Comparison of Statistical Methods for Delay Measurement between Heart Sound Signals

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Comparison of Statistical Methodsfor Delay
Measurement between Heart Sound Signals
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Outline

• Arterial stiffness
• Heart Carotid sounds
• Methods
• TF Estimation Welch, Regression, Ridge
  Regression
• Phase Delay
• Cross Correlation with Predicted Signal
• Results
• Simulation, Healthy, Cardiac patients
• Discussion Conclusions

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Arterial Stiffness - Definition
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Arterial Stiffness - Control

• Goal distribute blood to active tissues by
  controlling smooth muscle constriction
• Metabolic control
• Heart, brain, contracting skeleton muscles
• Neural control (mostly sympathetic) -
• Skin, resting skeletal muscles
• Arterioles, muscular arteries, large arteries
• Long term (tonic) and short term (phasic)
• Other affecting factors (age, disease, BP)

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Arterial Stiffness - Evaluation

• Goal prognostic and therapeutic information
  beyond blood pressure measurements
• Direct methods
• Change of arterial dimensions in response to
  pressure change (US echo-tracking, MRI)
• Indirect methods
• Pulse contour analysis (Pulse wave, Finger IR)
• Pulse wave velocity (Tonometry, QKd, MRI, Doppler
  US)
• Pulse wave velocity
• Pulse pressure wave low frequency signal
• Time-delay between two places
• Foot-to-toot, peak-to-peak, cross correlation

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Heart Sounds Mechanical Correlations
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Heart Sounds Auscultation Areas
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Heart sounds PCG, ECG and CP
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Heart sounds PCG, ECG and BP
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Carotid Artery Sounds (CAS)
Taken from Hasegawa,1991
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Carotid Sounds PCG and CAS
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Methodology
Welch, Regression or Ridge
BPF
phase
slope
TFE
BPF
TD filter
Pred
Env
Peak
CC
Env
Peak
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TFE General FIR Model
v(n)
h

x(n)
y(n)
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TFE Model - Welch

• The periodogram
• Welchs method for PSD estimation
• windowing and averaging
• Welchs transfer function estimator
• The Coherence function

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TFE Model Regression and Ridge

• Multiple regression model
• (y Carotid Signal, X Heart Sound)
• Multiple regression solution
• Ridge regression solution

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Delay Estimation Phase Data

• Calculated between the S1/S2 complex at the heart
  and carotid
• Time delay calculation
• method I
• Method II Linear regression over phase data
• Main difficulty How to choose relevant
  frequencies for optimal Time Delay Estimation
• Solution frequency range of linear phase and
  high coherence values (30-90Hz, 30-120Hz)

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Simulation - Phase Data
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Simulation Prediction (15dB)
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Simulation - GCC Envelope
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Healthy Subject No Breathing
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Healthy Subject Two Peaks
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Healthy Subject S1 Removed
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Healthy Subject One Peak
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Healthy Subject Phase Coherence
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Healthy Subject - Breathing Noise
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Breathing Noise GCC
Before BPF
After BPF
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Breathing Noise Phase
Before BPF
After BPF
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Breathing Noise Carotid Prediction
Aligned with caS2
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Patient Missing S1, Short S2 Delay
Patient Recordings Were Provided by MediMon Inc.
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Patient GCC
Regress
Welch
Ridge
No TFE
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Patient Time Domain Filters
Regress
Welch
Ridge
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Discussion Conclusions

• Time-delay estimation of propagating heart pulse
  pressure wave is useful for monitoring short-term
  changes of arterial stiffness.
• Heart and carotid sounds may be used instead of
  pressure wave, as demonstrated by Hasegawa.
• GCC (Generalized Cross Correlation) of heart
  sound signal and predicted carotid signal
  according to Welch TFE (GCC) is sensitive to
  multiple delays, breathing noise, frequency
  filters etc.
• Linear regression of Welchs TFE phase requires
  frequency selection, and is not reliable when
  coherence is low (patient 1).
• GCC with Ridge Regression TFE is the most stable
  method.

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Future Directions

• Check if propagation speed of heart sounds
  reflects arterial stiffness.
• Validate results on larger population
• Simulate of real events
• Combine with pre-segmentation of S1 S2
• Check adaptive methods
• Synchronized averaging of Welchs TFE

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Patient Welch Prediction
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Patient Ridge Prediction
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Patient Regression Prediction
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Patient 1 Low Coherence
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Patient 1 Ridge More Stable
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Patient 1 Opposite time delays
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Time Domain Filter Envelope (0dB)
Regress
Welch
Ridge
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Time Domain Filter Envelope (15dB)
Regress
Welch
Ridge