pith. sign in

arxiv: 1907.06617 · v1 · pith:32V4TH72new · submitted 2019-07-15 · ⚛️ physics.med-ph

Technical Report: Time-Activity-Curve Integration in Lu-177 Therapies in Nuclear Medicine

Theresa Ida G\"otz This is my paper

Pith reviewed 2026-05-24 20:52 UTC · model grok-4.3

classification ⚛️ physics.med-ph
keywords particle filtertime-activity curvesLu-177 therapySPECT dosimetryvoxel-wise analysismono-exponential fitde-noisingnuclear medicine
0
0 comments X

The pith

Particle filtering reduces noise in voxel time-activity curves for Lu-177 dosimetry.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This technical report tests whether a particle filter can clean up noisy time-activity curves measured at individual voxels from serial SPECT scans in Lu-177 therapies. Direct fitting of mono-exponential curves to each voxel produces many half-lives that deviate strongly from the organ average and some that are physically implausible. The particle filter applies a mono-exponential evolution model to regularize the curves, yielding half-lives clustered nearer the organ mean and fewer outliers. The work matters because voxel-level dosimetry promises more precise dose estimates than whole-organ methods, but noise has blocked its use. Data from 26 patients with four time points each were processed, with tuned noise parameters showing the filter's advantage in consistency metrics.

Core claim

When a particle filter based on a mono-exponential decay model is applied to voxel-wise time-activity curves from four serial SPECT acquisitions, the resulting time-integrated activities produce half-life distributions closer to organ averages and contain fewer implausibly long values than those from independent mono-exponential fits to each voxel.

What carries the argument

Particle filter that regularizes each voxel's time-activity curve using a mono-exponential decay evolution model

Load-bearing premise

The time-activity curves are assumed to follow a mono-exponential decay, which is used both as the particle filter's evolution model and as the comparison method.

What would settle it

Obtain or simulate SPECT data with known true time-activity curves per voxel and measure whether the particle filter recovers the true half-lives more accurately than direct fitting.

Figures

Figures reproduced from arXiv: 1907.06617 by Theresa Ida G\"otz.

Figure 2.1
Figure 2.1. Figure 2.1: CT-image, SPECT-image and hyprid SPECT/CT-image as shown in [PITH_FULL_IMAGE:figures/full_fig_p009_2_1.png] view at source ↗
Figure 2.2
Figure 2.2. Figure 2.2: The four SPECT-images, the CT-image and the corresponding seg￾mentation map illustrated for one slice of one patient. 9 [PITH_FULL_IMAGE:figures/full_fig_p010_2_2.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Time activity curve for one kidney: f(0) = 1%IA, T1/2 = 77.9h. a(0) of the Time Activity Curve (TAC) is different for every voxel. Note that a(0) is different from the initially injected activity A0 and generally unkown. 4.1.1 State evolution model (SEM) For each voxel of the kidney an own State Evolution Model (SEM) is computed. At the beginning, the four activity values of the same voxel plus an additi… view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Shown are two histogramms of voxelactivities: Left side with a [PITH_FULL_IMAGE:figures/full_fig_p029_4_2.png] view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: Variation of the number of particles. values is colored in grey. Through particle filtering, the outlier at the second time point could be eliminated very well [PITH_FULL_IMAGE:figures/full_fig_p033_5_1.png] view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: Time activity curves for two different voxels at four time steps. [PITH_FULL_IMAGE:figures/full_fig_p033_5_2.png] view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: One slice of the results for the particle filtering method (left) and the [PITH_FULL_IMAGE:figures/full_fig_p034_5_3.png] view at source ↗
Figure 5.4
Figure 5.4. Figure 5.4: Histograms of number of decays per voxel for the particle filter method [PITH_FULL_IMAGE:figures/full_fig_p035_5_4.png] view at source ↗
Figure 5.5
Figure 5.5. Figure 5.5: Histograms of halflives per voxel for the particle filter method (blue) [PITH_FULL_IMAGE:figures/full_fig_p035_5_5.png] view at source ↗
read the original abstract

