PPG Heart Rate Sensing and Calibration
Heart rate can be measured in a variety of different ways. The method that is used in critical medical cases is the electrocardiogram (ECG). This method utilizes electrodes which are placed across the chest area and measure voltage changes which are generated by the heart muscle. This method is cumbersome and sensitive to high levels of activity in which the electrodes may see artifacts related to motion or even fall off due to the buildup of sweat. Another method of measuring heart rate is the photoplethysmogram (PPG). This method uses optics to measure changes in blood volume of which heart rate can be extracted. PPG sensing is not cumbersome since a PPG sensor can be made very small and does not require two electrical connections across the chest. PPG sensors do not require calibration like other instruments do.
How does PPG heart rate sensing work?
On a high level, PPG heart rate sensing works by shining light at the skin surface and measuring the reflectance with a light sensitive photodiode. Green light is often used in PPG sensors because it is absorbed well by hemoglobin which is the protein in red blood cells that carries oxygen. Changes in blood volume create changes in the reflectance of light inside the skin. Heart rate can be measured by looking for periodic changes in blood volume. The reflected light is measured by the voltage across the sensing photodiode. These voltages are recorded and processed to generate a heart rate measurement. Heart rate is a relatively low frequency signal and because of this, blood volume does not have to be sampled continuously. This is why PPG sensors often flash since they are taking samples by turning their green light emitters on and off very quickly to conserve power.
Why do some sensors and systems require calibration?
All sensors have a “characteristic curve” which defines their response to inputs. In the case of the PPG sensor, blood volume is the input, and voltage across the light sensing photodiode is the output. There are three aspects of a sensor's characteristic curve that can create a need for calibration. These are: sensitivity, offset, and linearity.
First let’s consider the case of the perfect sensor. A perfect sensor would have a perfectly linear characteristic curve with no offset and a slope of 1. In this case there is a perfect mapping between the blood volume input to the sensor, and the output voltage of the photodiode. This is shown in the figure below.
Next, let’s consider the case of a sensor that has a linear characteristic curve with a different sensitivity. In this case where the input remains the same, the output will be scaled differently as seen below.
Next let’s consider the case of a sensor that has both a different sensitivity (slope) as well as a different offset from the perfect sensor example. In this case where the input remains the same, the output will be scaled differently as well as shifted vertically from the output that was described in the perfect sensor example.
Finally, we can examine the case where the characteristic curve of the sensor is non-linear and has an offset. This is almost always the case with real sensors as most sensing mechanisms are non-linear in some way. A non-linear characteristic curve essentially means that the sensitivity changes with different levels of input. In some regimes the sensitivity could be low, in other regimes the sensitivity can be high. Non-linear characteristic curves change the shape of the output in a non-uniform way.
Why do gas sensors require regular calibration?
The purpose of most gas sensors is to measure the absolute value of a target gas concentration. A gas sensor takes the input of a target gas concentration and gives an output as a voltage across the sensing element consisting of two electrodes in a special electrolyte. At the manufacturing facility, the sensors are initially calibrated to account for different sensitivities, offsets, and non-linear aspects of the characteristic curves. This calibration adjusts for these imperfections and results in a sensor that gives accurate measurements of gas concentration. Over time the characteristic curve of the sensor can change due to aging which involves slow chemical changes in the sensing element. Re-calibration is needed because the characteristic curve changes over time which would otherwise make the output inaccurate.
Why do PPG heart rate sensors NOT require calibration?
PPG Heart Rate sensors do not require calibration. In the above images, it is shown that imperfections and changes to the characteristic curve indeed affect the blood volume to voltage output relationship, however the same exact periodic heart rate can be seen in the voltage output in every example. In technical terms, heart rate sensors perform continuous automatic zero calibration (removing the offset). They do this by only looking at relative changes in blood volume and not the absolute value. The measurement also does not require sensitivity accuracy since changes in sensitivity do not affect the sensor’s ability to see periodic changes in blood volume. This can be seen in the second figure. The sensitivity scales the output voltage down, but the heart rate is still present in the output data.