Is Attention all You Need in Medical Image Analysis? A Review.

Medical imaging is a key component in clinical diagnosis, treatment planning and clinical trial design, accounting for almost 90% of all healthcare data. CNNs achieved performance gains in medical image analysis (MIA) over the last years. CNNs can efficiently model local pixel interactions and be trained on small-scale MI data. Despite their important advances, typical CNN have relatively limited capabilities in modelling "global" pixel interactions, which restricts their generalisation ability to understand out-of-distribution data with different "global" information. The recent progress of Artificial Intelligence gave rise to Transformers, which can learn global relationships from data. However, full Transformer models need to be trained on large-scale data and involve tremendous computational complexity. Attention and Transformer compartments ("Transf/Attention") which can well maintain properties for modelling global relationships, have been proposed as lighter alternatives of full Transformers. Recently, there is an increasing trend to co-pollinate complementary local-global properties from CNN and Transf/Attention architectures, which led to a new era of hybrid models. The past years have witnessed substantial growth in hybrid CNN-Transf/Attention models across diverse MIA problems. In this systematic review, we survey existing hybrid CNN-Transf/Attention models, review and unravel key architectural designs, analyse breakthroughs, and evaluate current and future opportunities as well as challenges. We also introduced an analysis framework on generalisation opportunities of scientific and clinical impact, based on which new data-driven domain generalisation and adaptation methods can be stimulated.

Large-scale deep learning analysis to identify adult patients at risk for combined and common variable immunodeficiencies.

BACKGROUND: Primary immunodeficiency (PI) is a group of heterogeneous disorders resulting from immune system defects. Over 70% of PI is undiagnosed, leading to increased mortality, co-morbidity and healthcare costs. Among PI disorders, combined immunodeficiencies (CID) are characterized by complex immune defects. Common variable immunodeficiency (CVID) is among the most common types of PI. In light of available treatments, it is critical to identify adult patients at risk for CID and CVID, before the development of serious morbidity and mortality. METHODS: We developed a deep learning-based method (named "TabMLPNet") to analyze clinical history from nationally representative medical claims from electronic health records (Optum® data, covering all US), evaluated in the setting of identifying CID/CVID in adults. Further, we revealed the most important CID/CVID-associated antecedent phenotype combinations. Four large cohorts were generated: a total of 47,660 PI cases and (1:1 matched) controls. RESULTS: The sensitivity/specificity of TabMLPNet modeling ranges from 0.82-0.88/0.82-0.85 across cohorts. Distinctive combinations of antecedent phenotypes associated with CID/CVID are identified, consisting of respiratory infections/conditions, genetic anomalies, cardiac defects, autoimmune diseases, blood disorders and malignancies, which can possibly be useful to systematize the identification of CID and CVID. CONCLUSIONS: We demonstrated an accurate method in terms of CID and CVID detection evaluated on large-scale medical claims data. Our predictive scheme can potentially lead to the development of new clinical insights and expanded guidelines for identification of adult patients at risk for CID and CVID as well as be used to improve patient outcomes on population level.

Primary immunodeficiencies (PI) are disorders that weaken the immune system, increasing the incident of life-threatening infections, organ damage and the development of cancer and autoimmune diseases. Although PI is estimated to affect 1-2% of the global population, 70-90% of these patients remain undiagnosed. Many patients are diagnosed during adulthood, after other serious diseases have already developed. We developed a computational method to analyze the clinical history from a large group of people with and without PI. We focused on combined (CID) and common variable immunodeficiency (CVID), which are among the least studied and most common PI subtypes, respectively. We could identify people with CID or CVID and combinations of diseases and symptoms which could make it easier to identify CID or CVID. Our method could be used to more readily identify adults at risk of CID or CVID, enabling treatment to start earlier and their long-term health to be improved.

An Automated Deep Learning Approach for Spine Segmentation and Vertebrae Recognition Using Computed Tomography Images.

