Development of a Mathematical Model of the Human Circulatory System

Interventional Removal of Travelling Microthrombi Using Targeted Magnetic Microbubble

Microthrombus is one of the major causes of the sequelae of Corona Virus Disease 2019 (COVID-19 and leads to subsequent embolism and necrosis. Due to their small size and irregular movements, the early detection and efficient removal of microthrombi in vivo remain a great challenge. In this work, an interventional method is developed to identify and remove the traveling microthrombi using targeted-magnetic-microbubbles (TMMBs) and an interventional magnetic catheter. The thrombus-targeted drugs are coated on the TMMBs and magnetic nanoparticles are shelled inside, which allow not only targeted adhesion onto the traveling microthrombi, but also the effective capture by the magnetic catheter in the vessel. In the proof-of-concept experiments in the rat models, the concentration of microthrombus is reduced by more than 60% in 3 min, without damaging the organs. It is a promising method for treating microthrombus issues.

Self-Regulating Adaptive Controller for Oxygen Support to Severe Respiratory Distress Patients and Human Respiratory System Modeling

Uncontrolled breathing is the most critical and challenging situation for a healthcare person to patients. It may be due to simple cough/cold/critical disease to severe respiratory infection of the patients and resulting directly impacts the lungs and damages the alveoli which leads to shortness of breath and also impairs the oxygen exchange. The prolonged respiratory failure in such patients may cause death. In this condition, supportive care of the patients by medicine and a controlled oxygen supply is only the emergency treatment. In this paper, as a part of emergency support, the intelligent set-point modulated fuzzy PI-based model reference adaptive controller (SFPIMRAC) is delineated to control the oxygen supply to uncomforted breathing or respiratory infected patients. The effectiveness of the model reference adaptive controller (MRAC) is enhanced by assimilating the worthiness of fuzzy-based tuning and set-point modulation strategies. Since then, different conventional and intelligent controllers have attempted to regulate the supply of oxygen to respiratory distress patients. To overcome the limitations of previous techniques, researchers created the set-point modulated fuzzy PI-based model reference adaptive controller, which can react instantly to changes in oxygen demand in patients. Nonlinear mathematical formulations of the respiratory system and the exchange of oxygen with time delay are modeled and simulated for study. The efficacy of the proposed SFPIMRAC is tested, with transport delay and set-point variations in the devised respiratory model.

Proposed mechanism for reduced jugular vein flow in microgravity

Internal jugular flow is reduced in space compared with supine values, which can be associated with internal jugular vein (IJV) thrombosis. The mechanism is unknown but important to understand to prevent potentially serious vein thromboses on long duration flights. We used a novel, microgravity‐focused numerical model of the cranial vascular circulation to develop hypotheses for the reduced flow. This model includes the effects of removing hydrostatic gradients and tissue compressive forces – unique effects of weightlessness. The IJV in the model incorporates sensitivity to transmural pressure across the vein, which can dramatically affect resistance and flow in the vein. The model predicts reduced IJV flow in space. Although tissue weight in the neck is reduced in weightlessness, increasing transmural pressure, this is more than offset by the reduction in venous pressure produced by the loss of hydrostatic gradients and tissue pressures throughout the body. This results in a negative transmural pressure and increased IJV resistance. Unlike the IJV, the walls of the vertebral plexus are rigid; transmural pressure does not affect its resistance and so its flow increases in microgravity. This overall result is supported by spaceflight measurements, showing reduced IJV area inflight compared with supine values preflight. Significantly, this hypothesis suggests that interventions that further decrease internal IJV pressure (such as lower body negative pressure), which are not assisted by other drainage mechanisms (e.g. gravity), might lead to stagnant flow or IJV collapse with reduced flow, which could increase rather than decrease the risk of venous thrombosis.

Assessment of biventricular hemodynamics and energy dynamics using lumen-tracking 4D flow MRI without contrast medium

BACKGROUND

Biventricular physiological interaction remains a challenging problem in cardiology. We developed a four-dimensional (4D) flow magnetic resonance imaging (MRI) scan and clinically available analysis protocol based on beat tracking of the cardiovascular lumen without contrast medium, which enabled measurement of the biventricular hemodynamics and energetic performance by calculating flow energy loss (EL) and kinetic energy (KE). The aim of this study was to observe the flow patterns and energy dynamics to reveal the physiology of the right and left ventricular systems.

