SUMMARYHaemodynamical simulations using one-dimensional (1D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. Recent interest in verifying 1D numerical schemes has led to the development of alternative experimental setups and the use of threedimensional numerical models to acquire data not easily measured in vivo. In most studies to date, only one particular 1D scheme is tested. In this paper, we present a systematic comparison of six commonly used numerical schemes for 1D blood flow modelling: discontinuous Galerkin, locally conservative Galerkin, Galerkin least-squares finite element method, finite volume method, finite difference MacCormack method and a simplified trapezium rule method. Comparisons are made in a series of six benchmark test cases with an increasing degree of complexity. The accuracy of the numerical schemes is assessed by comparison with theoretical results, three-dimensional numerical data in compatible domains with distensible walls or experimental data in a network of silicone tubes. Results show a good agreement among all numerical schemes and their ability to capture the main features of pressure, flow and area waveforms in large arteries. All the information used in this study, including the input data for all benchmark cases, experimental data where available and numerical solutions for each scheme, is made publicly available online, providing a comprehensive reference data set to support the development of 1D models and numerical schemes.

Simulation platforms are increasingly becoming complementary tools for cutting-edge cardiovascular research. The interplay among structural properties of the arterial wall, morphometry, anatomy, wave propagation phenomena, and ultimately, cardiovascular diseases continues to be poorly understood. Accurate models are powerful tools to shed light on these open problems. We developed an anatomically detailed computational model of the arterial vasculature to conduct 1-D blood flow simulations to serve as simulation infrastructure to aid cardiovascular research. An average arterial vasculature of a man was outlined in 3-D space to serve as geometrical substrate for the mathematical model. The architecture of this model comprises almost every arterial vessel acknowledged in the medical/anatomical literature, with a resolution down to the luminal area of perforator arteries. Over 2000 arterial vessels compose the model. Anatomical, physiological, and mechanical considerations were employed for the set up of model parameters and to determine criteria for blood flow distribution. Computational fluid dynamics was used to simulate blood flow and wave propagation phenomena in such arterial network. A sensitivity analysis was developed to unveil the contributions of model parameters to the conformation of the pressure waveforms. In addition, parameters were modified to target model to a patient-specific scenario. On the light of the knowledge domain, we conclude that the present model features excellent descriptive and predictive capabilities in both patient-generic and patient-specific cases, presenting a new step toward integrating an unprecedented anatomical description, morphometric, and simulations data to help in understanding complex arterial blood flow phenomena and related cardiovascular diseases.

Development of blood flow distribution criteria is a mandatory step toward developing computational models and numerical simulations of the systemic circulation. In the present work, we (i) present a systematic approach based on anatomical and physiological considerations to distribute the blood flow in a 1D anatomically detailed model of the arterial network and (ii) develop a numerical procedure to calibrate resistive parameters in terminal models in order to effectively satisfy such flow distribution. For the first goal, we merge data collected from the specialized medical literature with anatomical concepts such as vascular territories to determine blood flow supply to specific (encephalon, kidneys, etc.) and distributed (muscles, skin, etc.) organs. Overall, 28 entities representing the main specific organs are accounted for in the detailed description of the arterial topology that we use as model substrate. In turn, 116 vascular territories are considered as the basic blocks that compose the distributed organs throughout the whole body. For the second goal, Windkessel models are used to represent the peripheral beds, and the values of the resistive parameters are computed applying a Newton method to a parameter identification problem to guarantee the supply of the correct flow fraction to each terminal location according to the given criteria. Finally, it is shown that, by means of the criteria developed, and for a rather standard set of model parameters, the model predicts physiologically realistic pressure and flow waveforms.

COVID-19 has caused great devastation in the past year. Multi-organ point-of-care ultrasound (PoCUS) including lung ultrasound (LUS) and focused cardiac ultrasound (FoCUS) as a clinical adjunct has played a significant role in triaging, diagnosis and medical management of COVID-19 patients. The expert panel from 27 countries and 6 continents with considerable experience of direct application of PoCUS on COVID-19 patients presents evidence-based consensus using GRADE methodology for the quality of evidence and an expedited, modified-Delphi process for the strength of expert consensus. The use of ultrasound is suggested in many clinical situations related to respiratory, cardiovascular and thromboembolic aspects of COVID-19, comparing well with other imaging modalities. The limitations due to insufficient data are highlighted as opportunities for future research.

A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro-and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force-and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the wellknown Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force-and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations.