What is Hemodynamics?

Hemodynamics is a branch of biomechanics, and its main task is to apply the theory and methods of fluid mechanics to study the causes, conditions, states, and various influencing factors of blood flow along the blood vessel circulation, in order to clarify the rules of blood flow, physiological significance, and Relationship of disease.

Chinese name: Hemodynamics
Belongs to: biology

main mission: Study blood flow along blood vessels, etc.
Content: Blood circulation consists of heart, blood and blood vessels

The blood circulation system consists of the heart, blood and blood vessels. Compared with the general fluid power system, the blood circulation system has many characteristics. First, blood vessels are elastic tubes with countless branches. Blood vessels transport blood to various organs in the body while maintaining integrity. Second, blood is a suspension containing a large amount of solid components (blood cells). Blood contains cells, proteins, low-density lipids, and ions needed to transport nutrients and discharge waste. Red blood cells make up about 40% of the entire blood volume. In most arteries, blood is characteristic of Newtonian fluid, and under normal hematocrit conditions, blood viscosity is 4 centipoise (cP). The non-Newtonian viscous fluid characteristics of blood are the research fields of biorheology, and a lot of research has been done. The heart is a very complicated pump controlled by neuro-humoral factors. The periodic motion of the heart pump creates pulsating conditions in the arteries. Therefore, blood flow cannot be considered simply as a steady flow, but as a pulsating flow.

Hemodynamics is the study of changes in the flow parameters (blood flow, flow rate, pressure, flow regime, viscosity, peripheral resistance, etc.) that characterize the human blood circulation system under physiological and pathological conditions. Vessel bifurcation and blood pulsation make the shear force of blood vessel wall surface change cyclically and non-uniformly. Normal arterial blood flow is laminar, accompanied by secondary flow at the bends and bifurcations, and the deviation of the velocity parabola will produce a small area of low wall shear force. Arterial blood vessels are adaptively adjusted and changed according to hemodynamic conditions, and non-conventional hemodynamic conditions also cause blood vessels to respond biologically.

The pulsatility of the blood is critical to the cardiovascular system and is the primary consideration in most analyses. In contrast, other factors of blood flow are ignored as secondary factors in many specific occasions, such as: wall elasticity, non-Newtonian fluid, suspended particles in the fluid, bulk force, and temperature, etc. Analysis of complex blood flow can be greatly simplified.

The shear force generated by the contact between the blood flow and the endothelium will slow down the flow. The wall shear force is proportional to the shear rate (velocity gradient). The velocity gradient is highly dependent on the shape of the velocity distribution curve and the distance between a certain velocity and the wall surface. In order to measure the pulsating flow wall shear force, it is necessary to accurately measure the velocity gradient near the wall surface, but this is not technically easy. At the same time, because the red blood cell concentration will decrease at the wall surface, and the blood viscosity near the wall surface is not easy to know, the prediction error of the wall shear force often reaches 20-50%, and the arterial wall shear force is usually maintained below 15dyn / cm. Endothelial cells respond to wall shear by adjusting tube diameter, intimal thickness, and platelet thrombosis. Therefore, wall shear is the most important influencing factor for blood vessels to respond to blood flow.

Another major hemodynamic factor that acts on blood vessels is the trans-wall pressure across the wall. The average transmural pressure of arteries is 100 mmHg, and the average transmural pressure of veins is 10 mmHg. For circular thin-walled pipes, the circumferential stress can be described by Laplace's law

Among them, t is the thickness of the wall surface, D is the inner diameter of the blood vessel, and P is the pressure across the wall. The most basic factor that determines smooth muscle cell response is the strain of these cells. The arterial wall responds to static and cyclic loads and reconstitutes the wall surface through the secretion and combination of collagen and elastin.

