Variability of cardiovascular
signals
Cardiovascular signal variability
• Cardiovascular signals (C-V signals)
• Easy to measure
• EGG: RR intervals, heart rate - HR (1/RR)
• Blood pressure: systolic (SBP), diastolic (DBP), mean (MAP), pulse
pressure (PP)
• Difficult to measure directly (bioimpedance method), can be
evaluated indirectly from blood pressure wave (Windkessel
model)
• Stroke volume (SV), cardiac output (CO), total peripheral resistance
(TPR)
• Very difficult to measure directly (invasive measurement)
• Blood flow and pressure in various places of vessels
Signal: time series
Beat to beat (for example 5 minutes)
• RR interval: 805, 820, 815, 817, 822, 816,….. ms
• Hear rate: 70, 73, 68, 65, 67, 71,….. bpm
• Systolic blood pressure: 115, 117, 120, 116, 121, 119,….. mmHg
SBP
[mmHg]
RR
[ms]
700
800
900
110
120
130
20 40 60 80 100 120 s
RR interval
R
ECG
SBP
Blood
pressure DBP
Signal: time series
Every 15 minutes
• 24-hour blood pressure measurement, ECG Holter
8 9 1110 12 13 14 1615 17 18 19 2120 22 23 24 21 3 4 5 76
120
140
100
80
60
[mmHg]
SBP
DBP
heart rate
vigil sleeping
Blood pressure
h
Variability of cardiovascular signals
• Cardiovascular system is regulated by negative feedback
• Negative feedback forms oscillations in the signals – the longer
feedback loop, the slower oscillations
• Analysis of oscillations in the C-V signals contains information
about regulatory mechanism
System B
Signal 2Signal 1
System A
Negative
feedback loop
Brief introduction in theory of systems
𝐴 𝑧 =
𝐴11 𝑧 𝐴12 𝑧
𝐴21 𝑧 𝐴22 𝑧
= 𝐴 𝑘 𝑧−𝑘
𝑝
𝑘=0
=
𝑎11,1 𝑧−1
+ 𝑎11,2 𝑧−2
+ ⋯ + 𝑎11,𝑛 𝑧−𝑝
𝑎12,1 𝑧−1
+ 𝑎12,2 𝑧−2
+ ⋯ + 𝑎12,𝑛 𝑧−𝑝
𝑎21,0 + 𝑎21,1 𝑧−1
+ 𝑎21,2 𝑧−2
+ ⋯ + 𝑎21,𝑛 𝑧−𝑝
𝑎22,1 𝑧−1
+ 𝑎22,2 𝑧−2
+ ⋯ + 𝑎22,𝑛 𝑧−𝑝
𝑆11 𝑓 = Δ 𝑧 2 ∙ 1 − 𝐴22 𝑧 2 𝜆1
2
+ 𝐴12 𝑧 2 𝜆2
2
,
𝑆22 𝑓 = Δ 𝑧 2
∙ 𝐴21 𝑧 2
𝜆1
2
+ 1 − 𝐴11 𝑧 2
𝜆2
2
𝑆12 𝑓 = Δ 𝑧 2 ∙ 1 − 𝐴22 𝑧 𝐴21 𝑧−1 𝜆1
2
+ 1 − 𝐴11 𝑧−1 𝐴12 𝑧 𝜆2
2
,
kde ∆ 𝑧 = 1 − 𝐴11 𝑧 1 − 𝐴22 𝑧 − 𝐴12 𝑧 𝐴21 𝑧
−1
.
𝐻 𝑓 = 𝐼 − 𝐴(𝑧) −1 =
𝐻11 𝑓 𝐻12 𝑓
𝐻21 𝑓 𝐻22 𝑓
𝑆 𝑓 = 𝐻 𝑧 ∙ Λ ∙ 𝐻′ 𝑧−1
=
𝑆11 𝑆12
𝑆21 𝑆22
,
Λ =
𝜆1
2
0
0 𝜆2
2
Brief introduction in theory of systems
𝐴 𝑧 =
𝐴11 𝑧 𝐴12 𝑧
𝐴21 𝑧 𝐴22 𝑧
= 𝐴 𝑘 𝑧−𝑘
𝑝
𝑘=0
=
𝑎11,1 𝑧−1
+ 𝑎11,2 𝑧−2
+ ⋯ + 𝑎11,𝑛 𝑧−𝑝
𝑎12,1 𝑧−1
+ 𝑎12,2 𝑧−2
+ ⋯ + 𝑎12,𝑛 𝑧−𝑝
𝑎21,0 + 𝑎21,1 𝑧−1
+ 𝑎21,2 𝑧−2
+ ⋯ + 𝑎21,𝑛 𝑧−𝑝
𝑎22,1 𝑧−1
+ 𝑎22,2 𝑧−2
+ ⋯ + 𝑎22,𝑛 𝑧−𝑝
𝑆11 𝑓 = Δ 𝑧 2 ∙ 1 − 𝐴22 𝑧 2 𝜆1
2
+ 𝐴12 𝑧 2 𝜆2
2
,
𝑆22 𝑓 = Δ 𝑧 2
∙ 𝐴21 𝑧 2
𝜆1
2
+ 1 − 𝐴11 𝑧 2
𝜆2
2
𝑆12 𝑓 = Δ 𝑧 2 ∙ 1 − 𝐴22 𝑧 𝐴21 𝑧−1 𝜆1
2
+ 1 − 𝐴11 𝑧−1 𝐴12 𝑧 𝜆2
2
,
kde ∆ 𝑧 = 1 − 𝐴11 𝑧 1 − 𝐴22 𝑧 − 𝐴12 𝑧 𝐴21 𝑧
−1
.
