Biomedical Engineering - Biomedical Signal Processing and Medical Images

Notes of Biomedical signal processing

Divided by topic

1 BIOMEDICAL SIGNAL S Mainly deterministic and mainly stochastic Biological systems are always characterized by a degree of uncertainty = biological systems that are strictly deterministic or stochastic do not generally exist , instead they are mainly deterministic (as ECG and ABP) or mainly stochastic (as EEG). The procedure to process and analyse mainly deterministic and mainly stochastic signals can be learned for a specific signal and then it can be applied to any other signal or image from the same category . General characteristics > High complexity > Dynamical behaviour > Adaptive (due to physiological regulation, sympathetic and parasympathetic arousal) > High variability both inter -individuals and intra - individual > Predictable (but not in an absolute sense = its general morphology is predictable if the signal is almost periodic and mostly deterministic (as ECG), but there is always the stochastic component that isn’t predictable (stochastic signals, as EEG, are not predictable at all) > Interact ions among systems (physical, chemical, metabolic, etc.) > Signals corrupted by the presence of noise Variability and complexity The intra -individual variability is caused by non -stationarity of the process. In analysing a biomedical signal, we assume it to be stationary and ergodic (weak sense), however this is actually not the case on the long period: ➔ patient status and environmental influences can change. ➔ all biological systems are close to periodicity an d close to stationarity, but none has those characteristics in strict sense That is due to Complexity of the biological system , and specifically to the mechanisms that act: ➔ Physiological a daptability in response to a great variety of stimuli and circumstances ➔ Pathological internal autoregulation mechanisms Prior knowledge to handle biosignals To perform signal processing properly some prior knowledge is required: > Anatomic -physiological, biological, physical, and chemical knowledge > Medical expertise (clinical, physio -pathological, statistic, epidemiological...) > Variability and disturbances/noise in the signals 2 Types of biosignals (overview) Take this table as a reference, the values are not definitive, they might change according to the circumstances and the application. Notes: - ECG starts at 0.05 Hz > 0 since it doesn’t contain any continuous component, while Blood Pressure and temperature for instance they have a continuous component (DC) since they never go down to 0 (constant bias > 0) - (ECG) for some applications we will work on a smaller BW (lower high limit): ECG analysis for diagnostic purpose BW up to 150/200 Hz, while for ECG monitoring for many hours a smaller BW is considered in order to deal with lighter datasets - ABP BW_invasive > BW_noninvasive - heart and breathing rate are usually obtained by ECG processing SIGNAL FREQUENCY BAND AMPLITUDE RANGE Electrocardiogram (ECG) 0.05 – 200 Hz 10 μV (fetal) ; 0.5 -5mV (adult) Electroencephalogram (EEG) 0.1 – 60/70 Hz 5/15 – 100/200 μV Electromyogram (EMG) 10 – 200/10000 Hz Function of the muscle activity and electrode placement Arterial Blood pressure Direct measurement: dc – 60 Hz Indirect measurement: dc – 50 Hz 10 -400 mmHg 25 -400 mmHg Venous Blood Pressure Dc – 50 Hz 0-50 mmHg Heart rate 45 – 200 beats/min Breathing rate 12 – 40 breaths/min Temperature Dc - 0.1Hz 32 – 41 ° 3 Decision procedure In taking a decision in biomedicine according to a signal the following workflow must be followed: I. Perform the measurement (obtain the signal) II. Data reduction III. Signal processing and parameters computation IV. Recognition / Interpretation → decision → experience (data collection) In this step two thing can be performed: • signal classification • pattern recognition V. Action: Therapy / treatment → back to measurement (to verify the effectiveness) 4 Signal acquisition ANALOG PART 1. Signal recording and transducing (if not electric al signal per se) ( → fc ) 2. Amplification : should be done as close to the source of the signal as possible to prevent any degradation of the signal. 3. Anti -aliasing filter : to cut -off high frequencies and be sure not to have alia sing in sampling the signal 4. Notch filter (at 60 Hz in US and 50H z in EU ) (This operation can be performed both on the analogic and digital signal, it is often the case that acquisition systems h ave insi de the analogic component , due to the standard operation and the low costs, but if this is n ot the case the stopband filtering must be performed later with a digital filter ) 5. Multiplexer (in case of multiple filters) The sampling frequency of the multiplexer with N channels must be N *(max_fs_ inputs): example: ECG: max_fc ~ 120 Hz => fs = 2*fc+e = 300 Hz => fn = fs/2 = 150 Hz ABP: max_fc ~ 60 Hz => fs = 2*fc+e = 160 Hz => fn = fs/2 = 80 Hz after multiplexing the sampling frequency should be 2 * max (300, 160) Hz → ECG wins x2 since there are 2 channels : fs_multiplexer = 600 H z the ABP will be oversampled, but it is ok, since otherwise the ECG would be under sampled and we would lose information !! FILTERING = SIGNA L MORPHOLOGY DISTORTION It is important to take into consideration the signal dynamics, before applying any pre -processing: if we modify the signal’s bandwidth , we consider only some components of the original signal . 6. A sample -and -hold circuit is required at the input of the A/D converter to hold the signal at a constant value during conversion. 5 7. A/D converter, performing quantization . The output of this component will be in a digital representation encoded in L bit. example: Being the max amplitude of the signal s about • ECG ( 5 mV) , resolution needed 0.5 mV → amplifi ed (1:10 0) • ABP ( 200 m mHg) , resolution needed 1 mmHg → amplifi ed (1:1) Then using L= 10 bit we will have 2 10=1024 levels , thus using a dynamic range , much wider to avoid saturation in case o f artifacts or a nomalies, of respectively: • 1000 mmHg → q=0.9 8 mmH g • 1 V → q= 0.9 8 mV (signal ranging up to 500 mV ) !! CLIPPING EFFECT If we amplify a signal over the limits of the A/D converter , the clipping effect occurs both as positive and as negative saturation (that means excluding the upper/lower part of the signal if it exceeds the given dynamic range) . The ampli fication must take into consideration the digital dynamic range. DIGITAL PART Once the digital signal has been obtained it can be analysed and processed wi th digital tools, but also stored and shared . Possible pipeline in digital processing: 8. Filtering : to work only on the most informative part of the signal (and cut out all the non - superimposed noise) o BANDPASS [f_low , f_high] if th e signal hasn ’t a dc component o LOWPASS [f_cut] if the signal is a non -zero mean process 9. Processing: apply algorithms to extract features or other signals from