Original article

A convolutional neural network-based system to estimate thearterial plasma radioactivity curve in 18F-FDG dynamic brain
PET study
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Keisuke Kawauchia, Mui Saitoa, Kentaro Nishigamia and Chietsugu Katohb
Purpose Quantitative images of metabolic activity
can be derived through dynamic PET. However, theconventional approach necessitates invasive blood
sampling to acquire the input function, thus limiting its
noninvasive nature. The aim of this study was to devise
a system based on convolutional neural network (CNN)
capable of estimating the time-radioactivity curve ofarterial plasma and accurately quantify the cerebral
metabolic rate of glucose (CMRGlc) directly from PET
data, thereby eliminating the requirement for invasive
sampling.
Methods This retrospective investigation analyzed
29 patients with neurological disorders who underwent
comprehensive whole-body 18F-FDG-PET/CT
examinations. Each patient received an intravenous
infusion of 185 MBq of 18F-FDG, followed by dynamic
PET data acquisition and arterial blood sampling. A CNN
architecture was developed to accurately estimate thetime-radioactivity curve of arterial plasma.
Results The CNN estimated the time-radioactivity curveusing the leave-one-out technique. In all cases, there wasat least one frame with a prediction error within 10% in at

Introduction

PET has been used in the realm of brain functional
imaging. Dynamic brain PET imaging using Fluorine-18
fluorodeoxyglucose (18F-FDG) permits the examinationof the cerebral metabolic rate of glucose (CMRGlc) [1].
Nevertheless, the conventional and widely accepted technique for analyzing the CMRGlc involves the extractionof arterial blood samples and the derivation of the time-radioactivity curve from arterial plasma, which necessitates
an invasive procedure for patients and exposes medical
personnel to radiation [2]. Consequently, the search fornoninvasive alternatives to generate input functions has
been underway [3,4]. Nonetheless, existing methods
suffer from limitations, such as insufficient sample sizeand diminished accuracy, thus failing to supplant blood
sampling. Therefore, we propose a novel approach that
employs a convolutional neural network (CNN)-based
This is an open-access article distributed under the terms of the Creative
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least one frame. Furthermore, the correlation coefficient
between CMRGlc obtained from the sampled blood and
CNN yielded a highly significant value of 0.99.
Conclusion The time-radioactivity curve of arterial
plasma and CMRGlc was determined from 18F-FDG
dynamic brain PET data using a CNN. The utilizationof CNN has facilitated noninvasive measurements of
input functions from dynamic PET data. This method
can be applied to various forms of quantitative analysis
of dynamic medical image data. Nucl Med Commun 44:
1029–1037 Copyright © 2023 The Author(s). Published byWolters Kluwer Health, Inc.
Nuclear Medicine Communications 2023, 44:1029–1037
Keywords: CNN, FDG dynamic brain PET, radioactivity curveaGraduate School of Biomedical Science and Engineering, Hokkaido
University and bFaculty of Health Sciences, Graduate School of Hokkaido
University, Sapporo, Japan
Correspondence to Keisuke Kawauchi, Graduate School of Biomedical Scienceand Engineering, Hokkaido University, N12, W5, Kita-Ku, Sapporo, Hokkaido,
060-0812 Japan
Tel: +81 117065152; e-mail: keisuke1.kawauchi@gmail.com
Received 7 April 2023 Accepted 15 August 2023.

system to estimate the time-radioactivity curve of arterial
plasma.
AI studies in the domain of PET have documented findings, including a study that automated the classificationof 18F-FDG whole-body PET images into three categories: benign, malignant, or equivocal [5]. FDG-PET/
computed tomography (CT) images of patients with lungcancer and lymphoma have demonstrated exceptional
diagnostic performance in fully automating the localization of FDG uptake patterns and identifying foci thatare either suspicious or nonsuspicious for cancer classification using a CNN [6]. Furthermore, a study reported
the generation of a 511-keV photon attenuation map
by inputting whole-body 18F-FDG-PET/CT images
from 100 patients with cancer into a CNN, which exhibited greater reliability than the four-fraction method
employed in current whole-body PET/MRI scans [7].
Moreover, a study detailed the classification of lung cancer foci on FDG-PET/CT images as either tumor stages
T1-2 or T3-4 by training a CNN on images obtained
from patients who underwent staging using FDG-PET/
CT images [8]. Hence, most reports in nuclear medicine,0143-3636 Copyright © 2023 The Author(s). Published by Wolters Kluwer Health, Inc.

