Hemodynamics
or haemodynamics are the
dynamics of blood flow. The
circulatory system
The blood circulatory system is a system of organs that includes the heart, blood vessels, and blood which is circulated throughout the entire body of a human or other vertebrate. It includes the cardiovascular system, or vascular system, tha ...
is controlled by
homeostatic
In biology, homeostasis (British also homoeostasis) (/hɒmɪə(ʊ)ˈsteɪsɪs/) is the state of steady internal, physical, and chemical conditions maintained by living systems. This is the condition of optimal functioning for the organism and ...
mechanisms of
autoregulation
Autoregulation is a process within many biological systems, resulting from an internal adaptive mechanism that works to adjust (or mitigate) that system's response to stimuli. While most systems of the body show some degree of autoregulation, it ...
, just as
hydraulic circuit
Hydraulic machines use liquid fluid power to perform work. Heavy construction vehicles are a common example. In this type of machine, hydraulic fluid is pumped to various hydraulic motors and hydraulic cylinders throughout the machine and b ...
s are controlled by
control systems. The hemodynamic response continuously monitors and adjusts to conditions in the body and its environment. Hemodynamics explains the
physical law
Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) ...
s that govern the flow of blood in the
blood vessel
The blood vessels are the components of the circulatory system that transport blood throughout the human body. These vessels transport blood cells, nutrients, and oxygen to the tissues of the body. They also take waste and carbon dioxide away ...
s.
Blood flow ensures the transportation of
nutrients,
hormone
A hormone (from the Greek participle , "setting in motion") is a class of signaling molecules in multicellular organisms that are sent to distant organs by complex biological processes to regulate physiology and behavior. Hormones are require ...
s, metabolic waste products,
oxygen
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as ...
, and
carbon dioxide
Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is trans ...
throughout the body to maintain cell-level
metabolism
Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run c ...
, the regulation of the
pH,
osmotic pressure and temperature of the whole body, and the protection from microbial and mechanical harm.
Blood is a
non-Newtonian fluid
A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, i.e., constant viscosity independent of stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Ketchup, for ex ...
, and is most efficiently studied using
rheology
Rheology (; ) is the study of the flow of matter, primarily in a fluid (liquid or gas) state, but also as "soft solids" or solids under conditions in which they respond with Plasticity (physics), plastic flow rather than deforming Elasticity (phy ...
rather than hydrodynamics. Because blood vessels are not rigid tubes, classic hydrodynamics and fluids mechanics based on the use of classical viscometers are not capable of explaining haemodynamics.
The study of the blood flow is called hemodynamics, and the study of the properties of the blood flow is called
hemorheology
Hemorheology, also spelled haemorheology (from Greek ‘αἷμα, ''haima'' 'blood' and rheology, from Greek ῥέω ''rhéō'', 'flow' and -λoγία, ''-logia'' 'study of'), or blood rheology, is the study of flow properties of blood and its ...
.
Blood
Blood is a complex liquid.
Blood
Blood is a body fluid in the circulatory system of humans and other vertebrates that delivers necessary substances such as nutrients and oxygen to the cells, and transports metabolic waste products away from those same cells. Blood in the cir ...
is composed of
plasma and
formed elements. The plasma contains 91.5% water, 7%
proteins and 1.5% other solutes. The formed elements are
platelet
Platelets, also called thrombocytes (from Greek θρόμβος, "clot" and κύτος, "cell"), are a component of blood whose function (along with the coagulation factors) is to react to bleeding from blood vessel injury by clumping, thereby i ...
s,
white blood cells, and
red blood cell
Red blood cells (RBCs), also referred to as red cells, red blood corpuscles (in humans or other animals not having nucleus in red blood cells), haematids, erythroid cells or erythrocytes (from Greek ''erythros'' for "red" and ''kytos'' for "holl ...
s. The presence of these formed elements and their interaction with plasma molecules are the main reasons why blood differs so much from ideal Newtonian fluids.
Viscosity of plasma
Normal
blood plasma
Blood plasma is a light amber-colored liquid component of blood in which blood cells are absent, but contains proteins and other constituents of whole blood in suspension. It makes up about 55% of the body's total blood volume. It is the intr ...
behaves like a Newtonian fluid at physiological rates of shear. Typical values for the
viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
of normal human plasma at 37 °C is 1.4 mN·s/m
2. The viscosity of normal plasma varies with temperature in the same way as does that of its solvent water; a 5 °C increase of temperature in the physiological range reduces plasma viscosity by about 10%.
Osmotic pressure of plasma
The osmotic pressure of solution is determined by the number of particles present and by the
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer.
Thermometers are calibrated in various Conversion of units of temperature, temp ...
. For example, a 1 molar solution of a substance contains molecules per liter of that substance and at 0 °C it has an osmotic pressure of . The osmotic pressure of the
plasma affects the mechanics of the circulation in several ways. An alteration of the osmotic pressure difference across the membrane of a blood cell causes a shift of water and a change of cell volume. The changes in shape and flexibility affect the mechanical properties of whole blood. A change in plasma
osmotic pressure alters the hematocrit, that is, the volume concentration of red cells in the whole blood by redistributing water between the intravascular and extravascular spaces. This in turn affects the mechanics of the whole blood.
