This chapter is vaguely relevant to Section G4(vi) of the 2017 CICM Primary Syllabus, which asks the exam candidate to "explain the factors that determine systemic blood pressures". Judging by their use of the plural "pressures", the college examiners were interested in the systolic, diastolic and mean arterial blood pressure parameters, rather than the concept of blood pressure as a whole. In addition to these characteristics which are mainly found in living pulsatile circulatory systems, the systemic circulation also has a mean systemic filling pressure and mean circulatory filling pressure, which become apparent in the absence of pulsatile flow. Because the discussion of those parameters is usually associated with the discussion of venous return and cardiac output, they have been banished into another section.
- Pressure is usually represented as force / surface area
- Blood pressure is represented as mmHg, where pressure is proportional to the gravitational force exerted by a displaced column of liquid mercury
- During a cardiac cycle,
- Systolic blood pressure is the maximum arterial pressure
- Diastolic blood pressure is the minimum pressure
- Mean arterial pressure is the area under the pressure/time curve, divided by the cardiac cycle time
- Overall, factors which determine arterial pressure are:
- Cardiac output, which is determined by preload afterload and contractility
- Peripheral vascular resistance, which is described by the Poiseuille equation, and is determined by
- Arteriolar radius
- Blood viscosity
- Length of the vascular tree
- Total energy gradient of blood flow, which is described by the Bernoulli equation, and which consists of:
- Elastic energy of the arterial circulation, which includes:
- Pressure generated by energy stored by the stroke volume through proximal arterial distension
- Pressure generated by constant vascular smooth muscle tone
- Reflected pressure waves
- Potential energy due to gravity, which contributes to the difference in blood pressure measured at different points of the circulatory system in the upright individual
- Kinetic energy of moving blood, which contributes minimally to the total energy of the system
- Systolic blood pressure is mainly determined by:
- Arterial elastance and compliance (major influence)
- Stroke volume, insofar as it affects elastance and compliance
- Total arterial peripheral resistance
- Diastolic blood pressure is mainly determined by:
- Total arterial peripheral resistance (major influence)
- Arterial elastance and compliance
- Time constant of the peripheral vessels (and therefore heart rate)
"Few subjects are more confidently discussed by some physiologists without any proper grasp of fundamentals than haemodynamics", snarked Burton in 1952, which demonstrates the toxicity of the trolling in professional literature on the subject. Dark forests teeming with enraged professors still await the reader who tries to understand this topic in any depth. If one can get a hold of it, "Arterial pressure" by George Stouffer (from Cardiovascular Hemodynamics for the Clinician, 2007) is probably the best introduction to this subject, followed closely by the 2018 article by Magder (the latter being more attractive by virtue of being free through Critical Care). In fact, anything written by Sheldon Magder seems to be gold. Dobrin's Mechanical Properties of Arteries is also excellent, in spite of its age (1978).
In general, there was no shortage of published material on the subject of blood pressure, but each resource seems to suffer from the same flaws. Each author takes a handful of ideas and throws them energetically at the reader. There, those are the factors that determine blood pressure, they say. Connect the dots yourselves. Little effort is made to develop any relationship between these difficult physical and mechanical concepts. The ambition of this chapter is not to surpass these scholarly works in clarity, but to explore the confusion and to revel in its abundance.
Before the craziness of the discussion which follows, it would be nice to take shelter in something comfortable and familiar. The terms used to describe blood pressure surely fit that description. Flow of blood in the non-VA ECMO version of the human circulation is pulsatile rather than constant, which gives two pressure values (a maximum and a minimum). These are the systolic and diastolic blood pressures. The difference between these is conventionally called the pulse pressure. Mean arterial pressure (MAP) is often incorrectly said to be (diastolic pressure + one third of the pulse pressure difference), but is in fact the area under the arterial pressure/time curve, divided by the cardiac cycle duration. This representative diagram is loosely borrowed from Gedde's Handbook of Blood Pressure Measurement.
