Ann Nucl Med (2014) 28:917–925 DOI 10.1007/s12149-014-0888-8

ORIGINAL ARTICLE

Quantification of myocardial blood flow using and population-based input function Kazuhiro Koshino • Kazuhito Fukushima • Masaji Fukumoto Yuki Hori • Tetsuaki Moriguchi • Tsutomu Zeniya • Yoshihiro Nishimura • Keisuke Kiso • Hidehiro Iida

201

Tl SPECT



Received: 26 January 2014 / Accepted: 12 July 2014 / Published online: 22 July 2014 Ó The Japanese Society of Nuclear Medicine 2014

Abstract Objectives Thallium-201 (201Tl) single photon emission computed tomography (SPECT) is an important tool in the diagnosis of ischemic heart disease. Absolute quantification of myocardial blood flow (MBF) has the potential to provide more useful information on myocardial perfusion than semi-quantitative assessments. This study aimed to validate the quantification of MBF using 201Tl cardiac SPECT based on a population-averaged input function (STD-IF) and one-point blood sample technique. Methods 201Tl emission and computed tomography (CT)based attenuation scans were performed on 11 healthy volunteers at rest using a SPECT/CT scanner. Individual input functions (IND-IFs) during the emission scans were based on arterial blood samples. The STD-IF technique was validated as follows: (1) optimal time to calibrate a STD-IF was determined to minimize differences between the calibrated STD-IF and the IND-IFs. (2) Tissue timeactivity curves (TTACs) were generated based on a singletissue compartment model for MBFtrue = 0.5, 1.0, 1.5, and 2.0 mL/min/g, a constant distribution volume of 45 mL/

K. Koshino (&)  Y. Hori  T. Moriguchi  T. Zeniya  H. Iida Department of Investigative Radiology, National Cerebral and Cardiovascular Center Research Institute, 5-7-1 Fujishirodai, Suita, Osaka 565-8565, Japan e-mail: [email protected] K. Fukushima  Y. Nishimura  K. Kiso The Department of Radiology, National Cerebral and Cardiovascular Center Hospital, 5-7-1 Fujishirodai, Suita, Osaka, Japan M. Fukumoto Department of Radiology, National Hospital Organization Osaka National Hospital, 2-1-14 Hoenzaka, Chuo-ku, Osaka-shi, Osaka, Japan

mL, and IND-IFs. The pseudo STD-IF for each subject was generated using the leave-one-out technique. Using the optimal calibration time and the pseudo STD-IFs, MBF values were estimated on the TTACs with an autoradiography method. Optimal mid-scan time (MST) with a fixed duration of 20 min was determined to minimize intersubject variation in estimated MBF errors, and (3) Global and regional MBF values estimated with pseudo STD-IFs were compared to those with IND-IFs using the optimal calibration time and MST. Results The optimal calibration time and MST were both 20 min after 201Tl injection. Global MBF determined using both IND-IFs and pseudo STD-IF showed significant correlations with rate-pressure products, R2 = 0.645; p \ 0.01 and R2 = 0.303; p \ 0.05, respectively. The mean percent error in regional MBF using pseudo STD-IFs was 0.69 ± 7.80 % (-12.80 to 14.25 %). No significant difference was observed between regional MBF values using IND-IFs and pseudo STD-IFs. Conclusion This study demonstrated that the proposed technique based on a STD-IF and one-point blood sample provided hemodynamically reasonable global MBF values and the regional MBF values comparable to those with IND-IFs. Keywords Myocardial blood flow  SPECT  Thallium201  Input function

Introduction Nuclear cardiac imaging provides information on biological functioning in vivo. The significance of absolute quantification of myocardial blood flow (MBF) and myocardial flow reserve (MFR) has been reported for

