The Transport of Low Density Lipoprotein in the human carotid model

4  
 
 
Abstract 
The accumulation of macromolecules such as LDL plays an important role in the information of the 
plaques in atherosclerosis disease.  The role of regional flow and wall fluid shear is fundamental to 
disease genesis and progress. In particular, the atherosclerosis shows predilection in regions of 
arterial tree with hemodynamics particularities, as local disturbances of wall shear stress and 
locally high concentration of LDL. The computational model included  a steady flow analysis with 
time varying inflow velocity and with the measured of LDL transport analysis.  The concentration 
of LDL is specified as a boundary condition through a definition of a  UDF and  the initial velocity is 
defined through the UDF, which permits to impose a sinusoidal development of the velocity . The 
results indicated that in the low wall shear regions, the reduced arterial flows enhanced LDL 
accumulation.
5 Chapter 1 
CHAPTER 1 
Introduction 
 
1.1 Anatomy of the cardiovascular system 
The cardiovascular system is composed of the heart, which pumps the blood and the network of 
blood vessels that convey blood to the body and drain it from the body tissues to the heart. 
1.1.1 The heart 
The heart is a muscular organ made of two synchronized pumps in parallel: the right side, which 
collects deoxygenated blood from the systemic venis and perfuses the lungs, and the left side, 
which collects oxygenated blood from the pulmonary venis and perfuses the rest of the body. The 
heart is comprised almost entirely of myocardium, specialized muscle cells, cardiomyocytes, that 
differ from other muscle cells in their contractibility, lower, and their resistance to fatigue. The 
heart has four cavities: upper left, LA, and right, RA, atria that collect the blood from the venis 
lower left, LV, and right, RV, ventricles, that contract to propel the blood in the systemic and 
pulmonary venis. the left ventricle, the largest chamber with the thickest walls, is located 
posteriorly and leftwards from the right ventricle , which can be thought of as a chamber wrapped 
around the right side of the left ventricle from the heart base to the apex. The two ventricles share 
a septum, which separates the heart into the left and right sides. the heart is surrounded by the 
pericardium, a serous, inelastic membrane that restricts excessive dilation of the heart and can 
limit ventricular filling.  There are four valves in the heart, one at the exit of each heart cavity. All 
of the valves are embedded in the fibrous skeleton of the heart, which divides the atria from the 
ventricles. The mitral valve, which presents blood from flowing back from the LV to the LA, has 
two leaflets and is prevented from prolapsing by the chordae tendons and papillary muscles 
running from the cups of the valve leaflets to the side of the LV. The aortic valve guards the exit of 
the LV into the aorta, the major systemic artery. It has three leaflets which are inserted into the 
walls of the sinus of Valsava, rougly hemispherical bulges at the root of the aorta. The aortic valve 
has three simple leaflets without any attachments that come together, providing mutual support 
when they are closed. The corresponding valves in the right heart are tricuspid valve between the 
RA and RV and the pulmonary valve between the RV and the root of the main pulmonary artery.
6 Chapter 1 
The heart itself is perfused by the right and the left coronary arteries, originating from two of the 
three sinuses of Valsava just above the aortic valves.  
 
Fig.1.1 The anatomy of the heart 
 
The large coronary arteries from the network that lies on the outer layer of the heart wall. The 
smaller arteries dive into the wall where they branch off to form the microcirculation of the 
myocardium. Because the myocardium lacks  the ability of other muscle cells to contract 
anaeorobically, without oxygen, the constant supply of oxygen by the coronary vessels is crucial to 
the regular function of the heart. The heart is innervated by both components of the autonomic 
nervous system: the parasympathetic and the sympathetic nerves. Normally, the parasympathetic 
innervation is the dominant neural influence on the heart.  
Deoxygenated blood from the head and the upper body and from the torso and lower limbs is 
brought to the right atrium by the superior and inferior venae cavae. While there are valves in the 
medium sized veins that prevent the back flow of blood, there are no valves between the venae 
cavae and the atria. This blood flows through the tricuspid valve into the RV. When the RV 
contracts, the tricuspid valve closes and the pulmonary valve opens, allowing the blood to flow 
into the main pulmonary artery. Oxygenated blood from the lungs flows into the LA through a 
variable number, most often 4, of pulmonary veins. There are no valves at the outlet of these
7 Chapter 1 
veins; it is difficult, in fact, to distinguish where the veins end and the atrium begins. This blood 
flows through the mitral valve into the LV. When the LV contracts, the mitral valve closes and the 
aortic valve opens, allowing the blood to flow into the aorta and thence the systemic circulation. 
 
