Recovering one irregular signal in the presence of another stronger one--*in utero* pulse ox

[Phil Hobbs]

Hi, all,

Hoping there are still some DSP folks round here despite the evil Google
ban. (But I repeat myself.)

I'm working on a completely noninvasive sensor for fetal blood oxygen,
using optical sensing through the mom's abdomen. It's a very low SNR
measurement on account of all the attenuation.

The mom's heartbeat modulates her pulse-ox signal, which is much
stronger than the fetus's on account of the scattering and absorption in
maternal tissue.

The data are several time series. The main issue is the variability of
both pulses, which smear out the spectra and therefore knock the peak
heights way down towards the noise. There are weak multiplicative
effects between maternal and fetal signals, as you'd expect.

What I'm looking to do is something like:

1. Use a digital PLL to find the time-dependent maternal pulse rate.

2. Resample the data accordingly, and notch out the first 5 or so mom
harmonics.

3. Do the PLL thing on the fetal pulse, and signal average to pull out
the average fetal pulse ox signal.

Extra credit: sometimes the baby's pulse can cross the first or second
harmonic of the mom's, and it would be good to preserve both pulse
shapes accurately.

Resampling a noisy signal isn't necessarily the most well-conditioned
operation, so I'd welcome suggestions for just how to do this.

Thanks

Phil Hobbs

[Eric Jacobsen]

On Tue, 18 May 2021 18:31:28 -0400, Phil Hobbs

Post by Phil Hobbs
Hi, all,
Hoping there are still some DSP folks round here despite the evil Google
ban. (But I repeat myself.)
I'm working on a completely noninvasive sensor for fetal blood oxygen,
using optical sensing through the mom's abdomen. It's a very low SNR
measurement on account of all the attenuation.
The mom's heartbeat modulates her pulse-ox signal, which is much
stronger than the fetus's on account of the scattering and absorption in
maternal tissue.
The data are several time series. The main issue is the variability of
both pulses, which smear out the spectra and therefore knock the peak
heights way down towards the noise. There are weak multiplicative
effects between maternal and fetal signals, as you'd expect.
1. Use a digital PLL to find the time-dependent maternal pulse rate.
2. Resample the data accordingly, and notch out the first 5 or so mom
harmonics.
3. Do the PLL thing on the fetal pulse, and signal average to pull out
the average fetal pulse ox signal.
Extra credit: sometimes the baby's pulse can cross the first or second
harmonic of the mom's, and it would be good to preserve both pulse
shapes accurately.
Resampling a noisy signal isn't necessarily the most well-conditioned
operation, so I'd welcome suggestions for just how to do this.
Thanks
Phil Hobbs

Would an Adaptive Noise Cancelling or Adaptive Noise Reduction
technique work? I'd guess that the mom's heartbeat could be isolated
reasonably well as the "noise" source with potentially a separate
sensor placed to minimize the fetal heartbeat, and use that as the
noise to be cancelled by the ANC/ANR?

Just a thought. Since the mom's heartbeat has higher SNR it seems
like it could be subtracted, and an ANR/ANC would be a pretty
well-established way to do that. If the mom's heartbeat needs more
SNR, or the fetal heartbeat rejected more for the noise reference
signal, a separate sensor or sensors might help with that.

Sounds like an interesting problem, regardless.

Eric

[Phil Hobbs]

Post by Eric Jacobsen
On Tue, 18 May 2021 18:31:28 -0400, Phil Hobbs

Post by Phil Hobbs
Hi, all,
Hoping there are still some DSP folks round here despite the evil Google
ban. (But I repeat myself.)
I'm working on a completely noninvasive sensor for fetal blood oxygen,
using optical sensing through the mom's abdomen. It's a very low SNR
measurement on account of all the attenuation.
The mom's heartbeat modulates her pulse-ox signal, which is much
stronger than the fetus's on account of the scattering and absorption in
maternal tissue.
The data are several time series. The main issue is the variability of
both pulses, which smear out the spectra and therefore knock the peak
heights way down towards the noise. There are weak multiplicative
effects between maternal and fetal signals, as you'd expect.
1. Use a digital PLL to find the time-dependent maternal pulse rate.
2. Resample the data accordingly, and notch out the first 5 or so mom
harmonics.
3. Do the PLL thing on the fetal pulse, and signal average to pull out
the average fetal pulse ox signal.
Extra credit: sometimes the baby's pulse can cross the first or second
harmonic of the mom's, and it would be good to preserve both pulse
shapes accurately.
Resampling a noisy signal isn't necessarily the most well-conditioned
operation, so I'd welcome suggestions for just how to do this.
Thanks
Phil Hobbs

Would an Adaptive Noise Cancelling or Adaptive Noise Reduction
technique work? I'd guess that the mom's heartbeat could be isolated
reasonably well as the "noise" source with potentially a separate
sensor placed to minimize the fetal heartbeat, and use that as the
noise to be cancelled by the ANC/ANR?
Just a thought. Since the mom's heartbeat has higher SNR it seems
like it could be subtracted, and an ANR/ANC would be a pretty
well-established way to do that. If the mom's heartbeat needs more
SNR, or the fetal heartbeat rejected more for the noise reference
signal, a separate sensor or sensors might help with that.
Sounds like an interesting problem, regardless.