Spine image analysis is based on the accurate segmentation and vertebrae recognition of the spine. Several deep learning models have been proposed for spine segmentation and vertebrae recognition, but they are very computationally demanding. In this research, a novel deep learning model is introduced for spine segmentation and vertebrae recognition using CT images. The proposed model works in two steps: (1) A cascaded hierarchical atrous spatial pyramid pooling residual attention U-Net (CHASPPRAU-Net), which is a modified version of U-Net, is used for the segmentation of the spine. Cascaded spatial pyramid pooling layers, along with residual blocks, are used for feature extraction, while the attention module is used for focusing on regions of interest. (2) A 3D mobile residual U-Net (MRU-Net) is used for vertebrae recognition. MobileNetv2 includes residual and attention modules to accurately extract features from the axial, sagittal, and coronal views of 3D spine images. The features from these three views are concatenated to form a 3D feature map. After that, a 3D deep learning model is used for vertebrae recognition. The VerSe 20 and VerSe 19 datasets were used to validate the proposed model. The model achieved more accurate results in spine segmentation and vertebrae recognition than the state-of-the-art methods.

Digital Transformation of Cancer Care in the Era of Big Data, Artificial Intelligence and Data-Driven Interventions: Navigating the Field.

OBJECTIVES: To navigate the field of digital cancer care and define and discuss key aspects and applications of big data analytics, artificial intelligence (AI), and data-driven interventions. DATA SOURCES: Peer-reviewed scientific publications and expert opinion. CONCLUSION: The digital transformation of cancer care, enabled by big data analytics, AI, and data-driven interventions, presents a significant opportunity to revolutionize the field. An increased understanding of the lifecycle and ethics of data-driven interventions will enhance development of innovative and applicable products to advance digital cancer care services. IMPLICATIONS FOR NURSING PRACTICE: As digital technologies become integrated into cancer care, nurse practitioners and scientists will be required to increase their knowledge and skills to effectively use these tools to the patient's benefit. An enhanced understanding of the core concepts of AI and big data, confident use of digital health platforms, and ability to interpret the outputs of data-driven interventions are key competencies. Nurses in oncology will play a crucial role in patient education around big data and AI, with a focus on addressing any arising questions, concerns, or misconceptions to foster trust in these technologies. Successful integration of data-driven innovations into oncology nursing practice will empower practitioners to deliver more personalized, effective, and evidence-based care.

A likelihood-based particle imaging filter using prior information.

BACKGROUND: Particle imaging can increase precision in proton and ion therapy. Interactions with nuclei in the imaged object increase image noise and reduce image quality, especially for multinucleon ions that can fragment, such as helium. PURPOSE: This work proposes a particle imaging filter, referred to as the Prior Filter, based on using prior information in the form of an estimated relative stopping power (RSP) map and the principles of electromagnetic interaction, to identify particles that have undergone nuclear interaction. The particles identified as having undergone nuclear interactions are then excluded from the image reconstruction, reducing the image noise. METHODS: The Prior Filter uses Fermi-Eyges scattering and Tschalär straggling theories to determine the likelihood that a particle only interacts electromagnetically. A threshold is then set to reject those particles with a low likelihood. The filter was evaluated and compared with a filter that estimates this likelihood based on the measured distribution of energy and scattering angle within pixels, commonly implemented as the 3σ filter. Reconstructed radiographs from simulated data of a 20-cm water cylinder and an anthropomorphic chest phantom were generated with both protons and helium ions to assess the effect of the filters on noise reduction. The simulation also allowed assessment of secondary particle removal through the particle histories. Experimental data were acquired of the Catphan CTP 404 Sensitometry phantom using the U.S. proton CT (pCT) collaboration prototype scanner. The proton and helium images were filtered with both the prior filtering method and a state-of-the-art method including an implementation of the 3σ filter. For both cases, a dE-E telescope filter, designed for this type of detector, was also applied. RESULTS: The proton radiographs showed a small reduction in noise (1 mm of water-equivalent thickness [WET]) but a larger reduction in helium radiographs (up to 5-6 mm of WET) due to better secondary filtering. The proton and helium CT images reflected this, with similar noise at the center of the phantom (0.02 RSP) for the proton images and an RSP noise of 0.03 for the proposed filter and 0.06 for the 3σ filter in the helium images. Images reconstructed from data with a dose reduction, up to a factor of 9, maintained a lower noise level using the Prior Filter over the state-of-the-art filtering method. CONCLUSIONS: The proposed filter results in images with equal or reduced noise compared to those that have undergone a filtering method typical of current particle imaging studies. This work also demonstrates that the proposed filter maintains better performance against the state of the art with up to a nine-fold dose reduction.

Pilot study of optical coherence tomography angiography-derived microvascular metrics in hands and feet of healthy and diabetic people.

