Abstract— Biomedical Signal and Image Processing (BSIP) constitutes a major ...
Measurements”, where advanced methods for biomedical signal and system ...
Biomedical Signal-Image Processing and Modelling Edited and presented by Sergio Cerutti1 with the contribution of: Giuseppe Baselli1, Anna Maria Bianchi1, Enrico Caiani1, Davide Contini2, Rinaldo Cubeddu2, Fabio Dercole3, Luca Di Rienzo4, Diego Liberati5, Luca Mainardi1, Paolo Ravazzani6, Sergio Rinaldi3, Maria Gabriella Signorini1, Alessandro Torricelli2 1) Dipartimento di Bioingegneria, Politecnico di Milano 2) Dipartimento di Fisica, Politecnico di Milano 3) Dipartimento di Elettronica e Informazione, Politecnico di Milano 4) Dipartimento di Elettrotecnica, Politecnico di Milano 5) CNR Consiglio Nazionale delle Ricerche, Istituto di Elettronica e di Ingegneria dell’Informazione e delle Telecomunicazioni e Istituto Nazionale di Fisica Nucleare, Milano 6) CNR Consiglio Nazionale delle Ricerche, Istituto di Ingegneria Biomedica, Milano Abstract— Biomedical Signal and Image Processing (BSIP) constitutes a major field of interest for both educational aspects and in research environment in Biomedical Engineering (BME). In fact, the physiological knowledge improvement in a wide variety of innovative research, as well as the implementation in many clinical procedures, make use extensively of these concepts in more or less sophisticated medical applications. In this paper, the important links between BSIP and physiological modelling and their important derived synergies will be particularly stressed. At this purpose, examples will be provided in the areas of cardiovascular system studying, as well as in neurosciences and in the field of functional imaging, by using different modalities, including time-resolved functional near infrared spectroscopy (fNIRS). Along this direction, the integration operation of the detected information between multiple signals, organs, modalities and across multiple scales (from gene/protein levels up to cell and organ levels) seems to be extremely promising. Further, advanced methods in the area of information treatment, like time-frequency, time-variant approaches will be investigated in the biomedical field together with the complexity measurements, most often carried out through nonlinear dynamical approaches where also in this context the integration between modelling and information processing plays a fundamental role. Finally, a few examples will be described in which the studying of electromagnetic fields (EMF’s), under the form of signals and images properly detected, might have a relevant impact into various biomedical applications.
I. INTRODUCTION Generally, “Physiological Modelling” and “Biomedical Signal Processing” constitute two important paradigms of Biomedical Engineering: their fundamental concepts are taught starting from undergraduate studies and are more completely dealt with in the last years of graduate curricula, as well as in PhD courses. Traditionally, these two cultural aspects were separated, being the first one more oriented to physiological issues and how to model them and the second one more dedicated to the development of processing tools
or algorithms to enhance useful information from clinical data. A practical consequence was that who did models did not do signal processing and viceversa. In the last years, instead, the need of obtaining a closer integration between signal processing and modelling of the relevant biological systems emerged very clearly (Cerutti et al., 2002, Bassingthwaighte et al., 2008). That it is not only true for training purpose, in order to properly prepare the new professional figures of Biomedical Engineering, but also for the development of newly conceived research projects in which the integration between “Biomedical Signal–Image Processing and Modelling” plays a crucial role. Just to give simply examples, topics like Brain-Computer Machine or Interfaces (BCM or BCI), Neuroengineering, Nonlinear Dynamical Analysis of Cardiovascular System, Integration of Sensory-Motor Characteristics aiming at the building of advanced prostheses and rehabilitation tools, Wearable Devices for vital sign monitoring and others, do require an intelligent fusion of modelling and signal processing competences which are certainly peculiar of our discipline of Biomedical Engineering (Cerutti, 2009). Further, this integration process could comprehend parameters and observations detected at different scales, at different organs and with different modalities (Cerutti et al., 2009). Such a paradigm is called the MMM-approach where it is clear how important information enhancement and synergy are certainly obtained when integrating Multivariate analysis (i.e. more signals from the same physiological system) with Multiorgan approach (i.e. correlating information derived from different organs, like in sleep), with integration between different modalities (i.e. signals with images, either anatomical or functional or both) and with Multiscale integration too (i.e. by finding relationships passing from gene- to protein-scale, to cellular scale, up to the entire organ level of detail). The following sections will deal with three basic topics: i.e. II) “Integration of Biomedical Signal-Image Processing
and Modelling”, where various contributions will approach different application fields in which the fusion of signal processing and modelling will be a recurrent keyword. Then III) “Advanced Algorithms for Biomedical Signal Processing: the Approaches of Time-Frequency and TimeVariant and of Nonlinear Dynamics Parameter Measurements”, where advanced methods for biomedical signal and system interpretation will be recalled (i.e. timefrequency and time-scale approaches, as well as complexity measurements derived from nonlinear dynamics) with a wide possibility of applications in biomedical field. Finally, IV) “Electromagnetic Field Imaging in Biomedical Applications” will deal with innovative electromagnetic mappings, which are finding a growing interest in both diagnostic and therapeutical applications. II. INTEGRATION OF BIOMEDICAL SIGNAL-IMAGE PROCESSING AND MODELLING
II.A Model Based Signal Processing of Cardiovascular (CV) Regulation The research line on heart rate variability (HRV) signal, started in the mid 1980s for the assessment of the autonomic control, was soon extended to other CV signals, mainly arterial pressure (AP) which at the time was invasively monitored (Pagani et al., 1986), while reliable non-invasive pletismographic recordings were being introduced. The availability of multiple contemporaneous signals containing information of different sites within CV regulation circuits (e.g. autonomic outflow to the heart by HRV, response to cardiac ejection combined to vasomotor activity by AP) rose the problem of a suitable analysis of the physiological interactions, which could be more specific to autonomic regulation compared to the information delivered by single signals or by a black-box multivariate analysis. The complexity of CV regulation renders it difficult to achieve a direct modeling; nonetheless, some physiological a-priori information can be easily included in the layout of multivariate closed-loop identification, as sketched by Fig.1. A first example was provided by a model of HRV– AP loop regulation (Baselli et al., 1988) which feeds back baroreflex responses on the heart, adjusting HR to correct AP in turn (see Fig.2). The proposed causal interaction lay– out and parametric structure considered an additional AP– AP loop, as well as an autoregressive structure the stochastic parts (i.e., unmeasured inputs) of both HRV and AP. A key point was the inclusion of respiration recording entering at both HRV and AP level. The advantage of this approach relies in augmenting the statistical power of data analysis by the inclusion of generally accepted knowledge, while living sufficient degrees of freedom for fitting individual or condition related features and to answer to
CNS supraspinal circuits baroreceptive mechanisms
cardiopulm. refl. respiration
HF
LF
HF
LF
phrenic n.
HF
LF
lungs
heart
spinal circuits
SN
LV
stroke volume
AB
heart rate
LF
LF
arterial pressure LF
LF
peripheral vascular districts
LF
vessels
LF LF
total peripheral conductance WK
Fig. 1. Causal structure (thick arrows) of respiration, AP, HRV interactions superimposed to a sketch of physiological mechanisms and neural structures: supraspinal circuits (mainly brainstem parasympathetic), spinal circuits (mainly sympathetic), outflow to Left Ventricle (LV), Sinus Node (SN), peripheral vascular districts, Low Frequency (LF) vasomotor activity, Windkessel (WK), Arterial Baroreceptors (AB) , Cardio Pulmonary reflexes.
unknown questions (e.g., level of baroreflex activity (Porta et al., 2000), gain of mechanical action of HR on AP (Baselli et al., 1994), resonance of loops and role in
Fig. 2. Translation of Fig.1 interactions into an identifiable linear parametric closed-loop model. Heart period (HP, t) series represents HRV and systolic AP (SAP, s) series represents AP variability. Deterministic blocks (Hst, Hts, Hss, Rs, and Rt) are moving average. Stochastic parts (Mt, Ms, and Mr) are autoregressive (AR). The overall structure is multivariate dynamic adjustment (alias ARXAR, AR eXogenous AR). From (Baselli et al., 1988).