Currently, there is a high interest in Lu-177 targeted radionuclide therapies, which could be attributed to favourable results obtained from Lu-177 compounds targeting neuroendocrine and prostate tumours. Generally, it has been recognized that a transition from dosimetry based on planar images towards based on fully-quantitative SPECT is beneficial in terms of increased accuracy. SPECT based dosimetry could not only be used for achieving accurate absorbed dose per-organ, but even for deriving dose values for individual voxels. However, a voxel-wise determination of TACs is problematic since several confounding factors exist, such as e.g. poor count-statistics or registration inaccuracies. A particle filter (PF) is a class of methods which applies regularization based on a model of a state's evolution over time. We applied PFs for de-noising the TACs of 26 patients, who underwent Lu-177-DOTATOC or -PSMA therapy. The TACs were obtained from four serial SPECT(/CT) data. The model used in the PF was a mono-exponential decay. The time-integrated activities (TIA) resulting from the PF were compared to the results of a monoexponential fit of the individual voxels in several volumes of interest. Optimal values for noise of observations and noise of the model were 0.25 and 0.5, respectively. The distribution of voxel-wise halflives resulting from the PFFit method were considerably closer to the organ average value and the number of implausibly long halflives was reduced. However, one has to admit that voxel-wise fitting generally lead to considerable deviations from the organ-average TIA as obtained by conventional whole-organ evaluation. Unfortunately, we did not have ground-truth TIA of our patient data and proper ground-truth could even be impossible to obtain. Nevertheless, there are strong indicators that Particle Filtering can be used for reducing voxel-wise TAC noise.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes applying particle filters (PF) with a mono-exponential decay evolution model to denoise voxel-wise time-activity curves (TACs) extracted from four serial SPECT/CT scans in 26 patients receiving Lu-177-DOTATOC or -PSMA therapy. Noise parameters are optimized to 0.25 (observations) and 0.5 (model); the resulting half-life distributions and time-integrated activities (TIAs) are compared to direct mono-exponential voxel fits, with the PF reported to yield values closer to organ averages and fewer implausibly long half-lives. The authors acknowledge the absence of ground-truth TIA values.

Significance. If the denoising effect can be confirmed independently, the approach would address a practical barrier to reliable voxel-level dosimetry in Lu-177 therapies, where poor count statistics and registration errors degrade direct TAC fitting. The work correctly identifies the regularization potential of state-evolution models but currently provides only indirect distributional evidence.

major comments (2)
  1. [Abstract (parameter optimization and evaluation)] The noise parameters (0.25 observation, 0.5 model) were selected to optimize closeness of voxel half-lives to organ averages on the identical 26-patient cohort used for all reported comparisons (abstract). Because the PF and the baseline comparator both enforce the same mono-exponential model, this procedure risks circularity: the metric used for optimization is also the primary evidence of improvement.
  2. [Abstract (results and discussion)] The central claim that PF reduces voxel-wise TAC noise rests on distributional shifts (closer to organ-average half-lives, fewer long half-lives) without any ground-truth TIA values, as the authors explicitly state. This leaves open whether the observed changes reflect genuine noise suppression or simply stronger enforcement of the shared mono-exponential assumption relative to unconstrained voxel fits.
minor comments (2)
  1. [Abstract] The term 'PFFit method' appears without prior definition; clarify whether it denotes the particle-filtered fit or another procedure.
  2. The manuscript would benefit from explicit reporting of the number of particles, resampling strategy, and any implementation details of the PF that are not already covered in the full text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment below and indicate where revisions will be made to the manuscript.

read point-by-point responses

  1. Referee: [Abstract (parameter optimization and evaluation)] The noise parameters (0.25 observation, 0.5 model) were selected to optimize closeness of voxel half-lives to organ averages on the identical 26-patient cohort used for all reported comparisons (abstract). Because the PF and the baseline comparator both enforce the same mono-exponential model, this procedure risks circularity: the metric used for optimization is also the primary evidence of improvement.

    Authors: The referee correctly identifies a limitation in our parameter selection process. The noise parameters were indeed tuned on the same 26-patient dataset to minimize deviation from organ-level averages. This choice was made because organ averages from conventional dosimetry provide an independent reference point, separate from voxel-wise fitting. However, we acknowledge the risk of circularity in using the same data for both optimization and evaluation. In the revised manuscript, we will explicitly state this limitation and recommend that future studies validate the parameters on an independent cohort. The primary comparison remains between the PF approach and direct mono-exponential fitting, both applied to the same TACs, showing reduced outliers with PF. revision: partial

  2. Referee: [Abstract (results and discussion)] The central claim that PF reduces voxel-wise TAC noise rests on distributional shifts (closer to organ-average half-lives, fewer long half-lives) without any ground-truth TIA values, as the authors explicitly state. This leaves open whether the observed changes reflect genuine noise suppression or simply stronger enforcement of the shared mono-exponential assumption relative to unconstrained voxel fits.

