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Nuclear Instruments and Methods in Physics Research A 580 (2007) 955–959

www.elsevier.com/locate/nima

vECTlab—A fully integrated multi-modality Monte Carlo simulationframework for the radiological imaging sciences

Jorg Peter�, Wolfhard Semmler

German Cancer Research Center (DKFZ), Division of Medical Physics in Radiology, Im Neuenheimer Feld 280, Heidelberg D-69120, Germany

Available online 6 July 2007

Abstract

Alongside and in part motivated by recent advances in molecular diagnostics, the development of dual-modality instruments for

patient and dedicated small animal imaging has gained attention by diverse research groups. The desire for such systems is high not only

to link molecular or functional information with the anatomical structures, but also for detecting multiple molecular events

simultaneously at shorter total acquisition times. While PET and SPECT have been integrated successfully with X-ray CT, the advance

of optical imaging approaches (OT) and the integration thereof into existing modalities carry a high application potential, particularly

for imaging small animals. A multi-modality Monte Carlo (MC) simulation approach at present has been developed that is able to trace

high-energy (keV) as well as optical (eV) photons concurrently within identical phantom representation models. We show that the

involved two approaches for ray-tracing keV and eV photons can be integrated into a unique simulation framework which enables both

photon classes to be propagated through various geometry models representing both phantoms and scanners. The main advantage of

such integrated framework for our specific application is the investigation of novel tomographic multi-modality instrumentation

intended for in vivo small animal imaging through time-resolved MC simulation upon identical phantom geometries. Design examples

are provided for recently proposed SPECT-OT and PET-OT imaging systems.

r 2007 Elsevier B.V. All rights reserved.

PACS: 07.05.Tp; 87.57. �s; 87.64.Aa; 87.64.Cc

Keywords: Monte Carlo simulation; Medical imaging; Computer tomography; Nuclear medicine instrumentation; Optical imaging

1. Introduction

Monte Carlo (MC) simulation [1] is a valuable tool forinvestigating complex physical and technological aspects ofnuclear medicine (positron emission tomography (PET),single photon computed tomography (SPECT)) and X-raycomputed tomography (CT) imaging instrumentation[2–4]. Data simulated by MC estimates are being oftenutilized also for performance evaluation of image recon-struction, scatter and attenuation correction, or otherrelated algorithms used in conjunction with those mod-alities, e.g. [5]. For comparative reviews on major MCcodes available for radiological imaging the reader isreferred to Refs. [6,7].

e front matter r 2007 Elsevier B.V. All rights reserved.

ma.2007.06.093

ing author.

ess: j.peter@dkfz.de (J. Peter).

/www.dkfz.de/petphysik/jpeter/ (J. Peter).

Optical imaging and possibly three-dimensional tomo-graphy (OT) is emerging as an alternative molecularimaging modality [8]. Besides modeling the internalprocesses of image formation to primarily aid instrumenta-tion and algorithm development, additional objectives arisewithin the context of simulating optical photon fluences.These pertain to gain insight into a more completeunderstanding of tissue optics, specifically to support theconstruction of mathematical models for light distributionwithin heterogeneous tissue and to better perceive theinverse relationship between measured light field and tissueoptical properties. If geometrically complex source dis-tributions within turbid media are involved, MC simula-tion is one of the most practical approaches to solving thetransport problem not only for isotopic and X-ray photonsbut also for optical photons, [9–11], without restrictionsand simplifications such as encountered with FEM-basedapproaches [12].

ARTICLE IN PRESSJ. Peter, W. Semmler / Nuclear Instruments and Methods in Physics Research A 580 (2007) 955–959956

Correlating metabolic information from SPECT or PETwith anatomical information from X-ray CT has demon-strated to improve and ease disease detection and localiza-tion in patients [13,14], with instruments also beingadapted recently for dedicated high-resolution SPECT-CT and PET-CT small animal imaging [15,16]. Dual-modality SPECT-OT and PET-OT systems appear also tocarry a multitude of advantages as compared to thesequential use of uni-modal devices, which initiated ourresearch on studying the feasibility of these integrationconcepts.

Therefore, the purpose of this work is to derive andintegrate device-specific MC algorithms for optical (eV)and for isotopic (keV) photons to be used for pre-constru-ction investigation and optimization of dual-modalitySPECT-OT and PET-OT instrumentation and associatedobjectives explained previously, and hence to enable time-resolved ray-tracing of both photon types within identicalphantom geometries. This is the first approach to simulateSPECT, PET, CT, and OT within a fully integratedframework.

