Recovering one irregular signal in the presence of another stronger one--_in utero_ pulse ox

Both pulse rates are going to change with time - the adult human pulse rate is constant over a roughly seven minute interval.

When I was working at EMI Central Research the body-scanner crew wanted to synchronously sample the heart position data, and the scheme fell down on exactly that point.

You are are going to need to have long strings of actual pulse signals - both for the mother and fetus over the same period - as well as an equally long string of O2 saturation data for the same period, and cross-correlate after you have collected it.

This may look clumsy, but it is the only approach that has a hope of working.

Forget the adaptive part. Just get the actual data and work with that.

That doesn't strike me as a good idea. The pulse data isn't all that regular.

Just measure what it is, and correlate with that.

The pulses aren't going to have a neat frequency spectrum

Why waste the time. The samples aren't going to be regular enough to make this a useful step.

Probably not a good idea. Cross-correlate the raw data

Sadly, the human pulse has got short term frequency stability.

You do need to think harder about that - and the nature of the pulse signals which you need to cross-correlate.

Won't work because maternal pulse rate isn't a constant frequency signal.

See above.

The fetal pulse rate probably isn't going to be a constant frequency signal either it might be a lot more stable than the mother's, but it is probably regulated by the same kind of slow feedback loop

Probably a bad idea. The maternal pulse rate isn't constant over periods shorter than about seven minutes.

An ecg will give you the exact time the maternal heart start contracting, and if you bin your optical data for specific intervals after that spike, you may be able to build a picture of the average transient in the maternal blood oxygenation.

Probably not a good idea.

Again the fetal pulse rate probably isn't going to be constant either.

Getting the fetal ecg isn't easy, but it can be done. If you can pick up the spike generated when the fetal heart starts contacting you could bin the optical data in a separate set of bins corresponding to a set of delays from the fetal heart contraction.

Sample the data separately - or at least set up two different banks of samples from the same data stream - based on what the maternal heart was doing at sampling time and and what the fetal heart was doing at that instant.

The key word might be "roughly".

I believe the inter-beat interval is normally chaotic, and a "too" constant interval indicates heart problems. Presumably the chaos reduces the problems of resonances etc.

I suspect that will significantly reduce the usefulness of FFT-based techniques.

Also be aware that you may have to work with normally low heart rates. My resting rate is normally ~52, and if I am very relaxed it can be 45. Fortunately the block doesn't have any (visible) symptoms.

The EMI story included a heart surgeon who took a drug to make his heart beat regularly enough for the synchronous imaging to work, and spent the rest of the week in bed until it wore off.

Who cares. Evolution doesn't have any kind of long term plan. What you see is what you have got.

Me too.

Fetal heart rates vary quite a bit during gestation. It starts off a close to the mother's heart rate, but then rises to peak at 175 beats per minute during the nineth week before starting to decrease.

No but he might be right that using the strong acoustic signal as a phase reference for the mothers heartbeat might give you a better steer on the phase and amplitude of the strongest component in the optical dataset to allow it to be more easily subtracted off.

Thinking about it overnight I concluded that you might be able to do well enough by ignoring the time when the main power stroke occurs and concentrating all your computational fire power on the inter pulse gap.

I thought babies heartbeats were typically in the range 2-3 Hz and perhaps a little higher during birth. My recollection of heartbeats is that their interval timing is just sufficiently irregular to make life difficult in the frequency domain. A heart beating at an exact frequency is already in serious trouble - that isn't natural behaviour.

FWIW my first instinct would be to lock onto the mothers heartbeat with a simplistic highest peak heuristic and average it into a buffer. Resampling it if necessary to adjust for any drift in frequency - basically building a template for the individuals heartbeat.

Subtract that off the raw data on a dot product correlation basis and what is left ought to be the babies component of the signal (or noise).

The simplest time domain regime that I think might work would be to run the raw data through a boxcar filter with a length matched to the babies power stroke. Heartbeats have a mark space ratio of 1:2 or higher so there should be enough almost baseline for the adult space to see the babies heartbeat on a fairly flat background most cycles.

I'm guessing that the ratio of their respective signals scales like body mass first and then depth of tissue being sampled so that the baby signal is 2-5% of the mothers. Give or take a factor of two.

_ | | __ | |/ \ Adult __| \_________________| etc.

Baby ____In_______In______In______

My instinct is that correlating the raw data against a filter matched for finding the babies heartbeat pattern and ignoring the zone where the mothers power stroke occurs entirely might be good enough. You can baseline correct either side of the detected babies peak signal.

Time domain will be competitive since the convolution kernel is quite short and the interval between peaks means that you don't have to work so hard most of the time. FFT will waste a lot of time and the jitter in the beat timings will make the frequency domain signal rather fuzzy.

Do you have to do it in realtime? A decent length dataset to look at offline is probably worth acquiring so you can see what might work. There may be two levels - good enough to make decisions and optimal.