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evaluation of myocardial perfusion, especially in multivessel coronary artery diseases [1–4]. Corrections for photon attenuation and scatter are essential in the accurate quantification of MBF, both with positron emission tomography (PET) and single photon emission tomography (SPECT). In cardiac SPECT as well as PET, X-ray computed tomography (CT)–based attenuation corrections have been developed using hybrid SPECT/CT systems [5–7]. Thallium-201 (201Tl) is a widely used myocardial perfusion tracer in clinical studies because of its relatively high first-pass extraction fraction, lack of metabolites, and well-known pharmacokinetics. In addition to qualitative and/or semi-quantitative evaluations of radioactivity concentrations in the myocardium, quantification of MBF using 201Tl and dynamic SPECT has been demonstrated using appropriate procedures such as corrections for attenuation and scatter. In a canine study with input functions (IFs) measured by frequent arterial blood sampling, a kinetic modeling approach provided accurate MBF values at rest, after beta-blocker administration and during adenosine infusion, and these were comparable to those measured in a microsphere experiment [8]. In myocardial perfusion studies with PET, image-driven IFs using time– activity curves of the left ventricular cavity and myocardium have been used as alternative and reliable approaches [9–11]. Application of the image-driven IF to cardiac SPECT could be difficult because of characteristics specific to SPECT. For instance, there is spillover from the myocardium to the ventricular cavity due to the higher distribution volume of SPECT tracers relative to those used in PET, and the lower spatial resolution with parallel collimators compared to PET. Although the use of IFs measured by frequent arterial blood sampling is considered to be the gold standard in cardiac SPECT, this approach involves complicated and invasive protocols. As an alternative approach to the measurement of individual input functions (IND-IFs), a standard input function (STD-IF) technique was shown to be feasible for quantifying regional cerebral blood flow [12–16]. A STD-IF is a time– activity curve consisting of population-averaged blood sample data and is calibrated with an one-point blood sample from the subject. The purpose of this study was to validate the quantification of MBF in 201Tl cardiac SPECT using STD-IF and an autoradiography method. First, using healthy volunteers at rest, we determined the appropriate one-point blood sampling time for calibrating a STD-IF and the scan start time relative to injection of 201Tl with a fixed scan duration. Then, by comparing MBF values with those obtained using IND-IFs determined with frequent blood sampling, we evaluated global MBF in terms of hemodynamics and assessed errors in regional MBF values using the STD-IF technique.

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Materials and methods Subjects Eleven healthy volunteers were enrolled. The subjects consisted of 7 men and 4 women; age range, 18–25 year; mean age ± SD, 21.4 ± 2.3 years; and mean weight ± SD, 55.4 ± 5.2 kg. None of the volunteers had signs or symptoms of ischemic heart disease. The study was approved by the ethics committee of the National Cerebral and Cardiovascular Center. All subjects gave written informed consent for participation in this study. Scanning protocols for human subjects All subjects were scanned at rest and in a supine position with arms up, using a hybrid SPECT/CT scanner, the Symbia T6 (Siemens, Knoxville, TN, USA). Hematocrit, hemoglobin values, hemodynamic parameters of heart rate, and systolic and diastolic blood pressures were measured prior to scans and 10 and 50 min after 201Tl injections. 99m Tc-based blank and transmission scans were performed, along with CT scout and breath-hold X-ray CT scans. The transmission system, filled with 99mTc, was removed from the SPECT detector before the following scans. The breathhold X-ray CT scans were acquired at end-inspiration, endexpiration, and the midpoint between these [7]. In this study, attenuation maps at the midpoint phase were employed for attenuation and scatter corrections during the reconstruction of SPECT images. CT acquisition parameters were described in detail in a previous work [7]. Dynamic SPECT was started 2 min before the start of the 2-min constant infusion of 111 MBq 201Tl. The detector heads were positioned opposite each other, with lowenergy, high-resolution collimators in continuous mode, a circular orbit, and a 34 % energy window centered on 77 keV [17, 18]. The scan sequence was 6 9 2 min and 8 9 5 min; number of views, degrees per view, matrix size, and enlargement factor were 45 views, 4° per view, 64 9 64, and 1.45, respectively. Arterial blood samples of approximately 1.5 mL were taken every 15 s for the first 4 min, every 30 s for 4–5 min, every 1 min for 5–8 min, every 2 min for 8–12 min, every 5 min for 15–20 min, and every 10 min for 20–50 min. In total, 29 samples were obtained from each subject. A whole blood aliquot of 200 lL was split from each subject’s sample, and the radioactivity was measured in a well counter that was cross-calibrated with the SPECT scanner. Plasma was separated immediately from the remaining sample by centrifugation, and the radioactivity of the plasma samples was measured in the well counter. Radioactivity concentrations of whole blood and plasma were calculated, with subtraction of corresponding

