Biomedical signal and image processing

Generally, physiological modeling and biomedical signal processing constitute two important paradigms of bio-medical engineering (BME): their fundamental concepts are taught starting from undergraduate studies and are more completely dealt with in the last years of gradu-ate curricula, as well as in Ph.D. courses. Traditionally,

these two cultural aspects were separated, with 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 those who did models did not do

By Sergio Cerutti, Giuseppe Baselli, Anna Maria Bianchi, Enrico Caiani, Davide Contini, Rinaldo Cubeddu, Fabio Dercole, Luca Di Rienzo, Diego Liberati, Luca Mainardi, Paolo Ravazzani, Sergio Rinaldi, Maria Gabriella Signorini, and Alessandro Torricelli

Digital Object Identifier 10.1109/MPUL.2011.941522

Date of publication: 2 June 2011

A Need for Close Integration

©BRAND X PICTURES, IMAGE SOURCE

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signal processing and vice versa. However, in recent years, the need for closer integration between signal processing and modeling of the relevant biological systems emerged very clearly [1], [2]. This is not only true for training pur-poses (i.e., to properly prepare the new professional mem-bers of BME) but also for the development of newly con-ceived research projects in which the integration between biomedical signal and image processing (BSIP) and model-ing plays a crucial role. Just to give simple examples, topics such as brain–computer machine or interfac-es, neuroengineering, nonlinear dynamical analysis of the cardiovascular (CV) system, integration of sensory-motor characteristics aimed at the building of advanced prosthe-ses and rehabilitation tools, and wearable de-vices for vital sign monitoring and others do require an intelligent fusion of modeling and signal processing competences that are cer-tainly peculiar of our discipline of BME [3].

This integration process could comprehend parameters and observations detected at differ-ent scales and organs and with different modalities [4]. Such a paradigm is called the multivariate, multimodality, multi-scale approach, where it is clear how important information enhancement and synergy are obtained with certainty when integrating multivariate analysis (i.e., more signals from the same physiological system) with a multiorgan approach (i.e., correlating information derived from different organs, such as 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).

This article deals with three basic topics, which are arranged as follows. In the “Integration of BSIP and Biomedical Mod-eling” section, various contributions will approach different application fields in which the fusion of signal processing and modeling will be a recurrent keyword. In the “Advanced Al-gorithms for Biomedical Signal Processing” section, advanced methods for biomedical signal and system interpretation will be recalled (i.e., time-frequency and time-scale approaches, as well as complexity measurements derived from nonlinear dynamics) with a wide possibility of applications in biomedical field. Fi-nally, the “Electromagnetic Field Imaging in Biomedical Appli-cations” section will deal with innovative electromagnetic map-pings, which are finding a growing interest in both diagnostic and therapeutic applications.

Integration of BSIP and Biological Modeling

Model-Based Signal Processing of Cardiovascular Regulation

The research line on heart rate variability (HRV) signal, started in the mid-1980s for the assessment of autonomic control, was soon extended to other CV signals, mainly arterial pressure (AP), which at the time was invasively monitored [5] while reliable noninvasive pletismographic recordings were being introduced. The availability of multiple contemporaneous signals contain-

ing information of different sites within CV regulation circuits (e.g., autonomic outflow to the heart by HRV and response to cardiac ejection combined to vasomotor activity by AP) brought forward the problem of a suitable analysis of the physiological interactions, which could be more specific to autonomic regula-tion compared with 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 identi-fication, as shown in Figure 1. A first exam-ple was provided by a model of HRV-AP loop regulation [6], which feeds back baroreflex responses on the heart, adjusting heart rate to correct AP in turn (see Figure 2). The pro-posed causal interaction layout and paramet-ric structure considered an additional AP-AP loop, as well as an autoregressive structure of the stochastic parts (i.e., unmeasured inputs) of both HRV and AP. A key point was the in-

clusion of respiration recording entering at both HRV and AP levels. The advantage of this approach relies in augmenting the statistical power of data analysis by the inclusion of gen-erally accepted knowledge while leaving sufficient degrees of freedom for fitting individual or condition-related features and as an answer to unknown questions (e.g., level of baro-reflex activity [7], including gain of mechanical action of HR on AP [8], resonance of loops and role in generating HRV rhythms versus spectral content of stochastic residuals [8], physiological pathways for respiratory sinus arrhythmia, and role of cardiopulmonary reflexes [9]).