generating HRV rhythms versus spectral content of stochastic residuals (Baselli et al., 1994), physiological pathways for respiratory sinus arrhythmia and role of cardiopulmonary reflexes (Lucini et al., 2000). In parallel with a linear analysis of causal interactions, the complexity of the system sketched in Fig.1 was investigated in several directions. Variable phase locking patterns between respiratory activity and sympathetic outflow was analyzed in decerebrate artificially ventilated cats under sympathetic or vagal activation (Porta et al., 1996) finding a rich variety of behaviors typical of complex non-linear interactions between oscillators at high frequency (HF) and LF under a forcing input. The synchronization/desynchronization conditions of distributed vasomotor low frequency oscillators were described in a simulation study (Baselli et al., 2006), showing the natural tendency to phase opposition of two peripheral districts and maximum phase distribution of many, when a sympathetic drive is switched off. The non-linear nature of peripheral resistances was further analyzed in a lumped model study of the vascular tree connected to peripheral districts with active auto-regulation (Aletti et al., 2009). The experimental analysis of non-linear interaction in short term (i.e., in few beats) variability has to overcome the necessity of processing limited data windows (typically few minutes or a few hundreds of beats) where autonomic and CV conditions can be considered stationary. Notoriously, black-box indexes used in the study of nonlinear series are considered to be robust over large amount of data. An elegant solution was proposed by (Porta et al., 1998) by a corrected conditional entropy of L-length patterns, CCEL/L-1; i.e. the entropy of the L-th sample given the previous L-1 ones, which equals the increase of length L entropy (HL) compared to length L-1 (HL-1). The notorious bias toward zero entropy (i.e., fake determinism) due to limited data was corrected by adding maximum uncertainty (i.e., unconditioned entropy H1) to the fraction of rare patterns (NRARE/N) appearing just once: CCEL / L1 H L H L1 ( N RARE N ) H1
As a result, CCEL/L-1, vs. pattern length L displays a minimum at the pattern length L for which the hidden determinism of the series can be robustly analyzed given the data length N (Fig.3). The conditional entropy approach has a direct link to prediction error methods (PEM) used in the parametric linear interaction analysis, since it is also structured in a prediction fashion from L-1 past samples to the actual L-th one. The difference lies in the fact that a prediction is actually not done; rather, its uncertainty is quantified by the conditional entropy. This permits the higher flexibility in order to capture deterministic effects, whether linear or not, and without a parametric structure. Both approaches share
Fig. 3. Beat-to-beat series of heart period, approximated as the time interval between two consecutive R peaks on the ECG (RR), in an healthy subject at rest and the relevant CCEL/L-1.
the ready extension to multivariate analysis of the interaction among more signals, since the past of another signal u can be easily considered in either the prediction of a signal y by a PEM or in the computation of a conditioned entropy. The similar framework also relates to the proposition of Granger causality from u to y, which states that causality is assessed when the prediction of y is improved by considering the past of u, which is respectively tested by a decrease of prediction error size or of prediction uncertainty (Porta et al., 2010). II. B Towards Systems Biology: Modeling Bio-Signals In this section, significant developments of biomedical signal processing and analysis will be stressed in a welldefined path towards the concept of System Biology. Linear Time Invariant multivariable models have been used ever since in investigating Central (Cerutti et al., 1985) and Autonomous (Baselli et al., 1986) Nervous Systems. Related improvements in Signal to Noise Ratio (Cerutti et al., 1987a) allowed to investigate trial by trial dynamics (Cerutti et al., 1987b, Liberati et al., 1997). Studies on multiple sclerosis and Alzheimer’s disease (Locatelli et al., 1998), as well as learning (Cerutti et al., 1988), stress (Pagani et al., 1991) and intention (Baraldi et al., 2007), benefit also by such techniques. De-convolution (De Nicolao and Liberati, 1993) has been successfully applied in reconstructing from blood concentration the course of the not directly accessible pituitary secretion (Sartorio et al., 2002). Compartmental models have been approached in (Liberati et al., 1993) as well as convolution modeling (Liberati and Turkheimer, 1999) in the study of dialysis. At a cellular level, prediction and understanding of solid tumor early stage growth has also been achieved (Chignola
et al., 2000). Even nonlinear influence, from a subsystem to another one, has thus been enhanced and studied via proper stimulation (Liberati et al., 1991b) and modeled via bicoherence analysis (Orizio et al., 1996). Artificial Neural Networks have been also investigated to identify nonlinear interactions in various application fields, namely in agro-biotechnology (Vercesi et al., 2000) and in prognostic factors in oncology (Drago et al., 2002). Logical Networks have been developed in order to infer (Muselli and Liberati, 2002) also prognostic factors in oncology (Paoli et al., 2000), besides selecting salient features, like via Adaptive Bayesian Networks (Bosin et al., 2006) and principal components analysis (Garatti et al., 2007). Time Variant dynamics has been initially modeled via Kalman filtering (Liberati et al., 1991a). PieceWise Affine identification (Ferrari-Trecate et al., 2003) of hybrid logical and dynamical processes has finally been developed in order to reduce the investigated problems as piecewise linear by identifying from data also switches among subsequent epochs. Various application are described in (Liberati, 2009a,b). Biophysics simulation of the modelled behaviour allows to in silico emulate patho-physiology (Milotti et al., 2008) toward systems biology (Sacco et al., 2010). II.C Clinical Parameter Detection through Cardiac Modelling The research activity at the Department of Biomedical Engineering in the field of cardiac image processing and modeling has been recently focused on the development and application of image processing techniques for diagnosis and support in mitral valve (MV) surgery repair procedures. Severe MV regurgitation associated to degenerative MV prolapse is one of the most common valvular pathologies in the industrialized countries, and it is characterized by high morbidity and mortality. The MV repair, with insertion of a prosthetic ring on the MV annulus (annuloplasty), is currently the primary surgical solution for this pathology. In this scenario, our efforts were aimed at characterizing the in-vivo behaviour of the prosthetic device, as well as at studying the effects of this surgery on left ventricular remodelling. Our innovative approach is based on the combined analysis and integration of the most advanced cardiac imaging techniques (real-time 3D echocardiography (RT3DE), cardiac magnetic resonance) with advanced image processing and finite element modelling techniques (Fig. 4), in order to obtain patient-specific information on the MV (see www.surgaid.org for more details). Mitral annulus was tracked frame-by-frame (Veronesi et al., 2008) in a 3D space from RT3DE datasets to evaluate the dynamic pattern of change of several geometric and
Displacement (mm) Displacement (mm)
13 13
0
0
0
0
Cardiac cycle (%)
Cardiac cycle (%)
100
100
Fig. 4. From RT3DE to finite element model of the MV (from top, clockwise): RT3DE dataset, extracted MV annulus, MV annulus displacement throughout the cardiac cycle and stress distribution computed from finite element model.
functional valvular parameters, and this information, together with papillary muscle tips position, was used as boundary condition in the definition of finite element structural models. This approach was applied in a group of patients with severe MV regurgitation receiving a flexible band (FLEX) or a complete rigid (RIG) ring, as well as in a control group (NL). As expected, in presence of MV regurgitation, annulus is enlarged and less planar compared to NL. Annuloplasty resulted in reduced areas both in RIG and FLEX and in a more planar annular shape. Preliminary results of the modelling approach are promising in order to utilize this patient-specific analysis also as in a surgical planning scenario, as a predictive tool (Votta et al., 2008). In the context of a nationally funded Project (PRIN 2007, www.surgaid.org) and in collaboration with Centro Cardiologico Monzino, Milan, an algorithm for left ventricular (LV) shape assessment from RT3DE data (Maffessanti et al., 2009) was developed, resulting in the computation of 3D shape indices of sphericity (S) and conicity (C), independent from LV dimensions. This methodology was applied to the same population of patients with severe MV regurgitation undergoing early MV repair. Results showed that prior to surgery, even in absence of worsening in LV function, S was elevated and C was decreased compared to NL. At 6 months, these changes were reversed with no further improvement at 12 months. MV repair in asymptomatic patients was associated with changes in LV shape which remodels to near normal morphology as a consequence of annuloplasty (Maffessanti et al., 2010). The obtained results give new insights in the in-vivo performance of the implanted rings and in the subsequent cardiac remodeling, offering new indices for the clinical decision process and follow-up. The developed approaches are novel and rather unconventional, being both interdisciplinary, involving electronic and mechanical biomedical engineering skills,
a
b
b Fig.5. PET/CT pulmonary patient data reconstructed with standard voxel based AWOSEM (a), and with AWOSEM-region (b).