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background concentrations. A STD-IF was calculated by averaging time courses of plasma counts normalized by the subjects’ weights and injected doses. Image reconstruction In human studies, quantitative SPECT images with pixel values expressed in Bq/mL were generated from projection data using a quantitative SPECT software package (QSPECT, National Cerebral and Cardiovascular Center and QSPECT group, Japan) [19]. The reconstruction algorithm used was ordered-subset expectation maximization reconstruction (3 iterations, 5 subsets using geometricmean projection and a post-smoothing Gaussian filter of 7.0 mm in full width at half maximum). Correction for photon attenuation and scatter was performed with a CTbased attenuation map. Methodological details regarding SPECT image reconstruction were described in our previous study [7]. Measurement of a recovery coefficient A phantom experiment was carried out to determine the recovery coefficient for correction the partial volume effect. The phantom provided a cardiac insert with variable wall thickness in lateral region, which was realized by moving a mimic of a left ventricular cavity along to lateral/ septal direction. We measured the recovery coefficient for 10-mm wall thickness. The mimic of myocardial wall filled with 29 MBq of 201Tl. There was no radioactivity in other regions inside and outside the myocardial mimic. Using the SPECT/CT scanner, we performed CT scan for attenuation and scatter corrections, and 10-min SPECT scan. Acquisition and reconstruction parameters were also the same as those of human studies. A 10-mm diameter circle was drawn as a region of interest on lateral myocardial region in the reconstructed image. Using true and image-derived radioactivity concentrations, the recovery coefficient was calculated. Data analysis We assumed that observed radioactivity concentrations in the myocardium were described by a two-compartment model with two parameters, K1 and k2, including a partial volume effect (a) and first-pass extraction fraction (EF) [8]: CðtÞ ¼ a  EF  K1  Ca ðtÞ  expðEF  K1 t=Vd Þ;

ð1Þ

where C(t) and Ca(t) denote the myocardial tissue time– activity curves (TTACs) measured by SPECT and the plasma input function, respectively. Vd = K1/k2 is the distribution volume, which was fixed to 45 mL/mL in this study. The value of Vd was derived from a previous work

