Research Article| Volume 96, P101-113, April 2022

# Modelling SPECT auto-contouring acquisitions for 177Lu & 131I molecular radiotherapy using new developments in Geant4/GATE

• Author Footnotes
1 List of authors in the MRTDosimetry Collaboration: Salvatore Berenato, Christophe Bobin, Marco Capogni, Sean Collins, Maurice Cox, Jérémie Dabin, Marco D’Arienzo, Ana M. Denis-Bacelar, Andrew J. Fenwick, Kelley M. Ferreira, Domenico Finocchiaro, Federica Fioroni, Elisa Grassi, Aida Hallam, Warda Heetun, Stephanie Jewitt, Maria Kotzassarlidou, Giuseppe Lorusso, Michael Ljungberg, Franz-Josef Maringer, Daniel R. McGowan, Darren Morgan, Andrew P. Robinson, Nathaniel Scott, James Scuffham, Vere Smyth, Jaroslav Šolc, Katarina Sjögreen Gleisner, Ludmila Štemberková, Jill Wevrett and Hannah Wiedner.
Open Access

## Highlights

• Auto-contour SPECT modelling (step & shoot acquisition).
• Phantom SPECT projection simulation and validation against experiments.
• Importance of auto-contour modelling on radionuclide with high septal penetration.
• Extend auto-contour modelling to a context of clinical dosimetry.

## Abstract

### Purpose

Monte Carlo modelling of SPECT imaging in Molecular Radiotherapy can improve activity quantification. Until now, SPECT modelling with GATE only considered circular orbit (CO) acquisitions. This cannot reproduce auto-contour acquisitions, where the detector head moves close to the patient to improve image resolution. The aim of this work is to develop and validate an auto-contouring step-and-shoot acquisition mode for GATE SPECT modelling.

### Methods

177Lu and 131I SPECT experimental acquisitions performed on a Siemens Symbia T2 and GE Discovery 670 gamma camera, respectively, were modelled. SPECT projections were obtained for a cylindrical Jaszczak phantom and a lung and spine phantom. Detector head parameters (radial positions and acquisition angles) were extracted from the experimental projections to model the non-circular orbit (NCO) detector motion. The gamma camera model was validated against the experimental projections obtained with the cylindrical Jaszczak (177Lu) and lung and spine phantom (131I). Then, 177Lu and 131I CO and NCO SPECT projections were simulated to validate the impact of explicit NCO modelling on simulated projections.

### Results

Experimental and simulated SPECT images were compared using the gamma index, and were in good agreement with gamma index passing rate (GIPR) and gammaavg of 96.27%, 0.242 (177Lu) and 92.89%, 0.36 (131I). Then, simulated 177Lu and 131I CO and NCO SPECT projections were compared. The GIPR, gammaavg between the two gamma camera motions was 99.85%, 0.108 for 177Lu and 75.58%, 0.6 for 131I.

### Conclusion

This work thereby justifies the need for auto-contouring modelling for isotopes with high septal penetration.

## Keywords

#### Abbreviations:

CO (Circular orbit), MC (Monte Carlo), MRT (Molecular radiotherapy), NCO (Non-circular orbit)

## Introduction

• Bardiès M.
• Buvat I.
Dosimetry in nuclear medicine therapy: what are the specifics in image quantification for dosimetry?.
].
Clinical dosimetry relies on the accuracy of each of these steps. However, due to the variety of protocols developed and used, there is a large heterogeneity in dosimetry approaches. A major issue today in clinical dosimetry is that no standard operating procedures exist [
• Sjögreen Gleisner K.
• Spezi E.
• Solny P.
• Gabina P.M.
• Cicone F.
• Stokke C.
• et al.
Variations in the practice of molecular radiotherapy and implementation of dosimetry: results from a European survey.
,
• McGowan D.R.
• Guy M.J.
Time to demand dosimetry for molecular radiotherapy?.
]. One of the reasons is difficulty in uncertainty assessment for every step of the clinical dosimetry workflow.
The DosiTest [

DosiTest project, www.dositest.com; 2020 [accessed 01 November 2020].

