This book is concerned with cardiovascular biomechanics; it is the study of the function and the structure of the cardiovascular system using the methods of mechanics. The forces perpendicular to the face cause compression of the material and this is the case whether the material is liquid or solid.
Solid Mechanics
- Young ’ s Modulus
- Poisson ’ s Ratio
- Models of Viscoelastic Behaviour
- Linear Elastic Theory (Isotropic)
- Linear Elastic Theory (Generalised)
- Constitutive Models for Non-linear Elasticity
- Materials in Practice
Young's modulus, E, is a measure of the elastic behavior of a material and is a fundamental mechanical property. Table 1.1 shows the number of elastic constants required for the constitutive model as a function of the number of dimensions and degree of anisotropy.
Fluid Mechanics
- Hydrostatic Pressure
- Shear Force and Strain Rate
- Viscosity
- Steady Flow in a Tube
- Reynolds Number and Flow States
- Unsteady Flow in Tubes
- Energy Considerations and the Bernoulli Principle
For a solid, a shear force causes a stress (represented by the angle θ in Fig.1.7); the greater the shear force, the greater the stress. At the entrance of a long pipe, the velocity profile flattens out initially, but after a certain length (called the 'inlet length') the velocity profile becomes parabolic and remains parabolic after this point.
Scientists Involved in the Development of Fluid and Solid Mechanics
Proposed a model describing the stress-strain behavior of materials with viscous and elastic behavior. Study the elastic behavior of materials formulating a model that can be used to describe the stress-strain behavior.
Relationships Between the 4 Elastic Constants for a Linear Isotropic Material
Components and Function
- Organisation of the Cardiovascular System
- Components of the Cardiovascular System
- Functions of the Cardiovascular System
The entry and exit of molecules into the cardiovascular system takes place through the capillary walls. The extracellular fluid consists of the fluid between cells (interstitial fluid), blood (in the cardiovascular system) and lymph (in the lymphatic system).
Physical Quantities
- Dimensions of the Systemic Circulation
- Pressure in the Systemic Circulation
- Pressure in Capillaries
- Flow and Velocity in the Systemic Circulation
Figures 2.4, 2.5 and 2.6 are based on the data in table 2.1 and show the change in the number, diameter and cross-sectional area of the vessels of the systemic circulation. The pressure in the venules and veins does not change much except with muscle action, as described in Chapter 7.
Constituents of Blood
- Plasma
- Macromolecules and Other Molecules
- Red Cells
- White Cells
- Platelets
Red cells are involved in the transport of oxygen from the lungs to the tissues, for which the iron in the red cell plays an important role. An increase in the volume fraction of white cells is a normal response to infection and is usually not harmful.
Forces on Blood Particles
- Forces Associated with Gravity
- Forces Associated with the Velocity and Shear Field at High Reynolds Number
- Forces Associated with the Velocity and Shear Field at Low Reynolds Number
- Chemical and Electrical Forces
- Forces Arising from Collision
If there is lateral motion of the particle (ie across streamlines) then this relative motion will also result in a drag force. All these forces are directed away from the wall resulting in movement of the particle away from the wall.
Viscous Behaviour of Blood
- Behaviour of Single Blood Cells
- Viscosity — Shear Rate Behaviour of Whole Blood
- Viscosity — Diameter Behaviour of Whole Blood
- Viscous Behaviour in Arteries
- Viscous Behaviour in Other Parts of the Cardiovascular System
The plasma layer near the wall moves at low speed, while the red blood cells in the center of the vessel move at high speed. In the expansion regime, there are stable vortices on both sides of the main flow. bVolume fraction of red blood cells.
Stiffness of Arteries
- Structure and Composition of Arteries
- Stress – Strain Behaviour in Arteries
In the left curve, the elastin has been removed by a chemical process, so that the mechanical behavior of the artery is controlled by the collagen. The artery is quite stiff, so a high load must be exerted to stretch the vessel. The artery is now quite elastic, so the small changes in stress result in large changes in diameter.
Pressure and Flow Waveforms in Arteries
- Windkessel Model
- Wave Propagation Model
- Propagation Model with Reflected Waves
- Pressure and Flow Waveforms at Different Distances from the Heart
Pressure and flow reach a maximum at the end of the ejection phase.cEjection of blood from the heart stops. Total resistance to flow is the sum of resistance in arteries and arterioles. The total flow rate is the ratio of the pressure gradient divided by the resistance to flow.
