Is your wrist pulse the signal that blood just arrived?
― The pulse is a "wave" that travels 20 times faster than blood
Press a finger to your wrist and you feel it: thump, thump. It's tempting to think that's the blood the heart just pushed out, arriving at your wrist. But that's not quite right. What you're actually feeling is a "bulge wave" travelling along the wall of the blood vessel. And the speed of that wave is an honest readout of how stiff your blood vessels are.
In a clinic waiting room, you press a finger to the inside of your wrist and count your pulse. About 70 beats a minute, pushing back against your finger with steady regularity.
Now try touching the pulse at the side of your neck with one hand, and the pulse at your wrist with the other, at the same time. The two pulses feel almost perfectly in sync.
But the distance from your heart to your wrist is about 80cm. Can blood really travel all the way to the tip of your arm that instantly?
Just two keys unlock the mystery of the pulse
When the heart pushes blood out, the vessel at its exit swells slightly. That bulge is handed off from one stretch of vessel to the next, all the way to your wrist. The blood itself, meanwhile, has only moved a few centimetres.
In a soft rubber tube, the wave travels slowly; in a stiff tube, it travels fast. As blood vessels stiffen with age, the pulse wave speeds up. Checkups even include a test that measures this speed.
Let's look at each in turn.
Blood moves slowly; the bulge moves fast
With each beat, the heart is thought to push around 70mL of blood into the aorta. The aorta is a vessel that stretches like rubber. To absorb the surge of incoming blood, the section near the exit swells first.
The wall of that swollen section, trying to spring back to shape, pushes the blood forward. That push swells the next stretch of vessel just ahead. This "swell, then spring back" is passed along one stretch at a time, travelling as a wave all the way to your fingertips.
In a young person's aorta, this wave is thought to travel at roughly 5–6 metres per second. That means it takes only about a tenth of a second to go from heart to wrist. The blood itself, by contrast, flows through the aorta at an average of only about 0.2–0.3 metres per second. The pulse wave is racing ahead at more than 20 times the speed of the blood.
Look at Figure 1. The instant the leading edge of the pulse wave reaches the wrist, the blood that just left the heart is still somewhere around the chest.
Think of a garden hose full of water. Turn the tap, and water comes out of the far end almost instantly. But that's the water that was already sitting at the far end of the hose. The water that just entered at the tap is still right there, near your hand. The pulse works the same way: what arrives first is the "push," not the water itself.
Stiffer vessels mean a faster pulse
How fast a wave travels depends on how forcefully the wall pushes back. A soft, balloon-like tube stretches a long way when pushed, absorbing the force and handing it on slowly. A stiff tube barely stretches and pushes back immediately, so the wave races ahead impatiently.
Blood vessel walls are thought to stiffen gradually with age, as the elastic fibres wear down and stiffer fibres make up a larger share of the wall. Long-term high blood pressure is also considered one cause of this stiffening.
That means measuring the speed of the pulse wave gives an external read on how stiff the vessels are. Many "vascular age" tests in medical checkups work by measuring the difference in arrival time between the pulse at the arm and at the ankle.
Stiff vessels bring another problem. Part of the pulse wave bounces back toward the heart at points where vessels branch. In a soft vessel, this reflected wave arrives only after the heart has finished pumping. In a stiff vessel, it bounces back faster, colliding with the outgoing push while the heart is still pumping — and is thought to push the systolic (upper) blood pressure even higher.
Thomas Young, the English scientist famous for demonstrating that light behaves as a wave, was also a physician. Around 1808, he is said to have estimated the speed of the pulse wave from the elasticity of the vessel wall. About 70 years later, the Dutch researchers Moens and Korteweg formulated this into the equation still used today.
Summary
The pulse at your wrist isn't a signal that blood has just flowed in from the heart. It's a bulge wave, carried forward as each heartbeat swells one stretch of vessel wall after another. Its speed is set by how stiff the vessel is — the stiffer it is, the faster it travels.
What the pulse announces isn't the arrival of blood, but the arrival of a push.
And its speed reveals how soft — or stiff — your vessels are.