    Authors: We agree that the evidence presented is indirect, as we have already noted in the manuscript that ground-truth voxel TIA values are unavailable. The observed shifts in half-life distributions and reduction in implausible values provide supportive but not definitive evidence of denoising. It is possible that part of the effect comes from the PF's stronger incorporation of the mono-exponential model through its state evolution. We will revise the discussion section to more explicitly discuss this ambiguity and the reliance on distributional evidence rather than direct validation. revision: yes

Circularity Check

1 steps flagged

Moderate circularity from fitting noise parameters to the evaluation metric used for the noise-reduction claim

specific steps
  1. fitted input called prediction [Abstract]
    "Optimal values for noise of observations and noise of the model were 0.25 and 0.5, respectively. The distribution of voxel-wise halflives resulting from the PFFit method were considerably closer to the organ average value and the number of implausibly long halflives was reduced."

    The noise parameters were selected as optimal on the patient cohort (using closeness to organ-average halflives as the optimization target); the reported improvement in halflife distribution is therefore partly enforced by construction of the parameter choice rather than emerging as an independent validation of the PF's denoising effect.

full rationale

The paper selects observation/model noise parameters (0.25/0.5) as optimal on the patient cohort and then reports that the PF (mono-exponential evolution) produces halflife distributions closer to organ averages than direct mono-exponential voxel fits. Because the same mono-exponential model is used both inside the PF and as the comparator, and because parameters were tuned to improve exactly the reported closeness metric, the 'strong indicators' of denoising reduce in part to the fitting process rather than an independent test. The paper itself notes the absence of ground-truth TIA, so the distributional comparison supplies only partial independent content. This matches the fitted-input-called-prediction pattern at moderate severity; no self-citation or uniqueness claims are involved.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The claim depends on the mono-exponential model assumption and on two tuned noise parameters whose values were chosen from the same patient data; no external validation set or independent evidence for the model form is provided.

free parameters (2)
  • noise of observations = 0.25
    Optimal value 0.25 selected for the particle filter observation noise.
  • noise of the model = 0.5
    Optimal value 0.5 selected for the particle filter model noise.
axioms (1)
  • domain assumption Time-activity curves follow a mono-exponential decay
    Invoked as the state-evolution model inside the particle filter and as the functional form for the direct voxel fits.

pith-pipeline@v0.9.0 · 5870 in / 1378 out tokens · 50000 ms · 2026-05-24T20:52:15.300524+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

32 extracted references · 32 canonical work pages

  1. [1]

    Douc and O

    R. Douc and O. Cappe. Comparison of resampling schemes for particle filtering. pages 64 – 69, 2005

    work page 2005

  2. [2]

    Doucet, N

    A. Doucet, N. de Freitas, and N. (Eds.) Gordon. Sequential Monte Carlo Methods in Practice. Springer, 2001

    work page 2001

  3. [3]

    A. Eberle. Markoc Processes, 2017

    work page 2017

  4. [4]

    G.S. Fishman. Monte Carlo - Concepts, Algorithms and Applications . Springer, 1996

    work page 1996

  5. [5]

    Gordon, D.J

    N.J. Gordon, D.J. Salmond, and A.F.M. Smith. Novel approach to nonlinear/non-gaussianbayesian state estimation. Radar and Signal Process- ing, IEEE Proceedings, 140(2):107–113, 1993

    work page 1993

  6. [6]

    Grassi, F

    E. Grassi, F. Fioroni, V . Ferri, E. Mezzenga, M.A. Sarti, T. Paulus, N. Lan- conelli, A. Filice, A. Versari, and M. Iori. Quantitative comparison between the commercial software stratos R⃝ by philips and a homemade software for voxel-dosimetry in radiopeptide therapy. Physica Medica: European Jour- nal of Medical Physics, 31(1):72–79, 2015

    work page 2015

  7. [7]

    Dose mapping after endoradiotherapy with 177lu- dotatate/dotatoc by a single measurement after 4 days

    Heribert Hänscheid, Constantin Lapa, Andreas K Buck, Michael Lassmann, and Rudolf A Werner. Dose mapping after endoradiotherapy with 177lu- dotatate/dotatoc by a single measurement after 4 days. Journal of nuclear medicine: official publication, Society of Nuclear Medicine , 59(1):75–81, 2018

    work page 2018

  8. [8]

    [177lu]-psma-617 radionuclide treatment in patients with metastatic castration-resistant prostate cancer (lupsma trial): a single-centre, single-arm, phase 2 study