the signal in time domain. examples are: - peak s de tection in ECG and HRV analysis - respira tion signal extraction from ECG - ectopic beats analysis and removal (NB: if more than 5 -10% are ectopic beats the signal is impaired 10. SPECTRAL ANALYSIS (Preliminary operations : - Check stationarity! - Detrend - resampling , if workin g with signals defined on uneven time intervals ) ➔ PSD ESTIMATION and CS ESTIMATION (among different derivatio ns or correlated signals) ➔ Features extra ction Instrumentation 6 Systems that produce per se electri cal signals (such as ECG , EMG and EEG) are recorded by means of electrodes placed either on the external surface (skin/scalp – Non -invasive techniques ) or inside the body (invasive techniques). Systems that can be observed by different ph ysical q uantities, such as Blood Pressure , require the employme nt of different sensors and then of transducers to derive the electrical signal to be digitalized. Derivations The electrodes position on the body affect s the m orphology of the signal recorde d. In particular , the relativ e position of the active electrode with respect to the reference electrode and to the source of the signal to be recorde d. Conversely, the rhythm (frequency ) of the signal remains unchanged . 7 NOISE Signals are corrupted by the presence of noise . Every biomedical signal recording comes with noise (such as powerline noise, or other physiological activities interaction or movement artifacts) → we should filter the original signal to keep only its informative part (= increase the SNR) . The noise can be : • ENDOGENOUS ( = internal to the biological organism) • EXOGENOUS (the origin is external) • Correlated with the signal (e.g., respiratory art ifacts in the ECG signal) • Uncorrelated with the signal (most often, e.g., quantization noise and other casual noises are not correlated with the signal ) The simplest signal/noise interaction model is the additive model (signal + noise): y(t) = x(t) + n(t) where y(t) is the detected signal, x(t) is the signal of interest and n(t) is the superimposed noise Reduction of the signal (S) -overlapping noise (N) → increase the signal -to-noise ratio (SNR). The aim is to have more Signal information than noise (= improve the SNR), hence we use low pass filtering, but: 1. the first case is the ideal one 2. the second case is the most common in real application , by filtering you manage to get rid of a consistent amount of noise, and significantly enhance the signal to noise ratio, losing a limited amount of signal information 3. the third case is the worst -case scenario , the superimposition between noise and signal is significant. Hence, in this case you usually accept to lose a lot of signal information to eliminate the major noise component 8 HEART The heart is the mus cle that pumps the blood throughout the circulatory syst em . The pumped blood carries oxygen and nutrients to the tissues and metabolic waste (such as carbon dioxide ) to the lungs . In humans , the heart is approximately the size of a closed fist and is located between the lungs, in the middle compartment of the chest . Cardiac excitation process The sinoatrial node is the pacemaker of the heart, is where the contraction originates. It is a small group of self -activating cells . (https://www.youtube.com/watch?v=WvvzODYqmbg ) Nodal cells initiate, synchronize, and generat e periodic action potentials → ex citation wave (whose pro pagation speeds varies along the heart to obtain a synchronized contraction ). Mean velocity in the myocard ium is overall around 0.5 m/sec . 9 1. SA node generates the action potential (about 1 m/s , employed time ≅ 80 ms) 2. excitation spreads t hrough atria → atria contraction → blood flows into ventricles 3. small delay to allow ventricles filling 4. excitation propag ates to the atrioventricular node (about 0.1 m/s ), and the n from there through his bundle branches (about 2 m/s ) 5. excitation spreads through ventricles → ventricles contra ction → blood e jection If all cells are successfully excited at the apex of the heart, the migration of the excitation wave will provide a smooth depolarization . Depolarization anomalies reflect anomali es in the ejection sequence. This propagating wave of the excitation can be modelled as a DIPOLE, described by a vector: 1. Origin in the Sinoatrial node (SA) 2. The dipole moment is a moving vector in the space defined per volume unit (= J) Therefore, the dipole moment (p) is the integration on the total volume crossed 3. In the end, the dipole moment it’s a moving vector in the space described by: - Application point - Module - Direction and orientation (azimuth and elevation) 10 ECG # Ecg is the most commonly biomedical signal used in cardiac diagnostic Electrocardiogram (ECG) is one of the main techniques for diagnosing heart disease thanks to the deduction of main electrical and mechanical defects . Acquisition • External electrodes The myocardial cells excitation can be modelled as dipole moment represented by a movi ng vector . This dipole is measured as voltage potential s ( ΔV) thanks to electrodes located on the bo dy surface. The so recorded signal shows positive deflection s when the dipole vector is directed toward the exploring electrode [+] (from the reference electrode [-]), and negative in the other case . • Derivations (or leads) An ECG lead is a graphical description of the electrical activity of the heart, and it is created by analysing several electrodes . The traditional ECG derivations are 12 divided as follows: EINTHOVEN’S TRIANGLE (VI, V II, V III) 3 leads of the limbs (Einthoven) These 3 leads provide information about the dipole evolution on the frontal plane : specifically, with on the triangle formed connecting the extremes of the limbs (right arm, left arm, left leg , the right leg is reference) . 11 Each lead is the projection of the dipole moment on the edges of the Einthoven ’s triangle ➔ the overall dipole ’s evolution in time (according to Kirchhoff’s law ) is given by the sum of the 3 derivations. GOLDBERG’S AUGMENTED LIMB LEADS (aVR, aVL, aVF) Improving the sensitivity by measuring each lead wrt t he average of the potential at the other two limbs instead of comparing it with the Cent ral Terminal . It is important to note that the three augmented leads, aVR, aVL, and aVF, are fully redundant with respect to the limb leads I, II, and III. But the augmented leads provide an easier interpretation of the signal thanks to their re ference system. the problem with these 2 is that they are measuring the signal from points that are not anatomically significant and far from the source of the e lectrical event PERICARDIAL LEADS (V1, V2, V 3, V4, V5, V6) 6 electrodes , placed in specific anatomical points, close to the heart . 