In the past, many vascular stress evaluation methods have been developed, such as: using the linearized blood-vascular coupled equation of motion Womersley's solution to obtain the green strain under blood pulsating pressure load, and using the vascular wall strain energy function to obtain vascular wall stress under pulsating pressure General expression of the distribution; Calculate the shear stress of the uniform arterial wall by measuring blood viscosity, blood flow velocity, pressure on the axis of the tube, and the diameter of the tube; use the pressure-volume (pV) of the vascular segment under the axial elongation ratio of the body The relationship between the data and the exponential function obtained the distribution of peripheral stress along the wall thickness of the vessel wall under a certain internal pressure. These methods for calculating vascular stress provide a powerful method for evaluating the response of blood vessels to blood flow in vivo and in vitro.

Hemodynamics I. Hemodynamics research methods

Due to the three-dimensional and multi-scale characteristics of the structure of the cardiovascular system, the mechanical phenomena generated by the cardiovascular system are very complicated. It is not enough to rely on previous computational mechanics and computational fluid dynamics (CFD) methods. Therefore, image-based 3D modeling, Fluid-solid-physiological coupling analysis techniques are indispensable for analyzing complex cardiovascular systems. Coupling analysis is not just fluid-solid coupling in the narrow sense, but the application of computational mechanics to explore the broad physical and chemical phenomena that make up the human system, and ultimately to the innovative application of biomedical technology.

In recent years, computed tomography (CT), magnetic resonance imaging (MRI), ultrasound (US), and digital subtraction imaging (DSA) and other medical imaging technologies (DSA) have provided a reliable way to build personalized 3D models based on precise anatomy. Data foundation. The development of computational fluid dynamics, finite element analysis, fluid-structure coupling technology, and high-performance computer hardware provides a strong theoretical basis for the analysis of hemodynamic characteristics.

Through reverse engineering technology, transparent silicone rubber can be used to make a variety of normal and diseased blood vessel models with real structure. Using PIV (Particle Imaging Velocimetry) visualization technology to observe blood flow characteristics in vitro, on the one hand, the validity of numerical simulation can be verified, and Aspects provide very useful tools for surgical design, drug development, and clinically trained intravascular procedures.

In addition, the one-dimensional and zero-dimensional cardiovascular system models can well describe the pulse wave transmission of the whole-body cardiovascular system and the phase changes of blood pressure and flow waves. They are very important and effective tools for studying hemodynamics.

After more than forty years of development, the one-dimensional model modeling method has been continuously improved. The shape of the velocity profile directly affects the form of the momentum equation and the evaluation of wall stress. Commonly used velocity profiles include flatness, parabola, power function, Stokes boundary layer, and periodic velocity profiles. The motion of the tube wall directly affects the propagation velocity and pulsation characteristics of the pressure wave. In the one-dimensional hemodynamic model, the wall motion is characterized by the equation of state, which is expressed as the relationship between the trans-wall pressure difference and the cross-sectional area. The equation of state derived from the Laplace equation of linear elasticity theory can better describe the blood flow characteristics under normal conditions.

Intra-arterial blood flow is mainly affected by arterioles, but the structure of arterioles is complex and difficult to observe, making it difficult to establish a suitable model to describe the effects of arterioles on the propagation of intra-arterial pulse waves. Considering small blood vessels and capillaries as extensions of large blood vessel exit boundaries, the effects of small arteries can be described using different exit boundary conditions. At present, there are three commonly used exit boundary conditions, including: pure impedance model, which uses only one impedance element to describe the relationship between pressure and flow at the exit, but this model cannot describe the phase delay characteristics of pressure waves and flow waves. The second is a three-element elastic cavity model. Although these two models are concise, the estimation of impedance and compliance under different physiological and pathological conditions is a difficult point. The small vessel tree model uses the type of the human arterial network to establish a binary tree structure, and then uses the theory of quasi-linear analysis to obtain the pressure and flow relationship at the aorta outlet. The structural tree model simulates the impedance of small vessel trees more comprehensively with fewer assumptions.

