beam–beam luminosity corrections. Contrary to the previous model with the
linear kick used at LHC in 2012–2019, it is based on the exact nonlinear
electrostatic force between the point and the Gaussian charge density, either
round 2.10 or elliptical 2.12. The perturbed particle trajectories are
followed in the accelerator assuming their ideal transverse betatron motion
with the known phase advances. The perturbed luminosity is calculated at the
interaction points with maximally focused beams, where the derivative of the
$\beta$-function is zero, and the elliptical phase-space trajectories of the
betatron motion become circular.

The luminosity corrections due to the perturbations of two bunches are
calculated separately and then summed. It is assumed that the bunch creating
the field is not disturbed by the beam–beam interaction. Therefore, the
coherent oscillation modes of the two beams are neglected.

The B*B simulation allows to correct the beam–beam luminosity bias in van der
Meer scan point-by-point and to remove it together with the associated $x$-$y$
non-factorizability. The bunch shapes may be approximated by an arbitrary sum
of Gaussians. The electrostatic field is pre-calculated and then the
interpolations are used to save CPU time. An arbitrary number of interaction
points is allowed. The simulation of different particles is parallelized in
the processors with multiple cores. The B*B code is written in C++. It can be
used as a standalone application or as a library available in four computer
languages: C, C++, python and R.

In section 3.6 it is shown that, for example, the first bunch phase-space
trajectories drawn in the complex planes
$\sqrt{\tilde{\epsilon}_{1x,1y}/Z_{1}Z_{2}N_{2}}\cdot e^{i\phi_{1x,1y}}$ are
determined only by the initial distribution of
$\tilde{\epsilon}_{1x,1y}/Z_{1}Z_{2}N_{2}$ ratios, by the phase advances and
$\beta_{1x}/\beta_{1y}$ ratios, if the normalized emittances
$\tilde{\epsilon}_{1x,1y}=\epsilon_{1x,1y}/(p_{1}/m_{1})$ are conserved. They
do not depend on the individual values of the beta-functions $\beta_{1x,1y}$,
the emittances $\epsilon_{1x,1y}$, the momentum $p_{1}$, the proton numbers
$Z_{1,2}$ or the number of particles in the opposite bunch $N_{2}$. This leads
to the corresponding invariance of the luminosity correction ratios.

For the bunch parameters from Table 1, ie. for the reference values of the old
model with the linear kick, the B*B simulation predicts 0.96% less van der
Meer cross-section correction than the old model. As one can see from Figure
3.8, the latter significantly overcorrects the bias. This needs to be
propagated to all LHC cross-sections after 2012 taking into account the bunch
parameters in the corresponding van der Meer calibrations. For other Run 2
proton–proton van der Meer scans the discrepancies are in the range
$0.8-1.4$%. The B*B predictions are going to be used at LHC in the future
calibration analyses, for example, they already appear in atlas20 .

###### Acknowledgements.

The author wishes to thank the members of LHC Luminosity Calibration and
Monitoring Working Group and, in particular, Guido Sterbini for calculating
the phase advances in Table 2 using LHC MAD-X software in July 2019 and
Tatiana Pieloni and Claudia Tambasco for confirming Figure 3.1 results using
COMBI simulation in August 2019.

