Experiencing the Oscillometric Method through Numbers: From Pulse Wave Data to Blood Pressure Measurements

In the previous article, “Deep Dive into the Oscillometric Method”, we explained everything from the physical principles of the oscillometric method to the overview of the algorithm, accuracy standards, and measurement limitations.

However, even if it is explained in words that “the algorithm calculates blood pressure values”, unless you can see exactly what numbers are processed and how the final blood pressure value is produced, you will not reach a true understanding.

Also, for the “micro perspective” of how the cuff pressure sensor captures and extracts “amplitude” per heartbeat in the first place, we explain it in detail in “What is the Blood Pressure Monitor Sensor Looking At? How “Amplitude” is Extracted from a Single Pulse”, so reading them together will deepen your understanding.

In this article, using simulated pulse wave data (oscillation amplitude), we will follow the calculation process step-by-step that is happening inside an electronic blood pressure monitor. Furthermore, in three clinically important scenarios—arteriosclerosis, cuff size mismatch, and wrist blood pressure monitors—we will confirm with interactive simulations how the shape of the envelope changes and what kind of errors occur in the calculated values.

1. Numerical Simulation of Normal Blood Pressure Measurement

1.1 Setting Up Simulated Data

First, we set the following conditions.

• Subject: Healthy Adult
• Actual Blood Pressure: Systolic Blood Pressure (SBP) = 120 mmHg, Diastolic Blood Pressure (DBP) = 80 mmHg
• Mean Arterial Pressure (MAP) = 93 mmHg

The electronic blood pressure monitor inflates the cuff pressure to about 160 mmHg, and then records the oscillation (vibration) amplitude of each heartbeat while gradually reducing the pressure. The following is simulated data obtained in that process. Note that this data is educational simulated data constructed based on the typical oscillometric envelope pattern reported in the literature¹²³.

These 14 steps of data points form the foundation of all calculations in the oscillometric method.

1.2 Visualization of the Oscillometric Envelope

Plotting the table above with cuff pressure on the horizontal axis and amplitude on the vertical axis gives a spindle-shaped curve bulging in the center - the oscillometric envelope.

Take a look at this graph. The three important points are as follows:

1. The maximum point of amplitude corresponds to MAP (93 mmHg) - This is the only blood pressure value that can be “directly determined” in the oscillometric method.
2. SBP is located on the rising side of the envelope (high-pressure side, left side).
3. DBP is located on the decaying side of the envelope (low-pressure side, right side).

However, SBP and DBP are not fixed at a single “point” on the graph. It is the algorithm that decides this.

2. Demonstration of Blood Pressure Calculation by the Fixed Ratio Method

2.1 Algorithm Procedure

Let’s actually calculate the blood pressure values using the Fixed Ratio Algorithm introduced in the previous article³.

In the fixed ratio method, a certain ratio to the maximum amplitude is used as a threshold, and SBP and DBP are determined from the intersection with the envelope.

Here, we will use the following ratios. These values are selected as intermediate values between SBP side ≈ 0.50, DBP side ≈ 0.80 reported in the original study by Geddes et al. (1982)¹, and 0.593 / 0.717 predicted by mathematical models by Drzewiecki et al. (1994)².

• Systolic Ratio: 0.55 (55% of the maximum amplitude)
• Diastolic Ratio: 0.75 (75% of the maximum amplitude)

2.2 Calculation Process

Step 1: Identify Maximum Amplitude

(Detected at a cuff pressure of 93 mmHg). This determines MAP = 93 mmHg.

Step 2: Calculate SBP Threshold

Look for the cuff pressure closest to an amplitude of 0.91 mmHg on the rising side (high-pressure side) of the envelope.

Checking the data:

• Cuff pressure 130 mmHg → Amplitude 0.60 (threshold not reached)
• Cuff pressure 120 mmHg → Amplitude 0.95 (exceeds threshold 0.91)

By interpolation, SBP ≈ 120 mmHg is calculated.

Step 3: Calculate DBP Threshold

Look for the cuff pressure closest to an amplitude of 1.24 mmHg on the decaying side (low-pressure side) of the envelope.

Checking the data:

• Cuff pressure 90 mmHg → Amplitude 1.60 (above threshold)
• Cuff pressure 80 mmHg → Amplitude 1.20 (falls below threshold 1.24)

By interpolation, DBP ≈ 80 mmHg is calculated.

2.3 Visualization of the Threshold Line

In the chart below, horizontal lines for the SBP threshold (0.91 mmHg) and DBP threshold (1.24 mmHg) are drawn over the envelope. The points where these horizontal lines intersect the envelope are the cuff pressures corresponding to SBP and DBP, respectively.

The point where the SBP threshold line (pink) intersects the rising side of the envelope is cuff pressure ≈ 120 mmHg (SBP), and the point where the DBP threshold line (yellow) intersects the decaying side of the envelope is cuff pressure ≈ 80 mmHg (DBP).