1 Hemodynamics 1 Hemodynamics of the arterial system

The bifurcation of the stiff arteries, abdominal aorta, left coronary arteries, heart and proximal aorta are the sites that are prone to lesions. Therefore, the normal and pathological hemodynamic characteristics of these sites have become the focus of attention.

Studies have shown that hemodynamic factors, such as wall shear stress (WSS), wall shear stress gradient (WSSG), flow separation, secondary flow, etc., can cause damage to arterial vascular endothelial cells, thickening of arterial intima, and intimal smooth muscle cells. Hyperplasia and blood cell aggregation have important effects.

1-1 atherosclerosis

The increasing incidence of cardiovascular and cerebrovascular diseases such as stroke and coronary heart disease caused by atherosclerosis has become the number one killer of the Chinese people, and the disability rate is extremely high, which places a heavy burden on families and social health resources. AS (atherosclerosis) originates from the bends, bifurcations and stenoses of arteries, such as the aortic arch, carotid branches, and abdominal aortic branches. In these sharply changed locations, the shear stress of the blood vessel wall will be weakened, the blood flow pattern will be abnormal, and the blood flow velocity will be reduced, which will cause harmful lipids in the blood flow to stay in this area for a long time, causing AS lesions. Low wall shear stress changes the function of endothelial cells and changes in the generation, secretion and expression of vasoactive substances, which affects the absorption and metabolism of lipoproteins and other macromolecular substances in the vascular wall, and then affects the structure and functional reconstruction of blood vessels.

The most prominent anatomical feature of the carotid artery is the presence of an arterial sinus on the internal carotid artery and the site of dilated blood vessels in the internal carotid artery downstream of the bifurcation. By using real pulsatile flow and pressure waveforms, numerical simulations of the local blood flow morphology, secondary flow, and wall shear force in the carotid sinus have been found. At certain times during the deceleration and diastole of the heart, the middle carotid sinus Flow separation will occur near the outer wall surface, forming a low-speed reflux region, resulting in a low wall shear oscillation of 2 to 6 dyn / cm, and the low wall shear stress oscillation is located exactly in the atherosclerotic lesion area (outside of the carotid sinus) In the same area, NMR velocity measurements also revealed a low-speed regurgitation during the deceleration phase of the heart. Furthermore, a finite element analysis of the oxygen transport characteristics of the carotid branches found that the low-speed return of the carotid sinus would reduce the oxygen transport at the entrance of the arterial sinus, thereby causing an atherosclerotic response in the arterial wall.

In recent years, after summarizing a large number of relationships between hemodynamics and material transport, researchers have proposed the lipid concentration polarization hypothesis: the semi-permeability of human blood vessels leads to low density lipoproteins in the blood circulation system (low density lipoprotein, LDL) is higher in the blood vessel wall than in the blood circulation body fluid. LDL stays for a long time in areas where the vascular geometry changes dramatically, providing a great opportunity for lipid penetration and deposition. At the same time, local differences in the flow field will also cause endothelial cell dysfunction, lipids will more easily enter the endothelium and accumulate under the endothelium, which will cause the occurrence and development of atherosclerosis. Lipid polarization not only explains the focal nature of atherosclerosis, but also explains why atherosclerosis does not occur in veins. The low pressure of the venous system makes it difficult for the lipid itself to enter the vascular endothelium. At the same time, because the venous wall is very thin, the lipid that enters the vascular endothelial layer can easily penetrate the outer wall of the vein and be taken away by the lymphatic system without being deposited in the venous wall. . Hemodynamic numerical simulations and in vitro cell experiments demonstrated that there is macromolecular infiltration and deposition associated with shear forces and semi-permeability on the endothelial surface.

Mathematical models based on non-linear stress-strain relationships can describe the characteristics of the vascular wall of atherosclerotic arteries, and the one-dimensional blood flow model can be used to analyze the effect of atherosclerotic arteries on blood flow in the cardiovascular system.

