Transcript Mechanical manifestation of human cardiovascular

Mechanical manifestation of human
cardiovascular dynamics
J.Kříž, P.Šeba
Department of physics,University of Hradec Kralove
and
K.Martiník, J. Šťásek
Faculty of Medicine, Charles University
QC workshop
“Spectra, Algorithms and Data Analysis“
February 28, 2006
Program
1.
2.
3.
4.
5.
6.
7.
8.
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
Force plate
Measured are the three force and three moment components,
i.e. a six dimensional multivariate time series
Force plate – typical signals
Force plate


FM
only five independent channels
Usual choice: force components + COP
Mx
My
y
.
x
,
Fz
Fz
Typical COP (120 s) – spaghetti diagram
Our equipment
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.
Typical measured signals
Periodic-like pattern of signals
Typical COP (10 s)
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.)
Method od data analysis
Multivariate signal – process: multidimensional timeparameterized 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.
Geometrical invariants of a curve
c: [a,b]
-> Rn …
Cn([a,b]) – mapping, such that
c' (t )  0, t  [a, b].
b
Length of a curve l 
 c' (t ) dt
a
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.
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
c' (t ), c' ' (t ), , c ( n1) (t )
independent t  [a, b].
are linearly
Geometrical invariants: curvatures
The Frenet Frame is the family of orthonormal vectors
{e1 (t ), e2 (t ), en (t ) | t [a, b]} called Frenet vectors. They are
constructed from the derivates of c(t) using the Gram-Schmidt
orthogonalization algorithm with
e1 (t ) 
c' (t )
,
c' (t )
e k (t ) 
e k (t )
e k (t )
k 1
, e k (t )  c ( k ) (t )   c ( k ) (t ), ei (t ) ei (t ), k  2, n  1,
i 1
e n (t )  e1 (t )  e 2 (t )   e n 1 (t ).
The real valued functions  j (t ), j  1,, n  1 are called
generalized curvatures and are defined as
 j (t ) 
e' j (t ), e j 1 (t )
c' (t )
.
The simplest cases
2 – dimensional curve
1
e1 (t ) 
c' (t )
c'1 (t ) 
c' (t ),
 2 
 (t )  1 (t ) 
1
e 2 (t ) 
c' (t )
 c'2 (t )
c' (t ) 
 1

 c' '1 (t )c'2 (t )  c' '2 (t )c'1 (t )
c' (t )
3
…tangent, normal
…curvature
3 – dimensional curve
e1 (t ) tangent, e 2 (t )normal, e3 (t )binormal
 (t )  1 (t ) 
 (t )   2 (t ) 
c' (t )  c' ' (t )
c' (t )
…curvature
3
c' (t )  c' ' (t ), c' ' ' (t )
c' (t )  c' ' (t )
2
…torsion
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
Given functions 1 ,  2 , ,  n 1 defined on some (a, b) with  j C n  j 1 - continuous
for j  1,, n  1 and with  j (t )  0 for j  1, , n  2 and t  (a, b). Then there
is unique (up to Eucleidian transform ations) n - dimensiona l curve c, so that
c' (t )  1 and c has curvatures 1 ,  2 , ,  n 1.
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
P-wave
(systola of atria)
R-wave
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
Results
The results are reproducible
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,...
Cardiac cycle
Total blood circulation:
Veins  right atrium  right ventricle  pulmonary artery  lungs
 pulmonary vein  left atrium  left ventricle  aorta 
branching to capillares  veins
Cardiac cycle
Pressures inside the Heart
Pressure wave propagation along aorta
Ejected blood propagets in the form of the pressure wave
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).
Aorta and major branchings
Aortic arch
Mesentric artery
Diaphragm
Coeliac artery
Abdominal
bifurcation
Iliac arteries
Renal
arteries
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
Cardiac Catheterization
For comparism we measured three volunteers on the force plate
in the same day as they were catheterized.
Cardiac Catheterization
Pressures inside the Heart
Pressures inside the Heart –
catheterization measurement
ECG
Aortic pressure
(aortal valve)
AVC
AVO
Ventricular
pressure
Pressures inside the Heart –
catheterization measurement
ECG
Aortic pressure
(abdominal
bifurcation)
Ventricular
pressure
Pressures in aorta
Aortic valve
Aortic arch
Pressures in aorta
Diaphragm
Renal arteries
Pressures in aorta
Abdominal bifurcation
Arteria femoralis
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
Pressure wave velocity
Depends on the elasticity of the arterial wall and on the
arterial pressure.
Pressure wave velocity