ORIGINAL 
Annals of Nuclear Medicine Vol.1, No. 1, 1-6, 1987 
Noninvasive quantification of regional myocardial blood flow and ammonia extraction fraction using Nitrogen-13 ammonia and positron emission tomography 
Masahiro ENDO,* Katsuya YOSHIDA,** Takeshi A. IINUMA,* Toshiro YAMASAKI,* Yukio TATENO,* Yoshiaki MASUDA** and Yoshiaki INAGAKI** 
*National Institute of Radiological Sciences, Chiba, Japan **Chiba University School of Medicine, Chiba, Japan 
This report describes the theoretical basis and a method to quantitate regional myocardial blood flow (RMBF) and ammonia extraction fraction (E) in man, noninvasively, with N-13 ammonia and positron emission tomography (PET). Two patients with hypertrophic cardio-myopathy, whose left ventricular (LV) walls were markedly thick, were employed in this study to avoid partial volume effects and cross contamination between LV walls and blood pool. RMBF and E were calculated from time-activity curves of myocardial tissue and left atrium derived from serial 6-second PET images of the heart. The time-activity curve of left atrium was used as an arterial input function. The results were RMBF=67+-4 ml/min/ 100 g, E=80+-13%; and 65+-10 ml/min/100 g, 81+-16% for each patient. The validity of the present method was discussed. 
Key words: Dynamic positron emission tomography, Regional myocardial blood flow, N-13 ammonia, Hypertrophic cardiomyopathy   
1. INTRODUCTION 
NONINVASIVE QUANTIFICATION of regional myocardial blood flow (RMBF) is necessary to facilitate detection and evaluation of cardiac pathophysiology. In animal experiments the microsphere technique has been regarded as the "gold standard". However because of high invasiveness, it is not easily available for clinical use. A positron-emitting blood flow tracer, N-13 ammonia, exhibits properties which to some extent resemble those of the radioactive microsphere. Recently Shah et al1 reported measurement of RMBF in dogs with N-13 ammonia and positron emission tomography (PET). Their method was much less invasive than the microsphere method, because it employed intravenous administration of N-13 ammonia and tissue radioactive concentration determined by PET scans. 
Received April 10, 1987 ; revision accepted June 8, 1987. For reprints contact : Masahiro Endo, Division of Clinical Research, National Institute of Radiological Sciences, 9-1, 4-chome Anagawa. Chiba, 260 JAPAN. 
But it still needed withdrawal of arterial blood to calibrate arterial input function. The newer generation positron tomographs, with much higher 'temporal resolution, make it possible to determine the arterial input function directly from regions of interest assigned to the cardiac cavity, and thus make this approach largely noninvasive. 
N-13 ammonia is extracted and fixed in myocardium in proportion to blood flow. However, a fraction of N-13 ammonia effectively retained in myocardium (net extraction fraction) is less than 100 %, decreases with higher flows, and may be influenced by blood pH, disturbance of glutamine synthesis in myocardial cells, etc.2,3 These findings need simultaneous determination of the RMBF and the extraction fraction of ammonia in myocardial tissue. The extraction fraction itself, if obtained, may provide an important physiologic and diagnostic indicator of the cellular viability in myocardium. Mullani et al4 and Goldstein et al5 suggested this possibility with rubidium extraction in dog. 
It is the purpose of our study to develop a method of quantitating the RMBF and the extraction fraction of ammonia in man with time-activity curves of cardiac cavity and myocardium, determined by fast dynamic PET scans after intravenous injection of N-13 ammonia. To avoid partial volume effects and cross contaminations between left ventricular (LV) walls and blood pool in reconstructed images, patients with markedly thick LV walls were employed in the present study. 
2. THEORY AND METHODS 
2.1. Compartmental model 
A model which characterizes physiologically correct processes of N-13 ammonia kinetics in myocardium seems to consist of at least three compartments, which are vascular, extravascular and cellular (metabolic) phases. But because of limited information obtained noninvasively by PET scans, analysis with the complicated models is difficult and it is necessary to employ an alternative simple functional model. 