for canines under conditions of resting, beta-blocker, and adenosine infusion [8]. Plasma flow K1 was estimated by autoradiography and table look-up (ARG) procedures. We calculated a look-up table relating theoretical myocardial counts to K1 values which were increased by 0.05 mL/min/ g, while the integration of Eq. 1 over scan period [T1, T2], that is, theoretical myocardial count, increased monotonically with given K1 values. Using this table and a cubic spline interpolation technique, a K1 value corresponding to observed myocardial count was estimated. An MBF value was obtained from the K1 value, corrected for EF and hematocrit (Hct) as MBF = K*1/EF, where EF ¼ 0:84  0:524  log10 ðK1 Þ; K1 ¼ K1 =ð1  HctÞ [20]. To determine the optimal time to calibrate the STD-IF for each subject, we introduced a metric between the INDand calibrated STD-input functions, which was defined as the following function for the i-th subject [13]: R  RT  T  100   0 ui ðTc Þ  AðsÞds  0 Cai ðsÞds i X ðTc Þ ¼ ; ð2Þ RT i 0 Ca ðsÞds where ui ðtÞ ¼ wi ðtÞ=wS ðtÞ is a calibration factor at time t, and wi(t) and wS ðtÞ are whole blood counts of the i-th subject and the STD-IF, respectively. T denotes the integral period (=50 min, whole-scan duration in this study), and Cai ðtÞ and A(t) are the i-th IND- and STD-IFs, respectively. In addition to the difference between the two kinds of IFs, the variations in radioactivity count ratios of plasma to whole blood were evaluated to assess the equilibrium time point for the ratios. A simulation study using an optimal calibration time was performed to optimize scanning time for minimizing inter-subject variation in MBF estimation errors due to use of a STD-IF. The pseudo STD-IF for each subject was constructed from the IND-IFs of the other 10 subjects, and was calibrated using the ratio of the subject’s whole blood count value, wi ðtOPT Þ; to the mean value of the other subjects, wS ðtOPT Þ; at the optimal calibration time, tOPT : Using Eq. 1, simulated TTACs of 50-min duration were generated using IND-IFs with the following parameters: MBF = 0.5, 1.0, 1.5, and 2.0 mL/min/g; Vd = 45 mL/mL; and a = 0.643, which was obtained from the cardiac phantom experiment. MBF values with the pseudo STD-IF were estimated on the simulated TTAC by the ARG method using a fixed scan duration, [T1, T2], of 20 min, and six mid-scan times (MSTs), (T1 ? T2)/2, of 10, 15, 20, 25, 30, and 35 min. The inter-subject variations were evaluated by SDs of percent errors in MBF values with pseudo STDIFs for the assumed MBFs and MSTs. Optimal scanning time was also assessed in term of image quality using ratios of radioactivity concentration in myocardia to that of left ventricular cavities, Rmyo/cav. For each subject, a static image was calculated by summing the dynamic image over

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the whole scan period. The dynamic and static images were reoriented to the short-axis using transformation parameters defined on the static image. A 14.8-mm diameter circle was drawn as a region of interest (ROI) on the left ventricular cavity in the static image. The ROI was superimposed on the dynamic image to calculate a TTAC. From the center of the ROI, a circumferential profile was obtained in a transverse slice at basal level with 1° of step angle. Using locations of sampling points of the profile, radioactivity concentration in the myocardium was averaged over the 360 samples for each dynamic frame. The averaged value was divided by the radioactivity concentration in the left ventricular cavity for each frame, and then a time course of Rmyo/cav was obtained. To evaluate errors in MBF estimated with a fixed Vd value, another simulation study was performed. Using Eq. 1, simulated TTACs of 50-min duration were generated using STD-IFs for MBF = 0.5, 1.0, 1.5, and 2.0 mL/ min/g and Vd = 35 to 55 mL/mL with step size = 1 mL/ mL. In calculating the TTACs, no calibration was applied to the STD-IF. For a fixed Vd = 45 mL/mL, MBFs were estimated on the TTACs by the ARG method. This simulation study was performed for the same MSTs and scan duration as the first simulation study. Using the optimized calibration and scan times, quantification of MBF was performed with the IND- and pseudo STD-IFs. For the optimal MST determined by the above procedures, pixel-by-pixel MBF images were produced from the re-oriented dynamic images by the ARG method using the IND- and pseudo STD-IFs, respectively. Myocardium in the MBF images was divided into 17 segments according to the AHA 17-segment model [21]. Global MBF was calculated by averaging the regional MBF values. Correlation of rate-pressure products (RPPs) and global MBF values with the two kinds of IFs was assessed. Global MBF values with IND-IFs, MBFIND and those values with pseudo STD-IFs, MBFPSTD were also compared directly using linear regression and Bland–Altman analyses. Regional MBF values with the two kinds of IFs were also statistically tested using the two-tailed paired t test for each segment. Percent difference between the regional MBFPSTD and MBFIND was calculated as 100  ðMBFPSTD - MBFIND Þ=MBFIND . A p value of less than 0.05 was considered statistically significant. Data are expressed as mean ± SD.

Results Hemoglobin and hematocrit values, as well as hemodynamic parameters, are summarized in Table 1. There was no statistically significant difference in hemodynamic parameters before and 10 min after 201Tl injection.

