Diffusion weighted (DW) imaging is a non-invasive method that allows to reconstruct quantitative maps sensitive to the underlying architecture of the tissue: the microscopic random diffusion of water molecules is exploited to obtain information on the microstructure of the brain. Diffusion abnormalities can reflect, at the macroscopic level, changes in microscopic tissue organization (Le Bihan et al., 1991; Jones, 2011).

DW imaging has the major benefit of providing data that can be used to derive quantitative maps. From the simplest formalism used to describe water diffusion in tissue, i.e., the diffusion tensor (DT) (Basser et al., 1994; Pierpaoli et al., 1996), it is possible to calculate maps of fractional anisotropy (FA), an index that is highly sensitive to microstructural damage of brain tissue due to pathological processes (Alexander et al., 2007). Mathematically, 7 DW volumes must be acquired to fully characterize the DT: 6 DW measurements along noncollinear directions and 1 with no DW, i.e., b-value = 0 (Tournier et al., 2011). It has been noted that limiting the number of diffusion directions to 6 can introduce directional biases in DT metrics. Many studies have shown that to avoid this problem, it is necessary to increase the number of DW directions that also contribute to improving the signal-to-noise ratio of the obtained maps (Giannelli et al., 2010; Zhan et al., 2011; Lebel et al., 2012). However, increasing the number of acquired DW images inevitably increases acquisition times. Some studies, therefore, have investigated the possibility of reducing the number of DWs to obtain FA by deep learning (DL) methods (Li et al., 2019; Aliotta et al., 2021; Gaviraghi et al., 2022).

Aliotta et al. (2021) developed a specific network for assessing FA in gliomas, without testing it on other clinical datasets nor on datasets acquired on other scanners or with different acquisition protocols. Li et al. (2019) developed a network by training it only on healthy subjects and did not test it on clinical cases or on other datasets. In our previous work (Gaviraghi et al., 2022) we optimized a “one-minute FA” DL network, which has the architecture of a U-net (Ronneberger et al., 2015) and requires 10 DW input volumes to output the FA map. This network was able to give as output FA maps that retained the quality of the FA maps obtained with the high-resolution fully DW sampled human connectome project (HCP) data (which has 288 DW volumes) (Van Essen et al., 2012; WU-Minn Consortium Human Connectome Project, 2017) used for model training. Differently from the previously mentioned papers, we also tested the generalizability of the network and its sensitivity to pathology in independent temporal lobe epilepsy (TLE) and multiple sclerosis (MS) datasets, acquired with different protocols on different scanners, without the need for retraining.

Recent work such as that of Aliotta et al. (2021) reconstructed the FA map from 3 DW volumes plus one b-value equal to 0, but did not show whether such network can be applied to unseen data acquired with different protocols and in different pathological cases. Moreover, given that the DT needs 6 DW directions to be defined, one may question how generalized this method really is. A fundamental characteristic of our “one-minute FA” DL network was that it was generalizable, i.e., applicable to datasets other than the one used to train the network. By reducing to extreme situations the input DW volumes, here we wanted to assess whether it was possible to retain output quality, sensitivity to pathology and generalisability. Indeed, it is by ensuring preservation of this fundamental characteristic of a DL network, i.e., generalisability, where the network becomes applicable to other, unseen datasets, where clinical translation becomes possible.

For medical images, data fidelity is essential, indeed it is necessary to avoid that in the images reconstructed by the DL networks there are pathological characteristics in the absence of the pathology and, on the other hand, non-pathological characteristics where there is pathology (Gassenmaier et al., 2021). Therefore, the main aim of the present work was to determine the minimal number of DW volumes required to maintain the clinical sensitivity of the reconstructed FA maps, independently from the specific pathology. More in detail, our goal here was to obtain a network able to output an FA map with the lowest possible number of DW volumes required as input, but at the same time able to maintain the same characteristics of the ground truth (GT) FA calculated with all volumes. The overall objective was to find a compromise between reducing the acquisition time and maintaining the original characteristics of the FA maps in healthy and pathological test sets.

For each number of N DW inputs, FA was successfully obtained for all HCP subjects of the test dataset and for all subjects belonging to the TLE and MS datasets. Table 1 show three performance metrics (RMSE; MAE; SSIM) for each network, and for each dataset.

Figures 2–4 show plots for each experiment, i.e., with N = 4, 7 and 10 input DW volumes, respectively. In each figure, the first row refers to a representative HCP test subject, the second row to the TLE dataset and the last row to the MS dataset. Each figure for each dataset reports, from left to right, the histogram, heatscatter plot (single level analysis) and the boxplot (group level analysis), all reporting WM FA values obtained with each method. The statistically significant group differences are reported as asterisks (p < 0.05). The R² coefficients are shown in Table 2.

When using 4 DW volumes (Figure 2) as input to the network, it is possible to appreciate that for the HCP test subjects the FA maps have similar characteristics to those calculated with the STANDARD method using all volumes. Conversely, the TLE dataset shows that statistical significance is lost between HC and LTLE and between HC and RTLE when using the network FA. For the MS dataset, between group differences are maintained, but NAWM FA values calculated with the network are much lower than with the STANDARD method.

Similar considerations can be made for FA values obtained with the 7 DW network (Figure 3) where for the HCP test subjects, FA maps have comparable characteristics to those calculated with the STANDARD method using all DW volumes. In contrast, for the TLE dataset, the statistically significant difference between HC and LTLE WM FA mean values was not reached when using WM FA values obtained using the network. For the MS dataset, the statistically significant difference between the HC and CIS was not reached when using WM FA values from the network.

