Jan Kříž

1. Detecting Targets in Human Body: What is the common property of radar systems and medical devices? Department of physics, University of Hradec Králové Doppler Institute for mathematical physics and applied mathematics Jan Kříž Joint work with Petr Šeba, Emil Doležal Tosa Yamada Sci-Tech Flash May 30, 2007 Kochi University of Technology

2. Program PART I • Introduction: What is the common property of radar systems and medical devices? Which types of targets are we detecting in human body? • Motivation: Why do we do this? • Results: Caridovascular dynamics Processes in the brain • Conclusions: What is it good for?

3. Program PART II • Warming up: forces, moments and COP • Filtering • Differential geometry and force plate data analysis: curvatures as geometric invariants • Maximum likelihood estimation

4. RADAR = Radio Detection and Ranging

5. RADAR = Radio Detection and Ranging

6. RADAR = Radio Detection and Ranging

7. EEG = Electroencephalographymeasures electric potentials on the scalp (generated by neuronal activity in the brain)

8. Multiepoch EEG: Evoked potentials = responses to the external stimulus (auditory, visual, etc.) sensory and cognitive processing in the brain

9. Force plate • Measured are the three force and three momentum components (on strain-gauge technology). • stability analysis (balance in upright stance) • gait analysis

10. Human cardiovascular dynamics measured by force plate

11. ECG – electrocardiographymeasures electrical activity of the heart over time

12. Cardiac catheterizatrion • 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 left ventricle and aorta

13. Cardiac Catheterization

14. Summary What is the output?

15. What is the common property of radar systems and medical devices? Output: multivariate time series • spatial–temporalcharacter • data of the form X = S + W • low signal to noise ratio(SNR) Signal processing: time series analysis Targets in human body: processes in the brain, haemodynamical events, …

16. MOTIVATION Is this a suitable topic for a physicist? YES !!! Multivariate time series themselves are analyzed in physics: geophysics, climatology, meteorology, astrophysics,… We exploit mathematical methods commonly used in quantum mechanics for data processing, namely: • Differential geometry: quantum waveguides theory • general theory of relativity • Maximum likelihood estimation: quantum state reconstruction • Random matrix theory: quantum billiards

17. MOTIVATION Example: JMA seismic intensity network Different types of rock layers filter the seismic waves. Aim of data analysis: • source localization • earthquake prediction

18. MOTIVATION Example: Positions of electrodes Bones and coeliolymph filter the electric waves. Aim of data analysis: • source localization • seiuzure prediction

19. MOTIVATION Why do we do this?

20. MOTIVATION Why do we do this? Quantum mechanics: no tradition in HK Medical research has been provided in HK for more than fifty years.

21. Force plate data analysis Typical signal measured during quiet standing

22. Force plate data analysis Postural requirements during quiet standing - support head and body against gravity - maintain COM within the base of support Postural control inputs Somatosensory systems(cutaneous receptors in soles of the feet, muscle spindle & Golgi tendon organ information, ankle joint receptors, proprioreceptors located at other body segments) Vestibular system(located in the inner ear) Visual system (the slowest one)

23. Force plate data analysis Typical COP (120 s) – spaghetti diagram

24. Force plate data analysis Motor strategies (to correct the sway) Ankle strategy(body = inverted pendulum, vertical forces) Hip strategy(larger and more rapid, shear forces) Stepping strategy

25. Force plate data analysis Postural control: Central nervous system (CNS) Spinal cord (reflex, 50 ms) Brainstem/subcortical(automatic response, 100 ms) Cortical(voluntary movements, 150 ms) Cerebellum • Our original goal:study CNS using force plate dataforce plate as mechanical analog of EEGwe have found some „strange“ latencies in the data.

26. Cardiovascular dynamics measured by force plate

27. Cardiovascular dynamics measured by force plate Experiment Using the force plate and a special bed we measured the force plate output and the ECG signal on 20 healthy adults. In such a way we obtained a 7 dimensional time series. The used sampling rate was 1000 Hz.The measurements lasted 8 minutes.

28. Cardiovascular dynamics measured by force plate Typical measured signals

29. Cardiovascular dynamics measured by force plate For a reclining subject the motion of the internal masses withinthe 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-likepattern.) The idea is not new. Ballistocardiography (=usage of mikromovements for extracting information on the cardiac activity) is known for more than 70 years.

30. Cardiovascular dynamics measured by force plate Cardiac cycle Total blood circulation: Veins  right atrium right ventricle pulmonary artery lungs  pulmonary vein left atrium left ventricle aorta branching to capillares veins

31. Cardiovascular dynamics measured by force plate Mechanical activity is triggered by electric one. Starting point of cycle: ventricle sys. ~ QRS 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 average over cardiac cycles is taken.

32. Cardiovascular dynamics measured by force plate Data Filtering Averaging Black box (Curvatures)

33. Cardiovascular dynamics measured by force plate

34. Cardiovascular dynamics measured by force plate Advantages of „Curvatures“ • give more (and more precise) information than averaged forces / COP • every curvature contains information on each measured channel • do not depend on the position of the volunteer on the bed and on the position of the heart inside the body

35. Cardiovascular dynamics measured by force plate Question of interpretation The curvature maxima correspond 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,... The assignment was done with the help of cardiac catheterization.

36. 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

37. Human multiepochEEG „The analysis of EEG has a long history. Being used as a diagnostic tool for 70 years it still resists to be a subject of strict and objective analysis.“

38. Human multiepochEEG Experiment:

39. Human multiepochEEG Common property of evoked potentialsand cardiovascular dynamics studied process is timelocked to some event. Cardiovascular dynamics is triggered by (QRS complex of) ECG signal. Evoked potentials are triggered by the instant of stimulus application. However, just described method does not work for evoked potentials.

40. Human multiepochEEG The reason si: low SNR Noise – everything what we are not interested in, i.e. not only noise caused by imperfection of data acquisition – measured signal contains also other processes (not of interest) running inside the brain, resp. the body Cardiovascular dynamics: respiration, stomach activity… Evoked potentials: background activity of neurons Filtering + averaging: cardiovascular dynamics: OK evoked potentials: (sometimes still low SNR)

41. Human multiepochEEG Data Filtering Averaging Black box (Curvatures) Black box 2 (Curvatures, RMT) Data Black box 1 (MLE)

42. Human multiepochEEG – nonperiodic reversal Results: channels 57-60

43. Human multiepochEEG – nonperiodic reversal Results: channels 25-28

44. Human multiepochEEG – nonperiodic reversal Results

45. Human multiepochEEG – needle sticking Results

46. Conclusions • BETTER RESULTS THAN FILTERING/AVERAGING: • low number of epochs • low SNR

48. Detecting Targets in Human Body:PART II Department of physics, University of Hradec Králové Doppler Institute for mathematical physics and applied mathematics Jan Kříž Joint work with Petr Šeba, Emil Doležal Tosa Yamada Sci-Tech Flash May 30, 2007 Kochi University of Technology

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

50. Filtering Generally, filtering is some mapping of a (univariate) time series: linear, nonlinear We need to filter out „unwanted“ frequencies: multiplying by a suitable function in the frequency domain.