Red blood cells
The
red blood cell
Red blood cells (RBCs), also referred to as red cells, red blood corpuscles (in humans or other animals not having nucleus in red blood cells), haematids, erythroid cells or erythrocytes (from Greek ''erythros'' for "red" and ''kytos'' for "holl ...
is highly flexible and biconcave in shape. Its membrane has a
Young's modulus
Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied le ...
in the region of 106
Pa. Deformation in red blood cells is induced by shear stress. When a suspension is sheared, the red blood cells deform and spin because of the velocity gradient, with the rate of deformation and spin depending on the shear rate and the concentration.
This can influence the mechanics of the circulation and may complicate the measurement of blood
viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
. It is true that in a steady state flow of a viscous fluid through a rigid spherical body immersed in the fluid, where we assume the
inertia
Inertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law ...
is negligible in such a flow, it is believed that the downward
gravitational
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
force of the particle is balanced by the viscous drag force. From this force balance the speed of fall can be shown to be given by
Stokes' law
:
Where ''a'' is the particle radius, ''ρ
p'', ''ρ
f'' are the respectively particle and fluid density ''μ'' is the fluid viscosity, ''g'' is the gravitational acceleration. From the above equation we can see that the
sedimentation velocity of the particle depends on the square of the radius. If the particle is released from rest in the
fluid, its sedimentation velocity ''U
s'' increases until it attains the steady value called the terminal velocity (U), as shown above.
Hemodilution
Hemodilution is the dilution of the concentration of red blood cells and plasma constituents by partially substituting the blood with
colloids or
crystalloids
A volume expander is a type of intravenous therapy that has the function of providing volume for the circulatory system. It may be used for fluid replacement or during surgery to prevent nausea and vomiting after surgery.
Physiology
When blood is ...
. It is a strategy to avoid exposure of patients to the potential hazards of
homologous blood transfusions.
Hemodilution can be normovolemic, which implies the dilution of normal blood constituents by the use of expanders. During acute normovolemic hemodilution (ANH), blood subsequently lost during surgery contains proportionally fewer red blood cells per milliliter, thus minimizing intraoperative loss of the whole blood. Therefore, blood lost by the patient during surgery is not actually lost by the patient, for this volume is purified and redirected into the patient.
On the other hand, hypervolemic hemodilution (HVH) uses acute preoperative volume expansion without any blood removal. In choosing a fluid, however, it must be assured that when mixed, the remaining blood behaves in the microcirculation as in the original blood fluid, retaining all its properties of
viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
.
In presenting what volume of ANH should be applied one study suggests a mathematical model of ANH which calculates the maximum possible RCM savings using ANH, given the patients weight ''H
i'' and ''H
m''.
To maintain the normovolemia, the withdrawal of autologous blood must be simultaneously replaced by a suitable hemodilute. Ideally, this is achieved by isovolemia exchange transfusion of a plasma substitute with a colloid
osmotic pressure (OP). A
colloid is a fluid containing particles that are large enough to exert an oncotic pressure across the micro-vascular membrane.
When debating the use of colloid or crystalloid, it is imperative to think about all the components of the starling equation:
:
To identify the minimum safe hematocrit desirable for a given patient the following equation is useful:
:
where EBV is the estimated
blood
Blood is a body fluid in the circulatory system of humans and other vertebrates that delivers necessary substances such as nutrients and oxygen to the cells, and transports metabolic waste products away from those same cells. Blood in the cir ...
volume; 70 mL/kg was used in this model and ''H
i'' (initial hematocrit) is the patient's initial hematocrit.
From the equation above it is clear that the volume of blood removed during the ANH to the ''H
m'' is the same as the ''BL
s''.
How much blood is to be removed is usually based on the weight, not the volume. The number of units that need to be removed to hemodilute to the maximum safe hematocrit (ANH) can be found by
:
This is based on the assumption that each unit removed by hemodilution has a volume of 450 mL (the actual volume of a unit will vary somewhat since completion of collection ais dependent on weight and not volume).
The model assumes that the hemodilute value is equal to the ''H
m'' prior to surgery, therefore, the re-transfusion of blood obtained by hemodilution must begin when SBL begins.
The RCM available for retransfusion after ANH (RCMm) can be calculated from the patient's ''H
i'' and the final hematocrit after hemodilution(''H
m'')
:
The maximum SBL that is possible when ANH is used without falling below Hm(BLH) is found by assuming that all the blood removed during ANH is returned to the patient at a rate sufficient to maintain the hematocrit at the minimum safe level
:
If ANH is used as long as SBL does not exceed ''BL
H'' there will not be any need for blood transfusion. We can conclude from the foregoing that ''H'' should therefore not exceed ''s''.
The difference between the ''BL
H'' and the ''BL
s'' therefore is the incremental surgical blood loss (''BL
i'') possible when using ANH.