] project initiated by our team aims to evaluate the impact of the various steps contributing to a dosimetry study by benchmarking approaches against Monte Carlo (MC) modelling.
This work highlights one specific aspect of the DosiTest project, i.e. improving quantitative imaging by modelling scintigraphic imaging in MRT. Scintigraphic imaging used in clinical dosimetry includes 2D planar imaging, modelling of which has already been addressed by Costa et al. [
• Costa G.C.A.
• Bonifácio D.A.B.
• Sarrut D.
• Cajgfinger T.
• Bardiès M.
Optimization of GATE simulations for whole-body planar scintigraphic acquisitions using the XCAT male phantom with 177Lu-DOTATATE biokinetics in a Siemens Symbia T2.
]. In this paper, we consider 3D scintigraphic imaging (Single Photon Emission Computed Tomography, or SPECT) modelling. SPECT is based on acquisitions performed using a detector or gamma camera rotating around the patient, either with a fixed radius or with a variable distance from the patient (auto-contouring). The trajectory of the detector around the patient affects the system resolution and sensitivity of the gamma camera as it is distance dependent, especially when radionuclides with high septal penetration are used. As a result, the image quality deteriorates, potentially impacting activity quantification, as the distance between source (patient/phantom) and detector increases.
Therefore, a non-circular detector orbit following the contour of the patient is typically used to optimize spatial resolution and uniformity [
• Gottschalk S.C.
• Salem D.
• Lim C.B.
• Wake R.H.
SPECT resolution and uniformity improvements by noncircular orbit.
,
• Heller S.L.
• Goodwin P.N.
SPECT instrumentation: performance, lesion detection, and recent innovations.
]. This acquisition mode is nowadays considered as the default for SPECT imaging [
• Dewaraja Y.K.
• Frey E.C.
• Sgouros G.
• Brill A.B.
• Roberson P.
• Zanzonico P.B.
• et al.
MIRD pamphlet No. 23: quantitative SPECT for patient-specific 3-dimensional dosimetry in internal radionuclide therapy.
,
• Sanders J.C.
• Kuwert T.
• Hornegger J.
• Ritt P.
Quantitative SPECT/CT Imaging of 177Lu with In Vivo Validation in Patients Undergoing Peptide Receptor Radionuclide Therapy.
].
The modelling of scintigraphic imaging is performed in our team using GATE (Geant4 Applications for Tomographic Emission) [
• Jan S.
• Santin G.
• Strul D.
• Staelens S.
• Assié K.
• Autret D.
• et al.
GATE: a simulation toolkit for PET and SPECT.
,
• Autret D.
• Bitar A.
• Ferrer L.
• Lisbona A.
• Bardiès M.
Monte Carlo modeling of gamma cameras for I-131 imaging in targeted radiotherapy.
,
• Buvat I.
• Lazaro D.
Monte Carlo simulations in emission tomography and GATE: An overview.
]. GATE is an open source platform that allows the easy design of different medical imaging devices for emission tomography. In addition, it permits the modelling of time dependent phenomena including detector motion, activity distribution over time, radioactive decay and patient motion in order to simulate realistic acquisition conditions.
Gamma camera modelling in GATE requires the explicit modelling of the collimator (low, medium or high energy), the NaI(Tl) crystal, and a back-compartment to account for the electronics and lead shield. The geometry and composition are modelled according to the manufacturer’s specifications. The back-compartment module is designed to model the light guide, photomultiplier tubes (PMTs) and associated electronics. The number of detector heads and their movement around the patient or phantom need to be described. Then, the behaviour of the electronics (digitization) must be modelled based on spatial and energy resolution, and the selected energy windows.
Modelling SPECT imaging requires not only the development of a gamma camera model (detector) but also the model of the imaged object, based on a patient or phantom (physical test object) used in experimental acquisitions.
In GATE, detector and patient are defined as two independent volumes (spaces). This allows for the implementation of the detector head movement around the patient without having to create a separate input file for each SPECT projection, which represents a major asset of GATE. However, the two volumes cannot overlap.
Until now, SPECT acquisition modelling with GATE only considered circular orbit (CO) movement of the detector around the patient, i.e. the detector rotation around the patient was performed with a fixed radius for every step angulation, large enough so that no detector/patient collision could occur. In that context, non-circular orbits (NCO) could not be modelled, despite being the standard SPECT acquisition in clinical practice. This paper focuses on the implementation of the auto-contouring motion in SPECT imaging in GATE, and assessing its impact on simulated projections.

## Materials and methods

Experimental imaging was performed for 2 isotopes (177Lu and 131I) on different gamma cameras and using different phantoms. This was further used to design and validate SPECT imaging simulations with GATE.
Experimental acquisitions with 177Lu were performed on a Siemens Symbia T2 camera, using a 2-organ phantom [

Robinson A. MRTDosimetry data repository, https://doi.org/10.17605/OSF.IO/69NGE; 2021 [accessed July 2021].

] (Fig. 1) developed during the joint research European project “Metrology for clinical implementation of dosimetry in molecular radiotherapy (MRTDosimetry)” [

MRT Dosimetry Project, http://mrtdosimetry-empir.eu/; 2020 [accessed 01 June 2020].

].
Experimental acquisitions with 131I were performed on a GE Discovery 670 camera, using an anthropomorphic SPECT torso phantom or lung spine phantom (ANT) [].
Next, to evaluate the importance of modelling auto-contouring motion, SPECT images were simulated using gamma camera models and a more realistic 4-organ phantom model, also designed during the MRTdosimetry (MRTD) project, with both CO and NCO motion, for the two radioisotopes considered experimentally.

### Validation of gamma camera models

#### Phantoms

A 3D printed phantom developed by The Christie NHS Foundation Trust, UK as part of the MRTD project was used in this work [

MRT Dosimetry Project, http://mrtdosimetry-empir.eu/; 2020 [accessed 01 June 2020].

,
• Tran-Gia J.
• Denis-Bacelar A.M.
• Ferreira K.M.
• Robinson A.P.
• Calvert N.
• Fenwick A.J.
• et al.
A multicentre and multi-national evaluation of the accuracy of quantitative Lu-177 SPECT/CT imaging performed within the MRTDosimetry project.
]. The 2-organ phantom includes two realistically shaped abdominal organs, namely a spleen and a two-compartment right kidney, inserted into a cylindrical Jaszczak phantom (with a diameter of 21.6 cm and height of 18.6 cm for the active volume) (Fig. 1). The kidney is divided into two compartments: medulla and cortex. Features such as base plates, screws and supports were added to complete the phantom.
The anthropomorphic lung and spine torso phantom (model ECT/TOR/P) consists of a large, body shaped cylinder with lungs, liver and spine inserts. A spherical “tumour” insert is placed in the liver. The phantom mimics the upper torso of an average to large male patient. The anterior-posterior and lateral outer phantom dimensions are 26 cm × 38 cm, while the inner dimensions are 24 cm × 36 cm. The wall thickness is 9.5 mm [] (Fig. 2).
Experimental SPECT acquisitions of the 177Lu-filled MRTD 2-organ phantom were performed at the University Hospital Würzburg (UKW), Germany on a dual-head Symbia T2 gamma camera (Siemens Healthineers, Germany) equipped with a medium energy (ME) collimator and a 15.8 mm (5/8″) crystal to derive the source distribution to be used in Monte Carlo simulations. Subsequently, a low-dose CT scan (130 kVp, 512 × 512 × 78 matrix, 0.98 × 0.98 × 5 mm resolution) was acquired for attenuation correction and as a template for geometry construction in Monte Carlo simulations.
Experimental 131I SPECT/CT acquisitions of the lung and spine ANT phantom were performed at The Christie (Manchester, UK) on a GE Discovery 670 (GE Healthcare, USA) equipped with a high energy (HE) collimator and a 9.5 mm (3/8″) crystal. The corresponding low-dose CT dataset was acquired with the following parameters: 120 kVp, 512 × 512 × 161 matrix, 0.98 × 0.98 × 2.5 mm resolution.
Table 1 and Table 2 show acquisition parameters for each phantom and gamma camera at UKW and The Christie, respectively. Sixty SPECT projections per head in step-and-shoot mode with an angular step of 3° (providing a total of 180° per head) were acquired in both cases. The choice of energy windows (both photopeak and scatter) and their width was made by each clinical centre and represents what is currently used in their clinical acquisition protocols.
Table 1Acquisition parameters for experiments at UKW.
UKW (Siemens Symbia T2 gamma camera with 177Lu)
PhantomAcquisition parameters
Matrix sizePixel size (mm2)Time per proj. (seconds)Energy windows
2-organ MRTD phantom128 × 1284.795 × 4.79520SC: 178 keV (166.14–186.9 keV)
PP: 208 keV (186.9–228.44 keV)
SC: 238 keV (228.44–249.2 keV)
SC: scatter window; PP: photopeak or main window.
Table 2Acquisition parameters for experiments at The Christie.
The Christie (GE Discovery 670 gamma camera with 131I)
PhantomAcquisition parameters
Matrix sizePixel size (mm2)Time per proj. (seconds)Energy windows
Lung and spine ANT phantom128 × 1284.418 × 4.41830SC: 317 keV (307.6–326.62 keV)
PP: 364 keV (328.05–400.95 keV)
SC: 414 keV (401.47–426.31 keV)
SC: scatter window; PP: photopeak or main window.