Optical coherence tomography angiography (OCTA) is a non-invasive, high-resolution imaging modality with growing application in dermatology and microvascular assessment. Accepted reference values for OCTA-derived microvascular parameters in skin do not yet exist but need to be established to drive OCTA into the clinic. In this pilot study, we assess a range of OCTA microvascular metrics at rest and after post-occlusive reactive hyperaemia (PORH) in the hands and feet of 52 healthy people and 11 people with well-controlled type 2 diabetes mellitus (T2DM). We calculate each metric, measure test-retest repeatability, and evaluate correlation with demographic risk factors. Our study delivers extremity-specific, age-dependent reference values and coefficients of repeatability of nine microvascular metrics at baseline and at the maximum of PORH. Significant differences are not seen for age-dependent microvascular metrics in hand, but they are present for several metrics in the foot. Significant differences are observed between hand and foot, both at baseline and maximum PORH, for most of the microvascular metrics with generally higher values in the hand. Despite a large variability over a range of individuals, as is expected based on heterogeneous ageing phenotypes of the population, the test-retest repeatability is 3.5% to 18% of the mean value for all metrics, which highlights the opportunities for OCTA-based studies in larger cohorts, for longitudinal monitoring, and for assessing the efficacy of interventions. Additionally, branchpoint density in the hand and foot and changes in vessel diameter in response to PORH stood out as good discriminators between healthy and T2DM groups, which indicates their potential value as biomarkers. This study, building on our previous work, represents a further step towards standardised OCTA in clinical practice and research.

Age-Dependent Decline in Common Femoral Artery Flow-Mediated Dilation and Wall Shear Stress in Healthy Subjects.

Femoral artery (FA) endothelial function is a promising biomarker of lower extremity vascular health for peripheral artery disease (PAD) prevention and treatment; however, the impact of age on FA endothelial function has not been reported in healthy adults. Therefore, we evaluated the reproducibility and acceptability of flow-mediated dilation (FMD) in the FA and brachial artery (BA) (n = 20) and performed cross-sectional FA- and BA-FMD measurements in healthy non-smokers aged 22−76 years (n = 50). FMD protocols demonstrated similar good reproducibility. Leg occlusion was deemed more uncomfortable than arm occlusion; thigh occlusion was less tolerated than forearm and calf occlusion. FA-FMD with calf occlusion was lower than BA-FMD (6.0 ± 1.1% vs 6.4 ± 1.3%, p = 0.030). Multivariate linear regression analysis indicated that age (−0.4%/decade) was a significant independent predictor of FA-FMD (R2 = 0.35, p = 0.002). The age-dependent decline in FMD did not significantly differ between FA and BA (pinteraction agexlocation = 0.388). In older participants, 40% of baseline FA wall shear stress (WSS) values were <5 dyne/cm2, which is regarded as pro-atherogenic. In conclusion, endothelial function declines similarly with age in the FA and the BA in healthy adults. The age-dependent FA enlargement results in a critical decrease in WSS that may explain part of the age-dependent predisposition for PAD.

Cocoa flavanol consumption improves lower extremity endothelial function in healthy individuals and people with type 2 diabetes.