:
When expressed in terms of the RCM
:
Where ''RCM
i'' is the red cell mass that would have to be administered using homologous blood to maintain the ''H
m'' if ANH is not used and blood loss equals BLH.
The model used assumes ANH used for a 70 kg patient with an estimated blood volume of 70 ml/kg (4900 ml). A range of ''H
i'' and ''H
m'' was evaluated to understand conditions where hemodilution is necessary to benefit the patient.
Result
The result of the model calculations are presented in a table given in the appendix for a range of ''H
i'' from 0.30 to 0.50 with ANH performed to minimum hematocrits from 0.30 to 0.15. Given a ''H
i'' of 0.40, if the ''H
m'' is assumed to be 0.25.then from the equation above the RCM count is still high and ANH is not necessary, if BL
s does not exceed 2303 ml, since the hemotocrit will not fall below H
m, although five units of blood must be removed during hemodilution. Under these conditions, to achieve the maximum benefit from the technique if ANH is used, no homologous blood will be required to maintain the ''H
m'' if blood loss does not exceed 2940 ml. In such a case, ANH can save a maximum of 1.1 packed red blood cell unit equivalent, and homologous blood transfusion is necessary to maintain ''H
m'', even if ANH is used.
This model can be used to identify when ANH may be used for a given patient and the degree of ANH necessary to maximize that benefit.
For example, if ''H
i'' is 0.30 or less it is not possible to save a red cell mass equivalent to two units of homologous PRBC even if the patient is hemodiluted to an ''H
m'' of 0.15. That is because from the RCM equation the patient RCM falls short from the equation giving above.
If ''H
i'' is 0.40 one must remove at least 7.5 units of blood during ANH, resulting in an ''H
m'' of 0.20 to save two units equivalence. Clearly, the greater the ''H
i'' and the greater the number of units removed during hemodilution, the more effective ANH is for preventing homologous blood transfusion. The model here is designed to allow doctors to determine where ANH may be beneficial for a patient based on their knowledge of the ''H
i'', the potential for SBL, and an estimate of the ''H
m''. Though the model used a 70 kg patient, the result can be applied to any patient. To apply these result to any body weight, any of the values BLs, BLH and ANHH or PRBC given in the table need to be multiplied by the factor we will call T
:
Basically, the model considered above is designed to predict the maximum RCM that can save ANH.
In summary, the efficacy of ANH has been described mathematically by means of measurements of surgical blood loss and blood volume flow measurement. This form of analysis permits accurate estimation of the potential efficiency of the techniques and shows the application of measurement in the medical field.
Blood flow
Cardiac output
![Diagram of human circulatory system](https://upload.wikimedia.org/wikipedia/commons/8/84/Diagram_of_human_circulatory_system.gif)
The heart is the driver of the circulatory system, pumping blood through rhythmic contraction and relaxation. The rate of blood flow out of the heart (often expressed in L/min) is known as the cardiac output (CO).
Blood being pumped out of the heart first enters the
aorta
The aorta ( ) is the main and largest artery in the human body, originating from the left ventricle of the heart and extending down to the abdomen, where it splits into two smaller arteries (the common iliac arteries). The aorta distributes o ...
, the largest artery of the body. It then proceeds to divide into smaller and smaller arteries, then into
arterioles
An arteriole is a small-diameter blood vessel in the microcirculation that extends and branches out from an artery and leads to capillaries.
Arterioles have muscular walls (usually only one to two layers of smooth muscle cells) and are the primar ...
, and eventually
capillaries
A capillary is a small blood vessel from 5 to 10 micrometres (μm) in diameter. Capillaries are composed of only the tunica intima, consisting of a thin wall of simple squamous endothelial cells. They are the smallest blood vessels in the body: ...
, where oxygen transfer occurs. The capillaries connect to
venules
A venule is a very small blood vessel in the microcirculation that allows blood to return from the capillary beds to drain into the larger blood vessels, the veins. Venules range from 7μm to 1mm in diameter. Veins contain approximately 70% of ...
, and the blood then travels back through the network of veins to the
right heart
The heart is a muscular organ in most animals. This organ pumps blood through the blood vessels of the circulatory system. The pumped blood carries oxygen and nutrients to the body, while carrying metabolic waste such as carbon dioxide to ...
. The micro-circulation — the arterioles, capillaries, and venules —constitutes most of the area of the vascular system and is the site of the transfer of O
2,
glucose
Glucose is a simple sugar with the molecular formula . Glucose is overall the most abundant monosaccharide, a subcategory of carbohydrates. Glucose is mainly made by plants and most algae during photosynthesis from water and carbon dioxide, u ...
, and
enzyme substrate
In chemistry, the term substrate is highly context-dependent. Broadly speaking, it can refer either to a chemical species being observed in a chemical reaction, or to a surface on which other chemical reactions or microscopy are performed.
