Biomedical Signal Processing and Control 5 (2010) 32–36

Measurement of cardiac synchrony using Approximate Entropy appliedto nuclear medicine scans

James Cullen a,*, Azeem Saleem a, Ric Swindell b, Paul Burt c, Chris Moore d

a Academic Radiation Oncology, University of Manchester, Christie Hospital NHS Foundation Trust, Withington, Manchester M20 4BX, UKb Medical Statistics, Christie Hospital NHS Foundation Trust, Withington, Manchester M20 4BX, UKc Clinical Oncology Department, Christie Hospital NHS Foundation Trust, Withington, Manchester M20 4BX, UKd Developing Technologies Section-RT Physics, North Western Medical Physics Department, Christie Hospital NHS Foundation Trust, Withington, Manchester M20 4BX, UK

A R T I C L E I N F O

Article history:

Received 9 November 2008

Received in revised form 14 June 2009

Accepted 22 July 2009

Available online 27 August 2009

Keywords:

Cardiac synchrony

Approximate Entropy

MUGA scan

Trastuzumab

A B S T R A C T

As cancer therapy becomes more effective, allowing patients to live longer, the long-term morbidity of

treatment assumes greater significance. Trastuzumab (Herceptin1), a monoclonal antibody that targets

the epidermal growth factor, has proven efficacy in breast cancer patients but is also known to be

cardiotoxic. Left ventricular ejection fraction (LVEF), a measure of cardiac function, is commonly used to

evaluate patients receiving trastuzumab by Multiple Gated Acquisition (MUGA) isotope scans. In this

paper, we have assessed the utility of previously published ventricular synchrony parameters in patients

undergoing trastuzumab therapy. In addition, we apply Approximate Entropy (ApEn) to MUGA images,

as a new measure of cardiac dysfunction and have evaluated its utility in the same patients. A significant

change in LVEF (p = 0.015) and ApEn (p = 0.020) but not ventricular synchrony measures were observed

over the course of treatment in these patients. The results suggest that ApEn provides a useful measure of

cardiac function and synchrony.

� 2009 Elsevier Ltd. All rights reserved.

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Biomedical Signal Processing and Control

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1. Introduction

Management of cancer has become increasingly ‘multimodal’over the years, with patients receiving a combination of therapiessuch as surgery, radiotherapy, chemotherapy and/or biologicalagents. At the same time, the outcome for patients diagnosed withcancer has also improved with a greater number of patients beingcured of cancer and living beyond the key 5 year point.Consequently, the side effects of treatment, especially long-termside effects assume greater significance, as they may impact onpatients’ quality of life and survival, potentially negating some ofthe benefits derived from treatment. This was observed in breastcancer patients who received adjuvant radiotherapy with oldertechniques. In these patients, despite a decrease in cancer-specificmortality, overall survival was unchanged due to an excess ofcardiac deaths [1–3], attributed to cardiac damage related toradiation dose, irradiated volume and delivery technique [4].

In addition to radiotherapy, certain chemotherapy agents arealso known to be particularly cardiotoxic, such as the anthracy-

Abbreviations: ApEn, Approximate Entropy; LVEF, left ventricular ejection fraction;

MUGA, Multiple Gated Acquisition.

* Corresponding author. Present address: Particle Physics Group, School of

Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK.

Tel.: +44 0161 275 4227; fax: +44 0161 446 8111.

E-mail address: james.cullen@manchester.ac.uk (J. Cullen).