12 ➔ 12 ECG LEADS The final solution is the superposition of the 3 techniques, resulting in 12 leads represented in the front al plan by vectorial representation as follows: 3 (Einthoven) + 3 (Goldberg) + 6 (Pericordial) = 12 leads Content of the signal ECG is the recording of the electrical activity related to the cardiac excitation process . It is the measurement of the excitation wave that spreads from the SA throughout the heart and that causes the myocardial contraction . Any deflection (positive or negative) from the baseline on the ECG signal determi nes an electrical event . The signal it’s almost periodic and deterministic (we know the evolution in time of the signal) and it is composed by a series of waves : P wave  atrial depolarization QRS complex  ventricular depolarization T waves  ventricular repolarization (to prepare the heart for the next contraction) 13 NORMAL ECG 1. Origin of the impulse and atrial depolarization . The impulse has origin in the SA node and the depolarization wave spreads across the atria, determining an electric vector directed downward to the left. This causes an upward deflection in the I and aVF leads (P wave). 2. Septal depolarizat ion . After a brief delay in the AV node, the impulse goes through the His bundle and through the branches of the bundle. Thus, it goes through the interventricular septum causing the myocardial depolarization with an electric vector directed downward and to right. This determines a slight negative deflection (downward directed) in the I lead (Q wave) and a positive deflection in the aVF lead (R wave) 3. Apical and early ventricular depolarization. The impulse continues along the conduction system, causing the depolarization of the apical ventricular myocardium with the electric vector downward directed and to the left. This determines a wide positive deflection (R wave) in the I lead that extends to the aVF lead. 14 4. Late vent ricular depolarization . When the depolarization continues in the ventricles, the vector moves upward and to the left, thus upward extending the R wave in the I lead and causing a negative deflection (S wave) in the aVF lead. 5. Repolarization When the heart is fully depolarized, from a brief time there is no electric activity (ST segment). Thus, the repolarization starts: is directed from the endocardium to the epicardium and produces a downward and to the left directed electric vector. This causes a positive deflection in the I and aVF leads (T waves). 6. After this, a time period in which there is no electric activity follows and the ECG tracing stays on the baseline until the next impulse has its origin in the SA node . Diagnostic s Any deviation from the typical ECG observed in the recorded electric depolarization signal (both in terms of morpholog y and sinus rhythm) is analysed and classified as a certain cardiac disorder . ➔ RHYTHM In physiological conditions , ANS ) we are supposed to have about 100 000 beats per day (roughly 65 bpm). 15 However, even under physiological control we can cave HR oscillations (slower/faster heartbeat ) according to the activity we perform along the day , due to the ANS arousals :  Sympathetic (increasing the HR, prevalent during daily activity)  Parasympathetic (slowing the Heartbeat, prevalent during sleep) BUT excessive or long -lasting changes in the r hythm or ver y irregular rhythm is an alert that something is wrong . NB: slight beat -to-beat variations are always present , but they are considered part of the heart rate variability (HRV) if they are limited to ±10% of the mean instantaneous cardiac frequency (HR ). Sinus Bradicardia : The impulses have their origin in the SA node with low frequency (< 60 bpm) Sinus Tachycardia: The impulses have their origin in the SA node with high frequency (> 100bpm) Sinus Arrhythmia: The impulses have their origin in the SA node with variable frequency 16 • ECTOPI C BEATS An ectopic beat is a disturbance of the romal cardiac rhyt hm caused by an an omalous electrical activity of the myc ardium . They are us ually caused by an increase of excita bility of the S A no de . An ectopic beat can be further classified according to where the prem ature contraction occurs : > Premature Ventricular Contraction (PV C) (or Ventricular extrasystole ) This PVC is often followed by a compensating longer than normal delay, imposed by the physiological control system. > Premature Atrial Contraction (PAC) Atrial non sinus rhythm (coronary sinus) : The impulses origin is not the SA node, but a poin t in the atria. This usually results in variations in the morphology of the P wave . Consequently, both the PP , the PR and the RR interval (so HR) are affect ed. Ventricular fibrillation: Ventricular chaotic depolarizat ion . Pacemaker rhythm: A transvenous pacemaker produces the beat in the right ventricle, but not at the supraventricular level and so the QRS complex is wide. Actually, we are currently provided by pacemakers that intervene only when it is detected that a heartbeat has been mis sed. 17 ➔ MORPHOLOGY Myocardial ischemia Ischemia happens when the provision of O2 to the myocardium is not sufficient in comparison with its requirements (can vary according to the health condition of the subject). In the most severe cases, myocardial ischaemia consists of a sudden reduction in the flow of oxygenated blood to the myocardium. This fatigues the myocardium, leading it to a state of distress. This can have significant consequences for the heart itself, which risks losing efficiency in its function as the body's pump. Effects on the ECG wave: • ST segment elev atio n NB: after some minutes i f the ischemia is not very severe it goes back to norm al. Acute Myocardial ischemia → Necrosis → Infarction We speak of a cute myocardial ischaemia when the condition is sudden but particularly severe and prolonged , so that the myocardium goes into necrosis . In such cases, it can degenerate into myocardial infarction. In case of infarction the slowing in the conduction at the border of the ischemic area allows a circular pathway of the impulse and a re -entry phenomenon with rapid repetitive depolarization . 18 Effects on the ECG wave: • HR > 120 bpm (Accelerated idioventricular rhythm (AIVR) ) • T and Q depression • Chaotic rhythm: Wide, rapid, and bizarre QRS complexes. To sum up. .. 19 Noise disturban ces The ECG can present multiple disturbances superimposed to the real signal : • baseline oscillation is physiological and is due to respiration • Very fast oscillations can be either caused by electrical activity from other muscle s or due to the powerline interference Signal analysis and processing 1. Signal acquisition and noise reduction ✓ Ba ndwidth ✓ Antialiasing filter : 200 /250 Hz (depending on the purpose of acquisition and the length of the signal ) ✓ Sampling frequency : 300 -500 Hz ✓ Quantization ~ 8-12 bits dynamic range: from 0. 