𝐻 𝑓 = 𝐼 − 𝐴(𝑧) −1 =
𝐻11 𝑓 𝐻12 𝑓
𝐻21 𝑓 𝐻22 𝑓
𝑆 𝑓 = 𝐻 𝑧 ∙ Λ ∙ 𝐻′ 𝑧−1
=
𝑆11 𝑆12
𝑆21 𝑆22
,
Λ =
𝜆1
2
0
0 𝜆2
2
MATRIXES !!! POLYNOMIALS!!!
poly…. WHAT?!
Brief introduction in theory of systems
• Biological systems are complex – more than one input, system
setting and outputs can change
• System transforms input signal into output signal – analysis of
input/output signals helps to understand the system
• noise: another input signal – we do not care about signal and/or
signal origin is unknown
System B
Signal 2Signal 1
System A
Feedback loop
Another source of
oscillations (noise)
Another source of
osculation (noise)
Source of oscillations
System B
Signal 2Signal 1
System A
Feedback loop
deflection
Transferred
deflection
Lag of system B
Oscillatory period – given by feedback length
Frequency of oscillation = 1/period
→ frequency (spectral) analysis
provides information about
system
Feedback loop - baroreflex
heart
signal: heart rate
arteries
signal: blood pressure
resistance arteries
signal: peripheral resistance CNS: vasomotor centre
CNS: kardiomotor centre
Sympathetic efferent pathways
Parasympathetic efferent pathways
Methods of the variability assessment
Time-domain methods Frequency-domain methods
Statistic methods Geometric methods
Non-linear methods
(index of ireversibility, entropy based indices, symbolic analysis…)
Statistic methods
Mean24-h ± SD24-h
SD24-h counted from
all RR-intervals in 24
hours
SD24-h counted from all
normal RR-intervals in
24 hours
Mean5 min
± SD5 min
Mean5 min
± SD5 min
Mean5 min
± SD5 min
Mean5 min
± SD5 min
……
SD counted from all
Mean5 min
SD counted from all
SD5 min
(Variations on Standard Deviation)
Geometric methods
840
828
760
756
808
856
768
780
808
756
708
728
756
732
708
x
y x
y x
y x
y x
y
RR (ms)
Geometric methods
Frequency domain methods – spectral analysis
Spectrum
Signal in frequency domain
Time series
Signal in time domain
Signal is decomposed in individual frequencies
amplitude
time (s)
504030200 10 0.50.40.30.20 0.1
amplitude
frequency (Hz)
Frequency domain methods – spectral analysis
Spectrum
Signal in frequency domain
Time series
Signal in time domain
Signal is decomposed in individual frequencies
amplitude
time (s)
504030200 10 0.50.40.30.20 0.1
amplitude
frequency (Hz)
amplitude
time (s) frequency (Hz)
T=50 s
T=10 s
T=3 s
a=0.5
a=0.3
a=0.2
period T amplitude a frequency f = 1/T
f = 1/3 = 0.33 Hz
f = 1/10 = 0.1 Hz
f = 1/50 = 0.02 Hz
0.5
0.2
0.3
+
+
=
+
+
=
0.5
0.2 0.3
0.330.02 0.1
f = 0,02 Hzf = 0,1 Hzf = 0,33 Hz
Spectrum
Frequency domainTime domain
How the spectrum is formed?
Blood pressure variability – spectrum of SBP
Signal: beat-to beat series of systolic blood pressure (5 minutes)
Ludwig (1847),
Einbrodt (1860)Traube (1865), Hering (1869),
Mayer (1876)
Not in spectrum
Frequency (Hz)
0.50.40.30 0.1 0.2
0
0,04
0,08
0,12
SpektcumSBP(n.u.)
