When designing a portable Near-Infrared Spectroscopy (NIRS) device for the measurement of muscle oxygenation, design engineers have plenty of factors to consider. They must think about battery life, portability, affordability, safety, and many other design criteria. Before considering many of these criteria, however, an engineer must design a working technology that is capable of actually measuring muscle oxygenation. Without this basic attribute, the device would be a complete failure. The basics for measurement of relative oxygenated and deoxygenated hemoglobin concentrations was introduced previously in the patent blog post, but the engineering design problem was mostly glossed over. This post will dive a little deeper into the quantitative nature of measurement of muscle oxygenation and what functions the design engineer must consider when designing a device that will operate properly and accurately. The main question to be answered is: how does an engineer use light to measure concentration of a particle in muscle?
Fig 1: Molecular Absorption Coefficient Profiles for Oxygenated and Deoxygenated Hemoglobin
As mentioned before, NIRS works by measuring the absorbance or attenuation of light as it passes through a sample to make a measurement of concentration of the absorbing analyte or particle. Also previously introduced were the benefits of using near-infrared light since it can pass through biological tissue and is primarily absorbed by hemoglobin. In an ideal world the absorbance is defined by the Beer-Lambert Law. According to this law, the absorbance of a particle is equal to the natural log of incident light over the detected light and this is further equal to the product of the molar absorbance coefficient, the concentration of the particle, and the mean path length of detected photons. In an ideal case this law works because it describes when light is shown through a glass cuvette with a solution with only one absorbance particle, but this is not helpful for a NIRS device for muscle oxygenation. Thus, for a NIRS device, the modified Beer-Lambert Law must be used, which is the same as the original equation but with an extra scattering term to account for photon scatter when passing through tissue like skin and muscle (Eqn. 1).
Here A is absorbance, I0 is incident (transmitted) light, I is detected light, ɛ is molar absorbance coefficient, c is concentration, L is mean path length, and G is the scattering term. This is great in theory because it appears that concentration can be calculated relatively easily, but there are further problems to solve. Start by considering the knowns and unknowns. The absorbance coefficient is a known value for any analyte given the wavelength of the laser used (Fig. 1), and the path length can easily be found from the distance between the light emitter and detector with some regards to the path shape which is known to be roughly banana shaped. This leaves two unknown terms: the unknown that to be measured, i.e. concentration, and the scatter term. The scatter term is unfortunately a problem. It varies by tissue and considering the device should be designed for consumers to use on different locations, different muscles, and different amounts of say fat that may lie in the way of the muscle, this G term will forever be changing. Thus, there needs to be a way to get rid of it. The easiest way to do this is to find change in absorbance so that G will be subtracted away. This uses the assumption that G is constant for a given location. The resulting equation will then give change in concentration as it is the only factor that changed between measurements 1 and 2 (usually an initial measurement and a second measure at a later time) (Eqn. 2). Notice that absorbance is now equal to the natural log of the first intensity detected divided by the second intensity measured based on the identity (log(x/y) = log(x)-log(y). Note that the need to get rid of G, because it cannot be calculated on every single consumer, leads to the fact that NIRS devices almost always measure change in concentration or relative concentration when measuring muscle oxygenation.
This equation looks great. So change in concentration as opposed to exact concentration is found, but so what, this is still a very helpful measure for oxygenation during exercise. BUT, this equation is not the whole story. NIRS works by measuring both oxygenated and deoxygenated hemoglobin (Hb). Both species of Hb contribute to absorbance in the near-infrared range. Thus the equation actually looks like this (Eqn. 3)
In this equation, subscript O is used for oxygenated Hb, and subscript Hb is used for deoxygenated Hb. Now there are two unknowns and only one equation. So what does a smart engineer do? They add more lights. By measuring multiple wavelengths, two changes in absorbance can be measured allowing both concentrations to be calculated by solving the system of equation (Eqn. 4-5).
In these equations, superscripts refer to the wavelengths of light 1 and 2. It must be remembered that absorbance coefficient, absorbance change, and path length will all vary based on wavelength. This clearly allows for the output of relative concentrations or total blood oxygen saturation percentage (oxyHb / [oxyHb + deoxyHb]). Here the assumption is that total Hb is equal to oxyHb plus deoxyHb. The last piece of the puzzle for an engineer is to decide on what wavelengths should be used for the lights. This is a very impactful decision in building the algorithm to calculate the outcome measures of the device since ɛ, A, and L all depend on wavelength. It should be noted based on Figure 1 that certain wavelengths will be better than others. For example, if 805 nm light is used, then the absorbance coefficients for both species of Hb will be the same. This leads to irrational answers for Equations 4 and 5, so this wavelength should be avoided. The best case is to pick a wavelength above and below this so that one is more sensitive to oxyHb and the other is more sensitive to deoxyHb. Thus, using 750 and 850nm could be viable options, and these are used in several current devices.
These results allow an engineer to design a device that will properly measure muscle oxygenation through the relative concentrations of oxygenated and deoxygenated Hb. A reminder that some of the assumptions that needed to be made were that the tissue was homogenous, that oxy and deoxy Hb are the only particles contributing to absorbance, that absorbance is constant in time when Hb concentrations do not change, that the scattering term remained constant, and that oxy + deoxy Hb is the total Hb. Realistically, tissue is not homogeneous, but this assumption causes smaller errors in the volumes being considered close to the skin surface. Unfortunately, Hb is not the only chromophore contributing to absorbance. Fat is a major problem because it shares a similar range of wavelengths for absorbance. Some devices take fat correction into account, but other do not, and papers have pointed this out. It is reasonable to assume that absorbance is constant in time when concentration is constant, but pulsatile flow can cause error here. The scattering term should remain constant if the position of the device is not changed, and it is also reasonable to assume that there are not Hb species besides oxy and deoxy in the muscle. Some of these do cause limitations to the design described here, and as already mentioned it will only measure change in concentration not the absolute value. In conclusion, two wavelengths of light are needed measure muscle oxygenation with NIRS.
References
[1]. Shimadzu Commercial Website https://www.ssi.shimadzu.com/products/imaging/labnirs-principle-of-operation.html
[2]. Kocsis, L., Herman, P., & Eke, A. (2006). The modified Beer-Lambert law revisited. Physics in Medicine and Biology, 51(5). http://doi.org/10.1088/0031-
[3]. Len-Carrin, J., & Len-Domnguez, U. (2012). Functional Near-Infrared Spectroscopy (fNIRS): Principles and Neuroscientific Applications. Neuroimaging – Methods. http://doi.org/10.5772/23146
[4]. McManus, C. J., Collison, J., & Cooper, C. E. (2018). Performance comparison of the MOXY and PortaMon near-infrared spectroscopy muscle oximeters at rest and during exercise. Journal of Biomedical Optics, 23(01), 1. http://doi.org/10.1117/1.jbo.23.1.015007