#### Activity distribution in different compartments of the phantoms

Activities (177Lu/UKW) in the spleen, right kidney cortex (RKC) and right kidney medulla (RKM) of the 2-organ phantom with the total activity in the phantom are reported in Table 3. These values are based on the activities of the stock solutions used in the SPECT/CT acquisition. They were determined using a VDC-405 dose calibrator with a VIK-202 ionization chamber (Comecer SpA), cross-calibrated to a high-purity germanium detector (Canberra Industries Inc.) whose energy-dependent efficiency was calibrated with several NIST and National Physical Laboratory–traceable standards over the energy range considered.
Table 3Activities (MBq) in the 2-organ MRTD phantom and the lung & spine ANT phantom.
CentrePhantomIsotopeLiverSpleenRKCRKMTumourBGTotal
UKWMRTD 2-organ177Lu178.6108.716.1303.4
The ChristieANT Lung & Spine131I51.65.06186.76243.42
RKC = Right Kidney Cortex; RKM = Right Kidney Medulla; BG = Background; Total = Total activity in the entire phantom.
Activities (131I/The Christie) for the lung and spine ANT phantom are also presented in Table 3. These values are based on the activity concentrations of the stock solutions and the weights of the compartments before and after filling. Activities were determined using a Capintec55t dose calibrator, whose calibration factors were calibrated with National Physical Laboratory–standards and a Fidelis secondary standard calibrator. Weights/volumes of the background and the cylinder were determined on a calibrated scale to 1 ml.

#### Simulations

Simulated SPECT imaging was designed and validated based on experimental acquisitions performed on the MRTD 2-organ phantom (Symbia T2 gamma camera and 177Lu) and the ANT lung & spine phantom (GE Discovery gamma camera and 131I).

#### Modelling the motion of gamma camera

The models of the Siemens Symbia T2 gamma camera and the GE Discovery 670 were derived from the previous works of Costa et al. [
• Costa G.C.A.
• Bonifácio D.A.B.
• Sarrut D.
• Cajgfinger T.
• Bardiès M.
Optimization of GATE simulations for whole-body planar scintigraphic acquisitions using the XCAT male phantom with 177Lu-DOTATATE biokinetics in a Siemens Symbia T2.
] and Autret et al. [
• Autret D.
• Bitar A.
• Ferrer L.
• Lisbona A.
• Bardiès M.
Monte Carlo modeling of gamma cameras for I-131 imaging in targeted radiotherapy.
] respectively.
To model NCO, information including radial position (radial distance of the detector from the centre of rotation), start angle (position of the detector around the patient at the start of the acquisition) and angular step (angular scan arc step between projections) were extracted from the experimental SPECT projection DICOM headers. Polar coordinates were converted to Cartesian coordinates to obtain the positions of the gamma camera head in ×, y and z as required by GATE using Python 3 [
• Van Rossum G.
• Drake F.L.
Python 3 Reference Manual.
]. The placements (positions along with the rotation angle, axis and time) of each detector head were written in a file format readable by the Generic Repeater Move class of GATE. This class allows the definition of repeated configurations with a list of transformations (translations and rotations) in time for the implementation of NCO acquisitions.
The patient table was not modelled in the simulations, however, the distances between the phantom and the camera head were obtained from the experimental conditions where the patient table was present. All energy windows considered for experimental acquisitions were modelled explicitly (see Table 1 & Table 2).

#### Phantom modelling and NCO implementation in GATE

Labelled voxelized models of the phantoms created from the acquired CT scans were used in simulations. They will be called “phantom models” in what follows, to make the distinction from the real phantoms (Fig. 1b) [
• Petoussi-Henss N.
• Bolch W.E.
• Eckerman K.F.
• Endo A.
• Hertel N.
• Hunt J.
• et al.
ICRP Publication 116–the first ICRP/ICRU application of the male and female adult reference computational phantoms.
].
By default, a phantom volume is a 3D square voxelized matrix with air around the phantom, as can be seen in Fig. 3. Hence, when the virtual gamma camera head approaches the phantom model, there is a collision between the two volumes (Fig. 3). This is a violation of Geant4/GATE conventions as different independent geometries cannot overlap.
This required a new approach in the definition of the phantom model geometry to accommodate the gamma camera head trajectory.
In order to solve this problem, the voxelized geometry definition was converted to a tessellated mesh phantom model. This concept of tessellation allows the subdivision of a geometry into finer meshes using triangle primitives or tetrahedral surfaces [

Renze KJ, Unstructured surface and volume decimation of tessellated domains, Retrospective Theses and Dissertations. 10713. https://doi.org/10.31274/rtd-180813-9973.