It would probably be natural for any discussion of blood pressure to begin with at least a brief explanation of what pressure actually is, and why we insist on measuring it in millimetres of mercury. Pressure is conventionally defined as a force distributed over a surface area, so why are we using units of length to describe it? To answer, the following long-winded explanation can be offered:
Thus, with all the other variables remaining constant (as manometers don't tend to change their shape in the course of their routine use),
In a different form, you can say that pressure is a force acting on the manometer which displaces a cylindrical column of fluid by a vertical length. That column of fluid has a mass, which means that under the effect of gravity, it exerts a force. That force is distributed over the crossectional area of the manometry cylinder, which is the definition of pressure. Ergo, the height of displacement is proportional to the pressure in the manometer. Theoretically, a diagram could help (a picture being worth etc etc) but in this case it probably only serves to muddle the concept yet further:
Anyway, that still does not offer much of an explanation as to why we use millimetres of mercury. In the unlikely case the reader's need for pointless trivia remains unsated, they can trace the use of mercury to Evangelino Toricelli (1644), who ended up having to use the heavier liquid when he found ten metre columns of water too unwieldy for his experiments. Because of the greater density of mercury, the same height displacement could be observed over the span of millimetres instead of centimetres, making the barometer much easier to work with.
Mercury manometry remained popular in multiple applications for a surprisingly long time; for instance, the US National Weather Service continued using it as a reference standard until 1977 (at which point it was replaced by a piezoelectric pressure transducer). In medicine, the mercury sphygmomanometer ("sphygmos" meaning "pulse") remained so ubiquitous and for so long that even in 2001 an AHA council group issued a statement warning against its premature retirement, insisting on "the use of mercury instruments for calibration of aneroid and electronic instruments". Hence, though most jurisdictions have banned the routine bedside use of mercury manometers and strain gauges (eg. the EU in 2012), they remain available for laboratory use and as a reference standard for calibrating other instruments.
Where blood pressure is discussed in textbooks, it is usually described in terms of the relationship between flow and resistance, crudely approximated using Ohm's law (Q=∆P/R), which describes the relationships of pressure resistance and flow:
Pressure is the product of resistance and flow:
Pa- Pv = QR,
- Pa- Pv = the pressure difference between the arterial and venous circulation
- Q = blood flow, and
- R = peripheral arterial resistance
Resistance is described by the classical Hagen-Poiseuille equation:
R = (8 l η) / πr4
- l = length of the vessel
- η = viscosity of the fluid
- r = radius of the vessel
Flow is the volume of blood moved over time, i.e. the cardiac output:
CO = HR × SV
- CO = cardiac output in ml/min
- HR = heart rate in beats /min
- SV = stroke volume in ml
The pressure described by this is Pa- Pv, the pressure difference between the arterial and venous circulation. However, though it is often said that flow in the circulatory system occurs because of this pressure gradient, in actual fact the physics purist would have to point out that an energy gradient is what really drives flow. In other words, there is an energy difference between Circulatory Point A and Circulatory Point B which produces flow.
How, then, do we discuss this energy difference? The total energy of a flowing fluid can be represented using a version of the Bernoulli equation, which at its most basic level looks like this:
Energy(point A) = Energy (point B)
where, in the classical version of the equation, the total energy remains the same everywhere (i.e it is the fluid version of the Law of Conservation of Energy). The total energy at each point is represented by the relationship,
Total energy = Ps + ρgh + ½ρv2
- Ps is the static pressure,
- ρ is the density of the fluid, or mass per volume,
- v is the flow velocity
- g is gravity and
- h is height of the measurement point above an arbitrary zero level.
One will immediately recognise that:
ρgh is (mass × height × gravity)
which is essentially the equation for potential energy, and
½ρv2 is (½ × mass × velocity squared)
which is obviously kinetic energy.
Thus, following from the Bernoulli equation, we can say that the total energy at a given point in a flowing fluid is the sum of several contributions:
However, the Bernoulli equation describes a highly idealised scenario, where a perfectly incompressible fluid is flowing frictionlessly through a totally rigid tube. None of that describes any of the natural characteristics of wet squishy biological systems. In the real circulatory system, Energy(point A) ≠ Energy (point B) because some of the energy of flowing blood is lost in activities like stretching the elastic walls of blood vessels, in friction against their sides, in deforming red cells, defeating the viscosity of plasma, and in forcing the distal blood volume through a reluctant system of ever-narrowing tubes. This energy difference between the energy of arterial and venous blood flow must mainly be expressed in the Ps parameter. Consider: the potential energy of blood depends only on height and gravity, which means it does not care about squishy vessel wall gymnastics, and kinetic energy is such a minor contributor to the total that it can be safely ignored (see below).