1.1.2 The large vessels 
The large vessels present the wall that is characterized by a circumferentially layered structure. 
The internal lumen layer is the intima made up of the endothelium attached to a basement 
membrane and a thin layer of connective tissue, subendothelium, connected to the internal elastic 
lamella. The internal elastic lamella delimits the intima from the media. the media is formed by 
layers of smooth muscle cells interspersed with elastic lamellae. These lamellae are about 15	 
thick and their structure is conserved across different sized arteries, larger arteries simply having 
more lamellae. The thickness of the media is ~10% of the internal diameter of the artery for the 
larger arteries. The outer limit of the media is delineated by the external elastic lamella. The outer 
layer of the arteries is the adventitia, consisting mainly of loose connective tissue with some 
smooth muscle cells. In larger vessels the adventitia contains nerves, vasa vasorum and lymphatic 
vessels. The adventitia is generally considered to play a minor role in the mechanics of the vessel 
wall, although damage to the adventitia can lead to chronic changes in the properties of the artery 
wall. There are subtle differences in the structure and properties of the large arteries at different 
locations in the arterial tree. Arteries proximal to the heart, particularly the ascending aorta, are 
known as elastic arteries. 
 
Fig. 1.2 the cross-section of a large artery
8 Chapter 1 
 
Their walls can be sigtly thinner than more distal arteries with a smaller fraction of smooth muscle 
cells. As a result they are more distensible and provide much of the Windkessel effect, which is 
defined as compliance chamber, whereby the starting-stopping nature of the blood flow expelled 
from the ventricle is smoothed out over the cardiac cycle to become pulsatile without any zero 
flow period downstream from the main elastic arteries. The more distal muscular arteries have a 
larger fraction of smooth muscle, a thinner internal elastic lamella and a much more clearly 
delineated external elastic lamella. the smooth muscle can alter the tone of the arteries and can 
respond to both neural and humoral stimuli in the control  of the cardiovascular system. The 
elastin compose a complex network of elastic tissue that forms a scaffold for the smooth muscle 
cells with many connections between the different lamellae. The elastic tissue can make up more 
than 50% of the dry weight of the large arteries. The collagen fibres are oriented in a roughly 
helical form around the artery and are generally tortuous under normal conditions. As the artery is 
distended, the collagen fibers straighten and, because of their large tensile strength, bear more 
and more of the load. Because of their variability and number, very little is known about the 
medium sized arteries. It is usually assumed that they resemble scaled down versions of the ore 
distal muscular arteries which have been studied. The walls of the large veins are thinner than 
their corresponding arteries and their bore is generally larger. The intima is very thin and the 
internal and external elastic lamellae are either absent or very thin. The media is thinner than the 
adventitia. Medium sized veins are characterized by the presence of valves that prevent blood 
from flowing distally during muscular compression of the veins. The largest veins of the abdomen 
and thorax have very thick adventitia, which contains bundles of longitudinal smooth muscle cells 
and vasa vasorum. Valves are absent. Venous valves are generally bicuspid and located in stiffer 
expanded segments of the vein. Venous Valves are made of connective tissue with elastic fibres 
and few smooth muscle cells, covered by the endothelium. Veins are often elliptical in cross 
section. Valve leaflefts are inserted on the lower curvature faces of the vein wall while tributary 
veins usually enter the edges with the higher curvature.
9 Chapter 1 
 
1.1.3 The small vessels 
The small vessels: Arterioles are usually defined as being less than 30 in diameter. They are 
composed of a continuous endothelium surrounded by one or two concentric layers of smooth 
muscle cells. Arterioles receive both sympathetic and parasympathetic innervation and are the 
principle regulators of local blood flow, through the action of muscular cells. Capillaries are small 
exchange vessels composed of endothelium surrounded by a basement membrane with three 
structural types.  
 
Fig. 1.3 the cross-section of a small blood vessel 
 
Continuous capillaries , found in muscle, skin, lungs and the central nervous system, have a 
continuous basement membrane and thight intercellular clefts between endothelial cells. They, 
thereby, have the lowest permeability. Fenestrated capillaries, found in endocrine glands, renal 
glomeruli, and intestinal mucosa, are characterized by perforations in the endothelium and, thus, 
by relatively higher permeability. Discontinuous capillaries, found in liver, spleen and bone 
marrow are defined by large gaps in the endothelium and basement membrane and, 
consequently, have very high permeability. Venules are composed of a continuous endothelium 
surrounded by a basement membrane for the post capillary venules and smooth muscle for the 
larger venules.  
Venules  have been classified into:
10 Chapter 1 
- microvenules  
- minivnules 
- venules. 
 