Schelbert et al2 made intensive experimental studies on N-13 ammonia kinetics in canine myocardium and obtained conclusions as follows : 
(1) N-13 ammonia freely crosses the capillary and is nearly 1OO % extracted during its initial capillary transit. (2) The rate of metabolic fixation appears to be the rate-limiting step. (3) N-13 ammonia is distributed in the extravascular space and back diffusion competes with metabolic trapping . 
These findings suggest that the physiological complicated model can be simplified to a functional two-compartment model shown in Fig. 1 , where the two compartments are free and trapped (metabolized) ammonia space. The present mokel is essentially the same as the one proposed by Mullani et al4 on Rb-82 kinetics in myocardium. The release of ammonia metabolites from the trapped compartment can be neglected in the present study, because it is a very slow process (its half-time averaged 273 minutes at control flows2) and our observation time is only two minutes after injection of ammonia. 
If amounts of N-13 ammonia in the free and trapped compartments for a unit volume of tissue are defined as Q1 and Q2 respectively, their relation-ships are given by, 
where we assume N-13 ammonia is 100% extracted during its initial capillary transit. k is a rate constant for the transport from the free to the trapped space. F is RMBF or perfusion and Ca(t) is an input function, which is arterial activity concentration as a function of time. Vd is a distribution volume of N-13 ammonia in the free compartment, which is the volume of tissue space in which the tracer in the free compartment would have been distributed with the same concentration as in venous blood at equilibrium. 
A time-activity curve of myocardium is given by, where fa is a fractional volume of arteries in  the region of interest. From the  solutions of eq. (1), Q(t) can be expressed as,   
where, and  denotes a convolution operation. From the eq. (4), RMBF is given by,  Net extraction fraction of ammonia (E) is a ratio of myocardial uptake to the product of RMBF and the integral of input function. The myocardial uptake is 
Therefore the net extraction fraction is given by, 
For simplicity the term "extraction fraction" is used instead of "net extraction fraction" in the rest of this paper. 
2.2 Methods 
N-13 was produced in the National Institute of Radiological Sciences medical cyclotron by the bombardment of pure water with proton beams by the 16O(p,a)13N reaction. The product was reduced to ammonia and collected in physiological saline. Radiochemical purity of N-13 ammonia was greater than 99.5 %.
Tomography was performed with POSITO-LOGICA-II6, which permitted serial acquisition of data in 6-second intervals and provided five trans-axial sections simultaneously. Midpoints of the sections are separated by 18mm. Sensitivities for a 
20cm diameter phantom are 22.5 and 33.6 kcps/uCi/ml for in- plane and cross- plane, respectively . 
About lOmCi N-13 ammonia was injected intravenously as a bolus from the antecubital vein. Serial PET imaging was initiated at the time of tracer injection, and twenty 6-second PET scans were performed without gating of cardiac cycle. 44 to 180 k counts were obtained per slice. Tomographic data were collected and reconstructed in 128 x 128 matrix. 
In the present study, the spatial resolution for reconstructed image was 13 mm FWHM at the center, and slice thicknesses were 13 mm and 10 mm for in-plane and cross-plane, respectively. To avoid partial volume effects and cross contaminations between left ventricular (LV) walls and blood pool, two patients with hypertrophic cardiomyopathy (HCM), whose LV wall thicknesses were more than twice the FWHM were employed. 
A time-activity curve of the myocardial tissue Q(t) was determined by assigning a region of interest (ROI) over the myocardium. The number of slices was three for each patient, and the number of ROls was three to five for each slice. An arterial input function Ca(t) was determined noninvasively by assigning a ROI over the left atrium, which was large enough to avoid the partial volume effects and cross contaminations. The sizes of ROIs were about 10x1O mm. Count losses in high count rate were corrected whit an object-independent method using a single count rate.7 Although the measured values were integrals of 6 second intervals, they showed enough temporal resolution for the present analysis. The parameters A, B, a and fa were estimated by fitting eq. (3) to the measured time-activity curve using a modified Gauss-Newton least-squares algorithm. The convolution in eq. (3) was calculated by a numerical integration. The curve-fitting algorithm was reproducible given the appropriate starting values for A, B, a and fa. Finally RMBF and extraction fraction of ammonia were calculated by the eqs. (5) and (7). Because RMBF thus obtained was in the unit volume of myocardium, it was corrected by a myocardial density (1.05 g/ml) and expressed as ml/min/100g. 