In parallel with a linear analysis of causal interactions, the complexity of the system shown in Figure 1 was investigated in several directions. Variable-phase locking patterns between respiratory activity and sympathetic outflow were analyzed in decerebrate artificially ventilated cats under sympathetic or va-gal activation [10], finding a rich variety of behaviors typical of complex nonlinear interactions between oscillators at high (HF) and low frequencies (LF) on a forcing input. The synchroniza-tion/desynchronization conditions of distributed vasomotor LF oscillators were described in a simulation study [11], showing the natural tendency to phase opposition of two peripheral dis-tricts and maximum phase distribution of many when a sympa-thetic drive is switched off. The nonlinear nature of peripheral resistances was further analyzed in a lumped model study of the vascular tree connected to peripheral districts with active autoregulation [12].

Toward Systems Biology: Modeling Biosignals

Linear time-invariant multivariable models have been used earlier to investigate central [13] and autonomic [14] nervous systems. Studies on multiple sclerosis and Alzheimer’s disease [15], learning and stress [16] as well as intention [17] also ben-efit from such techniques. Deconvolution [18] has been suc-cessfully applied in reconstructing the course of the not directly accessible pituitary secretion from blood concentration [19].

Linear time-invariant multivariable models have been used ever since in investigating

central and autonomic nervous systems.

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Logical networks have been developed to infer prognostic factors in oncology [20], besides selecting salient features, such as principal components analysis [21]. Time-variant dynamics has been initially modeled via Kalman filtering [22].

Piecewise affine identification [23] of hybrid logical and dy-namical processes has been finally developed to reduce the in-vestigated problems as piecewise linear by identifying data from switches among subsequent epochs. Various applications are described in [24] and [25].

Biophysics simulation of the modeled behavior allows to in silico emulate pathophysiology [26] toward systems biology [27].

Clinical Parameter Detection

Through Cardiac Modeling

The research activity at the Department of Biomedical Engi-neering 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 re-gurgitation associated with degenerative MV prolapse is one of the most common valvular pathologies in the industrialized

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FIGURE 2 Translation of Figure 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 vari-ability. 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 [6].

FIGURE 1 Causal structure (thick arrows) of respiration, AP, and 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 barorecep-tors (AB), and cardiopulmonary reflexes.

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countries, and it is characterized by high mor-bidity and mortality. The MV repair, with in-sertion of a prosthetic ring on the MV annulus (annuloplasty), is currently the primary surgi-cal solution for this pathology. In this scenario, our efforts were aimed at characterizing the in vivo behavior of the prosthetic device as well as studying the effects of this surgery on left ven-tricular (LV) remodeling.

Our innovative approach is based on the combined analysis and integration of the most advanced cardiac imaging techniques [real-time three-dimensional (3-D) echocardiogra-phy (RT3DE), cardiac magnetic resonance] with advanced image processing and finite element modeling tech-niques (Figure 3), to obtain patient-specific information on an MV (see www.surgaid.org for more details).

Mitral annulus was tracked frame by frame [28] in a 3-D space from RT3DE data sets to evaluate the dynamic pattern of change of several geometric and functional valvular parameters, and this information, together with papillary muscle tips posi-tion, was used as a boundary condition in the definition of fi-nite element structural models. This approach was applied in a group of patients with severe MV regurgitation receiving a flex-ible (FLEX) band or a complete rigid (RIG) ring, as well as in a

control group (NL). As expected, in the presence of MV regurgitation, annulus is enlarged and less planar compared with NL. Annuloplasty resulted in reduced areas in both RIG and FLEX and in a more planar annular shape. Preliminary results of the modeling approach are also promising to use this patient-specific analysis in a surgical planning scenario as a predictive tool [29].

