Leveraging radiomics and machine learning to differentiate radiation necrosis from recurrence in patients with brain metastases.

OBJECTIVE: Radiation necrosis (RN) can be difficult to radiographically discern from tumor progression after stereotactic radiosurgery (SRS). The objective of this study was to investigate the utility of radiomics and machine learning (ML) to differentiate RN from recurrence in patients with brain metastases treated with SRS. METHODS: Patients with brain metastases treated with SRS who developed either RN or tumor reccurence were retrospectively identified. Image preprocessing and radiomic feature extraction were performed using ANTsPy and PyRadiomics, yielding 105 features from MRI T1-weighted post-contrast (T1c), T2, and fluid-attenuated inversion recovery (FLAIR) images. Univariate analysis assessed significance of individual features. Multivariable analysis employed various classifiers on features identified as most discriminative through feature selection. ML models were evaluated through cross-validation, selecting the best model based on area under the receiver operating characteristic (ROC) curve (AUC). Specificity, sensitivity, and F1 score were computed. RESULTS: Sixty-six lesions from 55 patients were identified. On univariate analysis, 27 features from the T1c sequence were statistically significant, while no features were significant from the T2 or FLAIR sequences. For clinical variables, only immunotherapy use after SRS was significant. Multivariable analysis of features from the T1c sequence yielded an AUC of 76.2% (standard deviation [SD] ± 12.7%), with specificity and sensitivity of 75.5% (± 13.4%) and 62.3% (± 19.6%) in differentiating radionecrosis from recurrence. CONCLUSIONS: Radiomics with ML may assist the diagnostic ability of distinguishing RN from tumor recurrence after SRS. Further work is needed to validate this in a larger multi-institutional cohort and prospectively evaluate it's utility in patient care.

Attenuation correction and truncation completion for breast PET/MR imaging using deep learning.

Objective. Simultaneous PET/MR scanners combine the high sensitivity of MR imaging with the functional imaging of PET. However, attenuation correction of breast PET/MR imaging is technically challenging. The purpose of this study is to establish a robust attenuation correction algorithm for breast PET/MR images that relies on deep learning (DL) to recreate the missing portions of the patient's anatomy (truncation completion), as well as to provide bone information for attenuation correction from only the PET data.Approach. Data acquired from 23 female subjects with invasive breast cancer scanned with18F-fluorodeoxyglucose PET/CT and PET/MR localized to the breast region were used for this study. Three DL models, U-Net with mean absolute error loss (DLMAE) model, U-Net with mean squared error loss (DLMSE) model, and U-Net with perceptual loss (DLPerceptual) model, were trained to predict synthetic CT images (sCT) for PET attenuation correction (AC) given non-attenuation corrected (NAC) PETPET/MRimages as inputs. The DL and Dixon-based sCT reconstructed PET images were compared against those reconstructed from CT images by calculating the percent error of the standardized uptake value (SUV) and conducting Wilcoxon signed rank statistical tests.Main results. sCT images from the DLMAEmodel, the DLMSEmodel, and the DLPerceptualmodel were similar in mean absolute error (MAE), peak-signal-to-noise ratio, and normalized cross-correlation. No significant difference in SUV was found between the PET images reconstructed using the DLMSEand DLPerceptualsCTs compared to the reference CT for AC in all tissue regions. All DL methods performed better than the Dixon-based method according to SUV analysis.Significance. A 3D U-Net with MSE or perceptual loss model can be implemented into a reconstruction workflow, and the derived sCT images allow successful truncation completion and attenuation correction for breast PET/MR images.

MRI radiomics for hamstring strain injury identification and return to sport classification: a pilot study.