]. With this, the labelled regions of interest in the phantom model can be extracted individually as meshes, thereby eliminating the air region outside the phantom boundaries. This enables the gamma camera head to move as close as possible to the phantom model without collision and overlap within the virtual GATE environment, thereby allowing the replication of the clinical situation.
In this work, triangular primitives were considered over tetrahedral mesh structures, in order to conform with GATE requirements. Triangular primitives were generated by first selecting the coordinates corresponding to each segmented and labelled compartment of interest from the phantom model. This was followed by the generation of a list of vertices and faces to create meshes for each compartment, using python scripts with the NumPy [
• Harris C.R.
• Millman K.J.
• van der Walt S.J.
• Gommers R.
• Virtanen P.
• Cournapeau D.
• et al.
Array programming with NumPy.
] and SimpleITK libraries [
• Yaniv Z.
• Lowekamp B.C.
• Johnson H.J.
• Beare R.
SimpleITK Image-Analysis Notebooks: a Collaborative Environment for Education and Reproducible Research.
].
The object files (.obj) generated by this python script were then imported in Blender, an open source 3D image software [
• Bücking T.M.
• Hill E.R.
• Robertson J.L.
• Maneas E.
• Plumb A.A.
• Nikitichev D.I.
• et al.
From medical imaging data to 3D printed anatomical models.
] to merge triangles on planar faces and linear edges. This was done by dissolving the internal vertices and edges, thereby preserving the outer mesh surface of the compartment. All faces were further triangulated and exported as stereolithographic (.stl) files, a triangular representation of 3D surface geometry. Fig. 4 shows the triangulated mesh surfaces of two organs along with the assembled phantom model. These individual compartmental mesh surfaces were imported in GATE and converted into individual volumes with individual materials using the Geant4 G4TessellatedSolid class. Materials were assigned to each volume based on information from the phantom CT.

#### Radionuclide emission modelling and data output

Two radionuclides were used in this work: 177Lu and 131I. 177Lu (half-life of 6.64 days) is a beta/gamma emitter with a growing number of indications (including neuroendocrine or prostate cancers). Emitted photons of 112.9 keV (6.2%) and 208.4 keV (10.4%) along with low energy X-rays can be used for diagnostic evaluation and dosimetry [

Ljungberg M, Celler A, Konijnenberg M, Eckerman KF, Dewaraja YK, Sjögreen-Gleisner K et al. MIRD Pamphlet No. 26: Joint EANM/MIRD Guidelines for Quantitative 177Lu SPECT Applied for Dosimetry of Radiopharmaceutical Therapy. Journal of nuclear medicine. 2016;57(1): 151-62 doi.org/10.2967/jnumed.115.159012.

].
131I (half-life of 8.02 days) is a beta/gamma emitter. It is the most commonly used radioisotope in MRT, primarily for treatment of thyroid diseases. Photons of 284.3 keV (6.1%), 364.5 keV (81.5%), 637 keV (7.2%) and 722.9 keV (1.77%) [

National Nuclear Data Center, MIRD format, https://www.nndc.bnl.gov/nudat2/mird/; 2020 [accessed 25 September 2020].

,
• Dewaraja Y.K.
• Ljungberg M.
• Koral K.F.
Characterization of scatter and penetration using Monte Carlo simulation in 131I imaging.
] are emitted, thus allowing scintigraphic imaging. The presence of high energy photons requires the use of a high energy collimator but yet may result in septal penetration artefacts in scintigraphic images.
Since gamma and X-ray photons contribute to the generation of SPECT images, only photon emissions were considered in the simulation: 0.172 gamma emissions and 1.374 x-ray emissions (total of 1.546 emissions) per disintegration were used for 177Lu and 1.007 and 0.818 emissions of gamma and x-ray emissions respectively (accounting for a total of 1.825 emissions) per disintegration in case of 131I. The emstandard_option3 Geant4 physics list was used as it considers all electromagnetic interactions needed for imaging. Production cuts in form of range cut-off are used in GATE, which are internally converted to energy for individual materials, to prevent the generation of secondary particles. In this work, a range of 1 mm was applied to all volumes (and corresponding materials). For example, in lead, this means that secondary photons with an energy level ≤ 100 keV will not be generated.
Different outputs were generated from GATE. A projection interfile (.raw) format suitable for acquisition protocols using a multi-headed rotating gamma camera was saved. The projections corresponding to the particular energy window can also be obtained, but only if it is specified in the simulation’s macro files.
GATE also permits the storage of hits and singles (output pulses) in the form of ROOT file (.root) to visualise and inspect the produced simulated data. This file contains information like position (in x, y, z), direction (dx, dy, dz), time, energy deposition and location of interaction, type of particle corresponding to each hit [
• Brun R.
ROOT — An object oriented data analysis framework.
]. This enables building projections for any energy window and width that may be required for scatter correction or further analysis.
For this work, projections corresponding to all energy windows specified in Table 1 and Table 2 were simulated individually for 177Lu and 131I, respectively.