In the context of a nationally funded project (PRIN 2007, www.surgaid.org) and in collabo-ration with Centro Cardiologico Monzino, Mi-lan, an algorithm for LV shape assessment from RT3DE data [30] was developed, resulting in the computation of 3-D shape indices of sphericity

(S) and conicity (C), independent of LV dimensions.The obtained results give new insight for the in vivo perfor-

mance of the implanted rings and for the subsequent cardiac re-modeling, offering new indices for the clinical decision process and follow-up.

Lesion Evaluation in Fluorodeoxyglucose-PET

The quantitative information theoretically delivered by positron emission tomography (PET) is consistently smeared by its limited resolution, with a high dependence on object (lesion and back-ground), position in the scanner, and count statistics.

FIGURE 3 From RT3DE to finite element model of an MV: (a) RT3DE data set, (b) extracted MV annulus, (c) stress distribution computed from finite element model, and (d) MV annulus displacement throughout the cardiac cycle.

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The theoretical framework provided by maximum likeli-hood [31] and the relevant iterative algorithm of attenuation-weighted ordered subset expectation maximization (AWOSEM) [32] provides a powerful means to deal with the Poissonian fea-tures of collected data. In this algorithm, the correction of count data, yi, by the specific attenuation correction factor, ACFi, is explicit in the iterations to preserve the Pois-sonian assumption. The elements of the system matrix, aij, link activity li in the jth image ele-ment (either voxel or basis function [33]) to the ith measure, yi. To preserve Poissonian features, AWOSEM avoids application of attenuation cor-rection, ACFi, on data, but it corrects system co-efficients, aij/ACFi, through an iterative formula.

Intensive research has been carried out in recent years to evaluate the benefits of in-cluding further features such as space-variant blurring for resolution recovery, regularizing factors through basis functions, and targeted object features; also, convergence properties [34] and their object/algorithm dependence have been ana-lyzed concerning their effects on lesion detectability and le-sion quantification.

The Department of Bioengineering in cooperation with the Nuclear Medicine Department, Fondazione IRCCS Ca’Granda Ospedale Maggiore Policlinico, has explored several aspects in this field, mainly centered on the construction, estimation, and validation of a parametric model of space-variant blur-ring in a 3-D modern scanner for resolution recovery [35]. A two-dimensional transaxial approach was used after a suitably optimized Fourier re-binning (FORE); nonetheless, a 3-D blurring model was worked out for a full resolution re-covery: radial, tangential, and axial.

The flexibility and robustness of the blur-ring model permitted a thorough analysis of convergence and its object dependence. The main conclusion of these studies was that res-olution recovery was able to improve the esti-mate of the total activity within a lesion, with better control over noise amplification (noise breakup) phenomena, as shown in Figure 4. However, the iterations required for quanti-fication did not improve the diagnostic read-ability compared with the standard clinical images that are smooth and far from conver-gence to avoid false positives.

Finally, an AWOSEM-region algorithm [36] was proposed, which considered few image ele-ments: 1) voxels 100% within lesion, 2) partial volume voxels, 3) transition region affected by lesion spill-out, and 4) background, i.e., the rest of image is frozen at low resolution. Iteration of this procedure with lesion segmentation ad-justment proved to recover blurring and partial volume effects, providing a reliable estimate of lesion volume and total activity.

Time-Resolved Functional

Near-Infrared Spectroscopy

Basic Principles and Instrumentation

Starting almost 30 years ago with the pioneering work of Jobsis [37], noninvasive functional near-infrared spectros-

copy (fNIRS) has been first used to inves-tigate, experimentally and clinically, brain oxygenation in neonates and adults and later used to assess muscle oxidative metabolism in pathophysiology [38]. An fNIRS employs optical radiation in the range 600–1,000 nm, where light attenuation by tissue con-stituents (water, lipid, oxyhemoglobin, and deoxyhemoglobin) is relatively low and ac-counts for an optical penetration through several centimeters of tissue. Absorption and scattering coefficient are measured to opti-cally characterize tissues: the first param-eter describes the tissue content while the

second characterizes the tissue structure. The difference in the absorption spectra of oxy- and deoxyhemoglobin 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 at-tenuation at two wavelengths between a couple of optical fibers, placed on the tissue surface, at a known relative dis-tance (typically 2–4 cm). The key limitations of CW fNIRS

FIGURE 4 PET/CT pulmonary patient data reconstructed with (a) standard voxel-based AWOSEM and (b) AWOSEM region.

