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A sphygmomanometer, a device used for measuring arterial pressure.
A sphygmomanometer, a device used for measuring arterial pressure.
Blood pressure (BP), sometimes referred to as arterial blood pressure, is the pressure exerted by circulating blood upon the walls of blood vessels, and is one of the principal vital signs. When used without further specification, "blood pressure" usually refers to the arterial pressure of the systemic circulation. During each heartbeat, blood pressure varies between a maximum (systolic) and a minimum (diastolic) pressure. The blood pressure in the circulation is principally due to the pumping action of the heart. 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 the resistance to flow presented by the blood vessels. Mean blood pressure decreases as the circulating blood moves away from the heart through arteries and capillaries due to viscous losses of energy. Mean blood pressure drops over the whole circulation, although most of the fall occurs along the small arteries and arterioles. Gravity affects blood pressure via hydrostatic forces (e.g., during standing) and valves in veins, breathing, and pumping from contraction of skeletal muscles also influence blood pressure in veins.
The measurement blood pressure without further specification usually refers to the systemic arterial pressure measured at a person's upper arm and is a measure of the pressure in the brachial artery, major artery in the upper arm. A person’s blood pressure is usually expressed in terms of the systolic pressure over diastolic pressure and is measured in millimetres of mercury (mmHg), for example 140/90.
|Category||systolic, mmHg||diastolic, mmHg|
The table on the right shows the classification of blood pressure adopted by the American Heart Association for adults who are 18 years and older. It assumes the values are a result of averaging blood pressure readings measured at two or more visits to the doctor.
While average values for arterial pressure could be computed for any given population, there is often a large variation from person to person; arterial pressure also varies in individuals from moment to moment. Additionally, the average of any given population may have a questionable correlation with its general health; thus the relevance of such average values is equally questionable. However, in a study of 100 human subjects with no known history of hypertension, an average blood pressure of 112/64 mmHg was found, which are currently classified as desirable or "normal" values. Normal values fluctuate through the 24-hour cycle, with highest readings in the afternoons and lowest readings at night.
Various factors, such as age and sex influence average values, influence a person's average blood pressure and variations. In children, the normal ranges are lower than for adults and depend on height. As adults age, systolic pressure tends to rise and diastolic tends to fall. In the elderly, blood pressure tends to be above the normal adult range, largely because of reduced flexibility of the arteries. Also, an individual's blood pressure varies with exercise, emotional reactions, sleep, digestion and time of day.
Differences between left and right arm blood pressure measurements tend to be random and average to nearly zero if enough measurements are taken. However, in a small percentage of cases there is a consistent difference greater than 10 mmHg which may need further investigation, e.g. for obstructive arterial disease.
The risk of cardiovascular disease increases progressively above 115/75 mmHg. In the past, hypertension was only diagnosed if secondary signs of high arterial pressure were present, along with a prolonged high systolic pressure reading over several visits. Regarding hypotension, in practice blood pressure is considered too low only if noticeable symptoms are present.
Clinical trials demonstrate that people who maintain arterial pressures at the low end of these pressure ranges have much better long term cardiovascular health. The principal medical debate concerns the aggressiveness and relative value of methods used to lower pressures into this range for those who do not maintain such pressure on their own. Elevations, more commonly seen in older people, though often considered normal, are associated with increased morbidity and mortality.
|Infants||1 to 12 months||75–100||50–70|
|Toddlers||1 to 4 years||80–110||50–80|
|Preschoolers||3 to 5 years||80–110||50–80|
|School age||6 to 13 years||85–120||50–80|
|Adolescents||13 to 18 years||95–140||60–90|
There are many physical factors that influence arterial pressure. Each of these may in turn be influenced by physiological factors, such as diet, exercise, disease, drugs or alcohol, stress, obesity, and so-forth.