3. RESULTS 
Figure 2 shows a 6-sec serial PET imaging with N-13 ammonia at the midventricular level in one of the HCM patients (patient #1) employed in this study. The numbers below the images show time (in sec) after intravenous injection of N-13 ammonia. The transit of N-13 activity through right ventricle, both lungs and left ventricle is visualized at the earlier images. Then clearance of N-13 activity occurs in the blood pools and lungs, and finally the myocardial image is delineated. The last two images represent 30-second PET scans taken just after the initial twenty 6-second PET scans were completed. 
Fig. 3 shows time-activity curves of septum and left atrium for patient #1. The solid line in the figure shows a time-activity curve of the left atrium which was used as an input function in the present analysis. The cross marks ( x ) show a measured time-activity curve of the myocardium, while the dotted line shows an estimated myocardial response. 
Fig. 4 shows estimated values of RMBF and extraction fraction of ammonia on the anatomical cross sections in patient #1. The sections correspond to high ventricular (atrial), mid-ventricular and low ventricular levels from left to right. The upper panel shows RMBF and the lower shows extraction fraction. Table 1 summarizes the estimated results. 
4. DISCUSSION 
In this paper we estimated RMBF and extraction fraction in man with intravenous injection of N-13 ammonia and PET. To our knowledge this is the first report describing noninvasive measurements of such physiologic parameters in man. Although we have no direct evidence to judge whether the results obtained here are true or not, they seem consistent with values obtained in animal experiments2 or by a much more invasive method in man.8 
Schelbert et al2 measured extraction fraction and clearance half-time of ammonia after coronary injection of N-13 ammonia in dog. Their results were summarized from our point of view as E=82% and a=0.027 sec-1 at the control flow of F= 100 ml/min/100g. Selwyn et al8 measured RMBF in man with human albumin microspheres labeled with C-11 and PET. Their results showed that RMBF was 82.0+-32.0 ml/min/1OOg in the normal myocardium. Although our results in Table 1 were obtained from the HCM patients, they seem to agree well with these values. The interpretation of this agreement needs further study. Fractional volume of vascular space in myocardium is usually about 10%.9 fa in Table 1 is much smaller than this value. However fa is a fractional volume of arterial space in the field of view. Because it does not include capillaries and veins the values in Table 1 seem reasonable. 
As described before, the present model is essentially the same as the one proposed by Mullani et al,4 and its validity might be further supported by the following discussion. From the eqs. (4), (5) and (7), k and Vd can be expressed as, 
If the average value of patient #1 is substituted in eq. (8), k=0.019 sec-1 (1.1 min-1) and Vd=2.5. 
Because Vd is the distribution volume of N-13 ammonia in the free compartment, the result (Vd= 2.5) means that at equilibrium N-13 ammonia in the free compartment would occupy 2.5 times of actual tissue space if its concentration were the same as the venous concentration. Frank and Langer10 measured extracellular space of perfused rabbit heart using radioactive La+++, and found that if La were distributed in free solution it would occupy 194% of total tissue water, discussing that it was due to extensive binding of La+++ to polyanionic extracellular structures of myocardium. In extracellular space N-13 ammonia exists in the chemical equilibrium of NH3 and NH4+, m which the prominent form is NH4+. The possibility of extracellular trapping of NH4+ just as La+++ suggests that N-13 ammonia concentration in the extracellular space may be greater than in veins, which supports our result of Vd=2.5 and the validity of the model. Further studies are required to interpret the values of k obtained here. 
The present method employed a time-activity curve of left atrium measured with PET as an arterial input function. Iida et al11 compared radial arterial curves with time-activity curves of left ventricle following intravenous injection of O-15 water, and concluded that the radial curve was significantly dispersed from the time-activity of left ventricle measured with PET. Their results suggest that the use of time-activity curve measured with PET as an input function not only is noninvasive but also may be more accurate, especially for arteries near the heart such as coronary artery. 
nother prolem on the input function is whether N-13 activity in the arterial blood is all due to ammonia or not. N-13 ammonia in the blood is rapidly uptaken and metabolized mainly by the liver, and its metabolites labeled with N-13 come into the blood. Lockwood et al12 examined contents of N-13 activity in the arterial blood after intravenous injection of N-13 ammonia in man, and concluded that the labeled metabolites were not detectable until after 3 min of injection. Because our study utilized the activity changes up to 2 min after injection, N-13 activity observed in the arterial blood seems substantially due to ammonia. 