1-2 Hemodynamic 1-2 arterial stenosis and its bypass graft bypass

Atherosclerosis causes local narrowing of the arteries and affects blood perfusion of downstream vessels. At the same time, after the formation of atherosclerotic plaques, as bulges on the vessel wall, they continue to be subject to shear stress, tube wall tension stress, cross-wall pressure, Variations in pulsating pressure during vasoconstriction and pressure changes during turbulence can cause plaque instability and even rupture.

Interaction between intimal hyperplasia, tube wall cavity shape change, and hemodynamics. To simulate the process of intimal hyperplasia, the researchers proposed a calculation method for cell filling. The threshold low shear stress condition is used to judge that when intimal hyperplasia occurs on the wall surface, the calculation unit near the wall surface is filled as a solid wall unit. It was found through simulation that the maximum stenosis rate was 34.4%, which occurred on the lateral wall of the sinus artery 5 mm from the bifurcation of the blood vessel.

To study the changes in local blood flow and endothelial cells after stenosis, animal and in vitro models can be established. Methods for constructing stenosis models include: Feeding animals with foods rich in protein and fat to keep them in the body for a relatively short period of time The endometrium is produced, which promotes its hyperplasia and stenosis; the surgical method damages the endometrium to make it hypertrophic and narrow; the circulatory constriction is used to narrow the blood vessels symmetrically. However, the hemodynamic simulation of carotid sinus ring contraction found that lipid deposition will develop symmetrically along the circumferential axis in the sinus downstream of the stenosis, and the top of the stenosis will not produce atherosclerosis due to high shear force. Therefore, asymmetric stenosis with uneven thickness should be used to artificially produce uneven stenosis.

Atherosclerosis causes local stenosis of the artery. For severe arterial blood vessels, artificial arterial blood vessels or autogenous vein blood vessels are often used for arterial bypass graft bypass grafting to restore normal blood supply to the vessels and tissues downstream of the narrowed artery. A major problem with arterial bypass surgery is the high incidence of postoperative vascular occlusion and the subsequent high cost of treatment. Intimal hyperplasia and the development of restenosis in the downstream suture area are the causes of surgical failure.

There are many factors affecting the success rate of arterial bypass surgery. The graft-host artery diameter ratio and suture angle are two important geometric factors. Hemodynamic analysis and surgical practice have shown that larger graft-host artery diameter ratio and smaller suture angle can minimize wall shear stress gradient and have better hemodynamic characteristics.

The study of hemodynamics in the suture area can help improve the clinical success rate of arterial bypass surgery. For example, when the important hemodynamic parameters of the suture zone lesion are determined, the doctor can choose the suture structure to achieve the optimal hemodynamics, thereby minimizing the pathological factors leading to intimal hyperplasia.

1-3 Hemodynamics 1-3 aneurysms

Cerebral hemangioma is a pathological swell of the cerebral blood vessels, which usually occurs at the site of the Willis ring. The Willis ring is a circular artery at the bottom of the brain that delivers arterial blood rich in oxygen and nutrients to brain tissue. It is mainly composed of the carotid, midbrain, forebrain, basilar, posterior cerebral, and three communicating arteries. At present, the commonly used clinical methods for treating aneurysms include aneurysm clipping and vascular embolization. However, before surgery, aneurysm rupture occurs during operation, and cerebral vasospasm may be caused during bleeding, which will increase the difficulty of surgery. And the risk of postoperative complications (such as cerebral infarction, cognitive dysfunction, etc.) and high mortality cannot be ignored. Clinical studies show that microsurgery and endovascular treatment of forebrain communication aneurysms can cause patients with different degrees of cognitive dysfunction. Therefore, there is an increasing tendency in clinical practice to detect rupturable aneurysms early and perform preventive surgery. Designing an effective surgical treatment plan requires a better understanding of the process of aneurysm formation, development, and rupture, but the development mechanism of this process is still not very clear.

