**1. Introduction**

296 Neuroimaging – Cognitive and Clinical Neuroscience

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Since the fifth Century Athens, when Hippocrates identified the brain as the source of thought and understanding, humanity has been preoccupied with its functions. Anatomical descriptions have been brought to modernity by Andreas Vesalius in the sixteenth century (Vesalius, 1543) while underlying mechanisms have awaited the discovery of "bioelectricity" by Luigi Galvani in the eighteenth century to emerge (Galvani, 1791). In the nineteenth century, famous physicians such as Paul Broca or Carl Wernicke have demonstrated the role of the brain in cognitive tasks, studying patients with neurological disorders (Broca, 2004; Wernicke, 1894). From the late twentieth century to present day, neuroimaging techniques have allowed explorations in healthy subjects providing very precise locations of brain regions involved in cognitive and motor functions.

For the advancement of theory it is essential to acknowledge the strengths and limitations of available neuroimaging techniques so that converging evidence on the basis of multiple modes of investigation can be brought to bear on current controversies in the literature. Electroencephalography (EEG) was chronologically the first technique to open the way to the study of brain functions in exercising subjects (Swartz and Goldensohn, 1998). While one of the most direct methods to non-invasively measure the electrical signal arising from the synchronous firing of neurons, spatial resolution and lack of information from areas deeper than the cortex are its main limitations. Magnetoencephalography (MEG) is also a direct measure of the electrical activity of neurons and has a better spatial resolution as compared with EEG. However, the lack of detection in deep brain structures and the threshold detection (at least 50,000 neurons active simultaneously are needed) make MEG main disadvantages (Shibasaki, 2008). Functional imaging such as positron emission tomography (PET), single photon emission computed tomography (SPECT) and functional magnetic resonance imaging (fMRI) overcome the EEG and MEG limitations as they can detect neuronal activity as deep in the brain as experimenters desire (Cui et al., 2011; Villringer, 1997). However, the measure is indirect as it relies on blood supply for fMRI or on radioactive tracers for PET and SPECT (Jantzen et al., 2008; Tashiro et al., 2008). Additionally, except for EEG, the experimental environments of the earlier described techniques are very restricting with regards to physical exercise. Subjects and experimenters are limited to sit or laid positions and to breathe, eye, wrist and ankle movements. Actually, *in vivo* determination of brain functions in humans requires flexible, accessible and rapid monitoring techniques (Kikukawa et al., 2008; Perrey, 2008;

What Does Cerebral Oxygenation Tell Us About Central Motor Output? 299

From equation 4 (illustrated by fig.1), the main idea of NIRS is to compute the concentration of species (c) by measuring the OD according to Bouguer's definition (eq.1) and, inserting the a priori known extinction coefficients for species and the path length of light (eq. 4).

Fig. 1. Illustration of the Beer-Lambert's law. In panel A, the medium has a low OD (transmitted light I1 is close to incident light I0); the concentration of absorbing species is low. In panel B, OD is higher (larger difference between I2 and I0 than between I1 and I0), so

At least six conditions have to be fulfilled in order for the Beer-Lambert's law to be valid:


Living tissues, especially in humans, are doubtlessly among the most structured and complex in the universe. Their characteristics do not match with the Beer-Lambert's law prerequisites on numerous points. Therefore, the modified Beer-Lambert's law has to be applied in NIRS. As stated in the fifth point of the prerequisites, the incident light must be monochromatic (i.e. only one wavelength λ). In human tissues, lots of chemical species absorb light and account for its loss when travelling. However, there is a range of wavelengths at which light travel is much facilitated. Intuitively, when, in a dark environment, one looks at a flashlight through his finger or his hand, red is invariably the dominant colour. The physical explanation is that the red light travel through the human tissues is easier than for any other wavelengths. Implicitly, in the red portion of the visible



is the concentration of absorbing species.

**2.2 Application of NIRS to living tissues** 

the medium;




Rasmussen et al., 2007). Near infrared spectroscopy (NIRS) is perhaps the technique which best gathers these qualities; which may account for the increasing popularity of NIRS among research teams in recent years.

#### **2. Near infrared spectroscopy in humans**

As suggested by its name, the NIRS technique relies on red and infrared light diffusion through the living tissues. Physically, NIRS systems consist of numerous probes designed to be attached directly on the skin, over the area(s) to explore. Either optical fibres or regular electrical wires link the probes to a dedicated hardware, which in turn feeds a computer with experimental data. Probes are made of light transmitters and light receivers; the light power emission, the receiver gain and the interoptode distance can be adapted to match with the characteristics and depth of the areas under investigation. However, those three parameters necessarily come as inputs for the NIRS dedicated software which drives the record session.