Waves travelling across the surface of water work the same way — it's the disturbance that moves, not the water itself (Why do throwing a stone into a pond create expanding circular ripples?). The heart rhythm that generates the pulse wave is covered in Why can the heart keep beating all by itself?, and the speed of a different kind of signal travelling through the body is covered in Why does the pain from stubbing your little toe arrive with a slight delay?.
- Gently place your index and middle fingers in the slight hollow on the inside of your wrist, on the thumb side. Pressing too hard actually makes the pulse harder to feel.
- With your other hand, touch the pulse at the side of your neck (just below the angle of the jaw) and compare its timing with the pulse at your wrist. You should feel them almost simultaneously. In that time, the blood has moved only a few centimetres.
- Sit with your legs crossed, and touch the pulse at your neck with one hand and the pulse on the inside of your ankle (just behind the anklebone) with the other. The ankle pulse may feel very slightly delayed compared to the neck. That's because the wave takes a little longer to arrive at the greater distance from the heart.
Touch the neck pulse only lightly. Pressing firmly on both sides of the neck at once can make you feel unwell. The delay at the ankle is thought to be about 0.1 seconds — not being able to feel it is perfectly normal.
Want to know more? ― Terminology, formulas, and links to the curriculumFrom junior-high science to university-level specialist subjects — each item is labelled by level
- JHSCovered in junior-high school science
- HSCovered in high-school "Physics" or "Biology"
- HS+Advanced high-school content, or textbook sidebar material
- Univ.Not covered in high school — university-level specialist content (biomechanics, circulatory physiology)
- ResearchNot yet settled even at university level — something researchers are actively investigating
JHSTerminology: this phenomenon has a name
- Pulse wave: the wave of vessel-wall bulging, generated by each heartbeat, that travels along an artery. This is what you feel as your pulse at the wrist.
- Pulse wave velocity: the speed at which the pulse wave travels along an artery. Used in checkups as a gauge of vessel stiffness.
- Arteriosclerosis: a condition in which artery walls become stiff and thickened. A cause of increased pulse wave velocity.
JHSHSCheck it with a formula: pulse wave speed and time to reach the wrist
The speed of a wave travelling through an elastic tube is set by the wall's stiffness, its thickness, and the weight of the fluid inside. Let's plug in values close to a young person's aorta and calculate the pulse wave speed itself.
| In symbols | c = √( E × h ÷ ( ρ × d ) ) |
| In words | Pulse wave speed = the square root of (wall stiffness × wall thickness) ÷ (blood density × vessel diameter) |
| Where it comes from | This formula balances the force of the stretched wall springing back against the inertia (weight) of the blood being moved. It's known as the Moens–Korteweg equation. |
| Symbol | Meaning and unit |
| c | Pulse wave speed (m/s) |
| E | Vessel wall stiffness (Young's modulus, Pa) |
| h | Vessel wall thickness (m) |
| ρ | Blood density (kg/m³) |
| d | Vessel diameter (m) |
| Wall stiffness (typical for a young aorta) | roughly 500000 Pa (0.5 MPa) |
| Wall thickness | roughly 0.002 m (2 mm) |
| Vessel diameter | roughly 0.025 m (2.5 cm) |
| Blood density | roughly 1060 kg/m³ |
| Distance from heart to wrist | roughly 0.8 m |
| Average aortic blood speed | roughly 0.3 m/s (approximate) |
| Stiffness × thickness | 500000 × 0.002 = 1000 |
| Density × diameter | 1060 × 0.025 = 26.5 |
| Ratio of the two | 1000 ÷ 26.5 ≒ 37.7 |
| Square root (pulse wave speed) | √37.7 ≒ 6.1 (6.1 m/s) |
| Time to reach the wrist | 0.8 ÷ 6.1 ≒ 0.13 s |
| Distance blood travels meanwhile | 0.3 × 0.13 ≒ 0.039 m |
| How many times faster the wave is than blood | 6.1 ÷ 0.3 ≒ 20 times |
| If the wall gets 4× stiffer, speed doubles | 6.1 × 2 = 12.2 |
The pulse wave travels at roughly 6 m/s, reaching the wrist from the heart in 0.13 seconds. In that time, blood moves only about 4cm. If the wall becomes 4 times stiffer, the pulse wave speeds up to roughly 12 m/s.