The stress-growth law is used to obtain the basic relationship of the local expansion of blood vessels and based on the hemodynamic equation, the analytical expressions of the flow velocity, pressure, and shear stress in the tube wall can be obtained based on the hemodynamic equation. The analysis results show that local expansion affects pressure The effect is not obvious, but it will cause the wall shear stress to be unevenly distributed-the shear stress in the gradually expanding section becomes very low, while the shear stress in the tapered section will increase to the maximum.

Due to the extremely high risk of rupture of aneurysms, attention to the factors of aneurysm rupture, and attempts to find methods for predicting risk factors have become a hot topic of research. The intima of the vessel wall where the aneurysm is usually thin or even missing is the root cause of aneurysm rupture.

The longitudinal blood flow will impact the distal end of the blood vessel, causing the elastic layer of the blood vessel to be destroyed, forming a sac-like protrusion. This sac-like protrusion can aggravate the blood vortex at this site, causing the vessel wall to oscillate and promote its degeneration. Over time, tube wall radius, pressure, shear stress, and tube wall brittleness will affect each other, resulting in increased pressure-increased tube diameter-reduced wall thickness-increased tube wall brittleness-reduced wall shear stress, forming Vicious circle, this is the progression of aneurysm. The most common location of aneurysm rupture is the apex, and the rupture process involves various material characteristics and hemodynamic factors.

In the study of the mechanism of aneurysm formation, aneurysm formation and cerebral vascular structural changes, such as the absence or stenosis of the Willis annulus, and the outward remodeling of the anterior communicating artery are associated with the occurrence of aneurysms. Animal experiments in rats have shown that systemic hypertension can produce aneurysms. Studies have shown that the flow pattern, velocity, and wall shear stress distribution of the mid-cerebral artery are related to the location of the aneurysm, and the geometry of the posterior communicating artery is related to the internal carotid artery and posterior communicating aneurysm. In the cerebral circulation, the morphological characteristics of the supplying arteries can determine whether the hemodynamic environment is easier or more difficult to form an aneurysm.

Because the Willis ring is a prone site for aneurysms, a large number of blood flow characteristics in the Willis ring are analyzed using concentrated parameters and a one-dimensional vascular network model, as well as three-dimensional fluid-structure analysis, such as: structural variations in the brain The effects of different Willis ring structures on blood flow balance during carotid stenosis and obstruction; the effects of forebrain communication aneurysms on Willis ring blood flow. One-dimensional hemodynamic modeling can also be used to investigate the effect of aneurysm on systemic pressure pulsation.

Figure 1. Different variants of the Willis ring a. Intact b. Forebrain artery missing c Forebrain artery stenosis

1-4 Hemodynamic 1-4 stent treatment

Vascular stent-based interventional therapy, with its microtrauma and high efficiency, has become an important method for the treatment of cardiovascular stenosis and coronary heart disease and aneurysms.

Early stent implantation technology brought about the problem of restenosis in the stent, which was due to the damage of the vessel wall and the change of the hemodynamic environment caused by interventional treatment, which caused thrombosis and intimal hyperplasia. Antiplatelet and anticoagulant drugs and drug-coated stents can greatly reduce restenosis due to vessel wall damage.

The hemodynamic research on the interventional treatment of aneurysm stent mainly includes the analysis of the blood flow velocity, the wall shear stress and the wall pressure of the tumor cavity after the stent implantation. The study found that the size of the stent filament had a significant effect on the eddy current status inside the tumor cavity. The triangular cross-section stent is better than the traditional circular cross-section stent in the treatment of meandering aneurysms.

A stent hemodynamic study of an aneurysm on the medial aortic arch showed that after implantation of the stent, the overall flow in the aortic arch did not change significantly, and blood flow in the aneurysm cavity was greatly weakened. Aneurysm wall pressure is reduced and pressure distribution is more balanced. Therefore, the markedly inhibited flow in the tumor cavity will lead to the formation of thrombus in the tumor cavity. This shows that stent implantation is beneficial to the atresia of aneurysms.