and multi-disciplinary, requiring a strong collaboration with heart surgeons and cardiologists. II.D Expectation Maximization Tomographic Reconstruction for Lesion Evaluation in FDG-PET The quantitative information theoretically delivered by Positron Emission Tomography (PET) is consistently smeared by the limited resolution, with a high dependence on object (lesion and background), position in the scanner, and count statistics. The theoretical framework provided by Maximum Likelihood (Lange et al., 1984) and the relevant iterative algorithm of Attenuation Weighted Ordered Subset Expectation Maximization (AWOSEM) (Liu et al., 2001) provides a powerful mean to deal with the Poissonian features of collected data. In this algorithm the correction of count data, yi, by the specific attenuation correction factor, ACFi, is explicit in the iterations in order to preserve the Poissionian assumption. The elements of the system matrix, aij, link activity, λi, in the j-th image element (either voxel or basis function (Carson, 1986) to the i-th measure, yi. To preserve Poissonian features, AWOSEM avoids to apply attenuation correction, ACFi, on data, but it corrects system coefficients, aij/ACFi. The iterations from step (n) to (n+1) are based on a fairly simple operation which weighs over a data subset the ratio between real data and those simulated predicted by the n-th reconstruction : a ACFi yi ~ yi( n) ( n 1) i ij i aij ACFi
i
In standard applications, normally available on commercial scanners, the system matrix includes only weighs describing the geometry of intersections between the line of responses of detector pairs and image elements. However, intensive research has been carried out in recent years in order to evaluate the benefits of including further features such as: space variant blurring for resolution
recovery, regularizing factors through basis functions, targeted object features, etc.; also, convergence properties (Liow et al., 1993) and their object/algorithm dependence have been analyzed concerning their effects on lesion detectability and lesion quantification. The Department of Bioengineering in co-operation with the Nuclear Medicine Department, Fondazione Ospedale Maggiore Policlinico, Mangiagalli e Regina Elena, has explored several aspects in this field, mainly centered on the construction, estimation, and validation of a parametric model of space variant blurring in a 3D modern scanner for resolution recovery (De Bernardi et al., 2007). A 2D transaxial approach was used after a suitably optimized FOurier REbinning (FORE); nonetheless, a 3D blurring model was worked out for a full resolution recovery: radial, tangential, and axial. The flexibility and robustness of the blurring model permitted a thorough analysis of convergence and its object dependence. The main conclusion of these studies was that resolution recovery was able to improve the estimate of the total activity within a lesion, with a better control over noise amplification (noise break-up) phenomena, as shown in Fig.5; however, the iterations required for quantification did not improve the diagnostic readability compared to the standard clinical images which are smooth and far from convergence to avoid false positives. Consequently, further work aimed at improving quantification by targeting an addressed lesion, assuming the quantification step to follow lesion detection on a standard clinical image by an expert viewer. An AWOSEMregion algorithm (De Bernardi et al., 2009) was proposed, which considered few image elements: 1) voxels 100% within lesion; 2) partial volume voxels; 3) transition region affected by lesion spill-out; 4) background, i.e. the rest of image frozen at low resolution. Iteration of this procedure with lesion segmentation adjustment, proved to well recover blurring and partial volume effects, providing a reliable estimate of lesion volume and total activity. The proposed strategy therefore contributes to the active research field on quantification of lesion uptake and volume (Tylski et al., 2010). II.E. Time-Resolved Spectroscopy
Functional
Near
Infrared
Basic Principles and Instrumentation Starting almost 30 years ago with the pioneering work of Jobsis (Jobsis, 1977), non-invasive functional near-infrared spectroscopy (fNIRS) has been used first to investigate experimentally and clinically brain oxygenation in neonates and adults, and later to assess muscle oxidative metabolism in pathophysiology (McCully et al., 2000). fNIRS employs optical radiation in the range 600-1000 nm where light attenuation by tissue constituents (water, lipid,
Fig.6. Time resolved fNIRS curve. The different penetration depth related to the arrival time of the photons is highlighted.
oxyhemoglobin and deoxyhemoglobin) is relatively low and accounts for an optical penetration through several centimeters of tissue. Absorption and scattering coefficient are measured in order to optically characterize tissues: the first parameter describes the tissue content, while the second the tissue structure. The difference in the absorption spectra of oxy- and deoxy-hemoglobin allows the separate measurements of the concentration of these two species. So far, the most common approach of fNIRS is in the continuous wave (CW) regime, that is to measure light attenuation at two wavelengths between a couple of optical fibers, placed on the tissue surface, at a known relative distance (typically 2-4 cm). The key limitations of CW fNIRS techniques are the coupling between the absorption and the scattering coefficient causing the lack of quantitative assessment and sensitivity. A possible way to uncouple absorption from scattering is based on the use of modulated laser sources, and on the measurement of signal phase and amplitude changes caused by propagation. The so called frequency-domain (FD) technique in fact extracts both the mean scattering coefficient and absorption coefficient of the probed medium provided that a non-trivial calibration of collection efficiencies is performed. The dual approach is the study of photon migration in the time domain. This approach is based on the detection of attenuation, broadening and delay experienced by a short (hundreds of picoseconds) laser pulse injected in a diffusive medium. Recently, some groups have developed compact systems for time-resolved (TR) fNIRS (Contini et al., 2006). fNIRS data Analysis In principle, FD- as TR-fNIRS provide a richer insight to the problem of non-invasively probing a diffusive medium. These approaches can discriminate between absorption and scattering contributions and derive absolute values for the hemodynamic parameters. The accuracy of hemodynamic parameters estimation depends mainly on three aspects: i) the accuracy of the theoretical model describing photon
propagation in a turbid medium like a biological tissue, ii) the knowledge of the real bulk optical properties of the tissue and iii) the knowledge of the real tissue structure. Analytical model for homogeneous medium or simple structured medium (e.g. layered medium) can be derived (Martelli et al., 2005). For a highly heterogeneous medium, like the human head, it is possible to use numerical methods like Monte Carlo or Finite Elements. These methods, for their practical and effective use with TR or FD set-up, require a large amount of computational time and a priori information about the structure of the head (e.g. the anatomical images provided by a MRI scan). Apart some technical problems for the implementation and integration of analytical or numerical methods with the real tissue structure, the main limitation of these approaches is the lack of knowledge about the in vivo bulk optical properties of the head, in fact, to this day no one accurately measured the optical properties of the different structures of the head (Comelli et al., 2007). In our opinion, TR should be preferred to FD fNIRS because TR techniques rely on an easier approach to the problem of depth sensitivity. A key point in TR-fNIRS is the ability to separate systemic hemodynamic changes, occurring in particular in the scalp, from functional changes related to brain activation. In fact, analyzing the first part of the TR curve (early gate) we consider photons that travel few hundreds of picoseconds into the tissue and, thus, have a low probability to reach the brain cortex, while, analyzing the tail of the TR curve (late gate) we consider photons with a higher probability to go deep into the tissue and bring information about brain activity (Fig. 6). Thus, exploiting the depth information, naturally encoded into photons arrival time, it is possible to discriminate extra- and intra-cerebral activity (Liebert et al., 2004; Contini et al., 2007). TR-fNIRS can be integrated with other functional technique like EEG in order to merge different type of data, for example to better explain the relation between electrical and metabolic brain activity (Molteni, 2010). TR fNIRS can be also integrated with fMRI in order to compensate for the lack of anatomical information (Caffini, 2010). III. ADVANCED ALGORITHMS FOR BIOMEDICAL SIGNAL PROCESSING: THE APPROACHES OF TIME-FREQUENCY, TIMEVARIANT
AND
NONLINEAR
DYNAMICS
PARAMETER
MEASUREMENTS
III.A Time-Frequency and Time-Variant Methods for Biomedical Signal Processing Many biomedical signals are characterized by oscillatory patterns (or rhythms) which carry relevant information for diagnostic and therapeutic purposes as well as for
understanding the underlying physiology. Typical examples are the δ, θ, α and β rhythms of the EEG and the Lowfrequency (LF) and High-Frequency (HF) components of the heart rate variability (HRV) signal. The analysis of these oscillatory patterns is usually performed by spectral analysis using both non-parametric (FFT based) and parametric (AR/ARMA model based) approaches. These tools require the signal to be stationarity in the analysis window. However, biomedical signals are characterized by transient waveforms of various nature (i.e. they are intrinsically nonstationary). As a result, the spectral features of these signals evolve with time, and the capability to track these changes is relevant for the characterization of the dynamics which occur in a wide range of clinical and physiological studies. The possibility to track spectral changes with time has been made possible by the application of time-frequency and time-variant methods. The Department of Bioengineering of Politecnico di Milano has been very active in this fields since the beginning and contributed with both methodological innovations and novel applications. A review of these activities in the analysis of HRV signals can be found in a few review papers (Cerutti et al., 2000; Mainardi, 2009; Mainardi et al., 2002). Here only a brief summary of the main findings will be reported. Methodologies The most diffused approaches for time frequency representation of a signal can be summarized in three main categories: i) linear decomposition; ii) quadratic distributions; iii) adaptive parametric models. Linear decomposition of the signal The fundamental mathematical tool for time-frequency analysis is based on signal expansion and inner product, according to proper orthogonal basis functions. In practice the signal is expressed as a linear combination of a set of elementary components. When the analysis functions are complex sinusoids, then we obtain the Fourier Transform (FT) of the signal, if the basis functions are localized both in time and in frequency, the coefficients of the decomposition constitute the time-frequency representation of the signal. An example is given by the Short Time Fourier Transform (STFT), in which the basis function are time windowed sinusoids. Time and frequency properties are not independent, in fact they are linked by the Heisenberg’s inequality, according to the following expression:
f t
1 4
The smaller the time duration of the basis functions, the better the time resolution (Δt), and the poorer the frequency resolution (Δf). Usually a signal is characterized by shorttime high-frequency components superimposed to longtime, low-frequency components, thus a compromise is