1746-8094/$ – see front matter � 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.bspc.2009.07.002

clines, doxorubicin and epirubicin. Anthracycline-associatedcardiac damage manifests as electrocardiogram (ECG) changes,arrhythmias, cardiomyopathy leading to congestive heart failureand most importantly cardiac contractile dysfunction and isrelated to the cumulative dose [5]. The reported incidence ofdoxorubicin-induced cardiac dysfunction varies from 4% to >36%in patients [6]. A particular anti-cancer agent commonly associatedwith the unpredicatbale appearance of cardiac side effects istrastuzumab (Herceptin1), a relatively novel monoclonal antibodythat targets breast cancer cells that overexpress the cancer growthprotein HER-2. Unlike anthracyclines, there is no dose–cardio-toxicity relationship with trastuzumab. Although trastuzumab-induced cardiotoxicity is known to generally respond to standardtreatment or the discontinuation of trastuzumab [7], the rever-sibility and long-term cardiac morbidity associated with trastu-zumab is unclear [8]. Telli et al. reported that a number of patientshad to discontinue trastuzumab therapy, despite obeying strictimaging or clinical criteria aimed to stop therapy beforeunacceptable toxicity was reached [8].

Left ventricular ejection fraction (LVEF) is commonly used as ameasure of cardiac efficiency since the left ventricle is the heart’smain pumping chamber, supplying the systemic circuit. LVEFmeasures the fractional volume of blood of the total left ventricularvolume pumped with each heartbeat. LVEF values range between55% and 70% in individuals with normal cardiac function. LVEF is ofprognostic value in the management and control of cardiovascular

J. Cullen et al. / Biomedical Signal Processing and Control 5 (2010) 32–36 33

disease [9] and is commonly measured by either echocardiographyor Multiple Gated Acquisition (MUGA) scans, which are low doseradioactive tracer investigations of heart function. Limitations inimaging place an error of �5% on MUGA reported LVEFs and greaterfor those from echocardiography [10]. In patients receiving trastu-zumab or cardiotoxic chemotherapy, LVEF is commonly assessedprior to and during therapy, so that any cardiac sequelae are detectedearly and further treatment is modified accordingly [8]. A number offactors such as ischaemia, hypertension, disturbances in cardiacrhythm and cardiac valvular disease may lead to cardiac dysfunctionand failure, which is manifested symptomatically and as a decrease inLVEF on imaging.

In addition to changes in LVEF, a lack of co-ordination in thecontraction and relaxation of the heart chambers is observed insome patients who develop cardiac failure. Variability in timing ofthe onset of contraction within a ventricle has been used as ameasure of cardiac synchrony and others have been suggested.O’Connell et al. [11] proposed a pair of measures, synchrony (S) andentropy (E), to quantify perturbation of cardiac contraction, whichdirectly impacts LVEF, based on functional images generated fromMUGA scans [12].

In this audit study, where LVEF changes have already beenidentified, we investigate if trastuzumab therapy also affected co-ordination of cardiac contraction. For this we evaluated serialchanges in LVEF and the quantitative parameters, synchrony andentropy defined by O’Connell et al. [11] from MUGA scans ofpatients on trastuzumab therapy. In addition, we have proposedand evaluated the utility of Approximate Entropy (ApEn), aregularity statistic previously used in other disciplines [13–15]primarily to measure patterns in time series data, as a measure ofcardiac synchrony. This is the first time ApEn has been used onmedical imaging data to quantify the adverse impact of drugs liketrastuzumab.

2. Theory

2.1. Synchrony and entropy

Intra-ventricular synchrony can be defined as the variability intiming of the onset of contraction within a ventricle [16]. Onequantitative measure of left ventricular synchrony is the standarddeviation of the left ventricle phase angles on the phase imagederived from a MUGA scan. O’Connell et al. proposed a pair ofmeasures based on the phase and amplitude images derived fromMUGA scans to quantify the synchrony of cardiac contraction [11].The approach is comparable with phase locking statistics [17]where separated amplitude and phase values are used to definesynchrony amongst multiple signals, e.g. in EEG studies [18].

For each corresponding pixel in the phase and amplitudeimages a vector vi is formed where the vector amplitude is thevalue for that pixel in the amplitude image and the vectorargument is the pixel value in the phase image. Synchrony is thendefined as

S ¼PN

i¼1 vi

��� ���PNi¼1 vij j

(1)

A synchrony value of 1 describes complete synchrony and a valueapproaching 0 describes asynchrony.