Background: diabetes and age are major risk factors for the development of lower extremity peripheral artery disease (PAD). Cocoa flavanol (CF) consumption is associated with lower risk for PAD and improves brachial artery (BA) endothelial function. Objectives: to assess if femoral artery (FA) endothelial function and dermal microcirculation are impaired in individuals with type 2 diabetes mellitus (T2DM) and evaluate the acute effect of CF consumption on FA endothelial function. Methods: in a randomised, controlled, double-blind, cross-over study, 22 individuals (n = 11 healthy, n = 11 T2DM) without cardiovascular disease were recruited. Participants received either 1350 mg CF or placebo capsules on 2 separate days in random order. Endothelial function was measured as flow-mediated dilation (FMD) using ultrasound of the common FA and the BA before and 2 hours after interventions. The cutaneous microvasculature was assessed using optical coherence tomography angiography. Results: baseline FA-FMD and BA-FMD were significantly lower in T2DM (FA: 3.2 ± 1.1% [SD], BA: 4.8 ± 0.8%) compared to healthy (FA: 5.5 ± 0.7%, BA: 6.0 ± 0.8%); each p < 0.001. Whereas in healthy individuals FA-FMD did not significantly differ from BA-FMD (p = 0.144), FA-FMD was significantly lower than BA-FMD in T2DM (p = 0.003) indicating pronounced and additional endothelial dysfunction of lower limb arteries (FA-FMD/BA-FMD: 94 ± 14% [healthy] vs. 68 ± 22% [T2DM], p = 0.007). The baseline FA blood flow rate (0.42 ± 0.23 vs. 0.73 ± 0.35 l min-1, p = 0.037) and microvascular dilation in response to occlusion in hands and feet were significantly lower in T2DM subjects than in healthy ones. CF increased both FA- and BA-FMD at 2 hours, compared to placebo, in both healthy and T2DM subgroups (FA-FMD effect: 2.9 ± 1.4%, BA-FMD effect 3.0 ± 3.5%, each pintervention< 0.001). In parallel, baseline FA blood flow and microvascular diameter significantly increased in feet (3.5 ± 3.5 µm, pintervention< 0.001) but not hands. Systolic blood pressure and pulse wave velocity significantly decreased after CF in both subgroups (-7.2 ± 9.6 mmHg, pintervention = 0.004; -1.3 ± 1.3 m s-1, pintervention = 0.002). Conclusions: individuals with T2DM exhibit decreased endothelial function that is more pronounced in the femoral than in the brachial artery. CFs increase endothelial function not only in the BA but also the FA both in healthy individuals and in those with T2DM who are at increased risk of developing lower extremity PAD and foot ulcers.

Discrete Shearlets as a Sparsifying Transform in Low-Rank Plus Sparse Decomposition for Undersampled (k, t)-Space MR Data.

The discrete shearlet transformation accurately represents the discontinuities and edges occurring in magnetic resonance imaging, providing an excellent option of a sparsifying transform. In the present paper, we examine the use of discrete shearlets over other sparsifying transforms in a low-rank plus sparse decomposition problem, denoted by L+S. The proposed algorithm is evaluated on simulated dynamic contrast enhanced (DCE) and small bowel data. For the small bowel, eight subjects were scanned; the sequence was run first on breath-holding and subsequently on free-breathing, without changing the anatomical position of the subject. The reconstruction performance of the proposed algorithm was evaluated against k-t FOCUSS. L+S decomposition, using discrete shearlets as sparsifying transforms, successfully separated the low-rank (background and periodic motion) from the sparse component (enhancement or bowel motility) for both DCE and small bowel data. Motion estimated from low-rank of DCE data is closer to ground truth deformations than motion estimated from L and S. Motility metrics derived from the S component of free-breathing data were not significantly different from the ones from breath-holding data up to four-fold undersampling, indicating that bowel (rapid/random) motility is isolated in S. Our work strongly supports the use of discrete shearlets as a sparsifying transform in a L+S decomposition for undersampled MR data.

A few-shot U-Net deep learning model for lung cancer lesion segmentation via PET/CT imaging.

Over the past few years, positron emission tomography/computed tomography (PET/CT) imaging for computer-aided diagnosis has received increasing attention. Supervised deep learning architectures are usually employed for the detection of abnormalities, with anatomical localization, especially in the case of CT scans. However, the main limitations of the supervised learning paradigm include (i) large amounts of data required for model training, and (ii) the assumption of fixed network weights upon training completion, implying that the performance of the model cannot be further improved after training. In order to overcome these limitations, we apply a few-shot learning (FSL) scheme. Contrary to traditional deep learning practices, in FSL the model is provided with less data during training. The model then utilizes end-user feedback after training to constantly improve its performance. We integrate FSL in a U-Net architecture for lung cancer lesion segmentation on PET/CT scans, allowing for dynamic model weight fine-tuning and resulting in an online supervised learning scheme. Constant online readjustments of the model weights according to the users' feedback, increase the detection and classification accuracy, especially in cases where low detection performance is encountered. Our proposed method is validated on the Lung-PET-CT-DX TCIA database. PET/CT scans from 87 patients were included in the dataset and were acquired 60 minutes after intravenous18F-FDG injection. Experimental results indicate the superiority of our approach compared to other state-of-the-art methods.

OCTAVA: An open-source toolbox for quantitative analysis of optical coherence tomography angiography images.