OBJECTIVE: To determine if MRI-based radiomics from hamstring muscles are related to injury and if the features could be used to perform a time to return to sport (RTS) classification. We hypothesize that radiomics from hamstring muscles, especially T2-weighted and diffusion tensor imaging-based features, are related to injury and can be used for RTS classification. SUBJECTS AND METHODS: MRI data from 32 athletes at the University of Wisconsin-Madison that sustained a hamstring strain injury were collected. Diffusion tensor imaging and T1- and T2-weighted images were processed, and diffusion maps were calculated. Radiomics features were extracted from the four hamstring muscles in each limb and for each MRI modality, individually. Feature selection was performed and multiple support vector classifiers were cross-validated to differentiate between involved and uninvolved limbs and perform binary (≤ or > 25 days) and multiclass (< 14 vs. 14-42 vs. > 42 days) classification of RTS. RESULT: The combination of radiomics features from all diffusion tensor imaging and T2-weighted images provided the most accurate differentiation between involved and uninvolved limbs (AUC ≈ 0.84 ± 0.16). For the binary RTS classification, the combination of all extracted radiomics offered the most accurate classification (AUC ≈ 0.95 ± 0.15). While for the multiclass RTS classification, the combination of features from all the diffusion tensor imaging maps provided the most accurate classification (weighted one vs. rest AUC ≈ 0.81 ± 0.16). CONCLUSION: This pilot study demonstrated that radiomics features from hamstring muscles are related to injury and have the potential to predict RTS.

Vagus nerve stimulation in the non-human primate: implantation methodology, characterization of nerve anatomy, target engagement and experimental applications.

BACKGROUND: Vagus nerve stimulation (VNS) is a FDA approved therapy regularly used to treat a variety of neurological disorders that impact the central nervous system (CNS) including epilepsy and stroke. Putatively, the therapeutic efficacy of VNS results from its action on neuromodulatory centers via projections of the vagus nerve to the solitary tract nucleus. Currently, there is not an established large animal model that facilitates detailed mechanistic studies exploring how VNS impacts the function of the CNS, especially during complex behaviors requiring motor action and decision making. METHODS: We describe the anatomical organization, surgical methodology to implant VNS electrodes on the left gagus nerve and characterization of target engagement/neural interface properties in a non-human primate (NHP) model of VNS that permits chronic stimulation over long periods of time. Furthermore, we describe the results of pilot experiments in a small number of NHPs to demonstrate how this preparation might be used in an animal model capable of performing complex motor and decision making tasks. RESULTS: VNS electrode impedance remained constant over months suggesting a stable interface. VNS elicited robust activation of the vagus nerve which resulted in decreases of respiration rate and/or partial pressure of carbon dioxide in expired air, but not changes in heart rate in both awake and anesthetized NHPs. CONCLUSIONS: We anticipate that this preparation will be very useful to study the mechanisms underlying the effects of VNS for the treatment of conditions such as epilepsy and depression, for which VNS is extensively used, as well as for the study of the neurobiological basis underlying higher order functions such as learning and memory.

Next-Generation Cancer Magnetic Resonance Imaging With Tumor-Targeted Alkylphosphocholine Metal Analogs.

OBJECTIVES: In an effort to exploit the elevated need for phospholipids displayed by cancer cells relative to normal cells, we have developed tumor-targeted alkylphosphocholines (APCs) as broad-spectrum cancer imaging and therapy agents. Radioactive APC analogs have exhibited selective uptake and prolonged tumor retention in over 50 cancer types in preclinical models, as well as over 15 cancer types in over a dozen clinical trials. To push the structural limits of this platform, we recently added a chelating moiety capable of binding gadolinium and many other metals for cancer-targeted magnetic resonance imaging (MRI), positron emission tomography imaging, and targeted radionuclide therapy. The aim of this work was to synthesize, characterize, and validate the tumor selectivity of a new broad-spectrum, tumor-targeted, macrocyclic MRI chelate, Gd-NM600, in xenograft and orthotopic tumor models. A secondary aim was to identify and track the in vivo chemical speciation and spatial localization of this new chelate Gd-NM600 in order to assess its Gd deposition properties. MATERIALS AND METHODS: T1 relaxivities of Gd-NM600 were characterized in water and plasma at 1.5 T and 3.0 T. Tumor uptake and subcellular localization studies were performed using transmission electron microscopy. We imaged 8 different preclinical models of human cancer over time and compared the T1-weighted imaging results to that of a commercial macrocyclic Gd chelate, Gd-DOTA. Finally, matrix-assisted laser desorption and ionization-mass spectrometry imaging was used to characterize and map the tissue distribution of the chemical species of Gd-NM600. RESULTS: Gd-NM600 exhibits high T1 relaxivity (approximately 16.4 s-1/mM at 1.5 T), excellent tumor uptake (3.95 %ID/g at 48 hours), prolonged tumor retention (7 days), and MRI conspicuity. Moreover, minimal tumor uptake saturability of Gd-NM600 was observed. Broad-spectrum tumor-specific uptake was demonstrated in 8 different human cancer models. Cancer cell uptake of Gd-NM600 via endosomal internalization and processing was revealed with transmission electron microscopy. Importantly, tissue mass spectrometry imaging successfully interrogated the spatial localization and chemical speciation of Gd compounds and also identified breakdown products of Gd species. CONCLUSIONS: We have introduced a new macrocyclic cancer-targeted Gd chelate that achieves broad-spectrum tumor uptake and prolonged retention. Furthermore, we have demonstrated in vivo stability of Gd-NM600 by ultrahigh resolution MS tissue imaging. A tumor-targeted contrast agent coupled with the enhanced imaging resolution of MRI relative to positron emission tomography may transform oncologic imaging.