Some physical factors are:
In practice, each individual's autonomic nervous system responds to and regulates all these interacting factors so that, although the above issues are important, the actual arterial pressure response of a given individual varies widely because of both split-second and slow-moving responses of the nervous system and end organs. These responses are very effective in changing the variables and resulting blood pressure from moment to moment.
Moreover, blood pressure is the result of cardiac output increased by peripheral resistance: blood pressure = cardiac output X peripheral resistance. As a result, an abnormal change in blood pressure is often an indication of a problem affecting the heart's output, the blood vessels' resistance, or both. Thus, knowing the patient's blood pressure is critical to assess any pathology related to output and resistance.
MAP can be approximately determined from measurements of the systolic pressure and the diastolic pressure while there is a normal resting heart rate,
The up and down fluctuation of the arterial pressure results from the pulsatile nature of the cardiac output, i.e. the heartbeat. The pulse pressure is determined by the interaction of the stroke volume of the heart, compliance (ability to expand) of the aorta, and the resistance to flow in the arterial tree. By expanding under pressure, the aorta absorbs some of the force of the blood surge from the heart during a heartbeat. In this way, the pulse pressure is reduced from what it would be if the aorta wasn't compliant. The loss of arterial compliance that occurs with aging explains the elevated pulse pressures found in elderly patients.
The pulse pressure can be simply calculated from the difference of the measured systolic and diastolic pressures,
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 mmHg, but may be increased in e.g. coarctation of the aorta.
The larger arteries, including all large enough to see without magnification, are conduits with low vascular resistance (assuming no advanced atherosclerotic changes) with high flow rates that generate only small drops in pressure. The smaller arteries and arterioles have higher resistance, and confer the main drop in blood pressure along the circulatory system.
Modern physiology developed the concept of the vascular pressure wave (VPW). This wave is created by the heart during the systole and originates in the ascending aorta. Much faster than the stream of blood itself, it is then transported through the vessel walls to the peripheral arteries. There the pressure wave can be palpated as the peripheral pulse. As the wave is reflected at the peripheral veins, it runs back in a centripetal fashion. When the reflected wave meets the next outbound pressure wave, the pressure inside the vessel rises higher than the pressure in the aorta. This concept explains why the arterial pressure inside the peripheral arteries of the legs and arms is higher than the arterial pressure in the aorta, and in turn for the higher pressures seen at the ankle compared to the arm with normal ankle brachial pressure index values.
The endogenous regulation of arterial pressure is not completely understood, but the following mechanisms of regulating arterial pressure have been well-characterized:
These different mechanisms are not necessarily independent of each other, as indicated by the link between the RAS and aldosterone release. Currently, the RAS is targeted pharmacologically by ACE inhibitors and angiotensin II receptor antagonists. The aldosterone system is directly targeted by spironolactone, an aldosterone antagonist. The fluid retention may be targeted by diuretics; the antihypertensive effect of diuretics is due to its effect on blood volume. Generally, the baroreceptor reflex is not targeted in hypertension because if blocked, individuals may suffer from orthostatic hypotension and fainting.
Arterial pressure is most commonly measured via a sphygmomanometer, which historically used the height of a column of mercury to reflect the circulating pressure. Blood pressure values are generally reported in millimetres of mercury (mmHg), though aneroid and electronic devices do not use mercury.
For each heartbeat, blood pressure varies between systolic and diastolic pressures. Systolic pressure is peak pressure in the arteries, which occurs near the end of the cardiac cycle when the ventricles are contracting. Diastolic pressure is minimum pressure in the arteries, which occurs near the beginning of the cardiac cycle when the ventricles are filled with blood. An example of normal measured values for a resting, healthy adult human is 120 mmHg systolic and 80 mmHg diastolic (written as 120/80 mmHg, and spoken [in the US and UK] as "one-twenty over eighty").
Systolic and diastolic arterial blood pressures are not static but undergo natural variations from one heartbeat to another and throughout the day (in a circadian rhythm). They also change in response to stress, nutritional factors, drugs, disease, exercise, and momentarily from standing up. Sometimes the variations are large. Hypertension refers to arterial pressure being abnormally high, as opposed to hypotension, when it is abnormally low. Along with body temperature, respiratory rate, and pulse rate, blood pressure is one of the four main vital signs routinely monitored by medical professionals and healthcare providers.
