198 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 40, NO. 2, APRIL 1993

Monte Carlo Simulation in SPECT: Complete 3D Modeling of Source,

Collimator and Tomographic Data Acquisition J. C. Yanch and A. B. Dobrzeniecki

Abstract-A sophisticated SPECT simulation package has been developed permitting full tomographic acquisition of data from physically realistic nonuniform and asymmetric 3D source ob- jects. The package is based on the Los Alamos code MCNP 111 (Monte Carlo for Neutron-Photon transport) which has been extensively modified by us to allow complete collimator and source modelling and direct manipulation of the geometric and physical parameters of the nuclear medicine experiment. In this paper we present a brief description of synthetic SPECT imag- ing system and of its capabilities. We will begin by describing the code MCNP, then we will provide details of the modifica- tions that have been necessary in order to run MCNP for this application. Preliminary experiments to verify the accurate mod- elling of the imaging situation have been successful and these will also be described. We will focus here on its ability to model two different collimator geometries (parallel-hole and cone- beam), and include steps taken to verify the models.

I. SPECT SIMULATION

E SPECT simulation package (“SimSPECT”) is T” based on a sophisticated 3D Los Alamos Monte Carlo code called MCNP. We have, however, extensively modi- fied the code in order to tailor it to the specific applica- tion of Nuclear Medicine Imaging.

MCNP (Monte Carlo for Neutron and Photon trans- port) represents the state-of-the-art in terms of the physics, cross-section data, and mathematical models necessary for neutron and photon Monte Carlo simulations. For the current application however the neutron generation capa- bility has been turned off and only photons are trans- ported. MCNP contains photon cross-section tables for elements Z = 1 to Z = 94. A composite material contain- ing any number of different elements can be easily mod- elled, as can source with any degree of non-homogeneity. The data in the photon interaction tables allow MCNP to automatically account for coherent and incoherent scat- tering, photoelectric absorption with characteristic X-ray

Manuscript received November 20, 1991. The authors are with the Department of Nuclear Engineering and

Whitaker College of Health Sciences and Technology, Massachussets Institute of Technology, Cambridge, MA 02140.

This paper was originally presented at the 1991 IEEE Nuclear Science Symposium (NSS ’91), held in Santa Fe, NM, November 5-8, 1991.

IEEE Log Number 9207254.

emission and pair production with local emission of anni- hilation quanta. Scattering distributions may be modified by atomic form factors and incoherent scattering functions.

MCNP has a generalized input file capability which allows the user to specify an infinite variety of source and detector conditions without having to make modifications to the Monte Carlo source code itself. The size, shape and spectrum of the radiation source, the composition and configuration of the medium through which photons are transported, and the collimator geometry and type are all user-defined parts of this input file.

To simplify the input file step we have constructed a “pre-processor” in which the user specifies collimator type (parallel, cone-beam), hole diameter, length and number, packing geometry, and overall dimensions. Here the user also completely defines the source geometry (patient or phantom) in three dimensions. The isotope used, energy windods), image pixel size and the number of tomo- graphic views required is also specified.

The pre-processor invokes the MCNP code which simu- lates the emission and the transport of photons through the geometry. All photon interactions are accounted for automatically within MCNP. The scintillation crystal, light pipe and photomultiplier tubes are not simulated via transport methods. Instead the camera is modelled as a plane with the same dimensions as the collimator being modelled, composed of a user-defined pixel number and size. The energy of each detected photon is sampled from the energy resolution function of the camera which is assumed to have a FWHM of 12% (also user-definable).

To simulate tomographic data acquisition in manage- able times we make use of multiple processes running on separate computers. The technique is illustrated in Fig. 1. One computer is designated the photon generator which tracks photon interactions within the patient or phantom. When the photon leaves the object and passes through a virtual sphere surrounding the object, its position, direc- tion, energy and scatter order are saved. The photon is then cloned and allowed to interact with the collimator for all views with which it would interact. This step is carried out by one or more photon consumers using separate CPUs. This method achieves a high degree of

0018-9499/93$03.00 0 1993 IEEE

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YANCH AND DOBRZENIECKI: MONTE CARLO SIMULATION IN SPECT 199

coarse-grained parallelism and can produce true tomo- graphic simulations in a reasonable time.

The SimSPECT environment also allows both on-line and post-acquisition processing of projection and recon- structed SPECT data; this environment consists of a vari- ety of tools for image display and image manipulation. Users can easily access data in a number of different formats, perform image filtering in a number of ways, carry out image arithmetic, control colormaps, and his- tograms and display image profiles and other properties; series of images can be combined into a cine loop that provides real-time display (animation) of sequential data. All such image manipulation can be carried out while the simulation is running. Such real-time interaction is helpful in that acquisition statistics can be easily confirmed during a long run. All runs can be stopped and restarted at any time. Our imaging environment also permits the recon- struction of any data (scatter, total counts, primary data, etc.) at any time while the simulation is running.

A. Simulation of Parallel-Hole Collimators With SimSPECT the collimator is physically modelled

in its entirety. The user simply specifies the number of holes, hole diameter and length, septal thickness, hole shape and packing arrangement.

