Feature-Based MRI Data Fusion for Cardiac

Arrhythmia Studies

Karl Magtibaya,1,∗, Mohammadali Beheshtia,Farbod Hosseyndoust Foomanya,2, Stephane Masseb, Patrick F.H. Laib,

Nima Zamirib,3, John Astab, Kumaraswamy Nanthakumarb, David Jaffrayc,Sridhar Krishnana, Karthikeyan Umapathya

aDepartment of Electrical and Computer Engineering, Ryerson University, 350 VictoriaSt., Toronto, Ontario, Canada, M5B2K3

bToby Hull Family Cardiac Fibrillation Management Laboratory, Toronto GeneralHospital, 200 Elizabeth St., Toronto, Ontario, Canada, M5G2C4

cPrincess Margaret Cancer Centre, Princess Margaret Hospital, 610 University Ave.,Toronto, Ontario, Canada, M5G2M9

Abstract

Current practices in studying cardiac arrhythmias primarily use electrical oroptical surface recordings of a heart, spatially-limited transmural recordings,and mathematical models. However, given that such arrhythmias occur ona 3D myocardial tissue, information obtained from such practices lack in di-mension, completeness, and are sometimes prone to oversimplification. Thecombination of complementary Magnetic-Resonance Imaging (MRI)-basedtechniques such as Current Density Imaging (CDI) and Diffusion TensorImaging (DTI) could provide more depth to current practices in assessingthe cardiac arrhythmia dynamics in entire cross sections of myocardium. Inthis work, we present an approach utilizing feature-based data fusion meth-ods to demonstrate that complimentary information obtained from electrical

∗K. Magtibay is the corresponding authorE-mail:karl.magtibay@gmail.com Tel.No.: +1-(416)-528-0906

1K. Magtibay is currently a Research Analyst at the Toby Hull Family Cardiac Fibril-lation Management Laboratory, 200 Elizabeth St., Toronto, Ontario, Canada, M5G2C4

2F.H. Foomany is currently the Lead Security Content Researcher at Security Compass,257 Adelaide Street West, Suite 500, Toronto, Ontario, Canada M5H1X9

3N. Zamiri is currently an Internal Medicine resident physician at McMaster UniversityMedical Centre, 1200 Main St. W, Hamilton, Ontario, Canada L8N3Z5

January 24, 2016

© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ (http://dx.doi.org/10.1016/j.compbiomed.2016.02.006)

current distribution and structural properties within a heart could be quan-tified and enhanced. Twelve (12) pairs of CDI and DTI image data sets weregathered from porcine hearts perfused through a Langendorff set up. Im-ages were fused together using feature-based data fusion techniques such asJoint Independent Component Analysis (jICA), Canonical Correlation Anal-ysis (CCA), and their combination (CCA+jICA). The results suggest thatthe complimentary information of cardiac states from CDI and DTI are en-hanced and are better classified with the use of data fusion methods. Foreach dataset, an increase in mean correlations of fused images were observedwith 38% increase from CCA+jICA compared to the original images whilemean mutual information of the fused images from jICA and CCA+jICAincreased by approximately three-fold. We conclude that MRI-based tech-niques present potential viable tools in furthering studies for cardiac arrhyth-mias especially Ventricular Fibrillation.

Keywords: Magnetic Resonance Imaging, Current Density Imaging,Diffusion Tensor Imaging, Data Fusion, Cardiac Arrhythmia, VentricularFibrillation

1. Introduction

Current techniques used to characterize cardiac arrhythmias such as surface[1,2] and transmural[3, 4, 5] mapping have been proven to provide meaningfulinformation on the electrical activity on and within regions of a myocardium.Cardiac models[6, 7, 8, 9, 10] have also been developed to mimic myocardialcharacteristics with which simulations are performed to study electrical dy-namics of cardiac arrhythmias. This allows researchers to study arrhythmiaswithout using biological samples or living subjects. However, applicationsof such techniques are spatially limited and are restricted by mathematicaloversimplifications while cardiac arrhythmias are complex global phenomena.