Measuring pressure invasively, by penetrating the arterial wall to take the measurement, is much less common and usually restricted to a hospital setting.
The noninvasive auscultatory and oscillometric measurements are simpler and quicker than invasive measurements, require less expertise, have virtually no complications, are less unpleasant and less painful for the patient. However, noninvasive methods may yield somewhat lower accuracy and small systematic differences in numerical results. Noninvasive measurement methods are more commonly used for routine examinations and monitoring.
A minimum systolic value can be roughly estimated by palpation, most often used in emergency situations, but should be used with caution. It has been estimated that, using 50% percentiles, carotid, femoral and radial pulses are present in patients with a systolic blood pressure > 70 mmHg, carotid and femoral pulses alone in patients with systolic blood pressure of > 50 mmHg, and only a carotid pulse in patients with a systolic blood pressure of > 40 mmHg.
A more accurate value of systolic blood pressure can be obtained with a sphygmomanometer and palpating the radial pulse. The diastolic blood pressure cannot be estimated by this method. The American Heart Association recommends that palpation be used to get an estimate before using the auscultatory method.
The auscultatory method (from the Latin word for "listening") uses a stethoscope and a sphygmomanometer. This comprises an inflatable (Riva-Rocci) cuff placed around the upper arm at roughly the same vertical height as the heart, attached to a mercury or aneroid manometer. The mercury manometer, considered the gold standard, measures the height of a column of mercury, giving an absolute result without need for calibration and, consequently, not subject to the errors and drift of calibration which affect other methods. The use of mercury manometers is often required in clinical trials and for the clinical measurement of hypertension in high-risk patients, such as pregnant women.
A cuff of appropriate size is fitted smoothly and snugly, then inflated manually by repeatedly squeezing a rubber bulb until the artery is completely occluded. Listening with the stethoscope to the brachial artery at the elbow, the examiner slowly releases the pressure in the cuff. When blood just starts to flow in the artery, the turbulent flow creates a "whooshing" or pounding (first Korotkoff sound). The pressure at which this sound is first heard is the systolic blood pressure. The cuff pressure is further released until no sound can be heard (fifth Korotkoff sound), at the diastolic arterial pressure.
The auscultatory method is the predominant method of clinical measurement.
The oscillometric method was first demonstrated in 1876 and involves the observation of oscillations in the sphygmomanometer cuff pressure which are caused by the oscillations of blood flow, i.e., the pulse. The electronic version of this method is sometimes used in long-term measurements and general practice. It uses a sphygmomanometer cuff, like the auscultatory method, but with an electronic pressure sensor (transducer) to observe cuff pressure oscillations, electronics to automatically interpret them, and automatic inflation and deflation of the cuff. The pressure sensor should be calibrated periodically to maintain accuracy.
Oscillometric measurement requires less skill than the auscultatory technique and may be suitable for use by untrained staff and for automated patient home monitoring.
The cuff is inflated to a pressure initially in excess of the systolic arterial pressure and then reduced to below diastolic pressure over a period of about 30 seconds. When blood flow is nil (cuff pressure exceeding systolic pressure) or unimpeded (cuff pressure below diastolic pressure), cuff pressure will be essentially constant. It is essential that the cuff size is correct: undersized cuffs may yield too high a pressure; oversized cuffs yield too low a pressure. When blood flow is present, but restricted, the cuff pressure, which is monitored by the pressure sensor, will vary periodically in synchrony with the cyclic expansion and contraction of the brachial artery, i.e., it will oscillate. The values of systolic and diastolic pressure are computed, not actually measured from the raw data, using an algorithm; the computed results are displayed.