The second parameter, entropy, is described by O’Connell et al.[11] as being of particular use in cases of low synchrony to helpdifferentiate between true asynchrony and opposed sub-regions.This entropy measure is a modified version of Shannon entropy[19], where phase angles are grouped into 30 equal units andnormalised for the number of phase angles in the ROI to give anentropy value between 0, representing complete order and 1,

representing random behaviour. O’Connell entropy is defined as

E ¼ �PM

i¼1 Pi log2ðPiÞ�log2ðMÞ

(2)

where M is the number of phase angle groups and Pi is theprobability of a phase angle being in the ith group.

2.2. Approximate Entropy

In the 1950s Kolmogorov and Sinai developed their KS entropystatistic intended for use with non-linear dynamic systemschanging from regular to irregular states. However, unrealisticallylarge amounts of data were required to determine KS. Subse-quently, Pincus developed a more pragmatic algorithm, which wascalled ‘approximate’ entropy, or ApEn [15]. The order in which thedata values appear assumes importance, which is a feature thatdistinguishes ApEn as a regularity rather than a variability statistic.Subsets of a predefined length of the data are used as a templateagainst which the whole dataset is compared. This matchingprocess is performed for each possible subset of consecutive pointsand the results used to derive ApEn. A dataset with a repeating datapattern will have a low ApEn value, a measure of its regularity.

Formally, the calculation of ApEn proceeds as follows. For N

data points {u(i)} = u(1), u(2), . . ., u(N) and starting with the ithpoint, the vector sequences x̃ðtÞ to x̃ðN �mþ 1Þ are formedcomposed of m consecutive u values x̃ðiÞ ¼ ½uðiÞ; . . . ;uðiþm� 1Þ�:The sequence, x̃ð1Þ; x̃ð2Þ; . . . ; x̃ðN �mþ 1Þ is used to constructCm

i ðrÞ values for each i � (N �m + 1);

Cmi ðrÞ ¼ number of j � ðN �mþ 1Þ such that

d½x̃ðiÞ; x̃ð jÞ�ðN �mþ 1Þ � r

� �

where d½x̃ðiÞ; x̃ð jÞ� is the distance between vectors, defined as themaximum difference in their scalar components. The Cm

i ðrÞ valuesmeasure, within a tolerance ‘r’, the frequency of sequencesoccurring in the dataset {u(i)} which are similar to the givensequence, x̃ðiÞ of length m. The Pincus Approximate Entropystatistic ApEn is then defined by;

ApEn ¼ �ðN �mÞ�1XN�m

i¼1

lnCmþ1

i ðrÞCm

i ðrÞ

" #(3)

Hence ApEn can be seen as a measure of the average logarithmiclikelihood, over all sequences x̃ð1Þ to x̃ðN �mþ 1Þ, such that anysequence in the data series {u(i)}, which is within a tolerance r ofthe given sequence x̃ðiÞ of length m, remains within the sametolerance when the length of both sequences is increased by onedata point. Tolerance r is proportional to the measured seriesstandard deviation s, i.e. r = ks where k is a constant. It is necessaryto determine k empirically so that the widest range of complexityvalues is achieved. In defining ApEn Pincus and Goldberger [20]suggest that it is most usefully applied to datasets that have aminimum of 10m data points.