In short, the efficacy of the stent is affected by many factors, such as the shape of the stent (spiral, grid), the diameter of the stent, the permeability, the position of the stent, the characteristics of the aneurysm and the degree of the lesion, local hemodynamics, and stent flexibility. Wait. To investigate the mechanical factors of stent design and its influence on hemodynamics after stent implantation can help the design of interventional treatment plan.

Hemodynamics II, Cardiac Hemodynamics

The heart is the driving force for blood circulation. The heart has a rhythmic contraction and relaxation, and a unidirectional flow of the heart valve, which ensures the power pump function of the heart in the blood circulation. The function of the heart pump is directly related to the amount of blood the heart delivers to the peripheral blood vessels. Clinically, the cardiac output is reduced due to cardiac pumping dysfunction, and the blood supply process that cannot meet the needs of systemic tissue metabolism is called heart failure.

Cardiac output is a basic indicator for measuring the pumping function of the heart, and usually refers to the amount of blood ejected within one minute of the heart beat or working time, including two basic indicators of stroke output and minute output. The stroke volume is the amount of blood ejected from the left and right ventricle sides during one cardiac cycle. Minute output is the product of heart rate per minute and stroke volume. The average heart rate of a healthy adult male at rest is 75 beats per minute and the stroke output is 65 mL, so the output per minute is about 4 L.
Because cardiac output is affected by the body surface area of an individual, the unit cardiac surface area to calculate cardiac output per minute is called the cardiac index. The average cardiac index of a normal-sized adult at rest is 3.0 ~ 3.56 L / (min · ).
Ejection fraction, which is the percentage of ventricular ejection volume to end-diastolic volume, is used to evaluate cardiac function. In healthy adults, the ejection fraction is 55% to 65%. In cardiac failure, due to the weakening of myocardial contractility, the stroke output decreases, but the end-diastolic change does not change significantly, so the ejection fraction decreases.

From the mechanism of myocardial subcellular excitation-contraction to organ-level hemodynamics and structural mechanics, the physiological functions of the heart include multi-scale and multi-physical processes. By establishing a model of the molecular mechanism of the cardiac excitation-contraction process, based on the finite element fluid-solid coupling analysis, the correlation between cardiac structure and function can be better analyzed, the left ventricular dilatation function can be evaluated, combined with ultrasound Doppler imaging and nuclear magnetic functional imaging, etc. , To obtain the material properties of the active and passive state of the myocardium, the thickness of the myocardial wall when the infarcted area of the left ventricle occurs. Multi-scale, multi-physical coupling model can also analyze left ventricular motion and intraventricular blood flow during myocardial infarction. Studies have shown that the area of the stress-tension closed loop during myocardial infarction is almost zero or negative, and the pressure-volume relationship is also very different from normal. End-diastolic left ventricular volume during acute and subacute myocardial infarction is greater than normal, but their tensile material properties are harder.

The aortic valve is composed of three semi-lunar membranes, located at the root of the aorta, with three dimples, called the Valsalva Sinus; the pulmonary valve structure is similar to the aortic valve; the mitral valve consists of two slightly trapezoidal It is composed of a thin film, the base is oval, and the membrane forms a cone-shaped structure when opened. The chordae are connected to the ventricular mastoid muscle at the edge of the membrane to prevent overturning. The tricuspid valve has three valves. The four valves of the heart are one-way valves for blood circulation and prevent blood from flowing back. Their opening and closing process is essential for the normal operation of the heart pump function.

The mechanism of heart valve opening and closing is controlled by hydrodynamics. When the decelerating blood flow before and after the heart valve causes a reverse pressure gradient, the heart valve closes.