[68 Ga]Ga-FAPI-46 PET for non-invasive detection of pulmonary fibrosis disease activity.

PURPOSE: The lack of effective molecular biomarkers to monitor idiopathic pulmonary fibrosis (IPF) activity or treatment response remains an unmet clinical need. Herein, we determined the utility of fibroblast activation protein inhibitor for positron emission tomography (FAPI PET) imaging in a mouse model of pulmonary fibrosis. METHODS: Pulmonary fibrosis was induced by intratracheal administration of bleomycin (1 U/kg) while intratracheal saline was administered to control mice. Subgroups from each cohort (n = 3-5) underwent dynamic 1 h PET/CT after intravenously injecting FAPI-46 radiolabeled with gallium-68 ([68 Ga]Ga-FAPI-46) at 7 days and 14 days following disease induction. Animals were sacrificed following imaging for ex vivo gamma counting and histologic correlation. [68 Ga]Ga-FAPI-46 uptake was quantified and reported as percent injected activity per cc (%IA/cc) or percent injected activity (%IA). Lung CT density in Hounsfield units (HU) was also correlated with histologic examinations of lung fibrosis. RESULTS: CT only detected differences in the fibrotic response at 14 days post-bleomycin administration. [68 Ga]Ga-FAPI-46 lung uptake was significantly higher in the bleomycin group than in control subjects at 7 days and 14 days. Significantly (P = 0.0012) increased [68 Ga]Ga-FAPI-46 lung uptake in the bleomycin groups at 14 days (1.01 ± 0.12%IA/cc) vs. 7 days (0.33 ± 0.09%IA/cc) at 60 min post-injection of the tracer was observed. These findings were consistent with an increase in both fibrinogenesis and FAP expression as seen in histology. CONCLUSION: CT was unable to assess disease activity in a murine model of IPF. Conversely, FAPI PET detected both the presence and activity of lung fibrogenesis, making it a promising tool for assessing early disease activity and evaluating the efficacy of therapeutic interventions in lung fibrosis patients.

Gadolinium-based contrast agent attenuation does not impact PET quantification in simultaneous dynamic contrast enhanced breast PET/MR.

PURPOSE: Simultaneous PET/MR imaging involves injection of a radiopharmaceutical and often also includes administration of a gadolinium-based contrast agent (GBCA). Phantom model studies indicate that attenuation of annihilation photons by GBCAs does not bias quantification metrics of PET radiopharmaceutical uptake. However, a direct comparison of attenuation-corrected PET values before and after administration of GBCA has not been performed in patients imaged with simultaneous dynamic PET/MR. The purpose of this study was to investigate the attenuating effect of GBCAs on standardized uptake value (SUV) quantification of 18 F-fluorodeoxyglucose (FDG) uptake in invasive breast cancer and normal tissues using simultaneous PET/MR. METHODS: The study included 13 women with newly diagnosed invasive breast cancer imaged using simultaneous dedicated prone breast PET/MR with FDG. PET data collection and two-point Dixon-based MR attenuation correction sequences began simultaneously before the administration of GBCA to avoid a potential impact of GBCA on the attenuation correction map. A standard clinical dose of GBCA was intravenously administered for the dynamic contrast enhanced MR sequences obtained during the simultaneous PET data acquisition. PET data were dynamically reconstructed into 60 frames of 30 s each. Three timing windows were chosen consisting of a single frame (30 s), two frames (60 s), or four frames (120 s) immediately before and after contrast administration. SUVmax and SUVmean of the biopsy-proven breast malignancy, fibroglandular tissue of the contralateral normal breast, descending aorta, and liver were calculated prior to and following GBCA administration. Percent change in the SUV metrics were calculated to test for a statistically significant, non-zero percent change using Wilcoxon signed-rank tests. RESULTS: No statistical change in SUVmax or SUVmean was found for the breast malignancies or normal anatomical regions during the timing windows before and after GBCA administration. CONCLUSIONS: GBCAs do not significantly impact the results of PET quantification by means of additional attenuation. However, GBCAs may still affect quantification by affecting MR acquisitions used for MR-based attenuation correction which this study did not address. Corrections to account for attenuation due to clinical concentrations of GBCAs are not necessary in simultaneous PET/MR examinations when MR-based attenuation correction sequences are performed prior to GBCA administration.