Heart rate variability (HRV)
Signal: beat-to-beat RR-intervals (5 min)
Frequency (Hz)
čas
RR-interval(ms)
0.50.40.30 0.1 0.2
0
100
200
300
PowerofRR(ms2)
Spestrum of RR intervals is
similar to the spectrum of
heart rate
Baroreflex
heart
signal: heart rate
arteries
signal: blood pressure
resistance arteries
signal: peripheral resistance CNS: vasomotor centre
CNS: kardiomotor centre
Sympathetic efferent pathways
Parasympathetic efferent pathways
peripheral (vascular, sympathetic) branch of
baroreflexu
Cardiac (parasympathetic) branch
Baroreflex
heart
signal: heart rate
arteries
signal: blood pressure
resistance arteries
signal: peripheral resistance CNS: vasomotor centre
CNS: kardiomotor centre
Physiological significance – frequency bands
High frequency (HF)
Intrathoracal pressure changes
influencing blood pressure
Very low
frequency (VLF)
Low frequency
(LF)
Slow hormonal changes, RAS, changes
of vascular tonus
Respiratory sinus arrhythmia
baroreflex
band:
baroreflex
Systolicblood
pressure
Heartrate
0.50.40.30 0.1 0.2
0
0,04
0,08
0,12
0
0,0
0,2
SpectrumSBP(n.u.)SpectrumHR(n.u.)
Variability source:
respiration
Variability
source:
High frequency (HF)
Intrathoracic pressure changes
influencing blood pressure
Very low
frequency (VLF)
Low frequency
(LF)
Respiratory sinus arrhythmia
baroreflex
band:
baroreflex
Systolicblood
pressure
Heartrate
0.50.40.30 0.1 0.2
0
0,04
0,08
0,12
0
0,0
0,2
SpectrumSBP(n.u.)SpectrumHR(n.u.)
parasympathetic activity
Time lag < 1 s
Time lag > 6 s
Slow oscillations
fast oscillations
High frequency (HF)
Very low
frequency (VLF)
Low frequency
(LF)
band:
Systolicblood
pressure
Heartrate
0.50.40.30 0.1 0.2
0
0,04
0,08
0,12
0
0,0
0,2
SpectrumSBP(n.u.)SpectrumHR(n.u.)
parasympathetic activity
Time lag < 1 s
Time lag > 6 s
Slow oscillations
fast oscillations
baroreflex
Mechanical
transfer
CNS (n. vagus)
Thoracic
pressure
changes
Changes of TPR
(sympathetic
nerves)
???
Variability changes: orthostatic challenge
Heart rate
Systolic pressure
frequency
↓HF-HR
↑LF-HR
↑LF-SBP
Orthostatic challenge:
• Increase of sympathetic activity → increase of low frequency HR and SBP
variability (LF-HR, LF-SBP)
• Decrease of parasympathetic activity → decrease of variability in respiratory
frequency (HF-HR)
analysis of autonomic nervous system function
Sympatho-vagal ratio LF-HR/HF-HR
Heart rate variability (HRV) changes
HRV in respiratory frequency decreases in
stress situations (↑sympathetic activity)
• Physiologically – sport, mental stress
• Pathologically – diabetes, hear failure
• Transplanted heart
• Predictor of the cardiovascular risk
heart
signal: RR intervals
arteries
signal: systolic
pressure (SBP)
CNS: kardiomotoric
centrum
Afferent neural
pathways
Efferent
neural
pathways
RR → SBP
SBP → RR
Evaluation of baroreflex function
Baroreflex sensitivity (BRS)
BRS: change of cardiac cycle
caused by change of SBP by 1
mmHg [ms/mmHg]
SBP
[mmHg]
RR
[ms]
700
800
900
110
120
130
20 40 60 80 100 120 s
RR interval
BRS:
slope
RR
SBP
R
ECG
SPB
Blood
pressure DBP
Cardiac baroreflex can
be evaluted by
analysis of SBP- HR
interaction
Laboratory methods:
- Phenylephrin application (standard)
- neck suction
- Valsalva manoeuvre
Spontaneous methods:
in time domain: sequence analysis
in spectral domain: cross-spectral analysis,
-index
Baroreflex sensitivity
0.50.40.30 0.1 0.2
0
0,04
0,08
0,12
0
0,0
0,2
SpectrumSBPSpectrumRRSpectral methods
BRS: change of RR caused by change of SBP by 1 mmHg [ms/mmHg]
• Change of RR – amplitude of RR in the spectrum of RR
• Change of SBP – amplitude of SBP in the spectrum of SPB
• → dividing of spectra→ alpha index
• Complication – not every oscillation in RR is caused by oscillation in SBP