3. Materials and methods

3.1. MUGA scan acquisition

Serial MUGA scans of patients receiving trastuzumab forprimary breast cancer were selected for analysis. A baseline scanwas performed to assess eligibility for treatment, primarilythrough LVEF, and repeated approximately every 3 months whilston treatment. Standard departmental MUGA scanning protocolswere followed. Briefly, a stannous chloride solution was injectedinto the patient followed 20 min later by 1000 MBq of technetium-99m pertechnetate. The patient lay prone on the scanning couchand a gamma camera was positioned over the heart. Detection of

J. Cullen et al. / Biomedical Signal Processing and Control 5 (2010) 32–3634

characteristic 140 keV decay photons was used as a surrogate forred blood cell position. Image acquisition was gated to the cardiaccycle, with 24 frames captured throughout the cardiac cycle. Scanswere terminated once 1 000 000 counts from the left ventricle hadbeen recorded. Amplitude and phase images were derived from thescans using Fourier analysis of the fundamental frequency (firstharmonic).

3.2. MUGA scan evaluation

Data from eight patients with several MUGA scans performed atthe Nuclear Medicine Department, Christie Hospital NHS Trust,Manchester, UK between September 2004 and January 2007 wererandomly selected. Each patient had multiple scans during thecourse of their treatment to monitor cardiotoxicity, as measured bya reduction in LVEF.

All MUGA scan images were assessed using a Xeleris Work-station (GE Healthcare, Chalfont St Giles, Buckinghamshire, UK).Regions of interest (ROIs) were semi-automatically drawn aroundthe left ventricle on the end diastolic and end systolic frames andused to calculate LVEF. The background ROI was shifted one pixelfrom the systolic ROI and located at a segment with the lowestaverage count rate. The background ROI is used by the program tocorrect all the frames for emission by underlying tissues. Thestandard practice required ROI delineation by up to fourexperienced staff from the nuclear medicine department. Scanswherein the left ventricle was clearly visible required fewerindividuals to draw an ROI than those scans where the left ventriclewas not as well defined. Table 1 shows the number of MUGA scanseach patient had and the total number of ROIs drawn on thosescans.

3.3. Left ventricle size and LVEF

Since the size of the left ventricle on a MUGA scan isproportional to the number of pixels in that ROI, we evaluated ifa correlation existed between the left ventricular size and thecardiac function. For this we used the Pearson product–momentcorrelation co-efficient to relate the number of pixels in the leftventricle ROI with LVEF.

3.4. Computation of synchrony, entropy and ApEn and time trends

calculation

In-house analytical software was written in the Interactive DataLanguage (IDL from ITT Visual Information Solutions, Boulder, CO,USA) data mining language, running on a PC (1.4 GHz Intel CeleronM, 512 MB RAM) with Microsoft Windows XP Professionaloperating system. This platform was used to calculate meanphase angle (mean f) and standard deviation of phase angles (SDf) from the MUGA scan data recovered from within the ROIs. Allpoints external to the ROI were set to zero. Any background pixelsin the phase image included in the ROI were removed. Data were

Table 1Number of MUGA scans and ROIs drawn per scan for all patients analysed in the

study.

Patient number Total number of MUGA scans Total number of ROIs

1 11 20

2 2 6

3 3 5

4 5 13

5 6 12

6 4 14

7 4 10

8 4 8

converted from polar to Cartesian coordinates for vector addition.Synchrony was determined as per Eq. (1). Phase angle data werethen grouped into 30 ‘bins’ of size 128 and entropy determined asper Eq. (2).

From the ROI phase data a one-dimensional array or vectorcontaining all points was created. Data were read in to the vectorfrom left to right, top to bottom of the ROI. The ROI phase data werethen stationarised by standard finite differencing. This removesspurious slow trends in the data prior to statistical processing.Approximate Entropy was then calculated using m = 2 andr = 0.16SD of the dataset, in line with the literature [20–22].

For each patient, the parameters LVEF, ApEn, mean f, SD f,synchrony and entropy were plotted against the number of dayselapsed since baseline scan. Each scan parameter was plottedindividually on the ordinate and scan date on the abscissa. Linearregression was then used to calculate the line of best fit employingtwo methods: (i) multiple parameter values calculated fromdifferent observer drawn ROIs on the same scan were averaged togive a single mean value for each scan, and (ii) all individual pointsfrom each different observer drawn ROIs were plotted. Thegradients of linear regression for each parameter using bothmethods were recorded. This method allows changes in para-meters over the course of scans to be calculated. Using SPSS version14.0 (SPSS Inc. Headquarters, 233 S. Wacker Drive, 11th floor,Chicago, IL) a one sample t-test was performed individually oneach parameter gradient for both of the linear regression methodsfor the group. A p value of �0.05 was considered significant.