5 mV to 5mV in adults required resolution : about 0.0 5 mV ✓ Notch filter ( at 50 Hz in EU or 60 Hz in U S) ✓ Pass ba nd: 0.05 Hz – 120 /200 Hz  baseline oscillation rem oval (if respiration is not of interest )  muscular artifacts removal 0.05 – 200 Hz → Diagnostic ECG 0.05 – 100 Hz → Holter ECG (24h monit oring ) 0.05 – 50 Hz → Monitoring ECG 20/30 – 0.5/1 kHz Functional physiological study or high -resolution ECG 20 2. Waves and fiducial marks identification Recognition of the QRS complex , P waves and T waves by means of algorithms. PAN -TOMPKINS ALGORITHM i. BANDPASS → QRS complex isolation band -pass filter (5-15 Hz) to isolate the interval of frequencies associated to the QRS com plex (and eventually removing baseline drift and high frequency noise if not done before). ii. DERIVATIVE FILTER → compute QRS slope iii. SQUARED RECTIFICATION → signal > 0 the filtered signal is squared point -by -point to make all data points positive and to enhance the dominant peaks (QRSs) . iv. MOVING AVERAGE → R peaks enhancement a moving average filter (low pass ) is applied to get rid of the noise , enhance only relevant peaks , an d provide information about t he duration of the QRS complex . v. FIDUCI AL MARKS IDENTIFICATION → possi ble QRS peaks identification 21 peaks are identif ied (on the low pass filtered signal ) as the points where the slope of the signal changes direction . After a detected peak a lock out time is set: no peaks can be detected within intervals < 200 ms due to p hysiological refractory period. vi. ADAPTIVE THRESHOLDING → QRS identification each identified peak is compare d to an a daptive threshold to decide if the fiduc ial mark corresponds to a QRS complex (>thr) or not ( BW_noninvasive what means that the invasive measurement provides a richer signal. NB: external measurements are known to slightly overestimate and underestimate respectively the diastolic and the systolic ABP (slightly reduced range in ampli tude) Non -standard methods: wearable sensors → ABP evaluation out of the medical facility Measurements performed by using electrodes integrated in patches that can be placed on the skin in a n easy manner (wearable sensors). ➔ Similar results to the non -invasive method , but with wave -shape slightly shifted in ampli tude or slightly different morphology (according to the body district where the patch is placed). (Black signal is the reference measurement with traditional medical instrumentation in the same place). 23 Content The evolution of the pressure on the artery , m easured in mmHg over time . Systole = ventricle contractio n and blood ejection Diastole = Aortic discharge of blood load ➔ Maximum = systolic abp ➔ Minimum = diastolic abp (always > 0) ➔ Dicrotic notch = opening and closing of the valve s ABP EVOLUTION DURING THE CARDIAC CYCLE: 1. Valves between the atrium and ventricles on both sides close → S1 (Tricuspid valve right A-V and Mitral valve left A -V) 2. Ventricular depolarization → left ventricular pressure increases 3. aor tic valve opens → blood ejection → aortic pressure increases and ventricular volume decreases 4. aor tic valve closes (sudden) → small in aortic pressure (followed by a gradual decrease ) and reverberation resulting in sound (S2 ) 5. mitral valve opens (S3) → blood flowing inside the ventricles → ventricle volume increases 6. Atria contraction → S4 The time between S1 and S2 is when the ventricles contract -> SYSTOLE The time between S2 and the next S1 is when the ventricles relax and are filled with blood -> DIASTOLE 24 Bandwi dth The bandwidth of the signal depends on the method used to obtain it: • Direct measurement: dc – 60 Hz • Indirect measurement: dc – 50 Hz but in any case, the constant (f=0) component is releva nt since ABP always higher than 0. Fiducial Points Fiducial points on the ABP signal are Systolic (maximum ) and Diastolic (minimum ) pressure values. From them we can obtain Systogram and Diastogram , respectively. 25 Autonomic Regulation Autonomic Nervous System (ANS) plays an important role on the HR control, thus on the HRV. It is divided into two branches: • Parasympathetic (vagal) → inhibitory function that decreases these cardiovascular activities (decreas e in frequency, contractility, conductivity, and excitability) • Orthosympathetic (sympathetic ) → excitation function over the cardiovascular system, increasing HR and blood pressure. The vag al nerve collects inputs from throughout the body and affects the cardiac rhythm acting with those 2 me chanism s on the Sinoatrial node : Parasympathetic activity: ↓ HR (RR interval in time increase) ↓ CONTRACTILITY ↓ CONDUCTIVITY ↓ EXCITABILITY Sympathetic activity: ↑ HR (RR interval in time increase) ↑ CONTRACTILITY ↑ CONDUCTIVITY ↑ EXCITABILITY 26 Baroreflex Baroreceptors are mechanoreceptors located in the carotid sinus and in the aortic arch. Their function is to sense pressure changes by responding to changes in the tension of the arterial wall. The baroreflex mechanism is a fast response to changes in blood pressure. Baroreflex Sensitivity (BRS) The Baro reflex Sen sitivity (BRS, often indicated with α) (also known as baroreflex gain |G|) is an index measuring the responsiveness of the ANS in the HR – Blood Pressure regulati on in a subject. It is defined as the variation in time of the RR interval (= adjustment of the HR) with respect to the variation in blo od pressure . Indeed, according to the baroreflex dynamics ➔ if blood pressure increases , then HR decrease s = the RR increases Thus , if we model the baroreflex as a black -box system, we can define the BRS as the gain of the system having as input th e variation in bl ood pressure and as ou tput the variation in the RR interval : ∆������� − − − [ ������ ]− −→ ∆�� ������ = ∆�� ∆������� [ �� ���� ] α = h ow much the system increases the RR interval having a unit ary increase in blood pressure NB: usually the Arterial Blood Pressure is used as blood pressure measure ment , and specifically the systolic (SAP) value is taken as re ference to me asure the variance in blood pressure. This choice is reasonable since the Systolic ABP is actually what the baroreceptor s are more sensible to (the majority of baroreceptor s are in the aorta right after the a ortic valve and the highest pressure the y are subjected to is the systolic one during ejection) 27 Physiological regulation • Normal HR (center) BP is normal → the Sinus impulse is regular at normal frequency the vagal activity is normal → vessels contrac tility is normal • Increased HR (right) BP increases (due to the faster ejection) → baroreceptors trigger → CNS increases the vagal activity and decreases the sympathetic one to compe nsat e → the HR decreases (thanks to the action of the vagal nerv e on the SA node) and the contractili ty of the vessels is decreased • Decreased HR (left) BP drops (due to the lower perfusion ) → to maintain cardiac output and perfusio n of noble organs the sympathetic activity is increased and the vagal one is reduced → the HR and the vasoconstriction increas e How to measure the BRS (Pharmacological method – quite deprecated) Baroreceptive gain is usually measured via the phenylephri ne test (generally performed as a