Hi Phil,

could cepstral analysis and tracking help to tell baby's and mom's pulses apart and suppress mom's?

All the best,

Dieter

Doggone, you are messing with my sleep patterns, and I had three other things going on already.

For starters, we could define a new-to-me function Timewarp that uses one waveform or time series dataset to modulate the timing of a second one. Like having arb1 feed the vco input of arb2.

I don't think I've seen that math function before. It's not in Signals And Systems For Dummies.

Your problem is the inverse, to figure out the arb1 waveform given only the timewarped output signal from arb2. This reminds me of my TDR deconvolution program... find the FIR filter that make an ugly waveform into a pretty waveform. But Timewarp.

Well, you actually get the summed output of two such systems and want to separate them all out. Even worse. Envision mathematical instabilities.

Evolution is survivor bias. Those without a chaotic heartbeat didn't survive.

Strange. But then Life (as we know it) Is Strange :)

PLLs aren't necessarily narrowband, and this one doesn't have to work in real time--we can use the maximum a posteriori (MAP) estimate, and align each beat using the accumulated reconstructed signal. That's probably an iterative procedure.

Cheers

Phil Hobbs

I can just imagine explaining that to the FDA. ;)

Three plus or minus 1.

Cheers

Phil Hobbs

The cepstrum could maybe be useful to separate out the variations of pulse shape and pulse rate--it's an interesting idea.

I'm doubtful that it would separate the two pulses, because their variations aren't independent.. For instance, during a contraction the mum's pulse rate goes up and the baby's usually goes down.

Cheers

Phil Hobbs

Prove it. What we can see is a system which regulates the heart beat closely enough to let people survive. This isn't evidence that there's anything in the system with a high enough Q to do anything odd if the heart-beat was more regular. Heart-lung machines don't seem to be designed to avoid regular pulsation.

The fetal heart is pushing a rather smaller blood volume through rather narrower arteries with a much smaller heart. It might have to beat more often to move enough blood, but this is pure speculation, if not as totally speculative as your imaginary resonances.

Right. There are two of them though. ;)

It's not quite that bad, because we have a measurement of just the mum to start with, as well as datasets corresponding to different typical depths. The maternal waveform and phase shift aren't necessarily the same in all datasets, at least not to the required accuracy, but we should be able to pull out the instantaneous maternal pulse rate more-or-less unambiguously.

Yup. Fortunately we get lots of chances for a given dataset.

Fun.

Cheers

Phil Hobbs

Why bother. The mother and the fetus are defining two different waveforms all the time - the maternal pulse and the fetal pulse.

Both are directly measurable (though keeping the maternal pulse out of the fetal pulse isn't easy).

Try "Unnecessary Signals for Management Clowns". <snip>

Not really. What Phil is looking at are blood oxygenation numbers that are influenced by the maternal heat beat - delivering fresh blood to the placenta - and the fetal heart beat - circulating blood through the placenta and the fetus where it gets deoxygenated (in the fetus) between contractions of the fetal heart.

Another exercise from "Unnecessary Signals for Management Clowns"

We get a nice strong maternal signal from the closer detectors, no worries.

That's why I want to resample to make the signals as close to perfectly periodic as possible. That way all the signal winds up in one frequency bin.

Exactly. The idea is to use that to strobe the noisy signal to improve SNR. That's usually good for 10-15 dB. The problem is that if (for instance) the child's running at very close to the second harmonic of the mum, the accumulated pulse shapes will be wrong. If we can extract the phases accurately enough, we can choose averaging windows (not necessarily contiguous) so that the interaction goes to zero.

Hopefully, if we get the mum's waveform close enough to right. The active noise cancellation (ANC) approach, which uses cross-correlation to find the right multiplier for the maternal signal to subtract from the combined signal, has been tried since 1999 that I know about, and hasn't been good enough for an actual product to result, despite a pressing and widely-recognized need.

Depends entirely on the measurement geometry and tissue parameters. The interrogated volume doesn't depend strongly on the difference in mass.

The dataset is 4 +-1 channels, sampled at a few kilohertz. An elevator controller can keep up with that. ;) Even if it needed a multicore GPU it wouldn't be a big problem.

Not exactly real time, but during labour a delay of a few minutes can be fairly serious. On the other hand, there will usually be lots of time to gather a baseline data set before anything starts really going south. So we can probably have our cake and eat it.

Fun problem.

Cheers

Phil Hobbs

That's the reason for resampling--to make the samples equally spaced in phase rather than time.

Probably not a lot of zombies are going to be giving birth. ;)

Cheers

Phil Hobbs

At pulse-ox wavelengths, melanin's absorptivity declines smoothly toward longer wavelengths.

Your generic pulse ox uses only two wavelengths, so it's hard for it to eliminate the melanin tail. Three wavelengths should work reasonably unambiguously.

Cheers

Phil Hobbs

Do the two heartbeats tend to synchronize? There are evolutionary issues if syncing or not has any advantage.