A key point in TR fNIRS is the ability

to separate systemic hemodynamic changes from

functional changes related to brain

activation.

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techniques are the coupling between the absorption and scattering coefficient, causing the lack of quantitative assess-ment 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 frequency domain (FD) technique extracts both mean scattering and absorption co-efficients of the probed medium, provided that a nontrivial 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 pi-coseconds) laser pulse injected in a diffusive medium. Recently, some groups have devel-oped compact systems for time-resolved (TR) fNIRS [39].

Continuous Wave fNIRS Data Analysis

In principle, FD and TR fNIRS provide a richer insight to the problem of noninvasively probing a diffusive medium. These ap-proaches can discriminate between absorption and scattering contributions and derive absolute values for the hemodynamic parameters. The accuracy of hemodynamic parameters estima-tion mainly depends on three aspects: 1) the accuracy of the theoretical model describing photon propagation in a turbid me-dium such as a biological tissue, 2) the knowledge of the real bulk optical properties of the tissue, and 3) the knowledge of the real tissue structure. Analytical model for homogeneous me-dium or simple structured medium (e.g., layered medium) can be derived [40]. For a highly heterogeneous medium, such as the human head, it is possible to use numerical methods such as Monte Carlo or finite elements. These methods, for their practical and effective use with TR or FD setup, require a large amount of computational time and a priori information about the structure of the head [e.g., the anatomical images provided by magnetic resonance imaging (MRI) scan]. Apart from 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 date, no one has accurately measured the optical properties of the different structures of the head [41].

In our opinion, TR should be preferred to FD fNIRS, be-cause TR techniques rely on an easier approach to the prob-lem of depth sensitivity. A key point in TR fNIRS is the abil-ity to separate systemic hemodynamic changes, occurring particularly in the scalp, from functional changes related to

brain activation. In fact, analyzing the first part of the TR curve (early gate), we consider pho-tons that travel few hundreds of picoseconds into the tissue and, thus, have a low probabil-ity 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 (Figure 5).

Thus, exploiting the depth information, naturally encoded into the photon’s arrival time, it is possible to discriminate extra- and intracerebral activities [42], [43].

TR fNIRS can be integrated with other functional techniques such as electroencephalography (EEG) to merge different types of data to better explain the relation between electrical and metabolic brain activity [44]. TR fNIRS can also be integrated with fMRI to compensate for the lack of anatomical informa-tion [45].

Advanced Algorithms for Biomedical Signal Processing

Time-Frequency and Time-Variant

Methods for Biomedical Signal Processing

Many biomedical signals are characterized by oscillatory pat-terns (or rhythms), which carry relevant information for diag-nostic and therapeutic purposes as well as for understanding the underlying physiology. Typical examples are the d, u, a, and b rhythms of the EEG and the LF and HF components of the HRV signal.

The analysis of these oscillatory patterns is usually per-formed by spectral analysis using both nonparametric [fast Fourier transform (FFT)-based] and parametric [autoregres-sive (AR)/moving average (ARMA) model based] approaches. These tools require the signal to be stationary in the analysis window. However, biomedical signals are characterized by tran-sient waveforms of various natures (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 that 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 Politec-nico di Milano has been very active in this field since the begin-ning and contributed with both methodological innovations and novel applications. A review of these activities in the analysis of HRV signals can be found in [46]–[48]. Here, only a brief sum-mary of the main findings will be reported.

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Many biomedical signals are

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Methods

The most diffused approaches for time-frequency representation (TFR) of a signal can be summarized in three main categories: 1) linear decomposition, 2) quadratic distributions, and 3) adaptive parametric models.

