myocardial blood volume activity might occur in correction for the spillover from the right heart. The blood radioactivity concentration in the RV chamber is lower than that in the LV chamber during the ¹⁵O₂ inhalation and at steady state, whereas the blood radioactivity is homogeneous during the recording of the [¹⁵O]CO scan. According to the simulation study (Fig 8a), overestimation in the blood volume by 10% corresponds to underestimation in rOEF by 10%.

Data were analyzed by use of transaxial images and regions drawn only for septal, anterior, and lateral areas of myocardium. We therefore do not have information about potential errors or difficulties that might arise from the close proximity of the abdominal organs and the spillover of signal from these regions.

Conclusions
The present study has shown the feasibility of making noninvasive quantitative measurements of OEF and MMRO₂ regionally in humans by use of ¹⁵O₂ inhalation and PET. Corrections were required for contamination of the myocardial signal by spillover of activity from vascular and pulmonary gas compartments. A novel method for the latter correction using the transmission data was developed and validated. After corrections for both spillover components, a clear myocardial signal could be distinguished in humans. This signal was amenable to analysis with a compartmental tracer kinetic model for the calculation of rOEF and rMMRO₂. The values of these parameters were concordant with those derived from invasive measurements using arterial–coronary sinus differences in oxygen content that have been reported previously. A theoretical simulation study was performed to investigate the effects of various possible sources of error and supports the notion that this technique is able to provide quantitative values of acceptable accuracy. Direct validation studies have been performed^{41 42} that demonstrate the accuracy of this technique under various hemodynamic conditions.

	Appendix 1

Top Abstract Introduction Methods Results Discussion Appendix 1 Appendix 2 References

 
Measurement of Oxygen Extraction Fraction
The compartmental model describing ¹⁵O₂ behavior in the myocardium is illustrated in Fig 9. ¹⁵O₂ gas, which is mostly bound to hemoglobin, enters through the arterial circulation, and the unextracted fraction leaves via the venous drainage. It is assumed that the rate of ¹⁵O₂ transfer into the tissue space is directly proportional to the arterial ¹⁵O₂ concentration, with the constant of proportionality being the product of the local fractional extraction of ¹⁵O₂ from arterial blood and regional blood flow. Once extracted into tissue, ¹⁵O₂ is assumed to be metabolized immediately to [¹⁵O]H₂O. [¹⁵O]H₂O is freely diffusible and equilibrates instantaneously in the myocardium³⁴ and washes out via the venous drainage of the heart according to the prevailing myocardial blood flow. In addition, the ¹⁵O signal measured in the arterial supply to the heart includes [¹⁵O]H₂O produced as a result of aerobic metabolism in the rest of the body. The kinetics of this recirculating [¹⁵O]H₂O in the heart is identical to that produced locally as a result of cardiac aerobic metabolism.^{9 10 11 12 13 14 15 16} Thus, the differential equation describing the myocardial kinetics of [¹⁵O]H₂O [C^myo(t)] after inhalation of ¹⁵O₂ gas can be written as

(E4)

Solving Equation 4 in terms of C^myo(t) gives

(E5)

where the asterisk denotes the convolution integral. During steady-state conditions, which can be reached during the continuous inhalation of ¹⁵O₂, the following relationship holds:

(E6)

View larger version (42K): [in this window] [in a new window]   Figure 9. A compartmental model to measure rOEF and rMMRO2 by use of PET and 15O2 inhalation. The myocardial ROI includes radioactivity in the myocardial tissue, spillover from the radioactivity of blood occupying the cardiac chamber, and spillover from radioactivity in the lung. The myocardial compartment consists of the tissue component and a vascular component (which includes arterial, capillary, and venous volumes). The hemoglobin-bound 15O2 is supplied to the capillary and diffuses into the tissue space, to be instantaneously converted into labeled water of metabolism ([15O]H2Omet). This diffusion process is assumed to be explained by an OEF. There is another input of radioactivity with a different chemical form, circulating [15O]H2O, which is assumed to be freely diffusible across the capillary membrane. This radioactivity is assumed to distribute in the same tissue space as [15O]HOmet and is washed out in proportion to the blood flow divided by the partition coefficient of water.

In cardiac PET studies, the measured myocardial signal described in Equations 5 and 6 is underestimated relative to the true radioactivity concentration because of cardiac wall motion and the small transmural heart wall thickness relative to the limited spatial resolution of the PET scanner. This is called the partial-volume effect^{17 18 19 20} and results in significant contamination of the measured myocardial signal by that originating from surrounding regions (such as the LV chamber and the lung) and vice versa. The ¹⁵O radioactivity concentration measured by PET in a myocardial ROI can therefore be expressed as the sum of the following three components: (1) the true myocardial tissue radioactivity described above, (2) radioactivity in the blood existing in the myocardial vascular space plus spillover from the heart chambers and the pulmonary vasculature, and (3) spillover from the ¹⁵O₂ activity present in the alveolar gas during inhalation. Then the measured radioactivity concentration in the myocardial ROI can be expressed as

(E7)

The ¹⁵O₂ molecular gas concentration is homogeneously distributed throughout all lung regions, and therefore, any observed regional difference in lung gas radioactivity is directly proportional to the topographical variation in lung gas volume.

The measured radioactivity concentration in the lung ROI can be expressed as

(E8)

where the contribution of radioactivity in the lung tissue can be neglected because of its low density and low molecular ¹⁵O₂ concentration. Therefore, th