Sleep 3.2 PPG Theory and Biophysics

• So the next topic is PPG theory and biophysics, and there are basically three ways in which light interacts with tissue. There's scattering, absorption, and reflection. And actually, reflection as a physics principle does not really occur prominently in PPG because the different tissue layers have relatively similar refractive indices, typically around like 1.3 to 1.4. So the small differences in refractive indices means the internal light reflection at tissue boundaries really do not typically occur. So when light enters human tissue with PPG measurements, it really primarily depends on the two of the three, scattering and absorption. 
• Scattering is particularly complex because it occurs several ways.
• First, is the Rayleigh scattering. This happens with particles much smaller than the wavelength of light and occurs with small cellular structures and proteins. Think of ribosomes and keratin. And this tends to create a more uniform scatter pattern. The second is Mie Scattering. This occurs when light interacts with particles similar to the light wavelength and in tissues, this mainly happens with larger protein structures like collagen fibers, which is prominent in the dermis layer of the skin.
• Mie Scattering creates a somewhat forward-directed, scattered pattern. And as a result of these two processes, you have an almost browning path like, path of light motion as shown here, and accounts for why the path of light travels traveling from the source of the light to the detector has a banana-shaped pattern to it after averaging over many photon paths.
• We will come back to why this is important. And one really important information to note is that Rayleigh scattering is inversely proportional to the light wavelength to the fourth power. This means that scattering for 400 nanometers is 9.4 times more likely than scattering of 700 nanometers light.
• So scattering plays a crucial role in determining how light of different wavelengths penetrates the skin. So for shorter wavelength light, such as blue shown here, the scattering is so strong that it only reaches the epidermis. It simply cannot penetrate any deeper. In contrast, the longer wavelength light, like red, can penetrate much deeper into the dermis, reaching the arterioles, where deeper physiological measurements can be obtained.
• And green light sort of falls between, somewhere in between. It penetrates to the upper dermis, where the capillaries are located. An easy way to remember the relationship between scattering and the light wavelengths is to think about sort of shining light through your hand. The light that emerges, on the other side is red because the longer wavelengths, like red, penetrate more deeper, deeply, while the shorter wavelengths are scattered or absorbed before they can reach to the other side.
• Now this comes to the other issue of light tissue interaction, which is absorption. Within the visible light spectrum, which spans wavelengths about 300 to 700 nanometers, melanin and hemoglobin are the dominant molecular absorbers. And you can see in this absorption versus light, wavelength plot that melanin has a higher absorption coefficient compared to hemoglobin.
• Actually, there's two types of melanin shown here. The one that you should probably focus on is the eumelanin, which is responsible for the skin tone. this one has to do with individual's red, hair, and, and freckles. so, You know, because you can see that the absorption of melanin has higher absorption compared to hemoglobin, but because it is confined to the thin epidermal layer of the skin, its overall influence on PPG light, its propagation is more limited than you would think.
• Now, that being said, melanin might reduce the accuracy of PPGs in certain individuals with darker skin, which I'll go into much more detail later. In contrast, hemoglobin is more widely distributed across the tissues, with volume, fractions typically ranging between one and five percent, and so may contribute to larger fractions of light absorption, particularly wavelengths that go into deeper tissue levels like red.
• So, as we move to higher wavelengths, beyond 1000 nanometers, water becomes a more significant absorber. And interestingly, there's a range called the optical window, somewhere between 750 and maybe 1400 nanometers, which is the near-infrared spectrum. And in this range, absorption by both the hemoglobin and water is reduced allowing for deeper light penetration in tissues. And so this is why near-infrared light is often used in medical and physiological monitoring devices, for, you know, measurements that require accessing deeper vascular structures. You can think of NEARs as an example. 
• So when you combine these two factors, scattering and absorption, you can then really appreciate how the light interacts with the skin.
• Scattering determines the depth of light penetration, and absorption determines what is being measured. So when you put these two things together, you see that blue light has high scattering and thus only reaches the epidermis. But as you can see in the blue light, it does get absorbed by both melanin and hemoglobin, but because the epidermis contains very little blood vessels, hemoglobin does not play a factor.
• For green light, green causes is scattered at moderate high levels, and thus it reaches the papillary dermis level to the upper blood vessels in the small plexus, where there's capillaries here. And so the major components that are being absorbed is capillaries. That absorbing the green light is melanin and hemoglobin.