DOI: 10.1097/MNM.0000000000001752

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particularly in the realm of PET, pertained to the classification of images and the extraction of lesions, withsome demonstrating efficacy in disease classification
and attenuation correction. Nevertheless, regression
analyses of data derived from images have seldom been
documented, despite the existence of studies that havereported regression prediction of age and weight basedon whole-body PET images [9].
This study aimed to devise a CNN-based framework
capable of estimating the time- radioactivity curveof arterial plasma and CMRGlc from PET data. Our
hypothesis posited that such an approach would facilitatea noninvasive and quantitative investigation of cerebral
energy metabolism.

Methods
Subjects

This study comprised a cohort of 29 patients diagnosed
with neurological disorders (mean age: 37.3 ± 13.2 years;
11 males and 18 females). The Ethics Committee of
Hokkaido University Hospital Medical Information
Network Clinical Trials Registry (UMIN000018160) provided approval for this study. All participants provided
written informed consent. Note however that this further
investigative study utilized previously acquired data retrospectively so the need for further ethical approval was
waived.
For each patient, an intravenous infusion of 185 MBq of
18
F-FDG was administered, followed by dynamic PET
data acquisition and arterial blood sampling. Dynamic
PET images of the brain were acquired over a periodof 60 min, with 22 frames. The time intervals for frame
collection were as follows: 20, 50, 70, 100, 140, 180, 220,
270, 330, 390, 450, 570, 750, 930, 1110, 1350, 1650, 1950,
2250, 2550, 2850, and 3150 s (Fig. 1). Concurrently, 1 mLof arterial blood was collected from the forearm artery via
an indwelling needle. Immediately after blood collection,

centrifugation was performed to separate the plasma andcellular components.
18

F-FDG dynamic imaging and blood sampling

Arterial plasma radioactivity counts were measured using
a counter (ARC-380CL manufactured by Aloka), and thearterial plasma time-radioactivity curve was obtained.
The arterial blood time-radioactivity curve is not an accurate input function for compartmental model analysis of18
F-FDG accumulation in the brain, because activity isalso taken up by erythrocytes. Therefore, we obtained
an accurate arterial plasma time-radioactivity curve byremoving erythrocyte radioactivity that did not enter
brain tissue.
Scanner configuration

PET investigations were performed employing an ECATEXACT HR+ scanner manufactured by CTI/Siemens,
which exhibited in-plane and axial resolutions of 4.8
and 5.6 mm, respectively. The field of view possessed adiameter of 23.4 cm. Through continuous axial motion of
the gantry, the PET scanner generated 63 tomographic
images at intervals of 2.425 mm. These image slices
were oriented parallel to the orbitomeatal line. To correct tissue attenuation, a transmission scan employing a
68-Ge line source was performed before emission scanning. PET images were reconstructed using the filtered
back projection method employing a ramp filter. The
resultant PET image from this device had a half width(FWHM) of 4.8 mm, and each pixel corresponded to an
actual length of 2.5 × 2.5 × 6.3 mm. The 22 frames of the
dynamic PET images were reconstructed using filtered
back projection with a similar matrix size of 128 × 128 in
the axial plane and a voxel size of 2.5 × 2.5 × 6.3 mm.
Convolutional neural network

A neural network represents a computational paradigm
that emulates the structure and functionality of neurons

Fig. 1(a) A typical example of slice images in which the internal carotid is most clearly depicted in each frame of 18F-FDG dynamic brain PET. (b) A typicalexample of the time-radioactivity curve of arterial plasma.

CNN-based system to estimate radioactivity curve Kawauchi et al.