Flow in Arteries
- Turbulence, Disturbed and Laminar Flow
- Rotating Versus Axial Flow
- Fully Developed Flow Versus Non-fully Developed
- Symmetric Versus Asymmetric Velocity Profiles
- Considerations for Measurement of Blood Velocity and Related Quantities
Rotation of the flow is induced in a curved tube and in the daughter arms of branch tubes. The left ventricle in the heart twists during contraction, which induces a rotational current component in the aorta. It is hypothesized that the presence of rotational flow acts to stabilize flow in the arterial system by reducing shear stress differences (Shipkowitz et al. 2000).
Physical Quantities for Selected Arteries
Introduction
- Historical Introduction
- Forces on Arteries
- Murray ’ s Law
- Brief Review of Wall Shear Stress
- The Law of Laplace
- Brief Review of Circumferential and Longitudinal Wall Stress
The WSS is the viscous resistance of blood on the wall and acts in the plane of the wall. The circumferential tension in the aortic wall increases with animal size (5 N m−1 for the mouse rising to 190 N m−1 for the pig). Thickening of the wall during embryonic development occurs due to an increase in the number of lamellar units.
Arterial System Growth and Adaptability
- Embryogenesis
- Fetal Growth
- Birth
- Childhood
- Adulthood
- Intervention and Disease
- Summary of the Control of Arterial Structure
The artery's response is to lengthen to normalize the longitudinal stress. The loss of the umbilical supply leads to an increase in pressure in the aorta and the reduction in pulmonary resistance leads to a decrease in pressure in the pulmonary artery. However, there is increase in the wall thickness of the aorta and decrease in the wall thickness of the pulmonary artery.
Principles of Mechanotransduction
- Mechanotransmission
- Mechanosensing
- Mechanosignalling
- Mechanoresponse
- Switch-Like and Dynamic Models of Mechantransduction
- Other Mechanosensory Mechanisms
A reduction in tethering forces does not lead to a reduction in the length of the artery; instead, the artery will lengthen. If activated, mechanosensors can signal to other parts of the cell that there has been a change in the mechanical environment. More commonly, the response involves pathways within the cell that involve the cell's nucleus as well as signaling to other cells.
Endothelial Mechanotransduction
- Effect of Wall Shear Stress on Endothelium
- Decentralised Model of Endothelial Mechanotransduction
- Potential Wall Shear Stress Mechanosensors
The glycocalyx is a layer of glycoproteins covering the surface of the endothelial cell that extends up to 4.5 microns. Age-related increase in wall stress of the human abdominal aorta: an in vivo study. Explain how the normal electrical activation sequence of the heart is disrupted in an arrhythmia, and give an example.
Overview of Cardiac Structure and Function .1 Cardiac Anatomy and the Cardiac Cycle
- Cardiac Cells and Tissue
- Myocardial Perfusion and Metabolism
Contraction of the LV then pushes the oxygenated blood through the aortic valve and into the systemic circulation. Figure 6.2 illustrates typical pressure and volume in the left side of the human heart during each beat. Venous blood collects in the coronary sinus, which is located around the back of the heart, near the valve surface.
Electrical Excitation
- The Cardiac Action Potential
- Activation Sequence for Normal Beats
- Origin of the Electrocardiogram
- Arrhythmias and Conduction Defects
Electrical activation of the sinus node and atria is recorded on the ECG as the P wave. The duration of the P wave reflects the conduction of the action potential through the atria, and the PQ interval (usually erroneously referred to as the PR interval) indicates the atrial activation time plus slow conduction through the atrioventricular node. Activation of the atrioventricular node is irregular, so ventricular beats occur at irregular intervals.
Excitation-Contraction Coupling
- Molecular and Cell Scale Mechanisms
- Biomechanics of Cardiac Cells and Tissue
Repeated cross-bridge cycles produce movement of the thick filaments relative to the thin ones, and thus generate tension in the sarcomere. Throughout the heart, isometric contraction corresponds to the isovolumetric phase of the cardiac cycle, before the valves open. In the middle of the ventricular wall, myocytes are oriented with their long axis aligned with the circumferential direction and producing a circumferential component to wall stress.
Control of Cardiac Output .1 Frank – Starling Mechanism
- Work in the Heart
- Regulation of the Heart
An increase in preload increases end-diastolic volume, and this is thus reflected as a rightward shift of the isovolumic contraction phase of the pressure-volume loop. Increased afterload (higher systolic arterial pressure) results in earlier closure of the aortic valve, and thus the isolvolumic relaxation phase of the pressure-volume loop is shifted to the right. Increased contractility shifts the end-systolic pressure-volume curve upward, and thus the isovolumemic relaxation phase of the pressure-volume loop is shifted to the left.
Cardiac Remodelling .1 The Remodelling Process
- Engineering Mechanics of Ventricular Remodelling
Increase in the size of the ventricles associated with the pathological response to altered physiological conditions is commonly referred to as ventricular hypertrophy. In general, we recognize the conditions of pressure overload and volume overload as causative factors in the remodeling of the ventricles. The role of the venous system is to return blood to the heart under low pressure conditions compared to the arterial system.
