Abstract

Introduction

PET kinetic modeling represents the ultimate foundations of PET imaging, namely to quantify in vivo a wide range of pathophysiological processes at the molecular level [1, 2]. By adjusting the measured signal from dynamic PET data to relevant mathematical models, parametric images may be generated, reflecting advanced biological processes with a high degree of precision [3–5]. From the late 1970s, such historical approaches were dedicated to research purpose only, due to PET gantry coverage, time processing, and practical issues. Over the past 25 years, PET imaging has become a key imaging modality in clinical practice, overwhelmingly favoring static acquisition schemes, which consist of taking a snapshot of the bio distribution of the radiotracer, after a standardized post-injection infusion delay. To note, visual and semi-quantitative metrics derived from static PET images are intrinsically limited, given the improvement of knowledge in molecular biology, the development of personalized therapies, and the emergence of predictive medicine based on statistical engineering.

The recent commercial availability of PET systems with large axial field of view (LAFOV) heralds a paradigm shift in future practice, thanks to their extended axial coverage characteristics and technical abilities [6, 7]. In particular, there are high expectations for PET parametric imaging [8–13]. To date, numerous research software packages have been proposed for regional or small organ-oriented analyses of 4D PET data [14–18]. The lack of simple ergonomics and inadequate computational efficiency at the entire FOV level preclude their use in routine standard practice. PET parametric imaging at any part of the body may become a future clinical reality. However, it will strongly remain dependent on the accessibility to dedicated processing on professional workstations (which are linked to the PET hardware renewal cycles), evidence-based results of its clinical relevance, and practice changes from the PET community worldwide. Since these three interlinked milestones may take a while to come, making parametric images easily accessible to all PET users may accelerate the whole process for the benefit of patients. In order to promote PET kinetic modeling in future practice regardless of whatever the body anatomical level, radiotracer properties, or PET gantry (short axial-SAFOV or LAFOV), we developed PET KinetiX, which is an undoubtedly user-oriented software package, allowing faster and easier generation of parametric images from any 4D-PET DICOM series, at the entire FOV level.

General Overview

The PET KinetiX package is an optimized PET imaging research software, currently built in the Osirix DICOM viewer environment, and therefore requires a Mac OS computer with an operational Osirix MD license. In order to support fast appropriation, PET KinetiX is fully user-oriented with intuitive ergonomics. It quickly generates parametric images of any reconstructed 4D-PET DICOM data at the whole FOV level, with minimal settings. The general processing workflow of PET KinetiX is illustrated in Fig. 1. Briefly, PET KinetiX requires the user to basically install the plug-in once in Osirix MD. For any data processing, the user has to import 4D-PET DICOM series of interest into Osirix and follow these few methodological steps:

• Choose a kinetic model from the five currently available in PET KinetiX.

• Define an input function (IF). For practical convenience (potential metabolite correction, population-based IF requirements, etc.), the IF may be defined either by directly uploading a csv file or by directly drawing a small sphere of interest onto a relevant vascular structure on the 4D-PET data through the graphical user interface of Osirix.

• Launch the computation.

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Fig. 1

PET KinetiX imaging workflow

The practical efficiency of the process allows the user to accelerate his 4D-PET clinical research workflow making PET kinetic modeling feasible in daily practice. Based on the well-grounded foundation of PET kinetic modeling, the following biological models are implemented off the shelf in the current version of PET KinetiX:

• Patlak plot linear analysis: used for radiotracers with irreversible distribution properties [19], which is defined as follows: $C\left(t\right)=Ki{\int }_0^t{C}_p\left(\tau \right)d\tau +V_0{C}_p(t)$, where $t$ is the time after the radiotracer injection, $C\left(t\right)$ is the amount of radiotracer in a voxel of interest, $C_p(t)$ is the IF, and $\mathit{Ki}$ and $V_0$ are the metabolized and the distribution volume ($\mathit{DV}$) of the radiotracer. PET KinetiX automatically provides the 3D parametric maps of $\mathit{Ki}$ and $\mathit{DV}$, together with two other 3D maps: the $T^{\ast }$ map, corresponding for each voxel to the time-to-equilibrium of the radiotracer retained for optimized fitting and the R-squared error map of the fits ($R^2$), computed for each voxel as follows: $R^2=1-\frac{{\sum }_{i=1}^N{(y_i-\widehat{y_i)}}^2}{{\sum }_{i=1}^N{(y_i-\overline{y_i})}^2}$, where $N$ is the number of frames, $y_i$ is the signal measured at each time point, ${\widehat{y}}_i$ is the signal computed by the model at each time point, and $\overline{y}$ is the average of signal values. To note, $T^{\ast }$ parameter can also be set initially by the user.