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in the brain. It comprises three fundamental layers: input,
hidden, and output layers. Each layer consists of interconnected nodes connected by edges. A ‘deep neural network’ (DNN) refers to a neural network that incorporates
multiple hidden layers. The use of DNNs in machinelearning is commonly known as ‘deep learning’. A CNN
stands as a specialized DNN variant that demonstrates
remarkable efficacy in tasks involving image recognition. Unlike traditional approaches for image recognition,
CNNs do not rely on predefined image features. In thisstudy, we proposed adopting a CNN for classifying FDGPET brain images.

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visualization technique known as Gradient-weighted
Class Activation Mapping (Grad-CAM) [16]. Grad-CAM
enables the identification of image regions that contribute to the activation of the neural network, thereby allowing for a visual understanding of the CNN’s estimationbasis. In this study, we employed Grad-CAM to predicteach test case and performed an additional experiment tovisualize the basis for the estimation results. Grad-CAM
assigns a continuous value to each pixel, and we applied athreshold of 90% of the maximum value to delineate theactivated area.
Hardware and software environments

Architectures

In this study, we used a network model based on the
Xception architecture [10]. Xception has exhibited
remarkable effectiveness in various medical imaging
domains, encompassing clinical images of basal cell carcinoma and pigmented nevi, v, and non-contrast-enhanced
CT images for identifying the ultra-high-density middle
cerebral artery sign in patients with acute ischemic stroke[11–13]. Xception is a model that optimizes parametercount and computational complexity by implementing
depth-wise separable convolutions.
Model training and testing

During the training phase of the model, we implemented an ‘early stopping’ technique to decrease overfitting. Early stopping serves to monitor the loss functionof both training and validation processes, allowing us tostop the learning process before it becomes excessively
focused. This approach has found applications in diverse
machine learning methodologies [14]. The CNN usedin this study was fed a complete set of image frames as
inputs. Specifically, we used 22-frame PET images in asingle axial plane, that captured on capturing the internal carotid most prominently. Given the use of regression models in this study, we supplemented the image
inputs with arterial plasma time- radioactivity curve data.
Furthermore, the output layer of the model was configured to consist of a single unit. In the model testing
phase, a regression model was created using a CNN topredict the arterial plasma time-radioactivity curve. For
training, validation, and evaluation, we employed theleave-one-out cross-validation (LOOCV) methodology[15]. Within the LOOCV framework, one case was chosen from 29 cases as the test case, while the remaining 28
cases were used for training and validation. Among the
28 cases, 21 were allocated for training and seven wereused for validation. This process was repeated for all test
cases, resulting in 29 iterations.
Gradient-weighted class activation mapping

To address the challenge of explaining the decision-making process in artificial intelligence (AI) models developed through deep learning, we have incorporated aThis experiment was performed in the following environments: operating system: Windows 10 pro 64 bit; CPU:Intel Core i9-10900K; GPU: NVIDIA GeForce RTX
3090 24GB; Framework: TensorFlow 2.5.0; Language:
Python 3.8.5.
3-compartment model analysis

For each patient, 100 regions of interest (ROIs) werepositioned on the cerebral images. The size of the
ROIs was one pixel, and the length of the pixel size was
2.5 × 2.5 × 6.3 mm. The time- radioactivity curve X(t) for
each ROI was calculated. The CMRGlc in each ROI was
measured using the following equation in the 3-compartment model analysis:
X (t) = Xe (t) + Xm (t)d Cp (t)= k 2  Xe (t)dt

K 1  Cp (t)d Xe (t)= K 1  Cp (t) + k 4  (t)dtd Xm (t)= k 3  Xw (t)dt(k 2 + k 3) Xe (t)k 4  (t)where Xe(t) and Xm(t) are the time-radioactivity curvesin the first and second tissue compartments, respectively.
Cp(t) is plasma activity (Fig. 2). K1 and k2 are the rate
constants of FDG uptake from the plasma into the tissue
and from the tissue back into the plasma, respectively.
k3 and k4 are the rate constants for the phosphorylationof FDG by hexokinase and dephosphorylation of FDG6-PO4 to FDG, respectively (Fig. 3).
Figure 4 also shows that tissues, such as the skull andscalp, have high k2 values due to low glucose uptake
and metabolism (relying predominantly on fatty acidmetabolism. Xm(t) indicates the tissue that requires glucose. The CMRGlc was calculated using the following
equation:
CM RGlc = Blood glucose level  K 1  k 3= (k 2 + k 3) =LC

where LC is a lumped constant of 0.89 [17].