Oscillometric monitors may produce inaccurate readings in patients with heart and circulation problems, which include arterial sclerosis, arrhythmia, preeclampsia, pulsus alternans, and pulsus paradoxus.
In practice the different methods do not give identical results; an algorithm and experimentally obtained coefficients are used to adjust the oscillometric results to give readings which match the auscultatory results as well as possible. Some equipment uses computer-aided analysis of the instantaneous arterial pressure waveform to determine the systolic, mean, and diastolic points. Since many oscillometric devices have not been validated, caution must be given as most are not suitable in clinical and acute care settings.
The term NIBP, for non-invasive blood pressure, is often used to describe oscillometric monitoring equipment.
For some patients, blood pressure measurements taken in a doctor's office may not correctly characterize their typical blood pressure. In up to 25% of patients, the office measurement is higher than their typical blood pressure. This type of error is called white-coat hypertension (WCH) and can result from anxiety related to an examination by a health care professional. The misdiagnosis of hypertension for these patients can result in needless and possibly harmful medication. WCH can be reduced (but not eliminated) with automated blood pressure measurements over 15 to 20 minutes in a quiet part of the office or clinic.
Debate continues regarding the significance of this effect. Some reactive patients will react to many other stimuli throughout their daily lives and require treatment. In some cases a lower blood pressure reading occurs at the doctor's office.
Ambulatory blood pressure devices that take readings every half hour throughout the day and night have been used for identifying and mitigating measurement problems like white-coat hypertension. Except for sleep, home monitoring could be used for these purposes instead of ambulatory blood pressure monitoring. Home monitoring may be used to improve hypertension management and to monitor the effects of lifestyle changes and medication related to blood pressure. Compared to ambulatory blood pressure measurements, home monitoring has been found to be an effective and lower cost alternative, but ambulatory monitoring is more accurate than both clinic and home monitoring in diagnosing hypertension. Ambulatory monitoring is recommended for most patients before the start of antihypertensive drugs.
Aside from the white-coat effect, blood pressure readings outside of a clinical setting are usually slightly lower in the majority of people. The studies that looked into the risks from hypertension and the benefits of lowering blood pressure in affected patients were based on readings in a clinical environment.
When measuring blood pressure, an accurate reading requires that one not drink coffee, smoke cigarettes, or engage in strenuous exercise for 30 minutes before taking the reading. A full bladder may have a small effect on blood pressure readings; if the urge to urinate arises, one should do so before the reading. For 5 minutes before the reading, one should sit upright in a chair with one's feet flat on the floor and with limbs uncrossed. The blood pressure cuff should always be against bare skin, as readings taken over a shirt sleeve are less accurate. During the reading, the arm that is used should be relaxed and kept at heart level, for example by resting it on a table.
Since blood pressure varies throughout the day, measurements intended to monitor changes over longer time frames should be taken at the same time of day to ensure that the readings are comparable. Suitable times are:
Automatic self-contained blood pressure monitors are available at reasonable prices, some of which are capable of Korotkoff's measurement in addition to oscillometric methods, enabling irregular heartbeat patients to accurately measure their blood pressure at home.
Arterial blood pressure (BP) is most accurately measured invasively through an arterial line. Invasive arterial pressure measurement with intravascular cannulae involves direct measurement of arterial pressure by placing a cannula needle in an artery (usually radial, femoral, dorsalis pedis or brachial).
The cannula must be connected to a sterile, fluid-filled system, which is connected to an electronic pressure transducer. The advantage of this system is that pressure is constantly monitored beat-by-beat, and a waveform (a graph of pressure against time) can be displayed. This invasive technique is regularly employed in human and veterinary intensive care medicine, anesthesiology, and for research purposes.
Cannulation for invasive vascular pressure monitoring is infrequently associated with complications such as thrombosis, infection, and bleeding. Patients with invasive arterial monitoring require very close supervision, as there is a danger of severe bleeding if the line becomes disconnected. It is generally reserved for patients where rapid variations in arterial pressure are anticipated.
