Commit fbed6e9b authored by Zach Fredin's avatar Zach Fredin

math formatting

parent 5d0977ee
......@@ -39,7 +39,7 @@ _Figure source: Bülbül, Ali & Küçük, Serdar. (2016). Pulse Oximeter Manufac
In order to differentiate the slight intensity change caused by varying blood oxygen concentration from errors related to skin absorbance and venous blood (whose oxygen has already been taken up by cells), the signal processing algorithm isolates the AC portion of the signal, since within a reasonable range (~0.5 - 3 Hz) this corresponds to blood rushing through arteries with each heartbeat. This _pulsatile arterial blood_ increases the optical path length of the measurement as blood pressure swells the arteries, producing periodic oscillations in the absorption signal. The other contributors to absorption, such as tissue and venous/capillary blood, are effectively constant in this frequency regime. By calculating the ratio of the AC and DC signals at each wavelength, then taking the ratio of these two absorption ratios, a value $`R`$ can be determined which is only related to the relative concentration of oxyhemoglobin (O2Hb) and reduced hemoglobin (Hb):
```math
R=A_{AC_{660}}/A_{DC{660}}/A_{AC_{940}}/A_{DC{940}}
R=\frac A_{AC_{660}}/A_{DC_{660}} A_{AC_{940}}/A_{DC_{940}}
```
As the photodiode sensor does not differentiate by wavelength, the device rapidly cycles between red, IR, and no LED, allowing the system to compensate for ambient light as well. The cycling speed must be substantially faster than the heart rate, since the ratio $`R`$ assumes absorption at all wavelengths is carried out simultaneously in order to cancel out path length.
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