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Fig. 2

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Arterial plasma time-radioactivity curve Cp(t) and tissue time-radioactivity curve X(t) at any position in the brain obtained from PET images.
Where Xe(t) and Xm(t) are the time-radioactivity curves in the first andsecond tissue compartments, respectively. X(t) is the sum of X e(t) andXm(t).

Fig. 3The diagram illustrates the velocity constants employed in the analysis ofa three-compartment model. Specifically, K1 and k2 represent the rate
constants governing the uptake of FDG from the plasma into the tissue
and its subsequent return from the tissue to the plasma, respectively.
Similarly, k3 and k4 denote the rate constants involved in the phosphorylation of FDG by hexokinase and the dephosphorylation of FDG6-PO4 to FDG, respectively. The unit of K1 is mL/min/g, while k1, k2,
and k3 are expressed in/min. These values serve as essential parameters
for the calculations performed in the three-compartment model analysis.

Results

The model underwent training for an average of 70 ± 27
epochs employing an early stopping algorithm. The training phase required an average of 560 ± 216 s, while prediction per patient took <0.1 s.
The time-radioactivity curve, estimated by the CNN
employing LOOCV, was compared with the corresponding curve derived from arterial blood. In eachcase, the prediction error was at least 10% in at least
one frame. In 21 cases, it was verified that >18 of the 22
frames exhibited a prediction error within a 10% margin. Nevertheless, the remaining eight cases showednumerous frames with prediction errors exceeding 10%(Table 1).

Figure 5 displays the arterial plasma time- radioactivity
curves acquired through both the CNN-based method
and traditional blood sampling. The accurate outcomeof our proposed methodology using a CNN has demonstrated the achievement of comparable fittings, independent of the acquisition of blood samples.
Two challenges commonly encountered in machine anddeep learning are underfitting and overfitting. Thesephenomena can be visualized by analyzing a loss curve
plotted against the number of epochs. In the case ofunderfitting, the loss curve continues to decrease for boththe training and validation datasets. Conversely, overfitting is characterized by a training loss curve approaching
100%, while the validation loss curve diverges from it.
Figure 6 illustrates the loss curve for one of the 29 trials
performed in this study. In this particular instance, thetraining and validation loss curves did not deviate significantly, indicating that the training process achieved
an optimal balance without underfitting or overfitting.
Similar trends were observed across the remaining 28
trials, further supporting the absence of underfitting or
overfitting.
Comparison with CMRGlc

In each test patient, 100 ROIs were strategically positioned within the brain (Fig. 7). These ROIs were automatically defined as single-pixel regions every 2 cm
along the vertical and horizontal axes, excluding thoselocated within the ventricles or outside the brain. Timeradioactivity curves were obtained from brain tissue,
and the CMRGlc was calculated using a 3-compartment
model. The results are presented in Fig. 8a. Notably,
the correlation coefficient between the CMRGlc values
derived from blood sampling and those estimated by
the CNN demonstrated a significantly high correlationof 0.99. According to established guidelines [18], a correlation coefficient of ≥0.5 indicates a strong correlation.
Figure 8b illustrates the Brand–Altman plot, where thevertical axis represents the difference (DIFF) between
the CMRGlc values obtained from blood sampling andthose estimated by the CNN, and the horizontal axis
represents the average (MMEAN) of these values. The
dashed line represents the limits of agreement (LOA),
calculated as ‘mean DIFF ± 1.96 × SD of DIFF’. If 95%
of the DIFF values fall within the LOA, it indicates thatthe error follows a normal distribution and can be considered consistent between the CMRGlc values obtained
from blood sampling and those estimated by the CNN.
The findings of this study demonstrated a high level ofconsistency, with 97% of the DIFF values falling within
the LOA.
Grad-CAM

We employed Grad-CAM to discern the precise anatomical
regions within the image from which the neural network
extracted the most salient information. Exemplary instances

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Fig. 4

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Distribution image of the rate constants K1, k2, k3, k4 in an exemplar series of 18F-FDG-PET brain images.