## References

  * (1) S. van der Meer, Calibration of the effective beam height in the ISR. Tech. Rep. CERN-ISR-PO-68-31, CERN, Geneva (1968). https://cds.cern.ch/record/296752
  * (2) V. Balagura, Non factorization in LHCb vdM scans: experience in Run-2, impact on luminosity calibration. Proceedings of LHC Lumi Days: LHC Workshop on LHC Luminosity Calibration (CERN, Geneva, 2019). https://indico.cern.ch/event/813285/contributions/3406097
  * (3) G. Carboni et al., Nucl. Phys. B 254, 697 (1984). https://cds.cern.ch/record/156499
  * (4) C. Rubbia, Measurement of the luminosity of p$\bar{\mathrm{p}}$ collider with a (generalized) Van der Meer Method. Tech. Rep. CERN-p$\bar{\mathrm{p}}$-Note-38, CERN, Geneva (1977). https://cds.cern.ch/record/1025746
  * (5) A. Drees, S. White, Vernier Scan Results from the First RHIC Proton Run at 250 GeV. Proceedings of International Particle Accelerator Conference, Kyoto, Japan, 2010, p. MOPEC013. https://cds.cern.ch/record/1307872
  * (6) A. Drees, Analysis of vernier scans during RHIC Run-13 (pp at 255 GeV/beam). Tech. Rep. BNL-102438-2013-IR, C-A/AP/488 (RHIC), BNL (2013). https://www.bnl.gov/isd/documents/83218.pdf
  * (7) S. White, R. Alemany-Fernandez, H. Burkhardt and M. Lamont, First Luminosity Scans in the LHC. Tech. Rep. CERN-ATS-2010-096, CERN, Geneva (2010), proceedings of International Particle Accelerator Conference, Kyoto, Japan, 2010, p. MOPEC014. https://cds.cern.ch/record/1271694
  * (8) R. Aaij et al. (LHCb Collaboration), JINST 7 (2012) P01010. https://arxiv.org/abs/1110.2866
  * (9) CMS Collaboration, CMS Luminosity Based on Pixel Cluster Counting – Summer 2013 Update, Tech. Rep. CMS-PAS-LUM-13-001, CERN, Geneva (2013). https://cds.cern.ch/record/1598864
  * (10) G. Aad et al. (ATLAS Collaboration), Eur. Phys. J. C73 (2013) 2518. https://arxiv.org/abs/1302.4393
  * (11) R. Aaij et al. (LHCb Collaboration), JINST 9 (2014) P12005. https://arxiv.org/abs/1410.0149
  * (12) Abelev et al. (ALICE Collaboration), JINST 9 (2014) P11003. https://arxiv.org/abs/1405.1849
  * (13) M. Aaboud (ATLAS Collaboration), Eur. Phys. J. C 76 (2016) 653. https://arxiv.org/abs/1608.03953
  * (14) J. Adam et al. (ALICE Collaboration), ALICE luminosity determination for pp collisions at $\sqrt{s}$=13 TeV. Tech. Rep. ALICE-PUBLIC-2016-002, CERN, Geneva (2016). https://cds.cern.ch/record/2160174
  * (15) CMS Collaboration, CMS luminosity measurement for the 2015 data-taking period. Tech. Rep. CMS-PAS-LUM-15-001, CERN, Geneva (2017). https://cds.cern.ch/record/2138682
  * (16) CMS Collaboration, CMS Luminosity Measurements for the 2016 Data Taking. Tech. Rep. CMS-PAS-LUM-17-001, CERN, Geneva (2017). https://cds.cern.ch/record/2257069
  * (17) CMS Collaboration, CMS luminosity measurement for the 2017 data-taking period at $\sqrt{s}=13~{}\mathrm{TeV}$. Tech. Rep. CMS-PAS-LUM-17-004, CERN, Geneva (2018). https://cds.cern.ch/record/2621960
  * (18) ATLAS Collaboration, Luminosity determination in $pp$ collisions at $\sqrt{s}=13$ TeV using the ATLAS detector at the LHC. Tech. Rep. ATLAS-CONF-2019-021, CERN, Geneva (2019). https://cds.cern.ch/record/2677054
  * (19) M. Ferro-Luzzi, Nucl. Instrum. Methods A553, 388 (2005). https://cds.cern.ch/record/844569
  * (20) C. Barschel, Precision luminosity measurement at LHCb with beam-gas imaging. PhD thesis, RWTH Aachen U., 2014, CERN-THESIS-2013-301. https://cds.cern.ch/record/1693671
  * (21) V. Balagura, Nucl. Instrum. Meth. A654, 634 (2011). https://arxiv.org/abs/1103.1129
  * (22) M. Zanetti, Beams Scan based Absolute Normalization of the CMS Luminosity Measurement. Tech. Rep. CERN-Proceedings-2011-001, Geneva (2011), p. 69, proceedings of LHC Lumi Days: LHC Workshop on LHC Luminosity Calibration (CERN, Geneva, 2012). https://cds.cern.ch/record/1357856
  * (23) M. Klute et al, JINST 12 (2017) P03018. https://arxiv.org/abs/1603.03566
  * (24) W. Herr, Beam–beam and dynamic beta. Proceedings of LHC Lumi Days: LHC Workshop on LHC Luminosity Calibration (CERN, Geneva, 2012). https://indico.cern.ch/event/162948/contributions/1417430
  * (25) P.A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020, 083C01 (2020). https://academic.oup.com/ptep/article/2020/8/083C01/5891211
  * (26) M. Bassetti, G.A. Erskine, Closed expression for the electrical field of a two-dimensional Gaussian charge. Tech. Rep. CERN-ISR-TH-80-06, ISR-TH-80-06, CERN, Geneva (1980). https://cds.cern.ch/record/122227
  * (27) K. Hirata, Nucl. Instrum. Meth. A269, 7 (1988). https://cds.cern.ch/record/179831
  * (28) V. Balagura, BxB standalone simulation and interfaces to C, C++ and phython languages (2020). https://github.com/balagura/beam-beam-simulation-for-vdM-scans-at-LHC
  * (29) V. Balagura, BxB simulation interface to R programming language (2020). https://github.com/balagura/BxB
  * (30) A.W. Chao, K.H. Mess, M. Tigner, F. Zimmermann, Handbook of accelerator physics and engineering, 2nd ed. (World Scientific, Singapore, 2013). https://cds.cern.ch/record/1490001
  * (31) ATLAS Collaboration, Luminosity determination for low-pileup datasets at $\sqrt{s}=5$ and 13 TeV using the ATLAS detector at the LHC. Tech. Rep. ATLAS-CONF-2020-023, CERN, Geneva (2020). https://cds.cern.ch/record/2725195


