First we find how much energy our head absorbs. Then how much will be the thermal stress based on temperature rise; and eventually how much will be the pressure of the "boiling wave".
It was described previously that cochlear ablation results in abolishment of microwave hearing. This means that during microwave exposure, somehow the cochlea is activated and that this takes place via a physical transduction mechanism.
James Lin, an investigator with extensive research in the microwave auditory phenomenon field, suggested three potential mechanisms:
He mentioned that based on his studies below, the thermoelastic pressures are one to three orders of magnitude greater than the other candidate mechanisms [Lin, 1976a,b].
Lin JC. 1976b. Microwave induced hearing sensation: Some preliminary theoretical observations. J Microwave Power 11:295–298 (free pdf).
He then went on to measure them. It was previously mentioned that these were measured in a salt solution using a hydrophone. We were wondering if we could measure similarly the thermoelastic waves that are generated in the brain. The answer is yes. The scientist and his colleagues used a hydrophone transducer (3 mm in diameter) which they implanted in the brains of cats, rats, and guinea pigs. The results [Olsen and Lin,1981, 1983; Su and Lin, 1987] showed sound/pressure frequencies that were in accordance with their predictions from the thermoelastic transduction theory. Below are their studies:
Olsen RG, Lin JC. 1983. Microwave-induced pressure wave in mammalian brain. IEEE Trans Biomed Eng 30:289–294.
Su JL, Lin JC. 1987. Thermoelastic signatures of tissue phantom absorption and thermal expansion. IEEE Trans Biomed Eng
They also measured the speed of thermoelastic pressure wave propagation in the brains of cats irradiated with pulsed microwaves and they found a value of 1523 m/s [Lin et al., 1988].
Lin JC, Su JL, Wang YJ. 1988. Microwave-induced thermoelastic pressure wave propagation in the cat brain. Bioelectromagnetics 9:141–147.
What is practically “sound pressure”? James Lin tells us that it is “loudness”. Interestingly the wider the pulse the greater the loudness up to a certain point; after this it decreases [Lin, 1977a,b,c cited in Lin JC, 2004. Studies on Microwaves in Medicine and Biology: From Snails to Humans Bioelectromagnetics 25:146-159.]
We will now proceed to humans. In experimental animals a hydrophone was used in the brain. The alternative to a hydrophone study is to create a model.
What will we be modelling?
We have electromagnetic radiation falling onto a human. Let us consider a human head.
We wish to calculate how much is absorbed. This is too general, we have to say how much is absorbed during a specific amount of time. The “how much” in “some time” is a rate. We will be calculating what is termed as a “Specific Absorption Rate” or SAR.
This is something that is very popular in engineering; for instance this is the kind of study you would do to find out if a mobile phone harms your brain. Also this is how international standards are set, e.g. for mobile phone companies.
A specific algorithm is used which is called Finite-Difference Time-Domain (FDTD) algorithm.
This is recommended by the IEEE and the Federal Communications Commission of the United States.
According to the Federal Communications Commission of the United States as stated in OET Bulletin 65, "Evaluating Compliance with FCC Guidelines for Human Exposure to Radiofrequency Electromagnetic Fields", Supplement C:
Currently, the finite-difference time-domain (FDTD) algorithm is the most widely accepted computational method for SAR modeling". Furthermore, in FCC Part 95 Section 603(f) it is stated: "Applications for equipment authorization of devices operating under this section must contain a finite difference time domain (FDTD) computational modeling report showing compliance with these provisions for fundamental emissions."
We will be presenting this study:
Yoshiaki Watanabe, Toshiyuki Tanaka, Member, IEEE, Masao Taki, and So-ichi Watanabe, Member, IEEE
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 48, NO. 11, NOVEMBER 2000
The first step is to calculate the SAR (Specific Absorption Rate) distributions using Maxwell’s equations. Absorption will lead to temperature rise, which will lead to thermal stress. The second step is to calculate the elastic waves generated by thermal stress using the elastic wave equation.
Initially, you could approach the human head as a sphere, one with a 7cm diameter for instance. However, this is not enough, as there are different tissue layers in the human head and each of those absorbs differently.
So you would need to know where is what in the head. You can do an imaging study, an MRI study and build a structural model of the head. This is what the company REMCOM has done using MRI data from the Hershey Medical Center of the Penn State University.
Here is the relevant link:
As mentioned in the study, this is a model which has a resolution of 3*3*3mm and consists of bone, brain, cartilage, eye, muscle, and skin (this is termed Model 1 in the study).
The conditions we will use for the model are:
915 MHz, pulse of 20us
First, an absorption index will be calculated, the Specific Absorption Rate (SAR). This is shown as an “imaging result” in figure 11.
As the head is irradiated from the back a large SAR appears on the back.
Absorption triggers thermoelastic waves, pressure waves.
We do a single pulse of 915Hz for 2μs and we find the pressure waveform at the cochlea, which is shown in Fig 12 (for Model 1). The peak pressure (Model 1) is 83μPa. It is noted that humans can hear sounds over 20μPa (this corresponds to the 0 of the Decibel scale).
The sequence of the distribution of pressure waves in the head is shown in Fig 15 (for Model 1). The pressure wave starts from the back as mentioned, focuses on the center and then reverberates (bounces) many times.
Comment: Notice the wave shown as white area at 20μs and follow its course.
From the power spectra of the pressure waves shown in figure 14 it is shown that the dominant frequency components are 7-9KHz. These peaks correspond to the resonant frequencies of pressure waves in the head.
This value is in accordance with the prediction that was mentioned in the previous section based on experiments with guinea pigs and cats.
What does this frequency mean? One peak every 111-143 μs. What happens if you provide another microwave pulse with duration in between, e.g. 50μs? This will enhance the thermoelastic wave because the energy of the pulse will be fully integrated in the wave. If the pulse is longer, cancellation will occur.