Invasive vascular pressure monitors are pressure monitoring systems designed to acquire pressure information for display and processing. There are a variety of invasive vascular pressure monitors for trauma, critical care, and operating room applications. These include single pressure, dual pressure, and multi-parameter (i.e. pressure / temperature). The monitors can be used for measurement and follow-up of arterial, central venous, pulmonary arterial, left atrial, right atrial, femoral arterial, umbilical venous, umbilical arterial, and intracranial pressures.
In pregnancy, it is the fetal heart and not the mother's heart that builds up the fetal blood pressure to drive its blood through the fetal circulation.
The blood pressure in the fetal aorta is approximately 30 mmHg at 20 weeks of gestation, and increases to approximately 45 mmHg at 40 weeks of gestation.
The average blood pressure for full-term infants:
Systolic 65–95 mm Hg
Diastolic 30–60 mm Hg
Blood pressure is the measurement of force that is applied to the walls of the blood vessels as the heart pumps blood throughout the body. The human circulatory system is 400,000 miles long, and the magnitude of blood pressure is not uniform in all the blood vessels in the human body. The blood pressure is determined by the diameter, flexibility and the amount of blood being pumped through the blood vessel. Blood pressure is also affected by other factors including exercise, stress level, diet and sleep.
The average normal blood pressure in the brachial artery, which is the next direct artery from the aorta after the subclavian artery, is 120mmHg/80mmHg. Blood pressure readings are measured in millimeters of mercury (mmHg) using sphygmomanometer. Two pressures are measured and recorded namely as systolic and diastolic pressures. Systolic pressure reading is the first reading, which represents the maximum exerted pressure on the vessels when the heart contracts, while the diastolic pressure, the second reading, represents the minimum pressure in the vessels when the heart relaxes. Other major arteries have similar levels of blood pressure recordings indicating very low disparities among major arteries. The innominate artery, the average reading is 110/70mmHg, the right subclavian artery averages 120/80 and the abdominal aorta is 110/70mmHg. 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 (4mm), therefore the resistance is low.
In addition, flow rate (Q) is also the product of the cross-sectional area of the vessel and the average velocity (Q=AV). Flow rate is directly proportional to the pressure drop in a tube or in this case a vessel. ∆P α Q. The relationship is further described by Poisseulle’s equation ∆P=8µlQ/πr^4. As evident in the Poisseulle’s equation, although flow rate is proportional to the pressure drop, there are other factors of blood vessels that contribute towards the difference in pressure drop in bifurcations of blood vessels. These include viscosity, length of the vessel, and radius of the vessel.
Factors that determine the flow’s resistance as described by Poiseuille’s relationship:
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:
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 obvserved 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 have the largest surface area in the vascular network. They are known to have the largest surface area (485mm) in the human vascular network. The larger the total cross-sectional area, the lower the mean velocity as well as the pressure.
Reynold’s number also affects the blood flow in capillaries. Due to its smaller radius and lowest velocity compared to other vessels, the Reynold’s number at the capillaries is very low, resulting in laminar instead of turbulent flow.
The Reynold’s 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:
The Reynold’s 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 Reynold’s 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. Turbulent flow is characterized as chaotic and irregular flow.
All levels of arterial pressure put mechanical stress on the arterial walls. Higher pressures increase heart workload and progression of unhealthy tissue growth (atheroma) that develops within the walls of arteries. The higher the pressure, the more stress that is present and the more atheroma tend to progress and the heart muscle tends to thicken, enlarge and become weaker over time.
Persistent hypertension is one of the risk factors for strokes, heart attacks, heart failure and arterial aneurysms, and is the leading cause of chronic renal failure. Even moderate elevation of arterial pressure leads to shortened life expectancy. At severely high pressures, mean arterial pressures 50% or more above average, a person can expect to live no more than a few years unless appropriately treated.