Evaluation of Data-Driven Rigid Motion Correction in Clinical Brain PET Imaging.

Head motion during brain PET imaging can significantly degrade the quality of the reconstructed image, leading to reduced diagnostic value and inaccurate quantitation. A fully data-driven motion correction approach was recently demonstrated to produce highly accurate motion estimates (<1 mm) with high temporal resolution (≥1 Hz), which can then be used for a motion-corrected reconstruction. This can be applied retrospectively with no impact on the clinical image acquisition protocol. We present a reader-based evaluation and an atlas-based quantitative analysis of this motion correction approach within a clinical cohort. Methods: Clinical patient data were collected over 2019-2020 and processed retrospectively. Motion was estimated using image-based registration on reconstructions of ultrashort frames (0.6-1.8 s), after which list-mode reconstructions that were fully motion-corrected were performed. Two readers graded the motion-corrected and uncorrected reconstructions. An atlas-based quantitative analysis was performed. Paired Wilcoxon tests were used to test for significant differences in reader scores and SUVs between reconstructions. The Levene test was used to determine whether motion correction had a greater impact on quantitation in the presence of motion than when motion was low. Results: Fifty standard clinical 18F-FDG brain PET datasets (age range, 13-83 y; mean ± SD, 59 ± 20 y; 27 women) from 3 scanners were collected. The reader study showed a significantly different, diagnostically relevant improvement by motion correction when motion was present (P = 0.02) and no impact in low-motion cases. Eight percent of all datasets improved from diagnostically unacceptable to acceptable. The atlas-based analysis demonstrated a significant difference between the motion-corrected and uncorrected reconstructions in cases of high motion for 7 of 8 regions of interest (P < 0.05). Conclusion: The proposed approach to data-driven motion estimation and correction demonstrated a clinically significant impact on brain PET image reconstruction.

18F-SynVesT-1 PET/MR Imaging of the Effect of Gut Microbiota on Synaptic Density and Neurite Microstructure: A Preclinical Pilot Study.

The gut microbiome profoundly influences brain structure and function. The gut microbiome is hypothesized to play a key role in the etiopathogenesis of neuropsychiatric and neurodegenerative illness; however, the contribution of an intact gut microbiome to quantitative neuroimaging parameters of brain microstructure and function remains unknown. Herein, we report the broad and significant influence of a functional gut microbiome on commonly employed neuroimaging measures of diffusion tensor imaging (DTI), neurite orientation dispersion and density (NODDI) imaging, and SV2A 18F-SynVesT-1 synaptic density PET imaging when compared to germ-free animals. In this pilot study, we demonstrate that mice, in the presence of a functional gut microbiome, possess higher neurite density and orientation dispersion and decreased synaptic density when compared to age- and sex-matched germ-free mice. Our results reveal the region-specific structural influences and synaptic changes in the brain arising from the presence of intestinal microbiota. Further, our study highlights important considerations for the development of quantitative neuroimaging biomarkers for precision imaging in neurologic and psychiatric illness.

PET/MR imaging in gynecologic cancer: tips for differentiating normal gynecologic anatomy and benign pathology versus cancer.

Positron emission tomography/magnetic resonance imaging (PET/MR) is used in the pre-treatment and surveillance settings to evaluate women with gynecologic malignancies, including uterine, cervical, vaginal and vulvar cancers. PET/MR combines the excellent spatial and contrast resolution of MR imaging for gynecologic tissues, with the functional metabolic information of PET, to aid in a more accurate assessment of local disease extent and distant metastatic disease. In this review, the optimal protocol and utility of whole-body PET/MR imaging in patients with gynecologic malignancies will be discussed, with an emphasis on the advantages of PET/MR over PET/CT and how to differentiate normal or benign gynecologic tissues from cancer in the pelvis.