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Ann Nucl Med (2014) 28:917–925 Table 1 Hemodynamic parameters Parameters

Pre

10 min after Tl injection

201

50 min after 201 Tl injection

HR (beats/min)

56 ± 6

56 ± 5

SBP (mm Hg)

106 ± 11

108 ± 9

117 ± 13*, 

DBP (mm Hg)

59 ± 6

61 ± 6

66 ± 5*, 

6005 ± 1078

6085 ± 834

7101 ± 1473*, 

RPP (mm Hg/min)

61 ± 9

HR heart rate, SBP systolic blood pressure, DBP diastolic blood pressure, PRR rate pressure product * p \ 0.05 vs. Pre;

 

p \ 0.05 vs. 10 min after

201

Tl injection

Table 2 Differences between individual and population based input functions Calibration time (min)

Percent difference (%)

2.25

16.6 ± 17.6

2.5

11.5 ± 12.1

2.75

6.7 ± 4.3

3

6.4 ± 6.2

3.25

9.8 ± 8.7

3.5

12.6 ± 9.1

3.75 4

13.3 ± 11.3 12.8 ± 11.4

4.5

12.8 ± 12.9

5

12.4 ± 13.5

6

8.2 ± 10.6

7

8.8 ± 8.2

8

7.3 ± 7.8

10

7.0 ± 6.2

12

6.1 ± 6.1

15

4.9 ± 4.6

20

3.9 ± 2.9

30

4.3 ± 3.4

40

4.5 ± 3.9

50

4.8 ± 3.1

However, systolic and diastolic blood pressures and RPPs at 50 min after 201Tl injection were increased significantly compared with before and 10 min after 201Tl injection. Differences between STD- and IND-IFs are listed in Table 2 as a function of calibration times. All percent differences below 5 % were observed with calibration times longer than 15 min. The optimal time was 20 min after 201Tl injection, where the minimum bias and a variation of percent difference of 3.9 ± 2.9 were obtained. Figure 1 shows the radioactivity count ratios of plasma to whole blood as a function of time. Excluding the first 2 min during 201Tl injection, the ratio reached a minimum at 7 min and achieved near equilibrium after 20 min.

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921 2.5

4 Myocardium / left ventricular cavity

3.5 Plasma / whole blood

3 2.5 2 1.5 1 0.5 0 -0.5 -1

0

10

20 Time after

30 201

40

50

SD of %error in MBF PSTD

MBF = 0.5 (mL/min/g) MBF = 1.0 (mL/min/g) MBF = 1.5 (mL/min/g) MBF = 2.0 (mL/min/g)

15

10

5

0

0

5

10

15

20

25

30

1.5

1

0.5

0 0

Tl injection (min)

Fig. 1 Plot of radioactivity count ratios of plasma to whole blood over time

20

2

35

40

Mid scan time (min)

Fig. 2 Simulated variation of estimation error in MBF with pseudo standard input functions, MBFPSTD

Figure 2 shows simulated variations in MBF estimation errors due to the use of pseudo STD-IFs. The SDs of the percent errors in MBF values were plotted as functions of the MSTs. For simulated MBF = 0.5 and 2.0 mL/min/g, the SDs decreased and increased monotonically, respectively. For MBF = 1.0 and 1.5 mL/min/g, the minimum SDs occurred at MST = 25 and 20 min, respectively. Figure 3 shows time course of the averaged ratios of radioactivity concentration in myocardia to that in left ventricular cavities over all subjects. In contrast to increasing tendency in the first 20 min after 201Tl injection, the ratio achieved near equilibrium at the following phase. Figure 4 shows a representative example of a dynamic SPECT image at basal level. The ratios, Rmyo/cav, obtained from the image were closest to the averaged Rmyo/cav in term of sum of squared differences between the individual

5

10

15

20 25 30 35 Mid scan time (min)

