The small animal imaging data used to train and evaluate the DLIF model was collected in retrospect from two independent cohorts, acquired at UiT The Arctic University of Norway (UiT) and Université de Sherbrooke (UdS). The same PET imaging system and radiotracer was used at both centers, however, there were some systematic differences in the experimental methods and available animal strains in the datasets (Table 1). The UiT dataset was used for training and initial evaluation of the model. Because a ground truth AIF was unavailable in this dataset, an IDIF was used as training targets. On the other hand, in the UdS dataset continuous arterial blood sampling was performed simultaneously with PET acquisition. This dataset was used for additional evaluation of the DLIF model.

The proposed DLIF model architecture is shown in Figure 1. First, the spatial dimensions of each of the 41 volumes associated to each of the time frames of a single sample are reduced, while at the same time relevant spatial information is extracted and noise filtered out. The main expedient consists of feeding the volumes in parallel to four layers of 3D convolutional filters coupled with batch normalization, rectified linear unit (ReLU) activation functions and finally, 3D maxpooling layers. Choices of the different components are well described in the literature (32), but for instance, batch normalization has been shown to speed up the training process and act as a regularizer to avoid overfitting (33), while ReLU seems the most reasonable choice for activation function when the input and output data are non-negative quantities (34). Also, halving the spatial dimensions with maxpooling while doubling the number of filters for each layer is a well-known approach for obtaining a rich yet compact representation of the input, and many well-known architectures adopt this strategy (35, 36). Once the smallest spatial dimensions are reached (4×3×3), these 41 volumes of 16 features are flattened, so that each time frame is represented by a vector of 576 features. These vectors are reduced to a length of 32 by two cascaded multilayer perceptrons. Subsequently, 16 filters of 1D convolution are applied along the time axis, to capture the temporal correlations among the neighboring time frames. Finally, a multilayer perceptron takes the 16×41 extracted features and outputs a 41 long vector as output, representing the predicted DLIF.

Two different training regimes were used. First, the DLIF model was trained and evaluated with the UiT dataset, using 17-fold cross validation. Cross validation is commonly applied for model performance evaluation in settings with limited available training data (37). By iteratively splitting the dataset to use 64 samples for training and 4 samples for testing in each of the 17 folds, this allowed to have all 68 available samples in the test set once. Next, a new DLIF model was trained using all samples from the UiT dataset, and subsequently tested on the UdS dataset. In this setting, 50 runs with different random initializations were performed to obtain statistics over the DLIF predictions.

In both training regimes the Adam optimizer (38) with standard hyperparameters was selected to perform the minimization of a mean square error loss between the ground truth and the DLIF. Training was performed for 200 epochs with a learning rate of 2⋅10−4.

The DLIF models were implemented in Python 3.11.5, using PyTorch 2.1.0.

For both training regimes, the DLIF-predicted curves were first compared point by point to the respective reference input function using orthogonal regression. Orthogonal regression was chosen when comparing the measured and the predicted input function during regression analysis, because it assumes measurement error in both variable pairs, as opposed to standard linear regression, which assumes measurement error in only the independent variable (39). Patlak modeling (5, 6) was implemented in an in-house developed script (Python 3.11.5) and used to calculate the influx rate constant, Ki, for each voxel, as well as for brain and myocardium tissues, using both the predicted DLIF and each reference input function. For the UdS dataset, the regional influx rate constants for brain and myocardium tissues were also calculated using the IDIF and compared to those obtained with the AIF.

DLIF- and IDIF-based influx estimates were compared to those obtained from respective reference input function using paired t-test (α=0.05) and orthogonal regression. Normality was assessed using quantile-quantile plots. All statistical analyses were implemented in an in-house developed script (Python 3.11.5).

The overall input function curve shape, with an early peak and a vanishing tail, is captured by the DLIF model, as shown for the three mouse scan examples in Figure 2. Investigating the data points from all samples, there is a strong overall linear relationship (slope: 0.84) and strong correlation (correlation coefficient: 0.91) between DLIF and IDIF (Figure 3A). The DLIF model slightly underestimates the IDIF peak, shown as a deviation from the linear model for data points with high SUV value in Figure 3A.