provocative test to artifici ally alter the physiologic sympatho -vagal balance are required ). Phenylephrine is a vasoconstrictor drug which causes a blood pressure increase . After this a certain number of beats is collected, they are plotted on graph (pression – RR) The gain is the slope of the regression line (Frequency domain methods – non -invasive ) (without perturbing the hemodynamic characteristics of the system ) Estimate the BRS by analysing spontaneous oscillations in systolic blood pressure and heart period time series → BRS is be computed from the Tachogram an d Systogram spectral density . Two approaches are possib le: • Spectral Index method : ������ = √ �������� ������������������� where ��� = ������� ������������� (�� ) ��� �������������� = ������� ������������� (��������) • Transfer Function method : ������ = �������� ,������������� ������������������� wher e ���,������������� = �������������� (�� ,��� ) ��� �������������� = ������� �������������(��������) exploiting the TF estimation rule from cross -spect ral analysis 28 PIPEL INE: 1. Obtain the Tachogram and the Systogram from your data In matlab to get both RR an d SAP from the ABP signal: Ons = wabp(abp) r = abpfeature(abp,Ons) 2. Detrend and interpolate to obtain the interval functions 3. Estimate their PSD 4. FIRST METHOD: Estimate the baroreflex sensitivity by computing the α index from PSD of HP SAP, as the square root of their ratio 5. SECOND METHOD: Estimate their transfer function and quadratic coherence Estimate the baroreflex sensitivity as the average of all TF modulus values NB: in both methods, there are 2 possible approaches: • considering the spectra only in the LF range • considering the spectra only in the LF range and only where cohe rence > 0.5 REMARK: LF = [0.04, 0.15] These methods envisage the BRS estimation as i f the system was in open loop (no feedback from ΔRR to ΔP). A more sophisticated model allows the closed -loop (considering feedback) computation of α α=|Hts| in closed loop s = systolic blood pressure t= tachogram Hst = non -neural effects of t on s Hts = baroreceptor and neural mechanisms Nt and Ns = disturbances Hyper tensive subjects: The baroreceptive gain is lower for subjects with hypertension than for normal subjects during the day, while during the night it is almost the same 29 TILT TEST It is a diagnostic procedure that alters the physiologic sympatho -va gal balance , by expos ing the patient to orthostatic stress. It is a procedure widely employed in patients in whom a neurologically mediated syncope is suspected. I. REST At first, the patient lays horizontally II. TILT Suddenly , the bad is put in vertical position, and so does the patient, but in a passive way (the patient reaches the upright posture without any active contribution) . Gravity forces a red istribution of the bloo d volume towards the lower limb s RESULTS: The upright posture obtaine d passively elicits an or thostatic st ress ➔ Physiological cardiovascular reflexes : to maintain cardiac output and perfusio n of noble organs (the brain!), the orthostatic stress is compensated by:  increase in heart rate (HR) = lower RR intervals  increase of vessels constriction ➔ higher LF/HF On the spectral density this results a s an increase of the LF component (~ symp athetic ar ousal ). The LF component increases significantly and becomes predominant (almost 3 times the HF) 30 HRV Heart rate variability signal (HRV) is a complex signal affected by several factors that act at different time scales and contains information about the nervous mechanisms controlling the cardiovascular system. Indeed, it is affected by : • Physiological autoregulation mech anisms (= sympatho -vagal balance ) which act in the short period can be evaluated by means of linear approaches , such as Fourier analysis . • Other factors ( humoral factors, metabolic activity, and others ) which have slower contributions ( act on the long period ) must be analysed by means of non -linear methods , such as the entropy measur ements . Influence of physiological control mechanism on the HRV HRV analysis provides information on system alterations diagnosis of cardiological pathologies not only caused by physi cal damages eventually before the physical damage of the organ occurs early diagnostic / dynamical disease s The HRV signals contain information only on the cardiac r hythm , n ot about ECG morphology in time . HRV signals (linear approaches) Time series that correlate different signals (ECG, ABP and Respiration) synchronizing them wrt to the heart beats , are useful to compare the variance in the cardiac system according to specific conditions, especially related to the analysis physiological cardiovascular reflexes mediated by the ANS (sympatho -vagal balance ). TACHOGRAM RR intervals are plotted versus the index of the corresponding heartbeat. - x-axis: number of beats equi -spaced (NOT EVENLY SPACED IN TIME) (as indi ces ) - y-axis: RR interval length in time > to obtain the x -axis reference in time we can multiply each beat for the length in time : �(������)= ��� (�(������)) ��� ��� ℎ ������ = 0,..,������ ����� > from ECG an algorithm to extract the fiducial point (R peak in the QRS complex) is required 31 SYST OGRAM and DIASTOGRAM These two signals are introduced by synchronizing the ECG with the ABP time evolution. For each identified beat (measured by RR duration: RR i) we identify: - Systolic Blood Pressure (SBP i) - Diastolic Blood Pressure (DBP i) during the i -th beat (RR i). Then we report on a graph that has on: - x-axis: the beats (as index i) - y-axis: the ABP value in mmHg and we obtain respectively the systogram and the diastogram: RESPIROGRAM It depicts the changes beat to beat of the respiration frequency. It reports on the x -axis the i -th beat index and on the y -axis the respiration frequency computed beat to beat on the downsampled (@R peaks) respiratory signal. The y -axis is often in A.U. s cale (Arbitrary Units) since what we obtain with this indirect measurement of the respiratory frequency isn’t something that can quantify a real measurement, it only depicts the variance in respiration frequency . 