40

45

50

Fig. 3 The averaged ratio of radioactivity concentration in myocardial regions to that in left ventricular cavities

and the averaged ratios. Myocardium and left ventricle with comparable radioactivity concentration were delineated at MST = 5 min. Figure 5 shows the errors in MBF estimations due to incorrect Vd values for MSTs of 10, 20, and 30 min. Larger errors were observed with delayed MSTs and higher MBFs. For MSTs of 15, 25, and 35 min, similar trends were also observed (omitted in Fig. 5). Ranges of the percent errors for MBF = 2.0 mL/min/g were (-6.0, 4.1), (-8.5, 6.0), (-12.2, 9.1), (-16.4, 13.1), (-20.8, 18.2), and (-25.3, 25.2) for MSTs of 10, 15, 20, 25, 30, and 35 min, respectively. Correlations of global MBFs using the 20-min MST with RPPs are shown in Fig. 6a, b for IND-IF (R2 = 0.645; p \ 0.01) and pseudo STD-IF (R2 = 0.303; p \ 0.05), respectively. The RPP values were calculated from heart rates and systolic blood pressures measured at 10 min after 201 Tl injections. Figure 7a shows correlations of global MBFPSTD with MBFIND (R2 = 0.533; p \ 0.01). Figure 7b shows differences between global MBFPSTD and MBFIND, which ranged from -0.053 to 0.051 mL/min/g (percent errors, -12.67 to 13.91 %). Regional MBFs using INDand pseudo STD-IFs are shown in Fig. 8a using polar map representation. The mean MBF values of the 17 segments were 0.407 ± 0.062 (0.335–0.520) and 0.407 ± 0.062 (0.327–0.508) mL/min/g for the two kinds of input functions, respectively. There was no significant difference between regional MBF values using the two kinds of input functions. Figure 8b shows bias and inter-subject variation of MBF estimation errors associated with use of pseudo STD-IFs in polar map representation. The mean bias was 0.69 % (-12.80 to 14.25 %) and the variation was 7.80 %. Both global and regional MBF values were obtained with an MST of 20 min.

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20

MBF = 0.5 (mL/min/g) MBF = 1.0 (mL/min/g) MBF = 1.5 (mL/min/g) MBF = 2.0 (mL/min/g)

10 0 -10 Assumed Vd = 45 (mL/mL)

-20

B

30 20

MBF = 0.5 (mL/min/g) MBF = 1.0 (mL/min/g) MBF = 1.5 (mL/min/g) MBF = 2.0 (mL/min/g)

10 0 -10 Assumed Vd = 45 (mL/mL)

-20

MST = 10 min

C

30

%Error in estimated MBF

30

%Error in estimated MBF

A %Error in estimated MBF

Fig. 4 A representative example of a dynamic SPECT image at basal level

20

0 -10 Assumed Vd = 45 (mL/mL)

-20

MST = 30 min

-30 40 45 50 True Vd (mL/mL)

10

MST = 20 min

-30 35

MBF = 0.5 (mL/min/g) MBF = 1.0 (mL/min/g) MBF = 1.5 (mL/min/g) MBF = 2.0 (mL/min/g)

55

-30 35

40 45 50 True Vd (mL/mL)

55

35

40 45 50 True Vd (mL/mL)

55

Fig. 5 Errors in MBF estimations due to incorrect Vd values for mid scan times (MSTs) of 10, 20, and 30 min

A

B

0.6

0.4 0.3 0.2

2

R =0.645, p < 0.01

0.1 0

0.4 0.3 0.2

2

R =0.303, p < 0.05

0.1

0

2000

4000

6000

8000 10000

Rate-pressure product

Discussion In this study we obtained 201Tl SPECT measurements of MBF in human subjects using IND-IFs and STD-IFs,

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0.6 0.5

MBFPSTD (mL/min/g)

0.5 MBFIND (mL/min/g)

Fig. 6 Correlation of ratepressure products and global MBF with 20-min mid scan time using individual input functions, MBFIND (a) and pseudo population averaged input functions, MBFPSTD (b), respectively. The rate-pressure products were calculated using heart rates and systolic blood pressures measured at 10 min after 201Tl injections

