Continuous wave  

Continuous wave (CW) system uses light sources with constant frequency and
amplitude. In fact, to measure absolute changes in HbO concentration with the
mBLL, we need to know photon path-length. However, CW-fNIRS does not provide
any knowledge of photon path-length, so changes in HbO concentration are
relative to an unknown path-length. Many CW-fNIRS commercial systems use
estimations of photon path-length derived from computerized  Monte-Carlo
simulations  and physical
models, to approximate absolute quantification of hemoglobin concentrations.

OD  =  ln  ⁡  (  I  0  /  I  )  =  ϵ  ⋅  [  X  ]  ⋅  l  ⋅  DPF  \+  G
{\displaystyle {\text{OD}}=\operatorname {ln} (I_{0}/I)=\epsilon \cdot
[X]\cdot l\cdot {\text{DPF}}+G}  ![{\\displaystyle {\\text{OD}}=\\operatorname
{ln} \(I_{0}/I\)=\\epsilon \\cdot \[X\]\\cdot l\\cdot
{\\text{DPF}}+G}](https://wikimedia.org/api/rest_v1/media/math/render/svg/19bdf284941c4b5773b962733a19dfef36d9c70a)

Where  OD  {\displaystyle {\text{OD}}}  
is the optical density or attenuation,  I  0  {\displaystyle I_{0}}

is emitted light intensity,  I  {\displaystyle I}  
is measured light intensity,  ϵ  {\displaystyle \epsilon }  
is the  attenuation coefficient  ,  [  X  ]  {\displaystyle [X]}  ![{\\displaystyle
\[X\]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fadb3aef0836cb1d004479f470703a45972bf8fe)
is the chromophore concentration,  l  {\displaystyle l}  
is the distance between source and detector and  DPF  {\displaystyle
{\text{DPF}}}  
is the differential path length factor, and  G  {\displaystyle G}

is a geometric factor associated with scattering.

When the attenuation coefficients  ϵ  {\displaystyle \epsilon }

are known, constant  scattering 
loss is assumed, and the measurements are treated differentially in time, the
equation reduces to:

Δ  [  X  ]  =  Δ  OD  ϵ  d  {\displaystyle \Delta [X]=\Delta {\frac
{\text{OD}}{\epsilon d}}}  ![{\\displaystyle \\Delta \[X\]=\\Delta {\\frac
{\\text{OD}}{\\epsilon
d}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a02d0a004d3011f7a93471acb7b21853a83fb96c)

Where  d  {\displaystyle d}  
is the total corrected photon path-length.

Using a dual wavelength system, measurements for HbO  2  and Hb can be solved
from the matrix equation:  [9]

(  Δ  OD  λ  1  Δ  OD  λ  2  )  =  (  ϵ  λ  1  Hb  d  ϵ  λ  1  HbO  2  d  ϵ  λ
2  Hb  d  ϵ  λ  2  HbO  2  d  )  (  Δ  [  X  ]  Hb  Δ  [  X  ]  HbO  2  )
{\displaystyle {\begin{pmatrix}\Delta {\text{OD}}_{\lambda _{1}}\\\\\Delta
{\text{OD}}_{\lambda _{2}}\end{pmatrix}}={\begin{pmatrix}\epsilon _{\lambda
_{1}}^{\text{Hb}}d&\epsilon _{\lambda _{1}}^{{\text{HbO}}_{2}}d\\\\\epsilon
_{\lambda _{2}}^{\text{Hb}}d&\epsilon _{\lambda
_{2}}^{{\text{HbO}}_{2}}d\end{pmatrix}}{\begin{pmatrix}\Delta
[X]^{\text{Hb}}\\\\\Delta [X]^{{\text{HbO}}_{2}}\end{pmatrix}}}
![{\\displaystyle {\\begin{pmatrix}\\Delta {\\text{OD}}_{\\lambda
_{1}}\\\\\\Delta {\\text{OD}}_{\\lambda
_{2}}\\end{pmatrix}}={\\begin{pmatrix}\\epsilon _{\\lambda
_{1}}^{\\text{Hb}}d&\\epsilon _{\\lambda
_{1}}^{{\\text{HbO}}_{2}}d\\\\\\epsilon _{\\lambda
_{2}}^{\\text{Hb}}d&\\epsilon _{\\lambda
_{2}}^{{\\text{HbO}}_{2}}d\\end{pmatrix}}{\\begin{pmatrix}\\Delta
\[X\]^{\\text{Hb}}\\\\\\Delta
\[X\]^{{\\text{HbO}}_{2}}\\end{pmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/233ca031c5dfffcfd7ef9b68b4a2524e79fe8e50)

Due to their simplicity and cost-effectiveness, CW-fNIRS is by far the most
common form of functional NIRS since it is the cheapest to make, applicable
with more channels, and ensures a high temporal resolution. However, it does
not distinguish between absorption and scattering changes, and cannot measure
absolute absorption values: which means that it is only sensitive to
_relative_ change in HbO concentration.

Still, the simplicity and cost-effectiveness of CW-based devices prove
themselves to be the most favorable for a number of clinical applications:
neonatal care, patient monitoring systems, diffuse optical tomography, and so
forth. Moreover, thanks to its portability, wireless CW systems have been
developed—allowing individuals to be monitored in ambulatory, clinical and
sports environments.  [10]  [11]  [12]