In the ...
s into the cells. The venous system returns the de-oxygenated blood to the right heart where it is pumped into the
lungs
The lungs are the primary organs of the respiratory system in humans and most other animals, including some snails and a small number of fish. In mammals and most other vertebrates, two lungs are located near the backbone on either side ...
to become oxygenated and CO
2 and other gaseous wastes exchanged and expelled during breathing. Blood then returns to the left side of the heart where it begins the process again.
In a normal circulatory system, the volume of blood returning to the heart each minute is approximately equal to the volume that is pumped out each minute (the cardiac output).
Because of this, the velocity of blood flow across each level of the circulatory system is primarily determined by the total cross-sectional area of that level.
Cardiac output is determine by two methods. One is to used the Fick equation:
The other thermodilution method is to sense the temperature change from a liquid injected in the proximal port of a Swan-Ganz to the distal port.
Cardiac output is mathematically expressed by the following equation:
:
where
* CO = cardiac output (L/sec)
* SV = stroke volume (ml)
* HR = heart rate (bpm)
The normal human cardiac output is 5-6 L/min at rest. Not all blood that enters the left ventricle exits the heart. What is left at the end of diastole (EDV) minus the stroke volume make up the end diastolic volume (ESV).
Anatomical features
Circulatory system of species subjected to orthostatic blood pressure (such as arboreal snakes) has evolved with physiological and morphological features to overcome the circulatory disturbance. For instance, in arboreal snakes the heart is closer to the head, in comparison with aquatic snakes. This facilitates blood perfusion to the brain.
Turbulence
Blood flow is also affected by the smoothness of the vessels, resulting in either turbulent (chaotic) or laminar (smooth) flow. Smoothness is reduced by the buildup of fatty deposits on the arterial walls.
The Reynolds number (denoted NR or Re) is a relationship that helps determine the behavior of a fluid in a tube, in this case blood in the vessel.
The equation for this dimensionless relationship is written as:
:
:* ''ρ'': density of the blood
:* ''v'': mean velocity of the blood
:* ''L'': characteristic dimension of the vessel, in this case diameter
:* ''μ'': viscosity of blood
The Reynolds number is directly proportional to the velocity and diameter of the tube. Note that NR is directly proportional to the mean velocity as well as the diameter. A Reynolds number of less than 2300 is laminar fluid flow, which is characterized by constant flow motion, whereas a value of over 4000, is represented as turbulent flow.
Due to its smaller radius and lowest velocity compared to other vessels, the Reynolds number at the capillaries is very low, resulting in laminar instead of turbulent flow.
Velocity
Often expressed in cm/s. This value is inversely related to the total cross-sectional area of the blood vessel and also differs per cross-section, because in normal condition the blood flow has
laminar characteristics. For this reason, the blood flow velocity is the fastest in the middle of the vessel and slowest at the vessel wall. In most cases, the mean velocity is used.
There are many ways to measure blood flow velocity, like videocapillary microscoping with frame-to-frame analysis, or
laser Doppler anemometry.
Blood velocities in
arteries
An artery (plural arteries) () is a blood vessel in humans and most animals that takes blood away from the heart to one or more parts of the body (tissues, lungs, brain etc.). Most arteries carry oxygenated blood; the two exceptions are the pu ...
are higher during
systole than during
diastole
Diastole ( ) is the relaxed phase of the cardiac cycle when the chambers of the heart are re-filling with blood. The contrasting phase is systole when the heart chambers are contracting. Atrial diastole is the relaxing of the atria, and ventri ...
. One parameter to quantify this difference is the pulsatility index (PI), which is equal to the difference between the peak systolic velocity and the minimum diastolic velocity divided by the mean velocity during the
cardiac cycle
The cardiac cycle is the performance of the human heart from the beginning of one heartbeat to the beginning of the next. It consists of two periods: one during which the heart muscle relaxes and refills with blood, called diastole, following ...
. This value decreases with distance from the heart.
:
Blood vessels
Vascular resistance
Resistance is also related to vessel radius, vessel length, and blood viscosity.
In a first approach based on fluids, as indicated by the
Hagen–Poiseuille equation
In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar fl ...
.
The equation is as follows:
:
:* ∆''P'': pressure drop/gradient
:* ''µ'': viscosity
:* ''l'': length of tube. In the case of vessels with infinitely long lengths, l is replaced with diameter of the vessel.
:* ''Q'': flow rate of the blood in the vessel
:* ''r'': radius of the vessel
In a second approach, more realistic of the
vascular resistance
Vascular resistance is the resistance that must be overcome to push blood through the circulatory system and create flow. The resistance offered by the systemic circulation is known as the systemic vascular resistance (SVR) or may sometimes be cal ...
and coming from experimental observations on blood flows, according to Thurston,
[GB Thurston, Viscosity and viscoelasticity of blood in small diameter tubes, Microvasular Research 11, 133 146, 1976] there is a plasma release-cell layering at the walls surrounding a plugged flow. It is a fluid layer in which at a distance δ, viscosity η is a function of δ written as η(δ), and these surrounding layers do not meet at the vessel centre in real blood flow. Instead, there is the plugged flow which is hyperviscous because holding high concentration of RBCs. Thurston assembled this layer to the flow resistance to describe blood flow by means of a viscosity η(δ) and thickness δ from the wall layer.