#### Computation of the primaries / particles

Considering the total activity in each phantom with 60 projections per head, 20 s or 30 s per projection (2-organ or ANT phantom, respectively) and 1.546 or 1.825 emissions per decay (177Lu or 131I, respectively), the total number of primaries to be used in the simulations was computed and reported in Table 4.
Table 4Conversion of activity to primaries.
2-organ303.4177Lu1.5465.63 × 1011
ANT243.42131I1.8258.00 × 1011

### CO vs NCO acquisitions: 177Lu and 131I modelling

For the comparison of circular detector motion and non-circular or auto-contouring detector motion, it is important to consider phantoms that mimic a realistic patient geometry. Clearly a cylindrical section phantom model is not adapted to the purpose. Hence, the elliptical 4-organ phantom (instead of the cylindrical 2-organ phantom) was used for generation of 177Lu NCO and CO SPECT projections with the Siemens Symbia T2 gamma camera model.
The 4-organ phantom includes spleen, kidneys, and liver inserted into an ellipsoid phantom (with short radii, long radii and height of 10.6 cm, 13.55 cm and 31.2 cm, respectively). A spherical tumour is present in the liver. Features such as base plates, screws and supports were added to complete the phantom (Fig. 5).
The activity distribution for each compartment in the 4-organ phantom was derived from the compartmental pharmacokinetic model of Brolin et al. [
• Brolin G.
• Gustafsson J.
• Ljungberg M.
• Gleisner K.S.
Pharmacokinetic digital phantoms for accuracy assessment of image-based dosimetry in (177)Lu-DOTATATE peptide receptor radionuclide therapy.
] assuming an administered activity of 7.4 GBq and adapted to reflect the volume of the individual compartments. A full set of time-activity curves (TAC) was generated for this realistic 4-organ phantom. For the purpose of NCO vs CO comparison, the activity distribution at 40 h post injection was considered to have sufficient statistics for simulations (Table 5). More information about the TACs considered is given the Discussion section. Acquisition parameters similar to that of the 2-organ phantom were used except for the time per projection which was set to 30 s. The number of primaries used for the 4-organ phantom is reported in Table 6.
Table 5Activity distribution (MBq) in the 4-organ MRTD phantom.
4-organ

MRTD
177Lu145.4154.631.915.0238.326.0327.3879.44388.11
RKC = Right Kidney Cortex; RKM = Right Kidney Medulla; LKC = Left Kidney Cortex; LKM = Left Kidney Medulla; BG = Background; Total = Total activity in the phantom.
Table 6Computation of primaries for the 4-organ phantom with 177Lu.
4-organ MRTD177Lu388.111.5461.08 × 1012
For 131I, simulated NCO and CO SPECT acquisitions were modelled with the same lung and spine phantom on a GE Discovery 670 model, as presented in part A. There was no need to change the phantom model as the section of the ANT phantom is realistic enough to compare CO/NCO acquisitions.
In case of NCO acquisitions, to generate the detector positions at different projection angles for both phantoms, information was extracted from acquisitions made experimentally with the 4-organ phantom and the ANT phantom at The Christie (radial positions from source to surface of the gamma camera).
For CO acquisitions, the largest distance between the phantom model and the surface of the gamma camera was obtained from experimental acquisitions.
For both acquisition types, the specific thickness of each gamma camera model was considered, to avoid any overlaps or collisions between phantom and detector volumes.

### Image comparison metrics

Image comparison was performed using a range of metrics including the difference in profile magnitudes and the gamma index.
Magnitude difference in profiles: For comparison of the series of 2D SPECT projections, flattened 1D profiles on the x-axis were created (for each projection) by summing all the counts along the y-axis. Then, the relative difference between profiles of experimental and simulated projections was calculated for each projection and a mean relative difference was computed considering all projections.
Gamma index: Gamma evaluation methods are widely used in intensity modulated radiotherapy (IMRT) to quantitatively compare absorbed dose distributions. This evaluation technique combines the absorbed dose difference (DD) criterion along with the distance to agreement (DTA) criterion to compare two absorbed dose distributions (namely reference or measured and evaluated or simulated absorbed doses). These criteria complement each other, thereby allowing access to the absorbed dose distribution calculation quality [
• Low D.A.
• Harms W.B.
• Mutic S.
• Purdy J.A.
A technique for the quantitative evaluation of dose distributions.
,
• Hussein M.
• Ebert M.A.
• Nisbet A.
• Clark C.H.
A comparison of the gamma index analysis in various commercial IMRT/VMAT QA systems.
]. The gamma index of the reference $γ(r→r)$ is defined as the minimum of generalised $Γ$ functions as represented in equations 1–4 [
• Wendling M.
• Zijp L.J.
• McDermott L.N.
• Smit E.J.
• Sonke J.-J.
• Mijnheer B.J.
• et al.
A fast algorithm for gamma evaluation in 3D.
]:
$γ(r→r)=min{Γ(r→e,r→r)}∀(r→e)$
(1)

$Γr→e,r→r=δ2(r→e,r→r)ΔD2+r2(r→e,r→r)Δd2$
(2)

$δr→e,r→r=Der→e-Drr→r$
(3)

$rr→e,r→r=r→e-r→r$
(4)

$Der→e$ and $Drr→r$ represent the evaluated and reference absorbed doses respectively, $r→e$ and $r→r$ are the vector positions of the evaluated and reference points respectively, and $ΔD$ and $Δd$ are the DD and DTA criteria respectively.
Hence, the gamma index is interpreted as the minimum distance between two distributions in a renormalized absorbed dose-distance space. Only if $γr→r≤1$ is the evaluated distribution accepted. This means that each point in evaluated distribution is assessed to see if both the criteria pass or fail the selected tolerances (for e.g. 2% DD and 2 mm DTA). The gamma index pass rate (GIPR) specifies a percentage of $γr→r≤1$ (indicating the points lying within the given DD/DTA acceptance criteria) [
• Low D.A.
Gamma Dose Distribution Evaluation Tool.
]. This gamma index was used as a comparison metric to compare the SPECT projections considering the difference in counts as DD criterion and the spatial difference as DTA criterion.
For the validation of the NCO implementation (i.e., experimental vs simulated 177Lu SPECT images of the 2-organ MRTD phantom), DTA was set to the maximum difference in pixels between experimental and simulated images, while DD (i.e. the acceptable difference in counts in our case) was set to 2%. For the validation of 131I SPECT images of the lung and spine ANT phantom, DD, DTA criteria of 2%, 1 pixel were considered.
Then, for studying the impact of NCO detector motion (i.e. CO vs NCO simulated SPECT images for 177Lu and 131I), DTA was set to 1 pixel (the maximum possible shift) and the DD criteria was set to 2%. In all cases, 2% was chosen as there is convergence of results above this value.

