1. 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

2. Program 1.What is a force plate? 2.How to study cardiovascular system using force plate? 3.Differential geometry – method of data analysis 4.Results 5.Cardiac cycle 6.Comparing results (cardiac catetherization) 7.Interpretation 8.Conclusions

3. Force plate Measured are the three force and three moment components, i.e. a six dimensional multivariate time series

4. Force plate – typical signals

5. only five independent channels Usual choice: force components + COP Force plate

6. Typical COP (120 s) – spaghetti diagram

7. Our equipment

8. 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.

9. Typical measured signals

10. Periodic-like pattern of signals

11. Typical COP (10 s)

12. 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.) Hypothesis

13. process 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. Method od data analysis

14. c: [a,b] -> R n … C n ([a,b]) – mapping, such that Length of a curve Curvatures: Geometrical invariants of a curve 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.

15. 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 c(t). Frenet frame Assume that are linearly independent To see a “Frenet frame” animation click herehere

16. 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 Geometrical invariants: curvatures

17. 2 – dimensional curve 3 – dimensional curve …curvature …tangent, normal …curvature …torsion The simplest cases

18. Relation between the local reference frame and its changes Main theorem of curve theory Curvatures are invariant under reparametrization and Eucleidian transformations! Therefore they are geometric properties of the curve. Frenet – Serret formulae

19. 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 Averaging The mean over cardiac cycles was taken. Length of the cycle: approximately 1000 ms P-wave (systola of atria) Q -wave R-wave S-wave T-wave (repolarization) QRS complex (systola of ventricles)

20. Results

21. The results are reproducible

22. 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,...

23. Total blood circulation: Veins  right atrium  right ventricle  pulmonary artery  lungs  pulmonary vein  left atrium  left ventricle  aorta  branching to capillares  veins Cardiac cycle

25. Pressures inside the Heart

26. Pressure wave propagation along aorta Ejected blood propagets in the form of the pressure wave

27. 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).

28. Aorta and major branchings Aortic arch Diaphragm Coeliac artery Mesentric artery Renal arteries Abdominal bifurcation Iliac arteries

29. 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

30. Cardiac Catheterization For comparism we measured three volunteers on the force plate in the same day as they were catheterized.

31. Cardiac Catheterization

32. Pressures inside the Heart

33. Pressures inside the Heart – catheterization measurement ECG Ventricular pressure Aortic pressure (aortal valve) AVO AVC

34. Pressures inside the Heart – catheterization measurement ECG Ventricular pressure Aortic pressure (abdominal bifurcation)

35. Pressures in aorta Aortic arch Aortic valve

36. Pressures in aorta Renal arteries Diaphragm

37. Pressures in aorta Arteria femoralis Abdominal bifurcation

38. 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 Conclusions

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