The accuracy with which SimSPECT models the re- sponse of the parallel-hole collimator in both planar and tomographic imaging was tested in two ways. First, the geometric response of the collimator was evaluated by placing a point source at different distances from the collimator face for different sizes of hole. The full-width at half-maximum (FWHM) of the resultant image of the point source was measured and plotted against distance from the collimator. A straight line should be the result if the collimator has been modelled correctly since the spa- tial resolution of the acquired image can be linearly expressed by a simple equation in terms of the source- collimator distance and collimator dimensions. That is,

d ( L + Z ) L

R =

where R is the spatial resolution, L is the hole length, d of the hole diameter, and Z the source-to-collimator distance [2]. A G E LEGP collimator containing 18,000 holes of diameter 25 mm and length 41 mm was simulated with SimSPECT. [Note that all 18,000 hexagonal holes were accurately modelled in hexagonal packed array.] Changes in FWHM as a result of adjusting the position of the point source or the hole size are shown in Fig. 2. Note that the expected relationship is observed.

To evaluate the accuracy of the tomographic capability of SimSPECT using a parallel-hole collimator we carried out both real and simulated tomographic acquisition of a water-filled cylindrical phantom containing four spheres filled with 99mTc. Sixty projection views were obtained into a 64 X 64 pixel array. Data were collected with a 20% energy window center on the 99m Tc photopeak. The radius

Photon

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Fig. 1. Schematic illustration of the generation of tomographic data through Monte Carlo simulation. Photons are generated and tracked in the object on CPU1 (the photon generator). Upon passing though a "virtual sphere" the photons' direction, position, energy and scatter order are recorded; the photon is cloned and redirected to all collimator positions with which that photon could have interacted. Photon tracking through collimator positions is carried out on one or more CPU's (photon consumers).

of rotation was set at 25 cm. A Siemens Rota Singlehead camera fitted with a LEHR collimator (825-004004) was used in the experimental acquisition (physically exact col- limator dimensions were used for the simulation). Real and simulated projection data were reconstructed using identical filtered backprojection algorithms and filter cut- off frequencies. Results are shown in Fig. 3. Line profiles taken through the smallest hot source (1.3 cm diameter) show a great deal of similarity between the real and the simulated images indicating the SimSPECT is accurately modelling the realistic SPECT situation of asymmetric sources.

The phantom modelled here, however, is a relatively simple three-dimensional object. One of the advantages of the simulation system is that it is fully capable of mod- elling any complicated three-dimensional object with a physical accuracy limited only by the dedication of the user. Fig. 4 illustrates another phantom geometry that was modelled; Fig. 4(b) shows a transaxial slice through a water-filled phantom containing two identical spheres. Each sphere consists of a 1-cm thick 99mTc-filled perime- ter with a 2-cm diameter water-filled center. Simulated tomographic data were reconstructed using the Maxi- mum-likelihood expectation-maximization (MLEM) algo- rithm [3], [4]. The line-length projector and backprojector (PLL and BLL) were used and the reconstructions were stopped after twenty iterations. A reconstructed transaxial image of the primary photons collected in the photopeak window is illustrated in Fig. 4(b). The scattered photons collected in this window are reconstructed and are shown in Fig. 4(c). Note that the ability to separate the scattered and unscattered components of the data is not possible experimentally.

200 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 40, NO. 2, APRIL 1993

(C) (d)

Fig. 2. Determination of the geometric response of a simulated parallel-hole collimator. (a) Spatial resolution (FWHM) versus source collimator distance (hole diameter = 1.11 mm, hole length = 2.36 cm), pixel resolution is 64 X 64. Note that the straight line relationship falls apart when the image of the point approaches the size of a single pixel (0.625 cm). (b) Spatial resolution (FWHM) versus source collimator distance (hole diameter = 1.11 mm, hole length = 2.36 cm), pixel resolution is 128 x 128. (c) Spatial resolution versus length of collimator hole (hole diameter = 1.11 mm, source-collimator distance is 20.0 cm), pixel resolution is 64 x 64. (d) Spatial resolution versus hole diameter for hole length of 2.36 cm and source-collimator distance of 10.0 cm, pixel resolution is 64 X 64.

Fig. 3. (a) Schematic diagram of the 19.5 cm diameter x 18.0 cm length cylindrical phantom. Four 99mTc-filled spheres (3.0, 2.5, 1.8, and 1.3 cm diameters) were placed at a radial position of 5.7 cm. Activity in each sphere was identical. (b) Experimental data: A transaxial slice through the center of the phantom. Total activity was approximately 720 MBq. A 20 second acquisition time per view lead to roughly 270 x lO/cubed, counts in each projection. (c) Reconstructed transaxial slice using Monte Carlo simulation data. (d) Horizontal profile through the smallest hot sphere in the reconstructed image of the experimentally obtained data. (e) Corresponding profile using simulated data.