The statistical methods used, in particular the regressionmethods, gave the best description of time trends in parameters,since the identity of outliners was not recorded. Regressionmethod (i) makes use of all data available evenly distributingparameter values. Method (ii) also makes use of all data, but onscans where there are more parameter values, due to clinicalpractice requirements, these extra values have a bias effect to theregression.

4. Results

4.1. LVEF

LVEF values for the study patients were mostly within thenormal range, with 6 out of 8 (75%) patients having LVEF�55 � 5%throughout the study duration. When the LVEF values in all the 39MUGA scans were assessed, 36 MUGA scans (92%) from the studywere observed to have LVEF values within the normal range.Similarly, the LVEF in 89% (78/88) of all the individual ROIs drawnon the MUGA scans were normal.

4.2. Left ventricle size and LVEF

A moderate but statistically significant (R2 = 0.5; p < 0.0001)negative correlation was observed between left ventricular sizeand LVEF (Fig. 1), suggesting that the ejection fraction was smallerin patients with larger ventricular size. The mean number of pointsin the ROIs studied was 313.99 (SD 61.98).

4.3. Scan parameters

Statistical significance values following a one sample t-test oflinear regression gradients to evaluate time-changes in variouscardiac parameters using mean parameter values (method (i)) andall individual parameter values (method (ii)), are shown in Table 2.We found a significant decrease in LVEF (p = 0.015 and p = 0.018, inmethods (i) and (ii), respectively) and a significant increase in ApEn(p = 0.020 and p = 0.032 using methods (i) and (ii), respectively) forthe group. Using both regression methods, every patient had a

Fig. 1. Scatter plot of left ventricle size versus LVEF. The line shows the negative

correlation between the parameters.

J. Cullen et al. / Biomedical Signal Processing and Control 5 (2010) 32–36 35

negative LVEF gradient, and 7/8 and 6/8 had positive ApEngradients using regression methods (i) and (ii), respectively. Meanf, SD f, synchrony and entropy varied arbitrarily across the groupwith no statistical significance (Table 2).

Table 3 shows the changes in LVEF and ApEn for all patientsfrom baseline to the end of study. All patients displayed a decreasein LVEF and 6/8 displayed an increase in ApEn. The mean time ontreatment was 444 days.

Fig. 2 shows the percentage change in LVEF and ApEn for eachpatient with respect to days on treatment.

5. Discussion

Side effects of therapy such as cardiotoxicity have a negativeimpact on the overall efficacy of treatment. An understanding ofthe mechanism of cardiotoxicity and its imaging surrogates willnot only allow monitoring of therapy but also be helpful in thedevelopment of cardio-protective drugs. Cardiac toxicity inpatients receiving anti-cancer therapy is conventionally assessedby quantifying the changes in the LVEF, measured either withMUGA scans or with echocardiography. Since the inter-observerdifferences with MUGA scans is less than with echocardiography, a

Table 2Statistical significance values following a one sample t-test of all eight patients’ gradie

Regression method p value

LVEF ApEn

Mean parameter values 0.015 0.020

All individual parameter values 0.018 0.032

Table 3Baseline, end of treatment and percentage change in LVEF and ApEn for all patients. M

Patient Days on treatment Baseline

LVEF ApEn

1 869 63.0 0.949313

2 118 69.5 0.794200

3 244 71.0 0.716189

4 533 68.0 0.696814

5 624 61.0 1.001086

6 276 56.3 0.748690

7 388 69.0 0.592999

8 498 64.0 0.890534

number of centres including ours have used MUGA scans tomonitor patients receiving potentially cardiotoxic therapy with aview to withholding therapy, if necessary. In order to understandfurther the mechanism of cardiotoxicity, we retrospectivelyaudited the MUGA scan imaging data of patients receivingtrastuzumab. In order to find out if there were also associatedchanges in cardiac synchrony, we calculated imaging parametersdescribed previously by O’Connell et al. [11] for the first time inpatients receiving trastuzumab. In addition, we have evaluated theutility of another parameter, ApEn, for the first time in imagingdata and report on our findings in this paper.

