A 1D-0D-3D coupled model for simulating blood flow and transport processes in breast tissue

Numerical simulation and fast method for the 0D-1D multi-scale coupled model and its application in ischemic brain tissue blood flow problems

As living standards rise, more and more people are paying attention to their own health, especially issues such as cerebral thrombosis, cerebral infarction, and other cerebral blood flow problems. An accurate simulation of blood flow within cerebral vessels has emerged as a crucial area of research. In this study, we focus on microcirculatory blood flow in ischemic brain tissue and employ a 0D-1D geometric multi-scale coupled model to characterize this process. Given the intricate nature of human cerebral vessels, we apply a numerical method combining the finite element method and the third-order Runge-Kutta method to resolve the coupled model. To enhance computational efficiency, we introduce a fast method based on the reduced-order extrapolation algorithm. Our numerical example underscores the stability of the method and convergence accuracy to O h 3 + τ 3 , while significantly improving the accuracy and efficiency of blood flow simulation, making the mechanism analysis more accurate. Additionally, we present examples detailing variations and distribution of intracranial pressure and blood flow in ischemic brain tissue throughout a cardiac cycle. Both reduced vascular compliance and vascular stenosis can have adverse effects on intracranial cerebral pressure and blood flow, leading to insufficient local oxygen supply and negative effects on brain function. Meanwhile, there will also be corresponding changes in volume flow and pulsatile blood pressure.

Review of cardiac-coronary interaction and insights from mathematical modeling

Cardiac-coronary interaction is fundamental to the function of the heart. As one of the highest metabolic organs in the body, the cardiac oxygen demand is met by blood perfusion through the coronary vasculature. The coronary vasculature is largely embedded within the myocardial tissue which is continually contracting and hence squeezing the blood vessels. The myocardium-coronary vessel interaction is two-ways and complex. Here, we review the different types of cardiac-coronary interactions with a focus on insights gained from mathematical models. Specifically, we will consider the following: (1) myocardial-vessel mechanical interaction; (2) metabolic-flow interaction and regulation; (3) perfusion-contraction matching, and (4) chronic interactions between the myocardium and coronary vasculature. We also provide a discussion of the relevant experimental and clinical studies of different types of cardiac-coronary interactions. Finally, we highlight knowledge gaps, key challenges, and limitations of existing mathematical models along with future research directions to understand the unique myocardium-coronary coupling in the heart. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Multi-scale simulations of pulmonary airflow based on a coupled 3D-1D-0D model

Pulmonary airflow simulation is a valuable tool for studying respiratory function and disease. However, the respiratory system is a complex multiscale system that involves various physical and biological processes across different spatial and temporal scales. In this study, we propose a 3D-1D-0D multiscale method for simulating pulmonary airflow, which integrates different levels of detail and complexity of the respiratory system. The method consists of three components: a 3D computational fluid dynamics model for the airflow in the trachea and bronchus, a 1D pipe model for the airflow in the terminal bronchioles, and a 0D biphasic mixture model for the airflow in the respiratory bronchioles and alveoli coupled with the lung deformation. The coupling between the different components is achieved by satisfying the mass and momentum conservation law and the pressure continuity condition at the interfaces. We demonstrate the validity and applicability of our method by comparing the results with data of previous models. We also investigate the reduction in inhaled air volume due to the pulmonary fibrosis using the developed multiscale model. Our method provides a comprehensive and realistic framework for simulating pulmonary airflow and can potentially facilitate the diagnosis and treatment of respiratory diseases.

Accelerated simulation methodologies for computational vascular flow modelling

Vascular flow modelling can improve our understanding of vascular pathologies and aid in developing safe and effective medical devices. Vascular flow models typically involve solving the nonlinear Navier-Stokes equations in complex anatomies and using physiological boundary conditions, often presenting a multi-physics and multi-scale computational problem to be solved. This leads to highly complex and expensive models that require excessive computational time. This review explores accelerated simulation methodologies, specifically focusing on computational vascular flow modelling. We review reduced order modelling (ROM) techniques like zero-/one-dimensional and modal decomposition-based ROMs and machine learning (ML) methods including ML-augmented ROMs, ML-based ROMs and physics-informed ML models. We discuss the applicability of each method to vascular flow acceleration and the effectiveness of the method in addressing domain-specific challenges. When available, we provide statistics on accuracy and speed-up factors for various applications related to vascular flow simulation acceleration. Our findings indicate that each type of model has strengths and limitations depending on the context. To accelerate real-world vascular flow problems, we propose future research on developing multi-scale acceleration methods capable of handling the significant geometric variability inherent to such problems.