    Michael S Hofman, John Violet, Rodney J Hicks, Justin Ferdinandus, Sue Ping Thang, Tim Akhurst, Amir Iravani, Grace Kong, Aravind Ravi Kumar, Declan G Murphy, Peter Eu, Price Jackson, Mark Scalzo, Scott G Williams, and Shahneen Sandhu. [177lu]-psma-617 radionuclide treatment in patients with metastatic castration-resistant prostate cancer (lupsma trial): ...

    work page 2018

  9. [9]

    Isard and A

    M. Isard and A. Blake. CONDENSATION– conditional density propagation of visual tracking. International Journal of Computer Vision , 29(1):5–28, 2001

    work page 2001

  10. [10]

    Jackson, J.M

    P. Jackson, J.M. Beauregard, M.S. Hofman, T. Kron, A. Hogg, and R.J. Hicks. An automated voxelized dosimetry tool for radionuclide therapy based on serial quantitative spect/ct imaging.Medical physics, 40(11), 2013

    work page 2013

  11. [11]

    R.E. Kalman. A new approach to linear filtering and prediction problems. J. Basic Engineering, pages 35–45, 1960

    work page 1960

  12. [12]

    Lutetium-labelled pep- tides for therapy of neuroendocrine tumours

    BLR Kam, JJM Teunissen, Eric P Krenning, Wouter W de Herder, Saima Khan, EI Van Vliet, and Dirk Jan Kwekkeboom. Lutetium-labelled pep- tides for therapy of neuroendocrine tumours. European journal of nuclear medicine and molecular imaging, 39(1):103–112, 2012

    work page 2012

  13. [13]

    Kanazawa, D

    K. Kanazawa, D. Koller, and S. Russell. Stochastic simulation algorithms for dynamic probabilistic networks. In Proceedings of the Eleventh Confer- ence on Uncertainty in Artificial Intelligence , UAI’95, pages 346–351, San Francisco, CA, USA, 1995. Morgan Kaufmann Publishers Inc

    work page 1995

  14. [14]

    S. D. Kost, Y .K. Dewaraja, R. G. Abramson, and M. G. Stabin. Vida: A voxel-based dosimetry method for targeted radionuclide therapy using geant4. Cancer Biotherapy and Radiopharmaceuticals, 30(1):16–26, 2015. PMID: 25594357

    work page 2015

  15. [15]

    D.J.C. MacKay. Information Theory, Inference and Learning Algorithms . Cambridge University Press, 2003

    work page 2003

  16. [16]

    Marcatili, C

    S. Marcatili, C. Pettinato, S. Daniels, G. Lewis, P. Edwards, S. Fanti, and E. Spezi. Development and validation of raydose: a geant4-based application for molecular radiotherapy. Physics in Medicine and Biology , 58(8):2491, 2013

    work page 2013

  17. [17]

    O’Hagan and J

    A. O’Hagan and J. Forster. Kendall’s Advanced Theory od Statistics, Vol. 2B: Bayesian Inference. Arnold Publishers, 1999

    work page 1999

  18. [18]

    Prideaux, H

    A. Prideaux, H. Song, R. Hobbs, B. He, E. Frey, P. Ladenson, R. Wahl, and Sgouros G. 3D radiobiologic dosimetry: application of radiobiologic modelling to patient-specific 3D imaging-based internal dosimetry. J. Nucl. Med,, 48:1008–1016, 2007

    work page 2007

  19. [19]

    P. Ritt, J. Hornegger, and T. Kuwert. Technik und physikalische aspekte der spect/ct. Der Nuklearmediziner, 34(01):9–20, 2011. 39

    work page 2011

  20. [20]

    Sanders, T

    J.C. Sanders, T. Kuwert, J. Hornegger, and Ph. Ritt. Quantitative SPECT/CT imaging of 177-lu with In Vivo Validation in Patients Undergoing Peptide Receptor Radionuclide Therapy. Mol. Imaging Biol, 2014

    work page 2014

  21. [21]

    Individualized dosimetry in patients undergoing therapy with 177 lu-dota-d-phe 1-tyr 3-octreotate

    Mattias Sandström, Ulrike Garske, Dan Granberg, Anders Sundin, and Hans Lundqvist. Individualized dosimetry in patients undergoing therapy with 177 lu-dota-d-phe 1-tyr 3-octreotate. European journal of nuclear medicine and molecular imaging, 37(2):212–225, 2010

    work page 2010

  22. [22]

    Individualized dosimetry of kidney and bone marrow in patients undergoing 177lu-dota-octreotate treatment