In this cohort of randomly selected patients who underwentserial MUGA scanning, the LVEF was within the normal range inmost (6 of 8) of the patients and in 92% of the scans done, inkeeping with their eligibility to receive trastuzumab. We were alsoable to confirm that trastuzumab resulted in a statisticallysignificant trend in decrease in LVEF for the group, as notedpreviously [8]. In keeping with previously observed findings, wealso found that left ventricular size negatively correlated with theLVEF [23], although considering all the LVEF values in this study asindividual events is not strictly valid as there were repeated andmultiple measures for the same scan with different observers. Thisrelationship between larger ventricular size or cardiac dilatationand impairment in cardiac function, is commonly observed inpatients with cardiac failure. Cardiac dilatation has many causes,including cardiotoxic chemotherapy [24] and in patients withcardiac failure is associated with a decrease in its efficacy as apump (and therefore LVEF).

In order to assess if there were associated changes in cardiacsynchrony, we used previously defined parameters indicative oflack of cardiac co-ordination including mean f, SD f and theparameters proposed by O’Connell et al. [11]. However, we did notobserve significant time trends in either O’Connell synchrony orentropy. This study reports the first results, outside of their originalpaper, where the O’Connell parameters were applied to patientswhere cardiac function is a clinical concern. The only otherpreviously published study where the O’Connell parameters havebeen used to quantify cardiac health were carried out in healthyvolunteers [25], wherein the results were reported as a set ofstandard synchrony and entropy indices for the description ofnormal ventricular contraction.

In addition, we did not observe any significant change in meanf or SD f over the same period. SD f has been used previously as ameasure of synchrony of contraction of the left ventricle [12,16].

nts for the six scan parameters using two regression methods.

Mean f SD f Synchrony Entropy

0.168 0.587 0.581 0.698

0.141 0.680 0.695 0.734

ean parameter values are shown.

End of study Percentage change

LVEF ApEn LVEF ApEn

58.5 0.820224 �7.14 �13.60

57.5 0.837807 �17.27 5.49

55.0 1.055375 �22.54 47.36

60.5 0.774318 �11.03 11.12

58.3 0.978550 �4.37 �2.25

38.0 0.987485 �32.44 31.90

44.3 0.834713 �35.75 40.76

52.5 1.089492 �17.97 22.34

Fig. 2. Scatter plot of percentage change in LVEF and ApEn from baseline to end of

study against time on treatment.

J. Cullen et al. / Biomedical Signal Processing and Control 5 (2010) 32–3636

Finally, we evaluated the utility of a novel parameter, ApEn, forthe first time in MUGA imaging data. We found an increase in ApEnin patients undergoing trastuzumab therapy. Since ApEn issensitive to grey scale structure or pattern in the MUGA scans,rather than purely random behaviour or noise, we speculate thatturbulent flow might be modulating the grey scale values of theMUGA scans. Refining the existing ApEn algorithm would benecessary to explore this further and relate it to precisephysiological effects. Nevertheless, ApEn quantification withm = 2, r = 0.16SD applied to stationary phase angle data is, togetherwith LVEF, an important indicator of cardiac dysfunction.

All patients experienced a decrease in LVEF from baseline to theend of the study, and 6/8 patients had an increase in ApEn (Table 3).Fig. 2 shows the percentage change in these parameters almostmirror each other. The largest percentage changes are seenbetween 200 and 400 days on treatment, gradually reducing after.This suggests that the cardiotoxic side effects of treatment aremost severe in this interval.

