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Autonomic CardiovascularModulation

We validated a symbolic approach to assess auto-nomic modulation from pulse interval (PI) andsystolic arterial pressure (SAP) series obtained

from an animal model of chronic heart failure(CHF). We studied three groups of rats: controls; CHF ani-mals; CHF animals treated with spironolactone (CHF-SP),reducing sympathetic activity in CHF. Simulations confirmedthat symbolic analysis captures modifications of cardiovascu-lar regulation in the case of fast dynamics and negligible var-iance. While spectral indexes did not reveal any significantdifference among groups, symbolic analysis pointed out thatsympathetic modulation is reduced in CHF group and restoredto basal values in CHF-SP one.

Several previous studies have investigated the autonomic car-diovascular regulation in rats, measuring heart rate and bloodpressure variability by means of spectral analysis. Althoughthere is no standard definition for the band limits in rats, thepower of the oscillations in the low-frequency (LF) band, morefrequently centered about 0.45 Hz, is considered as a marker ofsympathetic modulation, whereas that in the high-frequency(HF) band is regarded as a marker of vagal modulation [1]–[5].

Several animal models have been adopted to mimic differentcardiovascular diseases, such as CHF, hypertension, and myo-cardial infarction. CHF is one of the most challenging pathologi-cal conditions associated with massive neurohumoral activationand drastic reduction in heart-rate variability (HRV). Particu-larly, the progression of CHF has been studied in rat modelsaccording to different techniques such as rapid ventricular pac-ing model or myocardial infarction, this latter based on the liga-tion of the left coronary artery leading to the development ofdilated cardiomyopathy and an altered autonomic regulation [6].

Concerning CHF, it is well known that the progression of thisdisease is characterized by an increase of sympathetic activityand an impairment of the baroreflex function [6]. Despite theseevidences, the evaluation of the autonomic control of heart rateand blood-pressure variability using spectral analysis in CHFrats was not able to show clear-cut changes in autonomic cardi-ovascular modulation [7]. However, it is unclear whether theabsence of neural changes might be due to technical limitationsof spectral analysis, emerging in conditions of very low

variance and high derangement of the oscillatory properties ofcardiovascular variability, such as those occurring in CHF.

Consequently, we use an approach based on symbolic analy-sis [8], [9], chosen among those present in literature [8]–[14], toevaluate autonomic control in a rat ischemic model of CHF. Sofar, this approach was able to identify the prevalence of sympa-thetic or parasympathetic modulation induced by pharmacolog-ical interventions, to detect nonreciprocal autonomic changesbefore major arrhythmias and track the progressive increase ofthe sympathetic modulation during head-up tilt as a function ofthe tilt table angle in humans [8], [9].

Therefore, the aim of our study was twofold: first, to validatesymbolic analysis as a tool capable of assessing autonomic car-diovascular regulation in rats and, second, to investigate neuralcardiovascular regulation during the progression of ischemic-induced CHF in two groups of rats, a control group and a grouptreated with chronic administration of the mineralocorticoidreceptor antagonist SP, a drug playing a protective role overcardiovascular regulation [15], [16].

Symbolic AnalysisSymbolic analysis is a nonlinear method based on the conversionof the series into a sequence of symbols. The full dynamics of theseries (the min–max range) is spread over six bins, each of whichis identified by a number (symbol) from 0 to 5. Original valuesinside each bin are substituted by the symbol defining the spe-cific bin, thus obtaining a symbolic series. The symbolic series isconverted into a series of patterns of three symbols. Four differ-ent families of patterns can be identified: 0V (patterns with novariation and all symbols are equal), 1V (patterns with one varia-tion, two consecutive symbols are equal, and the remaining oneis different), 2LV (patterns with two like variations, the secondand the third symbol change with respect to the previous one,and the changes have the same sign), and 2UV (patterns with twounlike variations, the second and the third symbol change withrespect to the previous one, and the changes have opposite sign).The rate of occurrence of each pattern is evaluated and indicatedas 0V, 1V, 2LV, and 2UV%. Symbolic analysis has beenrecently applied to evaluate cardiac autonomic control fromHRV in humans. It has been demonstrated that, in physiologicalcondition, 0V% is a marker of sympathetic modulation, whereas2UV% is a marker of vagal modulation [8], [9].