Linear Decomposition of the Signal

The fundamental mathematical tool for time-frequency analy-sis 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, we obtain a Fourier transform (FT) of the signal; if the basis functions are localized in both time and frequency, the coefficients of the decomposition constitute the TFR of the signal. An example is given by the short-time FT (STFT) in which the basis functions are time-windowed sinusoids. Time and frequency properties are not independent; in fact, they are linked by the Heisenberg’s inequality according to the fol-lowing expression:

Df # Dt $1

4p.

The smaller the time duration of the basis functions, the better the time resolution (Dt) and poorer the frequency resolution (Df). Usually, a signal is characterized by short-time, HF components superimposed to long-time, LF com-ponents; thus, a compromise is needed in the choice of the proper basis. To overcome this limitation, a multiresolution decomposition can be achieved through the wavelet trans-form (WT), where the decomposition basis is obtained from a mother wavelet (or function) that is stretched or shrunk in time to obtain orthonormal bases characterized by different time-frequency resolutions.

Quadratic Distributions

A quadratic TFR is usually associated with the concept of in-stantaneous power spectral density (PSD). Two popular exam-ples of quadratic distributions are the spectrogram and scalo-gram, obtained by squaring the coefficients of 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 (WD) distribution. Different versions of WD have been proposed in literature to reduce the presence of cross terms in the time-frequency plane, and these are en-closed in the Cohen class.

Adaptive Parametric Models

The parametric approach to the estimation of PSD assumes that the time series under analysis is the output of a given process, whose parameters are, however, unknown. Usually, the model

is independent of the physiology or the anatomy of the bio-logical 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: 1) choice of the correct model for the description of the data, 2) estimation of the model parameters based on the recorded data, and 3) calculation of the 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 PSD can be calcu-lated for each new sample in the data. A forget-ting factor can be added in the estimation proce-dure to make the updating parameter procedure more dependent on the more recent data while the oldest ones are forgotten with an exponen-tial decay. In such a way, the sample-by-sample

estimation is able to track changes in the signal characteristics, and a TFR of the signal is obtained.

Applications

Spontaneous Myocardial Ischemia

An interesting field of application is the study of relationships between autonomic nervous system (ANS) and myocardial ischemia, either spontaneous or induced. An early result, ob-tained by AR-based time-varying methods [49], puts into evi-dence an LF increase within the 2 min preceding the ischemic attack. When different ischemic events are considered, different trends were observed, all documenting an important involve-ment of ANS in either generating or sustaining the attack. In particular, a different interplay between ANS and variant or stable angina was documented [50]. An example of HRV signal analysis during stable angina is presented in Figure 6.

Provocative Tests

Many clinical tests (such as stress test) induce changes in ANS modulation of the heart beat. The response is depen-dent on the amplitude of the stimulus: a faster (and larger) sympathetic response was observed for more pronounced tilt angles [47]. When the tilt was prolonged, oscillations and nonstationarity characterized the trend of the LF components, being more evident in patients with syncope [51]. The study also documented a sympathetic withdrawal preceding syncope, which may be either sudden or pro-gressive. In addition, using the time-variant model in the bivariate form, an autonomic mismatch between HR and blood pressure regulation was also observed before synco-pe [52]. 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 ischemia, but preceding the ST displacement on the ECG [53]. The time-variant pa-rameters were therefore documented to be an early sign of ischemia of clinical interest.

A quadratic TFR is usually associated with the concept of

instantaneous power spectral density.


Sleep Studies

Sleep is a physiological condition that can be altered by many pathological events. Even if sleep evaluation is mainly based on the analy-sis of EEG, it also affects the peripheral systems and the related signals, such as the HRV and the respiration signal. Thus, the typical param-eters that quantify the dynamical changes of the HRV signal, namely LF and HF powers, significantly change in the different sleep stages and in the presence of pathological events such as sleep apneas and mi-croarousals. As the HRV signal is highly nonstationary dur-ing sleep, time-frequency methods are required for correct analysis. Time-variant AR model has been used for automatic sleep classification [54] and for apnea detection [55] from the HRV, while smoothed pseudo-Wigner-Ville was used for the characterization of ANS during microarousals [56].