Optical coherence tomography angiography (OCTA) performs non-invasive visualization and characterization of microvasculature in research and clinical applications mainly in ophthalmology and dermatology. A wide variety of instruments, imaging protocols, processing methods and metrics have been used to describe the microvasculature, such that comparing different study outcomes is currently not feasible. With the goal of contributing to standardization of OCTA data analysis, we report a user-friendly, open-source toolbox, OCTAVA (OCTA Vascular Analyzer), to automate the pre-processing, segmentation, and quantitative analysis of en face OCTA maximum intensity projection images in a standardized workflow. We present each analysis step, including optimization of filtering and choice of segmentation algorithm, and definition of metrics. We perform quantitative analysis of OCTA images from different commercial and non-commercial instruments and samples and show OCTAVA can accurately and reproducibly determine metrics for characterization of microvasculature. Wide adoption could enable studies and aggregation of data on a scale sufficient to develop reliable microvascular biomarkers for early detection, and to guide treatment, of microvascular disease.

Utility of diffusion MRI characteristics of cervical lymph nodes as disease classifier between patients with head and neck squamous cell carcinoma and healthy volunteers.

Diffusion MRI characteristics assessed by apparent diffusion coefficient (ADC) histogram analysis in head and neck squamous cell carcinoma (HNSCC) have been reported as helpful in classifying tumours based on diffusion characteristics. There is little reported on HNSCC lymph nodes classification by diffusion characteristics. The aim of this study was to determine whether pretreatment nodal microstructural diffusion MRI characteristics can classify diseased nodes of patients with HNSCC from normal nodes of healthy volunteers. Seventy-nine patients with histologically confirmed HNSCC prior to chemoradiotherapy, and eight healthy volunteers, underwent diffusion-weighted (DW) MRI at a 1.5-T MR scanner. Two radiologists contoured lymph nodes on DW (b = 300 s/m2 ) images. ADC, distributed diffusion coefficient (DDC) and alpha (α) values were calculated by monoexponential and stretched exponential models. Histogram analysis metrics of drawn volume were compared between patients and volunteers using a Mann-Whitney test. The classification performance of each metric between the normal and diseased nodes was determined by receiver operating characteristic (ROC) analysis. Intraclass correlation coefficients determined interobserver reproducibility of each metric based on differently drawn ROIs by two radiologists. Sixty cancerous and 40 normal nodes were analysed. ADC histogram analysis revealed significant differences between patients and volunteers (p ≤0.0001 to 0.0046), presenting ADC distributions that were more skewed (1.49 for patients, 1.03 for volunteers; p = 0.0114) and 'peaked' (6.82 for patients, 4.20 for volunteers; p = 0.0021) in patients. Maximum ADC values exhibited the highest area under the curve ([AUC] 0.892). Significant differences were revealed between patients and volunteers for DDC and α value histogram metrics (p ≤0.0001 to 0.0044); the highest AUC were exhibited by maximum DDC (0.772) and the 25th percentile α value (0.761). Interobserver repeatability was excellent for mean ADC (ICC = 0.88) and the 25th percentile α value (ICC = 0.78), but poor for all other metrics. These results suggest that pretreatment microstructural diffusion MRI characteristics in lymph nodes, assessed by ADC and α value histogram analysis, can identify nodal disease.

Quantification of T1, T2 relaxation times from Magnetic Resonance Fingerprinting radially undersampled data using analytical transformations.

Quantitative magnetic resonance imaging (MRI) estimates magnetic parameters related to tissue, such as T1, T2 relaxation times and proton density. MR fingerprinting (MRF) is a new concept that uses pseudo-random, incoherent measurements to create a unique fingerprint for each tissue type to quantify magnet parameters. This paper aims to enhance MRF performance by investigating (i) the most suitable acquisition trajectory, and (ii) analytical transformations, suitable for radial acquisitions. Highly undersampled MRF brain (k, t)-space data have been simulated and non-linearly reconstructed to exploit the low-rank property of dynamic imaging. Based on our findings, the radial trajectory is the most suitable for MRF compared to Cartesian and spiral acquisitions. Perhaps this is due to the fact that its aliasing artifacts are more noise-like, and that unlike spiral trajectories, it can use analytical transformations that do not require re-gridding. One such analytical algorithm is the spline reconstruction technique (SRT) that is based on a novel numerical implementation of an analytic representation of the inverse Radon transform. Here, for the first time, this algorithm is applied to MR radial data. Reconstructions using SRT were compared to the ones using filtered back-projection. SRT provided images of higher contrast, lower bias, which resulted in more accurate T1, T2 values.