Given the limited number of patients retrospectively auditedplus the lack of information on patient demographics and previoustreatment, though some would have previously received anthra-cyclines and partial cardiac irradiation, we are unable to makedefinite conclusions on the precise mechanisms of trastuzumabrelated toxicity. However, this study has provided importantinsights on the changes in imaging parameters in patientsreceiving cardiotoxic therapy. Larger controlled and prospectivestudies in patients undergoing cardiotoxic therapy will however beable to provide more definitive answers. We therefore recommendthat ApEn should also be prospectively evaluated in such patientsundergoing serial MUGA scans and plan to do so in future at ourcentre.

6. Conclusions

The parameters suggested by O’Connell et al. synchrony andentropy for quantification of ventricular synchrony gave negativeresults in this study. Neither quantity changed significantly overtime, whereas a significant decrease in LVEF was observed.Interestingly SD f, a parameter which has widely been usedpreviously as a measure of cardiac synchrony, does not changesignificantly over time either. For the first time, we also observed a

significant increase in ApEn over the course of trastuzumabtreatment. These results show that the application of ApEn to thisimage data is a valid technique for evaluating order and ultimatelysynchrony in the heart.

Acknowledgements

The authors would like to thank Dr Jill Tipping and Brian Murbyof the Nuclear Medicine Department, Christie Hospital, Manche-ster, UK for their help with data used in the study.

References

[1] J. Cuzick, H. Stewart, R. Peto, M. Baum, B. Fisher, H. Host, J.P. Lythgoe, G. Ribeiro, H.Scheurlen, A. Wallgren, Overview of randomized trials of postoperative adjuvantradiotherapy in breast cancer, Cancer Treat. Rep. 71 (1) (1987) 15–29.

[2] J. Cuzick, H. Stewart, R. Peto, B. Fisher, S. Kaae, H. Johansen, J.P. Lythgoe, R.J.Prescott, Overview of randomized trials comparing radical mastectomy withoutradiotherapy against simple mastectomy with radiotherapy in breast cancer,Cancer Treat. Rep. 71 (1) (1987) 7–14.

[3] J. Cuzick, H. Stewart, L. Rutqvist, J. Houghton, R. Edwards, C. Redmond, R. Peto, M.Baum, B. Fisher, H. Host, et al., Cause-specific mortality in long-term survivors ofbreast cancer who participated in trials of radiotherapy, J. Clin. Oncol. 12 (3)(1994) 447–453.

[4] M.J. Adams, P.H. Hardenbergh, L.S. Constine, S.E. Lipshultz, Radiation-associatedcardiovascular disease, Crit. Rev. Oncol. Hematol. 45 (1) (2003) 55–75.

[5] T.M. Suter, B. Meier, Detection of anthracycline-induced cardiotoxicity: is therelight at the end of the tunnel? Ann. Oncol. 13 (5) (2002) 647–649.

[6] P.K. Singal, N. Iliskovic, Doxorubicin-induced cardiomyopathy, N. Engl. J. Med. 339(13) (1998) 900–905.

[7] D.L. Keefe, Trastuzumab-associated cardiotoxicity, Cancer 95 (7) (2002) 1592–1600.

[8] M.L. Telli, S.A. Hunt, R.W. Carlson, A.E. Guardino, Trastuzumab-related cardio-toxicity: calling into question the concept of reversibility, J. Clin. Oncol. 25 (23)(2007) 3525–3533.

[9] C. Leclercq, D.A. Kass, Retiming the failing heart: principles and current clinicalstatus of cardiac resynchronization, J. Am. Coll. Cardiol. 39 (2) (2002) 194–201.