This is the essence of the calculations taking place inside an electronic blood pressure monitor.

3. “Manufacturer Differences” Created by Differences in Ratios

3.1 Why Values Differ Among Manufacturers

As mentioned in the previous article, the ratios of the fixed-ratio method differ by manufacturer and are non-public. In the literature, the values for the systolic ratio are reported to be in the range of 0.45 to 0.73, and the diastolic ratio is 0.69 to 0.83³⁴.

This difference in ratios is one of the causes of the values disagreeing when measuring the same person with blood pressure monitors from different manufacturers.

3.2 Comparison with 3 Sets of Ratios

Let’s see how the calculated results change with the following 3 sets of ratios:

From the same pulse wave data, there is a maximum difference of 15 mmHg for SBP and a maximum difference of 6 mmHg for DBP.

In this chart, three different SBP thresholds are superimposed as horizontal lines on the same envelope. As the threshold lowers (smaller ratio), the intersection with the envelope shifts to the high-pressure side, visually confirming that the SBP is calculated higher.

Clinical Significance: This “manufacturer difference” is especially important for patients near the diagnostic threshold for hypertension (140/90 mmHg)⁵. An individual may be judged “normal” by one manufacturer’s blood pressure monitor but “hypertensive” by another—such a situation can actually occur. It was also confirmed in a comprehensive analysis by Babbs (2012) that differences in fixed ratios create clinically significant differences⁴.

4. Simulation of Arteriosclerosis and Pseudohypertension

4.1 Effect of Arteriosclerosis on the Envelope

In patients with advanced arteriosclerosis, particularly calcium deposition (calcification) in the vascular wall, the vascular wall stiffens, and the artery cannot be completely occluded even when compressed with a cuff⁶⁷.

This causes the following changes in the envelope for the oscillometric method⁷:

1. The entire envelope shifts to the high-pressure side - Because a higher cuff pressure than the actual blood pressure is required to finally occlude the artery.
2. The amplitude generally decreases - Because a stiff vascular wall is hard to expand, the fluctuation amplitude due to pulsation is small.
3. The shape of the envelope becomes broader - Due to the reduced compliance of the vascular wall, the curve of amplitude change becomes less sharp.

4.2 Numerical Simulation

Below is simulated data for two subjects with the same actual blood pressure of 120/80 mmHg. This data is educational data constructed based on the mechanisms of pseudohypertension reported in the literature⁶⁷. Clinical studies have reported that the difference between cuff pressure and intra-arterial pressure in patients with pseudohypertension can range from 10 to 54 mmHg⁶:

In this simulation, even though the actual blood pressure within the blood vessels is identical at 120/80 mmHg, in a patient with arteriosclerosis:

• MAP is detected elevated from 93 to 133 mmHg
• Calculated using the fixed-ratio method (Ratio B: SBP 0.55, DBP 0.75):
  • SBP ≈ 160 mmHg (Actually 120 → overestimation of +40 mmHg)
  • DBP ≈ 120 mmHg (Actually 80 → overestimation of +40 mmHg)

This is pseudohypertension⁶. Even though blood pressure is normal, the blood pressure monitor indicates “severe hypertension”. The +40 mmHg overestimation in this simulation is an educational example within the 10-54 mmHg range reported in literature⁶.

Clinical Importance: Pseudohypertension requires special attention in the elderly (prevalence around 5-15%), dialysis patients, and diabetic patients⁶⁸. When unnecessary antihypertensive drugs are prescribed based on pseudohypertension, it can lead to excessive blood pressure drops (hypotension), presenting a risk of complications like falls or dizziness⁸.

5. Cuff Size Mismatch Simulation

5.1 Relationship Between Cuff Size and Accuracy

The accuracy of the oscillometric method is highly dependent on the match between the cuff size and the thickness of the arm⁸⁹.

Source: Pickering et al. (2005) AHA Scientific Statement⁸

If the cuff size is inappropriate, the following effects occur⁹¹⁰:

• When the cuff is too small: the compression area of the cuff is insufficient, and a higher cuff pressure than actual is needed to occlude the artery → blood pressure is overestimated
• When the cuff is too large: the compression area of the cuff is excessive, and the artery is occluded at a lower cuff pressure than actual → blood pressure is underestimated

5.2 Numerical Simulation

Below is simulated data for different sized cuffs used for the same subject (actual blood pressure 120/80 mmHg). The Cuff(SZ) randomized crossover trial by Ishigami et al. (2023) reported an overestimation of SBP by +4.8 mmHg with a cuff one size smaller, and SBP by +19.5 mmHg with a cuff two sizes smaller⁹. Also, Sprafka et al. (1991) reported an overestimation of SBP by +2 to 6 mmHg with a cuff one size smaller¹⁰. The value of this simulation (SBP +8 mmHg) is within a range consistent with these clinical data:

Calculated using the fixed-ratio method (Ratio B):

Just a mismatch in cuff size alone yields a maximum difference of 16 mmHg in SBP. This is an error that cannot be ignored against the diagnostic criteria for hypertension (140/90 mmHg)⁵.