Synthetic Computed Tomography Generation from 0.35T Magnetic Resonance Images for Magnetic Resonance-Only Radiation Therapy Planning Using Perceptual Loss Models.

PURPOSE: Magnetic resonance imaging (MRI) provides excellent soft-tissue contrast, which makes it useful for delineating tumor and normal structures in radiation therapy planning, but MRI cannot readily provide electron density for dose calculation. Computed tomography (CT) is used but introduces registration uncertainty between MRI and CT. Previous studies have shown that synthetic CTs (sCTs) can be generated directly from MRI images with deep learning methods. However, mainly high-field MRI images have been validated. This study tested whether acceptable sCTs for MR-only radiation therapy planning can be synthesized using an integrated MR-guided linear accelerator at 0.35T, using MRI images and treatment plans in the liver region. METHODS AND MATERIALS: Two models were investigated in this study: a convolutional neural network (Unet) with conventional mean square error (MSE) loss and a Unet using a secondary convolutional neural network for perceptual loss. A total of 37 cases were used in this study with 10-fold cross validation, and 37 treatment plans were generated and evaluated for target coverage and dose to organs at risk (OARs) in the MSE loss model, perceptual loss model, and original CT. RESULTS: The sCTs predicted by the perceptual loss model had improved subjective visual quality compared with those predicted by the MSE loss model, but both were similar in mean absolute error (MAE), peak-signal-to-noise ratio (PSNR), and normalized cross-correlation (NCC). The MAE, PSNR, and NCC for the perceptual loss model were 35.64, 24.11, and 0.9539, respectively, and those for the MSE loss model were 35.67, 24.36, and 0.9566, respectively. No significant differences in target coverage and dose to OARs were found between the sCT predicted by the perceptual loss model or by the MSE model and the original CT image. CONCLUSIONS: This study indicated that a Unet with both MSE loss and perceptual loss models can be used for generating sCT images from a 0.35T integrated MR linear accelerator.

A Path to Qualification of PET/MRI Scanners for Multicenter Brain Imaging Studies: Evaluation of MRI-Based Attenuation Correction Methods Using a Patient Phantom.

PET/MRI scanners cannot be qualified in the manner adopted for hybrid PET/CT devices. The main hurdle with qualification in PET/MRI is that attenuation correction (AC) cannot be adequately measured in conventional PET phantoms because of the difficulty in converting the MR images of the physical structures (e.g., plastic) into electron density maps. Over the last decade, a plethora of novel MRI-based algorithms has been developed to more accurately derive the attenuation properties of the human head, including the skull. Although promising, none of these techniques has yet emerged as an optimal and universally adopted strategy for AC in PET/MRI. In this work, we propose a path for PET/MRI qualification for multicenter brain imaging studies. Specifically, our solution is to separate the head AC from the other factors that affect PET data quantification and use a patient as a phantom to assess the former. The emission data collected on the integrated PET/MRI scanner to be qualified should be reconstructed using both MRI- and CT-based AC methods, and whole-brain qualitative and quantitative (both voxelwise and regional) analyses should be performed. The MRI-based approach will be considered satisfactory if the PET quantification bias is within the acceptance criteria specified here. We have implemented this approach successfully across 2 PET/MRI scanner manufacturers at 2 sites.

Robustifying Deep Networks for Medical Image Segmentation.

