Pressure and flow: We’re one, but we’re not the same

One of the most useful applications of physics in critical care is its utility in describing how fluids—either gasses or liquids—move from place to place. For those with a bent towards math, this can often be quantified, but in most cases that’s not necessary. What is necessary is grasping it on a qualitative, intuitive level, because that’s what helps us to understand what we’re doing to our patients and appreciate the response.

A particularly important, but often misunderstood aspect of fluid behavior in physiology is the relationship between pressure and flow. Perhaps you think you understand this—you know that pressure is the force exerted by the fluid against its vessel (or vice versa, if you prefer), and flow is the rate at which it moves from place to place.

Perhaps you know that their relationship is typically modeled using Poiseuille’s law, which for these purposes can be reduced to simply say this: the direct relationship between pressure and flow is limited by the variable of resistance. That is, as resistance increases (for instance, due to a smaller-radiused lumen or a higher-viscosity fluid), a greater pressure is needed to achieve the same flow, or the same flow will generate a higher pressure.

Perhaps you know that for many purposes in ICU physiology, pressure and flow are closely linked, and so they can often be conflated. However, if you’re wise, you also know that this simplification can create confusion.

Let’s consider a couple of thought experiments, and we’ll see how your intuitive understanding holds up.

Scenario 1: The cardiogenic shock patient

A 65-year-old male is admitted for altered mental status. On evaluation, their blood pressure is 120/80—that is, normal. However, they are cold in the extremities, with thready pulses, and their labs show signs of organ dysfunction (acute kidney injury, elevated lactate, climbing transaminases). Echocardiography reveals an ejection fraction of 10%, and a diagnosis is made of cardiogenic shock.

Scenario 2: The vasculopathic arterial line

You are placing a radial arterial line in a 70-year-old patient with severe peripheral vascular disease. Even using ultrasound, you have great difficulty entering the vessel, and when you do place the cannula, the blood bubbles out sluggishly. Since the flow doesn’t look “arterial,” you wonder if you have inadvertently cannulated a vein.

Scenario 3: The lumbar puncture

You are performing an LP on a patient with concern for cryptococcal meningitis. Upon entering the spinal canal, CSF drips out slowly and positionally; you assume that the opening pressure is very low. However, your colleague suggests that you transduce it anyway, in case the weak flow is not necessarily indicative of a low pressure.

Pressure is not Flow

Most of you probably understood the first scenario easily. This patient has a low cardiac output despite a normal blood pressure. This is a completely normal finding in cardiogenic shock, which is a “pump failure”—a lack of forward flow—rather than a hypotensive state.

Arterial blood pressure is primarily maintained by vasomotor tone, which is why most of the shock we see is distributive (i.e. vasodilatory) in nature. In Guytonian physiology, the vascular pressure in the absence of any flow—the “mean systemic filling pressure”—is not zero, but it is very low (<20 mmHg). Low flow can eventually be a primary cause of arterial hypotension, but only in end stages; most cardiogenic shock is normotensive, or even hypertensive. As always, the wild card is vascular resistance, which can vary in either a compensatory or decompensated manner.

To make a long story short, flow and pressure are largely independent in cardiogenic shock, which means that we can no longer use blood pressure as a surrogate for flow—a simplification to which we’ve grown accustomed in other shock states, such as sepsis. In the septic, distributive shock patient, peripheral blood flow is pressure-dependent, so the BP on the monitor tends to correlate well with tissue perfusion. But that ain’t always so.

So it’s clear that pressure and flow are variables that, like a Venn diagram, overlap but remain distinct. We generally understand this is cardiogenic shock. But what about in other situations?

In Scenario 2, we cannulated a vessel and found its flow to be very poor. We assumed this to mean that its source could not be arterial. Why? Because arteries should have a high pressure. But we just agreed that these things don’t necessarily go together, didn’t we?

Covering the outlet of the cannula with a finger, you feel blood pulsating firmly against it. Skeptically, you hook it to the transducer, revealing an (obviously arterial) pressure of 100/60, despite the weak flow.

In Scenario 3 we discovered something similar. Lumbar punctures are performed using long, small-bore needles, which create a high-resistance “choke point.” Poiseuille tells us that flow through such a spinal needle will always be poor, unless the ICP is astronomical. A dribble of flow doesn’t mean the pressure head is not pathologically high; for enough pressure to create truly brisk flow through such a high-resistance lumen, you’d need to hook it to a fire hose. Here, flow tells us almost nothing about pressure.

You attach the fluid column manometer to your needle, and it fills very slowly. However, it keeps climbing and climbing, and by the time it finally levels out, it shows a severely elevated opening pressure of 30 cmH2O.

Conclusions

What’s the point of all this?

Pressure isn’t flow. Flow isn’t pressure.

We conflate them in many situations, and many times the simplification holds true. But they aren’t the same, and forgetting the additional variable of resistance can lead you to some very poor assumptions in the ICU.

To paraphrase Albert Einstein, everything—including our physiologic models—should be made as simple as possible… but no simpler.