2. Methods

A MC simulation framework, termed vECTlab (virtualemission computed tomography lab) has been developed.The transport problem is solved for optical photons(400–950 nm) as well as isotopic and X-ray photons(10–800 keV) by means of a statistical estimates to thecorresponding Boltzmann equations which is the essence ofthe MC method.

2.1. Ray-tracing of keV photons

Given the range of photon energies sampled, thefollowing Boltzmann-type transport equation is solvedmodeling Compton scattering, Rayleigh scattering, andphotoelectric absorption processes at every interaction inthe media

qLðr;O;E; tÞqt

¼1

4psðrÞdðE � E0Þ

� cmðr;O;EÞLðr;O;E; tÞ � cOrrLðr;O;E; tÞ

þ c

ZE

dE0Z4p

dOKðO;E;O0;E0jr; tÞ

�Lðr;O0;E0; tÞ,

whereby L is the photon density, r is the position vector, Oand O0 are the unit vectors of beam direction prior andafter interaction, E and E0 are the photon energies at r andafter interaction, and s is the spatio-temporal sourcedistribution. The first term represents the source sample,the second and third are the attenuated and scatteredfluxes, respectively, and the integral term is the fluxscattered into the differential volume. Angular distri-bution of scattered X-rays and gamma-rays by Comptoninteraction is characterized by the Klein–Nishina formula.

In case positrons are emitted the positron path length issampled from an energy-dependent three-dimensionalGaussian [17].

2.2. Ray-tracing of eV photons

Optical photons are treated as classical particles andlight-matter interactions are characterized by elasticscattering. In case the scatterer is macroscopic in relationto the photon, e.g. at media boundaries, reflection andrefraction is applied. In all other cases, the specific type ofscattering—Rayleigh, Mie, Stokes Raman, etc.—is notmodeled directly. Rather, macroscopic measures such asattenuation coefficient ma, scatter coefficient ms and aniso-tropy g of the media, like those published in Ref. [18], areused to define probability density functions from whichthe photon path length and direction is sampled. Forpropagation of optical photons the following Boltzmann-type transport equation is sampled:

qLðr;O; tÞqt

¼ � cmtLðr;O; tÞ � cOrLðr;O; tÞ

þ cms

ZLðr;O0; tÞf ðO;O0ÞdO0 þ csðr;O; tÞ

with the transport coefficient mt ¼ ma þ ms and f being theprobability of scattering from O into O0.

2.3. Phantom representation

The geometrical scene representation model is crucial forrealistic study setup. We implemented fully time-resolvedray-tracing calculation algorithms upon any hybrid combi-nation of tomographic volumes, analytical surfaces asdefined by super-quadric shapes, and higher order surfacesin the form of closed point meshes, as illustrated in Fig. 1,that incorporate sampling strategies and variance reduc-tion techniques optimized for both photon classes.Analytical representation allows for precise, simple-geo-metry phantom setup and is used primarily to assess theperformance of imaging systems simulated and to verifythe MC algorithm. Segmented tomographic data andhigher-order surfaces yield superior anatomical detail.Point meshes can be derived from CT or MRI data, e.g.[19], and carry the advantage of being more easilyexpendable for dynamic phantom creation.Each particular shape representation is considered a

phantom simploid that can be intrinsically translated,rotated, or scaled arbitrarily in space during simulationtime, allowing for approximation of cardiac and respira-tory motion [20], tumor-growth dynamics [21], or non-static scanner geometries. Every simploid as well assub-regions thereof can contain multiple associatedparameter dynamics such as marker density or scattercoefficient which allows for approximation of organ-specific tracer kinetics [22] or fluorochrome bleaching.Inter-simploid relationships of any order are defined bymeans of a simploid-reference table which contains the

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Fig. 1. Phantom model representation examples: (a) analytical surface (super-ellipsoid); (b) higher order surface (kidney tetrahedron mesh); and

(c) tomographic volume (one transversal slice of a voxelized thorax phantom).

J. Peter, W. Semmler / Nuclear Instruments and Methods in Physics Research A 580 (2007) 955–959 957

logical replacement dependencies between simploids. Toimprove computational performance efficient rejectiontesting according to [23] and further strategies as describedin [24] were applied. A modified Siddon algorithm [25] isimplemented for ray-tracing tomographic volumes.

2.4. Camera and external source representation

Depending on study setup, imaging system componentscan be defined either by means of probability densityfunctions or through direct geometrical representation.Direct geometrical representation implies that not only theimaged object is described by geometrical models but alsothe imager or parts therefrom such as transmission sources,crystals, or collimators. This enables the definition of awide variety of particular realizations of PET, SPECT, CT,and optical camera systems. Exemplarily, by using a directgeometric representation model for phoswich crystals(SPECT, PET) and solving the transport equation notonly for the incoming high-energy photon but also for thereleased optical photons generates more precise binningimages since effects such as inter-crystal particle penetra-tion and scattering are better approximated.