• Logan plot linear analysis: used for radiotracers with reversible distribution properties [20], which is defined as follows: $\frac{{\int }_0^t{C}_T(\tau )d\tau }{C_{T(t)}}=K\frac{{\int }_0^t{C}_p\left(\tau \right)d\tau }{C_T(t)}+b$, where $t$ is the time after the radiotracer injection, $C_T\left(t\right)$ is the amount of radiotracer in a voxel of interest, $C_p(t)$ is the IF, and $K$ is the total distribution volume ($\mathit{Vt}$) of the radiotracer. PET KinetiX automatically provides the 3D parametric map of $\mathit{Vt}$, together with the 3D maps of $T^{\ast }$ and $R^2$.

• First-pass model for the estimation of blood flow: as defined in [21]: $F=\frac{P(t_m)}{{\int }_0^m{C}_p\left(t\right)dt}$, where $t_m$ is the peak-counts time after the radiotracer injection, and $C_p(t)$ is the IF. PET KinetiX automatically provides the 3D parametric map of$F$.

• Tissue compartment modeling: for any compartment model of interest (1, 2, 3, or more), the signal measurement from 4D-PET data in a voxel of interest is driven by the general equation: $C_{\mathrm{PET}}\left(t\right)=\left(1,-,v_b\right)C_{\mathrm{Tissue}}\left(t\right)+v_b{C}_{\mathrm{Blood}}(t)$, where the amount of radiotracer activity measured by PET $C_{\mathrm{PET}}\left(t\right)$ is a mix of radiotracer activities extracted into tissue $C_{\mathit{Tissue}}$(t) and circulating within the blood $C_{\mathrm{Blood}}(t)$, and $v_b$ represents the fractional blood volume [1, 2]. In the current version, PET KinetiX provides 1TCM and 2TCM:

  • – 1TCM: for which $C_{\mathrm{Tissue}}$(t) is defined as follows: $\frac{d{C}_{\mathrm{Tissue}}(t)}{\mathit{dt}}=K_1{C}_p\left(t\right)-k_2{C}_{\mathrm{Tissue}}\left(t\right)$, where $t$ is the time after the radiotracer injection, $C_p(t)$ is the IF, and $K_1$ and $k_2$ represent the influx (perfusion-dependent) and efflux rates of radiotracer, respectively. PET KinetiX automatically provides the $K_1$, $k_2$, and $v_{\mathrm{b}}$ 3D parametric maps, together with the normalized root mean squared error 3D map of the fits (n $\mathit{RMSE}$), computed for each voxel as follows: $nRMSE=\frac{\sqrt{\frac{{\sum }_{i=1}^N{(y_i-{\widehat{y}}_i)}^2}{N}}}{\overline{y}}$, where $N$ is the number of frames, $y_i$ is the signal measured at each time point, ${\widehat{y}}_i$ is the signal computed by the model at each time point, and $\overline{y}$ is the average of signal values.
  • – $2\mathrm{TCM}(k_4=0)$ for which $C_{\mathrm{Tissue}}\left(t\right)=C_{\mathrm{Free}}(\mathrm{t})+C_{\mathrm{Bound}}(\mathrm{t})$ is defined as follows:
    $$\left\{\begin{array}{c}\frac{d{C}_{\mathrm{Free}}(t)}{\mathit{dt}}=K_1{C}_p\left(t\right)-{(k}_2+{k_3)C}_{\mathrm{Free}}\left(t\right)\\ \frac{d{C}_{\mathrm{Bound}}(t)}{\mathit{dt}}=k_3{C}_{\mathrm{Free}}\left(t\right)\end{array}\right)$$

where $t$ is the time after the radiotracer injection, $C_p(t)$ is the IF, $C_{\mathrm{Free}}(t)$ and $C_{\mathit{Bound}}(t)$ are the unmetabolized and metabolized fractions of radiotracer in the tissue compartment, $K_1$ and $k_2$ are the influx (perfusion-dependent) and efflux rates of radiotracer, respectively, and $k_3$ is an intracellular enzymatic activity of interest related to the radiotracer properties (for example, hexokinase activity for ¹⁸F-FDG). PET KinetiX automatically provides the $K_1$, $k_2$, $k_3$, and $v_b$ 3D parametric maps, together with the $K_i$ map (the net influx rate, defined as $\frac{K_1{k}_3}{k_2+k_3}$) and the $\mathit{nRMSE}$ map.

For any model of interest (Patlak and Logan plots, first pass model, 1TCM, 2TCM), all the 3D parameter and error maps are automatically estimated and written in DICOM format by PET KinetiX.