Following DLIF prediction, Patlak modeling was performed to investigate the potential usefulness of the DLIF model for glucose metabolic rate measurements. Figure 3B displays all voxel-wise Ki data points as scatterplot, using DLIF and IDIF as input function, respectively, while Table 2 and Supplementary Figure S2 presents statistics and data from the regional Ki values, for brain and myocardium tissues, respectively. The voxel-wise influx rate constants displayed a strong linear relationship (slope: 1.05) and a strong correlation (correlation coefficient: 0.94) for the majority of the mouse scans. A few outlier cases are obvious as colored data points deviating from the identity line in Figure 3B. Nevertheless, visual comparison of the voxel-wise influx rate constants calculated with IDIF and DLIF, respectively, for the mouse scan with minimum and maximum errors from Figure 2, still show promising similarities (Figure 4). The regional Patlak analysis (Table 2 and Supplementary Figure S2) indicated good agreement between the population average influx rate constants for brain and myocardium tissues (average errors: ≤10%) and a strong correlation (correlation coefficient: 0.78–0.95). The obtained P values, surpassing the significance level, suggested insufficient evidence to reject the null hypothesis of significant differences between the groups.

A DLIF model trained on the full UiT dataset was applied to the UdS data for the purpose of external evaluation. The general curve shape is captured by the DLIF model and is in good agreement for some mouse scans (Figure 5A). However, there are also examples where the DLIF model fails to predict the tail (Figure 5B) or the peak (Figure 5C) in this external dataset. The predictions for all test mouse scans are shown in Supplementary Figure S1. For most mouse scans, the DLIF model is unable to predict the AIF peak, while the tail regions are generally in better agreement with the mean DLIF curve (Supplementary Figure S1). This is also visible in the comparison of individual data points (Figure 6A). There is a strong correlation between the data points (correlation coefficient: 0.70), with a linear tendency (slope: 0.61), although with discrepancies, especially around the peak, corresponding to high data point values.

The influx rate constant from Patlak modeling, obtained using DLIF and reference AIF as input function, respectively, showed a strong linear relationship (slope: 1.12) and a strong correlation (correlation coefficient: 0.90) for the voxel-wise calculations (Figure 6B). Visual comparison of the voxel-wise influx rate constants calculated with AIF and DLIF, respectively, for the mouse scan with minimum and maximum errors from Figure 5, also show promising similarities (Figure 7). The regional comparisons for brain and myocardium tissues (Table 2 and Supplementary Figure S3) indicated average errors of 20% and−3%, respectively, with a strong correlation (correlation coefficient: 0.91–0.94). The obtained P values for brain and myocardium tissues, surpassing the significance level, suggested insufficient evidence to reject the null hypothesis of significant differences between the groups. Table 2 and Supplementary Figure S4 also displays the corresponding comparisons between Ki obtained with the reference AIF and the one obtained using the IDIF in the UdS dataset. These results indicate similar agreement for the brain region compared to DLIF (mean error: −9%, correlation coefficient: 0.84, P value: 0.36), while for myocardium tissues, larger and significant deviations from the reference AIF were obtained, compared to DLIF (mean error: −17%, correlation coefficient: 0.97, P value: 0.09).