Thanks. The ANC thing has been tried, and helps a fair amount, but so
far not enough on account of the low SNR of both parts of the signal.

Folks have been trying to do this for over 20 years--their papers always
declare victory, but there are no commercial products despite a
widely-recognized need. (This is my first whack at it.)

The instantaneous SNRs of both signals are frequently way, way down in
the mud, like 2 dB for the baby and 15 dB for the mum. Thus the
uncertainty in the maternal pulse signal can make a mess of the remainder.

The pulse waveforms themselves are slowly varying, but the pulse rates
can change +-20% within 10 beats or so. Thus my hope is to do the DPLL
thing to get the phase vs. time for the mom's pulse, do some signal
averaging on the resampled signal to recover a decent estimate of the
'true' maternal signal.

Thanks again

Phil Hobbs

[Christian Gollwitzer]

Post by Phil Hobbs
I'm working on a completely noninvasive sensor for fetal blood oxygen,
using optical sensing through the mom's abdomen.  It's a very low SNR
measurement on account of all the attenuation.
The mom's heartbeat modulates her pulse-ox signal, which is much
stronger than the fetus's on account of the scattering and absorption in
maternal tissue.
The data are several time series.  The main issue is the variability of
both pulses, which smear out the spectra and therefore knock the peak
heights way down towards the noise.  There are weak multiplicative
effects between maternal and fetal signals, as you'd expect.

How about using a second channel to detect the mother's heartbeat? For
example an ECG channel? It's not perfectly synchronized, though, the
delay between ECG and pulse oxymetry is influenced by the blood
pressure. So it only works if the blood pressure is constant.

Christian

[Phil Hobbs]

Post by Christian Gollwitzer

Post by Phil Hobbs
I'm working on a completely noninvasive sensor for fetal blood oxygen,
using optical sensing through the mom's abdomen.  It's a very low SNR
measurement on account of all the attenuation.
The mom's heartbeat modulates her pulse-ox signal, which is much
stronger than the fetus's on account of the scattering and absorption
in maternal tissue.
The data are several time series.  The main issue is the variability
of both pulses, which smear out the spectra and therefore knock the
peak heights way down towards the noise.  There are weak
multiplicative effects between maternal and fetal signals, as you'd
expect.

How about using a second channel to detect the mother's heartbeat? For
example an ECG channel? It's not perfectly synchronized, though, the
delay between ECG and pulse oxymetry is influenced by the blood
pressure. So it only works if the blood pressure is constant.
    Christian

Thanks. We can isolate the mom's pulse-ox signal, and as Eric
suggested, it's possible to use that for adaptive noise cancellation
except that (as far as we gather from the literature) it doesn't work
well enough for a technological measurement. We can get the mom's pulse
rate vs. time from that, which will be a big help.

We really need to resample at the child's pulse rate in order to
concentrate its signal into as narrow a bandwidth as possible to improve
the SNR.

Folks have been trying this sort of thing since the late '90s without
producing a commercial instrument. Despite the optimistic tone of all
scientific papers, this leads me to suppose that although an expert can
make it work once or twice, getting it to work many times in non-expert
hands is hard.

There's also a lot of physiological variability, including thickness of
skin and subcutaneous fat, presentation (normal, breech, reverse, etc.)

When you're working with 150-dB path loss, a 2% change will lose you
half your signal. :(

Cheers

Phil Hobbs

[Les Cargill]

Post by Phil Hobbs
Hi, all,
Hoping there are still some DSP folks round here despite the evil Google
ban. (But I repeat myself.)
I'm working on a completely noninvasive sensor for fetal blood oxygen,
using optical sensing through the mom's abdomen.  It's a very low SNR
measurement on account of all the attenuation.
The mom's heartbeat modulates her pulse-ox signal, which is much
stronger than the fetus's on account of the scattering and absorption in
maternal tissue.
The data are several time series.  The main issue is the variability of
both pulses, which smear out the spectra and therefore knock the peak
heights way down towards the noise.  There are weak multiplicative
effects between maternal and fetal signals, as you'd expect.
1. Use a digital PLL to find the time-dependent maternal pulse rate.
2. Resample the data accordingly, and notch out the first 5 or so mom
harmonics.
3. Do the PLL thing on the fetal pulse, and signal average to pull out
the average fetal pulse ox signal.
Extra credit: sometimes the baby's pulse can cross the first or second
harmonic of the mom's, and it would be good to preserve both pulse
shapes accurately.
Resampling a noisy signal isn't necessarily the most well-conditioned
operation, so I'd welcome suggestions for just how to do this.
Thanks
Phil Hobbs

I'd be tempted to take a cuff-style/smartwatch heartrate reading from Ma
and use that as the top of a search tree for the other frequencies. "Top
of a search tree" isn't really all that much help but it's a start.