This "static pressure" is defined as the pressure measured at a single point of the circulatory system by a barometer which is moving in the direction of flow (to eliminate the kinetic element). In short, this Ps parameter is probably where the resistance to blood flow factors into the energy equation. Magder (2018) also seems to have attributed it to the elastic elements of the circulation, which incorporated the contributions of all the mentioned factors (pulsatile flow, reflected waves, etc). Or at least, that is what it seems like from the structure of his article, as the connection is never explicitly stated.
So. The difference between arterial and venous pressure is cardiac output multiplied by vascular resistance, where "pressure" is the static pressure at a given point in the circulatory system; and added to this pressure is the contribution of kinetic energy and gravity. Clearly it would be madness to try to unite all these concepts into one big unifying tableaux (we say clearly because no serious publication has ever done this), but here's what that would look like if you tried:
This probably needs to be unpacked in some considerable detail, but the real question is how. There is no specific well-accepted method of joining all these concepts together. The contribution of the factors is unequal and difficult to measure experimentally in the living organism, where blood pressure is tightly controlled by cardiovascular reflexes. Moreover, some factors may contribute differently at different points in the cardiac cycle - some might be more important in systole, and others in diastole. No convenient narrative solution comes to mind which might be suited to unravelling this wirrwarr. For lack of a better option, the author has resigned himself to listing the factors which are involved, and discussing how they contribute to each blood pressure parameter (systolic, diastolic, mean), referring to experiments wherever possible.
Elastic energy comes from the pressure exerted by arterial walls on their contents. The term usually applied here is arterial elastance, because elastance described the resistance to stretch (i.e pressure generated by a change in volume), whereas compliance describes a change in volume in response to pressure which would make no sense in the context of this blood-pressure-focused chapter. The bottom line is that there is a pressure which is generated by the arterial walls' reluctant deformation in response to being occupied by a volume. This takes several forms:
In case this was not confusing enough or insufficiently generous with broad inaccurate approximations, here is a diagram to amplify those characteristics:
Potential energy, or perhaps is it better to call it "pressure due to the weight of blood", is actually an extremely important contributor to total blood pressure, depending on where you measure it. In the upright person, the circulatory system can be crudely represented as a vertical column occupied by fluid. Between the top and the bottom of this column, there will be a pressure difference proportional to its height, which is about 73.5 mmHg per every 100 cm of blood. Classically, textbooks describe a 182 cm tall upright person with a mean arterial pressure of 83 mmHg at the level of the heart, which increases to 171 mm Hg at their feet and decreases to 39 mmHg at their brain. This specific example seems to be repeated constantly and seems to come from Burton's Physiology and biophysics of the circulation, a textbook from 1965 which is quoted literally everywhere when the subject of hydrostatic pressure distribution comes up. Uncharacteristically, Φ will not perpetuate this process by stealing this famous image and reproducing it here. Instead, here's a diagram comparing mean arterial pressures of the upright human with those of a giraffe:
These are not computations based on simplistic cylinder models, but true life measurements. Heroically, Hargens et al (1987) collected their data directly from the arteries a real live giraffe. The stoic authors made no mention of the undoubtedly daunting logistical challenge of keeping the anaesthetised animals in a stationary upright position while having their arteries cannulated. They observed that, in order to achieve a mean arterial pressure of 110 mmHg at the head, the MAP at the level of the heart had to be 190 mmHg, and 260 mmHg at their feet. Interestingly, though one might expect there to be some sort of linear progression of MAP across the large range of vertebrate body sizes, that does not appear to be the case: the MAP of a mouse (about 70 mmHg) and the MAP of an African elephant (about 100 mmHg) are not much different in spite of a five-order-of-magnitude difference in mass.
Anyway. From the discussion above, the takeaway point is that gravity influences arterial pressure. Mean, systolic and diastolic are all affected equally (however the act of measuring the pressure at different points in the circulatory system will yield different systolic and diastolic values for a completely different reason, because of distal systolic pulse amplification). The venous circulation is also affected, and the influence of hydrostatic pressure on the circulatory system has implications for the cardiovascular adaptation to changes in posture, which is discussed in more detail elsewhere.