needed in the choice of the proper basis. In order to overcome this limitation a multi-resolution decomposition can be achieved through the wavelet transform (WT), where the decomposition basis is obtained from a “mother” wavelet (or function), that is stretched or shrunk in time in order to obtain an ortho-normal bases characterized by different time-frequency resolutions. Quadratic distributions A quadratic time-frequency representation (TFR) is usually associated to the concept of instantaneous power spectral density. Two popular example of quadratic distributions are the spectrogram and the scalogram, obtained by squaring the coefficients of the STFT and WT respectively. An alternative quadratic distribution is obtained by calculating the FT of the instantaneous autocorrelation function (ACF) of the signal, which preserves both the time and the frequency information of the signal. This is the well known Wigner-Ville Distribution (WD). Different versions of the WD have been proposed in literature, in order to reduce the presence of cross terms in the time frequency plane, and these are enclosed in the Cohen class. Adaptive parametric models The parametric approach to the estimation of the power spectral density assumes that the time series under analysis is the output of a given process, whose parameters are, however, unknown. Usually the model is independent from the physiology or the anatomy of the biological process generating the data, and its formulation is based on the input-output relationships, according to the so called black box approach. Thus, the process is completely described by the model parameters. The parametric spectral approach is a procedure that can be summarized in three steps: i) choice of the correct model for the description of the data; ii) estimation of the model parameters based on the recorded data; iii) calculation of the power spectral density (PSD) through proper equations (according to the selected model). The parameter estimation can be made recursive and a new model can be estimated each time a new sample of the signal is made available; thus a new power spectral density can be calculated for each new sample in the data. A forgetting factor can be added in the estimation procedure in order to make the updating parameter procedure more dependent on the more recent data, while the oldest ones are forgotten with an exponential decay. In such a way, the sample by sample estimation is able to track changes in the signal characteristics and a time-frequency representation of the signal is obtained. The recursive estimation procedure is summarized in Fig.7. Applications - Spontantaneous Myocardial Ischaemia An interesting field of application is the study of relationships between ANS and myocardial ischaemia,
either spontaneous or induced. An early result, obtained by AR-based time-varying methods (Bianchi et al., 1993), puts into evidence a LF increase within the 2 min preceding the ischaemic attack. When different ischaemic events are considered, different trends were observed (Bianchi et al., 1997), all documenting an important involvement of ANS in either generating or sustaining the attack. In particular a different interplay between ANS and variant or stable angina was documented (Bianchi et al., 1997). An example of HRV signal analysis during stable angina is presented in Fig.7 (right panel). - Provocative tests. Many clinical tests (such as tress-test) induce changes in ANS modulation of the heart beating. The response is dependent on the amplitude of the stimulus: a faster (and larger) sympathetic response was observed for more pronounced tilt angles (Mainardi et al., 2002). When the tilt was prolonged, oscillations and non-stationarity characterized the trend of the LF components, being more evident in patients with syncope (Furlan et al., 1998). The study also documented a sympathetic withdrawal preceding syncope, which may be either sudden or progressive. In addition, using the time-variant model in the bi-variate form, an autonomic mismatch between HR and blood pressure regulation was also observed before syncope (Mainardi et al., 1997). During pharmacological tests (dipyridamole-stress test), the trend of spectral parameter puts into evidence an increase of the LF component in coincidence with the echocardiographic marker of ischaemia, but preceding the ST displacement on the ECG (Petrucci et al., 1996). The time-variant parameters were therefore documented to be an early sign of ischaemia of clinical interest. In a recent study time-frequency approach based on
III.B Complexity in Biomedical Systems and Nonlinear Parameters Measurements
y(t) e(t) +
Smoothed-Pseudo Wigner Ville (SPWV) has been applied to stress-test to assess the dynamic evolution of Respiratory Sinus Arrhythmia (RSA) and its links to ventilation during the effort. In this context some novel methodological innovations have been proposed to include information related to respiratory frequency (Bailon et al., 2010). - Sleep studies Sleep is a physiological condition, that can be altered by many pathological events. Even if sleep evaluation is mainly based on the analysis of the EEG, it affects also peripheral systems and the related signals, such as the HRV and the respiration signal. Thus, the typical parameters that quantify the dynamical changes of the HRV signal, namely LF and HF powers, significantly change in the different sleep stages and in presence of pathological events such as sleep apneas and micro-arousals. As the HRV signal is highly non stationary during sleep, time-frequency methods are required for correct analysis. Time-variant AR model have been used for automatic sleep classification (Mendez et al., 2010) and for apnea detection (Mendez et al., 2009) from the HRV, while SPWV was used for the characterization of the ANS during microarousals (Mendez et al., 2008). - EEG processing It is well known that during the execution of voluntary movements or even only during motor imagery, there is a power decreasing in the alpha range (alpha desynchronization or alpha ERD, event related desynchronization) related to the beginning of the movement, but preceding its execution and a marked power increasing in the beta range (beta ERS) at the end of the movement. In a recent paper such dynamics are quantified through time-frequency techniques through adaptive parametric models that are particularly suitable for this application, because in this way it is possible to put into evidence both power and frequency changes in the rhythms of interest (Foffani et al., 2004).
updating algorithm
a(t)
+
a(t)
z -1
y(t) + a(t-1) (t) = [y(t-1) y(t-2) … y(t-n)]
Fig.7. Left panel: recursive algorithm for the time-variant estimation of AR model coefficients. Right panel: Sequence of the PSD’s as output of the recursive algorithm, during a stable angina episode. Each PSD corresponds to a single sample in the signal.
Methods and Modelling Approach The research group at the Department of Electronics and Information (DEI) at the Politecnico has been actively working on the methodologies for the analysis of complex signals and systems. In the area of bifurcation analysis (Meijer et al., 2009; Dercole et al., 2010), studies have yield theoretical contributions (Kuznetsov et al., 2001, 2003; Colombo et al., 2010), numerical methods (Dercole et al., 2005; Dercole 2008), and applications in diverse fields. As far as signal analysis is concerned, peak-to-peak analysis and symbolic methods have been proposed as systematic tools for modelling, parameter estimation, and control of chaotic systems (Candaten et al. 2000; Piccardi,
2006). Epidemic spreading is one of the areas where the above methods have been exploited. The full two-parameter bifurcation analysis of the classical SIR/SEIR models has disclosed and classified many epidemiological regimes that are observed in real-world data (Kuznetsov et al. 1994), and has paved the way to classical (i.e., PID) and fuzzy control schemes for reducing the impact of epidemics (Ghezzi et al., 1997; Piccardi et al., 1998). The most recent trends in the study of epidemics are based on the theory of complex networks: in this context, the study of the spreading of some specific disease has pointed out some nontrivial interplay between network topology and infection peculiarities (Piccardi et al., 2008). Bifurcation theory has been successfully applied to the analysis of evolutionary processes in biology. In particular, the research group has contributed to the methodological development and to the application of the approach known as Adaptive Dynamics. The results (collected in several papers in leading international journals and in a book (Dercole et al., 2008) range from the classification of the evolutionary regimes of resource-consumer systems and the evolutionary origins of cooperative and cannibalistic attitudes, to the discovery of the first chaotic evolutionary attractor (Dercole et al., 2010). The study of networks of dynamical systems has attracted a lot of attention in the last decade in very diverse fields, among which bioengineering, and several methods of analysis have been developed, so that many phenomena that crucially characterize network dynamics can now be rigorously studied. An important class of networks is that in which each node is an oscillator (e.g., a neuron), namely a dynamical system that behaves periodically or chaotically when isolated (perhaps by producing recurrent spikes or bursts). A huge number of systems naturally call for this modelling, in particular in neurosciences. In this context, one of the main issues is the study of synchronization, i.e., the possibility that all the systems oscillate in unison, since this fact is of paramount importance in many applications, including the study of many pathologies (e.g., Parkinson disease and epilepsy). The results obtained within the research group on this issue have been collected in a series of papers (Colombo et al., 2008; Torri et al., 2003; Maggi et al., 2006; Dercole et al., 2007; Belykh et al., 2009; Rinaldi, 2009), but they have been also described in detail in plenary lectures at the 2006 International Symposium on Nonlinear Theory and its Applications (NOLTA06, Bologna), at the 6th European Conference on Ecological Modelling (ECEM07, Trieste), and at the “International Meeting on Chaos and Dynamics in Biological Networks” (Cargese, Corsica, 2008). Time-Series Analysis The modern signal processing approach to the
biomedical time series received a significant improvement by the development of the nonlinear dynamical system analysis. This has led to the introduction of a large amount of signal analysis techniques aimed at the extraction of nonlinear parameters from experimental time series. As in biological field the system model is often unknown, the measured signals are the only information we can have about the system itself. This is precisely the case of the human life support systems among which the heart plays a dominant role. The complex structure of the Heart Rate Variability signal (HRV) has been widely studied in order to identify the “complex” nature of its control mechanisms. The aim was to investigate the structure of the physiological rhythms of the cardiac system by assessing how the presence of nonlinear deterministic phenomena could affect the HRV signal both in short and long temporal windows. The analysis of HRV signal, through classical linear methods, either in time, or in frequency domain, provided two main outcomes: that the quantification of some important properties of the regulating action performed by the ANS in the short period and that the information carried by this signal may not be totally explained by a linear approach (Kantz et al., 1998). This second statement confirms the value of the analysis approach through nonlinear methods. Results on HRV signal analysis have shown that its dynamic behavior involves nonlinear components that also contribute in the signal generation and control (Cerutti et al., 2007). The signal shows apparently erratic behavior but abrupt changes and patterns are also present in which a more regular behavior is detectable. The evaluation of the HRV signal characteristics by a nonlinear approach is based on different methods investigating both geometric and dynamic signal features. Important indications can be extracted from parameters estimating nonlinear characteristics and their statistical use is of great importance improving diagnostic performances and helping the clinical knowledge of analysis methods for different cardiovascular pathologies (Cerutti et al., 2007, Signorini et al., 2003). At first, methods based on the reconstruction of the HRV time series in an embedding space, such as Fractal Dimension and Lyapunov Exponents were computed. Their estimation must be associated to a determinism test based on surrogate data confirming that is a deterministic mechanism instead of a linear correlation that controls the HRV dynamics. Surrogate data are series of casual data sharing some linear properties (mean, variance, Fourier spectrum) with original series. The null hypothesis the test wants to reject is: “A stochastic linear process generates the HRV time series” (Schreiber et al., 2000).