Various medical imaging modalities may provide an alternative tool notonly to improve on the spatial resolution of current mapping techniques butalso information on tissue anatomy on which they occur such as fibre ori-entation and anisotropy. A joint analysis of anatomical and electrophysio-logical information within a myocardium could provide further insights onthe structural and functional nature of cardiac arrhythmias. As an exam-ple, Ultrasound Imaging has been used in in-vivo cardiac mapping studiessuch as creation of local activation maps through Electromechanical Wave

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Imaging[12, 11].Another medical imaging modality, Magnetic Resonance Imaging (MRI),

has been thoroughly used in research and clinical practice to study and/ordiagnose a wide array of human patho-physiologies. Some MRI techniques,such as Functional MRI[13] and Diffusion Weighted Imaging[14], are heav-ily used in neurological studies techniques. Moreover, techniques such asMagnetic Resonance Angiography[15], Myocardial Tagging[16] and MagneticResonance Perfusion Imaging[17] have been widely used in cardiovascularstudies.

In this work, we take advantage of two MRI techniques to identify func-tional and structural characteristics of different cardiac states, Current Den-sity Imaging (CDI)[18, 19] and Diffusion Tensor Imaging (DTI)[14], respec-tively. On one hand, CDI was developed to detect changes in the magneticfield induced by electrical currents and was previously used to study elec-trical current distribution and pathways in biological samples[19, 20, 21].On the other hand, DTI further builds on the concept of Diffusion WeightedImaging which provides micro-structural information of tissues based on ten-sors derived from water molecules diffusion within a sample. DTI has beenlong used in cardiac studies, exploring contributions of myocardial ischemiaand/or infarction to cardiac arrhythmias[23, 24, 25].

Treating CDI and DTI as complementary tools for myocardial assessmentmay be beneficial in providing more in-depth understanding of cardiac ar-rhythmias most especially Ventricular Fibrillation (VF) since its electricaldynamics are poorly understood hence considered most lethal of the ventric-ular arrhythmias. Feature-based data fusion methods such as Joint Indepen-dent Component Analysis (jICA), Canonical Correlation Analysis (CCA),and the combination of the latter two (jICA+CCA), which have been usedfor neurological studies in the past[26, 27, 28, 29, 30, 31, 32], could be usefulto jointly analyze cardiac data from CDI and DTI. Therefore, we aim todemonstrate the combined capability of MRI techniques, CDI and DTI, tocapture unique characteristics of cardiac states by using feature-based datafusion methods. Through these methods, we can then quantify and enhanceinformation acquired from different cardiac states.

To the best of our knowledge data fusion as applied to cardiac imagingdata collected through CDI from live biological samples is novel. We havepresented a preliminary study of fusing CDI and DTI data using jICA for asmaller database[33]. This work greatly expands on these initial results andanalysis to a larger database, the addition of CCA and jiCA+CCA as fusion

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Figure 1: Timeline for porcine heart experiment protocols execution: from organ harvestto imaging

methods, and metrics of comparison for the said data fusion methods. Thispaper is organized as follows: Section 2 will outline our protocol for acquiringand preprocessing CDI and DTI datasets and introduce mathematical foun-dations of data fusion methods. In Section 3, we present the results of ourexperiments and application of fusion algorithms. We provide an analysisour results in Section 4. We summarize our findings and discuss future workin section 5. Finally, we provide some limitations of our study in Section 6.

2. Methods

We obtained structural (from DTI) and functional (from CDI) imagingdata sets associated to a maximum of two out of three cardiac states ona porcine heart: normal sinus (NM), asystolic (AS), and VF. These stateswere verified accordingly with corresponding electrograms (EGMs). Overall,10 porcine hearts were used in experiments from which 12 datasets wereobtained, 4 datasets for each said cardiac state. Each experiment lasted from2.5 hours to a maximum of 4 hours. A timeline of the protocol executionfollowed for each experiment is shown in Fig. 1

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2.1. Data Acquisition

With an approved Animal Use Protocol from Toronto General Hospi-tal (TGH), ex-vivo studies were performed on porcine hearts. Each heartwas surgically harvested from healthy anesthetized male yorkshire pigs, eachabout 60 kg in body weight. Each heart was aortically cannulated andmounted to a mobile Langendorff perfusion system (shown in Fig. 2A).The heart was perfused with carbogenated (95% O2 and 5% CO2) Krebs-Henseleit solution maintained at 37◦C. The beating heart was allowed tostabilize for 10 minutes. Bipolar EGMs were monitored and recorded to con-firm the state of the heart. Examples of acquired bipolar EGMs are shownin Figs. 3A (NM) and B (VF).

Three pairs of copper and brass electrodes were attached to the heartas shown in Fig. 2B: a pair for current injection (C; one pierced throughthe base and one pierced through the apex of the heart), a pair for electri-cal stimulation (S; stitched on the surface of the epicardium), and a pair ofcopper plates, wrapped around the ventricles, to monitor ventricular electro-grams which also acted as defibrillating pads (E/D). The heart was fitted into a protective MRI phantom (shown in Fig. 2C). The protective phantomallows for subject rotation, as per CDI requirements [19], with minimal axialdisplacement.

