high pass filter with cutoff set at 0.003Hz

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paul kaam 2016-2-16

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评论： Star Strider 2016-3-4

Hi,

I have a data set consisting of a mean bloodpressure and I want to high-pass-filter this signal with a DC cutoff set at 0.003 Hz. I'm not really familiar with signal processing (filter type, freq domain etc) so if anyone could help me out a bit, that would be great.

thanks in advance,

Paul

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Answer 1

Star Strider 2016-2-16

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My filter design procedure is here: How to design a lowpass filter for ocean wave data in Matlab?

Before you design a filter with such a low stopband, consider your sampling frequency. If you have a ‘high enough’ sampling frequency, consider a Chebyshev Type II filter.

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Star Strider 2016-2-16

A sampling interval of 1 Hz is not high enough to design a filter with a stopband as low as you want it. (I actually did that experiment with different filter designs, the reason for the delay in my reply. None worked.)

I would consider one of two options:

1. Simply subtract the mean from the signal to eliminate the d-c offset;

2. If you have a varying baseline, use the Savitzky-Golay filter on the baseline to model it, then subtract the filter output from your signal to eliminate the baseline drift.

Most filter design requires experimenting to get the best result, including the Savitzky-Golay filter.

I don’t know what experiment you are doing, but mean blood pressure is normally relatively stable in healthy individuals, unless you are doing something deliberately to perturb it (alpha or beta adrenergic receptor antagonists or agonists, rapid postural changes, etc.) so filtering out the baseline drift could filter out much of your signal as well.

A third possibility (that I do not recommend) is to resample it to a higher sampling frequency. The problem with such significant interpolation is that you are creating data where none actually exist.

Star Strider 2016-2-23

在 MATLAB Online 中打开

Actually, it was a hydraulic chamber with two valves, the pressure in the chamber driven by a reciprocating cylinder. (The basic design existed before I got there.) The idea was to get away from from flexing the tubing with the fracturing, shearing, and particle liberation inherent in that technology. We had very low hemolysis values and good results in the animal studies. I wrote the protocols and guided the R&D effort in the preclinical trials, including the data analysis and writing the IDE. The benefit here is that I know a bit about the technology and physiology involved.

I did some analysis on your signal. Looking at the fft in figure(3), virtually all your signal energy is below 0.003 Hz. If you filtered it out with a high-pass filter, you would have only noise left.

My guess is that the paper sampled at a much faster rate, and therefore could sample with such a low frequency to eliminate baseline drift and d-c offset. I still wonder if their experimental setup was similar to yours, because a highpass filter with a 0.003 Hz cutoff makes no sense to me with your data. A lowpass filter with the same cutoff (assuming designing one is possible with such a low sampling frequency) definitely does. Let me know what you want to do.

The code:

[MAP,s,r] = xlsread('paul kaam MAPdata.xlsx');
L = length(MAP);
Ts = 1;                                                         % Sampling Interval (sec)
Fs = 1/Ts;                                                      % Sampling Frequency (Hz)
Fn = Fs/2;                                                      % Nyquist Frequency (Hz)
t = 0:Ts:L-1;
figure(1)
plot(t, MAP);
grid
title('Time Domain Plot Of Unprocessed MAP')
xlabel('Time (sec)')
ylabel('MAP (Torr?)')
FMAP = fft(MAP)/L;                                              % FFT Of Raw Data
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                             % Frequency Vector
Iv = 1:length(Fv);                                              % Index Vector
figure(2)
plot(Fv, 2*abs(FMAP(Iv)))
grid
axis([0  0.01    ylim])
title('Frequency Domain Plot Of Unprocessed MAP')
xlabel('Frequency (Hz)')
ylabel('Amplitude (Torr?)')
MAP0 = MAP-mean(MAP);                                           % Subtract d-c Offset
FMAP0 = fft(MAP0)/L;
figure(3)
plot(Fv, 2*abs(FMAP0(Iv)))
grid
axis([0  0.01    ylim])
title('Frequency Domain Plot Of Mean-Corrected MAP')
xlabel('Frequency (Hz)')
ylabel('Amplitude (Torr?)')