Heart valve disease refers to the organic disease of the heart valve due to congenital abnormalities or acquired diseases, often manifested as stenosis or incomplete closing of the valve. Valvular heart disease causes abnormal cardiac hemodynamics, increases atrial and ventricular load, causes corresponding atrial and ventricular hypertrophy deformation (compensation period), and does not appear obvious symptoms of blood circulation disorders; when the disease is aggravated (entering decompensation period) Symptoms and signs of pulmonary and systemic circulation disorders, and even life-threatening.

A common method for numerical simulation of heart valves is to build a valve structure model from magnetic resonance images of the heart valve, apply finite element analysis to describe the valve structure mechanics, and apply the immersion boundary method to describe the blood flow and valve interaction. This provides a unique perspective for understanding the dynamics of the valve under normal and pathological conditions.

The centralized parameter model can not only describe the whole body vascular system, but also can better simulate the heart function. Based on the centralized parameter model of the total circulation system, through appropriate modification of the transvalvular flow equation, the effects of ventricular preload, postload, and myocardial contractile force on the left ventricular pressure-volume relationship can be simulated, and mitral valve stenosis and mitral Left ventricular pressure-volume loops for valve insufficiency, aortic valve stenosis, and aortic valve double lesions.

Based on the centralized parameter model, a systemic simulation experiment system can also be designed. In the experimental simulation, the atrium, ventricle, and aortic arch test sections are made of latex, and the geometry is similar to the physiological section 1: 1. The atrioventricular valve and aortic valve use yak pericardial biological valve, and drive the piston in the system to move the piston up and down to make the ventricle. Do exercises that approximate natural systole and diastole. The remaining arteries are connected to the damping valve and the sealed air cavity with a thick-walled latex tube. This system simulates the hemodynamic characteristics of the left ventricle and the aortic arch, and at the same time, it can simulate the basic characteristics of the blood pressure pulse wave at the left subclavian artery and the atria. This experimental device provides a good experimental method for studying the pressure wave transmission of the cardiovascular system and the effect of vascular parameters on blood flow.

Hemodynamics III. Venous system hemodynamics

The return of venous blood from the lower limbs to the heart requires the help of a pump structure, because the force generated by the heart alone cannot transport blood from the toes to the brain. This pumping action on the deep veins is provided by the muscles. Muscle compression squeezes the blood back to the heart through higher pressure. As long as the venous valve and muscle pump are working well, blood can be returned to the heart.

Lower extremity venous diseases are mainly classified into two major categories: venous reflux disease and reflux disorder. The former is mainly characterized by primary deep venous insufficiency of the lower extremity, and the latter is represented by deep vein thrombosis of the lower extremity.

"Economy Class Syndrome" refers to sitting in a narrow position of an aircraft for a long time, with little space for movement of the feet, resulting in poor venous blood flow. In addition, the re-filtered dry air is continuously inhaled during the flight, which increases the blood viscosity and can cause depth Venous thrombosis. These blood clots run along the bloodstream to the lungs and cause pulmonary vascular embolism, resulting in dyspnea and death in severe cases.

Fluid-structure analysis is also applicable to the flow of blood in the venous system. At this time, the effects of gravity, vascular collapse, respiration, and venous valves need to be considered. The role of a venous valve can be thought of as a boundary that changes over time. When the velocity near the valve is positive, the venous valve is fully open, otherwise it is closed. When in a pathological state, the boundary representing the venous valve cannot be completely closed, and reflux will occur.

Portal hypertension (PHT) is a group of symptoms that result in increased pressure in the portal vein and its branches due to obstruction of the blood flow in the portal pulsation system and / or increased blood flow. Sustained portal hypertension can easily lead to esophageal, gastric varices rupture and bleeding, ascites, hypersplenism, hepatic encephalopathy and other complications. The current treatment is not satisfactory. The portal vein hemodynamics is in a special state of coexistence of high pressure and continuous high blood flow during PHT. The relationship between the portal vein zero stress state during the formation of intrahepatic portal hypertension and the dynamic change of the tensile stress-elongation ratio during axial tension Observation found that the stiffness of the portal vein vessel wall increased, presumably due to the high stress caused by the uneven growth of the composition of the vessel wall, and the relatively fixed composition ratio was broken.

