Near infrared light
Absorption of light by blood
Blood
Interpolation
Cerebral Cortex
fMRI
MEG
PET
Now we would like to explain the physical background of the optical topography system. Though near infrared light used by this system passes through human brain it does not pass transparently. Almost all of the light illuminated on scalp is absorbed and scattered by the brain tissue. An extremely small amount of the initial light is reflected back to the scalp. In adults, the light attenuates to a level as low as a hundred millionth or even a billionth of the irradiated light.

Amount of the detected light with the wavelength at each measurement position is expressed by the following equation approximately.


where,
: Amount of irradiation light,
and : Molecular absorption coefficient of oxy- and deoxy-hemoglobin at wavelength
: Concentration of oxy- and deoxy-hemoglobin,
d: Effective optical path length in active region of cerebral cortex,
: Attenuation due to light absorption by pigments except hemoglobin ( such as cytochrome aas)
: Attenuation due to light scattering by tissues,
When stimulation is given to the brain, the concentration and oxygenation of hemoglobin changes, and the amount of detected light changes accordingly as follows:
where, the character superscript "s" represents a value of each variable under stimulation.
Because the total light absorption by hemoglobin in live body in the near-infrared region is about 10 times greater than that of cytochrome aasthat is the major term of, neglecting change in caused by stimulation, an assumption of is given.

Furthermore, by subtracting the equation (1) from the equation (2), the following equation can be obtained,
where, we defined follows:
Since it is actually difficult to obtain the effective length d of the optical path in the active region of cerebral cortex, relative changes in concentration of hemoglobin associated with brain activity are obtained in (mM)x(mm) unit.
means the proportional value of the sum above, in other words, the proportional value of the change of the blood volume.
The measurement with dual wavelength at each measurement position allows the solution of of simultaneous equation (3) for , as follows:


where,

As we can see in formula (4), the value are given in (5)(6)(7), which are denoted as the products of (hemoglobin concentration)x(effective light path).

So, we adopt the unit of -as (mmol)x(mm) .
Conventionally, hemoglobin concentration in blood is used (g/dl), and adopting the molecular weight of hemoglobin is 64,000, the conversion of (g/dl) is as follows: 1g/dl = 0.156mmol or 1mmol = 6.4g/dl

Reference:
Mean hemoglobin density of human adult
male 15g/dl = 2.34mmol
female 13g/dl = 2.03mmol