METHODS

4D flow MRI studies were performed in 19 healthy volunteers including 11 male and 8 female. The right and left ventricular systems were segmented to visualize the flow patterns and to quantify the hemodynamics and energy dynamics.

RESULTS

A large vortex was observed in the left ventricle (LV), along the longitudinal axis, during end diastole and early systole. At early systole, the vortex appeared to facilitate smooth ejection with little EL. In contrast, in the right ventricle (RV), there were vortices near the free wall in both the short and long axes during the diastolic filling phase. Mean EL index during a single cardiac cycle in the right and left heart systems was 0.63 ± 0.16 (0.42-0.99) mW/m², and 1.02 ± 0.26 (0.58-1.58) mW/m², respectively. EL is inevitable loss caused by the vortex flow to facilitate smooth right and left ventricular function and left-sided EL tended to correlate positively with heart rate and right ventricular stroke volume. Kinetic energy at the aortic valve was influenced by LV end-diastolic volume/stroke volume. No gender difference was observed.

CONCLUSIONS

The RV appears to function as a regulator of the energy dynamics of the LV system.

A computer simulation of short-term adaptations of cardiovascular hemodynamics in microgravity

Astronauts in the microgravity environment experience significant changes in their cardiovascular hemodynamics. In this study, a system-level numerical model has been utilized to simulate the short-term adaptations of hemodynamic parameters due to the gravitational removal in space. The effect of lower body negative pressure (LBNP) as a countermeasure has also been simulated. The numerical model was built upon a lumped-parameter Windkessel model by incorporating gravity-induced hydrostatic pressure and transcapillary fluid exchange modules. The short-term (in the time scale of seconds and minutes) adaptations of the cardiac functions, blood pressure, and fluid volumes have been analyzed and compared with physiological data. The simulation results suggest microgravity induces a decrease in aortic pressure, heart rate, lower body capillary pressure and volume, and an increase in stroke volume, upper body capillary pressure and volume. The activation of LBNP causes an immediate increase in lower body blood volume and a gradual decrease in upper body blood volume. As a result, the fluid shift due to microgravity could be reversed by the LBNP application. LBNP also counters the impacts of microgravity on the cardiac functions, including heart rate and stroke volume. The simulation results have been validated using available physiological data obtained from spaceflight and parabolic flight experiments.

A computational fluid dynamics simulation study of coronary blood flow affected by graft placement†

OBJECTIVES

To determine the effect of graft placement and orientation on flow rates through a partially obstructed coronary artery.

METHODS

A numerical, parametric study of blood flow in the human coronary artery was conducted using computational fluid dynamics simulation. A cylindrical approximation of the coronary artery with varying degrees of stenosis, with and without a bypass graft, was modelled to determine trends in volumetric flow rates. Steady and transient simulations were conducted for geometric variations of percentage of blockage, length and shape of stenosis, graft position relative to the coronary blockage and graft orientation. Accurate simulations were performed using a non-Newtonian fluid model and pressure-driven viscous flow.

RESULTS

Simulations demonstrate, as expected, that total outlet flow rates of grafted arteries are consistently improved for upstream stenosis varying between 0 and 90% blockage. Grafts angled towards the artery provided increased total outflow. However, flow rates in the coronary artery upstream of the graft are substantially reduced in comparison with the non-grafted configuration due to competing flows. For some configurations (reduced blockage, graft placed close to long grafts), flow rates in the graft are below that of the flow rate through the stenosis. In general, a graft angled more towards the artery increased flow rates upstream of the graft.

CONCLUSIONS

Placement and orientation of a graft may adversely affect upstream flow, with the degree of effect dependent on geometric factors of downstream position and graft angle.