32 Acquisition Single channel – only from ECG 1. ECG recording (a) 2. R peaks detection (by means of classical algorithms, such as Pan -Tompinks) 3. RR interval computation (computation of the time between two successive R peaks expressed in milliseconds) ➔ RR intervals become the samples of a new signal ➔ by plotting the RR intervals on the time at which the heartbeat occurs (= reporting the same time information on both axis), we obtain a new time series: RR interval time series (b) ➔ The problem here is that samples are not equally spaced on the x -axis. Solution 1: 4. Interpolation of the RR series 5. re-sampling @ fs > 2* HR to be compliant with Nyquist theorem and to be sure to not eliminate any information (in case of humans, where HR is about 1.5 Hz, fs about 3 Hz might be a good choice) ➔ Interval function (c) Solution 2: 4. Plot the RR series versus the index of the corresponding heartbeat (not considering it in time, but only as a sequence on the respective index) ➔ Tachogram (c) Optio n 3: Plot the RR interval series in time on the x -axis (as in b) and a unitary value on the y -axis (= Series of Dirac Delta functions marking beats in time, so placed in correspondence of R peaks in time) → Dirac delta function (d) Could be useful for spe cific application, but we are NOT considering this. 33 Multiple channel – ECG + ABP (+ Respiration) Systogram, Diastogram and Respirogram can be physically obtained by using a multiple channel system, recording synchronously ECG, ABP and eventually the Respir atory signal. Once the multiple channel signal has been obtained, the following algorithm is used: 1. analyse the ECG an d find the R peaks 2. compute the RR intervals : RR i ➔ TACHOGRAM : plot the RR values over the i -th index 3. for each identified R peak, identify the corresponding sample on the ABP signal: ABP i 4. starting from ABP i open a time window and analyse the ABP sig nal looking for the maximum (SBP i) and the minimum (DBP i) (**) ➔ SYSTOGRAM and DIASTOGRAM : plot SBP i and DBP i with respect to i -th index to obtain respectively 5. then you move to the third channel, and you select on the Respira tory signal only the samples corresponding to the R peak (downsampling the respiratory signal in correspondence to R peaks) 6. from the downsampled signal extract the respiration frequency beat to beat ➔ RESPIROGRAM : report the respiration frequency beat to beat over the i -th beats index to (**) the ABP signal has always Dicrotic notch, the algorithm used to find the max and min must consider and handle this aspect to find only the systolic and diastolic values. To deal with this probl em we might consider the a priori knowledge we have about ABP morphology. NB: it is important to have the same sampling frequency (the highest required) for all channels to allow this comparison, in this case would be the ECG’s one. [ Respiration (< 20 Hz) ; ABP ( < 50/60 Hz) ; ECG (< 200 Hz) ] 34 Alternative plots HISTOGRAM Consider the Relative frequency of occurrence of a specific RR interval duration per second. - x-axis : RR interval duration - y-axis : number of beats h aving that RR interval duration (reported on the x -axis) NB: the y axis is often normalized on the total duration of the observation to have comparable results on different realizations (relative frequenc y over seconds) SCATTERGRAM Consider the variation of the RR interval duration between consequent beats . - x-axis : RR interval (i) duration - y-axis : RR interval (i+1) duration ➔ Isolat ed points represent extra systolic beats. ➔ the more the HRV is spread al ong the bisector (high variability) the more the ANS seems to work properly in adjusting the RR according to the needs. ➔ Conversely, the h igher the regularity in the plot (linear increase or almost constant RR intervals) the higher the risk of heart failure. 35 If points are mostly located close to the origin, then the action of parasympathetic system is prevalent, since the parasympathetic action slows the Heartbeat, thus it increases the RR interval between consequent beats. It they are spread out sympathetic is more active. Real a pplications HRV in 24h – Normal vs Transplanted 24h Holter recording = record the ECG in a subject over 24h (the number of R -R intervals is near 100k ) • normal subject In a normal subject in a time window of about 24h we usually can recognize two main HRV components: - Low bpm  longer RR intervals (RED section)  associated to sleeping - High bpm  shorter RR intervals (BLUE segment)  associated to awake and active state • transplanted subject A transplanted heart is not innervated , thus they show less variabil ity (lower HRV due to the abse nce of the physiological control mech anisms) Indeed , in frequency it results a single main peak at shorte r RR intervals . 36 NB: the RR intervals in a normal subject range from 600 to 1200 ms , while in a transplanted subject the range is from 450 to 800 (shif t towards shorter intervals and less variability ) RESULTS: 37 Spectral analysis Analysis of the spectral co mponents of the HRV, how the RR interval duration changes along time. To perform the spectra l analysis o f the HR evolution the RR time series must be defined on even ly spaced in time samples, thus we must work with interval functions . Then to estimate t he PSD , parametric approaches are usually employed . Main ly because the number of peaks of interest is known (→ order can be easily estimated ) + they provide smoother results (more interpretable ) (see below the comparison) . The HRV r esults to have 3 main harmonic components: • VLF range (0 -0.04 Hz) represents slow components, circadian rhythms, non -linear contributions • LF range (0.04 -0.15 Hz) represents the activity of the sympathetic syste m and vasomotion • HF range (0.15 -0.4 Hz) represents the vagal system control and the respiration activity NB: x -axis i n normalized frequency – y-axis can be either in a.u. or in sec 2/Hz 38 (**) Parametric vs non -parametric spectral analysis Given this RR serie s, the PSD have been estimated using both approaches : Parametric Non -parametric order 9 (3 harmonic compone nts) Whiteness Test over Prediction Error (PEWT) passed Optimal Order Test (OOT) passed Welch method Hann window → less clear LF / HF ratio It is a measurement of the sympatho -vagal balance (the closer to 1 the higher the balance). It is common an increase in the LF component , thus LF/HF > 1, during: tilt test, upright position, and moderate exercise and mental stress . An increase in the HF component is caused by : controlled breathing, cold facial stimulation, and rotational movement stimulation. Based on literature data, it is evident that LF values increase, and HF values decrease during sympathetic stimulation and the opposite phenomenon occurs during vagal stimulation. Cross -spectral analysis – HR, ABP and Respiratory variability Useful to analyse physiological cardiovascular reflexes mediated by the ANS (sympatho -vagal balance ). To perform cross -spectral analysis over H eart Rate Variability , Blood Pressure Vari ability and Respiratory Variability, the Interval functions obtained respectively resampling the Tachogram , the Systogram/Diastogram (**) and the Respirogram can be used. Necessary bandwidt h is usually 10 harmonics more than the fundamental frequency: in case of a 120 bpm heart rate (=2 Hz), the bandwidth is 20Hz. In applications such as dP/dt measurement (to study contractility of myocardium), at least 20 harmonics are required. NB: it is important to re sample the 3 at the same frequency to have results referr ing to the same time scale . 