Table 1

Mean error and percentage of slices within 10% error

Patient_01
Patient_02
Patient_03
Patient_04
Patient_05
Patient_06
Patient_07
Patient_08
Patient_09
Patient_10
Patient_11
Patient_12
Patient_13
Patient_14
Patient_15
Patient_16
Patient_17
Patient_18
Patient_19
Patient_20
Patient_21
Patient_22
Patient_23
Patient_24
Patient_25
Patient_26
Patient_27
Patient_28
Patient_29

Mean error %Percentage of slices within 10% error

3.9
6.1
1.6
5.0
4.2
1.7
3.3
4.3
3.3
17.3
3.3
5.5
2.5
17.6
9.0
5.1
12.6
3.5
8.4
3.4
3.0
2.9
2.7
33.8
4.2
47.3
30.2
34.5
2.7

100%
86%
100%
86%
95%
100%
100%
95%
100%
32%
100%
91%
100%
41%
64%
91%
64%
95%
77%
100%
100%
100%
100%
18%
100%
14%
18%
9%
95%

of this analysis are illustrated in Fig. 9. It is noteworthy thatall patients presented at least one image where an activation region encompassing the vicinity of the internal carotid

Fig. 5The arterial plasma time-radioactivity curve presents the calculated
mean and SD from the analysis of all 29 cases. This visual representation underscores the exceptional uniformity observed in the fitting of
the curves.

artery was clearly evident. Conversely, Fig. 10 provides anexample of Grad-CAM highlighting areas other than theinternal carotid artery. Specifically, (A) delineates enhanced
regions surrounding the optic nerve, while (B) identifies
enhanced areas adjacent to the cerebellum. These particular images manifest notable prediction errors.

Discussions

In this study, we employed a CNN architecture known as
Xception that leverages depth-wise separable convolution

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effectively diminishing the number of parameters andcomputational complexity compared with conventional
approaches. Consequently, in 21 cases, we ascertainedthat >18 of the 22 frames manifested a prediction error
within a range of 10%. Moreover, the correlation coefficient between the estimated CMRGlc derived from blood
samples and those acquired from the CNN exhibited ahighly significant value of 0.98. These compelling findings indicate that the CNN can accurately estimate thearterial plasma time-radioactivity curve using 18F-FDG
Fig. 6

An example of a training and verification loss curve is in this study. The
vertical axis represents the value of the loss function, the horizontal
axis represents the number of epochs, and the blue and orange colors
depict the training and validation loss curves, respectively. The training
was completed at 70 ± 27 epochs due to early stopping, and both thetraining and evaluation gradually declined.

dynamic brain PET data, thereby enabling noninvasive
quantitative analysis of diverse dynamic imaging data.
We performed deep learning analysis to estimate thearterial blood time-radioactivity curve from dynamic
brain 18F-FDG-PET images specifically targeting theinternal carotid region. As a straightforward approach,
we postulated that the arterial blood time-radioactivity
curve can be derived by setting the ROI encompassing
the internal carotid in the dynamic image and computing the maximum radioactivity at each timepoint. This
choice is motivated by the fact that the PET device usedin this study had an FWHM of 4.8 mm, while the pixel
size of the PET image output was 2.5 mm. Furthermore,
the inner diameter of the internal carotid in the skull
ranges from approximately 2–3 mm, and considering thepartial volume effect, accurate quantification of arterial
blood radioactivity passing through the internal carotid
lumen is unfeasible with an image possessing an FWHM
of 4.8 mm. The desired parameter for analysis is not thecomplete time-radioactivity curve of whole blood, butrather the arterial plasma’s time-radioactivity curve after
the removal of erythrocytes. Given that blood cell components are not taken up by brain tissue, the time-radioactivity curve of 18F-FDG absorbed by blood cells should
be excluded from the input function during compartment
model analysis. Therefore, in this study, we developed a
CNN model that estimates the arterial plasma time-radioactivity curve, instead of the arterial blood time-radioactivity curve, using dynamic brain PET images of18
F-FDG.
Numerous techniques have been reported in the literature or estimating the input function in brain PET using
image data. Typically, these approaches involve defining
an ROI encompassing the relevant vascular structures in a

Fig. 7100 regions of interest (ROI) in the brain of each case. ROIs in the image were automatically set to 1-pixel ROIs every 2 cm in the vertical and horizontal directions. However, the ROIs inside the ventricle and outside the brain were excluded.