EEG Processing

It is well known that, during the execution of voluntary move-ments or even during motor imagery, there is a power decreas-ing in the alpha range [alpha desynchronization or alpha event-related desynchronization (ERD)] related to the begin-

ning of the movement, but preceding its ex-ecution, and a marked power increasing in the beta range [beta event-related synchronization (ERS)] at the end of the movement. In a recent article, such dynamics are quantified through the time-frequency technique, namely adaptive parametric models that are particularly suit-able for this application, because in this way it is possible to put into evidence both power and

frequency changes in the rhythms of interest [57].

Complexity in Biomedical Systems

and Nonlinear Parameters Measurements

Methods and Modeling Approach

The research group at the Department of Electronics and Information at Politecnico has been actively working on the methodologies for the analysis of complex signals and sys-tems. In the area of bifurcation analysis [57], [58], studies have yielded theoretical contributions [59]–[61], numerical methods [62], [63], 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

Bifurcation theory has been successfully

applied to the analysis of evolutionary

processes in biology.

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FIGURE 6 (a) Recursive algorithm for the time-variant estimation of AR model coefficients. (b) Sequence of the PSDs as output of the recursive algorithm during a stable angina episode. Each PSD corresponds to a single sample in the signal.


for modeling, parameter estimation, and con-trol of chaotic systems.

Epidemic spreading is one of the areas where the earlier methods have been exploited. The full two-parameter bifurcation analysis of the classi-cal SIR/SEIR models has disclosed and classified many epidemiological regimes that are observed in real-world data [64] and has paved the way to classical (i.e., proportional integral derivative) and fuzzy control schemes for reducing the im-pact of epidemics. 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 [65].

Bifurcation theory has been successfully applied to the analysis of evolutionary processes in biology. In particular, the research group has contributed to the methodological de-velopment 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 [66]) 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 [58].

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 (per-haps by producing recurrent spikes or bursts). A huge num-ber of systems naturally call for this modeling, in particular in neurosciences. In this context, one of the main issues is the study of synchronization, i.e., the possibility that all the sys-tems oscillate in unison, since this fact is of paramount im-portance in many applications, including the study of many pathologies (e.g., Parkinson’s disease and epilepsy). The results obtained within the research group on this issue have been collected in a series of papers [67]–[70], but they have also been described in detail in plenary lectures at the 2006 Inter-national Symposium on Nonlinear Theory and its Applications (NOLTA 2006, Bologna), at the 6th European Conference on Ecological Modeling (ECEM 2007, Trieste), and at the Interna-tional 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 nonlinear dynamical system analysis. This has led to the in-troduction of 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 hu-man life support systems among which the heart plays a dominant role. The complex structure of the HRV signal has been widely studied to identify the complex nature of its con-

trol mechanisms. The aim is 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 sig-nal, through classical linear methods, either in time or FD, provided two main outcomes: the quantification of some important properties of the regulating action performed by the ANS in the short period and the information carried by this signal may not be totally explained by

a linear approach [71].This second statement confirms the value of the analysis

approach through nonlinear methods. Results on HRV sig-nal analysis have shown that its dynamic behavior involves nonlinear components that also contribute in the signal gen-eration and control [72]. 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 the different methods investigating both geometric and dy-namic signal features.

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 with a determinism test based on surrogate data confirming that it 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, and Fourier spectrum) with original series. The null hypothesis the test wants to reject is, “a stochastic lin-ear process generates the HRV time series” [73].

Results in 24-h HRV series have shown that the structure generating the signal is neither linear nor stochastic. Further-more, methods quantifying fractal and self-similar monofractal characteristics [1/f a spectrum, detrended fluctuation analysis (DFA)] and regularity and complexity statistics (approximate and sample entropy: ApEn, SampEn as well as Lempel-Ziv com-plexity) allow to characterize the HRV signal distinguishing pathological from healthy subjects [74]. Figure 7(a) reports a 24-h HRV signal recorded from a Holter tape in a normal case compared with a transplanted heart patient [Figure 7(b)]: a-power law coefficient in 24 hours is significantly different in the two cases.

Among other applications, examples of this approach con-cern CV pathologies and fetal heart rate analysis.

