Why does Near Infrared (NIR) light allow deeper imaging in biological tissue in Multiphoton Microscopy?

Question

I have been reading this paper on multiphoton microscopy (https://www.nature.com/articles/nphoton.an.2010.2) and I am very confused about something. Here is a quote from the paper:

"The NIR excitation enhances the ability to image deeper into a sample through a reduction light scattering proportional to the fourth power of the excitation wavelength."

Why is this true? Why can longer wavelength light penetrate further into biological tissue? Is this generally true for any wave, that a higher wavelength means a higher Transmission coefficient (I thought the opposite was true)?

Is this a material-dependent phenomenon, and it just so happens that in biological tissue NIR can penetrate further, and there's no good explanation why?

I do not know much about QM so would appreciate an intuitive, less technical answer, thanks.

Answer 1

I can't provide a general correlation between the transmission coefficient and wavelength due to numerous factors influencing transmission. For instance, when a certain type of polar molecule within the material resonates with the incoming electromagnetic waves, the transmission coefficient tends to significantly decrease at that specific wavelength.

The interaction between electromagnetic waves and materials is very complex, particularly in the realm of absorbing materials (mainly focusing on microwaves), there are various dielectric losses (such as condutive loss and polarization loss) and magnetic loss (such as hysteresis loss and eddy current loss) mechanisms. Each of these mechanisms exhibits distinct frequency-dependent behavior. For instance, magnetic losses usually become insignificant at higher frequencies. While in the very high energy range, the $\gamma$-ray interact with materials through three primary mechanisms: Compton scattering, photoelecric effect and electron pair effect. Therefore, determining which mechanism dominates within a specific wavelength range is crucial.

Fortunately, a reference (Deep tissue multiphoton microscopy using longer wavelength excitation) in the article you provied identified the primary influencing factor by comparing the free paths associated with different processes.

As a result of the large difference between scattering mean free paths (MFPs) and absorption lengths in brain tissue, scattering dominates over absorption by water and intrinsic molecules in determining the attenuation factor for wavelengths between 350 nm and 1300 nm.

Although I have no idea about what is acting as a scatterer in the biological tissue, the description in the article, which states that the scattering is proportional to the fourth power of the wavelength, implies that these scatters should have a considerable sub-wavelength scale. This specific relationship exactly corresponds to the widely recognized Rayleigh scattering law of subwavelength particle scattering.

Now I will give a brief review of the Rayleigh scattering. When an electromagnetic wave with a wavelength $k$ incident upon a small dielectric (or PEC) particle with radius $a$, If $ka\ll 1$ holds, only the lowest multipoles responeses, usually electric and magnetic dipoles, are important. The contribution of such dipole response gives a total scattering cross-section of $\sigma \propto k^4a^6$. For describing the scattering of small particles, Rayleigh's law usually works well when resonance scattering does not occur (or if the static dipole moment of the particle vanishes, the scattering caused by it may also be smaller).

So in this scenario, we can consider the tissue as a low absorption medium. The subwavelength disorder and defects function as scatterers, causing light attenuation due to scattering during propagation. Evidently the $k^4$ dependence means that higher wavelength light penetrate further into biological tissue in such a specific wavelength range. At this point, we could compare the tissue to foggy weather. Similar to how fog scatters light differently across the spectrum, with red being scattered least and violet most, causing red signals to travel farther and be easier to detect during foggy conditions.

Answer 2

In a general case, you are right that shorter wavelengths better penetrates materials, because simply they have more energy as per $E=hc/\lambda$. It's same like if you would throw a snowball faster and it would penetrate snow wall more deeply, making deeper hole in it. However, if human body has to be modelled as a black body, then according to Wien's displacement law, our bodies mostly radiates in wavelengths of :

$$\approx \frac {3~mK·m}{37^\circ C} = 10~\mu m \tag 1$$

So it happens so, that our body must be relatively transparent to IR radiation, otherwise infrared frequencies from deep body tissues would not reach surface of our body,- skin and would not escape into the wild. You can look at it also other way,- as when in cold winter we like to warm up by the fireplace. This means that our bodies "absorb" infrared waves and transfer them to deeper tissues pretty well too.

If we shift wavelengths, there's also some inverse tendencies. Short UV spectrum waves are pretty good absorbed by our skin, so that it cancels ultraviolet radiation completely. That's why it's pretty dangerous to be in the Sun in a very hot summer days for very long time periods, because you can even get a skin cancer.

Anyway, when in biological tissue spectroscopy you shift working wavelengths slightly to NIR range, which is about $1~\mu m$, you get to the transmittance window, which our bodies allows. This is because we are mostly composed of water, and water have several low absorption coefficient regions, such as at $1\mu m ;~ 10\mu m$. This is illustrated by water absorption spectrum :

So yes, it's a material-dependant feature, which must be exploited for deeper EM visual spectroscopy.