CNN-based system to estimate radioactivity curve Kawauchi et al.

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Fig. 8Downloaded from http://journals.lww.com/nuclearmedicinecomm by BhDMf5ePHKav1zEoum1tQfN4a+kJLhEZgbsIH
o4XMi0hCywCX1AWnYQp/IlQrHD3i3D0OdRyi7TvSFl4Cf3VC4/OAVpDDa8KKGKV0Ymy+78= on 10/26/2023(a) Scatter plot of the time-radioactivity curve of arterial plasma from blood sampling and by CNN. The correlation coefficient is 0.99, indicating that
there is a strong correlation between the two. (b) The Brand–Altman plot (vertical axis; DIFF) (difference between CMRGlc obtained from blood
sampling data and estimated by CNN), horizontal axis: MMEAN (average of CMRGlc obtained from blood sampling data and estimated by CNN).
The results obtained in this study were consistent because 97% of DIFF was included in the LOA.

Fig. 9

Typical examples of Grad-CAM: CNN was found to respond to the internal carotid in slices containing the internal carotid.

PET scan to generate an input function. However, a persistent challenge lies in generating a metabolite-corrected
plasma curve from a whole blood curve. Consequently,
reliance on arterial or venous blood sampling remains
necessary [2]. In the proposed methodology, blood sampling is used to train the CNN. Nevertheless, the findings of this study suggest that the use of a well-trained

CNN might obviate the need for blood sampling during
examinations.
On the contrary, the criteria employed by the CNN remain
opaque, making the cause behind the heightened prediction error in the eight cases unknown. Nevertheless, it
was observed that in instances where the prediction was
unsuccessful, the visibility of the internal carotid was

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Fig. 10

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There were cases in which Grad-CAM enhanced areas other than the internal carotid. (a) The area around the optic nerve is enhanced. (b) The areaaround the cerebellum was enhanced.

diminished compared with other cases. Furthermore, as
depicted in Fig. 9, Grad-CAM exhibited a proclivity tofocus on regions beyond the internal carotid. Based onthese observations, it is plausible to speculate that thechallenge in visualizing the internal carotid may havecontributed to the diminished prediction accuracy,
despite our efforts to identify frames where the internal
carotid was most prominently discernible. To address
this, we propose that augmenting the number of images
showcasing characteristics similar to those of the training
data would prove useful.
CNNs are renowned for their ability to classify images
based on distinctive features present within them.
Grad-CAM, a visualization technique, can illuminate
the ‘region of AI focus’ and holds promise in promoting
the development of explainable AI, in contrast to theconventional ‘black box’ paradigm, thereby fostering
increased user confidence. The findings of this investigation substantiate that in numerous instances, CNNs
exhibit discernible responses to the internal carotid,
as exemplified in Fig. 9. Nonetheless, there were certain cases where Grad-CAM accentuated regions distinct from the internal carotid, as illustrated in Fig. 10.
Consequently, this study validates the potential for
visualizing the AI’s zone of interest, enabling further exploration of the foundations underpinning its
predictions.
Conclusion

The use of a CNN has demonstrated the potential for
estimating time- radioactivity curves in arterial vessels
derived from 18F-FDG brain PET dynamic data. Thisapplication of CNNs offers a noninvasive method forquantifying input functions extracted from dynamic
PET data, thereby presenting an effective approach forthe quantitative analysis of various dynamic medical
imaging datasets.

Acknowledgements

This study was supported by the Japan Society for the
Promotion of Science (JSPS N0.22K0765802).
All procedures performed in studies involving humanparticipants were by the ethical standards of the institutional and/or national research committee and with the1964 Helsinki Declaration and its later amendments orcomparable ethical standards.
The institutional review board of Hokkaido University
Hospital approved the study (UMIN000018160) andwaived the need for written informed consent from eachpatient because the study was conducted retrospectively.
Conflicts of interest

There are no conflicts of interest.

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