Performances Compared to a Reference Standard in Clinical Research Practice

In order to assess the performance of PET KinetiX, the parametric maps of the net influx constant Ki (in mL/min/cm³), estimated both from Patlak (Ki_Patlak, the time to equilibrium T star being fixed at 20 min) and the irreversible 2 tissue compartment model (Ki_2TCM), were computed from 4D-PET real life data (1-h dynamic thoracic PET acquisitions from 12 patients who had prospectively undergone an FDG PET/MR for thoracic oncology purpose, Signa PET/MR, Waukesha, USA) (refs PhD) and compared voxel-wise with those provided by PMOD (PKIN, PMOD Technologies LLC 1996–2022, Zurich, Switzerland). For this purpose, and since our version of PKIN is not able to compute more than 10,000 voxels, the comparisons were made for each patient within three small volumes of interest (VOI<300 voxels)—tumor, tissue, and bone targets, respectively (Fig. 2). The comparison included the time efficiency (defined by the number of voxels estimated per second), the number of aberrant Ki values (defined by voxel values<0 or>1), and the absolute percent bias of PET KinetiX compared to the reference (PMOD), defined by the following formula: bias (%)=(PET_KinetiX−PMOD)/PMOD×100. Finally, the consistency between Ki_Patlak and KI2TCM was assessed for PET KinetiX and PKIN-PMOD as follows: bias (%)=(Ki_Patlak−Ki_2TCM)/Ki_2TCM×100. The results are provided in Table ​Table11 and Fig. 2. In terms of time efficiency, PET KinetiX computed 83,000 and 27,000 voxels per second, respectively, for Ki_Patlak and Ki_2TCM. On the other hand, 25 and 0.4 voxels per second were computed by PKIN-PMOD for Ki_Patlak and Ki_2TCM, respectively. For Ki_Patlak (T star fixed at T=20 min), the number of aberrant voxels were 205 (3.9% of the dataset) and 612 (11.7% of the dataset), respectively, for PET KinetiX and PKIN-PMOD; the absolute bias (median, (IQR)) was 0.1% (0.05–0.25). For Ki_2TCM, the number of aberrant voxels was 165 (3.2% of the dataset) and 587 (11.3% of the dataset), respectively, for PET KinetiX and PKIN-PMOD; the absolute bias at the 80th percentile was 5.8% (3.3–12.3). Finally, the consistency between Ki_Patlak and Ki_2TCM was similar for both software: |Bias|_{80th percentile}=35.3% (15.8–73.0) and 36.1% (16.2–70.8), respectively, for PET KinetiX and PKIN PMOD. Ki_Patlak and Ki_2TCM parametric maps of the whole FOV level are provided in Fig. 3.

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Fig. 2

A VOIs (small red spheres) used to compute the Ki_Patlak and Ki_2TCM for comparison analyses. B Results of the Ki computed with PET KinetiX and PMOD within the VOIs. Each dot represents a voxel of interest

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Fig. 3

Comparison between Ki_Patlak and Ki_2TCM parametric maps (in mL/min/cc) computed with PET KinetiX

Illustrative Cases on Different PET System with Various Dynamic Acquisition Schemes

Figures 4, ​,5,5, ​,6,6, ​,7,7, and ​and88 show various PET parametric maps computed with PET KinetiX from different 4D-PET DICOM data. In Figs. 4, ​,5,5, and ​and6,6, whole-FOV parametric maps were derived from single-bed single-pass dynamic PET data, respectively, acquired on a Signa PET/MRI (GE Healthcare, Waukesha, USA, ¹⁸F-FDG, Patlak, Fig. 4), a PET/CT Biograph mCT Flow (Siemens Healthineers, Erlangen, Germany, ¹⁸F-FDG, 2TCM, Fig. 5), and a PET/CT Vision 600 (Siemens Healthineers, Erlangen, Germany, ⁶⁸ Ga-MAA, 1TCM, Fig. 6). In Fig. 7, whole-body parametric maps were derived from multi-bed multipass dynamic PET data acquired on a SAFOV PET/CT system (Vision 600, Siemens Healthineers, Erlangen, Germany, ¹⁸F-FDG, Patlak). In Fig. 8, whole-FOV parametric maps were derived from single-bed single-pass dynamic PET data acquired on a LAFOV PET/CT system (Biograph Quadra, Siemens Healthineers, Erlangen, Germany, ¹⁸F-FDG, 2TCM). In each case, the overall computation time at the whole FOV level (standard or extended FOV PET systems) took around 3 min on a MacBook pro (Apple M1 or M2 max, 64 Go RAM).