The thing I'd wonder is whether the fetal ox cycle isn't a harmonic of
Ma's respiratory cycle. Actually, if it's not that's kind of an even
more interesting question.

Post by Phil Hobbs
There are weak multiplicative
effects between maternal and fetal signals, as you'd expect.

This makes me think of an old Stroboconn/Peterson tuner. Obviously,
those are solving a much simpler problem. I'd be tempted to play
with the aliasing/sidebands.

The peterson/Stroboconn had a base model of the frequency under
measurement and provided a visual , intentionally aliased display
of the difference. It literally wagonwheeled.

This probably isn't much help, but it's clearly a profound problem.
Seems like a thing more for metaphor than for mechanism. Find the story
and the mechanism reveals itself. I'd almost bet that there's a model in
the brain of every neonatalist.

[Phil Hobbs]

Post by Les Cargill

Post by Phil Hobbs
Hi, all,
Hoping there are still some DSP folks round here despite the evil
Google ban. (But I repeat myself.)
I'm working on a completely noninvasive sensor for fetal blood oxygen,
using optical sensing through the mom's abdomen.  It's a very low SNR
measurement on account of all the attenuation.
The mom's heartbeat modulates her pulse-ox signal, which is much
stronger than the fetus's on account of the scattering and absorption
in maternal tissue.
The data are several time series.  The main issue is the variability
of both pulses, which smear out the spectra and therefore knock the
peak heights way down towards the noise.  There are weak
multiplicative effects between maternal and fetal signals, as you'd
expect.
1. Use a digital PLL to find the time-dependent maternal pulse rate.
2. Resample the data accordingly, and notch out the first 5 or so mom
harmonics.
3. Do the PLL thing on the fetal pulse, and signal average to pull out
the average fetal pulse ox signal.
Extra credit: sometimes the baby's pulse can cross the first or second
harmonic of the mom's, and it would be good to preserve both pulse
shapes accurately.
Resampling a noisy signal isn't necessarily the most well-conditioned
operation, so I'd welcome suggestions for just how to do this.
Thanks
Phil Hobbs

I'd be tempted to take a cuff-style/smartwatch heartrate reading from Ma
and use that as the top of a search tree for the other frequencies. "Top
of a search tree" isn't really all that much help but it's a start.

We get the mum's pulse more or less for free, right on her abdomen.
That has the added advantage that it has the right phase and pulse
shape, so that we can strobe the signal to increase the SNR. (You win
by multiplying the signal by a cleaned-up version of itself.)

Post by Les Cargill
The thing I'd wonder is whether the fetal ox cycle isn't a harmonic of
Ma's respiratory cycle. Actually, if it's not that's kind of an even
more interesting question.

Nope, they both vary independently, with the child's running about 1.5x
and 2d the mum's unless the child is in respiratory distress, when they
can cross over. That's obviously an important constraint, because you
_really_ need a good measurement then.

Post by Les Cargill

Post by Phil Hobbs
There are weak multiplicative
effects between maternal and fetal signals, as you'd expect.

This makes me think of an old Stroboconn/Peterson tuner. Obviously,
those are solving a much simpler problem. I'd be tempted to play
with the aliasing/sidebands.
The peterson/Stroboconn had a base model of the frequency under
measurement and provided a visual , intentionally aliased display
of the difference. It literally wagonwheeled.
This probably isn't much help, but it's clearly a profound problem.
Seems  like a thing more for metaphor than for mechanism. Find the story
and the mechanism reveals itself. I'd almost bet that there's a model in
the brain of every neonatalist.

So overall it looks like the best-guess algorithm is something like:

Use one set of LEDs and several photodetectors at different spacings
(corresponding to different depths)

Oversample several channels massively

Run a digital PLL on the mum and reconstruct a filtered pulse shape.

Strobe the data with the reconstructed pulse, and refine the mum's pulse
rate vs. time.

Resample the noisy data so that the mum's pulse is perfectly periodic

Notch her out of the picture, and (possibly) resample back to the
original uniform spacing

Repeat the two-step DPLL/strobe thing on the child's pulse

Resample the data so the child's pulse is periodic

Average N periods to improve SNR, possibly using a data window sideways
if the noise floor isn't flat (That is, if there are K samples in each
of N periods, use a window function W(n), not W(k).)

Extract the child's pulse ox signal.

There may be some stable iterative way of improving the pulse rate
estimates, I don't know. We'll have probably a good 15 minutes' worth
of data, and perhaps several hours.

Fun problem--tire kicking welcome.

Cheers

Phil Hobbs