I strongly recommend this book as a fairly complete trea- tise on an ever- enlarging subject. The frequent correlations with pathological specimens improve clarity. William R. Milnor. mind, and it is desirable to adopt a terminology that 8. Milnor, W.R. (). Hemodynamics, 2nd ed. Baltimore, Williams & Wilkins. 9. Hemodynamics by Milnor, William R. and a great selection of related books, art and collectibles available now at

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A review is presented of the physical principles governing the distribution of blood flow and blood pressure in the vascular system. The main factors involved are the pulsatile driving pressure generated by the heart, the flow characteristics of blood, and the geometric structure and mechanical properties of the vessels. The relationship between driving pressure and flow in a given vessel can be understood by considering the viscous and inertial forces acting on the blood. Depending on the vessel diameter and other physical parameters, a wide variety of flow phenomena can occur.

In hemoodynamics arteries, the propagation of the pressure pulse depends on hekodynamics elastic properties of the artery walls. In the microcirculation, the fact that blood is a suspension of cells strongly influences its flow properties and leads to a non-uniform distribution of hematocrit among microvessels. The forces acting on vessel walls include shear stress resulting from blood flow and circumferential ,ilnor resulting from blood pressure.

Biological responses to these forces are important in the control of blood flow and the structural remodeling of vessels, and also play a role in major disease processes including hypertension and atherosclerosis. hemodynammics

Consideration of hemodynamics is essential hemodyamics a comprehensive understanding of the functioning of the circulatory system. The circulatory system consists of the heart and an extensive branched system of vessels containing blood, whose primary function is the transport of oxygen, nutrients he,odynamics other substances and heat throughout the body. According to this definition, the emphasis is on the fluid and miknor mechanics of the system. While numerous biological processes have important interactions with hemodynamic effects, these processes are not discussed in depth.

Furthermore, the fluid and solid mechanics of the heart are not addressed here, as they are described in other articles in this series. The study of hemodynamics has a long history. The quantitative reasoning of William Harvey — led in hemodynamlcs the concept that blood continuously circulates InStephen Hales — reported direct measurements of arterial pressure Among his many scientific contributions, Thomas Young — established the relationship between the elastic properties of arteries and the propagation speed of the arterial pulse Through meticulous experiments, J.

Poiseuille — in established the fourth-power relationship between flow rate and diameter for a tube subject to a fixed pressure gradient along hemovynamics length One of the several contributions of Otto Frank — to physiology was his development of the Windkessel model to describe the mechanical interaction between the ejection of blood from the left ventricle during systole and the elasticity of the aorta and the major arteries In this model, the elastic arteries are considered as a single compliant compartment.

## Hemodynamics

The modern era of theoretical hemodynamics can be considered to begin in the s with the work of John R. Womersley — and Donald A. McDonald —who observed and analyzed the time-dependent motion of blood in an elastic artery driven by a fluctuating pressure gradient 63 Its various editions contain detailed reviews of the history of hemodynamics.

For further historical information, see also 2466 This review starts with a discussion of some basic concepts of hemodynamics, considering the relationship between pressures and flows in a hdmodynamics of blood vessels. Next, an introduction to the concepts of continuum mechanics is provided, including fluid and solid mechanics.

Aspects of blood flow mechanics specific to arteries are considered next, including pulsatile flow, arterial compliance, propagation of the pulse wave, and effects of specific geometrical features of the arteries. Distinctive characteristics of blood flow in the veins are briefly considered.

The microcirculation is discussed with emphasis on the consequences of the suspension characteristics of blood, including strong variations in the flow properties of blood and non-uniform distribution of hematocrit in hemoxynamics networks. More detailed discussions of many of the topics mentioned here can be found in several books 71228646671 At a fundamental level, the study of hemodynamics is concerned with the distribution of pressures and flows in the circulatory system.

However, milhor can equivalently be considered as internal mechanical energy per unit volume. By pressurizing blood, the pumping heart provides it with this internal energy that is available to drive its motion hemdynamics the circulation. These quantities should be carefully distinguished. In discussions of hemodynamics, an analogy with electric circuits is commonly introduced.

In this analogy, the pressure at a point in the circulation corresponds to the voltage Hemodnamics energy per unit charge at a point in a circuit, and milbor volume flow rate corresponds milnoor the current I charge per unit time in the circuit.

This relationship is strictly valid only when flow does not vary with time.

### Hemodynamics / William R. Milnor – Details – Trove

In a time-varying flow, the driving pressure includes a component related to the acceleration of blood. Under a broad range of conditions, the flow resistance of mlinor blood vessel is approximately independent of the flow rate, and depends only on the geometrical properties of the vessel and on the viscosity of blood, as discussed below.

In this approximation, the vascular system or a subset of it can be viewed as a network of resistances, fed and drained by known pressures Figure 1A. The flow rates in each segment of the network can be calculated using basic principles, such as the laws for the combined resistance of resistors connected in series or in parallel, namely. Many important phenomena in the circulatory system hwmodynamics be understood from the perspective of a hemodynmics of resistors.

For example, an increase in flow resistance of an individual segment, resulting from constriction or from partial blockage by a hemocynamics or lesion, causes a decrease in flow in all dependent segments of a tree-like vascular structure Figure 1B. Schematic representation of the systemic circulation as a network of resistances.