Imaging
Fig.8. Log-log spectra calculated in 24 hours HRV signal in a normal subject (upper panel) and in a patient after heart transplant (lower panel). The slope represents α coefficient in α-power law spectrum.
Results in 24 hours HRV series have shown that the structure generating the signal is neither linear nor stochastic. Furthermore, methods quantifying fractal and self-similar “monofractal” characteristics (1/fα spectrum, Detrended Fluctuation Analysis, DFA) and regularity and complexity statistics (Approximate and Sample Entropy: ApEn, SampEn as well as Lempel-Ziv complexity) allow to characterize the HRV signal distinguishing pathological from healthy subjects (Ferrario et al., 2006). Fig.8 reports a 24h HRV signal recorded from a Holter tape in a normal case (upper panel), compared to a transplanted heart patient (lower panel): α-power law coefficient in the 24h is significantly different in the two cases. HRV signal regulation certainly involves nonlinear contributions. Nonlinear time series analysis allows extracting signal characteristics of physiologic and clinical relevance. Results in the HRV signal analysis confirm the presence of a nonlinear deterministic structure in time series. Moreover, nonlinear parameters can be used to separate normal from pathological subjects leading to best classification of different pathological states.. Among other applications, examples concerning cardiovascular pathologies and fetal heart rate analysis might be cited. All these examples and results in physiological and pathological conditions, confirm that nonlinear dynamic analysis to biological time series can be useful explaining regulating mechanisms of cardiovascular system.
Magnetocardiographic field imaging (MFI) is a technique used to record contact-free the magnetic field distribution and estimate the underlying source distribution in the heart (Leder et al., 1998). Typically, the cardiomagnetic fields are recorded with superconducting quantum interference devices (SQUIDs) (Andrä et al., 2006). SQUIDs are restricted in their positioning to cryostats, since they require liquid helium (low temperature superconductors) or nitrogen (high temperature superconductors) cooling. Recently, however, new technologies of magnetic sensor systems for magnetocardiography make feasible a less restrictive sensor positioning. Therefore, the general question arises how to optimally place the sensors obeying a technical minimum distance between them. To this end, a typical goal function used in sensor array optimization is the condition number (CN) of the kernel (leadfield) matrix. More sophisticated Figures of Merit (FOM) to compare sensor arrays efficiency have been introduced (Di Rienzo et al. 2006, 2007). Since the generation of the kernel matrix for a given position of magnetic sensors is computationally expensive, a pre-computation for a dense enough grid of sensor positions and orientations is needed. Consequently, the search space of the optimization scheme is discretized. Simulation setup A three compartment boundary element (BE) model of the torso (conductivity 0.2 S/m) and lungs (0.04 S/m) is created from a T1-weighted MRI of a 72 year old participant (Fig. 9). We model the cardiac sources with 13 dipoles arranged regularly around the left ventricular blood mass. The measure of averaged heart cycle (PQRST) data from the patient (195-channel vectorial magnetometer system Argos200, AtB SrL, Italy) serve for the estimation of the orientation of the dipoles with a minimum norm
IV. ELECTROMAGNETIC FIELD IMAGING IN BIOMEDICAL APPLICATIONS
IV.A
Magnetocardiographic Field and Diagnostic
Fig.9. Boundary Element Model (BEM) and source model.
approach with L-curve regularization. The sensors are modeled as a coil with a single winding and a diameter of 1 cm. Comparison of existing sensor arrays Using different FOMs, we compare three different SQUID sensor set-ups: one realistic and two idealized ones. The idealized set-ups are an 8x8 three-axial (measuring 3 magnetic field components) magnetometers array and a 14x14 mono-axial magnetometers array (in figures “14x14 1D”), covering the same area. The realistic set-up is the ARGOS 200 comprising 65 three-axial sensors. All set-ups provide approximately the same number of measurement channels and are positioned in front of the chest of a healthy volunteer (Di Rienzo et al., 2006, 2007). Optimization procedure for the design of a new measurement system In order optimize the sensor setup we use tabu search optimization (Lau et al., 2008) and particle swarm technique, obtaining similar results. IV.B Safety of Electromagnetic Field Exposure and Biomedical Applications of Electromagnetic Fields The Milan Unit of the CNR Institute of Biomedical Engineering (ISIB CNR) is internationally acknowledged for their studies on the effects of the human exposure to electromagnetic fields (EMF) and on computational modeling of the interaction between EMF and the dielectrically inhomogeneous human body. Numerical modeling of that interaction provides a unique way for assessing the resulting spatial distribution of internal EMF, currents and rate of energy deposition within the human body caused by the exposure to such EMF. Knowledge of these parameters is of crucial importance in understanding such interactions and is a prerequisite when assessing the impact of EMF exposure on health or when assessing or
0.073 (A/m)
0
Fig.10. On the left: electric field distribution on the head tissues on a transversal plane passing through the anode during transient Direct Current Stimulation of the primary motor cortex; on the right: distribution of the magnetic field in a whole body newborn model, generated by a RFID identity reconfirmation system.
optimizing therapeutic or diagnostic medical application that employ EMF. The main results of the ISIB Unit in this area were on: 1) Numerical estimation (using FIT techniques) of the radiofrequencies EMF distribution in human head or trunk by devices and systems for mobile communication, specially on mobile phones and Wi-Fi. This includes also the computational estimation of the coupling of environmental EMF with active and passive medical implants in the human body, focusing mainly on cochlear implants and neural stimulators (Parazzini et al., 2010ab, Sibella et al., 2009, Parazzini et al., 2007a). In particular the main recent findings of these studies were related to the quantitative confirmation that the EMF fields and the specific absorption rates SAR at the level of the peripheral hearing organs in humans due to exposure to mobile phones at GSM and UMTS frequencies are extremely lower than the current exposure limits. Moreover, the ISIB Unit quantitatively demonstrated that the use of mobile phones and the exposure to WiFi network do not interfere with the functionality of implanted cochlear implants. 2) Optimization of health support systems and procedures that make use of EMF, such as cochlear implants, electric (tDCS transient Direct Current Stimulation) and magnetic stimulation, deep brain stimulation, RFID applications in health environment and electromagnetic sensor (Lopresto et al., 2007; Tura et al., 2010; Tognola et al., 2005, 2007). The main recent findings were related to the quantitative estimation of the current density in terms of pattern and values in the cochlear tissue around the cochlear implant electrode array, in the evaluation of the electric fields and current densities generated by brain stimulators in the cortex and white matter, indentifying the different influence on the fields due to the use of different electrodes in terms of size and shape in tDCS and in the assessment of the exposure to passive RFID reader during newborn-mother identity reconfirmation procedure in neonatal clinics. In this latter case sensitive levels of exposure of the newborns were identified and an innovative relationship between the maximum generated magnetic fields and the time of use of the device close to the body was proposed. See Fig. 10 as an illustrative example. 3) Study of the potential health effects of exposure of biological systems to electromagnetic fields (Galloni et al., 2009, 2005ab; Parazzini et al., 2009; Parazzini et al., 2010ab, Parazzini et al., 2007bcd, Paglialonga et al. 2007, Repacholi and Ravazzani, 2006, Ravazzani, 2008). The main findings were related to the study of the effects of the exposure of the animal and human hearing system to mobile phones radiation at GSM (900-1800 MHz) and UMTS (around 2.0 GHz) frequencies. In particular, no acute effect was found on the main audiological measure both in animals and humans, considering controlled exposure to