3. Application examples and results

Besides other studies, we have used this simulationframework to design a small animal SPECT-OT imagerand to investigate instrumentation integration conceptsfor small animal PET-OT systems. Results presented inthe following sub-sections only unfold a fraction of thecapabilities of the simulation framework. Because of therecapitulatory nature of this article and limited spaceavailable a full validation of the codes implemented,although of central importance, will not be presented here.

3.1. Dual-modality SPECT-OT small animal imager

Primary objective for this simulation study was toinvestigate the imaging performance of the SPECT sub-system which directly effected construction of the camera,

specifically the collimator. Since algorithms for imagereconstruction from light projection data distributionswithin heterogeneous media are not yet available theoptical sub-system was investigated especially to study lightfluence within well-defined phantom conditions. In short,the SPECT sub-system is modeled by a pixelized scintilla-tor array consisting of 66� 66 individual 1:3� 1:3�6mm3 NaI(Tl) crystal elements, pitched at 1.5mm, yieldinga total array size of 9:9� 9:9 cm2. The crystal array isorthogonally distanced at 7.5 cm focal length from thecenter of a 1.0mm knife-edged tungsten pinhole collimator.The collimator shielding has reflective surfaces mountedatop of it, rendered in Fig. 2(a), to filter out opticalphotons from the multi-energetic photon flux. Simulationresults using a hybrid, double-labeled mouse brainphantom, Fig. 2(b), are shown in Fig. 2(c)–(e).

3.2. Dual-modality PET-OT small animal imager

This MC simulated dual-modality system imaging,rendered in Fig. 3(a), is different from the previouslysimulated system in that the optical sensor does not employa lens-coupled camera for light detection. Rather, it uses aradial cylindrical lattice of micro lens arrays which isallocated in front of PET detector blocks. A network ofoptical fibers is assigned on a multi-hole plate such that thefocal points of the individual micro lenses correspondlocally to single fiber ending points. Depending onoperation mode each individual micro lens-optical fibercompartment either transmits light from the imagedobject to a photon detector, or light from a laser sourceis tracked to the imaged object for fluorochrome excitation.Simulation results for this detector system are shown inFig. 3(c)–(e).

4. Discussion

Fully integrated multi-modality simulation studies facili-tate the investigation of hybrid imaging systems we willlikely see in the near future. However, the value of the MCsimulation approach is not only broadened by this feature.

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Fig. 2. Simulation of a SPECT-OT small animal imager: (a) Dual-modality instrumentation design sketch. Indicated is the superimposed field-of-view of

the optical sub-system; (b) Hybrid mouse phantom which assimilates two eV photon emitting point sources (spheres, ; ¼ 0:1mm) that are placed within a

tomographic phantom (assumed: keV tracer distribution according to gray scale, ma ¼ 0:25 cm�1, ms ¼ 12:5 cm�1, g ¼ 0:01); (c) optical fluence distributionresulting from the two emitting point sources (10,000 photon emissions, each, log. scale); (d) reconstructed image of a SPECT simulated 125I activity

distribution (500,000 emissions per projection, 120 projections); and (e) simulation of the same setup in dual-modality mode.

Fig. 3. Simulation of a PET-OT small animal imager proposition: (a) rendered view of the dual-modality imaging concept; (b) rendering of the quadric-

based Derenzo-like phantom which was used for this simulation; (c) reconstructed image slice of a PET simulation (2.2E109 total positron emission

histories); (d) distribution of optical power flux resulting from uniformly sampled photon emissions within the internal rods (5.0E106 total light photon

histories, 5 ns time window, ma ¼ 0:2=0:8 cm�1, ms ¼ 100=1000 cm�1, g ¼ 0:8, rod/cylinder, log. scale); and (e) detected light projection images of the

optical sub-system (1mm micro lens ;; images: log. scale, independently scaled, interpolated).

J. Peter, W. Semmler / Nuclear Instruments and Methods in Physics Research A 580 (2007) 955–959958

ARTICLE IN PRESSJ. Peter, W. Semmler / Nuclear Instruments and Methods in Physics Research A 580 (2007) 955–959 959

We have seen a steadily increasing interest in using thisframework for the exploration of optical properties ofvarious tissue models, particularly for heterogeneous mediacompositions, and their contribution to the solvability ofthe inverse problem as image reconstruction of diffuseoptical probes in whole animals has not been solved yet.

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