The blood resistance law appears as R adapted to blood flow profile :
:
where
* R = resistance to blood flow
* c = constant coefficient of flow
* L = length of the vessel
* η(δ) =
viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
of blood in the wall plasma release-cell layering
* r = radius of the blood vessel
* δ = distance in the plasma release-cell layer
Blood resistance varies depending on blood viscosity and its plugged flow (or sheath flow since they are complementary across the vessel section) size as well, and on the size of the vessels.
Assuming steady, laminar flow in the vessel, the blood vessels behavior is similar to that of a pipe. For instance if p1 and p2 are pressures are at the ends of the tube, the pressure drop/gradient is:
:
The larger arteries, including all large enough to see without magnification, are conduits with low
vascular resistance
Vascular resistance is the resistance that must be overcome to push blood through the circulatory system and create flow. The resistance offered by the systemic circulation is known as the systemic vascular resistance (SVR) or may sometimes be cal ...
(assuming no advanced
atherosclerotic
Atherosclerosis is a pattern of the disease arteriosclerosis in which the wall of the artery develops abnormalities, called lesions. These lesions may lead to narrowing due to the buildup of atheromatous plaque. At onset there are usually no ...
changes) with high flow rates that generate only small drops in pressure. The smaller arteries and arterioles have higher resistance, and confer the main blood pressure drop across major arteries to capillaries in the circulatory system.
![Blausen 0092 BloodPressureFlow](https://upload.wikimedia.org/wikipedia/commons/0/0c/Blausen_0092_BloodPressureFlow.png)
In the arterioles blood pressure is lower than in the major arteries. This is due to bifurcations, which cause a drop in pressure. The more bifurcations, the higher the total cross-sectional area, therefore the pressure across the surface drops. This is why the arterioles have the highest pressure-drop. The pressure drop of the arterioles is the product of flow rate and resistance: ∆P=Q xresistance. The high resistance observed in the arterioles, which factor largely in the ∆''P'' is a result of a smaller radius of about 30 µm. The smaller the radius of a tube, the larger the resistance to fluid flow.
Immediately following the arterioles are the capillaries. Following the logic observed in the arterioles, we expect the blood pressure to be lower in the capillaries compared to the arterioles. Since pressure is a function of force per unit area, (''P'' = ''F''/''A''), the larger the surface area, the lesser the pressure when an external force acts on it. Though the radii of the capillaries are very small, the network of capillaries has the largest surface area in the vascular network. They are known to have the largest surface area (485 mm^2) in the human vascular network. The larger the total cross-sectional area, the lower the mean velocity as well as the pressure.
Substances called
vasoconstrictor
Vasoconstriction is the narrowing of the blood vessels resulting from contraction of the muscular wall of the vessels, in particular the large arteries and small arterioles. The process is the opposite of vasodilation, the widening of blood vess ...
s can reduce the size of blood vessels, thereby increasing blood pressure.
Vasodilators (such as
nitroglycerin) increase the size of blood vessels, thereby decreasing arterial pressure.
If the blood viscosity increases (gets thicker), the result is an increase in arterial pressure. Certain
medical conditions
A disease is a particular abnormal condition that negatively affects the structure or function of all or part of an organism, and that is not immediately due to any external injury. Diseases are often known to be medical conditions that a ...
can change the viscosity of the blood. For instance, anemia (low
red blood cell
Red blood cells (RBCs), also referred to as red cells, red blood corpuscles (in humans or other animals not having nucleus in red blood cells), haematids, erythroid cells or erythrocytes (from Greek ''erythros'' for "red" and ''kytos'' for "holl ...
concentration) reduces viscosity, whereas increased red blood cell concentration increases viscosity. It had been thought that
aspirin
Aspirin, also known as acetylsalicylic acid (ASA), is a nonsteroidal anti-inflammatory drug (NSAID) used to reduce pain, fever, and/or inflammation, and as an antithrombotic. Specific inflammatory conditions which aspirin is used to treat inc ...
and related "
blood thinner
Anticoagulants, commonly known as blood thinners, are chemical substances that prevent or reduce coagulation of blood, prolonging the clotting time. Some of them occur naturally in blood-eating animals such as leeches and mosquitoes, where th ...
" drugs decreased the viscosity of blood, but instead studies found that they act by reducing the tendency of the blood to clot.
To determine the systemic vascular resistance (SVR) the formula for calculating all resistance is used.
This translates for SVR into:
Where
* SVR = systemic vascular resistance (mmHg/L/min)
* MAP = mean arterial pressure (mmHg)
* CVP = central venous pressure (mmHg)
* CO = cardiac output (L/min)
To get this in Wood units the answer is multiplied by 80.
Normal systemic vascular resistance is between 900 and 1440 dynes/sec/cm−5.
Wall tension
![Circumferential stress](https://upload.wikimedia.org/wikipedia/commons/1/1f/Circumferential_stress.svg)
Regardless of site, blood pressure is related to the
wall tension of the vessel according to the
Young–Laplace equation
In physics, the Young–Laplace equation () is an algebraic equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or w ...