BY ELEONORA TOBALDINI, NICOLA MONTANO,SHUN-GUANG WEI, ZHI-HUA ZHANG,JOSEPH FRANCIS, ROBERT M. WEISS,KARINA R. CASALI, ROBERT B. FELDER,AND ALBERTO PORTA

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Symbolic Analysis of the Effects of CentralMineralocorticoid Receptor Antagonistin Heart Failure Rats

Digital Object Identifier 10.1109/MEMB.2009.934620

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SimulationsTo simulate time series exhibiting oscillations at the samefrequency of those usually found in short-term heart-period varia-bility in rats, we summed two zero mean uncorrelated second-order autoregressive processes. The two autoregressive processeshad central frequencies at fLF ¼ 0.1 and fHF ¼ 0.25 cycles/beat,respectively. The pole modulus of the two processes was equaland selected from the set {0.85, 0.9, 0.95}. The sum processes, s,were rescaled to have a mean of 180 ms and a variance of 10 ms2

that are typical values for the mean and variance of the shortheart-period series in rats. Given a mean heart period of 180 ms,fLF¼ 0.1 and fHF¼ 0.25 cycles/beat correspond to 0.55 and 1.39Hz, which are typical LF and HF in rats. Two types of simulationswere considered: 1) a process with the LF component with var-iance two times the variance of the HF one, termed as sLF, simu-lating heart-period series with dominant slow oscillations; 2) aprocess with the opposite balance between the variance of the LFand HF components, termed as sHF, simulating heart-period serieswith dominant fast oscillations. Simulations were carried out inthe absence or presence of additive Gaussian white noise, uncor-related to sLF (or sHF) and with variance equal to a fixed percent-age of the sLF (or sHF) variance (i.e., 20, 40, 60, 80, and 100%).For each simulation, we generated 20 different realizations.

Experimental Preparation,Protocol, and Data AnalysisA group of adult Sprague-Dawley rats underwent surgical oper-ation to induce heart failure (n ¼ 14). Rats were anesthetizedwith ketamine (100 mg/kg ip), intubated, and mechanicallyventilated with room air. Then, the heart was exposed by a left

thoracotomy, the pericardium was opened, and the heart wasexteriorized. The left anterior descending coronary artery wasligated between the pulmonary outflow tract and left atrium.Sham-operated rats (SHAM, n ¼ 7) were prepared in the samemanner but did not undergo coronary artery ligation. Aftersurgery, animals were given benzathinepenicillin and lidocaine.Approximately 24 h after the surgery, an echocardiographicassessment was performed to confirm the extent of the ischemicinjury: animals with an ischemic area more than 40% of leftventricular wall were included in the study (CHF, n¼ 14).

Seven out of 14 CHF rats were treated with SP (CHF-SP,n ¼ 7). A stainless steel 23-gauge cannula was implanted intothe third ventricle using stereotaxic coordinates, and SP wasinfused at a dose of 100 ng/h for four weeks through mini-pumps. Four weeks after the coronary ligation, the CHF ratswere reanesthetized to implant arterial and venous cannulas.Blood pressure was recorded in the conscious, freely movingrats, 4 h after recovery from anesthesia. The data reported herewere obtained from SHAM (n ¼ 7), CHF (n ¼ 7), and CHF-SP (n ¼ 7) rats. The blood pressure was recorded through afemoral artery catheter, and PI was derived from the interdias-tolic interval with a resolution of 0.8 ms. SAP values werederived as the maximum of the blood pressure inside the PI.

Symbolic indexes were compared with more traditionalindexes derived from autoregressive spectral analysis [3]. Theidentification of the autoregressive coefficients was carriedout using Levinson-Durbin recursion. The best model orderwas automatically selected using the Akaike figure of merit inthe range of 8–14 (4–14 in case of simulations). The sum ofthe power of the autoregressive components, the central

frequency of which were be-tween 0.2 and 0.8 Hz, was la-beled as LFa and that between0.8 and 2 Hz was labeled asHFa. The LFa and HFa pow-ers were expressed in normal-ized units as well (i.e., LFnu¼ 100 Æ LFa/(LFa þ HFa) andHFnu¼ 100 ÆLFa/(LFaþHFa)).According to [9], we calcu-lated over the PI series LFnuand HFa powers considered asindexes of sympathetic and va-gal modulations directed theheart, respectively, and overthe SAP series the LFa powerregarded as an index of sympa-thetic modulation directed to thevessels. Symbolic and spectralanalyses were carried out overthe same sequences of PI andSAP values. The sequencelength ranged 150–200 cardiacbeats, and the sequences werelinearly detrended.