GSM and UMTS phones at the maximum permitted power. Currently ISIB CNR is serving as Central Coordinator of the Project EFHRAN (European Health Risk Assessment Network on Electromagnetic Fields Exposure, 2009-2012), in the framework of the Programme of Community Action in The Field of Health, Health 2008, aimed to provide the health risk assessment about the exposure to EMF fields in Europe. In the last years ISIB CNR served has Central Coordinator of three multicentric projects funded by the European Commission. GUARD (FP5) and EMFnEAR (DG Health and Consumer Protection) were focused on mobile phone exposure and hearing; EMF-NET (FP6) was a large Coordination Action aimed to interpret the mass of results of scientific research on EMF and health impact, to provide input for policy maker and health authorities in Europe. REFERENCES Section I - Baselli G, Caiani E, Porta A, Montano N, Signorini MG, Cerutti S, Biomedical signal processing and modeling in cardiovascular systems, Crit Rev Biomed Eng, 30:55-84, 2009 - Bassingthwaighte JB, Chizeck HJ, The Physiome projects and multiscale modeling, IEEE Sig Proc Mag 25:121-144, 2008 - Cerutti S, In the spotlight: Biomedical signal processing: a well established discipline or a paradigm to promising integrated visions?, IEEE Review on Biom Engin, 7-11, 2009 - Cerutti S, Hoyer D, Voss A, Multiscale, multiorgan and multivariate complexity analyses of cardiovascular regulation, Philos. Trans. A Math. Phys. Eng. Sci, 367:1337-1358, 2009 Section II.A - Aletti F, Lanzarone E, Costantino ML, Baselli G, Simulation study of autoregulation responses of peripheral circulation to systemic pulsatility, Nonlinear Biomedical Physics, 3:7,2009 - Baselli G, Cerutti S, Civardi S, Malliani A, Pagani M, Cardiovascular variability signals: towards the identification of a closed-loop model of the neural control mechanisms, IEEE Trans. Biomed. Eng. BME, 35:1033-1046, 1988 - Baselli G, Cerutti S, Badilini F, Biancardi L, Porta A, Pagani M, Lombardi F, Furlan R, Malliani A, Model for the assessment of heart period and arterial pressure variability interactions and of respiration influences, Med.& Biol.Eng.& Comput, 32:143-52, 1994 - Baselli G, Porta A, Pagani M, coupling arterial windkessel with peripheral vasomotion: modeling the effects on low frequency oscillations, IEEE Trans. Biomed. Eng, 53:53-64, 2006 - Lucini D, Porta A, Milani O, Baselli G, Pagani M, Assessment of arterial cardiopulmonary baroreflex gains from simultaneous recordings of spontaneous cardiovascular and respiratory variability, J. Hypertension, 18:281-286, 2000 - Pagani M, Lombardi F, Guzzetti S, Rimoldi O, Furlan R, Pizzinelli P, Sandrone G, Dell'Orto S, Picalunga E, Turiel M, Baselli G, Cerutti S, Malliani A, Power spectral analysis of heart rate and arterial blood pressure variabilities as a marker of sympatho-vagal interaction in man and in conscious dog, Circ. Res, 59:178-193, 1986 - Porta A, Baselli G, Montano N, Gnecchi-Ruscone T, Lombardi F, Malliani A, Cerutti S, Classification of coupling patterns among spontaneous rhythms and ventilation in the sympathetic discharge of decerebrate cats, Biol Cybern, 75:163-172, 1996 - Porta A, Baselli G, Liberati D, Montano N, Cogliati C, GnecchiRuscone T, Malliani A, Cerruti S, Measuring the degree of
synchronisation by means of a corrected conditional entropy in sympathetic outflow, Biol Cybern, 78:71-78, 1998 - Porta A, Baselli G, Rimoldi O, Malliani A, Pagani M, Assessing baroreflex gain from spontaneous variability in conscious dogs: role of causality and respiration, Am J Physiol, 279:H2558-H2567, 2000 - Porta A, Tobaldini E, Gnecchi-Ruscone T, Montano N, RT variability unrelated to heart period and respiration progressively increases during graded head-up tilt, Am J Physiol, 298:H1406-H1414, 2010
Section II.B Baraldi P, Manginelli AA, Maieron M, Liberati D, Porro CA, An ARX model-based approach to trial by trial identification of fMRI-BOLD responsens, NeuroImage 37: 189–201, 2007 Baselli G et al, Spectral and cross-spectral analysis of heart rate and arterial blood pressure variability signals, Comput Biomed Res 19 520-534, 1986. Bosin A, Dessì N, Liberati D, Pes B, Learning Bayesian classifiers from gene-expression microarray data, Lecture Notes in Artificial Intelligence, 3849: 297 – 304, Springer-Verlag, 2006 Cerutti S, Liberati D, Mascellani P, Parameters extraction in EEG processing during riskful neurosurgical operations, Signal Processing, 9: 25-35, 1985 Cerutti S, Bersani V, Carrara A, Liberati D, Analysis of visual evoked potentials through Wiener filtering applied to a small number of sweeps, J Biomed Eng., 9: 3-12, 1987a. Cerutti S, Baselli G, Liberati D, Pavesi G,Single sweep analysis over visual evoked potentials through a model of parametric identification, Biol Cybern, 56: 111-120, 1987b. Cerutti S, Chiarenza G, Liberati D, Mascellani P, Pavesi G, A parametric method of identification of the single trial event related potentials in the brain, IEEE Trans BioMed Eng 35: 701-711, 1988. Chignola R et al, Forecasting the growth of multicell tumour spheroids: implications for the dynamic growth of solid tumours, Cell Proliferat 33:219-229, 2000 De Nicolao G and Liberati D, Linear and nonlinear techniques for the deconvolution of hormone time-series, IEEE Trans BioMed Eng 40: 440-455, 1993 Drago GP, Setti E, Licitra L and Liberati D, Forecasting the performance status of head and neck cancer patient treatment by an interval arithmetic pruned perceptron, IEEE Trans BioMed Eng 49:782-787, 2002 Ferrari Trecate G, Muselli M, Liberati D, Morari M, A clustering technique for the identification of piecewise affine systems,Automatica 39: 205-217, 2003. Garatti S, Bittanti S, Liberati D, Maffezzoli P, An unsupervised clustering approach for leukemia classification based on DNA microarrays data, Intelligent Data Analysis, 11:175-188, 2007 Liberati D et al, Parametric method for the detection of inter and intrasweep variability in VEP's processing, Med Biol Eng Comput 29:159166, 1991a. Liberati D et al, A model for the cortico-cortical neural interaction in multisensory evoked potentials, IEEE Trans BioMed Eng 38:879-890, 1991b. Liberati D et al, A new compartmental model approach to dialysis, Med Biol Eng Comput 31:171-179, 1993. Liberati D et al, Total and partial coherence of spontaneous and evoked EEG by means of multi-variable autoregressive processing, Med Biol Eng Comput 35:124-130, 1997. Liberati D and Turkheimer F, Linear spectral deconvolution of catabolic plasma concentration decay in dialysis, Med Biol Eng Comput 37:391-395, 1999. Liberati D, Piece-wise affine identification in dialysis, Nonlinear Analysis: Hybrid Systems 3:708-712, 2009a Liberati D. Biomedical applications of piece-wise affine identification
for hybrid systems, Annals of Biomedical Engineering, 37:18711876, 2009b Locatelli T, Cursi M, Liberati D, Franceschi M, Comi G, EEG coherence in Alzheimer's disease, Electroen Clin Neuro 106:229-237, 1998 Milotti E, Chignola R, Dalla Pellegrina C, Del Fabbro A, Farina M, Liberati D, VBL: Virtual Biophysics Lab, Il Nuovo Cimento 31 C (1): 109, 118, 2008 Muselli M and Liberati D, Binary rule generation via Hamming Clustering, IEEE T Knowl Data En 14;1258-1268, 2002 Orizio C, Liberati D, Locatelli C, DeGrandis D, Veicsteinas A, Surface mechanomyogram reflects muscle fibres twitches summation, J Biomech 29:475-481, 1996. Pagani M et al, Sympatho-vagal interaction during mental stress: a study employing spectral analysis of heart rate variability in healty controls and in patients with a prior myocardial infarction, Circulation, 83:43-51, 1991. Paoli G, Muselli M, Bellazzi R, Corvo’ R, Liberati D, Foppiano F, Hamming Clustering techniques for the identification of prognostic indices in patients with advanced head and neck cancer trated with radiation therapy, Med Biol Eng Comput, 38:483-486, 2000 Sacco E et al, A deterministic model describing intra-molecular regulation of hSos1, the major activator of the proto-oncoprotein Ras, BioMed@POLIMI, 2010 Sartorio A, De Nicolao G and Liberati D, An improved computational method to assess pituitary responsiveness to secretagogue stimuli, Eur J Endocrinol, 147: 323-332, 2002. Vercesi A, Sirtori C, Vavassori A, Setti E and Liberati D: Estimating germinability of Plasmopara Viticola oospores by means of neural networks, Med Biol Eng Comput 38:109-112, 2000 Section II.C Maffessanti F, Lang RM, Corsi C, MorAvi V, Caiani EG, Feasibility of left ventricular shape analysis from transthoracic realtime 3D echocardiographic