Machine learning for proton path tracking in proton computed tomography.

A Machine Learning approach to the problem of calculating the proton paths inside a scanned object in proton Computed Tomography is presented. The method is developed in order to mitigate the loss in both spatial resolution and quantitative integrity of the reconstructed images caused by multiple Coulomb scattering of protons traversing the matter. Two Machine Learning models were used: a forward neural network (NN) and the XGBoost method. A heuristic approach, based on track averaging was also implemented in order to evaluate the accuracy limits on track calculation, imposed by the statistical nature of the scattering. Synthetic data from anthropomorphic voxelized phantoms, generated by the Monte Carlo (MC) Geant4 code, were utilized to train the models and evaluate their accuracy, in comparison to a widely used analytical method that is based on likelihood maximization and Fermi-Eyges scattering model. Both NN and XGBoost model were found to perform very close or at the accuracy limit, further improving the accuracy of the analytical method (by 12% in the typical case of 200 MeV protons on 20 cm of water object), especially for protons scattered at large angles. Inclusion of the material information along the path in terms of radiation length did not show improvement in accuracy for the phantoms simulated in the study. A NN was also constructed to predict the error in path calculation, thus enabling a criterion to filter out proton events that may have a negative effect on the quality of the reconstructed image. By parametrizing a large set of synthetic data, the Machine Learning models were proved capable to bring-in an indirect and time efficient way-the accuracy of the MC method into the problem of proton tracking.

Statistical limitations in ion imaging.

In this study, we investigated the capacity of various ion beams available for radiotherapy to produce high quality relative stopping power map acquired from energy-loss measurements. The image quality metrics chosen to compare the different ions were signal-to-noise ratio (SNR) as a function of dose and spatial resolution. Geant4 Monte Carlo simulations were performed for: hydrogen, helium, lithium, boron and carbon ion beams crossing a 20 cm diameter water phantom to determine SNR and spatial resolution. It has been found that protons possess a significantly larger SNR when compared with other ions at a fixed range (up to 36% higher than helium) due to the proton nuclear stability and low dose per primary. However, it also yields the lowest spatial resolution against all other ions, with a resolution lowered by a factor 4 compared to that of carbon imaging, for a beam with the same initial range. When comparing for a fixed spatial resolution of 10 lp cm-1, carbon ions produce the highest image quality metrics with proton ions producing the lowest. In conclusion, it has been found that no ion can maximize all image quality metrics simultaneously and that a choice must be made between spatial resolution, SNR, and dose.

Deep learning magnetic resonance spectroscopy fingerprints of brain tumours using quantum mechanically synthesised data.

Metabolic fingerprints are valuable biomarkers for diseases that are associated with metabolic disorders. 1H magnetic resonance spectroscopy (MRS) is a unique noninvasive diagnostic tool that can depict the metabolic fingerprint based solely on the proton signal of different molecules present in the tissue. However, its performance is severely hindered by low SNR, field inhomogeneities and overlapping spectra of metabolites, which affect the quantification of metabolites. Consequently, MRS is rarely included in routine clinical protocols and has not been proven in multi-institutional trials. This work proposes an alternative approach, where instead of quantifying metabolites' concentration, deep learning (DL) is used to model the complex nonlinear relationship between diseases and their spectroscopic metabolic fingerprint (pattern). DL requires large training datasets, acquired (ideally) with the same protocol/scanner, which are very rarely available. To overcome this limitation, a novel method is proposed that can quantum mechanically synthesise MRS data for any scanner/acquisition protocol. The proposed methodology is applied to the challenging clinical problem of differentiating metastasis from glioblastoma brain tumours on data acquired across multiple institutions. DL algorithms were trained on the augmented synthetic spectra and tested on two independent datasets acquired by different scanners, achieving a receiver operating characteristic area under the curve of up to 0.96 and 0.97, respectively.

Covid-19: predictive mathematical formulae for the number of deaths during lockdown and possible scenarios for the post-lockdown period.