We first trained and evaluated the DLIF model on 68 mouse scans with IDIF targets using cross-validation. These experiments indicated that DLIF could capture the overall input function curve shape, with an early peak and a vanishing tail, and as such, could be a useful approach for estimating an IDIF (Figure 2). Data points between DLIF and IDIF input functions showed a linear behavior and were highly correlated (Figure 3A). As the input function curve itself is not the interesting result in most dynamic PET studies, we evaluated the influx rate constant, Ki, from Patlak modeling using the reference IDIF as input function, and compared it to the corresponding Ki, when using DLIF as input function. This analysis was done on both voxel-wise (Figures 3B and 4), and on a regional level for brain and myocardium tissues (Table 2, Supplementary Figure S2). In the voxel-wise scatterplot (Figure 3B), each mouse scan is displayed with a different color. The individual slope coefficients for the majority of mouse scans were around 1, however, 10 (15%) of the 68 mouse scans had more severe deviations from the identity line, with slope values outside the range of 1±0.4 (Supplementary Table S1). One of these was attributed to tracer injection problems (yellow data points in Figure 3B). Six of the 10 outliers (60%) were BALB/c mice. This strain was represented by only 17 (25%) of the 68 mouse scans in the training data. It is well known that tracer kinetics and glucose metabolism can vary significantly between different mouse strains, especially for diseased strains (40, 41). Based on the unbalanced number of samples from the two strains, we hypothesize that the DLIF model is sensitive to differences in uptake pattern between different mouse strains, and thus is unable to learn the possible variations among the samples. Among the remaining 3 outliers, 2 mouse scans were attributed to significantly higher myocardium uptake, which could partly explain why the DLIF model was less accurate for these samples. The remaining outlier had an unusual positioning in the mouse bed with its spine being curled, and not elongated, as for most other mice, which could affect the DLIF model output (42). Also note that the small P-values found in Figure 3 (P<0.01) are expected for comparisons of large sample sizes (43).

The regional analysis indicated similar mean values for brain and myocardium tissues, with mean errors below 10 %, strong correlation (correlation coefficients: brain: 0.78, myocardium: 0.95), and non-significant differences between the influx rate constants derived using DLIF and reference IDIF as input function (Table 2 and Supplementary Figure S3). These findings were similar to our previously published MLDIF model for brain, where we reported correlation coefficients of 0.56 for brain, and 0.90 for myocardium, with average errors of 7% and 4%, respectively [Table 3 in (25)]. The MLDIF model, however, was based on extracted time-activity curves from 5 manually defined tissue regions (myocardium, brain, liver, muscle and brown fat) as model input. Although the results were similar when using DLIF instead of MLDIF, DLIF undoubtedly overcomes the time-consuming need for manual tissue region delineation in the input images. This removes potential bias in the delineation step, and significantly simplifies the processing pipeline, as well as shortens the application time required to use the DLIF model.

The DLIF model, was trained with reference IDIF data targets due to the limited availability of high quality and high quantity small animal PET datasets with ground truth arterial blood sampling. To investigate the potential application of DLIF to predict a useful blood input function, we performed model training on the full 68 mouse scan dataset with IDIF targets, and subsequently evaluated the performance on the external UdS dataset, which contained continuous arterial blood samples as ground truth. The predicted DLIF curves were in good agreement with the ground truth AIF for some mouse scans in the UdS dataset (Figure 5), while there were larger discrepancies for others (Supplementary Figure S1). In general, the tail of the DLIF prediction was in better agreement compared to the peak. This discrepancy could be explained by a larger variation in the peak region for the UdS data (Figure 6A). There were several systematic differences in the data collection methodology between the UiT training data and the UdS test data, which could explain these deviations. Most importantly, the UdS mice were not fasted before the experiments, which is reflected in the slightly higher blood glucose values of the UdS data. It is well known that fasting affects the glucose metabolism in mice, and contributes to reducing the variability between samples (44–47), and specifically, myocardium uptake is affected by fasting, a region that we have shown is important for the prediction of the input function (25). Another difference between the studies was that the injection volume in the UdS data was not fixed. Four mice were injected using 100 μl, while four mice were injected with 200 μl. This volume difference could most likely introduce a variability in the peak of the input function, which was not accounted for in the training data used for the DLIF model. Also, for the UdS data, no attenuation or scatter correction was performed, because an associated CT scan was missing from the dataset. This could introduce underestimations of the measured activity concentration depending on tissue position (48), something which is not accounted for by the DLIF model. Lastly, the UdS test mice were of three different strains, and four of the mice could not be traced to a specific animal supplier, which could introduce additional bias in the data.

Despite these discrepancies, following Patlak modeling, the voxel-wise influx rate constants obtained using DLIF and reference AIF as input function for the UdS data showed an overall strong linear relationship and strong correlation (Figure 6B), even though systematic deviations are obvious for different mice. We found small but systematic underestimations of the slope coefficient for all BALB/c mice (n=3, average slope coefficient: 0.8), while the slope coefficients for C57/BL/6 (n=2, average slope coefficient: 1.4) and CD-1 (n=3, average slope coefficient: 1.5) were larger and systematically overestimated (Supplementary Table S2). While 17 (25%) of the 68 mouse scans used for training of the DLIF model were from the BALB/c strain, the C57/BL/6 and CD-1 strains were not represented among the training data. Similar to our discussion around Figure 3B, this further indicates that the DLIF model is sensitive to uptake patterns in mouse strains that were not part of the training data.