Star Strider 2016-2-23

在 MATLAB Online 中打开

My pleasure!

No papers, and I wasn’t allowed to take anything with me. (That was more than 30 years ago, so much of the technology is obsolete, and any patents — as well as my non-disclosure and non-competition agreements — have long since expired.) You might be able to get the IDE application from the FDA, but I doubt it would be of much help if it was in any way redacted. I did get high praise from the FDA reviewers and the cardiovascular life support devices advisory group for my experimental design, protocols, and data analysis though, so those might be helpful. I advocated replacing the piston pump with an oscillating roller pump, so the shards of tubing stayed in the drive system and not in the blood, but that idea got shot down quickly.

‘... sampled with an analog-to-digital converter at 60 Hz and then processed ...’

That is of course 60 times per second, not 1 time per second. If you have the opportunity to revise your experimental protocol, amend it to increase the sampling frequency to 60 Hz from 1 Hz. Then you can filter at 0.003 Hz easily.

The filter for a 60 Hz sampling frequency is easy to design:

Fs = 60;                                                    % Sampling Frequency (Hz)
Fn = Fs/2;                                                  % Nyquist Frequency (Hz)
Wp = 0.005;                                                 % Passband Frequency (Hz)
Ws = 0.003;                                                 % Stopband Frequency (Hz)
Rp =     1;                                                 % Passband Ripple (dB)
Rs =    20;                                                 % Stopband Ripple (dB)
[n,Wn] = buttord(Wp, Ws, Rp, Rs);                           % Optimal Filter Order
[b,a]  = butter(n,Wn, 'high');                              % Calculate Filter Coefficients For Highpass Filter
[sos,g] = tf2sos(b,a);                                      % Convert To Second-Order-Sections For Stability
figure(1)
freqz(sos, 2048, Fs)                                        % Assess Filter Passband & Stability

Then use filtfilt for the actual filtering.

I would still do the fft analysis first, to be certain you are not filtering out relevant parts of your signal, and not only the baseline drift and d-c offset. That the paper chose those parameters does not mean they are appropriate for your experimental design or instrumentation.

Star Strider 2016-2-24

Not really strange if you knew that company (now long out of business).

My pleasure.

I’m confused. If your data is already filtered, then it is likely not necessary to filter it. The problem is that you don’t know what the original data were, and what was filtered out. What is gone may or may not be important. I like to have all the original data so that I can decide what is important and what isn’t. Baseline drift (low-frequency components of your signal) could be important if those signals are actual data and not extraneous noise.

Haemodilution should either initially increase or have no effect on MABP, depending on how rapidly the saline is infused. There will be ‘third-spacing’ of the saline because the plasma oncotic pressure will not be enough to counter the physical intravascular pressure, favouring transudation of the saline at the onset of bypass. So MABP will decline once the third-spacing has equilibrated and plasma oncotic pressure once again is enough to oppose significant transudation. Blood transfusions may increase MABP depending on whether it is whole blood or packed erythrocytes. Cooling will cause peripheral vasoconstriction, and rewarming peripheral vasodilatation, so those will have an effect.

There is some pulsatile component of even older (I would like to believe obsolete) constant-flow roller pump designs, so you may have to take that into account as well. If you are using a pulsatile pump, you need to track the pulse rate, pulse pressure and pulse contour as well, because the vascular systems of animals with complex hearts evolved to provide optimal systemic perfusion with pulsatile blood flow, exemplified in the technological superiority of a-c over d-c for long-distance electrical distribution systems. The same principles apply to cardiovascular physiology.

You need the perfusionist’s and anaesthesiologist’s records as to what was infused when,, the pump and other settings, what vasoactive drugs were given, and all other information. I can guarantee you that what you are doing is not trivial! Physiology is absolutely fascinating, but it can be frustrating to analyse from an engineering perspective, much less model.

