Mechanical manifestation of human cardiovascular dynamics

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Mechanical manifestation of human cardiovascular
dynamics

• J.Krí, P.eba
• Department of physics,University of Hradec
  Kralove
• and
• K.Martiník, J. tásek
• Faculty of Medicine, Charles University

QC workshop Spectra, Algorithms and Data
Analysis February 28, 2006
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Program

• What is a force plate?
• How to study cardiovascular system using force
  plate?
• Differential geometry method of data analysis
• Results
• Cardiac cycle
• Comparing results (cardiac catetherization)
• Interpretation
• Conclusions

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Force plate
Measured are the three force and three moment
components, i.e. a six dimensional multivariate
time series
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Force plate typical signals
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Force plate
only five independent channels
Usual choice force components COP
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Typical COP (120 s) spaghetti diagram
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Our equipment
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Experiment Using the force plate and a special
bed we measured the force plate output and the
ECG signal on 20 healthy adults. In three cases
we measured also the heart sounds. In such a way
we obtained a 7 or 8 dimensional time series.
The used sampling rate was 1000 Hz. The
measurements lasted 8 minutes.
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Typical measured signals
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Periodic-like pattern of signals
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Typical COP (10 s)
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Hypothesis
For a reclining subject the motion of the
internal masses within the body has a crucial
effect. Measured ground reaction forces contain
information on the blood mass transient flow at
each heartbeat and on the movement of the heart
itself. (There are also other sources of the
internal mass motion that cannot be suppressed,
like the stomach activity etc, but they are much
slower and do not display a periodic-like
pattern.)
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Method od data analysis
Multivariate signal process multidimensional
time-parameterized curve. Measured channels
projections of the curve to given axes. Example
changing the position of an electrode within EEG
measurement changes the measured voltage. The
measured process remains unchanged. Measured
forces and moments (projections) depend on the
position of the pacient on the bed and on the
position of the heart inside the
body. Characterizing the curve geometrical
invariants.
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Geometrical invariants of a curve
c a,b -gt Rn Cn(a,b) mapping, such that
Length of a curve Curvatures
The main message of the differential geometry
It is more natural to describe local properties
of the curve in terms of a local reference system
than using a global one like the euclidean
coordinates.
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Frenet frame
Frenet frame is a moving reference frame of n
orthonormal vectors ei(t) which are used to
describe a curve locally at each point c(t).
To see a Frenet frame animation click here
Assume that are linearly independent
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Geometrical invariants curvatures
The Frenet Frame is the family of orthonormal
vectors called Frenet vectors. They are
constructed from the derivates of c(t) using the
Gram-Schmidt orthogonalization algorithm with
                                           
                                                  
                             

• The real valued functions are called
  generalized curvatures and are defined as

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The simplest cases
2 dimensional curve
tangent, normal
curvature
3 dimensional curve
curvature
torsion
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Frenet Serret formulae
Relation between the local reference frame and
its changes
Curvatures are invariant under reparametrization
and Eucleidian transformations! Therefore they
are geometric properties of the curve.
Main theorem of curve theory
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Averaging
The 5 curvatures were evaluated from 6 force
plate signals.
Starting point of the cardiac cycle QRS complex
of ECG. Length of the cycle approximately 1000
ms
R-wave
P-wave (systola of atria)
T-wave (repolarization)
Q -wave
S-wave
QRS complex (systola of ventricles)
The mean over cardiac cycles was taken. Length
of the cycle approximately 1000 ms
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Results
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The results are reproducible
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The question of interpretetion
The curvature maxima correspond to sudden changes
of the curve, i.e. to rapid changes in the
direction of the motion of internal masses within
the body. The curvature maxima are associated
with significant mechanical events, e.g. rapid
heart expand/contract movements, opening/closure
of the valves, arriving of the pulse wave to
various aortic branchings,...
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Cardiac cycle
Total blood circulation
Veins ? right atrium ? right ventricle ?
pulmonary artery ? lungs ? pulmonary vein ? left
atrium ? left ventricle ? aorta ? branching to
capillares ? veins
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Cardiac cycle
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Pressures inside the Heart
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Pressure wave propagation along aorta
Ejected blood propagets in the form of the
pressure wave
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Pressure wave propagation along aorta
On branching places of large arteries the pulse
wave is scattered and the subsequent elastic
recoil contribute to the force changes measured
by the plate. A similar recoil is expected also
when the artery changes its direction (like for
instance in the aortic arch).
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Aorta and major branchings
Aortic arch
Mesentric artery
Diaphragm
Coeliac artery
Renal arteries
Abdominal bifurcation
Iliac arteries
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Cardiac Catheterization

• involves passing a catheter ( a thin flexible
  tube) from the groin or the arm into the heart

• produces angiograms (x-ray images)
• can measure pressures in the left ventricle and
  the aorta

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Cardiac Catheterization
For comparism we measured three volunteers on the
force plate in the same day as they were
catheterized.
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Cardiac Catheterization
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Pressures inside the Heart
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Pressures inside the Heart catheterization
measurement
ECG
Aortic pressure (aortal valve)
AVC
Ventricular pressure
AVO
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Pressures inside the Heart catheterization
measurement
ECG
Aortic pressure (abdominal bifurcation)
Ventricular pressure
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Pressures in aorta
Aortic valve
Aortic arch
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Pressures in aorta
Diaphragm
Renal arteries
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Pressures in aorta
Abdominal bifurcation
Arteria femoralis
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Conclusions

• What is it good for?
• Measuring the pressure wave velocity in large
  arteries
• Observing pathological reflections (recoils)
• Testing the effect of medicaments on the aortal
  wall properties
• Testing the pressure changes in abdominal aorta
  in pregnant women
• etc. and all this fully noninvasively.
  Cooperation of the patient is not needed

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Pressure wave velocity
Depends on the elasticity of the arterial wall
and on the arterial pressure.
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Pressure wave velocity