(assuming that the thickness of the vessel wall is very small as compared to the diameter of the
lumen):
:
where
* ''P'' is the blood pressure
* ''t'' is the wall thickness
* ''r'' is the inside radius of the cylinder.
*
is the
cylinder stress
In mechanics, a cylinder stress is a stress distribution with rotational symmetry; that is, which remains unchanged if the stressed object is rotated about some fixed axis.
Cylinder stress patterns include:
* circumferential stress, or hoop stres ...
or "hoop stress".
For the thin-walled assumption to be valid the vessel must have a wall thickness of no more than about one-tenth (often cited as one twentieth) of its radius.
The
cylinder stress
In mechanics, a cylinder stress is a stress distribution with rotational symmetry; that is, which remains unchanged if the stressed object is rotated about some fixed axis.
Cylinder stress patterns include:
* circumferential stress, or hoop stres ...
, in turn, is the average
force exerted circumferentially (perpendicular both to the axis and to the radius of the object) in the cylinder wall, and can be described as:
:
where:
* ''F'' is the
force exerted circumferentially on an area of the cylinder wall that has the following two lengths as sides:
* ''t'' is the radial thickness of the cylinder
* ''l'' is the axial length of the cylinder
Stress
When force is applied to a material it starts to deform or move. As the force needed to deform a material (e.g. to make a fluid flow) increases with the size of the surface of the material A.,
the magnitude of this force F is proportional to the area A of the portion of the surface. Therefore, the quantity (F/A) that is the force per unit area is called the stress. The shear stress at the wall that is associated with blood flow through an artery depends on the artery size and geometry and can range between 0.5 and 4
Pa.
:
.
Under normal conditions, to avoid atherogenesis, thrombosis, smooth muscle proliferation and endothelial apoptosis, shear stress maintains its magnitude and direction within an acceptable range. In some cases occurring due to blood hammer, shear stress reaches larger values. While the direction of the stress may also change by the reverse flow, depending on the hemodynamic conditions. Therefore, this situation can lead to atherosclerosis disease.
Capacitance
Veins are described as the "capacitance vessels" of the body because over 70% of the blood volume resides in the venous system. Veins are more compliant than arteries and expand to accommodate changing volume.
Blood pressure
The blood pressure in the circulation is principally due to the pumping action of the heart.
The pumping action of the heart generates pulsatile blood flow, which is conducted into the arteries, across the micro-circulation and eventually, back via the venous system to the heart. During each heartbeat, systemic arterial blood pressure varies between a maximum (
systolic) and a minimum (
diastolic
Diastole ( ) is the relaxed phase of the cardiac cycle when the chambers of the heart are re-filling with blood. The contrasting phase is systole when the heart chambers are contracting. Atrial diastole is the relaxing of the atria, and ventricu ...
) pressure. In physiology, these are often simplified into one value, the
mean arterial pressure (MAP), which is calculated as follows:
where:
* MAP = Mean Arterial Pressure
* DP = Diastolic blood pressure
* PP = Pulse pressure which is systolic pressure minus diastolic pressure.
Differences in mean blood pressure are responsible for blood flow from one location to another in the circulation. The rate of mean blood flow depends on both blood pressure and the resistance to flow presented by the blood vessels. Mean blood pressure decreases as the
circulating blood moves away from the
heart
The heart is a muscular organ in most animals. This organ pumps blood through the blood vessels of the circulatory system. The pumped blood carries oxygen and nutrients to the body, while carrying metabolic waste such as carbon dioxide to t ...
through arteries and
capillaries
A capillary is a small blood vessel from 5 to 10 micrometres (μm) in diameter. Capillaries are composed of only the tunica intima, consisting of a thin wall of simple squamous endothelial cells. They are the smallest blood vessels in the body: ...
due to
viscous
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
losses of energy. Mean blood pressure drops over the whole circulation, although most of the fall occurs along the small arteries and
arteriole
An arteriole is a small-diameter blood vessel in the microcirculation that extends and branches out from an artery and leads to capillaries.
Arterioles have muscular walls (usually only one to two layers of smooth muscle cells) and are the primar ...
s.
Gravity affects blood pressure via
hydrostatic
Fluid statics or hydrostatics is the branch of fluid mechanics that studies the condition of the equilibrium of a floating body and submerged body "fluids at hydrostatic equilibrium and the pressure in a fluid, or exerted by a fluid, on an imme ...
forces (e.g., during standing), and valves in veins,
breathing, and pumping from contraction of skeletal muscles also influence blood pressure in veins.
The relationship between pressure, flow, and resistance is expressed in the following equation:
:
When applied to the circulatory system, we get:
:
where
* CO = cardiac output (in L/min)
* MAP = mean arterial pressure (in mmHg), the average pressure of blood as it leaves the heart
* RAP = right atrial pressure (in mmHg), the average pressure of blood as it returns to the heart
* TPR =
total peripheral resistance
Vascular resistance is the resistance that must be overcome to push blood through the circulatory system and create flow. The resistance offered by the systemic circulation is known as the systemic vascular resistance (SVR) or may sometimes be cal ...
