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Nuclear Instruments and Methods in Physics Research A 513 (2003) 70–73

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doi:10.1016

Sinogram-based dynamic imaging using a slow positroncamera rotation

Antonello E. Spinelli*, Robert J. Ott, Antigoni Divoli, Gail R. ter Haar

Joint Department of Physics, Institute of Cancer Research, Royal Marsden Hospital, Downs Road, Sutton, Surrey SM2 5PT, UK

Abstract

The PETRRA positron camera was used for dynamic imaging using a continuous slow camera rotation. There are

different approaches to performing dynamic studies on projections directly, most of which are valid for specific

assumptions (tracer kinetic model). Our approach is to obtain a time–activity curve (TAC) directly from the sinogram.

Assuming that the function representing the activity distribution is separable in time and space, the integral of the

spatial part with respect to each bin is constant so that there is a linear relationship between the integral of the

projections and the temporal part of the activity distribution function. If there are a few high activity regions

distinguishable on the sinogram, a TAC can be obtained for each one. By dividing each projection by the TAC it is

possible to obtain a time-independent sinogram and using an analytic or iterative algorithm it is possible to perform

image reconstruction. We conclude that this new method might be useful where a blood vessel, heart or tumour is in the

field of view.

r 2003 Elsevier B.V. All rights reserved.

PACS: 87.58.Fg

Keywords: Positron emission tomography; Dynamic imaging; Time activity curve; Sinogram; Image reconstruction

1. Introduction

In order to study the kinetics of tracers it isimportant to acquire an image every few seconds(10 or less). This is very difficult to achieve using arotating dual head PET or SPECT camera due tothe poor statistics of the resulting images.

Our idea is to develop a method to acquirespatial and time information using slow camerarotation, more precisely to obtain a time–activity

onding author. Tel.: +44-20-8661-3023; fax: +44-

2.

ddress: spinelli@icr.ac.uk (A.E. Spinelli).

- see front matter r 2003 Elsevier B.V. All rights reserve

/j.nima.2003.08.004

curve (TAC) directly from the sinogram. There area series of different approaches to performingdynamic studies directly on projections. Most ofthem are valid for a specific pharmacokineticmodel [1], an explicit functional dependence [2]or a monotonic variation of the radiotracerconcentration in the tissue [3]. Our approach doesnot assume any particular model.

In the following we will introduce very brieflythe theory for TAC measurements and imagingreconstruction using a slowly rotating camera. Aseries of simulations and experimental resultsusing tracer dispersion in tubes and a phantomwill then be described.

d.

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A.E. Spinelli et al. / Nuclear Instruments and Methods in Physics Research A 513 (2003) 70–73 71

2. Theory

2.1. TAC measurement

The spatial and temporal distribution of a highactivity region A in the patient can be given by

Aðx; y; z; tÞ ¼ lðtÞIðx; y; zÞ ð1Þ

where we assume that the activity distributionfunction is separable. lðtÞ represents the tracerconcentration in the tissue and Iðx; y; zÞ is thespatial distribution function where the uptaketakes place.

A projection P is defined as the integral along aline of Eq. (1)

Pðr; y; t; zÞ ¼ lðtÞZ

Iðx; y; zÞ ds ð2Þ

where s is the integration variable, r is the bincoordinate and y is the angle between the bin andthe x-axis. Thus the projection is dependent uponlðtÞ and the integral of I along the directionnormal to the projection.

The integral of I is constant for circular objectsbut this is not true for an object of arbitrary shape.Thus a change in the projection values can be dueto a time variation of the tracer concentration inthe tissue, the angular dependence of the projec-tion or both. To solve this problem we note thatthe integral of the projection spatial componentwith respect to each bin r should be invariant withangle if an attenuation correction is performed,and the integral of the projection is dependent onlðtÞ only

P�ðtÞ ¼ lðtÞZ Z

Iðx; y; zÞ ds dr ¼ klðtÞ ð3Þ

where k is a constant (for a given slice z) equal to

k ¼Z Z

Iðx; y; zÞ ds dr: ð4Þ

Using a continuous camera rotation we canobtain a one-to-one relation between the cameraangle y and time t: Combining this relation andEq. (3) it is possible to obtain a TAC.

2.2. Dynamic imaging and image reconstruction at

the same time using a slow rotation of the camera

In Section 2.1 we discussed a simple method formeasurement of the TACs if there are few hotspots in the field of view (FOV). A rapid change oftracer concentration during image acquisitionproduces artefacts in the reconstructed images ifthe time frame is long compared to the tracerkinetics. We here propose a correction methodbased on TAC measurements from a dynamicsinogram.

