Rubicon wrote: ↑Fri Dec 02, 2022 2:44 am
Wondering1 wrote: ↑Thu Dec 01, 2022 7:24 pm
To get to a better understanding I asked the folks over at Apneaboard about the misnaming of the graph:
Yeah that's a thread that's definitely going to make "Best of AB":
Other flow rates in Oscar include the tidal volume (milliliters/second) ...
To fully refute the contention that the graph represents "Flow", the flow being measured is a volume (milliliters). Without time, or zero, we have a divide by zero error. Give that a try and you are left with a meaningless static measurement.
Ok, I guess this quote comes from apneaboard. Just like here, I can no longer access my robysue account over there and for the same reason: I don't remember the password and the email account that I used back then is on a computer that has long since went to the great computer trash heap in the sky. And I haven't felt inclined to create a robysue1 over there.
But I have to say, this piece of nonsense is
almost enough for me to do that.
First of all: Whoever posted this nonsense hasn't looked at the units for the Tidal Volume graph in Oscar: They're clearly labeled as mL, not mL/sec. So that immediately calls into mind the competence and/or overall intelligence of the poster.
And then, there's the stuff about "divide by zero" nonsense. Once again my heart is going pitter-patter because I have a chance to talk about Calculus in a public forum full of non mathematicians. Today's topic is the
derivative.
The
derivative is exactly how mathematicians, starting with Isaac Newton and Gottfried Leibniz, get around the need to "divide by zero" in order to both define and calculate
instantaneous rates of change for functions that are defined either algebraically or graphically. If
f(t) is the
quantity function (i.e.
f might represent the
volume of air in your lungs at time
t), then the
instantaneous rate of change in
f with respect to
t, which is called the derivative and which is denoted by
f ' (t), is defined as a
limit as the difference in time goes to zero. In formal mathematical language:
Graphically, the fraction
represents the slope of the line through the points
(x, f(x)) and
(t, f(t)). Analytically this fraction represents
the average rate of change in
f(t) over the interval between time =
x and time =
t. When we take the limit as the denominator goes to zero, we get the slope of the line that is
tangent to
y = f(t) at the point
(t, f(t)). The limiting process allows us to avoid the "divide by zero" problem and still find the rate the function
f(t) is changing
instantaneously at the point in question.
It's also worth noting that computing the value of
for specific values of
x and
t that are extremely close to each other gives a pretty good approximation of the value of
f ' (t). It gives an even better approximation of the value of
f ' (m) where
m = (x-t)/2---i.e. where
m is the midpoint between
x and
t.
Now in some
real world problems, it is actually easier to compute/evaluate the derivative
f ' (t) or get an extremely accurate approximation of the derivative directly from measurement devices than it is to compute the quantity function
f(t). As a basic example, the speedometer in your car is designed to measure your speed, and speed is the derivative of the position function. (Well, technically velocity is the derivative of speed, and velocity's plus/minus sign is used to indicate which way you are traveling---i.e. on an east/west interstate, a velocity of +70 mph indicates you are traveling in east at 70 mph and a velocity of -70 mph indicates you are traveling west at 70 mph.)
Likewise, engineers long ago cracked the problem of coming up with a reasonably accurate way of measuring airflow---the volume of air being moved by a fan with respect to time---i.e. air flow always measured units like L/min.
And in xPAP, we have a pressurized system with a leak comprising the blower unit (i.e. fan), the hose, the mask, and the patient's respiratory system where the leak is the combination of the intentional leak built in the mask along any unintentional leaks.
Since the critical idea in a pressurized system with a leak is to maintain the pressure by blowing air into the system at the rate that air is being lost, the blower (i.e. fan) in the CPAP is the driving force in the system. Because the rate of flow needed to maintain the desired pressure depends on the flow of air into and out of the lungs, the designers of xPAP equipment were able to easily figure out a way of measuring that air flow into and out of the lungs. Tracking that data and analyzing it in real-time is necessary for an xPAP machine both to flag events and to auto-adjust the pressure in an appropriate fashion for APAPs.
In other words, from an engineering point of view, it is easy to measure the
flow of air into and out of the lungs. And this flow is, in fact, measured in L/min. And this flow is the derivative of the volume of air in the lungs at time
t, which cannot easily be measured directly.
Now to tie this all back to wondering1's mistaken notion that tidal volume (i.e. the amount of air inhaled in one inhalation) is somehow a "flow" function. The amount of air inhaled in one inhalation, or the tidal volume, is the
net increase in volume of air in the lungs over the course of one inhalation. And that is a definite integral of the flow curve. In other words, we can say:
where flow(
t) is the flow (or flow rate) function and
a is the time the inhalation starts and
b is the time the inhalation ends. A technical note: Since flow is measured in L/min, this definition of TV gives the TV measured in L, not mL. You still need to do a unit conversion to get the actual numbers given in the TV graph as shown in Oscar, SleepHQ and ResScan where TV is measured in mL. If I recall correctly, however, TV is usually averaged over several breaths in the data presented as the TV graph in Oscar, SleepHQ, and ResScan.
But the fundamental problem that wondering1 still has is that he simply will not accept that the sleep medicine community long ago decided that the definitions of apnea and hypopnea should be based on the air
flow into the lungs---i.e. the
rate function, and not the volume of air in the lungs or the "net increase in volume" (i.e. TV).
I'll end with this: If anybody wants to "steal" this post and put it on apnea board, feel free to do so.
If you really think I should do it, let me know that and I'll reconsider registering over there under a new (robysue1) name since I can't recover my old robysue account over there.
Joined as robysue on 9/18/10. Forgot my password & the email I used was on a machine that has long since died & gone to computer heaven.
Correct number of posts is 7250 as robysue + what I have as robysue1
Profile pic: Frozen Niagara Falls
<3