B. Simulation of Cone-Beam Collimator the heart and brain. Cone-beam collimation also leads to a large increase in sensitivity-a factor of 2-3 more counts from the organ reach the detector as compared with conventional parallel-hole collimation [5 ] , [6]. This increased sensitivity and magnification has been shown to lead to significant improvements in lesion detectability [7].

Cone-beam collimation was also investigated. A cone- beam collimator is one in which the holes converge to a single point behind the collimator. This leads to a magni- fication, on the detection plane, of small organs such as

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YANCH AND DOBRZENIECKI: MONTE CARLO SIMULATION IN SPECT

Focal Colllmator Hole Hole Shape Length Thickness Diameter

(an) (an) (an)

2.46 0.115 p a d e l hexagonal - hole

cone hexagonal 5 0 4.06 0.190 bum

(d) (e)

Fig. 4. Hollow spheres simulated phantom; each sphere is water filled, with activity present in a 0.5 cm thick annulus. The spheres are inside a cylindrical container, also filled with water. (a) Schematic diagram of the phantom (b) Maximum likelihood reconstruction of simulation data using scattered and unscattered photons in the photopeak window. (c) Profile through the reconstructed image. (d) Maximum likelihood reconstruction using only unscattered photons in the photopeak window. (e) Maximum likelihood reconstruction using only scattered photons in the photopeak window.

Sept.1 Thickness

(an)

0.015

0.025

40 0 0 0

30 U al 0

al

c.

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202 IEEE TRANSACTIONS O N NUCLEAR SCIENCE, VOL. 40, NO. 2, APRIL 1993

t

(d) (e)

Fig. 6. The “cross-talk’ phantom consisting of seven parallel discs of equal activity lying parallel to the axis of rotation. (a) 2D plot through the phantom as provided by MCNPs internal routine. (b) Planar image of the simulated phantom. (c) Profile through a planar image. (d) Sagittal view through the center of the reconstructed image. (e) Profile through the sagittal image. Note the cross-talk artifact producing elongation of the structure in the axial direction and corresponding reduction in counts.

SimSPECT is capable of modelling any cone-beam col- limator. For the purposes of model verification and pre- liminaq testing a collimator described in the literature was modelled [61. [Details of collimator dimensions are provided with Fig. 5.1 To verify the accuracy of the simu- lated cone-beam collimator we measured its sensitivity as a function of source-detector distance. For comparison, the sensitivity of a low-energy high-resolution parallel-hole collimator as also tested. Results are shown in Fig. 5. Note the large increase in the number of counts reaching the detector as the point source is moved further away. As expected, this increase reaches a factor of two at a dis- tance of roughly 20 cm [6].

Initial verification of the accuracy of SimSPECT in modelling SPECT using a cone-beam collimator was car- ried out by simulating the “slice-to-slice cross-talk’’ phan- tom [8], [9]. If simulated reconstructed cone-beam data show the same artifacts as seen with real cone-beam imaging this would further verify the accuracy of the simulation model. A phantom well-suited for showing the cross-talk artifact consists of seven radioactive discs lying in a transverse plane, each with a diameter of 20 cm and a thickness of 2 cm. Fig. 6(a) shows a two-dimensional cut through the simulated phantom as provided by MCNP’s internal plotting routine. Sixty projection views

image of this phantom as simulated by SimSPECT. Reconstruction via the Feldkamp algorithm [lo] is ex-

pected to show both spatial distortion away from the center of the image and an underestimate of activity which becomes worse with distance away from the center. The artifact is clearly seen in the reconstructed sagittal view of the simulated data as shown in Fig. 6(c). A profile through this image is given in Fig. 6(d).

11. COMPUTATIONAL TIMES The simulation system currently runs on SUN SPARC

workstations and Silicon Graphics Personal IRIS ma- chines. Communication within and between processes (photon generators and consumers) is via TCP/IP sock- ets. All image manipulation and display is carried out under X Windows. The code requires 15 MByte of RAM when executing.

The time required to carry out the simulation shown in Fig. 3 was approximately 200 CPU hours on each of two IRIS workstations leading to approximately 2,000 counts in each of 60 tomographic views. Modifications were sub- sequently made to the SPECT simulation system to im- prove efficiency. Images shown in Fig. 6 took 36 h of CPU time leading to approximately 60,000 counts/view.

were simulated over 360” and acquired in a 64 x 64 pixel array. Data were collected in a 20% energy window cen- tered on the 99mTc photopeak. Collimator to phantom center distance was 25 cm. Fig. 6(b) shows a projection

111. CONCLUSIONS Verification tests of the accuracy of SimSPECT in simu-

lating the realistic Nuclear Medicine acquisition of tomo-

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YANCH AND DOBRZENIECKI: MONTE CARLO SIMULATION IN SPECT

graphic data will continue. Initial results, however, appear extremely promising and suggest that with both parallel- hole or cone-beam collimation SimSPECT is producing accurate projection data. Future work with the simulation method will involve the development and evaluation of collimator design, and the quantitative assessment of cor- rection algorithms for photon scatter and photon attenua- tion in asymmetric, non-homogeneous source objects.

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