Kinetic energy comes from the velocity of flowing blood. That flowing blood has kinetic energy will be no surprise to anybody who has ever lost a pair of shoes to the removal of an IABP. There are probably two parts to this:
Considering that the velocity of blood drops markedly in the peripheral circulation, the kinetic energy of the whole blood column is probably rather low. Most of the kinetic energy in the bloodstream is therefore invested in the volume of blood ejected from the LV with each beat. Though the velocity of the stroke volume often quite high (McDonald et al in 1952 recorded a peak of 60cm/sec) the mass is usually modest (i.e. at maximum, the stroke volume - around 70-100g of blood). Thus, the kinetic energy of blood contributes very little to blood pressure. Magder (2018) gives 3% as its contribution to the total, which is a figure he probably got from Prec et al (1949). These investigators measured the kinetic energy of an angiographically measured stroke volume, and arrived at a figure of around 290-590 grams per cm, or 1.4-3.1% of the total energy in the system (derived from the Bernoulli equation). The contribution of kinetic energy to blood pressure must surely play more of a role in patients who have a higher cardiac output (eg. those in the early hyperdynamic stages of septic shock), as increased flow equals increased velocity. Thus, the stroke volume is probably the most important determinant of this energy contribution.
Stroke volume: the volume of blood in the arterial circulation generates a pressure, and this relationship (change in pressure due to change in volume) is generally referred to as elastance. Thus, any increase in volume will change the pressure in the arteries. Stroke volume generally increases with increased preload and contractility, and so does blood pressure, which means this assertion probably meets the test of logic.
Arterial elastance: the property which influences how much the pressure changes when the volume changes is clearly also important. This is the rigidity of the arterial tree. Obviously, as the arteries become more rigid, so the pressure generated by the same stroke volume will increase. This relationship can be observed in the different pressure-volume curve measured from the supple arteries of young people and the crusty arteries of the elderly by Hermann Bader (1967), whose original diagram is presented here in a severely vandalised form:
Peripheral vascular resistance: as was already stated, the addition of a stroke volume to the arterial blood volume increases the pressure by distending the vessel walls. However, the aorta is not crossclamped. As a stroke volume is propelled into the aorta, not all of it is accommodated by the stretching of proximal arteries - some of it (apparently about 50%) actually displaces blood further into the distal circulation and into the capillaries. Thus, volume is constantly being removed from the arterial circulation, as well as added. The rate of this "removal" depends on the size of the bathtub drain, i.e on the resistance to the outflow of blood from the arterial circulation. In their model Stergiopulos et al (1996) were able to produce this relationship between peripheral vascular resistance and systolic blood pressure:
Reflected waves: because blood vessels are not infinitely elastic, they do not stretch perfectly to absorb the pressure wave sent to them by the ventricle, and some of that wave is reflected off their various arterial surfaces and branching points. The images below were stolen from Murgo et al (1980), who demonstrated that reflected waves increase the systolic pressure in the aorta by about 10 mmHg when manual pressure occludes the femoral arteries.
The reflected wavefront, as returns to the aorta, adds only a little extra pressure to the total. In a nice healthy circulation, these waves are slow and mainly augment the pressure in diastole, contributing to coronary filling. In a diseased atheromatous circulation, the rigid arteries send back rapid reflected waves, which add to the systolic pressure, and therefore increase afterload.
Kinetic energy of the blood also adds something to systolic pressure (or, at least, more than it does to the diastolic), but its contribution to blood pressure in general is so miniscule that it is barely worth discussing in this section. It would be strictly limited to something you mention in an exam situation.
Stroke volume has some minimal relationship with diastolic blood pressure, mainly because of how it fills the windkessel. As diastole begins, about 50% of the stroke volume remains in the proximal arteries which distended elastically in response. In diastole, this volume will be slowly squeezed out into the distal vessels by the gradual return of these arteries to their pre-systolic dimensions. Thus, insofar as it influences systolic arterial distension, the stroke volume also influences diastolic pressure.
Arterial elastance is probably the most important determinant of diastolic blood pressure. As already discussed above, this property determines how much the pressure in the vessels changes in response to the stroke volume. It also determines how rapidly they change in pressure when the stroke volume is "lost" (i.e. when it disappears into the peripheral circulation). This means that poor arterial compliance (high elastance) will result in a lower diastolic blood pressure, all other parameters remaining equal:
There appears to be some experimental evidence in support of this. Elzinga & Westerhof (1973) determined that increased aortic elastance (decreased compliance) results in a faster drop of diastolic pressure, because the aortic pressure-volume curve in a poorly compliant aorta is so steep. In fact, the magnitude of the diastolic decrease was twice the magnitude of the systolic increase, i.e. peripheral vascular resistance played a more important role in diastole than in systole.