𝑎𝑙𝑝ℎ𝑎 𝑖𝑛𝑑𝑒𝑥 =
𝑠𝑝𝑒𝑐𝑡𝑟𝑢𝑚 𝑅𝑅
𝑠𝑝𝑒𝑐𝑡𝑟𝑢𝑚 𝑆𝐵𝑃
Spectral methods
Cross -spectrum RR and SBP:
• Contains inly these frequencies occurring in both signals
simultaneously
• Advantage – we can analyse only special frequencies asociated
with baroreflex
0.50.40.30 0.1 0.2
spectrumSBPcros-spectrumSBPxRR
𝒈𝒂𝒊𝒏 =
𝒄𝒓𝒐𝒔𝒔 − 𝒔𝒑𝒆𝒄𝒕𝒓𝒖𝒎 𝑹𝑹 𝒙 𝑺𝑩𝑷
𝒔𝒑𝒆𝒄𝒕𝒓𝒖𝒎 𝑺𝑩𝑷
LF
BRS
0.50.40.30 0.1 0.2
0
4
8
12
Gain(ms/mmHg)
Baroreflex sensitivity – physiological significance
• Baroreflex function – regulation of blood pressure changes by
changes of HR and TPR
• Cardiac branch of baroreflex is mediated by vagal nerves
→ BRS is increased in higher vagal activity and decreased in sympathetic
activity
→ BRS is decreased in stress
→ BRS depends on RR interval length
• Long-time decreased BRS reflects dysfunction in blood pressure
regulation – cardiovascular risk
normal
BRS
RR
SBP
RR
SBP
decreased
BRS
Decreased BRS
• Physiologically
• psychic stress – increased sympathetic
activity
• Physical exercise – increased
sympathetic activity
• In old age
• Pathologically
• hypertension – decreased baroreceptor
sensitivity (atherosclerosis, increased
arterial stiffness)
• diabetes – neuropathy of autonomic
nervous system
• Chronic depression (neurogenic)
• Heart insufficiency/failure – heart do
not response
• Transplanted heart - denervation
• Myocardial infarction – heart do not
response
Disadvantages of methods
• Only sinus rhythm without ectopic beats can be analysed
• Long recording >5min, stationary signal
• BRS is a parameter of cardiac baroreflex function, information
about vascular part of baroreflex is missing
• Causality of RR-SBP is neglected
Blood pressure signal (270 s) - example
time (s)
Bloodpressure(mmHg)Krevnítlak(mmHg)
Sitting, paced breathing
Standing, paced breathing
Meyer waves (10 s rhythm)
respiration
sequentions of SBP, DBP and inter-beat intervals (IBI) - example
time (s)
BP
(mmHg)
Sitting, paced breathing
Standing, paced breathing
IBI(ms)
BP
(mmHg)IBI(ms)
Spectra of SBP and IBI - example
SBP
Sitting, paced breathing
Standing, paced breathing
0,1 Hz
Sympathetic activity
Respiratory frequency
vagal activity
IBI
↓symp. act., ↑vagal act.
↑ symp. act., ↓vagal act.
frequency (Hz)
SBPIBI
Coherence a BRS - example
frequency (Hz)
Sitting, paced breathing
Standing, paced breathing
coherence
BRS
(ms/mmHg)
coherence
BRS
(ms/mmHg)
0,1 Hz
baroreflex
Respiratory frequency
coherence: synchronization
between signals (correlation
on particular frequency)
Take home message 1
• Variability of cardiovascular signals contain information about
regulatory mechanisms
• Analysed signals: time series
• ECG: beat-to-beat RR intervals, heart rate (HR)
• Continual record of blood pressure: beat-to-beat systolic
pressures (SBP)
• Main methods of variability analysis
• Standard deviations and derived parameters
• Spectral analysis
• Analysis of RR-SBP interaction: baroreflex sensitivity
(definition: change of RR caused by change of SBP by 1 mmHg)
• Heart rate variability (HRV) – assessment of ANS activity
• decreased – increased cardiovascular risk
• Blood pressure variability (less analysed)
• increased – increased cardiovascular risk
• Baroreflex sensitivity (BRS)
• normal(> 4 mmHg) – baroreflex function is OK
• decreased (< 3 mmHg) – increased cardiovascular risk
• Hypertension, diabetes, heart failure, stress
• Predictors od sudden cardiac death: zero values of BRS and HRV
• Spectra RR and SBP
• Frequency bands (VLF, LF a HF)
• HF (0.15-0,5Hz): parasympathetic activity, respiration
• LF (around 0,1 Hz): sympathetic/parasym. activity, baroreflex
• VLF (< 0,03): low changes in vascular system (hormones, TPR,
RAS,…)
Take home message 1
Thank you
Thank you