Mechanical manifestation of human hemodynamics

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Mechanical manifestation of human hemodynamics

• J.Kríž, P.Šeba
• Department of physics,University Hradec Kralove
• and
• K.Martiník
• Faculty of Medicine, Charles University

arXiv physics/0507135
15. konference ceských a slovenských
fyziku 7.9.2005
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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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Typical data
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Force plate
Measured are the three force and three moment
components , i.e. a six dimensional multivariate
time series
only five independent channels
Usual choice three force components point of
application of the force COP
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Typical data COP (120 s)
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Our equipment
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Measurements Using the force plate and a special
bed we measured the force plate output and the
ECG signal on 17 healthy adult males. 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.
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Typical data COP (10 s)
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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.
)
Starting point of the cardiac cycle the R wave
of the ECG signal. Length of the cycle 1000 ms
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Multivariate signal process
multidimensional time-parameterized
curve. Measured channel projection of the curve
to a given axis Changing the position of an
electrode within EEG measurement changes the
measured voltage. The measured process remains
unchanged.
Characterizing the curve geometrical invariants
c a,b? ?n Cn(a,b) mapping, such that
examples of geometrical invariants length of
a curve Curvatures
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Frenet frame A Frenet frame is a moving reference
frame of n orthonormal vectors e_i(t) which are
used to describe a curve locally at each point
?(t).
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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Assume that are linearly independent 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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Special cases 2 dimensional curve
tangent, normal
curvature
3 dimensional curve
curvature
torsion
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Frenet-Serret Formulas 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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The 5 curvatures were evaluated at each cycle and
the mean over cycles was taken. The measurement
lasted 8 minutes
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The results are reproducible
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What does it mean? Are the curvature peaks linked
to some physiological events?
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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 aortal arc).
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Pressure wave oscillations
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Pathology abdominal aneurism
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volunteer
pacient
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Scattering of the pressure wave on the artery
branchings / bendings leads to forces and
moments measured by the force plate.
Pressure wave velocity Depends on the
elasticity of the arterial wall and on the
arterial pressure.
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Pulse wave velocity on large arteries is not
directly accessible.
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Timing and consistency Pulse wave velocity
cL/T L0.7 m
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Magnetic resonace measurements
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• 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
• etc. and all this fully noninvasively.
  Cooperation of the patient is not needed