## Results

### Validation of gamma camera (experimental vs simulated projections)

#### Siemens Symbia T2 for 177Lu with 2-organ MRTD phantom

SPECT projections were simulated for the 2-organ phantom model considering NCO or auto-contouring motion. Fig. 6 shows the movement of the gamma camera model containing the collimator and crystal along with the PMTs and electronics around the phantom model. From Fig. 6a to Fig. 6c, the camera head moves from 0° to 45° and 90°. As the camera rotates, each head moves independently moving close or further from the phantom model. As can be seen in Fig. 6b, the camera heads are not equidistant from the centre of rotation, thus validating the auto-contouring acquisition mode (or non-circular movement) of the gamma camera in simulations.
Simulated SPECT projections for the 2-organ phantom model (containing the spleen and the right kidney) are shown in Fig. 7. These projections were modelled from 0° to 360° with an angular step of 3°, thereby generating 120 projections in total (60 projections per head). The projections represented in this figure correspond to 0°, 90°, 180° and 270° from Fig. 7a to Fig. 7d, respectively. 0° and 180° projections correspond to the position of the gamma camera head below and above the table respectively. The gamma camera moves in a clockwise direction, which explains the appearance of the right kidney in the second and the spleen in the last projection individually.
The measured (at UKW, Germany) and simulated energy spectra of 177Lu (with two major gamma peaks at 113 keV and 208 keV, and the low energy X-ray peak at around 50 keV along with the Compton continuum) are shown in Fig. 8a, illustrating the similarity between experiments and measurements, especially within the energy windows considered. The simulated non-circular detector movement in Fig. 8b shows the rotation of the camera heads around the phantom with each thin blue line representing the gamma camera plane at their respective 3° angular step. It can be clearly seen that the gamma camera follows a non-circular trajectory. When the camera head passes above the phantom in a positive y position, it is possible to get closer to the patient than when passing below the phantom due to the presence of the table. This explains the lower activity observed in Fig. 7a for 0°, compared to Fig. 7c for 180°.
The experimental projections and the simulated projections for the 2-organ phantom (model) are shown in Fig. 9.
Profiles were drawn for both sets of projections to assess their similarity (Fig. 10). The two peaks in the profiles (Fig. 10a and Fig. 10c) represent the spleen and right kidney, respectively. This difference in counts between spleen and right kidney arises due to higher spleen activity (Table 3). As the camera moves from 0° to 90°, the right kidney is more prominently seen (Fig. 7b), thus explaining the presence of only one peak in the projection at 90° (Fig. 10b). Similarly, a mirror image of the projection at 0° is seen for the projection at 180°, and when the camera moves further from 180° to 270°, the spleen is more visible (Fig. 7d), thereby explaining the single peak for the projection at 270° (Fig. 10d).
While comparing experimental and simulated profiles, projections at 0° and 180° are quite similar except for the peak of the spleen at 0°. In case of the projections at 90° and 270°, an offset of approximately 6 pixels between experimental and simulated profiles was seen, which was likely due to the centering uncertainties of the phantom during image acquisition (a tilt of a few degrees in the phantom positioning along the table axis was observed in the phantom CT). The simulated projections were adjusted for this shift, and therefore the simulated profiles at these angles are now closer to the experimental profiles.
The distance to agreement (DTA) in the gamma index was set to 6 pixels (as per the maximum shift observed in profiles) to understand the impact of the shift in the comparison of experimental vs. simulated projections. The acceptable difference in counts was 2% of the maximum count of the experimental image. The GIPR (gamma < 1) for the 2D global gamma index 2% − 6 pixels was 96.27% with gammaavg of 0.242. The corresponding gamma index map is shown in Fig. 9c. This reveals the high similarity between the images, thereby validating our gamma camera model.

#### GE Discovery 670 for 131I with the lung and spine ANT phantom

The auto-contouring motion modelling for the GE Discovery 670 SPECT system with the lung and spine phantom was performed as explained previously for 177Lu imaging.
Experimental vs. simulated SPECT images for the lung and spine ANT phantom are shown in Fig. 11. The tumour with high activity concentration can be seen in the liver. The other regions with activity include liver and background.
Profiles were drawn for both sets of projections to assess the similarity as shown in Fig. 12. As can be seen, the profiles for projections at all angles are quite similar. A small dip in counts at the central × axis is observed in profiles at 180° due to the presence of the cylinder representing the spine in the phantom.
The gamma index metric was used with 2%, 1 pixel criteria (DD, DTA). The GIPR (gamma index passing rate) with gamma < 1 for 2D global gamma index 2% − 1 pixel was 92.89% with an average gamma of 0.36. The gamma index map in Fig. 11c reveals good similarity, thereby validating our GE Discovery 670 gamma camera model.

### Simulation time

The time required to complete the simulation without any optimisation (variance reduction technique) was estimated to 2.24 to 3.25 years on a single CPU core with 2,6GHz, 16 GB, thereby justifying the access to large computing resources. Brute-forced simulation of SPECT projections required from 12 to 16 h of computation time using from 1620 to 1800 CPU cores at the regional high-performance computing (HPC) centre CALMIP [

CALMIP, https://www.calmip.univ-toulouse.fr/ ; 2004-2020 [accessed 01 November 2020].

]. Simulation time varied between simulations, depending on the availability of cluster cores.