MIDLMedical Imaging with Deep Learning 2019 MIDL 2019 – Extended Abstract
Track Yngve Mardal Moe1<EMAIL_ADDRESS>
Aurora Rosvoll Groendahl1
Martine Mulstad1
Oliver Tomic1
Ulf Indahl1
Einar Dale2
Eirik Malinen3,4
Cecilia Marie Futsaether1
1 Faculty of Science and Technology, Norwegian University of Life Sciences,
Aas, Norway.
2 Department of Oncology, Oslo University Hospital, Oslo, Norway.
3 Department of Medical Physics, Oslo University Hospital, Oslo, Norway.
4 Department of Physics, University of Oslo, Oslo, Norway.

# Deep learning for automatic tumour segmentation in PET/CT images of patients
with head and neck cancers

###### Abstract

An automatic segmentation algorithm for delineation of the gross tumour volume
and pathologic lymph nodes of head and neck cancers in PET/CT images is
described. The proposed algorithm is based on a convolutional neural network
using the U-Net architecture. Several model hyperparameters were explored and
the model performance in terms of the Dice similarity coefficient was
validated on images from 15 patients. A separate test set consisting of images
from 40 patients was used to assess the generalisability of the algorithm. The
performance on the test set showed close-to-oncologist level delineations as
measured by the Dice coefficient (CT: $0.65\pm 0.17$, PET: $0.71\pm 0.12$,
PET/CT: $0.75\pm 0.12$).

##  1 Introduction

Radiotherapy (RT) is standard treatment for patients with inoperable head and
neck cancers (HNC). An essential part of RT planning is delineation of
tumours, metastatic lymph nodes and organs at risk. This task is done
manually, which is time-consuming, labour-intensive and prone to inter- and
intra-observer differences [Gudi et al.(2017)Gudi, Ghosh-Laskar, Agarwal,
Chaudhari, Rangarajan, Paul, Upreti, Murthy, Budrukkar, and Gupta]. Finding
robust and precise methods to automate delineation is, therefore, of great
importance.

In this work, we used a deep convolutional neural network to automatically
delineate the gross tumour volume (GTV) and pathologic lymph nodes in patients
with HNC.

##  2 Methods

Oncologist delineations of gross tumour volume and pathologic lymph nodes were
extracted from 197 HNC patients planned for radiotherapy at Oslo University
Hospital between January 2007 and December 2013. FDG-PET co-registered to
contrast enhanced CT images were available for all patients. The dataset was
split into a training (142 patients), validation (15 patients) and test (40
patients) set, stratified by tumour T-stage. The Regional Ethics Committee
approved the study.

The ground truth segmentation masks were defined as the union of the
oncologist delineated GTV and pathologic lymph nodes. Images were cropped to
reduce their size whilst retaining a sufficiently large region of interest
(ROI) of the head and neck region (see fig:results). The network was trained
on transversal image slices.

A U-Net architecture [Ronneberger et al.(2015)Ronneberger, Fischer, and Brox]
with zero padded convolutions was trained using the Adam optimiser [Kingma and
Ba(2014)] with a learning rate of $10^{-4}$ and standard $\beta$ parameters.
Batch normalisation [Ioffe and Szegedy(2015)] was used after each activation
function to ensure stable training. Cross entropy loss and the Dice loss were
tested [Milletari et al.(2016)Milletari, Navab, and Ahmadi].