In a recent article, we introduced two novel mathematical expressions and a deep learning algorithm for characterizing the dynamics of the number of reported infected cases with SARS-CoV-2. Here, we show that such formulae can also be used for determining the time evolution of the associated number of deaths: for the epidemics in Spain, Germany, Italy and the UK, the parameters defining these formulae were computed using data up to 1 May 2020, a period of lockdown for these countries; then, the predictions of the formulae were compared with the data for the following 122 days, namely until 1 September. These comparisons, in addition to demonstrating the remarkable predictive capacity of our simple formulae, also show that for a rather long time the easing of the lockdown measures did not affect the number of deaths. The importance of these results regarding predictions of the number of Covid-19 deaths during the post-lockdown period is discussed.

Molière maximum likelihood proton path estimation approximated by cubic Bézier curve for scatter corrected proton CT reconstruction.

A maximum likelihood approach to the problem of calculating the proton paths inside the scanned object in proton computed tomography is presented. Molière theory is used for the first time to derive a physical model that describes proton multiple Coulomb scattering, avoiding the need for the Gaussian approximation currently used. To enable this, the proposed method approximates proton paths with cubic Bézier curves and subsequently maximizes the path likelihood through parametric optimization, based on the Molière model. Results from the Highland formula-based Gaussian approximation are also presented for comparison. The simplex method is utilized for optimisation. The scattering properties of the material(s) of the scanned object are taken into account by appropriately calculating the scattering parameters from the stopping power map that is calculated/updated at every iteration of the algebraic reconstruction process. Proton track length constraint imposed by the proton energy loss is accounted for. The method is also applied in the case that no exit angle data are measured. Geant4 Monte Carlo simulations were performed for model validation. Our results show that use of Molière probability density function for modelling the multiple Coulomb scattering presents a modest 2% accuracy improvement over the Gaussian approximation and most-likely-path method. Simulations of voxelized phantom showed no essential benefit from the inclusion of the material information into the optimization, while path optimization with energy constraint slightly increased path resolution in a bone/water interface phantom. Method error was found to depend on energy, proton track-length within the medium, and proportion of data filtering.

Stochastic Gradient Langevin dynamics for joint parameterization of tracer kinetic models, input functions, and T1 relaxation-times from undersampled k-space DCE-MRI.

Dynamic Contrast Enhanced (DCE) Magnetic Resonance Imaging (MRI) is an important diagnostic technique that can quantify the structure and function of microvasculature processes, using T1 relaxation times and tracer kinetic maps. However, a series of methodological limitations affect both the accuracy and standardisation of the quantified maps, and consequently their diagnostic ability. The main methodological challenge in the quantification of tracer kinetics is a multi-parameter optimization, with correlated parameters that have different scales, which results in local minima particularly when measurements are highly undersampled. This work suggests a novel data driven optimization scheme, based on a variation of the Stochastic Gradient Langevin dynamics (SGLD) Markov chain Monte Carlo algorithm, which combines stochastic gradient descent and Langevin dynamics. The proposed SGDL algorithm avoided local minima and accurately quantified proton density, T1 relaxation times and tracer kinetics. Joint direct parameterization significantly benefited the quantification of proton density, T1 relaxation times, and the selection of a suitable tracer kinetic model per tissue type. Model based arterial and portal vein input functions were automatically determined during the joint direct parameterization. Observations made on simulated fully and highly undersampled liver DCE MRI data were confirmed on acquired clinical data.

Statistical limitations in proton imaging.

Proton imaging is a promising technology for proton radiotherapy as it can be used for: (1) direct sampling of the tissue stopping power, (2) input information for multi-modality RSP reconstruction, (3) gold-standard calibration against concurrent techniques, (4) tracking motion and (5) pre-treatment positioning. However, no end-to-end characterization of the image quality (signal-to-noise ratio and spatial resolution, blurring uncertainty) against the dose has been done. This work aims to establish a model relating these characteristics and to describe their relationship with proton energy and object size. The imaging noise originates from two processes: the Coulomb scattering with the nucleus, producing a path deviation, and the energy loss straggling with electrons. The noise is found to increases with thickness crossed and, independently, decreases with decreasing energy. The scattering noise is dominant around high-gradient edge whereas the straggling noise is maximal in homogeneous regions. Image quality metrics are found to behave oppositely against energy: lower energy minimizes both the noise and the spatial resolution, with the optimal energy choice depending on the application and location in the imaged object. In conclusion, the model presented will help define an optimal usage of proton imaging to reach the promised application of this technology and establish a fair comparison with other imaging techniques.