Statistical AnalysisOne-way analysis of variance(ANOVA; Bonferroni’s test)was used to test the differen-ces between indexes derivedfrom different groups (SHAM,

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Fig. 1. Realizations of (a) sLF and (b) sHF processes are shown. Their autoregressive compo-nents have pole modulus equal to 0.9. The bar graphs show mean (þSD) of (c) 0V%, 1V%,2LV%, and 2UV% and of (d) LFa and HFa powers relevant to 20 realizations of sLF and sHF

processes (solid and open bars, respectively). The symbol * indicates a significant differencebetween sLF and sHF processes with P < 0.05.

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CHF, and CHF-SP). If the normality test was not fulfilled,Kruskal–Wallis one-way ANOVA on ranks was used (Dunn’stest). One-way ANOVA (Dunnett’s test) was used to assessdifferences between parameters derived from simulationswith different pole modulus. When normality test failed, theKruskal–Wallis one-way ANOVA on ranks was used (Dun-nett’s test). The aggregate significance level was set at P <0.05. Unpaired t test was used to test differences betweenparameters extracted from simulated sLF and sHF noisy real-izations. If the normality test was not fulfilled, the Mann–Whitney rank sum test was used. The significance level wasset at P< 0.05 for pairwise comparisons. Data were presentedas mean� SD.

Results

Simulation ResultsFigure 1(a) and (b) shows the realization of sLF and sHF proc-esses, respectively, with pole modulus equal to 0.9. The sLF

series simulated a LF-dominant oscillation in the presence of asmaller HF component, such as those present in case of asignificant shift of the syma-thovagal balance toward sym-pathetic predominance, whereasthe sHF series simulated aHF-dominant rhythm in thepresence of a smaller LFcomponent, such as thoseobservable in the presenceof a reverse situation, char-acterized by a predominantvagal modulation. Resultsrelevant to the applicationof symbolic analysis to 20realizations of sLF and sHF

processes are shown in Fig-ure 1(c). The index 0V%was significantly higher in thepresence of dominant slowoscillations (i.e., sLF, solidbars) than in the presenceof dominant fast oscillations(i.e., sHF, open bars). Theopposite result was found incase of 2UV%. The index1V% was significantly largerin case of sLF series than inthe case of sHF ones. Differ-ences between 2LV% valuesderived from sLF and sHF

realizations were negligible.By construction, the powerin the LF band was two timesgreater than that in theHF band in the case of sLF

series, whereas the reverse sit-uation was found in the caseof sHF [Figure 1(d)].

Figure 2 shows the effectsof additive noise to sLF andsHF processes on spectral andsymbolic parameters. The pole

modulus of the uncorrupted sLF and sHF processes was set at 0.9.While increasing the noise variance, 0V% decreased [Figure2(a)]. In addition, the difference between 0V% derived from sLF

and sHF processes declined more and more and became insignifi-cant when the percentage of the variance added to the uncor-rupted signal was larger than 80% [Figure 2(a)]. The parameter1V% followed a parallel trend, but the difference between 1V%derived from sLF and sHF processes became insignificant wellbefore [above 40%, Figure 2(b)]. On the contrary, 2UV% fol-lowed the reverse trend [i.e., it increased as a function of the noisevariance, Figure 2(d)]. Similarly to 0V%, differences between2UV% derived from sLF and sHF processes became insignificantabove 80% [Figure 2(d)]. The index 2LV% tended to decreasewith the noise variance, and differences between processes werenever significant [Figure 2(c)]. Spectral parameters followedthe same trend of 2UV% [Figure 2(e) and (f)], and differencesbetween sLF and sHF processes were always significant.

Figure 3 shows the ability of the symbolic analysis to trackchanges of regularity (or it is opposite, complexity). Symbolicparameters (i.e., 2LV% and 2UV%) could detect the decreaseof complexity (i.e., the increase of regularity) when the pole

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Fig. 2. The bar graphs show the mean (þSD) of (a) 0V%, (b) 1V%, (c) 2LV%, (d) 2UV%, (e) LFa,and (f) HFa powers relevant to 20 realizations of sLF and sHF processes (solid and open bars,respectively) corrupted by additive white Gaussian noise uncorrelated to original series. Thevariance of the noise was set as an assigned percentage of the variance of the uncorruptedseries. The percentages were 0, 20, 40, 60, 80, and 100%, where 0% means that no noise wasadded. The autoregressive components of the uncorrupted sLF and sHF processes have polemodulus equal to 0.9. The symbol * indicates a significant difference between sLF and sHF

processes with P < 0.05.