(in mmHg * min/L)
A simplified form of this equation assumes right atrial pressure is approximately 0:
:
The ideal blood pressure in the
brachial artery, where standard blood pressure cuffs measure pressure, is <120/80 mmHg. Other major arteries have similar levels of blood pressure recordings indicating very low disparities among major arteries. In the innominate artery, the average reading is 110/70 mmHg, the right subclavian artery averages 120/80 and the abdominal aorta is 110/70 mmHg.
The relatively uniform pressure in the arteries indicate that these blood vessels act as a pressure reservoir for fluids that are transported within them.
Pressure drops gradually as blood flows from the major arteries, through the arterioles, the capillaries until blood is pushed up back into the heart via the venules, the veins through the vena cava with the help of the muscles. At any given pressure drop, the flow rate is determined by the resistance to the blood flow. In the arteries, with the absence of diseases, there is very little or no resistance to blood. The vessel diameter is the most principal determinant to control resistance. Compared to other smaller vessels in the body, the artery has a much bigger diameter (4 mm), therefore the resistance is low.
The ''arm–leg (blood pressure) gradient'' is the difference between the blood pressure measured in the arms and that measured in the legs. It is normally less than 10 mm Hg,
but may be increased in e.g.
coarctation of the aorta
Coarctation of the aorta (CoA or CoAo), also called aortic narrowing, is a congenital condition whereby the aorta is narrow, usually in the area where the ductus arteriosus (ligamentum arteriosum after regression) inserts. The word ''coarctation' ...
.
[
]
Clinical significance
Pressure monitoring
Hemodynamic monitoring
Monitoring may refer to:
Science and technology Biology and healthcare
* Monitoring (medicine), the observation of a disease, condition or one or several medical parameters over time
* Baby monitoring
* Biomonitoring, of toxic chemical compounds, ...
is the observation of hemodynamic parameters over time, such as blood pressure and heart rate
Heart rate (or pulse rate) is the frequency of the heartbeat measured by the number of contractions (beats) of the heart per minute (bpm). The heart rate can vary according to the body's physical needs, including the need to absorb oxygen and excr ...
. Blood pressure can be monitored either invasively through an inserted blood pressure transducer assembly (providing continuous monitoring), or noninvasively by repeatedly measuring the blood pressure with an inflatable blood pressure cuff
A sphygmomanometer ( ), a blood pressure monitor, or blood pressure gauge, is a device used to measure blood pressure, composed of an inflatable cuff to collapse and then release the artery under the cuff in a controlled manner, and a mercury o ...
.
Hypertension is diagnosed by the presence of arterial blood pressures of 140/90 or greater for two clinical visits.
Pulmonary Artery Wedge Pressure can show if there is congestive heart failure, mitral and aortic valve disorders, hypervolemia
Hypervolemia, also known as fluid overload, is the medical condition where there is too much fluid in the blood. The opposite condition is hypovolemia, which is too little fluid volume in the blood. Fluid volume excess in the intravascular compa ...
, shunts, or cardiac tamponade.
Remote, indirect monitoring of blood flow by laser Doppler
Noninvasive hemodynamic monitoring of eye fundus vessels can be performed by Laser Doppler holography, with near infrared light. The eye offers a unique opportunity for the non-invasive exploration of cardiovascular diseases
Cardiovascular disease (CVD) is a class of diseases that involve the heart or blood vessels. CVD includes coronary artery diseases (CAD) such as angina and myocardial infarction (commonly known as a heart attack). Other CVDs include stroke, ...
. Laser Doppler imaging
Laser Doppler imaging (LDI) is an imaging method that uses a laser beam to scan live tissue. When the laser light reaches the tissue, the moving blood cells generate doppler components in the reflected ( backscattered) light. The light that comes ...
by digital holography Digital holography refers to the acquisition and processing of holograms with a digital sensor array, typically a CCD camera or a similar device. Image rendering, or reconstruction of object ''data'' is performed numerically from digitized interfero ...
can measure blood flow in the retina
The retina (from la, rete "net") is the innermost, light-sensitive layer of tissue of the eye of most vertebrates and some molluscs. The optics of the eye create a focused two-dimensional image of the visual world on the retina, which then ...
and choroid, whose Doppler responses exhibit a pulse
In medicine, a pulse represents the tactile arterial palpation of the cardiac cycle (heartbeat) by trained fingertips. The pulse may be palpated in any place that allows an artery to be compressed near the surface of the body, such as at the n ...
-shaped profile with time[Puyo, Léo, Michel Paques, Mathias Fink, José-Alain Sahel, and Michael Atlan. "Waveform analysis of human retinal and choroidal blood flow with laser Doppler holography." Biomedical Optics Express 10, no. 10 (2019): 4942-4963.] This technique enables non invasive functional microangiography
Microangiography ( ) is a type of angiography that consists of the radiography of small blood or lymphatic vessels of an organ. While most other types of angiography cannot produce images of vessels smaller than 200 µm in diameter, microang ...
by high-contrast measurement of Doppler responses from endoluminal blood flow profiles in vessels in the posterior segment of the eye. Differences in blood pressure drive the flow of blood throughout the circulation. The rate of mean blood flow depends on both blood pressure and the hemodynamic resistance to flow presented by the blood vessels.