Electromagnetic Field Imaging

in Biomedical Applications

Magnetocardiographic Field and Diagnostic Imaging

Magnetocardiographic field imaging (MFI) is a technique used to record the contact-free magnetic field distribution and esti-mate the underlying source distribution in the heart [75]. Typi-cally, the cardiomagnetic fields are recorded with superconduct-ing quantum interference devices (SQUIDs) [76]. SQUIDs are

Recently, new technologies of

magnetic sensor systems for

magnetocardiography make feasible a less

restrictive sensor positioning.


restricted in their positioning to cryostats, since they require liquid helium (low-temperature superconductors) or nitrogen (high-temperature superconductors) cooling.

However, recently, new technologies of magnetic sensor sys-tems for magnetocardiography make feasible a less restrictive sensor positioning. Therefore, the general question arises: how to optimally place the sensors obeying a technical minimum dis-tance 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 [77], [78]. Since the generation of the kernel matrix for a given position of magnetic sensors is computationally expensive, a precomputation for a dense enough grid of sensor positions and orientations is needed. Consequently, the search space of the op-timization scheme is discretized.

Simulation Setup

A three-compartment boundary element model (BEM) of the torso (conductivity 0.2 S/m) and lungs (0.04 S/m) is cre-ated from a T1-weighted MRI for a 72-year-old participant (Figure 8). We model the cardiac sources with 13 dipoles regularly arranged around the LV blood mass. The measure of the averaged heart cycle (PQRST) data from the patient (195-channel vectorial magnetometer system Argos200, AtB SrL, Italy) serves for the estimation of the orientation of the dipoles with a minimum norm approach with L-curve regu-larization. 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 sen-sor setups: one realistic and two idealized ones. The idealized setups are an 8 3 8 three-axial (measuring three magnetic field components) magnetometers array and a 14 3 14 mono-axial magnetometers array (in Figure 8, 14 3 14 1-D), cover-ing the same area. The realistic setup is the Argos200 compris-ing 65 three axial sensors. All setups provide approximately the same number of measurement channels and are posi-tioned in front of the chest of a healthy volunteer [77], [78].

Electromagnetic Field Exposure

and Biomedical Applications

The Milan Unit of the CNR Institute of Biomedical Engineer-ing (ISIB CNR) is internationally acknowledged for their studies on the effects of human exposure to electromagnetic fields (EMFs) and on computational modeling of the interac-tion between EMF and the dielectrically inhomogeneous hu-man 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 an 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 as-sessing or optimizing therapeutic or diagnostic medical appli-cation that employ EMF.FIGURE 8 The BEM and source models.

8

6

4

2

0

–2

0

–1

–2

–3

–4

–5

–6

–7

–8

–4–6 –5 –4 –3 –2 –1 0

log (Hz)

–5 –4 –3 –2 –1 0log (Hz)

(a)

(b)

log

(sec

2 /H

z)lo

g (s

ec2 /

Hz)

R = 0.34Slope = –1.08

R = 0.59Slope = –1.66

Normal Subject

Heart-Transplanted Subject

R = 0.34RSlope = –1.08

R = 0.59RSlope = –1.66

FIGURE 7 (a) Log–log spectra calculated in 24-h HRV signal in a normal subject and (b) in a patient after heart transplant. The slope represents the α coefficient in α-power law spectrum.


The main results of the ISIB unit in this area were on:1) Numerical estimation (using finite integration techniques)