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Fig. 4

Single-bed single-pass PET parametric imaging of non-small cell lung cancer of the right upper lobe and regional lymph node (¹⁸F-FDG, Patlak) by using PET KinetiX. From the BioMAPS lab, Orsay, France

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Fig. 5

Single-bed single-pass PET parametric imaging of a duodenal tumor (¹⁸F-FDG, 2TCM) by using PET KinetiX (PET and fused PET/CT data in axial views). From the Department of Nuclear Medicine, Hôpitaux Universitaires Paris Saclay, CHU Bicêtre, AP-HP, France

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Fig. 6

Single-bed single-pass PET parametric imaging of lung perfusion (⁶⁸ Ga-labeled macroaggregated albumin MAA, 1TCM) by using PET KinetiX. Courtesy of Pierre-Yves Le Roux, MD-PhD, Ronan Abgral, MD-PhD, Pierre-Yves Salaün MD-PhD, and David Bourhis, PhD, from the Service de Médecine Nucléaire, Centre Hospitalier Régional Universitaire de Brest, Brest, France

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Fig. 7

Multi-bed multi-pass PET parametric imaging of a metastatic melanoma (¹⁸F-FDG, Patlak) by using PET KinetiX. Courtesy of Pierre-Yves Le Roux, MD-PhD, Ronan Abgral, MD-PhD, Pierre-Yves Salaün MD-PhD, and David Bourhis, PhD, from the Service de Médecine Nucléaire, Centre Hospitalier Régional Universitaire de Brest, Brest, France

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Fig. 8

Single-bed single-pass PET parametric imaging of the body (¹⁸F-FDG, 2TCM) by using PET KinetiX. Courtesy of Dr. Alessia Artesani, Dr Joyce van Sluis and Professor Tsoumpas from the Department of Nuclear Medicine and Molecular Imaging, University Medical Center Groningen (UMCG), Groningen, Netherlands

Discussion

Stimulated by the capabilities of recent LAFOV PET systems, several academic initiatives have emerged to accelerate, within the technical community of molecular imaging, the development and diffusion of processing tools, educational contents, or resources dedicated to PET kinetic modeling (https://nmmitools.org and https://www.openkmi.org/openkmi). Although these initiatives must be greatly welcomed, they nevertheless remain currently addressed to an expert research community exclusively: either open source or proprietary software solutions, and none of them are currently designed for clinical research practice, which would require very simple user-oriented interface with minimum technical configuration, as well as highly efficient computation time to quickly generate parametric images at the whole FOV level. On the other hand, the leading manufacturers are gradually offering dedicated solutions on their clinical proprietary systems. However, they are prototypes under proprietary license, as well as inherently dependent on the hardware renewal cycle. In order to generate more resources for clinical research, promote evidence-based results, and validate its use in future practice, PET kinetic modeling must be accessible within the medical imaging community, regardless of the PET system or manufacturer.

PET KinetiX addresses these challenges and proposes a fully independent software solution allowing, whatever the PET system (SAFOV/LAFOV) or acquisition scheme (single-bed single-pass, multi-bed multipass), the computation of 4D PET parametric maps at the whole FOV level in less than 5 min. Compared on real-life ¹⁸F-FDG 4D-PET data to the current research reference standard (PMOD PKIN 4.4, 12 patients acquired on a Signa PET/MRI, GE Healthcare, Waukesha), PET KinetiX provided excellent accuracy both for Patlak and 2TCM kinetic methods. Also tested on three other PET systems (two SAFOV and one LAFOV PET/CT systems, Siemens Healthineers, Germany), in different acquisition schemes (single-bed single-pass and multi-bed multipass, ¹⁸F-FDG, 2TCM), PET KinetiX provided in less than 5 min parametric maps of 1TCM, 2TCM, and Patlak methods with excellent visual quality and consistency in each case.

For the sack of rapid accessibility and simplicity to use, PET KinetiX is currently designed as a plugin for the widely known Osirix GUI (MD license). In the near future, the solution could be implemented on other operating systems and potentially designed as a software or as a service, depending on the needs. Furthermore, as an evolving software solution and based on potential academic collaborations requirements as well as in order to improve the performance of kinetic modeling, PET KinetiX could integrate cutting-edge methods/technology such as delay correction or model selection at a regional level [12, 22, 23].

Conclusion

PET KinetiX has been designed as an easy-to-install and user-friendly software solution, enabling fast PET parametric imaging at the whole FOV level on standard and extended PET gantries. The objective of PET KinetiX is to universally promote the accessibility to PET kinetic modeling in future clinical research practice.

Copyright and Collaboration

PET KinetiX is a proprietary software which has been developed and led by Florent L. Besson, MD, PhD, and Sylvain Faure, PhD, at Paris-Saclay University. In its current version, the software is for “educational” or “research” purposes only, under academic collaborations. More information at (http://www.petkinetix.fr) or on request by contacting the two co-inventors.

Acknowledgements

Funding

This research was funded by the French National Centre for Scientific Research (Programme Prématuration CNRS Innovation, 2022–2023) and supported by Institut National des sciences Mathématiques et de leurs interactions (INSMI) and laboratoire d’imagerie Multimodale Paris Saclay (BIOMAPS).

Data Availability

The data that support the findings of this study are available from the corresponding author, [F.L.Besson], upon reasonable request.

Footnotes

References