Glossary
;ANH:Acute Normovolemic Hemodilution
;ANHu:Number of Units During ANH
;BLH:Maximum Blood Loss Possible When ANH Is Used Before Homologous Blood Transfusion Is Needed
;BLI:Incremental Blood Loss Possible with ANH.(BLH – BLs)
;BLs:Maximum blood loss without ANH before homologous blood transfusion is required
;EBV:Estimated Blood Volume(70 mL/kg)
;Hct:Haematocrit Always Expressed Here As A Fraction
;Hi:Initial Haematocrit
;Hm:Minimum Safe Haematocrit
;PRBC:Packed Red Blood Cell Equivalent Saved by ANH
;RCM:Red cell mass.
;RCMH:Cell Mass Available For Transfusion after ANH
;RCMI:Red Cell Mass Saved by ANH
;SBL:Surgical Blood Loss
Etymology and pronunciation
The word ''hemodynamics'' () uses combining forms of '' hemo-'' (which comes from the ancient Greek ''haima'', meaning blood) and '' dynamics'', thus "the dynamics of blood
Blood is a body fluid in the circulatory system of humans and other vertebrates that delivers necessary substances such as nutrients and oxygen to the cells, and transports metabolic waste products away from those same cells. Blood in the cir ...
". The vowel of the ''hemo-'' syllable is variously written according to the ae/e variation.
* Blood hammer
* Blood pressure
* Cardiac output
* Cardiovascular System Dynamics Society The Cardiovascular System Dynamics Society (CSDS), founded on 5 October 1976 in Philadelphia, Pennsylvania, by organ system physiologist and biomedical engineers, was a historic first in its mathematical and quantitative approach to cardiovascular m ...
* Electrical cardiometry
* Esophogeal doppler
* Hemodynamics of the aorta
* Impedance cardiography
Impedance cardiography (ICG) is a non-invasive technology measuring total electrical conductivity of the thorax and its changes in time to process continuously a number of cardiodynamic parameters, such as stroke volume (SV), heart rate (HR), car ...
* Photoplethysmogram
A photoplethysmogram (PPG) is an optically obtained plethysmogram that can be used to detect blood volume changes in the microvascular bed of tissue. A PPG is often obtained by using a pulse oximeter which illuminates the skin and measures cha ...
* Laser Doppler imaging
Laser Doppler imaging (LDI) is an imaging method that uses a laser beam to scan live tissue. When the laser light reaches the tissue, the moving blood cells generate doppler components in the reflected ( backscattered) light. The light that comes ...
* Windkessel effect
Windkessel effect is a term used in medicine to account for the shape of the arterial blood pressure waveform in terms of the interaction between the stroke volume and the compliance of the aorta and large elastic arteries (Windkessel vessels) ...
* Functional near-infrared spectroscopy
Functional near-infrared spectroscopy (fNIRS) is an optical brain monitoring technique which uses near-infrared spectroscopy for the purpose of functional neuroimaging. Using fNIRS, brain activity is measured by using near-infrared light to estimat ...
Notes and references
Bibliography
* Berne RM, Levy MN. Cardiovascular physiology. 7th Ed Mosby 1997
* Rowell LB. Human Cardiovascular Control. Oxford University press 1993
* Braunwald E (Editor). Heart Disease: A Textbook of Cardiovascular Medicine. 5th Ed. W.B.Saunders 1997
* Siderman S, Beyar R, Kleber AG. Cardiac Electrophysiology, Circulation and Transport. Kluwer Academic Publishers 1991
American Heart Association
* Otto CM, Stoddard M, Waggoner A, Zoghbi WA. Recommendations for Quantification of Doppler Echocardiography: A Report from the Doppler Quantification Task Force of the Nomenclature and Standards Committee of the American Society of Echocardiography. J Am Soc Echocardiogr 2002;15:167-184
* Peterson LH, The Dynamics of Pulsatile Blood Flow, Circ. Res. 1954;2;127-139
Hemodynamic Monitoring
Bigatello LM, George E., Minerva Anestesiol, 2002 Apr;68(4):219-25
* Claude Franceschi; Paolo Zamboni Principles of Venous Hemodynamics Nova Science Publishers 2009-01 ISBN Nr 1606924850/9781606924853
* WR Milnor: Hemodynamics, Williams & Wilkins, 1982
* B Bo Sramek: Systemic Hemodynamics and Hemodynamic Management, 4th Edition, ESBN 1-59196-046-0
External links
Learn hemodynamics
{{Cardiovascular physiology
Fluid mechanics
Computational fluid dynamics
Cardiovascular physiology
Exercise physiology
Blood
Mathematics in medicine
Fluid dynamics