0

0

2000

4000

6000

8000 10000

Rate-pressure product

calibrated with one-blood-sample and ARG techniques. The optimal blood sampling time to calibrate a STD-IF was considered to be 20 min after 201Tl injection, because as shown in Table 2, STD-IFs calibrated with radioactivity

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B

0.6 0.5 0.4 0.3 0.2 MBFPSTD=0.098 + 0.760 MBFIND

0.1

R2=0.533, p < 0.01

0

MBFPSTD - MBFIND (mL/min/g)

A MBFPSTD (mL/min/g)

Fig. 7 Comparison between global MBF using pseudo population averaged input functions, MBFPSTD, and those values with individual input functions, MBFIND. Linear correlation (a) and differences by Bland–Altman analysis (b). Dashed line in (b) represent mean ± 1.96 SD

923 0.10

0.000 +/- 0.033 (mL/min/g) 0.05

0.00

-0.05

-0.10 0

0.1

0.2

0.3

0.4

MBFIND (mL/min/g)

Fig. 8 a Regional MBF estimated using individual and pseudo standard input functions. b Bias and inter-subject variation of MBF estimation errors associated with use of pseudo standard input functions. IF denotes an input function

blood counts sampled at 20 min resulted in minimum biases and variations between STD-IFs and IND-IFs. In addition, as shown in Fig. 1, the radioactivity count ratio of plasma to whole blood achieved near equilibrium after that time. Blood sampling at the ratio’s equilibrium was expected to suppress intersubject variations in the ratio, that is, to reduce errors by calibrating STD-IFs using the whole blood count for each subject. From Table 1, intersubject variation of IFs during the early phase was relatively large, as was the radioactivity ratio of plasma to whole blood in Fig. 1. For fixed scan durations, MBF measurements with early scan times were sensitive to the intersubject variations in IFs. To determine optimal scan time or MST with a fixed scan duration of 20 min, we performed a simulation study for assumed MBF values of 0.5, 1.0, 1.5, and 2.0 mL/min/g, using pseudo STD-IFs based on leave-one-out cross-validation. As shown in Fig. 2, minimum variations in estimation errors were

0.5

0.6

0.0

0.1

0.2

0.3

0.4

0.5

0.6

MBFIND (mL/min/g)

obtained with an MST of 25 min for MBF = 1.0 mL/min/ g and an MST of 20 min for MBF = 1.5 mL/min/g. The monotonically decreasing variation for MBF = 0.5 mL/ min/g indicated that later scan times could better minimize the error variation. However, as shown in Fig. 5, errors in MBF estimation were enhanced by ambiguity of Vd values at later scan times. Furthermore, the radioactivity concentration given by the integral on the right side of Eq. 1 was nonlinearly related to K1, and thus MBF. Employing later scan times enhanced the differences between STD-IF and IND-IF in estimating MBF through the nonlinear relation; thus the error variation was increased. From the error analysis with various Vd and MSTs, estimated MBF values were less sensitive to the ambiguity of the Vd value for early MSTs. However, as shown in Figs. 3 and 4, relatively low contrast between myocardial walls and left ventricular cavities was observed in early phase. Furthermore, from Fig. 4, radioactivity concentration in those regions varied obviously at phase from MST = 1 to 7 min. With a fixed scan duration of 20 min, it was indicated that employing the latter MST could contribute to improve myocardial image quality rather than early MST. Therefore, we considered that an appropriate MST was 20 or 25 min for a fixed duration of 20 min. Using the IND-IFs with the optimal MST of 20 min on the quantitative SPECT images, the obtained global MBF values were considered to be reasonable hemodynamically because these flow values correlated significantly with RPPs (R2 = 0.645; p \ 0.01). Global MBF values with the pseudo STD-IFs calibrated using the optimal blood counts also showed significant correlation with RPPs (R2 = 0.303; p \ 0.05). In addition, as shown in Fig. 8, no significant difference was observed between regional MBF values with IND-IFs and those with the pseudo STD-IFs for each segment. Although we observed lower correlation of global MBFPSTD with RPPs rather than global MBFIND (Fig. 6) and a non-zero intercept in the relation between global MBFPSTD and MBFIND (Fig. 7), the values of MBFPSTD