Basic elements of the systemic circulation. The pressure gradient between arterial pressure P A generated by the left heart and venous pressure P V drives blood through a network of blood vessels, consisting of the arteries, the microcirculation and the veins. Vascular segments are indicated by zigzag symbols, as in electrical circuits. The pulmonary circulation not shown has the same overall structure. Arrays of dots signify additional levels of branching in the network. The concept of flow resistance can also be applied to the peripheral circulation as a whole, considered as a single resistance, giving.

The total peripheral resistance at any moment depends on the geometric properties of the vascular system, including effects of vascular tone on vessel diameter, and on the flow properties of blood. It determines the pressure that the left heart must generate in order to provide a given level of cardiac output.

The PWP is measured by wedging a pulmonary catheter with an inflated balloon in a small pulmonary arterial branch, and measuring the pressure downstream of the occlusion.

It provides an estimate of pulmonary venous pressure. The pressure drop across the lungs typically about 10 mmHg is much lower than the drop across the systemic circulation typically about mmHg. The adequate distribution of blood flow to all parts of the body, so as to meet the changing needs of the tissues for oxygen and other nutrients and for removal of waste products, represents the most essential function of the circulatory system.

Considering the circulation as a network of interconnected resistors is simplistic for many reasons, some of which are addressed in the following sections. Nonetheless, it provides an essential basis for understanding how the distribution of blood flow can be controlled by the active contraction or dilation of blood vessels, and how it can be disturbed by disease processes leading to vessel blockage. In practice, this approach is not feasible for a system such as an artery containing flowing blood because the number of molecules in the system is too large.

Instead, a continuum approach is generally adopted, in which the physical properties of a material component of the system, such as its velocity, density or temperature, are represented as continuous functions of position.

The value of a given variable at a point then represents a local average of the variable over a small region. Fluctuations on smaller scales, arising for example from thermal motion of molecules, are not explicitly represented. Instead, the forces acting in a continuum are described using the concept of stress, as defined below.

This dependence is expressed in mathematical form using constitutive equations, which depend on the type of material under consideration. The size of the region is then considered to approach zero. In this limit, a system of partial differential equations is derived, relating the stress to the motion at each point in the material. These equations can be combined with the constitutive equations of the material to yield the governing equations of the continuum, which again take the form of partial differential equations.

The discussion of the key concepts of continuum mechanics, as introduced above, is expanded in the following paragraphs. The study of continuum mechanics is necessarily mathematical, requiring the use of vector calculus and partial differential equations to describe the spatial distributions of material motion and deformation. In this review, only a few key elements of the mathematical treatment are introduced.

Emphasis is placed on providing physical insights into the phenomena involved, so that mathematical expertise is not essential for gaining an appreciation of the subject.

For treatments of continuum mechanics in more mathematical detail, with an emphasis on applications in biomechanics, see 27 The hempdynamics forces in a continuum are represented using the concept of stress, which can be defined as follows. The local stress vector or traction T is defined as the force per miljor area acting on the surface. Given a system x 1x 2x 3 of Cartesian coordinates in three dimensions, T can be represented in terms of its components Imlnor 1T 2T 3 or briefly as T i where i is understood to take the values 1, 2 or hemodynamica.

Generally, T depends on the orientation of the surface being considered. A tensor is a generalized form of a vector that allows the representation of additional levels of directional information. This particular tensor is of second rank, i. Each component represents the traction force in the i th coordinate direction acting on a surface whose normal vector is in the j th coordinate direction Figure 2B.

Then the traction vector T acting on hemdoynamics arbitrarily oriented surface is given by. Bemodynamics of concepts underlying the definition of the stress tensor in a material. In general, this vector has components parallel to the surface shear force and normal to the surface normal force.

The net force on a small cuboid of material resulting from a stress in the material is zero if the stress is uniform, because the traction vectors acting on opposite faces of the cuboid are equal and opposite. However, if the stress distribution is not uniform, the traction vectors do not cancel and a net force is generated. Such a stress component is referred hemodynmaics as a mlinor stress, because it acts normal perpendicular to the surface. Such a stress component acts parallel to the surface and is referred to as a shear stress.

Although the definition of the stress tensor does hemodyna,ics depend on the specific coordinate system chosen, the components of the tensor do vary according to the choice of coordinates, except in the case of isotropic stress. A normal stress component in one coordinate system may appear as a shear stress component in a different rotated coordinate system.

Caution is needed in interpreting the physical significance of normal and shear stresses. Besides the Cauchy stress, other measures of miknor are commonly used, particular in the study of large deformation elasticity, such as the Piola-Kirchhoff stresses. These are not discussed here.

In summary, the stress tensor represents the forces per unit area acting on a small surface at a point in a continuum. Pa, PascalmmHg and cmH 2 O. This requires consideration of the net force acting on a piece of material, resulting from the stress in the material. In particular, consider a small cuboidal region aligned with the coordinate axes Figure 2C.

Suppose first that the stress tensor is uniform in space, i. In that case, the forces acting on any two opposite faces of the cuboid are jilnor and opposite according to Eq.