[10] J.F. Debatin, S.N. Nadel, J.F. Paolini, H.D. Sostman, R.E. Coleman, A.J. Evans, C. Beam,C.E. Spritzer, T.M. Bashore, Cardiac ejection fraction: phantom study comparingcine MR imaging, radionuclide blood pool imaging, and ventriculography, J. Magn.Reson. Imaging 2 (2) (1992) 135–142.

[11] J.W. O’Connell, C. Schreck, M. Moles, N. Badwar, T. DeMarco, J. Olgin, B. Lee, Z.Tseng, U. Kumar, E.H. Botvinick, A unique method by which to quantitatesynchrony with equilibrium radionuclide angiography, J. Nucl. Cardiol. 12 (4)(2005) 441–450.

[12] A. Muxi, P. Paredes, L. Mont, F.J. Setoain, J. Duch, S. Fuertes, J. Ortin, E. Diaz-Infante,F. Pons, Left ventricular function and visual phase analysis with equilibriumradionuclide angiography in patients with biventricular device, Eur. J. Nucl. Med.Mol. Imaging 35 (5) (2008) 912–921.

[13] C. Moore, K. Manickam, T. Willard, S. Jones, N. Slevin, S. Shalet, Spectral patterncomplexity analysis and the quantification of voice normality in healthy andradiotherapy patient groups, Med. Eng. Phys. 26 (4) (2004) 291–301.

[14] C.J. Moore, K. Manickam, N. Slevin, Collective spectral pattern complexity analysisof voicing in normal males and larynx cancer patients following radiotherapy,Biomed. Signal Process. Control 1 (2) (2006) 113–119.

[15] S.M. Pincus, Approximate entropy as a measure of system complexity, Proc. Natl.Acad. Sci. U.S.A. 88 (6) (1991) 2297–2301.

[16] W.F. Kerwin, E.H. Botvinick, J.W. O’Connell, S.H. Merrick, T. DeMarco, K. Chatter-jee, K. Scheibly, L.A. Saxon, Ventricular contraction abnormalities in dilatedcardiomyopathy: effect of biventricular pacing to correct interventricular dys-synchrony, J. Am. Coll. Cardiol. 35 (5) (2000) 1221–1227.

[17] B. Hong, S. Acharya, N. Thakor, S. Gao, Transient phase synchrony of independentcognitive components underlying scalp EEG, Conf. Proc. IEEE Eng. Med. Biol. Soc. 2(2005) 2037–2040.

[18] J.P. Lachaux, E. Rodriguez, J. Martinerie, F.J. Varela, Measuring phase synchrony inbrain signals, Hum. Brain Mapp. 8 (4) (1999) 194–208.

[19] C.E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27(1948), 379–423, 623–656.

[20] S.M. Pincus, A.L. Goldberger, Physiological time-series analysis: what does reg-ularity quantify? Am. J. Physiol. 266 (4 Pt 2) (1994) H1643–H1656.

[21] S.M. Pincus, I.M. Gladstone, R.A. Ehrenkranz, A regularity statistic for medical dataanalysis, J. Clin. Monit. 7 (4) (1991) 335–345.

[22] S.M. Pincus, R.R. Viscarello, Approximate entropy: a regularity measure for fetalheart rate analysis, Obstet. Gynecol. 79 (2) (1992) 249–255.

[23] K. Chatterjee, J.E. Rame, Systolic heart failure: chronic and acute syndromes, Crit.Care Med. 36 (1 Suppl.) (2008) S44–S51.

[24] A. Negro, B.K. Brar, K.F. Lee, Essential roles of Her2/erbB2 in cardiac developmentand function, Recent Prog. Horm. Res. 59 (2004) 1–12.

[25] L. Jimenez-Angeles, V. Medina-Banuelos, R. Valdes-Cristerna, E. Vallejo, Analysisof ventricular contraction by factorial phase imaging with equilibrium radio-nuclide angiography, Conf. Proc. IEEE Eng. Med. Biol. Soc. 1 (2006) 1081–1084.