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correlated significantly with those of MBFIND (p \ 0.01) within errors of ±14 %. In addition, regional MBF errors by the pseudo STD-IF technique ranged from -12.80 to 14.25 %.Therefore, our results indicated that the proposed STD-IF technique in 201Tl cardiac SPECT provided potentially accurate quantitative assessment of MBF. It was noted that the proposed protocol was optimized for 20-min scan duration using the SPECT data collected over 60 min. Shortening examination time was considered to be reasonable because it could reduce patients’ discomfort and improve examination throughput. In addition, it was expected to suppress patient body movement caused by discomfort. The patient movement induced incorrect attenuation corrections, which led to spurious defects in myocardial walls and deterioration of MBF estimation accuracy [6, 22–25]. A limitation of this study was the use of a fixed recovery coefficient for partial volume effects, which depended on thicknesses and motions of myocardial walls. When the fixed recovery coefficient is used, careful interpretation of MBF might be needed since values might be over- or underestimated, especially in hypertrophic cardiomyopathy or cardiomegaly patients, respectively. Image reconstruction methods with spatial resolution recovery offer a potential solution for partial volume effects [26]. These methods may also reduce scan duration and spillover from the ventricular cavity to the myocardium, effects that were not investigated in this study. It was expected that the STD-IF, which is derived from the IND-IFs of healthy volunteers at rest, could be applicable to MBF measurement in ischemic and infarcted patients at rest and under stress. This is because the slow infusion and relatively slow pharmacokinetics of 201Tl could suppress differences in IND-IFs, and thus the differences between individual patients’ IFs and the STD-IF. The magnitude of the STD-IF was calibrated by the whole blood count taken at the optimized sampling time. Furthermore, the scan time was optimized to minimize variation of errors in MBF estimation. Use of a fixed value of Vd was considered to be acceptable for measuring blood flow in ischemic and infarcted myocardia. The concept underlying Vd is the ability of myocardial tissues to retain 201Tl. Ischemic regions of the myocardium are characterized by low flow and maintained Vd. Infarcted regions correspond to low flow and low Vd. Due to the slow pharmacokinetics of 201Tl, the initial uptake of tracer into myocardial tissue mainly reflects flow rather than Vd [19]. Scan time investigated in this study were earlier than temporary phases, in which effects of Vd were dominant on radioactivity concentrations in myocardial tissues. The assumed value of Vd, 45 mL/mL, in this study was derived from the previous canine study [8]. Although, to our knowledge, values of Vd for human subject have not been reported, we expected that

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species difference in distribution volumes between human and canine was relatively small. As shown in Fig. 5, variation of Vd by ±20 % corresponded to about ±10 % error in MBF estimates for relatively high MBF (2.0 mL/min/g) at an MST of 20 min. Therefore, even though the assumed value of Vd differed from a true value in human subjects and/or infarcted patients, MBF quantification with the proposed scan time could be less sensitive to changes in Vd. However, further improvement of the proposed method obviously requires comparison with a more accurate technique such as 15O-water cardiac PET, which provides corrections for the partial volume effect and spillover from ventricular cavities [27, 28]. Impact of our method on clinical diagnosis is to be evaluated in future work.

Conclusion In this study, a protocol was determined for measuring MBF using a population-averaged input function and one-point blood sampling in 201Tl cardiac SPECT. The estimated accuracy of MBF can be reasonably high. The protocol is expected to contribute to the quantification of absolute MBF and assessment of MFR in ischemic patients. Acknowledgments This research was partially supported by a 2013 Grant-in-Aid for Young Scientists (B), no 13308422, from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

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Quantification of myocardial blood flow using (201)Tl SPECT and population-based input function.

Thallium-201 ((201)Tl) single photon emission computed tomography (SPECT) is an important tool in the diagnosis of ischemic heart disease. Absolute qu...
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