The purpose of this study is to investigate the robustness of a commonly used convolutional neural network for image segmentation with respect to nearly unnoticeable adversarial perturbations, and suggest new methods to make these networks more robust to such perturbations. In this retrospective study, the accuracy of brain tumor segmentation was studied in subjects with low- and high-grade gliomas. Two representative UNets were implemented to segment four different MR series (T1-weighted, post-contrast T1-weighted, T2-weighted, and T2-weighted FLAIR) into four pixelwise labels (Gd-enhancing tumor, peritumoral edema, necrotic and non-enhancing tumor, and background). We developed attack strategies based on the fast gradient sign method (FGSM), iterative FGSM (i-FGSM), and targeted iterative FGSM (ti-FGSM) to produce effective but imperceptible attacks. Additionally, we explored the effectiveness of distillation and adversarial training via data augmentation to counteract these adversarial attacks. Robustness was measured by comparing the Dice coefficients for the attacks using Wilcoxon signed-rank tests. The experimental results show that attacks based on FGSM, i-FGSM, and ti-FGSM were effective in reducing the quality of image segmentation by up to 65% in the Dice coefficient. For attack defenses, distillation performed significantly better than adversarial training approaches. However, all defense approaches performed worse compared to unperturbed test images. Therefore, segmentation networks can be adversely affected by targeted attacks that introduce visually minor (and potentially undetectable) modifications to existing images. With an increasing interest in applying deep learning techniques to medical imaging data, it is important to quantify the ramifications of adversarial inputs (either intentional or unintentional).

Anatomy and Physiology of Artificial Intelligence in PET Imaging.

Artificial intelligence (AI) has seen an explosion in interest within nuclear medicine. This interest is driven by the rapid progress and eye-catching achievements of machine learning algorithms. The growing foothold of AI in molecular imaging is exposing nuclear medicine personnel to new technology and terminology. Clinicians and researchers can be easily overwhelmed by numerous architectures and algorithms that have been published. This article dissects the backbone of most AI algorithms: the convolutional neural network. The algorithm training workflow and the key ingredients and operations of a convolutional neural network are described in detail. Finally, the ubiquitous U-Net is explained step-by-step.

Artificial Intelligence-Based Data Corrections for Attenuation and Scatter in Position Emission Tomography and Single-Photon Emission Computed Tomography.

Recent developments in artificial intelligence (AI) technology have enabled new developments that can improve attenuation and scatter correction in PET and single-photon emission computed tomography (SPECT). These technologies will enable the use of accurate and quantitative imaging without the need to acquire a computed tomography image, greatly expanding the capability of PET/MR imaging, PET-only, and SPECT-only scanners. The use of AI to aid in scatter correction will lead to improvements in image reconstruction speed, and improve patient throughput. This article outlines the use of these new tools, surveys contemporary implementation, and discusses their limitations.

Initial Experience With Low-Dose 18F-Fluorodeoxyglucose Positron Emission Tomography/Magnetic Resonance Imaging With Deep Learning Enhancement.

OBJECTIVE: To demonstrate the utility of deep learning enhancement (DLE) to achieve diagnostic quality low-dose positron emission tomography (PET)/magnetic resonance (MR) imaging. METHODS: Twenty subjects with known Crohn disease underwent simultaneous PET/MR imaging after intravenous administration of approximately 185 MBq of 18F-fluorodeoxyglucose (FDG). Five image sets were generated: (1) standard-of-care (reference), (2) low-dose (ie, using 20% of PET counts), (3) DLE-enhanced low-dose using PET data as input, (4) DLE-enhanced low-dose using PET and MR data as input, and (5) DLE-enhanced using no PET data input. Image sets were evaluated by both quantitative metrics and qualitatively by expert readers. RESULTS: Although low-dose images (series 2) and images with no PET data input (series 5) were nondiagnostic, DLE of the low-dose images (series 3 and 4) achieved diagnostic quality images that scored more favorably than reference (series 1), both qualitatively and quantitatively. CONCLUSIONS: Deep learning enhancement has the potential to enable a 90% reduction of radiotracer while achieving diagnostic quality images.

Application and Construction of Deep Learning Networks in Medical Imaging.

Deep learning (DL) approaches are part of the machine learning (ML) subfield concerned with the development of computational models to train artificial intelligence systems. DL models are characterized by automatically extracting high-level features from the input data to learn the relationship between matching datasets. Thus, its implementation offers an advantage over common ML methods that often require the practitioner to have some domain knowledge of the input data to select the best latent representation. As a result of this advantage, DL has been successfully applied within the medical imaging field to address problems, such as disease classification and tumor segmentation for which it is difficult or impossible to determine which image features are relevant. Therefore, taking into consideration the positive impact of DL on the medical imaging field, this article reviews the key concepts associated with its evolution and implementation. The sections of this review summarize the milestones related to the development of the DL field, followed by a description of the elements of deep neural network and an overview of its application within the medical imaging field. Subsequently, the key steps necessary to implement a supervised DL application are defined, and associated limitations are discussed.