    Mattias Sandström, Ulrike Garske-Román, Dan Granberg, Silvia Johansson, Charles Widström, Barbro Eriksson, Anders Sundin, Hans Lundqvist, and Mark Lubberink. Individualized dosimetry of kidney and bone marrow in patients undergoing 177lu-dota-octreotate treatment. Journal of Nuclear Medicine, 54(1):33–41, 2013

    work page 2013

  23. [23]

    Sarrut, J.N

    D. Sarrut, J.N. Badel, A. Halty, G. Garin, D. Perol, P. Cassier, J.Y . Blay, D. Kryza, and A.L. Giraudet. 3d absorbed dose distribution estimated by monte carlo simulation in radionuclide therapy with a monoclonal antibody targeting synovial sarcoma. EJNMMI Physics, 4(1):6, Jan 2017

    work page 2017

  24. [24]

    Sarrut, A

    D. Sarrut, A. Halty, J.N. Badel, L. Ferrer, and M. Bardis. V oxel-based mul- timodel fitting method for modeling time activity curves in spect images. Medical Physics, 44(12):6280–6288, 2017

    work page 2017

  25. [25]

    Sgouros, K

    G. Sgouros, K. S. Kolbert, A. Sheikh, K. S. Pentlow, et al. Patient- specific dosimetry for 131-i thyroid cancer therapy using 124-i pet and 3- dimensional-internal dosimetry (3d-id) software. The Journal of Nuclear Medicine, 45(8):1366, 2004

    work page 2004

  26. [26]

    Siegel, S.R

    J.A. Siegel, S.R. Thomas, J.B. Stubbs, M.G. Stabin, M.T. Hays, K.F. Koral, J.S. Robertson, R.W. Howell, D. R. Wessels, B. W .and Fisher, et al. Mird pamphlet no. 16: techniques for quantitative radiopharmaceutical biodistri- bution data acquisition and analysis for use in human radiation dose esti- mates. Journal of Nuclear Medicine, 40(2):37S, 1999

    work page 1999

  27. [27]

    Kunz, Matthew H

    Jonathan Strosberg, Ghassan El-Haddad, Edward Wolin, Andrew Hendi- far, James Yao, Beth Chasen, Erik Mittra, Pamela L. Kunz, Matthew H. Kulke, Heather Jacene, David Bushnell, Thomas M. O Dorisio, Richard P. Baum, Harshad R. Kulkarni, Martyn Caplin, Rachida Lebtahi, Timothy Hob- day, Ebrahim Delpassand, Eric Van Cutsem, Al Benson, Rajaventhan Srira- jaskan...

    work page

  28. [28]

    Vicini, A

    P. Vicini, A. B. Brill, and A. Stabin, M.and Rescigno. Kinetic modeling in support of radionuclide dose assessment. Seminars in nuclear medicine, 38(5):335–346, 2008

    work page 2008

  29. [29]

    Results of individual patient dosimetry in peptide recep- tor radionuclide therapy with 177lu dota-tate and 177lu dota-noc

    Christiane Wehrmann, Stefan Senftleben, Carolin Zachert, Dirk Müller, and Richard P Baum. Results of individual patient dosimetry in peptide recep- tor radionuclide therapy with 177lu dota-tate and 177lu dota-noc. Cancer biotherapy & radiopharmaceuticals, 22(3):406–416, 2007

    work page 2007

  30. [30]

    Wilderman, A.M

    S.J. Wilderman, A.M. Avram, J. Kritzman, R. Ackerman, and Y .K. De- waraja. Dosimetry in 131i internal emitter therapy using voxel dependent integrated time-activities derived from multiple, registered spect and ct im- ages. In Nuclear Science Symposium Conference Record, 2006. IEEE, vol- ume 6, pages 3492–3496. IEEE, 2006

    work page 2006

  31. [31]

    Yushkevich, J

    P.A. Yushkevich, J. Piven, H. Cody Hazlett, R. Gimpel Smith, S. Ho, J.C. Gee, and G. Gerig. User-guided 3D active contour segmentation of anatomi- cal structures: Significantly improved efficiency and reliability.Neuroimage, 31(3):1116–1128, 2006

    work page 2006

  32. [32]

    Zaknun, L

    John J. Zaknun, L. Bodei, J. Mueller-Brand, M. E. Pavel, R. P. Baum, D. Hörsch, M. S. O’Dorisio, T. M. O’Dorisiol, J. R. Howe, M. Cremonesi, and D. J. Kwekkeboom. The joint iaea, eanm, and snmmi practical guidance on peptide receptor radionuclide therapy (prrnt) in neuroendocrine tumours. European Journal of Nuclear Medicine and Molecular Imaging, 40(5):8...

    work page 2013