39 (**) Tachogram vs Systogram - CTS ✓ it sho ws more defined peaks and clearer coherence Tachogram vs Dia stogram - CTD • NORMAL SUBJECTS Estimating the PSD on the Tachogram vs Systogram interval function s on a healthy subject the expected result is the following: • RR intervals and ABP systolic and diastolic values present similar variability: they both have two main components in frequency LF and HF, respectively associated to sympathetic and vagal action. While VLF are due to hormonal effects and are different in the two signals. • The respirat ion signal presents a single frequency component in correspondence with the HF (it is the biological signal which gets closest to an ideal sinusoid ) ➔ proof that respiration influences the cardiac rhythm at HF ➔ Respiratory sinus arrhythmia: duri ng inspiration heart rate increases, during expiration it decreases Example of spectral analysis during exercise (sympathetic action): Analysing the RR time series on a normal subject under stress test (cycloergometer) it is possible to highl ight an increase of the HR and a decrease in HRV as the test ’s power demand increases ➔ RR intervals become shorter and more regular along the test. 40 Downward trend is evident in the tachogram (RR duration decreases  HR increases) as load increases . As load increases the LF/HF ratio increases (sympathetic action is prevalent ) and VLF (constant downward trend) and decrease in amplitude case specifics: - RR time series over 1536 beats - cycloer gometer test, with increasin g load ( (6 conditions expressed in Watt on the right axis ) (a) Tachogram (b) 6 spectra (shown in a pseudo -tridimensionality) calculated via AR identification on 6 subsets of 256 samples (6 consecutive recordings) each one corresponding to a different load condition. PATHOLOGI C SUBJECTS 41 Entropy (non -linear approaches ) Recent re sults show the heart rate variability signal (HRV) does not only contain linear harmonic contributions (traditionally identified through spectral analysis techniques) but it possesses a fractal like geometry. Fractal = repetitions that are not harmonic rhythms, but that are unpredictable (not periodic, randomness) PATHOLOGIC BREAKDOWN of FRAC TAL DYNAMICS In healthy conditions the ANS physiological control works properl y an d the fractal like geometry of the Heart Rate is physiological. (Top) But, when some cardiac pathologies arise, the frac tal dynamic is affe cted . Ultimately , pathologies can either lead to : • hig hly periodic HR (as in case of heart failure) (Down -left) • uncorrelated r andomness (as in case of Atrial fibrillation) (Down -right) To analyse those components non -linear approaches , as entropy related methods can be used. MULTISC ALE ENTROPY ( INITIAL SLOPE ) In particular , the Multiscale Entropy measures the self -similarity of a signal at differen t scale factors , and it has been demonstrated that this self -similarit y is af fected by pathological con ditions ( especially for low scale factors). Using the Muti Scale Entropy to discriminate among diff erent groups : ➔ the MSE values for the initial factors ( the initial slope ) was particularly informative . 42 Even in fetuses , it was possib le to find some ApEn parameters to estimate the entropy at different scale factors to di scriminate among pathologic fetuses to normal ones: • Approximate Entropy to inspect HRV at night vs day 43 24 h HRV recording ApEn parameters : Here we have results opposite of what we expect: it results that during day the heartbeat is more regular , while the signal results more complex (less regular) at night . 44 FETAL ECG By recording the ECG signal on a pregnant woman, we end up recording the heartbeat of both the mom and the baby  Abdominal ECG lead v(t) with maternal and fetal ECG superimposed . Depending on the lead we observe the baby’s one can be more or less evident . The fetal ECG differs fr om the maternal ECG, due to : lower amplitude, higher HR (about 2 -2.4 Hz) , usually no respiratory component (no HF component on the HRV spectral analysis ) NB: maternal and fetal ECG are electrically uncorrelated. (a) the arrow indicates a case of superimposition of maternal and fetal QRS complexes (b) MQRS identification: 1. digital filtering the signal in the maternal ECG bandwidth by means of Weber -Cappellini low -pass FIR (cut -off at 20Hz) 2. successive averaging on the signal synchronized on the maxima of the QRS complexes (c) FQRS identification: subtracting the maternal ECG from the original signal, the fetal ECG can be recognized 45 HRV Maternal (a) and fetal (b) RR time series (Interval functions) for a total period of 5 minutes (after the low pass filtering ). The mean value M an d the variance σ2 of the two signals are reported. Fetuses show : - lower H R variability - higher HR (on avg) Maternal PSD Fetal PSD the fetal PSD presents no significant components at HF since the fetus usually doesn’t breathe inside the amniotic sac. Cross -Spectrum (amplitude) Phase and Coherence as usually phase shift is valid only where coherence is > 0.5 46 Fetal states identification (HRV based) Two main fetal states can be identified: Quite Respiratory movements LF is predominant - f = 0.35 Hz  21 bmp Which are movements emulating respiration that the fetus does to get used to breathing (not to actually breat he, since inside the amniotic sac it cannot breathe).  Compressed spectral array of the breath signal recorded from fetus sheep. A phase of respiration (in the range of 0,35 Hz, equivalent to 20 breaths per minute) can be recognized, followed by a phase of non -breathing. These are respiratory movements that f etus performs to “get used” to breathing, even though the baby can’t breathe inside the amniotic sac. 47 RESPIRATORY SIGNAL It is a regular signal ( the biomedical si gnal close st to a sinusoid) with a slow oscillation. As all signals it comes with noise, so as shown by the figure it must be filtered. Direct estimation (multiple possible body districts ) - nasal cavity by using fiber -optic respiratory sensors or temperature transducer - thorax by using belts containing respiratory piezoelectric transducers - abdomen by using fiber -optic respiratory sensors Indirect estimation REMARK: respiration and cardiac cycle are strictly connected , and the ECG presents a ver y slow baseline oscillation related with respiration . Estimation o f the respiratory activity from the ECG signal before high -pass filtering , by means of R peaks inter polation . ➔ this technique provides only information about frequency of respiration , no information about the respiratory signal morphology. 