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modulus of sLF and sHF processes was increased from 0.85 to0.95 in steps of 0.05 [Figure 3(a) and (b)]. While decreasingthe complexity of the series, 2LV% and 2UV% exhibited oppo-site courses: indeed, 2LV% increased and 2UV% decreased. Byconstruction, the power of the LF and HF components wasunchanged [Figure 3(c) and (d)].

Experimental ResultsFigure 4(a)–(c) shows examples of PI series ina SHAM, CHF, and CHF-SP animals, respec-tively. The values of symbolic and spectralindexes derived from the series depicted inFigure 4(a)–(c) are shown in Figure 4(d) and(e). The index 0V% tended to decrease in CHFanimals with respect to SHAM and to increasein CHF-SP group. Similar changes were ob-servable in the case of 1V%. On the contrary,2UV% increased in CHF group and decreasedin the CHF-SP one. The changes of the LFnuand HFa powers [Figure 4(e)] matched withthose of 0V% and 1V%, respectively [Fig-ure 4(d)].

The results relevant to spectral and symbolicindexes derived from PI series are summarizedin Table 1. Symbolic analysis revealed a de-crease of 0V% on PI series in CHF group withrespect to SHAM animals and its succeedingnormalization after the SP treatment (0V%was similar in the SHAM and CHF-SP groups).The parameter 1V% underwent a similar trend.On the other hand, CHF animals were charac-terized by a significant increase of 2UV%,whereas in CHF-SP animals, 2UV% was simi-lar to SHAM group. Spectral parameters on PIseries did not show any significant differenceamong groups.

Figure 5(a)–(c) shows examples of SAP series in SHAM,CHF, and CHF-SP animals, respectively. The symbolic andspectral indexes derived from the series depicted in Figure5(a)–(c) are shown in Figure 5(d) and (e), respectively. Modi-fications of 0V%, 2LV%, and 2UV% are comparable withthose reported in Figure 4. The changes of the LFa powers

[Figure 5(e)] matched with those of 0V%,although less clearly [Figure 5(d)].

The trends reported in Table 2 are similar tothose presented in Table 1, with the sole ex-ception for the significant modification of2LV% in CHF group with respect to SHAMand CHF-SP. As in Table 1, the spectralindexes in Table 2 did not reveal any differ-ence among the groups.

Discussion

Symbolic Analysis inSimulated Variability SeriesSymbolic analysis has been applied to simulatedvariability series to evaluate its ability in assess-ing the autonomic cardiovascular regulation inconditions of fast dynamics, very low variance,and in the presence of both LF and HF rhythms.Slow LF oscillations with an amplitude largerthan faster HF oscillations, usually present duringexperimental conditions enhancing a sympatheticmodulation [8], [9], and fast HF rhythms moreimportant than slower LF ones, such as thoseobserved during controlled respiration and/orexperimental conditions evoking an importantvagal modulation [9], were simulated according

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Fig. 3. The bar graphs show the results of (a) and (b) symbolic and (c) and (d)spectral analyses. The mean (þSD) of 0V%, 1V%, 2LV%, and 2UV% derived fromsLF and sHF processes is shown in (a) and (b), respectively, whereas the mean(þSD) of LFa and HFa powers is depicted in (c) and (d), respectively. Indexesare derived from sLF and sHF processes with different pole modulus of their autor-egressive components (i.e., pole modulus equal to 0.85, 0.9, and 0.95 corre-sponds to black, gray, and dark gray bars, respectively). The symbol * indicatesa significant difference (P < 0.05) with respect to indexes derived from realiza-tions with pole modulus equal to 0.85.

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Fig. 4. Example of PI series in (a) SHAM, (b) CHF, and (c) CHF-SP rat. Indexesderived from symbolic analysis (i.e., 0V%, 1V%, 2LV%, and 2UV%) relevant toSHAM, CHF, and CHF-SP PI series (black, gray, and dark gray bars, respec-tively) are shown in (d), whereas indexes derived from spectral analysis (i.e.,LFnu and HFa powers) are depicted in (e).