Practical Advice: When purchasing a home electronic blood pressure monitor, first measure your arm circumference and check if it fits the size range of the included cuff⁸. Many blood pressure monitors come with a standard cuff (compatible with an arm circumference of approx. 22-32 cm), but those with thicker arms need to swap for a larger cuff. Ishigami et al.’s study reported that although 55% of the subjects needed a large or extra-large cuff, only a standard cuff was used in some cases⁹.

6. Wrist-type vs Upper Arm-type Differences

6.1 Structural Issues of Wrist-type Blood Pressure Monitors

Although wrist blood pressure monitors use the same oscillometric method as upper-arm types, they have the following structural differences due to the difference in the measurement site¹¹:

① Differences in arteries

Whereas the upper-arm type measures a single brachial artery, the wrist type measures the wrist where two arteries, the radial artery and the ulnar artery, run parallel. Because the signals from the two arteries are mixed, the shape of the envelope differs from that of the upper arm.

② Signal attenuation

Because tendons and skeletal structures in the wrist are in close proximity to the arteries, the swing width of the pulsation is smaller than in the upper arm. This causes overall oscillation amplitudes to decrease, making them more susceptible to noise.

③ Difference in height relative to the heart

This is the biggest problem with wrist types.

6.2 Pressure Correction According to Height Differences

According to the hydrostatic principle, the further the measurement site is from heart level, the greater the error in the blood pressure measurement value¹².

Where:

• $\Delta P$: Pressure difference (Pa)
• $\rho$: Density of blood ≈ 1060 kg/m³¹³
• $g$: Gravitational acceleration ≈ 9.81 m/s²
• $h$: Difference in height (m)

Calculating this out:

In other words, for every 10 cm away from the heart, a pressure difference of about 7.8 mmHg occurs. This value is broadly consistent with the actual measurement (~0.735 mmHg/cm) taken by Netea et al. (2003)¹².

6.3 Numerical Simulation

The simulation below compares baseline data for the upper-arm type with three envelope patterns for the wrist type (level with the heart, 15 cm above, 15 cm below).

The envelope of the wrist type has the following features compared to the upper arm type:

• Genereally smaller amplitude (Signal attenuation)
• Pressure offset by height difference shifts the peak position of the envelope.

The standard result when calculated with the fixed-ratio method (Ratio B) is as follows:

A difference of up to 23 mmHg in SBP occurs simply by changing the wrist position 15 cm above or below the heart.

Why the guidelines recommend the upper-arm type: With an upper-arm blood pressure monitor, the measurement site naturally falls roughly at heart level if the arm is placed on a desk while sitting. There is no need for conscious posture adjustments, and errors due to hydrostatic pressure are minimized. With the wrist type, the wrist must be accurately held at heart level, a condition difficult to meet in daily routine measurement. Both the 2017 AHA/ACC guidelines⁵ and the Japanese Society of Hypertension Guidelines (JSH2019)¹¹ recommend the use of an upper arm cuff-type monitor for home blood pressure measurement.

Summary: What the Simulations Teach Us

Through the simulations in this article, the following facts became clear:

1. Electronic blood pressure monitor values are “estimations”, not “measurements”

The only thing that can be directly determined by the oscillometric method is MAP (mean arterial pressure). SBP and DBP are estimator values from an algorithm, and the results vary depending on the ratio employed.

2. Differences in algorithm ratios produce clinically meaningful differences

A choice in fixed ratio alone can yield a difference of up to 15 mmHg in SBP. This is one of the real reasons behind the “difference in measurement values due to differing manufacturers.”

3. Arteriosclerosis can trigger severe overestimation

Clinical studies report that pseudohypertension calculates values 10-54 mmHg higher than actual blood pressure⁶⁷. There is a risk that this will lead to the prescription of unnecessary blood pressure-lowering drugs.

4. Cuff size mismatch is a routine source of error

The selection of appropriate cuff size is the most fundamental requirement for accurate blood pressure measurement.

5. The position error in wrist type monitors is equal to or greater than other sources of error

A height difference of merely 15 cm produces an error of over 10 mmHg. Here lies the scientific ground on which the guidelines recommend the upper-arm type.

Related Articles

• Deep Dive into the Oscillometric Method: How Electronic Blood Pressure Monitors Were Born, What They Measure, and What Are Their Limitations?
• Deep Dive into Korotkoff Sounds: How Are Systolic and Diastolic Blood Pressures Measured?
• A Journey to Measure Blood Pressure: Why Did Humanity Try to Measure Blood Pressure?

References