In the present study to avoid partial volume effects and cross contamination of activity, we employed the HCM patients with a marked increase in LV mass and showed the reliable results as discussed so far. However we did not analyze normal cases and patients with ischemic heart diseases, which are the most important in clinical practice. 
In order to apply the present method to these cases, we must correct the partial volume effects and cross contamination. Henze et al9 proposed a deconvolution technique that permitted calculation of spillover fractions from geometric measurement of the imaged cross section and the spatial resolution of tomograph. Recently Carson13 applied the EM (estimation maximum) algorithm to emission tomographic estimation of ROI activity and showed excellent results almost free from the partial volume effects. As the next step we will combine these techniques and the present method to analyze normal cases and patients with ischemic heart disease. 
ACKNOWLEDGMENT 
This research was done as a part of the research project 'Medical application of accelerated heavy particles' at the National Institute of Radiological Sciences (principal researcher Dr. H. Tsunemoto). The authors thank all the members of the project, especially Drs. N. Fukuda, T. Matsumoto and H. Shinoto for fruitful collaboration. They also thank Drs. T. Himi and A. Kagaya in the Chiba University School of Medicine for their clinical assistance. 
REFERENCES 
1. Shah A, Schelbert HR, Schwaiger M, et al : Measurement of regional myocardial blood flow with N-13 ammonia and positron-emission tomography in intact dogs. J Am Coll Cardiol 5: 92-100, 1985 
2. Schelbert HR, Phelps ME, Huang SC, et al : N-13 ammonia as indicator of myocardial blood flow. Circulation 63 : 1259-1272, 1981 
3. Rauch B, Helus F, Grunze M, et al: Kinetics of 13N-ammonia uptake in myocardial single cells indicating potential limitations in its applicability as a marker of myocardial blood flow. Circulation 71 : 387-393, 1985 
4. Mullani NA, Goldstein RA, Gould KL, et al: Myocardial perfusion with rubidium-82. I. Measurement of extraction and flow with external detectors. J Nucl Med 24: 898-906, 1983 
5. Goldstein RA, Mullani NA, Marani SK, et al: Myocardial perfusion with rubidium-82. ‡U. Effects of metabolic and pharmacologic interventions. J Nucl Med 24: 907-915, 1983 
6. Tanaka E, Nohara N, Tomitani T, et al : A whole body positron tomograph, POSITOLOGICA-II -Design and performance evaluation-. In : Proceedings of the Third World Congress on Nuclear Medicine and Biology, August-September, 1982, Pergamon Press, Paris, pp. 535-538 
7. Endo M, Nohara N, Iinuma TA, et al : Count rate characteristics arid count loss correction of POSITOLOGICA II: a whole body positron emission tomograph. Radioisotopes 36 : 227-231, 1987 
8. Selwyn AP, Shea MJ, Foale R, et al : Regional myocardial and organ blood flow after myocardial infarction : Application of the microsphere principle in man. Circulation 73 : 433-443, 1986 
9. Henze E, Huang SC, Ratib O, et al : Measurements of regional tissue and blood-pool radiotracer concentrations from serial tomographic images of the heart. J Nucl Med 24: 987-996, 1983 
10. Frank JS, Langer GA : The myocardial interstitium : Its structure and its role in ionic exchange. J Cell Biol 60: 586-601, 1974 
11. Iida H, Kanno I, Miura S, et al: Error analysis of a quantitative CBF measurement using H2 15O autoradiography and positron emission tomography with respect to the dispersion of the input function. J Cereb Blood Flow Metabol, 1986: in press. 
12. Lockwood AH, McDonald JM, Reiman RE : The dynamics of ammonia metabolism in man : Effects of liver disease and hyperammonemia. J Clin Invest 63 : 449-460, 1979 
13. Carson RE: A maximum likelihood method for region-of-interest evaluation in emission tomography. J Comput Assist Tomogr 10: 654-663, 1986