### Auto-contouring motion vs. Circular camera motion using 177Lu and 131I

SPECT projections of the 4-organ phantom were simulated with non-circular camera motion for 177Lu as shown in Fig. 13. The spherical tumour present in the liver has the highest activity concentration and can be seen in the figure. The other coloured regions represent the different organs and background.
Profiles were generated for NCO and CO gamma camera motion corresponding to both the 177Lu 4-organ MRTD and the 131I ANT phantom model.
177Lu profiles at two gamma camera positions (0° and 60°) are displayed in Fig. 14a and Fig. 14b. At gamma camera position 0°, the effective radius (distance from the centre of rotation to the surface of the detector) is 197 mm and 325 mm for NCO and CO, respectively. At 60° gamma camera position, this distance for both motions is 325 mm, hence the profiles are similar.
Similarly, profiles at gamma camera positions 0° and 240° for 131I are displayed in Fig. 15. The respective effective radii for NCO and CO correspond to 271 mm and 434 mm at 0°. The same effective radii of 434 mm are observed for both NCO and CO at 240° in case of the ANT phantom.
The total magnitude difference between the profiles was computed. In the case of 177Lu, this maximum difference (over all projections) was around 2.6%. However, in the case of 131I, this difference increased up to 13.13%.
For the gamma index, DTA was set to 1 pixel (kept as minimum since there is no shift between the simulated geometries) and DD (here, counts) was 2% of the maximum counts of the experimental image. The GIPR (gamma < 1) in case of 177Lu for the 2D global gamma index 2% − 1 pixel was 99.85% with gammaavg of 0.108. However, in case of 131I, if the same 2% − 1pixel parameter is considered, the GIPR (gamma < 1) was 75.58% with a gammaavg of 0.6. This shows that there is a difference in the simulated 131I SPECT images between the CO and NCO acquisitions.
Knowing that the mean relative difference between counts from profiles for 131I is around 13%, if a 2D global gamma index with 13% DD and 1 pixel DTA is considered, GIPR (gamma < 1) rises to 96.79%, with gammaavg decreasing to 0.35. This indicates that if a count difference of 13% between images is acceptable, then 96.79% of points in the profiles agree. Therefore, it can be said that there is at least a difference of around 13% between CO and NCO gamma camera motion.

## Discussion

The optimisation of the clinical dosimetry workflow may require the modelling of realistic SPECT images [
• Ligonnet T.
• Pistone D.
• Auditore L.
• Italiano A.
• Amato E.
• Campennì A.
• et al.
Simplified patient-specific renal dosimetry in 177Lu therapy: a proof of concept.
,
• Kayal G.
• Chauvin M.
• Vergara-Gil A.
• Clayton N.
• Ferrer L.
• Moalosi T.
• et al.
Generation of clinical 177Lu SPECT/CT images based on Monte Carlo simulation with GATE.
]. This work presents the new developments done in GATE to model the step-and-shoot auto-contouring motion of the gamma camera for generation of SPECT imaging. Step-and-shoot mode (static data acquisition) was adopted in this work because it is commonly used in clinical settings. Continuous acquisition mode (dynamic data acquisition) has been discussed in the literature [
• Cao Z.
• Maunoury C.
• Chen C.C.
• Holder L.E.
Comparison of continuous step-and-shoot versus step-and-shoot acquisition SPECT.
] as a means to improve image quality and may potentially be simulated in Geant4/GATE with more research and validation.
Extraction of information from the experimental DICOM images for modelling the movement of gamma camera around the object (phantom or patient) was quite challenging as the same tag may not reference the same property between manufacturers. For example, a gamma camera head rotating with 3° angular step and generating a total of 60 projections per head would have 60 radial positions per head. However, the tag ‘Radial position’ in one manufacturer can contain 60 values while for the other can have just 1 value (which has to be adjusted with another tag containing 60 offset values). Therefore, careful observation and analysis of the DICOM headers from different manufacturers for simulations is paramount.
The generation of individual tessellated meshes for each volume of interest was introduced in this work. The use of tessellated meshes instead of a voxelized phantom geometry enabled the detector head to approach the phantom model without collision in the GATE environment, thereby allowing for the modelling the auto-contouring detector motion. It is often asserted that mesh modelling of individual regions of interest and consequently the whole phantom is a time-consuming and cumbersome process in comparison to the use of voxelized phantoms. However, with the advancement of computational techniques, this step can be easily automated nowadays (using a python script for example). To avoid degrading simulation performance, each mesh compartment was optimized in Blender by reducing the number of vertices, faces, and edges to facilitate rapid geometry initialization in GATE.
As the patient table was not modelled in simulations, any attenuation caused by the patient table was disregarded. This is not deemed to have a significant influence in our study, however it could be included in the future if necessary.
The scatter-energy-window settings used for the simulations (±5% in case of 177Lu and ± 3% in case of 131I) were provided by the nuclear medicine departments in accordance with their local clinical procedures.
The energy spectrum of 177Lu derived from simulations was compared to the experimental measured spectrum and was found to be fairly consistent (except in the lead x-ray region of the spectrum, since secondary photons with energy < 100 keV were not simulated in lead). Following this, simulated 177Lu SPECT projections were validated against experimental projections for the main energy window only i.e. 208 keV ± 10%. Yet, the projections for the scatter energy windows i.e. the 178 keV ± 5% and 238 keV ± 5% as mentioned in the Table 1 were also simulated to correct for scatter during reconstruction (when it is performed).
In the context of 131I SPECT imaging, the experimental energy spectrum was not available. Despite the fact that a simulated 131I energy spectrum was generated, this study is limited as no comparison to a measured spectrum was performed, thereby providing a limited validation for the main photopeak energy window (364 keV ± 10%). Yet, the full energy spectrum comparison was presented in the work of Autret et al. [
• Autret D.
• Bitar A.
• Ferrer L.
• Lisbona A.
• Bardiès M.
Monte Carlo modeling of gamma cameras for I-131 imaging in targeted radiotherapy.
], on which the gamma camera model is based, for both collimated and uncollimated detector heads.
Simulations were performed using computational hours provided freely by the regional high-performance computing centre CALMIP. This facilitated the generation of simulated datasets within a reasonable timeframe. However, variance reduction techniques such as splitting, Russian roulette, or fixed forced detection, available in GATE, could be implemented to accelerate the simulations if needed.
To highlight the relevance of modelling this acquisition mode, comparison of CO vs NCO was performed for both radionuclides. For 177Lu, the ellipsoidal 4-organ cross-sectional MRTD model was chosen over the cylindrical 2-organ phantom model as it is closer to the representation of an actual patient.
Activity selected was derived from that presented in Brolin et al. [
• Brolin G.
• Gustafsson J.
• Ljungberg M.
• Gleisner K.S.
Pharmacokinetic digital phantoms for accuracy assessment of image-based dosimetry in (177)Lu-DOTATATE peptide receptor radionuclide therapy.
] and adapted to reflect the volumes of the individual compartments. Time activity distribution were then generated representing the activity in each organ and tumour as a part of the MRT Dosimetry project. The time-activity table is presented below (Table 7). From this table, the activity distribution at 40 h post injection was selected, as it provided sufficient statistics for simulations. It is believed that the results presented would not be significantly impacted by the variation in activity in the different organs of the phantom model.
Table 7Activity (in MBq) in 4-organ phantom model corresponding to 177Lu pharmacokinetics.
Time (h)LiverSpleenRK CRK MLK CLK MTumourBGTotal
1149.1647.1448.287.6057.979.1230.62840.431190.32
24180.5563.2839.346.1947.247.4330.11108.25482.39
40145.4054.6031.915.0238.326.0327.3879.44388.10
72109.9039.5520.803.2724.983.9322.2757.64282.34
14461.2319.118.071.279.691.5313.8429.02143.76
LK C, LK M - left kidney cortex and medulla respectively; RK C, RK M - right kidney cortex and medulla respectively; BG – background.
Acquisition modelling was done for two radionuclides: 177Lu and 131I. For 177Lu, CO and NCO acquisition modelling yields equivalent results, whereas for 131I relative differences are more pronounced. Also, the differences observed are more important for some angles. This can be explained in Fig. 16. The blue circle represents the circular motion of the gamma camera whereas the dark grey motion is the auto-contouring orbit. The patient (in this case phantom) is lying on the table.
At angles 231°, 240°, or 112° (in green radii), it is clear that the distance between the centre of rotation and the gamma camera head is almost the same for CO and NCO, and hence the projections at these angles are reasonably similar. However, for projections at 0° (or 180°), the distance between the center of rotation and the gamma camera head for CO and NCO are different, and therefore the projections will be impacted (more for 131I) due to septal penetration. As a nod to the fact, 177Lu has main photon emission peaks at 113 keV (∼6%) and 208 keV (∼10.4%), and maximum gamma energy of 321.3 keV (∼0.2%) while 131I emits photons at 364 keV (∼81.7%), 637 keV (∼7.2%) and 723 keV (∼1.8%). Even though the yield of 131I high energy photons is quite low, these photons have the possibility to cross through the collimator septa, thus reducing the image resolution and degrading the image quality [