Properties and Function of the Venous System
- Venous Composition and Compliance
- Vessel Collapse and Nonlinear Pressure – Area Relationship
- Resistance to Flow and Supercritical Flow in Collapsed Veins
- Venous Return
- Calf Muscle Pump
- The Respiratory Pump
The response of the finite element model shows significant changes in the cross-sectional geometry when the transmural pressure becomes negative. The anatomy of the sword muscle pump, which makes the most important contribution, is shown in Figure 7.5. The presence of valves in the veins of the legs and the reduction of pressure in the chest encourage flow towards the heart.
The Role of Venous Valves
- Valve Geometry
- Valve Locations and Incidence
- Dynamic Valve Behaviour
- Influence of Postural Changes
The leaflets do not fully open to the vein wall, resulting in a reduction in vessel diameter, as shown in cross-section in Figure 7.8a. Due to the extensibility of the venous system, changes in hydrostatic pressure lead to significant changes in venous volume. These effects have also been reported for deep circulatory veins with elevation changes of the leg (Cirovic et al.2006).
Biomechanics of Venous Disease .1 Venous Insuf ficiency
- Varicose Veins
- Deep Vein Thrombosis
DVT is the development of thrombus within the deep veins, typically of the calf or thigh. Effects of elastic compression stockings on wall shear stress in deep and superficial veins of the calf. The origin and development of the venous valves, with particular reference to the saphenous district.
Structure and Function of the Microcirculation .1 Structure
- Functions
Narrowing of the precapillary sphincters results in most of the flow passing through the preferential channel rather than the capillary bed. This allows control of the pressure at the capillaries and the flow rate through the capillary bed. The exchange of fluid and key molecules occurs through the walls of the capillaries.
Haemodynamics and Mechanics .1 Pressure and Velocity
- Blood Flow
- Myogenic Effect and Bayliss Effect
- Vessel Wall Mechanics
- Vasomotion
- Flow Pulsatility
- Wall Stress and Adaptability
Platelets in yellow occur mainly in the cell-free region (which has been pushed there by the RBCs). After an increase in blood pressure there is a decrease in diameter caused by constriction of the smooth muscle cells in the media. This is followed by constriction of the smooth muscle cells in the medial layer leading to a decrease in diameter over a period of 1–2 s.
Molecular Transport
- Starling ’ s Equations
- Molecular Movement Across the Capillary Wall
Conversely, when the net hydrostatic pressure is less than the net osmotic pressure, water will flow from the surrounding tissue into the capillary. The flow of fluid into or out of the capillaries requires that the blood pressure at the level of the capillaries be maintained at a stable level. In contrast, water-soluble molecules diffuse through the gaps (cuts or larger pores) in the capillary wall.
Control of Flow
- Metabolic Control
- Shear Stress Control
- Myogenic Control
Both CO2 and O2 are lipid soluble and thus can diffuse from the blood into the extracellular space across the lipid bilayer of the endothelium. A vesicle is a fluid-filled structure formed from the cell's membrane (lipid bilayer). Describe the principles of imaging of the different types of medical imaging systems (X-ray imaging techniques, MRI, ultrasound, PET, gamma camera imaging and SPECT).
Principles of Medical Imaging
- X-Ray Techniques
- Magnetic Resonance Imaging (MRI)
- Ultrasound
- Gamma Camera Imaging and Positron Emission Tomography
- Contrast Agents for Ultrasound and MRI
- Comparison of Medical Imaging Systems
- Catheter-Based Imaging — IVUS and OCT
This is a variant of angiography in which the tube and detector are rotated 180° around the patient (Figure 9.1d). A coil emitting in the radio frequency range is used to change the direction of proton magnetization (Figure 9.3b). The behavior of microbubbles in the acoustic field depends on the maximum sound pressure (Figure 9.10).
Measurements and Applications
- Geometry and Motion
- Blood Velocity and Related Quantities
- Strain
- Stiffness
- Functional Imaging in Cardiovascular Disease
3D time-varying data from the aorta can be obtained, allowing measurement of changes in diameter and length of the vessel over the cardiac cycle. Strain imaging is also widely used in elastography, which deals with the measurement of tissue stiffness (Hoskins 2012). Measuring tissue stiffness using imaging is called elastography.
Introduction to Cardiovascular Modelling .1 Model Definition
- Model Complexity
- Modelling
The complexity of the model depends on the needs of the problem to be solved. It is the analyst's responsibility to identify the purpose of the model and the level of complexity necessary to determine relevant data. An example of a specific question is determining the distribution of pressure and flow in the arterial system.
