The AHI measurement capability has to be my favorite of all those upgrades, Banned. What a cool machine!
DSM, I forgot to mention... Yes, thank you for correcting that "dead space" term for me. Indeed, volumetric space is really what I had in mind. I thought I was using the proper biomedical term when, in fact, dead space refers to a biologically-related space in which CO2 is retained after expiration.
SAG wrote:It is more accurately represented as the determination of the Sum of Flows (Turbulent + Laminar).
Agreed, SAG. Forgetting, for just a moment, about what gets measured by Learn Circuit, where, and why... I'd like to do some semi-amusing manipulation with that first Ohm's equation you presented. Then I'd like to apply that manipulated Ohm's equation to the above turbulent + laminar flow relationships.
Regarding Ohm's Law SAG Correctly wrote:(Pmachine - Pprox) / Flow = Resistance)
So Ohm's law shows a relationship among: 1) pressure, 2) flow, and 3) resistance. "(Pmachine - Pprox)" can be expressed as "delta
P sub tube") as it is in the very first equation presented in this post. From now on, let's just call that "
Pdelta" to make typing easier. So I'd like to manipulate the Ohm's law equation by multiplying both sides by "flow" to yield the following Ohm's equation:
Pdelta=(Flow) x (Resistance)
(We'll be using that relationship to manipulate that first equation a bit)
In that first equation, the term "sign(Fturbine)x" translates to either a positive or a minus, depending on the flow direction of the turbine (the word turbine meaning "CPAP impeller"). So let's work the positive or forward-flow case. That makes "sign(Fturbine)x" the same as 1x, which can be dropped as an implied positive sign. That yields the following equation, which we intend to break up into two Ohm's-based equations or components (I'll write
Fturbine simply as "Flow"):
Pdelta= (K1 x Flow^2) + (K2 x Flow)
SAG correctly points out that the K1 part of the equation on the left speaks of turbulent flow. He also correctly points out that the K2 part of the equation on the right speaks of laminar flow. Remember that Ohm's Law said that pressure equals flow times resistance. We have some pressure on the left side of that equation and some flow as well as presumable resistance on the right side of the equation. So let's break the above two part equation into two separate Ohm's equations, one for laminar and one for turbulent. Here's the laminar Ohm's expression first since that one's clean and simple so to speak:
Pdelta= (K2 x Flow)
If Ohm's law says that pressure equals resistance times flow, then K2 above must be resistance for the respiratory laminar flow model. Let's do similar Ohm's manipulation with turbulent flow below:
Pdelta= (K1 x Flow^2)
Let's rewrite that as:
Pdelta= K1 x Flow x Flow and then as
Pdelta= (K1 x Flow)Flow
If Ohm's law says that pressure equals resistance times flow, then let's first rewrite the turbulent-case relationship as:
Pdelta= (turbulent resistance) x Flow
(turbulent resistence)=(K1 x Flow) in this fluid-dynamics dirty math trick
A turbulence resistance can be
approximately thought of as having a dynamic value as some constant (K1) times Flow. Of course, that's not at all a neat solution in "real" fluid dynamics. Turbulent and laminar flow calculations are nowhere near as simple as the very viable approximations used in respiratory equations. But this rough and extremely dirty math may yield some intuitive insight that a dynamic pressure/flow circuit can be thought of as having some dynamic resistance and some static resistance. The respective resistances are implicitly represented in that K1 and K2 equation that reflects turbulent and laminar flow. Using Ohm's and distributive properties, that very first equation can be viewed with the same "dirty math" to get a feel that (K1 x Flow) more or less represents a dynamic or turbulence-related resistance in that equation while K2 represents a fixed or laminar-related resistance.
Learn Circuit claims to measure circuit impedance to factor in pressure delivery. Regarding "dirty math" toward a paradigm change, you can for all practical purposes think of total circuit impedance in this forward-flow case as being "(K1 x Flow) plus K2". And total circuit impedance in the reverse turbine-flow case can, in similar practicality, be thought of as "negative (K1 x Flow) plus K2". Bearing in mind that fluid dynamics doesn't even come
close to being that simple (Poiseuille's and Reynold's aren't even accurate here, but very workable!). The "dirty math" relationship is a very convenient and intuitive approximation regarding a working or practical view of "sum-total dynamic and fixed resistances".
Here's a nice presentation about turbulent and laminar flow in the basic respiratory paradigm or model (for general readership):
http://www.lib.mcg.edu/edu/eshuphysio/p ... ch2_45.htm
Bear in mind the presentation talks about turbulent and laminar flow in the human airway, while this thread has been focusing on similar flow factors inside the machine (with human respiration factored out and turbine rotation factored in).
Entertainment value only, and only intended for those who are not fluid-dynamics purists. If you are a fluid dynamics purist, please let me know so that I can run for cover when I see you or your posse on the streets.