Finite element modelling of pulsatile blood flow in idealized model of human aortic arch: study of hypotension and hypertension

A three-dimensional computer model of human aortic arch with three branches is reproduced to study the pulsatile blood flow with Finite Element Method. In specific, the focus is on variation of wall shear stress, which plays an important role in the localization and development of atherosclerotic plaques. Pulsatile pressure pulse is used as boundary condition to avoid flow entry development, and the aorta walls are considered rigid. The aorta model along with boundary conditions is altered to study the effect of hypotension and hypertension. The results illustrated low and fluctuating shear stress at outer and inner wall of aortic arch, proximal wall of branches, and entry region. Despite the simplification of aorta model, rigid walls and other assumptions results displayed that hypertension causes lowered local wall shear stresses. It is the sign of an increased risk of atherosclerosis. The assessment of hemodynamics shows that under the flow regimes of hypotension and hypertension, the risk of atherosclerosis localization in human aorta may increase.

Mathematical modeling and experimental testing of three bioreactor configurations based on windkessel models

This paper presents an experimental study of three bioreactor configurations. The bioreactor is intended to be used for the development of tissue-engineered heart valve substitutes. Therefore it must be able to reproduce physiological flow and pressure waveforms accurately. A detailed analysis of three bioreactor arrangements is presented using mathematical models based on the windkessel (WK) approach. First, a review of the many applications of this approach in medical studies enhances its fundamental nature and its usefulness. Then the models are developed with reference to the actual components of the bioreactor. This study emphasizes different conflicting issues arising in the design process of a bioreactor for biomedical purposes, where an optimization process is essential to reach a compromise satisfying all conditions. Two important aspects are the need for a simple system providing ease of use and long-term sterility, opposed to the need for an advanced (thus more complex) architecture capable of a more accurate reproduction of the physiological environment. Three classic WK architectures are analyzed, and experimental results enhance the advantages and limitations of each one.

Mathematical multi-scale model of the cardiovascular system including mitral valve dynamics. Application to ischemic mitral insufficiency

Background

Valve dysfunction is a common cardiovascular pathology. Despite significant clinical research, there is little formal study of how valve dysfunction affects overall circulatory dynamics. Validated models would offer the ability to better understand these dynamics and thus optimize diagnosis, as well as surgical and other interventions.

Methods

A cardiovascular and circulatory system (CVS) model has already been validated in silico, and in several animal model studies. It accounts for valve dynamics using Heaviside functions to simulate a physiologically accurate "open on pressure, close on flow" law. However, it does not consider real-time valve opening dynamics and therefore does not fully capture valve dysfunction, particularly where the dysfunction involves partial closure. This research describes an updated version of this previous closed-loop CVS model that includes the progressive opening of the mitral valve, and is defined over the full cardiac cycle.

Results

Simulations of the cardiovascular system with healthy mitral valve are performed, and, the global hemodynamic behaviour is studied compared with previously validated results. The error between resulting pressure-volume (PV) loops of already validated CVS model and the new CVS model that includes the progressive opening of the mitral valve is assessed and remains within typical measurement error and variability. Simulations of ischemic mitral insufficiency are also performed. Pressure-Volume loops, transmitral flow evolution and mitral valve aperture area evolution follow reported measurements in shape, amplitude and trends.

Conclusions

The resulting cardiovascular system model including mitral valve dynamics provides a foundation for clinical validation and the study of valvular dysfunction in vivo. The overall models and results could readily be generalised to other cardiac valves.

An extended computational model of the circulatory system for designing ventricular assist devices

An extended computational model of the circulatory system has been developed to predict blood flow in the presence of ventricular assist devices (VADs). A novel VAD, placed in the descending aorta, intended to offload the left ventricle (LV) and augment renal perfusion is being studied. For this application, a better understanding of the global hemodynamic response of the VAD, in essence an electrically driven pump, and the cardiovascular system is necessary. To meet this need, a model has been established as a nonlinear, lumped-parameter electrical analog, and simulated results under different states [healthy, congestive heart failure (CHF), and postinsertion of VAD] are presented. The systemic circulation is separated into five compartments and the descending aorta is composed of three components to accurately yield the system response of each section before and after the insertion of the VAD. Delays in valve closing time and blood inertia in the aorta were introduced to deliver a more realistic model. Pump governing equations and optimization are based on fundamental theories of turbomachines and can serve as a practical initial design point for rotary blood pumps. The model's results closely mimic established parameters for the circulatory system and confirm the feasibility of the intra-aortic VAD concept. This computational model can be linked with models of the pump motor to provide a valuable tool for innovative VAD design.