images, Ultrasound Med Biol 35:1953-1962, 2009 Maffessanti F, Caiani EG, Tamborini G, Muratori M, Sugeng L, Weinert L, Alamanni F, Zanobini M, Mor-Avi V, Lang RM, Pepi M, Serial changes in left ventricular shape following early mitral valve repair, Am J Cardiol 106:836-42, 2010 Veronesi F, Corsi C, Sugeng L, Caiani EG, Weinert L, Mor-Avi V, Cerutti S, Lamberti C, Lang RM, Quantification of mitral apparatus dynamics in functional and ischemic mitral regurgitation using realtime 3-dimensional echocardiography, J Am Soc Echocardiogr, 21:347-54,2008. Votta E, Caiani E, Veronesi F, Soncini M, Montevecchi FM, Redaelli A, Mitral valve finite-element modelling from ultrasound data: a pilot study for a new approach to understand mitral function and clinical scenarios, Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 366:3411-34, 2008 Section II.D Carson RE, A maximum likelihood method for region of interest evaluation in emission tomography, J Comp Assist Tomogr 10:654663, 1986. De Bernardi E, Mazzoli M, Zito F, Baselli G, Resolution recovery in PET during AWOSEM reconstruction: a performance evaluation study, IEEE Trans Nuc Sci 54:1626-1638, 2007. De Bernardi E, Faggiano E, Zito F, Baselli G, Lesion quantification in oncological Positron Emission Tomography: a maximum likelihood partial volume correction strategy, Med Phys 36:3040-3049, 2009. Lange K, Carson R, EM reconstruction algorithms for emission and transmission tomography, J. Comp. Assist. Tomogr., 8:306-316, 1984 Liow JS, Strother SC, The convergence of object dependent resolution in maximum likelihood based tomographic image reconstruction, 38:55-70, 1993. Liu X, Comtat C, Michel C, Kinahan P, Defrise M, Townsend D
Comparison of 3-D reconstruction with 3D-OSEM and with FORE+OSEM for PET, IEEE Trans. Med. Imag., 20:804–814, 2001. Tylski P, Stute S, Grotus N, Doyeux K, Hapdey S, Gardin I, Vanderlinden B, Buvat I, Comparative assessment of methods for estimating tumor volume and standardized uptake value in 18F-FDG PET, J Nuclear Med, 51, 2010 Section II.E – Caffini M, Anatomical Brain Atlas for NIRS Measurements of Brain Activation”, BioMed@POLIMI, Nov 2010 – Contini D, Torricelli A, Pifferi A, Spinelli L, Paglia F, Cubeddu R., Multi-channel time-resolved system for functional near infrared spectroscopy, Optics Express 14: 5418-5432, 2006 – Contini D, Spinelli L, Torricelli A, Pifferi A, Cubeddu R, Novel method for depth-resolved brain functional imaging by time-domain NIRS, Proc. SPIE 6629: 662908, 2007 – Comelli D, Bassi A, Pifferi A, Taroni P, Torricelli A, Cubeddu R, Martelli F, Zaccanti G, In vivo time-resolved reflectance spectroscopy of the human forehead, Appl Opt 46:1717-1725, 2007 – Jobsis FF, Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters, Science 198:1264-1267, 1977 – Liebert A, Wabnitz H, Steinbrink J, Obrig H, Möller M, Macdonald R, Villringer A, Rinneberg H, Time-resolved multidistance nearinfrared spectroscopy of the adult head: intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons, Applied Optics 43:3037-3047, 2004 – Martelli F, Del Bianco S, Zaccanti G, Perturbation model for light propagation through diffusive layered media, Phys. Med. Biol. 50: 2159, 2005 – McCully KK, Hamaoka T, Near-infrared spectroscopy: what can it tell us about oxygen saturation in skeletal muscle?, Exerc Sport Sci Rev 28:123-127, 2000 – Molteni E, Co–Registration of EEG and Time–Domain fNIRS during a Divided Attention Task, BioMed@POLIMI, Nov 2010 Section III.A - Bailón R, Mainardi L, Orini M, Sörnmo L, Laguna P, Analysis of heart rate variability during exercise stress testing using respiratory information, Biomedical signal processing and control, 5:299–310, 2010. - Bianchi A, Mainardi LT, Petrucci E, Signorini M, Mainardi M, Cerutti S. Time- variant power spectrum analysis for the detection of transient episodes in HRV signal. IEEE Trans. Biomed. Eng. 40:136– 144, 1993 - Cerutti S, Bianchi AM, Mainardi LT. Advanced spectral methods for detecting dynamic behaviour. Auton Neurosci. 90:3-12, 2000. - Bianchi A, Mainardi LT, Meloni C, Chierchia S, Cerutti S. Continuous monitoring of the sympatho-vagal balance through spectral analysis. IEEE EMBS Mag. 16:64–73, 1997. - Foffani G, Bianchi AM, Priori A, Baselli G, Adaptive autoregressive identification with spectral power decomposition for studying movement-related activity in scalp EEG signals and basal ganglia local field potentials, J Neural Eng., 1:165-173, 2004. - Furlan R, Piazza S, Dell’Orto S, Barbic F, Bianchi A, Mainardi LT, Cerutti S, Pagani M, Malliani A, Cardiac autonomic patterns preceding occasional vasovagal reactions in healthy humans, Circulation 98:1756–176, 1998 - Kortelainen JM, Mendez MO, Bianchi AM, Matteucci M, Cerutti S, Sleep staging based on signals acquired through bed sensor, IEEE Trans Inf Technol Biomed., 14:776-85, 2010 - Mainardi LT, Bianchi AM, Furlan R, Piazza S, Barbieri R, di Virgilio V, Malliani A, Cerutti S, Multivariate time-variant identification of cardiovascular variability signals: a beat-to-beat spectral parameter estimation in vasovagal syncope, IEEE Trans. Biomed. Eng. 44:978– 989, 2007
- Mainardi L, On the quantification of Heart Rate Variability spectral parameters using time-frequency and time-varying methods, Phil. Trans. R. Soc. A, 367:255–275, 2009 - Mainardi LT, Bianchi AM, Cerutti S, Time–frequency and timevarying analysis for assessing the dynamic responses of cardiovascular control, Crit. Rev. Biomed. Eng. 30:175–217, 2002. - Mendez MO, Bianchi AM, Montano N, Patruno V, Gil E, Mantaras C, Aiolfi S, Cerutti S, On arousal from sleep: time-frequency analysis, Med Biol Eng Comput 46:341-51, 2008 - Mendez MO, Bianchi AM, Matteucci M, Cerutti S, Penzel T, Sleep apnea screening by autoregressive models from a single ECG lead. IEEE Trans Biomed Eng, 56:2838-50, 2009 - Petrucci E, Mainardi LT, Balian V, Ghiringhelli S, Bianchi AM, Bertinelli M, Mainardi M, Cerutti S, Assessment of heart rate variability changes during dipyridamole infusion and dipyridamoleinduced myocardial ischemia: a time variant spectral approach, J. Am. Coll. Cardiol. 28:924–934, 1996. Section III.B - Belykh I, Piccardi C, Rinaldi S, Synchrony in tritrophic food-chain metacommunities, Journal of Biological Dynamics, 3, 497-514, 2009. - Candaten M, Rinaldi S, Peak-to-peak dynamics: A critical survey, International Journal of Bifurcation and Chaos, 10:1805-1819, 2000. - Cerutti S, Esposti F, Ferrario M, Sassi R, Signorini MG. Long-term invariant parameters obtained from 24-h Holter recordings: a comparison between different analysis techniques. Chaos, 17:015108, 2007 - Colombo A, Dercole F, Discontinuity induced bifurcations of nonhyperbolic cycles in nonsmooth systems, SIAM Journal on Applied Dynamical Systems, 9:62-83, 2010. - Colombo A, Dercole F, Rinaldi S, Remarks on metacommunity synchronization with application to prey-predator systems, The American Naturalist, 171:430-442, 2008. - Dercole F, BPcont: an auto driver for the continuation of branch points of algebraic and boundary-value problems, SIAM Journal on Scientific Computing, 30:2405-2426, 2008. - Dercole F, Ferriere R, Rinaldi S, Chaotic Red Queen coevolution in three-species food chains, Proceedings of the Royal Society of London B, 277:2321-2330, 2010. - Dercole F, Kuznetsov Y, SlideCont: An Auto97 driver for bifurcation analysis of Filippov systems, ACM Transactions on Mathematical Software, 31:95-119, 2005. - Dercole F, Loiacono D, Rinaldi S, Synchronization in ecological networks: a byproduct of Darwinian evolution?, International Journal of Bifurcation and Chaos, 17:2435-2446, 2007. - Dercole F and Rinaldi S, Analysis of evolutionary processes: the adaptive dynamics approach and its applications, Princeton University Press, Princeton, NY, 2008. - Dercole F and Rinaldi S, Dynamical systems and their bifurcations, in Advanced Methods of Biomedical Signal Processing, S Cerutti and C Marchesi (eds.), IEEE-Wiley Press, New York, 2010. - Ferrario M, Signorini MG, Magenes G, Cerutti S, Comparison of entropy-based regularity estimators: application to the fetal heart rate signal for the identification of fetal distress, IEEE Trans Biomed Eng., 53: 119-25, 2006. - Ghezzi L and Piccardi C, PID control of a chaotic system: an application to an epidemiological model, Automatica, 33:181-191, 1997. - Kantz H, Kurths J, Mayer-Kress G (Eds) Nonlinear analysis of physiological data, Springer-Verlag Berlin Heidelberg New-York, 1998 - Kuznetsov Yu A, De Feo O, and Rinaldi S, Belyakov homoclinic bifurcations in a tritrophic food chain model, SIAM Journal on Applied Mathematics, 62:462-487, 2001.