48 CENTRAL NERVOUS SYSTEM . CNS composed by: - Brainstem - Cerebellum - Brain (superior functions) Brainstem Phylogenetically the oldest part of the CNS. Its functions are: 1. Connecting the spine with the brain and cerebellum 2. Integrating visceral functions 3. Integrating centre of the motor reflexe Sensorial stimuli are catch from the periphery and processed at central level, by the CNS . Conversely, m otor inputs go from the CNS to the periphery 49 EEG The E EG signal is a stochastic (pseudorandom) stationary signal (if considered in a short -duration time window) → it’s impossible to predict the future of the signal knowing its past. NB: in the brain this apparent disorder is related to the proper function of the brain. If we have an ordered signal, we are in presence of pathology (e.g. epileptic seizure). We use the regularity or not of the signal to study the nervous system, monitoring of sleep stages, biofeedback and control, and diagnosis of diseases such as epilepsy. Acquisition The standard in ele ctrode positioning for the measurement of EEG signals is the 10 -20 system, in which there are 21 leads . The name 10 - 20 indicates the electrodes position : • taking as reference nasion (top of the nose) and the inion (base of the skull in the midline at the back of the head) and defining their connections from the midline to bot h sides of the scalp • electrodes are placed at 10,20,20,20,20, 10 % of the distance to the closest reference point NB: each derivati on is independent from the others. We can estimate the PS for each derivation. • The anterior -posterior measures are based on the distance between nasion and inion along the median line which passes through the vertex • Measures on the coronal plane are based on the distance between the right and left pre -auricular points along the line which passes through the vertex The leads can be bipolar or unipolar: bipolar → measure the potential difference between two electrodes, unipolar → that one between one electrode and a reference (in general the central one or the one set inside the foramen magnum) 50 Content The EEG signal is generated by the electrical activity of the CNS , recorded via some electrodes placed around the brain/head (cerebral cortex) (either on the scalp or placed directly inside the brain, in invasive procedures). The Reticular Activating System (RAS) is a network of interconnected neurons located in the brain stem that generates radially oriented electric dipoles. The EEG signal is a result of a synchronized and/or desynchronized activity of the cortical and subco rtical cells of the RAS in correspondence of the electrode → an ensemble of excitatory or inhibitory post -synaptic potentials . It is a mainly stochastic signal . However, it contains some oscillatory patterns that can be r ecognized : NB: each brain wave is defined in a specific characteristic bandwidth 51 Consciousness EEG activity is dependent on the level of consciousness : SLEEP STAGES The EEG changes significantly during different sleep stages and it has been proven that the EEG evolution during the sleep stages is very informative with respect to the evaluation of patie nt with respect to many neural pathologies . We are not completely sure this is a correct/complete categorization of sleep stages, but 6 stages have been identified : • Awake : alpha and beta waves , desynchronized (= small amplitude) • Stage 1 : theta, more synchronous • Stage 2 : irregular with periods of theta activity, sleep spindles, and K complexes • Stage 3 : high amplitude delta (20 -50%) – slow wave sleep • Stage 4 : more than 50% delta – slow wave sleep, synchronized • REM : beta and theta waves, desynchronized (= small amplitude) 52 Signal analysis and processing ACQUISITION and PRE - PROCESSING > bandwidth : 0.1 – 60/70 Hz > Anti -Aliasing Analog filter: cut -off @ 100 -200 H z > Sampling frequency: 300 -400 Hz (often 500 Hz to be sure) > Dynamic range: ( -100, 100) μV > Quantization: a precision of 8 -12 bits > often many derivations together → multiplexing ANALYSIS EEG is a pseudorandom sign al: ➔ assumed to be generated by - a stationary (if a small enough time window is considered, and with an appropriate confidence interval) - and Gaussian stochastic process ➔ processed with statistical methods rather than with deterministic ones Statistical methods • Deviation from the Gaussian hypothesis (using all statistical mome nts, included kurtosis and skewness ) • Normality Test ( χ2 or Kolmogorov -Smirnov) • Stationarity and ergodicity Time -domain • auto - and cross correlation (ACF and CCF) -> EEG are usually acquired simultaneously over multiple channels • zero -crossing -> instants at which the EEG and its derivatives cross the x axis • slope descriptors • waveform recognition -> pattern recognition (te mplate matching) by means of cross correlation → Pattern recognition of spike -and -wave complexes, useful for identification of epileptic behaviour , is carried out by analysing the cross -correlation with the expected pattern, the time relationship between the zero -crossings of the signal and of its first and second derivative Frequency domain • Spectral analysis (Fourier, cross -spectrum etc) • Brainwaves discrim ination by means of band selective filters in EEG bands (δ, θ, α, β) 53 Diagnostics EEG WAVES can be classified in: • Spontaneous Non -Paroxysmal (as those non induced by specific stimuli and with non -statistically significant changes in tim e) • Spontaneous (as those non induced by specific stimuli , but presenting spikes and recognizable complexes) • Evoked (as those waveforms voluntarily induced by specific st imuli) Paroxysmal : (in medicine ) a sudden violent event , (as of a disease) a fit, attack, or sudden increase or recurrence of symptoms By analysing the EEG signal many things can be inferred : • Spectral density reflects the energy distribution among brain characteristic bands (brainwave s intensity/presence) . Thus, the spect ral analysis of the EEG can provide information about:  level of consc iousness of the subject (as in anaesthesia or during sleep )  level of concentration/focalization (as in mental tasks)  sleep quality /patholo gies • Cross -spectral density among different derivation can provide information about:  brain area synchronization/correlation  functional activity  Lateralization of the rhythms (asymmetry of right and left hemispheres) EPILEPSY DIAGNOSTICS For epilepsy diagnosis, pattern recognition of spike -and -wave is used over an EEG signal. 54 It is performed by means of the time relations between zero -crossing for - the signal itself - its first - its second derivatives. ➔ The results are then plot together. This a pproach is used instead of the frequency one. The autocorrelogram , built from the autocorrelation function, highlights α activity over the EEG in occipital and parietal lobes. MONITORING AN AEST HESIA LEVELS EEG reflects brain activity and neurons synchronization and is correlated with consciou sness levels of the subject. Thus, it can be used to monitor the de pth of the induced sleep during surgery. Indeed, an aesthesia levels are defined on a scale of 7 values, going from the awake state to the deep anesthesia . These states have decreasing consiousness results on an EEg wave that has: • higher amplitude • lower frequency 55 BRAIN -COMPUTER INTERFACE (BCI) 56 Evoked Potentials Evoked potentials are generated after the stimulation of a sensory organ (sens