of the radio frequencies EMF distribution in human head or trunk by devices and systems for mobile communication, es-pecially on mobile phones and wireless fidelity (WiFi). This also includes the computational estimation of the coupling of environmental EMF with active and passive medical implants in the human body, mainly focusing on cochlear implants and neural stimulators [79]–[82]. In particular, the main re-cent findings of these studies were related to the quantita-tive confirmation that the EMFs and the specific absorption rates (SARs) at the level of the peripheral hearing organs in humans due to exposure to mobile phones at global system for mobile communication (GSM) and universal mobile tele-communications system (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 [transient direct current stimulation (tDCS)] and magnetic stimulation, deep brain stimulation, radio frequency identi-fication (RFID) applications in health environ-ment, and electromagnetic sensor [83], [84]. 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, evaluation of the electric fields and cur-rent densities generated by brain stimulators in the cortex and white matter, identifying the different influence on the fields because of the use of different electrodes in terms of size and shape in tDCS, and the assessment of the exposure to passive RFID reader during new-born–mother identity reconfirmation pro-cedure in neonatal clinics. In the latter case, sensitive levels of exposure of the newborns were identified, and an innovative relation-ship between the maximum generated magnetic fields and the time of use of the device close to the body was proposed. See Figure 9 for an illustrative example.

3) Study of the potential health effects of exposure of biological systems to EMFs [79], [80], [85]–[88]. The main findings were related to the study of the effects of exposure of the animal and human hearing system to mobile phone radiation at GSM (900–1,800 MHz) and UMTS (around 2.0 GHz) frequencies. In particu-lar, no acute effect was found on the main audiologi-cal measure in both animals and humans, considering controlled exposure to GSM and UMTS phones at the maximum permitted power.

Currently, ISIB CNR is serving as a central coordinator of the European Health Risk Assessment Network on Electromag-netic Fields Exposure (EFHRAN) Project, 2009–2012, and has previously served as a central coordinator of three multicen-

tric projects funded by the European Commission: GUARD (FP5) and EMFnEAR (DG Health and Consumer Protection) that were focused on mobile phone exposure and hearing; EMF-NET (FP6) was a large coordination action aimed to in-

terpret the mass of results of scientific research on EMF and health impact.

Summary and Conclusions

BSIP constitutes a major field of interest in both educational aspects and research environments in BME. In fact, the physiological knowledge improvement in a wide variety of innova-tive research as well as the implementation in many clinical procedures extensively makes use of these concepts in more or less sophisti-cated medical applications. In this article, the important links between BSIP and physiological modeling and their important derived synergies are particularly stressed. In support of this aim, examples have been provided in the areas of CV system studies, as well as in neurosciences

and functional imaging, by using different modalities, including TR fNIRS. Along this direction, the integration operation of the detected information between multiple signals, organs, modali-ties, 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, such as time-frequency and time-variant approaches, have been investi-gated in the biomedical field together with the complexity mea-surements, most often carried out through nonlinear dynamical approaches where, also in this context, the integration between modeling and information processing plays a fundamental role. Finally, a few examples have been described in which the study of EMFs, in the form of signals and images properly detected, have a relevant impact on various biomedical applications.

Sergio Cerutti, Giuseppe Baselli, Anna Maria Bianchi, Enrico Caiani, Luca Mainardi, and Maria Gabriella Signorini are with

0.073 (A/m)

00 1.57 V/m

(a) (b)

0 1.5

FIGURE 9 (a) Electric field distribution on the head tissues on a transversal plane passing through the anode during tDCS of the primary motor cortex; (b) distribution of the magnetic field in a whole-body newborn model generated by an RFID identity reconfirmation system.

The ISIB unit quantitatively demonstrated

that the use of mobile phones and the

exposure to WiFinetwork do not

interfere with the functionality of

implantedcochlear implants.


the Dipartimento di Bioingegneria, Politecnico di Milano, Mi-lano. Davide Contini, Rinaldo Cubeddu, and Alessandro Tor-ricelli are with the Dipartimento di Fisica, Politecnico di Milano, Milano. Fabio Dercole and Sergio Rinaldi are with the Diparti-mento di Elettronica e Informazione, Politecnico di Milano, Mi-lano. Luca Di Rienzo is with the Dipartimento di Elettrotecnica, Politecnico di Milano, Milano. Diego Liberati is with CNR Con-siglio Nazionale delle Ricerche, Istituto di Elettronica e di In-gegneria dell’Informazione e delle Telecomunicazioni e Istituto Nazionale di Fisica Nucleare, Milano. Paolo Ravazzani is with CNR Consiglio Nazionale delle Ricerche, Istituto di Ingegneria Biomedica, Milano.

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Biomedical signal and image processing