| 6 m/s | Fast enough to run 100m in about 17 seconds — roughly a sprinting elementary-school kid |
| 0.13 s | About the same as a single blink (0.1–0.15 seconds) |
HSHS+The same shape as a wave on a string
HSIn high-school physics, you learn that the speed of a wave on a string is "the square root of tension ÷ linear density." The stronger the restoring force, the faster; the heavier the thing being moved, the slower. The pulse formula has the same shape: wall stiffness and thickness play the role of "restoring force," while blood density and vessel width play the role of "weight."
HS+Vessel wall stiffness isn't constant. The higher the blood pressure and the more the wall is stretched, the larger the share of the load taken up by stiffer fibres, making the wall effectively stiffer. That's why, even in the same person, the pulse wave travels faster when blood pressure is higher. This is also why checkups measure blood pressure at the same time.
Univ.The reflected wave and the shape of systolic pressure
In university-level circulatory physiology, the blood pressure waveform is treated as the superposition of the wave leaving the heart (the forward wave) and the wave bouncing back from branch points (the reflected wave). How much the reflected wave boosts systolic pressure is called the augmentation index. As a method for measuring pulse wave velocity, carotid-femoral pulse wave velocity — measured between the neck and the groin — is considered the research standard. In Japan, measurement between the upper arm and ankle is more commonly used. The formula is derived by combining the equation of motion for a thin-walled elastic tube with the continuity equation for blood flow.
📖 For the derivation and further detail: Moens–Korteweg equation (English Wikipedia) ／ Pulse Wave Velocity (Japanese Wikipedia)
ResearchWhat's still not fully understood
- Can stiffened vessels be made soft again? There are reports that exercise, cutting salt intake, and medication can lower pulse wave velocity. But how far the wall's underlying structure can actually be rejuvenated is still debated.
- Can blood pressure be measured without a cuff? Efforts are underway to estimate blood pressure from pulse wave arrival time and measure it continuously with wrist-worn devices. However, correction varies by person and over time, making this still a research-stage technology in terms of accuracy.
- Where exactly does the reflection happen? The reflected wave is often simplified as "bouncing back from a single point," but in reality it returns gradually from countless branch points. Several different models exist for capturing the overall picture.
In other words, even this article describes things "as currently understood." Real blood vessels vary in width and stiffness from place to place, and the calculations here are approximations based on a simplified, uniform straight tube.
Links to the curriculum (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| JHS | Science (Field 2): blood circulation, heart function | The section on the heart pushing blood out and feeling it as a pulse |
| HS | Physics: how waves travel, speed of a wave on a string | That what's moving is a "bulge," not blood itself, and the shape of the formula |
| HS+ | Biology: the circulatory system, vessel structure | The relationship between blood pressure and stiffness, and age-related change |
| Univ. | Biomechanics / circulatory physiology | The Moens–Korteweg equation, forward and reflected waves |
| Research | Vascular aging, continuous blood pressure measurement | Whether vessel stiffness can be reversed, cuffless blood pressure monitors |
| ― | Everyday connections | The "vascular age" test in checkups, how to take your own pulse |
- Japanese Wikipedia, "Pulse Wave Velocity" (脈波伝播速度)
- Wikipedia, "Moens–Korteweg equation"
- Nichols WW, O'Rourke MF, et al., McDonald's Blood Flow in Arteries, Hodder Arnold
- Laurent S et al. (2006) Expert consensus document on arterial stiffness: methodological issues and clinical applications. European Heart Journal 27: 2588–2605
- Japanese Society of Hypertension (日本高血圧学会), Guidelines for the Management of Hypertension 2019 (高血圧治療ガイドライン2019)
※This article is a general-audience science explainer. The figures given are approximations meant to aid understanding of the underlying mechanism. If you have any concerns about your blood vessels or blood pressure, please consult a doctor.