- Kuznetsov Y and Piccardi C, Bifurcation analysis of periodic SEIR and SIR epidemic models, Journal of Mathematical Biology, 32:109121, 1994. - Kuznetsov Yu A, Rinaldi S, and Gragnani A, One-parameter bifurcations in planar Filippov systems, International Journal of Bifurcation and Chaos, 13:2157-2188, 2003. - Maggi S and Rinaldi S, Synchronization and peak-to-peak dynamics in networks of low-dimensional chaotic oscillators, International Journal of Bifurcation and Chaos, 16:3631-3642, 2006. - Meijer HGE, Dercole F, Oldeman BE, Numerical bifurcation analysis, in Encyclopedia of Complexity and System Science, RA Meyers (ed.), Springer-Verlag, Berlin, 2009. - Piccardi C, On parameter estimation of chaotic systems via symbolic time series analysis, Chaos, 16, 043115/1-10, 2006. - Piccardi C and Casagrandi R, Inefficient epidemic spreading in scalefree networks, Physical Review E, 77, 026113/1-4, 2008. - Piccardi C and Lazzaris S, Vaccination policies for chaos reduction in childhood epidemics, IEEE Transactions on Biomedical Engineering, 45: 591-595, 1998. - Rinaldi S, Synchrony in slow-fast metacommunities, International Journal of Bifurcation and Chaos, 19:2447-2453, 2009. - Schreiber T, Schmitz A, Surrogate time series, Physica D, 142:346382, 2000. - Signorini MG, Magenes G, Cerutti S, Arduini D, Linear and nonlinear parameters for the analysis of fetal heart rate signal from cardiotocographic recordings, IEEE Trans Biom Eng, 50:365-374, 2003. - Torri G, Rinaldi S, Piccardi C, Imperfect phase synchronization in the locomotor behavior of Halobacterium salinarium, International Journal of Bifurcation and Chaos, 13:3085-3092, 2003. Section IV.A - Andrä W. and Nowak H., Magnetism in Medicine, Weinheim: WileyVCH, 2006. - Di Rienzo L. and Haueisen J., Theoretical lower error bound for comparative evaluation of sensor arrays in magnetostatic linear inverse problems, IEEE Transactions on Magnetics, 42:3669-3673, 2006. - Di Rienzo L. and Haueisen J., Numerical comparison of sensor arrays for magnetostatic linear inverse problems based on a projection method, COMPEL, The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 26:356-367, 2007. - Lau S., Eichardt R., Di Rienzo L., Haueisen J., Tabu search optimization of magnetic sensor systems for magnetocardiography, IEEE Transactions on Magnetics, 44:1442-1445, 2008. - Leder U., Haueisen J., Huck M., Nowak H., Non-invasive imaging of arrhythmogenic left-ventricular myocardium after infarction, Lancet, 352:1825-1825, 1998. Section IV.B - Galloni P, Parazzini M, Piscitelli M, Pinto R, Lovisolo GA, Tognola G, Marino C, Ravazzani P, Electromagnetic fields from mobile phones do not affect the inner auditory system of Sprague-Dawley rats, Radiat. Res., 164:798-804, 2005a - Galloni P, Lovisolo GA, Mancini S, Parazzini M, Pinto R, Piscitelli M, Ravazzani P, Marino C, Effects of 900 MHz electromagnetic fields exposure on cochlear cells’ functionality in rats: evaluation of distortion product otoacoustic emissions. preliminary results. Bioelectromagnetics, 26:536-547, 2005b. - Galloni P, Lopresto V, Parazzini M, Pinto R, Piscitelli M, Ravazzani P, Marino C, No effects of UMTS exposure on the function of rat outer hair cells, Bioelectromagnetics, 30:385-392, 2009 - Lopresto V, Pinto R, De Vita A, Mancini S, Galloni P, Marino C, Ravazzani P, Lovisolo GA, Exposure setup to study potential adverse effects at GSM 1800 and UMTS frequencies on the auditory systems
of rats, Radiat Prot Dosimetry, 123:473-82, 2007 - Paglialonga A, Tognola G, Parazzini M, Lutman ME, Bell SL, Thuroczy G, Ravazzani P, Effects of mobile phone exposure on time frequency fine structure of transiently evoked otoacoustic emissions, J. Acoust. Soc. Am., 122: 2174-2182, 2007 - Parazzini M, Bell S, Thuroczy G, Molnar F, Tognola G, Lutman ME, Ravazzani P, Influence on the mechanisms of generation of distortion product otoacoustic emissions of mobile phone exposure Hear. Res. 208:68-78, 2005. - Parazzini M, Tognola G, Franzoni C, Grandori F, Ravazzani P, Modelling of the internal fields distribution in human inner hearing system exposed to 900 and 1800 MHz, IEEE Trans. Biomed. Eng., 54:39-48, 2007a. - Parazzini M, Ravazzani P, Tognola G, Thuroczy G, Molnar F, Sacchettini A, Ardesi G, Mainardi LT, Electromagnetic fields produced by GSM cellular phones and heart rate variability, Bioelectromagnetics, 28:122-129, 2007b. - Parazzini M, Brazzale AR, Paglialonga A, Tognola G, Collet L, Moulin A, Lutman ME, Bell SL, Thomas NA, Uloziene I, Uloza V, Thuroczy G, Tavartkiladze G, Tsalighopoulos M, Kyriafinis G, Ravazzani P, Effects of GSM cellular phones on human hearing: the European project “GUARD”, Radiat. Res., 168:608-613, 2007c. - Parazzini M, Galloni P, Piscitelli M, Pinto R, Lovisolo GA, Tognola G, Ravazzani P, Marino C: Possible combined effects of 900 MHz continuous wave electromagnetic fields and gentamicin on the auditory system of rats, Radiat Res., 167:600-605. 2007d - Parazzini M, Sibella F, Lutman ME, Mishra S, Moulin A, SliwinskaKowalska M, Woznicka E, Politanski P, Zmyslony M, Thuroczy G, Molnár F, Kubinyi G, Tavartkiladze G, Bronyakin S, Uloziene I, Uloza V, Gradauskiene E, Ravazzani P, Effects of UMTS Cellular Phones on Human Hearing: Results of the European Project “EMFnEAR”, Rad. Res., 172 :244-251, 2009. - Parazzini M, Lutman ME, Moulin A, Barnel C, Sliwinska-Kowalska M, Zmyslony M, Hernadi I, Stefanics G, Thuroczy G, Ravazzani P, Absence of short-term effects of UMTS exposure on the human auditory system, Rad. Res., 173:91-97, 2010a. - Parazzini M, Sibella F, Paglialonga A, Ravazzani P, Assessment of the exposure to WLAN frequencies of a head model with a cochlear implant. Bioelectromagnetics, 31:546-555, 2010b - Ravazzani P, The interpretation of the results of the research on electromagnetic fields and health in Europe: the EC Coordination Action EMF-NET, Annals of Telecommunications, 63:11-15, 2008. - Repacholi MH, Ravazzani P, Proceedings of WHO-sponsored symposium on Sensitivity of Children to EMF Exposure – Preface (Erratum of Bioelectromagnetics 2005, 26 (S7), S2-S4), Bioelectromagnetics, 27:430-430, 2006. - Sibella F, Parazzini MA, Paglialonga A, Ravazzani P, Assessment of SAR in the tissues near a cochlear implant exposed to radiofrequency electromagnetic fields, Phys. Med. Biol., 54:135-141, 2009. - Tognola G, Burdo S, Caponio M, Norgia M, Parazzini M, Ravazzani P, Grandori F, Svelto C, Measurement of electrode current pulses from cochlear implants, IEEE Trans. Instrumentation and Measurement, 54:2105-2112, 2005. -Tognola G, Pesatori A, Norgia M, Parazzini M, Di Rienzo L, Ravazzani P, Burdo S, Grandori F, Svelto C, Numerical modeling and experimental measurements of the electric potential generated by cochlear implants in physiological tissues, IEEE Trans. Instrum. Measur., 56:187-193, 2007. - Tura A, Sbrignadello S, Cianciavicchia D, Pacini G, Ravazzani P: A low frequency electromagnetic sensor for indirect measurement of glucose concentration: in vitro experiments in different conductive solutions, Sensors, 10:5346-5358, 2010.