Models were trained using solely CT images (CT-only), solely PET images (PET-
only) or both CT images and PET images (PET/CT). Benefits of using CT
windowing to highlight soft tissue were examined. Window widths of $100$ HU
and $200$ HU and centres of $60$ HU and $70$ HU were tested.

Models with all hyperparameter combinations were trained twice with different
random seeds. The Dice similarity coefficient on the validation set was used
for model comparisons. Models with the highest validation Dice coefficient for
each image modality were assessed on the test set.

fig:results [CT][htbp]  [PET][htbp]  [PET/CT][htbp]

Figure 1: The ground truth and predicted segmentation masks for each model.

##  3 Results

Models trained with CT windowing consistently outperformed those trained
without. Windowing parameters did not affect performance. Models using both
PET and windowed CT images achieved the overall highest performance, followed
by PET-only models which outperformed CT-only models. Loss function choice did
not affect performance.

Performance metrics obtained on the test set are shown in tab:results. In
comparison, a study of interobserver variability in HNC GTV delineation
reported a mean Dice coefficient between radiation oncologists of $0.56$ and
$0.69$ for CT-only and PET/CT images, respectively [Gudi et al.(2017)Gudi,
Ghosh-Laskar, Agarwal, Chaudhari, Rangarajan, Paul, Upreti, Murthy, Budrukkar,
and Gupta].

fig:results shows the oncologist ground truth delineations and the CNN
predicted segmentations superimposed on input images, for a case with moderate
CNN performance (Dice coefficient in the range 0.65-0.72).

tab:results  Modality Sensitivity Specificity Dice PPV CT-only $0.68\pm 0.18$
$0.99\pm 0.014$ $0.65\pm 0.17$ $0.67\pm 0.20$ PET-only $0.68\pm 0.17$ $0.99\pm
0.003$ $0.71\pm 0.12$ $0.78\pm 0.11$ PET/CT $0.74\pm 0.16$ $0.99\pm 0.007$
$0.75\pm 0.12$ $0.78\pm 0.15$

Table 1: Performance metrics (mean $\pm$ standard deviation) on the test set.

##  4 Conclusion

A deep convolutional neural network using the U-Net architecture was developed
for automatic delineation of head and neck cancers in PET and CT images. The
CNN required no user involvement or feedback during training and provided
close-to-oncologist level performance.

This study was funded by the Norwegian Cancer Society (Grant Number
160907-2014 and 182672-2016). We thank Disruptive Engineering and Eik
Ideverksted for letting us use their hardware.

## References

  * [Gudi et al.(2017)Gudi, Ghosh-Laskar, Agarwal, Chaudhari, Rangarajan, Paul, Upreti, Murthy, Budrukkar, and Gupta] S. Gudi, S. Ghosh-Laskar, J.P. Agarwal, S. Chaudhari, V. Rangarajan, S.N. Paul, R. Upreti, V. Murthy, A. Budrukkar, and T. Gupta.  Interobserver variability in the delineation of gross tumour volume and specified organs-at-risk during IMRT for head and neck cancers and the impact of FDG-PET/CT on such variability at the primary site.  _Journal of Medical Imaging and Radiation Sciences_ , 48(2):184–192, 2017.
  * [Ioffe and Szegedy(2015)] S. Ioffe and C. Szegedy.  Batch normalization: Accelerating deep network training by reducing internal covariate shift.  In _Proceedings of the 32nd International Conference on Machine Learning_ , pages 448–456, 2015.
  * [Kingma and Ba(2014)] D.P. Kingma and J. Ba.  Adam: A method for stochastic optimization.  _arXiv:1412.6980v1_ , 2014.
  * [Milletari et al.(2016)Milletari, Navab, and Ahmadi] F. Milletari, N. Navab, and S.A. Ahmadi.  V-net: Fully convolutional neural networks for volumetric medical image segmentation.  In _Proceedings of the Fourth International Conference on 3D Vision (3DV)_ , pages 565–571. IEEE, 2016.
  * [Ronneberger et al.(2015)Ronneberger, Fischer, and Brox] O. Ronneberger, P. Fischer, and T. Brox.  U-net: Convolutional networks for biomedical image segmentation.  In _Medical Image Computing and Computer-Assisted Intervention-MICCAI 2015_ , pages 234–241. Springer, 2015.