Star Strider 2016-2-25

Interesting. When we were doing preclinical trials with the pulsatile pump on 70 kg male Holstein calves, we monitored internal carotid blood flow with an electromagnetic flowmeter (we used the same technology to monitor all flows in our system), and found that shortly going on bypass, carotid blood flow declined to undetectable levels, yet the animals suffered no neurologic injury as determined by intraoperative EEG and post-recovery neurologic examination (by a veterinary anaesthesiologist with particular skills in this area). In our FDA filings, I cited some papers that went into some detail on cerebrovascular autoregulation, and the FDA was happy. I also pointed out that in most tissues, the mitochondrial cytochrome chain is usually saturated at a PO2 of 10 mm Hg (and 5 mm Hg in the liver), so as long as arterial PO2 remains high enough and flow high enough, hypoxia is unlikely.

The problem is relying on the patient monitoring system for your data. They are heavily filtered, because they are intended for clinical interpretation in real time, not research. You should be collecting your signals independently. (I’m not quite sure how I would monitor cerebral blood flow in a clinical situation, perhaps bilateral internal carotid ultrasound to replace the electromagnetic flowmeter, since ultrasound transducers and signal processors are significantly more sophisticated than in the mid-1980s.) Their use of transcranial ultrasound monitoring only the middle cerebral artery involves significant assumptions.

Notably:

‘Analog arterial pressure data from the operating room hemodynamic monitor, TCD, and NIRS signals were sampled with an analog-to-digital converter at 60 Hz ...’

So they got their signals directly from the analogue instrumentation and digitised them with their own equipment. They also used a moving average filter, something that I never advocate. I want to design my filters with specific frequency characteristics so I know what I’m doing with my signals.

I don’t quite follow some of their derived indices and statistics. It seems consulting with a statistician, and a biomedical engineer with expertise in instrumentation, before they designed their study would have been beneficial.

That cerebral blood flow (CBF) as determined by their indices decreases as MAP increases mirrors my own experience.

I haven’t kept up with the cardiopulmonary bypass (CPB) literature since my experience with it. (I’m a Board-Certified M.D. Internal Medicine Physician and M.S. Biomedical Engineer, not a cardiovascular surgeon.) However it saddens me that everyone continues to use peristaltic continuous-flow pumps when true pulsatile pumps provide much better clinical outcomes.

Star Strider 2016-2-29

Pulsatile is definitely the way to go, since it also makes the transition off the pump easier. A correctly-designed pulsatile pump also reduces haemolysis, although the correct valve design is critical. I believe a valve-based design is better than a pulsatile roller pump because the roller pump stresses the tubing too much, and causes plastic embolisation.

I would do what the authors of the paper did — multiplex off the analogue instrumentation signals digitising them with their own equipment. (That also has the advantage that the analogue hardware incorporate a hardware threshold to prevent the instruments from being wiped out by the Bovie (electrocautery) signals.)

I guarantee you 1 Hz is definitely too low a sampling frequency. I always suggest at least 250 Hz, because physiological signals are generally band-limited by the physiology of excitable membranes to about 100 Hz, so you’ll have a high enough Nyquist frequency (at least 125 Hz) to allow for a stable filter. Besides, disk storage is inexpensive enough these days to allow you to write to an outboard 1 TB disk drive, large enough to hold even data from long pump time. Record all your unfiltered signals with your own digitising equipment, and do the processing offline. You need to be certain that your ADC board can handle the voltages you’re receiving from the analogue sensors, but other than that, you should have no problems.

I don’t see any serious deficiencies with their comparing MAP and TCD with MAP and NIRS (I like their experimental setup), although I’d likely have opted for a different statistical design (and the assistance of a biostatistician, since it seems they didn’t). I believe these are valuable, although I might record EEG as well (since I believe that’s becoming standard practice in anaesthesiology). More data is generally better than less data.

I believe the essence of your study is correct. You just need to record the correct signals correctly.

paul kaam 2016-3-4

Thanks star stider! You've been a great help to me!

Star Strider 2016-3-4

My pleasure.

I know I couldn’t design your filter because of the low sampling frequency. If I was enough help, I would appreciate it if you would Accept my Answer.

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high pass filter with cutoff set at 0.003Hz

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high pass filter with cutoff set at 0.003Hz

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