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to the sum of the two autoregressive processes with differentvariances. The sum process was rescaled to have mean, var-iance, LF, and HF typical for short-term HRV in rats. Theindex 0V% was higher in the case of dominant LF rhythmsthan in the case of dominant HF oscillations. The reverse sit-uation was observed in the case of 2UV%. These data supportthe hypothesis that symbolic parameters 0V% and 2UV% canevidence the presence of slow and fast oscillations even in thepresence of fast dynamics and very low variance. It can bedemonstrated that the same performances can be obtained forany series in which LF and HF were set in terms of normalizedfrequencies at 0.1 and 0.25 cycles/beats (e.g., 0.1 and 0.25 Hzwith a mean heart period of 1,000 ms). The good performanceof symbolic analysis in the case of very low variance could beforeseen: indeed, the procedure of uniformly assigning thevalues of the full dynamical range (the min–max range) to sixbins renders this specific symbolic approach independent ofthe variance of the signal.

Simulations demonstrated that symbolic analysis was reli-able in distinguishing a process with dominant LF rhythmsfrom that with dominant HF oscillations even in the presenceof additive noise. Indeed, the two processes can be distin-guished using 0V% and 2UV% until the variance of the noisewas smaller than 80% of the variance of the uncorruptedseries. It is worth noting that spectral parameters performedbetter than symbolic indexes in the presence of additive noise,but they failed to assess the increase of regularity (or, con-versely, the decrease of complexity) obtained by increasingthe pole modulus of the autoregressive components towardone [17]. This last simulation suggests that the symbolic index2UV% is a very powerful measure of the complexity (or regu-larity) of a series.

Autonomic Control in aModel of CHF in RatsCHF is associated with impor-tant alterations of the cardiacautonomic regulation. Previousstudies have shown an increaseof sympathetic activity inCHF, accompanied by animpaired sympathetic modula-tion of HRV and blood-pres-sure variability. In our study,symbolic analysis showed a de-crease of 0V% both on PI andSAP variabilities. In agree-ment with data reported inhumans, these results couldindicate a decrease of sympa-thetic modulation, probably dueto the loss of rhythmical proper-ties of the sympathetic branchdirect to the periphery, notwith-standing the increased sympa-thetic activity.

On the other hand, we testedthe hypothesis that SP treatmentcould play a role in normalizingthe autonomic modulation inCHF. Indeed, previous studiessuggested that SP is capable of

reducing sympathetic overactivity in CHF rats [15], [16], whereasno data are available on the effects of this drug on autonomicmodulation. Symbolic analysis revealed that 0V% is similar inCHF-SP and SHAM groups, thus indicating that SP seems to becapable of preserving the physiological sympathetic modulationthat is lost in CHF.

It is worth noting that two parameters derived from spectralanalysis (i.e., LFnu power derived from PI series and LFa powerderived from SAP series) underwent the same trend as 0V%, butthe differences among groups were not significant. Since simu-lations proved that spectral analysis is more reliable with respect

Table 1. PI spectral and symbolic parameters in SHAM,CHF, and CHF-SP groups.

PISHAM(n ¼ 7)

CHF(n ¼ 7)

CHF-SP(n ¼ 7)

Mean (beats/min) 437 � 51 427 � 30 425 � 14Variance (ms2) 2.03 � 1.53 1.44 � 0.8 2.7 � 3.10V% 17.9 � 1.3 6.6 � 2.6*# 14.7 � 6.71V% 45.3 � 3.5 31.9 � 9.2*# 38.4 � 3.92LV% 9.16 � 3.4 11.2 � 3.2 12.3 � 6.32UV% 29.4 � 4.5 50.2 � 11.8*# 34.4 � 5.7LF (Hz) 0.42 � 0.15 0.48 � 0.23 0.55 � 0.19LFnu 20.6 � 17 14.7 � 7.1 20.1 � 8HF (Hz) 1.4 � 0.28 1.6 � 0.5 1.7 � 0.5HFa (ms2) 0.6 � 0.5 0.6 � 0.5 0.9 � 0.7

All values were expressed as mean � SD.*P < 0.05 CHF versus SHAM; #P < 0.05 CHF versus CHF-SP.

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Fig. 5. Example of SAP series in a (a) SHAM, (b) CHF, and (c) CHF-SP rat. Indexes derived fromsymbolic analysis (i.e., 0V%, 1V%, 2LV%, and 2UV%) relevant to SHAM, CHF, and CHF-SP SAPseries (black, gray, and dark gray bars, respectively) are shown in (d), whereas LFa powerderived from spectral analysis is depicted in (e). Only LFa power was considered as an indexof neural autonomic modulation over SAP series.