#### **2.1 Principles of physics underlying the NIRS technique**

Back in the eighteenth century, the brilliant French scientist Pierre Bouguer (1698-1758) is probably the true father of photometry (Bouguer, 1729). The goal of his publication entitled *"Essais sur la gradation de la lumière"* in 1729 was to quantify how much light is lost when travelling through a given atmospheric layer. To achieve his work, he empirically characterizes materials with an optical density (OD) as follows:

$$\text{OD} = \log\left(\frac{\text{I}\_0}{\text{I}}\right) \tag{1}$$

where I0 is the intensity of the incident light and I the intensity of the transmitted light. More than one hundred years later, the German scientist August Beer (1825-1863), based on Jean-Henri Lambert's (1728-1777) and Pierre Bouguer's works, published *"Einleitung in die höhere Optik"* (1853), where he defined transmittance of light rather than its loss when travelling through a tissue (Beer, 1853). What is now known as the Beer-Lambert's law is a different version of Bouguer's idea (eq.1). The Beer-Lambert's law (eq.2) states that there is a logarithmic dependence between the transmission of light (T) and the product of the absorption coefficient of the substance the light travelled through (α) and the distance travelled by the light (also called path length, l).

$$\mathbf{T} = \mathbf{1}0^{\text{st}!} \tag{2}$$

In turn, the absorption coefficient α depends on the product of the extinction coefficients (ε) and the concentration (c) of the absorbers in the material. In liquids, the Beer-Lambert's law is often written as follows:

$$\mathbf{T} = \mathbf{10}^{\text{ecl}} \tag{3}$$

Equations 1 and 3 imply that there is a linear relationship between Bouguer's optical density and the concentration of species in the material explored:

$$\text{OD} = \text{acl} \tag{4}$$

From equation 4 (illustrated by fig.1), the main idea of NIRS is to compute the concentration of species (c) by measuring the OD according to Bouguer's definition (eq.1) and, inserting the a priori known extinction coefficients for species and the path length of light (eq. 4).

298 Neuroimaging – Cognitive and Clinical Neuroscience

Rasmussen et al., 2007). Near infrared spectroscopy (NIRS) is perhaps the technique which best gathers these qualities; which may account for the increasing popularity of

As suggested by its name, the NIRS technique relies on red and infrared light diffusion through the living tissues. Physically, NIRS systems consist of numerous probes designed to be attached directly on the skin, over the area(s) to explore. Either optical fibres or regular electrical wires link the probes to a dedicated hardware, which in turn feeds a computer with experimental data. Probes are made of light transmitters and light receivers; the light power emission, the receiver gain and the interoptode distance can be adapted to match with the characteristics and depth of the areas under investigation. However, those three parameters necessarily come as inputs for the NIRS dedicated software which drives the

Back in the eighteenth century, the brilliant French scientist Pierre Bouguer (1698-1758) is probably the true father of photometry (Bouguer, 1729). The goal of his publication entitled *"Essais sur la gradation de la lumière"* in 1729 was to quantify how much light is lost when travelling through a given atmospheric layer. To achieve his work, he empirically

OD = log 0I

where I0 is the intensity of the incident light and I the intensity of the transmitted light. More than one hundred years later, the German scientist August Beer (1825-1863), based on Jean-Henri Lambert's (1728-1777) and Pierre Bouguer's works, published *"Einleitung in die höhere Optik"* (1853), where he defined transmittance of light rather than its loss when travelling through a tissue (Beer, 1853). What is now known as the Beer-Lambert's law is a different version of Bouguer's idea (eq.1). The Beer-Lambert's law (eq.2) states that there is a logarithmic dependence between the transmission of light (T) and the product of the absorption coefficient of the substance the light travelled through (α) and the distance

In turn, the absorption coefficient α depends on the product of the extinction coefficients (ε) and the concentration (c) of the absorbers in the material. In liquids, the Beer-Lambert's law

Equations 1 and 3 imply that there is a linear relationship between Bouguer's optical density

OD = εcl (4)

I 

(1)

T = 10*<sup>l</sup>* (2)

T = <sup>ε</sup>cl 10 (3)

NIRS among research teams in recent years.

record session.

**2. Near infrared spectroscopy in humans** 

**2.1 Principles of physics underlying the NIRS technique** 

characterizes materials with an optical density (OD) as follows:

travelled by the light (also called path length, l).

and the concentration of species in the material explored:

is often written as follows:

Fig. 1. Illustration of the Beer-Lambert's law. In panel A, the medium has a low OD (transmitted light I1 is close to incident light I0); the concentration of absorbing species is low. In panel B, OD is higher (larger difference between I2 and I0 than between I1 and I0), so is the concentration of absorbing species.