As evident from Figure 6A, the lower SUV values originating from the input function tail are closer to the identity line, compared to larger SUV values, belonging to the peak. The linear fit during Patlak graphical analysis is based on the steady state part following the input function peak (6). Although the integral of the full input function is present in the equation, the impact of the peak on the Ki is minimal, and consequently, this method is robust to noise and bias around the input function peak. This could explain why the Patlak Ki scatterplot (Figure 6B) still showed high correlation in the voxelwise analysis, despite the discrepancy of many of the peak regions (Supplementary Figure S1). The regional comparison of Ki calculated using reference AIF and DLIF (Table 2 and Supplementary Figure S2) indicated mean errors of 20% and −3% in Ki for brain and myocardium regions, respectively, with a strong correlation, and non-significant differences between the groups. These differences could be expected because of the mentioned differences between the UiT training data, and the UdS test data. Still, while DLIF-based calculation of Ki showed slightly larger errors for brain tissue, compared to IDIF, both results were non-significantly different from the influx derived with the AIF. For myocardium tissue, the average error in the DLIF-based calculation of Ki was similar to the error obtained during cross-validation experiments, while the corresponding error for the IDIF-based calculation was larger and significantly different from the AIF-based influx. Interestingly, although IDIF is a commonly used method for AIF estimation in the literature (16, 49), our results indicate that there might still be significant discrepancies between IDIF and AIF for myocardium tissues, which could be overcome by using the DLIF method. Again, we note that the small P-values found in Figure 6 (P<0.01) are expected for comparisons of large sample sizes (43). With all these mentioned limitations and differences between the UiT training data and the UdS test data, we argue that the DLIF model trained on IDIF reference targets still shows promising potential when compared to the external UdS data with reference AIF targets.

As depicted in Figures 3A and 6A, the DLIF model sometimes over- or underestimates the reference input function in early time frames, evident as vertical and horizontal data points around t=0, respectively. For these cases, we hypothesize that the DLIF model is unable to handle slight time-shifts in the input data. This will be investigated in future research. Our results furthermore indicate that the DLIF approach is sensitive to the specific mouse strain that it was trained on. Further prerequisites for the DLIF approach is that representative training data have been collected for the specific tracer, imaging system, and imaging protocol.

Although our work provided a comparison between DLIF and an AIF in the UdS test data, these findings must be further investigated in future research because of the large differences between the experimental methods in the UiT and UdS datasets. For instance, future work could include studying the dependency of the DLIF model to factors such as tracer, mouse strain, and variations in different experimental conditions and imaging protocols. Future research must also evaluate a DLIF model trained on a reference AIF measured in arterial blood.

The DLIF approach was in this work evaluated with [¹⁸F]FDG on a specific small animal PET imaging system. With further comprehensive validation, we suggest that the DLIF model could be retrained for other tracers and imaging systems. It is also conceivable that tracers requiring metabolite-correction may be modelled. DLIF could also have relevant applications in clinical human PET imaging (26). The accuracy of the DLIF models for a particular PET application will, in the end, depend on the quality, quantity and relevance of the available training data. Nevertheless, if properly validated, DLIF could provide a simplified, low-bias method for performing quantitative and longitudinal PET imaging studies in mice.

In conclusion, we demonstrated that our non-invasive DLIF prediction method may be a viable alternative to arterial blood sampling in [¹⁸F]FDG imaging of mice. The proposed approach does not require manual segmentation for model input, and it is not depending on a late calibration blood sample or any partial-volume correction. The resulting influx rate constants from Patlak modeling agreed well with image-derived reference values and promising agreement was obtained when comparing to data with continuous arterial blood sampling. With further validation, DLIF could overcome the need for arterial cannulation and allow fully quantitative and longitudinal experiments in PET imaging studies of mice.