Hemodynamics IV, microcirculation hemodynamics

Microcirculation is the blood circulation in the capillaries between the arterioles and venules. It is the part of the circulation after the free blood vessels in the large circulation enter each organ. It is the most basic structural and functional unit in the circulatory system. The entire circulatory system is a delivery device that supplies oxygen, essential nutrients and corresponding amounts of blood to the body's tissues. Microcirculation is the blood circulation between arterioles and venules in tissues and organs. It forms a microcirculation functional unit with microlymphatic vessels. It is responsible for the exchange of oxygen, essential nutrients and metabolites, energy and information transmission between blood and tissue fluid. , Responsible for blood circulation, distribution, tissue perfusion, and a series of feedback regulation, internal environment stabilization mechanisms. Therefore, the microcirculation is not only the peripheral part of the overall circulatory system, but also an independent functional unit in many organs. It plays a prominent role in maintaining the normal physiological function of the human body, the occurrence, development of various diseases, and the mechanism of drug action. Under normal circumstances, the microcirculation blood flow is adapted to the metabolism level of human tissues and organs, so that the physiological functions of various organs in the human body can operate normally. Once the human body's microcirculation is disturbed, its corresponding tissue system or internal organs will be affected and fail to perform normal functions, which will easily lead to aging of the human body, immune system disorders and diseases.

The flow of fluid through the capillaries can be regarded as the pressure-driven Stokes flow. The penetration of fluid through the capillary wall to the surrounding tissue can be considered as the Stokes flow in the osmotic tube. This type of problem can be solved by the boundary integral method with limited use. The element method can also analyze the Stokes / Darcy flow in the blood vessels with complex structures.

Tumor blood vessels are very different from normal tissue blood vessels in both morphology and function. Structurally, the morphology of most tumor vessels is distorted, swollen, cystic, the connection between vascular branches is disordered, the morphology of endothelial cells distributed along the blood vessels is distorted, the surrounding cells supporting endothelial cells are distributed or loose or absent, and the thickness of the vascular basement membrane is thin Inhomogeneity or even lack, large gaps in the vessel wall, macromolecular substances easily leak out of the blood vessels and showed "high leakage." These structural abnormalities lead to uneven blood flow distribution within the tumor.

Figure 3. Normal blood vessels and tumor blood vessels

The three-layer porous media model can describe fluid movement in solid tumors. Microvessels, lymphatic vessels, and tissues are considered to be porous media in which blood flow, lymph fluid and interstitial fluid flow. The flow of fluid and lymph fluid follows Darcy's law and the flow of interstitial fluid follows Starling's law. Theoretical analysis results show that higher interstitial fluid pressure is the main obstacle for macromolecular drugs to enter tumor tissues. This model combines fluid motion, porous media theory, and material transport theory well, and is an effective method for studying microcirculation.

Angiogenesis is the growth of a new capillary network from existing blood vessels, which is closely related to tumor growth. By considering endothelial cell diffusion movement, extracellular matrix linear elasticity, chemotaxis response of tumor blood vessels, tactile response of adhesion proteins, and convective movement, tumor angiogenesis can be simulated; on this basis, anti-tumor can be established Angiogenesis and tumor hemodynamics model, analyze the role of endostatin in inhibiting neovascular proliferation, bifurcation, and reducing blood perfusion rate and interstitial hypertension in tumors.

Hemodynamics summary

In short, the traditional continuum mechanics method for hemodynamic analysis will be developed through the integration of highly developed computational science technology, medical imaging technology, advanced flow field testing technology, animal experiments and cardiovascular system modeling. More personalized, low-invasive or non-invasive auxiliary solutions for cardiovascular disease treatment, solving more clinical treatment scientific problems.

Hemodynamics Further Reading

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