Combining Eqs. (2) and (3) we can obtain atime-independent projection equal to

*Pðr; yÞ ¼lðtÞ

klðtÞ

ZIðx; y; zÞ ds

¼1

k

ZIðx; y; zÞ ds: ð5Þ

Inverting Eq. (5) it is possible to obtain I :The procedure then becomes:

1. Acquisition of the projections.2. Measurement of the TAC using Eq. (3).3. Division of the projections using the TAC.4. Reconstruction of the image.

In this study the images are reconstructed usingfiltered back projection [4], however this methodcan also be applied to iterative techniques.

3. Simulations

In order to test the theory introduced in Section2.1 we have simulated a dynamic sinogram of twohot spots (a circle and an ellipse) with differenttracer kinetics using a one-compartment model [5].It is important to stress here that the choice of themodel is not unique and we chose this model forsimulation purposes only.

Fig. 1 shows the original TAC and the sinogramderived TAC for the elliptical hot spot obtainedusing the method described in Section 2.1.

Fig. 1 shows that it is possible using thesinogram method to obtain accurate TAC.

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Fig. 1. Original and recovered TACs. The curves are almost

indistinguishable.Fig. 2. An example tube TAC obtained using the sinogram

method (dotted curve) and the NaI(Tl) scintillator (continuous

curve). The flow rate was equal to 0.68ml/s.

Fig. 3. Phantom used in the experiments (dimensions are in

mm). The tracer flow into chamber 1 diffuses into chamber 2

through small holes, and finally flows out through the second

chamber. The main goal of this phantom is to mimic the tracer

dispersion in the heart.

A.E. Spinelli et al. / Nuclear Instruments and Methods in Physics Research A 513 (2003) 70–7372

4. Experimental results using PETRRA

4.1. Tracer dispersion in a tube

In order to verify experimentally the theoryintroduced in Section 2 we acquired a series ofdynamic images of a tube and a phantom using thegas detector based PET scanner PETRRA [6]. Thecirculation of the liquid (water) was obtained usinga peristaltic pump at different flow rates. In thissection we will present tube dispersion resultsobtained by injecting an activity of 1.5–2MBq of68Ga into a tube placed in the centre of the cameraFOV.

By integrating every projection of the sinogram(Eq. (3)) it is possible to obtain a sinogram-derivedtube TAC shown in Fig. 2.

The TAC shown in Fig. 2 has a shape similar tothe TAC obtained using a NaI(Tl) scintillator [7].

4.2. Dispersion using a phantom

In a similar way to the tube, a series of dynamicimages were acquired using the phantom shown inFig. 3.

The phantom TAC can be fitted using a modelintroduced in Ref. [7]:

lðtÞ ¼ wðt � t0Þe�ðt�t0Þ=b ð6Þ

where t0 is the arrival time and b and w are fittingparameters. The agreement between Eq. (6) and

the sinogram derived TAC is good, the correlationcoefficient r is being equal to 0.998.

In order to test the artefacts correction proce-dure described in Section 2.2, PET images of across-section of the phantom’s second chamberhave been acquired by injecting 6–8MBq of 68Ga(Fig. 4).

As one can see looking at Fig. 5 the artefactscorrection procedure reduces the artefacts due tothe tracer variation during the camera rotation.

Analogously to the tracer dispersion in the tubeit is interesting to compare the TAC obtained

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Fig. 4. Cross-section of the phantom, the image is obtained

without artefact correction.

Fig. 5. Cross-section of the phantom, the image is obtained by

correcting for the tracer variation, using the theory described in

Section 2.

Fig. 6. Time intensity curve obtained using the sinogram

method (dotted line) and using a NaI(Tl) probe. The flow rate

was 9ml/s.

A.E. Spinelli et al. / Nuclear Instruments and Methods in Physics Research A 513 (2003) 70–73 73

using a NaI(Tl) probe with the sinogram derivedTAC.

Fig. 6 shows that the agreement between theprobe and sinogram derived TAC is good.

5. Conclusion

In this paper a new method for dynamic imaginghas been introduced. Its validity was tested bymeans of simulated and real images obtained usingrotating planar detectors. A comparison of theexperimental TAC obtained using a NaI(Tl) probeshow good agreement. A correction procedureallows removal of the artefacts due to tracerconcentration variation during the camera rotation.It is now intended to assess this method in the clinic.

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