1.2 The blood 
Blood contains living cells and plasma. The plasma represents ~55% of the blood volume with 
remaining being the cells. the volume fraction of the cells is called the hematocrit. Because 
erytrocites, red blood cells, represent 97% of the cell volume, the haematocryt is variously defined 
as red blood cell volume fraction. The plasma contains ~92% water with the rest being made up 
of proteins, small molecules and ion. The major electrolytes in blood are the cations 
  ,  ,  ,	  and the anions    ,   ,   		   .  Small sugars and 
carbohydrates are transported in the blood. Blood glucose is the most important of the small 
molecules and its concentration, which is defined glycaemia, depends upon the exogenous supply 
and the degredation of the hepatic glycogen and it is controlled by the hormone insulin. The 
circulating blood proteins include fibrinogen and other clotting factors. Albumin is the main 
plasma protein, synthesized in the liver. It binds many small molecules for transport through the 
blood. Albumin, together with the electrolytes, is the main determinant of the osmotic pressure of 
the blood, which maintains the water balance between blood and the tissues. The non-protein 
nitrogen in the blood is contained in the urea, uric acid, creatine, creatinine, ammonium salts and 
amino acids. Lipid are essential for the formation and repair of cell membrane but are higly 
hydrophobic. They are transported in the blood in the liporpoteins, which are classified by their 
size and density; chylomicrons are the largest and are many involved in the transport of 
hydrophobic molecules from the small intestine to the liver where they are sequestred and 
processed. Very low density lipoproteins, VLDL, are synthetized in the liver and contain lipids, 
triglycerids and cholesterol esters. VLDL is converted into intermediate density lipoprotein, ILDL 
and low density lipoprotein, LDL, through a complex cascade. LDL is the primary mode of transport 
of lipid and colestherol through the body. Most cells have LDL receptors that are involved in the 
transport of lipids.  High density lipoprotein, HDL, a separate lipoprotein also synthetized in the 
liver, is primarily involved in the transport of the excess lipids and cholesterol from the tissue to 
the liver for storage or excretion. There are three main kinds of blood cells:
11 Chapter 1 
1) erythrocrytes, which are higly specialized cells that contain  neither a nucleus nor 
mitochondria. They consist of a bilipid membrane and membrane cytoskeleton 
surrounding a solution of haemoglobin. At the rest they assume a bioconcave discoid 
shape approximately 8	 in diameter and 2 in thick. Since the capillary diameters are 
often smaller than 6,	 the cells must deform considerably during their passage through 
the microcirculation. Haemoglobin is a protein with a high affinity for oxygen and most 
oxygen is transported from the lungs to the tissues via this route. Erythrocytes have an 
average life span of ~	3 months and they are constantly being generated by the bone 
marrow, ~6∗10
	
  ⁄ . The high cell content of the blood means that it has very 
complex rheological properties associated with cell deformability and aggregation  
 
2) leukocytes, or white blood cells, which are globular cells principally involved in the 
immune defence of the body and they have an average life span of only a few days. There 
are five types of leukocytes: 
 
a) neutrophils consist of 50−70%	 of all leukocytes and they have a diameter equal to 
8−15.	 Otherwise they are able to phagocytes foreign cells, toxins and viruses; 
b) eosinophils are less than 5% of all leukocytes, have a diameter equal to ~15	 and 
they phagocytes antigen-antibody complexes; 
c) basophils are less than 1% of all leukocytes , have a diameter equal to ~12−15	 
and release preformed granule associated mediators, include histamine, which cause 
vasodilatation, serotonin, bradykinin, heparin, which is anticoagulant and cytokines 
and newly generate mediators, such as prostaglandins and leukotrienes.  
The lymphocytes, 25−35% of hall leukocytes, have a diameter equal to ~15	 , also 
play an important role in the immune response by providing antigen specific acquired 
immunity, in other words they represent the immunological memory. The monocytes, 
3−9% of hall leukocytes, have a diameter equal to ~15−25	 , give rise to mature 
macrophages that reside in the tissues and defend the body against viruses and bacteria.  
 
3) platelets, of thrombocytes, which have a diameter equal to 2−4 , are non-nucleated 
cells with an average life span of 10 days, that are involved in coagulation. Platelets are 
dense in granules which contain serotonin, granulophysin, P-slectin, growth factors, 
clotting molecules and chemostatic compounds. Circulating platelets are kept in an
12 Chapter 1 
inactive state particularly by prostacyclin and no release by the endothelium. Platelet 
activation is affected by haemodynamics forces. At site of injury, the platelet adhere to 
the exposed sub-endothelium, aggregate and initiate the coagulation cascade. Platelets 
are also active in inflammation, synthesizing proteins involved in the inflammatory 
pathways.  
 