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to additive noise, the better performance of symbolic analysiscannot be explained in terms of capability of dealing with noise.We can speculate that the better performance of symbolicapproach can be related to specific features of symbolic analysis[9], [18]: 1) it captures nonlinear dynamics present in the series;2) it does not require the predefined definition of frequencybands; and 3) it can describe conditions characterized by non-concomitant increase or decrease of the autonomic modulationsof both autonomic branches. In addition, the simulations testingthe performance of symbolic analysis in following changes ofdynamical complexity of a process suggests that symbolic anal-ysis might be more adequate than spectral analysis in interpret-ing the complexity of short-term heart-period sequences in rats.

The other major finding of our study is represented by the pre-dominant presence of 2UV pattern in CHF rats. It has beenrecently observed in healthy subjects that this pattern, consistingof fast and irregular alternations (long–short–long or short–long–short intervals), decreases with increasing tilt table angles, thussuggesting a progressive loss of vagal modulation. However, ithas also been demonstrated that the percentage of this pattern isincreased in patients with CHF [18]. In pathological conditions,it could be hypothesized that the 2UV pattern is linked to othermechanisms different from the autonomic cardiovascular con-trol, such as mechanoelectrical or pulsus alternans [19], phenom-ena that are present in CHF. Conversely, 2UV% in theSP-treated group was similar to that occurring in SHAM group,revealing that SP can normalize 2UV% in PI and SAP series.

In conclusion, symbolic analysis seems to be a valid tool forthe investigation of the autonomic modulation in an experi-mental model of CHF in rats. In addition, the treatment withSP seems to restore a more physiological autonomic cardio-vascular modulation, as demonstrated by the increased pres-ence of patterns indicating slow modulations in PI and SAPseries and by the reduced presence of patterns indicating fastalterans in PI and SAP series.

AcknowledgmentsThis work was partly supported by a FIRST 2006 University ofMilan Grant and Italian Space Agency Research DCMC Grant,and National Institutes of Health (NIH) RO1 HL-063915.

Eleonora Tobaldini graduated in medicine and surgery fromthe University of Milan, Milan, Italy, in 2006. She is currentlya resident in internal medicine at the Internal Medicine Unit,

Sacco Hospital, University of Milan. Since2004, she has been a research fellow at theCardiovascular Physiopathology Labora-tory, Department of Clinical Sciences,University of Milan. Her research interestsare in the field of the autonomic control ofcardiovascular regulation in health anddisease, linear and nonlinear analysis of

cardiovascular variability, and cardiac autonomic regulationduring sleep.

Nicola Montano graduated in medicinefrom the University of Milan in 1988. Hereceived his Ph.D. degree in clinical physi-opathology from the University of Milanin 1994. He is currently an associate pro-fessor of internal medicine at the Univer-sity of Milan. His research interestsinclude the field of neural control of cardi-

ovascular function, mainly related to the relationship betweenneural and cardiovascular oscillatory patterns and the auto-nomic cardiac regulation during sleep in health and disease.

Shun-Guang Wei graduated in biologyfrom Fudan University, Shanghai, China,and obtained his master’s degree of medi-cine in cardiovascular physiology fromShandong Medical University, Jinan, China.He received his Ph.D. degree in neuro-science from the University of Iowa in2007. He is currently a research fellow in

the Laboratory of Signal Transduction at National Institute ofEnvironmental Health Sciences of NIH. His research interestsinclude central neural mechanisms involved in the regulation ofcardiovascular function in heart failure and hypertension withspecial attention to the role of brain renin-angiotensin systemand the angiotensin II cell signaling.

Zhi-Hua Zhang graduated in medicinefrom Taishan Medical School, Shandong,People’s Republic of China, in 1985. Hereceived the Ph.D. degree in neurophysi-ology from Shanxi Medical University,Taiyuan, China, in 1993. He joined theUniversity of Iowa Cardiovascular Cen-ter in 1999 as a research scientist after

finishing four years postdoctoral fellowship at Johns Hop-kins Medical Institution. His research interests include cen-tral mechanisms involving neurohumoral regulation underphysiological and pathophysiological conditions, such asheart failure.