This behavior was not detected in the case of network FA values obtained when inputting 10 DW volumes to the network (Figure 4); indeed, for all three datasets FA maps displayed similar characteristics as the FA calculated with the STANDARD method using all volumes and the clinical dataset displayed the same statistically significant differences (p < 0.05) between groups when using either the STANDARD method WM FA or the network WM FA.

Considering the Bland–Altman plots for each dataset (Figures 5–7), by increasing the number of DW volumes from 4 to 10, the number of outliers decreases. The outliers are almost all distributed at the interface between white matter and gray matter or between white matter and cerebrospinal fluid (CSF).

As the number of input DW volumes decreased, performance worsened evaluated using each performance metric (Table 1). All networks (4 DW, 7 DW and 10 DW) performed well on the test HCP data demonstrating the ability of the network to learn the mapping between a very reduced DW input dataset and GT FA. Conversely, for the clinical datasets, the sensitivity to pathology was partially lost with extremely reduced input datasets to the networks, i.e., 4 and 7 DW volumes.

Indeed, when using the 4 DW network FA no statistical differences were detected between HC and TLE patients; statistically significant differences between HC and MS patients were still detected, but NAWM FA values were much lower than those calculated with the STANDARD method. Interestingly, the standard deviation of the network FA in the SPMS group was increased compared to the STANDARD one, possibly due to a greater level of tissue heterogeneity typical of this group, due to severe pathological damage, not fully captured by training the network on limited input volumes of healthy subjects. When using 7 DW input volumes to the network, a similar drawback was observed: indeed, in the TLE dataset, the network FA did not identify differences between HC and LTLE, and in the MS dataset, differences were not found between HC and CIS patients.

In the experiments with 4 and 7 DW input volumes, the same hyperparameters of the network calculated with 10 DW were used (Gaviraghi et al., 2022). The fact that the performance is excellent on the HCP test subjects suggests that retraining hyperparameters would not provide an improvement of performance on the validation of unseen clinical datasets.

On the other hand, when the network is trained on more than the minimum number of DW volumes required to define the diffusion tensor, clinical sensitivity is maintained as it was the case for the 10 DW network (our proposed “one-minute” FA network).

Varying the number of inputs volumes to 4 and 7 showed us how an extreme reduction of the input information passed to the network may affect the network capability of generalization. Our previously proposed “one-minute FA” network can, therefore, extract FA from a reduced set of 10 DW volumes, not only on test data with identical acquisition properties as the training data, but also on test data with different diffusion-encoding directions and, most importantly, on data acquired on different scanners, with different DW directions and different b-values (Gaviraghi et al., 2022).

The WM FA values obtained from the network, as can be seen from the boxplots, are always lower than in the standard method with all volumes, except in the case of the HCP test set. This could be due to the fact that only the HCP dataset was used for training the network, or it could be a partial volume effect with gray matter or even CSF due to the fact that the voxel size of the clinical datasets (> 2.2 mm) is larger than that of the HCP training data (1.25 mm) (hence reducing the number of voxel with high FA). Interestingly, our data shows that the number of outliers, i.e., the voxels that behave differently than the FA calculated with all data available, decreases as more DW volumes are used for the deep learning network. Moreover, the outliers seem to be distributed exactly in regions of greater partial volume effect (between WM and gray matter or CSF or between crossing fibers). This could be further tested by acquiring data with the same voxel resolution as the HCP data, but using a different scanner (Fujiwara et al., 2008).

In this work we did not change the resolution of the training dataset to match the clinical dataset because we wanted to assess whether the network could learn the non-linear relationship between the low and high quality scans and consequently be applied to any dataset, independently of the acquisition parameters, we believe that as FA is derived from the DT model, training the DL network on data with lower DW directions than the minimum required for its mathematical definition, it cannot capture in full signal changes caused by different underlying microstructure scenarios. Nevertheless, in future, to investigate how much the resolution impacts on the network’s performance, training could be performed again by resampling the diffusion images of the HCP dataset to different resolutions. In this way, it could be understood whether performance improves by training the network at the resolution of the clinical images.

In future work, different architectures could also be explored, such as CycleGAN (Zhu et al., 2017), to investigate whether the performance improves. In addition, as future work, the number of subjects used for training could be expanded, including also subjects with different pathologies to investigate whether the performance improves, without compromising generalizability.

In conclusion, here we investigated the dependency of DL network FA maps on the number of DW volumes used as input. With 4 or 7 DW volumes, clinical sensitivity of the network FA decreases compared to that of the GT FA. Reducing the data required as input to DL networks trained to obtain quantitative maps such as FA is an appealing proposal in term of scan time and cost/benefit evaluations, but reducing the input data to extreme cases can have a detrimental effect on obtaining a network capable of generalization. When developing DL methods for clinical adoption it is important to reach a good compromise between data acquisition time, generalizability, and clinical sensitivity of the network output.

The original contributions presented in this study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author.

The studies involving humans were approved by the University College London IRCCS Mondino Foundation. The studies were conducted in accordance with the local legislation and institutional requirements. The participants provided their written informed consent to participate in this study.

MG: Conceptualization, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing. AR: Conceptualization, Methodology, Writing – review & editing. FuP: Data curation, Resources, Writing – review & editing. WB: Data curation, Resources, Writing – review & editing. PV: Resources, Writing – review & editing. FeP: Conceptualization, Data curation, Writing – review & editing. BK: Conceptualization, Data curation, Supervision, Writing – review & editing. CGW-K: Conceptualization, Funding acquisition, Methodology, Resources, Supervision, Writing – original draft, Writing – review & editing.