• For red light, the scatter is moderate and so it can reach the deeper levels, particularly the reticular levels where you have the deep blood vessels, where you have the arterioles. And thus, the absorption of red light is dominated mostly by hemoglobin and for near-infrared, as mentioned before, it sort of penetrates the deepest, because it has the lowest amount of scattering, and it gets mostly absorbed by water and hemoglobin.
• Now, since I'm talking about the physics of PPG, I can't not include some mathematical equations here, and so one of the fundamental principles underlying PPG is the Beer-Lambert Law. This law describes the relationship between light transmission and the properties of the medium through which it passes.
• Specifically, it shows that light intensity decreases exponentially as it travels through tissue, and can partly explain why PPG and other photonic-based diagnostic devices are so sensitive to light intensity. Generally, the brighter the light, the better the device functions. And so, this exponential attenuation depends on epsilon, which is the attenuation coefficient, the path length of light traveling through the tissue, and the concentration of the absorbing and scattering particles.
• And the attention coefficient and path lengths are dependent on wavelength of light. And the effect of attenuation is a summation of all the absorbing scattering processes that occur with different particles. Now the reason why, this is labeled as modified Beer-Lambert Law is that when it comes to PPG, we're not really interested in the absolute attenuation light, but more in the relative attenuation of light.
• We're focusing on the dynamic changes in the attenuation with respect to time. And so the biggest factor here in terms of absorption light by hemoglobin, which varies by the blood volume changes with each heartbeat. And this is what forms the basis for measuring, metrics like heart rate and oxygen saturation.
• So when it comes to absorption and scattering, there are non-pulsatile or static components and a pulsatile or dynamic component. The static component includes skin, bone, and muscle. Venous blown blood here is also kind of categorized as static, although it's probably more pseudostatic or dynamic, since it certainly varies with time.
• Then there's arterial blood with blood, which has both a non-pulsatile and a pulsatile component. Now, during systole, there is more blood in the skin and thus greater absorption of light, which leads to less light being registered at the sensor. So, during systole, the light being registered at the sense and sensor is actually at the minimum.
• So what's typically done is that the signal from the sensor is then inverted to then reflect the amount of blood in the skin. And this provides the PPG waveform that we typically see and so that's shown here.
• I just wanted to give you an example of what a raw waveform actually looks like. And you can see that in addition to the pulsatile components that you see in the arteries, you see, a lot more fluctuations of the wandering baseline than you would anticipate. And you can see the respiration components here too.
• There are a number of factors in addition to the arterial blood, pulsatile component, that need to be considered, but are often filtered out when we actually see the, PPG signals in the medical setting. 
• So, PPG, can be collected by two ways. One is the transmission, transmittance way, and the other is the reflectance.
• The transmittance way is basically having a source on one side of light, and then that light transmits through the median or whatever tissue that you might have, and then the detector on the opposite side. And so an example of this is the finger PPG. You can see this in any area of the body, which has sort of a thin depth, which includes sort of fingertip, ear lobes, and even toes in infants.
• For the reflectance mode, we basically have the source, light source, and the detector happening on the same side. And this is what we see in watches, you know, that we see in the consumer wearables. And the reflectance approach can be found in all different types of sites, including wrist, forehead, which is imaged here, torso, arms, legs, and even the ear canals, which are accounted for, so the earables that we increasingly hear about.
• Also, it can be used for the scalp of fetus during labor. And also, if you have endoscopy, you could be using, these, reflectance PPG to, evaluate blood flow in the esophagus and the bowel wall. 
• Now, the core part of the PPG hardware incorporates a number of components. The first part is sort of the light-emitting diode for emitting the light.
• Then you have the photo-detector for detecting the emitted light, a filter to remove noise and enhance signal quality, an amplifier, and an ADC or analog to digital converter, and a microprocessor that signal, that processes the signal, and then the emitter driver, which is then modified by the signal processing, to, modify the intensity of the light generated by the LED.
• Now, consumer wearables actually have different arrangements of the LED and the photodiodes and, and different filtering mechanisms than so, themselves. And you can see sort of the different arrangements here. It might be a little hard to see, but this is the Samsung Galaxy Watch. You can see a single LED with four photodiodes.
• The Garmin actually has four LEDs with one photodiode, and the Apple Watch, I think, has like several LED lights and several, photodiodes. So, these different arrangements do cause different results from these different devices.

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