1.3  The cardiovascular physiology 
The cardiovascular system is divided into the systemic circulation supplied by the left ventricle, LV, 
and the pulmonary circulation supplied by the right ventricle, RV. Each circulation can be divided 
conveniently into 4 parts: 
1. the corresponding heart pump; 
2. the arteries; 
3. the microcirculations; 
4. veins. 
This is a closed system with each part interacting with every other part more or less strongly. For 
example, over time the same amount of blood must flow through the left and the right side of the 
heart. There can be transient variations which lead to the redistribution of blood within the 
circulatory system, but these differences cannot be sustained for long and haemostasis will soon 
be reestablished. The heart is a single organ that is divided into the left and right sides. The 
arteries are the larger blood vessels that carry blood from the heart to the microcirculation in the 
tissue to be perfused and then the veins carry the blood back to the heart. In terms of mechanics, 
the large arteries and veins are differentiated from other vessels by their size and predominance 
of inertial effects over viscous effects in the flow blood in them. This is characterized by relatively 
large values of Reynolds number: 
 =
  
(1.1) 
 
It is a dimensionless number that depends on the diameter vessel D, the mean blood velocity u, 
the density ρ and the viscosity μ. The large difference in Re results in profoundly different fluid 
mechanics characteristics in the large and small vessels and so it is usual to threat them 
separately.
13 Chapter 1 
 
 
1.3.1 The cardiac cycle 
The cardiac cycle is the sequence of events that occurs when the heart beats. There are two 
phases of the cardiac cycle. In the diastole phase, the heart ventricles are relaxed and the heart 
fills with blood. In the systole phase, the ventricles contract and pump blood to the arteries. One 
cardiac cycle is completed when the heart fills with blood and the blood is pumped out of the 
heart. The events of the cardiac cycle described below trace the path of the blood as it enters the 
heart, is pumped to the lungs, travels back to the heart and is pumped out to the rest of the body. 
It is important to note that the events that occur in the first and second diastole phases actually 
happen at the same time. The same is also true for the events of the first and second systole 
phases. The frequency of the cardiac cycle is described by the heart rate. Each beat of the heart 
involves five major stages. The first two stages, often considered together as the "ventricular 
filling" stage, involve the movement of blood from atria into ventricles. The next three stages 
involve the movement of blood from the ventricles to the pulmonary artery (in the case of the 
right ventricle) and the aorta (in the case of the left ventricle). The first, "early diastole", is when 
the semilunar valves close, the atrio-ventricular (AV) valves are open, and the whole heart is 
relaxed. The second, "atrial systole", is when the atrium contracts, and blood flows from atrium to 
the ventricle. The third, "iso-volumic ventricular contraction", is when the ventricles begin to 
contract, the AV and semilunar valves close, and there is no change in volume. The fourth, 
"ventricular ejection", is when the ventricles are empty and contracting, and the semilunar valves 
are open. During the fifth stage, "Iso-volumic ventricular relaxation", pressure decreases, no blood 
enters the ventricles, the ventricles stop contracting and begin to relax, and the semilunar valves 
close due to the pressure of blood in the aorta. 
Throughout the cardiac cycle, blood pressure increases and decreases. The cardiac cycle is 
coordinated by a series of electrical impulses that are produced by specialized heart cells found 
within the sinoatrial node and the atrio-ventricular node. The cardiac muscle is composed of 
myocytes which initiate their own contraction without help of external nerves (with the exception 
of modifying the heart rate due to metabolic demand). Under normal circumstances, each cycle 
takes approximately one second.
14 Chapter 1 
 
Fig. 1.4 A sketch of the events occurring during the cardiac cycle: The cardiac cycle diagram shown to the 
right depicts changes in aortic pressure (AP), left ventricular pressure (LVP), left atrial pressure (LAP), left 
ventricular volume (LV Vol), and heart sounds during a single cycle of cardiac contraction and relaxation. 
These changes are related in time to the electrocardiogram. 
 
Atrial systole is the contraction of the heart muscle (myocardia) of the left and right atria. 
Normally, both atria contract at the same time. The term systole is synonymous with contraction 
(movement or shortening) of a muscle. Electrical systole is the electrical activity that stimulates 
the myocardium of the chambers of the heart to make them contract. This is soon followed by 
Mechanical systole, which is the mechanical contraction of the heart. 
As the atria contract, the blood pressure in each atrium increases, forcing additional blood into the 
ventricles. The additional flow of blood is called atrial kick. 
80% of the blood flows passively down to the ventricles, so the atria do not have to contract a 
great amount. 
Atrial kick is absent if there is loss of normal electrical conduction in the heart, such as during atrial 
fibrillation, atrial flutter, and complete heart block. Atrial kick is also different in character 
depending on the condition of the heart, such as stiff heart, which is found in patients with 
diastolic dysfunction. The detection of atrial systole consist of the electrical systole of the atria 
begins with the onset of the P wave on the ECG. The wave of bipolarization (or depolarization) 
that stimulates both atria to contract at the same time is due to sinoatrial node which is located