Lewis DP, Tsui BMW, Tocharoenchai C, Frey EC. Characterization of medium and high energy collimators using ray-tracing and Monte Carlo methods. 1998 IEEE Nuclear Science Symposium Conference Record. 1998 IEEE Nuclear Science Symposium and Medical Imaging Conference (Cat. No.98CH36255). 1998; 3:2026-2030. doi.org/ 10.1109/NSSMIC.1998.773931.

]. This may elucidate why the impact of varying source-detector distance is more pronounced on 131I compared to 177Lu.

## Conclusion

A new auto-contour step-and-shoot acquisition mode was developed in GATE. SPECT projections of different phantoms were modelled, and validated against experimental acquisitions for two gamma camera models, the Siemens Symbia T2 (with 5/8″ crystal thickness and ME collimator for 177Lu imaging) and the GE Discovery 670 (with 3/8″ crystal thickness and HE collimator for 131I imaging).
Simulations of CO and NCO acquisition modes were performed for 177Lu and 131I, and the projections were compared for each radionuclide to highlight the importance of modelling auto-contouring motion in GATE. The maximum relative difference in profiles between CO and NCO differences was 2.6% in case of 177Lu and around 13% in case of 131I. This justifies the use of NCO acquisition mode in simulations especially for radionuclides featuring high septal penetration, for example, in the case of 131I SPECT/CT acquisitions for MRT clinical dosimetry. In that context, the potential activity underestimation caused by the use of a CO acquisition mode in simulations may impact the absorbed dose determination. Implementation of the auto-contouring motion was made for three phantom models. This work can be further extended to model patient SPECT imaging with various gamma camera models and radionuclides.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgement

This work was performed and supported by the MRT-Dosimetry project http://mrtdosimetry-empir.eu. This project has received funding from the EMPIR programme co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation programme (15HLT06), European Union. This work has also received funding from the Euratom research and training programme 2014-2018 under grant agreement No 755523. This work is dedicated to Maria Kotzassarlidou, an active member of MRT Dosimetry project who passed away during the first COVID wave. She will be remembered, not only for her essential contribution in the project, but also for her positive and caring personality and her fabulous hospitality during the project meetings held in her beloved city of Thessaloniki, Greece.
This work has been partially supported by the ENEN + project that has received funding from the Euratom research and training Work programme 2016-2017-1 #75576).
The simulations of this work have been performed on the HPC centre CALMIP. We thank them wholeheartedly for their support and coordination.
The author expresses sincere gratitude to Gustavo Costa from UC Davis, USA for providing the macros for gamma camera model and Michael Ljungberg from LUND University, Sweden for helping decipher the GE DICOM header for gamma camera positions.

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