Peripheral vascular resistance influences the rate of diastolic emptying. Recall once more the tired old analogy of the bath tub, emptying though a small drain hole. Clearly, a smaller drain hole (higher resistance) will keep the pressure in the bath tub higher, for longer. For the diastolic pressure, this means a slower rate of diastolic pressure decrease. Again, going back to the same study (and in fact the same graph) from Stergiopulos et al (1996), this is the relationship between peripheral vascular resistance and diastolic pressure:
Obviously, when you talek about the rate of something, time is a factor which must be considered. Which brings us to our next point:
The time constant of the peripheral vessels represents the interaction between elastance and resistance, and describes the relationship between diastolic pressure and heart rate. Compliance (the inverse of elastance) multiplied by resistance produces the time constant of the arterial vessels, i.e. the time required to achieve 63% of the new steady state after a step change in conditions. What does that mean? In summary, it means that, at any given elastance and resistance, the slower the heart rate the lower the diastolic pressure. Observe:
Throughout the rest of this chapter the discussion had focussed on the gradient of pressure between the arterial and venous circulation, as if that is the only gradient available. Realistically, that is the pressure difference we mortals end up using when we try to estimate the ineffable mystery of peripheral vascular resistance, which is usually calculated by taking the arterial pressure and the central venous pressure (both being easily available in the ICU). However, in actual fact, the real pressure gradient is between the aorta and whatever part of the circulation is producing the resistance, where the critical closing pressure is being experienced.
That would usually be somewhere among the arterioles. There, pressure of the surrounding tissues and the arteriolar tone itself can cause the collapse of the vessels, making them the site of maximum resistance. Permutt & Riley wrote about this in 1962, describing it as a"vascular waterfall" or Starling resistor. The discovery of this phenomenon was made by researchers who, plotting the experimental results for the pressure-flow relationships of the arterial circulation, found that the x-axis intercept (where flow was zero) did not fall on the venous pressure value, but usually higher. The range for that intercept pressure was quite wide. Bellamy (1978), for example, ended up with a value of around 45 mmHg when studying the coronaries of the dog:
Others got very different numbers; for example Magder (1990) quotes a range from 40 to 75 mmHg, and there are many other examples. This is something that is clearly going to have different values depending on which tissue and which vascular bed you are sampling. The basis of this effect is external compression of the vessel. If the arterioles are collapsed, then it does not matter what the venous pressure is - the flow will not increase irrespective of how low that venous pressure value will be.
The pressure gradient to calculate resistance should therefore be between the arterial pressure and the arteriolar closing pressure, not venous. The use of the venous pressure could introduce a significant error into vascular resistance calculations. Here's an example:
As you can see, the conventional calculation leads you to believe that the SVR is increased and the patient is vasoconstricted ("quick, let's grab some milrinone"), whereas the One True SVR is in fact totally normal (within the range of 700 to 1,500 dynes/seconds/cm-5).
Clearly, critical closing pressure would be a handy parameter to have in one's haemodynamic assessment tool kit. However, measuring this closing pressure is a challenge in the animal preparation, let alone in the living human patient. Measuring between two points in the arterial circulation (for example, systolic and diastolic) is not really going to yield an accurate representation of this value because of the influence of heart rate and the arterial time constant. The only way to really measure this "waterfall pressure" is by means of a terrifying Flatliners-style experiment where all the pulsatile elements of the arterial pressure are eliminated by circulatory arrest, and the unadulterated influence of arterial tone and tissue pressure can be directly measured. Kottenberg-Assenmacher et al (2009) were actually able to perform this experiment in ten consenting humans who were going to have a controlled cardiac arrest anyway during the implantation of an AICD. They found that the normally accepted methods of "guessing" the critical closing pressure tended to overestimate it by a factor of two:
In summary, this is an important variable to know about, and an important limitation of conventional SVR calculations to understand. We know that vasoactive substances, exercise and body temperature affect the critical closing pressure, but we have no convenient method of measuring it.
A major point of difference encountered by junior non-ICU staff rotating through the ICU is the intensivists' preoccupation with the mean arterial pressure, whereas the rest of the hospital usually looks at the systolic and diastolic. Why, they often ask, do we obsess so over this variable, whereas apparently nobody else does? Why is mean arterial pressure important?
There are several reasons for this.