In the past, most attention was paid to diastolic pressure; but nowadays it is recognised that both high systolic pressure and high pulse pressure (the numerical difference between systolic and diastolic pressures) are also risk factors. In some cases, it appears that a decrease in excessive diastolic pressure can actually increase risk, due probably to the increased difference between systolic and diastolic pressures (see the article on pulse pressure). If systolic blood pressure is elevated (>140) with a normal diastolic blood pressure (<90), it is called "isolated systolic hypertension" and may present a health concern.
For those with heart valve regurgitation, a change in its severity may be associated with a change in diastolic pressure. In a study of people with heart valve regurgitation that compared measurements 2 weeks apart for each person, there was an increased severity of aortic and mitral regurgitation when diastolic blood pressure increased, whereas when diastolic blood pressure decreased, there was a decreased severity.
Blood pressure that is too low is known as hypotension. The similarity in pronunciation with hypertension can cause confusion. Hypotension is a medical concern if it causes signs or symptoms, such as dizziness, fainting, or in extreme cases, shock.
When arterial pressure and blood flow decrease beyond a certain point, the perfusion of the brain becomes critically decreased (i.e., the blood supply is not sufficient), causing lightheadedness, dizziness, weakness or fainting.
Sometimes the arterial pressure drops significantly when a patient stands up from sitting. This is known as orthostatic hypotension (postural hypotension); gravity reduces the rate of blood return from the body veins below the heart back to the heart, thus reducing stroke volume and cardiac output.
When people are healthy, the veins below their heart quickly constrict and the heart rate increases to minimize and compensate for the gravity effect. This is carried out involuntarily by the autonomic nervous system. The system usually requires a few seconds to fully adjust and if the compensations are too slow or inadequate, the individual will suffer reduced blood flow to the brain, dizziness and potential blackout. Increases in G-loading, such as routinely experienced by aerobatic or combat pilots 'pulling Gs', greatly increases this effect. Repositioning the body perpendicular to gravity largely eliminates the problem.
Other causes of low arterial pressure include:
Shock is a complex condition which leads to critically decreased perfusion. The usual mechanisms are loss of blood volume, pooling of blood within the veins reducing adequate return to the heart and/or low effective heart pumping. Low arterial pressure, especially low pulse pressure, is a sign of shock and contributes to and reflects decreased perfusion.
If there is a significant difference in the pressure from one arm to the other, that may indicate a narrowing (for example, due to aortic coarctation, aortic dissection, thrombosis or embolism) of an artery .
Normal fluctuation in blood pressure is adaptive and necessary. Fluctuations in pressure that are significantly greater than the norm are associated with greater white matter hyperintensity, a finding consistent with reduced local cerebral blood flow and a heightened risk of cerebrovascular disease. Within both high- and low-blood pressure groups, a greater degree of fluctuation was found to correlate with an increase in cerebrovascular disease compared to those with less variability, suggesting the consideration of the clinical management of blood pressure fluctuations, even among normotensive older adults. Older individuals and those who had received blood pressure medications were more likely to exhibit larger fluctuations in pressure.
|Central venous pressure||3–8|
|Right ventricular pressure||systolic||15–30|
|Pulmonary artery pressure||systolic||15–30|
|Left ventricular pressure||systolic||100–140|
Blood pressure generally refers to the arterial pressure in the systemic circulation. However, measurement of pressures in the venous system and the pulmonary vessels plays an important role in intensive care medicine but requires an invasive central venous catheter.
Venous pressure is the vascular pressure in a vein or in the atria of the heart. It is much less than arterial pressure, with common values of 5 mmHg in the right atrium and 8 mmHg in the left atrium.
Variants of venous pressure include:
Increased blood pressure in the capillaries of the lung cause pulmonary hypertension, with interstitial edema if the pressure increases to above 20 mmHg, and to frank pulmonary edema at pressures above 25 mmHg.
Regardless of site, blood pressure is related to the wall tension of the vessel according to the Young–Laplace equation (assuming that the thickness of the vessel wall is very small as compared to the diameter of the lumen):
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.