Joseph Francis received his bachelor ofveterinary medicine in animal husbandryand master’s in veterinary virology andimmunology from Madras Veterinary Col-lege, Madras, India, in 1991 and 1994,respectively. He received his Ph.D. degreein neuroendocrinology from Kansas StateUniversity, Manhattan, Kansas, in 1999.

After completion of his doctoral research, he joined Rob-ert Felder’s laboratory at the University of Iowa, for a

Table 2. SAP spectral and symbolic parameters in SHAM,CHF, and CHF-SP groups.

SAPSHAM(n ¼ 7)

CHF(n ¼ 7)

CHF-SP(n ¼ 7)

Mean (mmHg) 121 � 6 107 � 5 114 � 7Variance (mmHg2) 14.2 � 9.5 9.04 � 2 14.1 � 8.50V% 20.2 � 6 10.1 � 7.5*# 13.4 � 9.061V% 51.1 � 2.3 29.6 � 7.2*# 47.1 � 5.42LV% 15.4 � 5.4 7.7 � 4.7*# 15.1 � 7.62UV% 13.2 � 6.9 54.9 � 23.0*# 26.4 � 12.8LF (Hz) 0.43 � 0.04 0.38 � 0.02 0.41 � 0.07LFa (mmHg2) 10.1 � 9.2 3.9 � 4.1 6.5 � 5.2

All values were expressed as mean � SD.*P < 0.05 CHF versus SHAM; #P < 0.05 CHF versus CHF-SP.

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postdoctoral fellowship in cardiovascular pathophysiology.He joined the faculty of Louisiana State University as anassistant professor in 2003. Currently, he is an associate pro-fessor in Comparative Biomedical Sciences Department atLouisiana State University, Baton Rouge, Louisiana. Hisresearch interests include understanding the role played bycentral nervous system cytokines in the pathophysiology ofcardiovascular diseases.

Robert M. Weiss received his M.D.degree from the University of Michigan in1982 and completed residency training atthe University of Vermont. After clinicaltraining in cardiovascular disease andresearch training in the laboratory of Dr.Melvin L. Marcus, he joined the faculty ofthe University of Iowa in 1989 and is cur-

rently a professor of medicine. His research interests includethe area of cardiovascular function in rodents, with emphasison design and implementation of novel imaging methods.

Karina R. Casali graduated in electronicengineering from the University of SantaMaria and received a master’s degree inbiomedical engineering from the Univer-sity of Sao Paulo, Sao Paulo, Brazil, in2001 and 2003, respectively. She receivedher Ph.D. degree in physiology from theUniversity of Rio Grande do Sul, Porto

Alegre, Brazil, in 2009. She has been a researcher in theCardiology Institute at Porto Alegre, applying signal process-ing techniques such as spectral analysis, time irreversibility,and other nonlinear analysis to biological time series inexperimental and clinical studies.

Robert B. Felder received his M.D.degree from the University of North Caro-lina in 1972 and completed a residency ininternal medicine and a fellowship in car-diovascular diseases at the University ofIowa Hospitals and Clinics in Iowa City,Iowa. He joined the faculty of the Univer-sity of Iowa in 1980. In 1981, he had an

additional year of research training in the laboratory of Prof.K.M. Spyer in the Physiology Department at the Royal FreeHospital School of Medicine, University of London, England.He is currently a professor in the Cardiovascular MedicineDivision of the Department of Internal Medicine in the Roy J.and Lucille A. Carver College of Medicine, University ofIowa. His research interests include the role of central nervoussystem mechanisms in the pathophysiology of heart failure.

Alberto Porta graduated in electronicengineering from Politecnico di Milano,Milan, Italy, in 1989. He received hisPh.D. degree in biomedical engineeringfrom Politecnico di Milano in 1998. Since1999, he has been with the Faculty ofMedicine, Universita degli Studi di Milano,where he has been a researcher since 2005.

Since 2006, he has been teaching medical physics andsince 2007 applied medical statistics in the same faculty.

His research interests include time series analysis, biomed-ical signal processing, complexity analysis, system identi-fication, and modeling applied to cardiovascular controlmechanisms.

Address for Correspondence: Alberto Porta, Laboratorio diModellistica di Sistemi Complessi, Dipartimento di Tecnolo-gie per la Salute, Istituto Ortopedico Galeazzi, Universitadegli Studi di Milano, Via R. Galeazzi 4, 20161 Milan, Italy.E-mail: alberto.porta@unimi.it.

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