All experiments performed for this study were accomplished under a 1.5TGE Signa MRI system. Working with implied biological and pulse sequenceparameter constraints, six 256-by-256 images were collected from the ven-tricles of each heart for CDI and 21 images encompassing the whole heartvolume for DTI, overlapping those collected for CDI, with a 17 pixels percm spatial resolution. On one hand, the following parameters were used forCDI: NEX (Number of Excitations): 3; repetition time (TR): 700 ms; echotime (TE): 40 ms; slice thickness: 7 mm; slice spacing: 0 mm; field of view(FOV): 15 cm; average current amplitude: 25 mA; As per CDI requirements,two phases of an electrical current waveform, shown in Fig. 2D, phase cycles1 and 2, were passed from the base to the apex of the heart. Phase cycleswere timed with respect to spin echo pulse sequence. Details of CDI proto-cols are described elsewhere [19]. On the other hand, following parameterswere used for DTI: NEX: 6; TR: 8300 ms; slice thickness: 7 mm; slice spac-ing: 0 mm; FOV: 15 cm; No. of Directions: 30; b-value: 1000 mm2/s. Allof the copper and brass electrodes and plates were removed before the DTIprotocol was executed to prevent artifacts.

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Figure 2: Ex-vivo porcine heart experimental set up: A) shows a mobile Langendorffsystem; B) shows an example of electrode placement on a heart; C) depicts the protectivephantom used in imaging experiments; D) shows the phase cycles (PC1 and PC2) ofelectrical current waveform required for CDI: a is the magnitude of the current, d is thedelay between two pulses, and Tw is the width of each pulse

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Figure 3: Sample bipolar EGMs collected from two separate porcine heart experiments.Panel A shows an organized and periodic EGM attributed to a normal sinus (NM). Thisis indicative of the successive depolarization at a constant rate as seen in the above figure.Panel B, on the other hand, shows an EGM corresponding to a VF as illustrated by a time-varying and chaotic EGM. The EGMs were recorded with AudacityTMthrough custom-made ECG circuit, sampled at 8 kHz, bandpass filtered (0.5-100 Hz), and cascaded witha notch filter (60 Hz)

2.2. Data Preprocessing

The procedure used to calculate current density maps are described else-where [18]. Since the rotations of the heart were constrained to only twoorientations, only two dimensional maps (J) were calculated for this study.A requirement for current density map calculation is masking off the back-ground of the MR phase image components using a mask derived from theMR magnitude image component. This was accomplished by selecting thevalue within the MR magnitude image histogram on which the individualhistograms of the object and background intersect so that the object withinthe image is preserved. A 3-by-3 Median filter was used for each CDI imageslice to eliminate outliers. An example of a set of calculated current densitymaps is shown on the top row of Fig. 4.

To calculate diffusion tensor images, an open-source program, 3D Slicer[34], was used. As shown on the bottom row of Fig. 4, the images are encodedunder an RGB scheme. Each channel of an RGB image encodes a particularfibre orientation based on the primary eigenvector of the diffusion tensor,D. Based on our previous report [35], encoded within the red, green, andblue channels are the medial-lateral, anterior-posterior, and superior-inferiorcomponents of the primary eigenvector, respectively. In order to match themanner in which CDI was collected, only the blue channel, B, is used inconjunction with J images.

Although the image slices for both modalities were acquired from compa-

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Figure 4: Example of CDI and DTI images slices showing J (top) and B (bottom) images;show from left to right is the succession of slices from the base (superior) to the apex(inferior) of the heart while LV and RV show the locations of the the left and rightventricle, respectively.

rable regions of the heart, the slice planning and re-planning performed in-between modalities do not guarantee to scan the exact same slices. To matchthe CDI and DTI image slices, a minimum-variance area ratio (MVAR) wasperformed on the corresponding masks of each image by measuring the vari-ance of the ratios of the calculated areas of 6 image masks in batches. As 6consecutive slices were collected for CDI, 6 consecutive slices must then bematched from DTI with CDI from a similar area which is near the base ofa heart. The batches ranged from the first 6 DTI slices to the last 6 DTIslices incrementing by a slice per batch. The variance of each batch is thencalculated such that Rk = var(r), where k = 1, 2, ...,M −N , the number ofbatches being matched. The batch of slices that are closest with each otheris the one with the lowest variance such that kmatch = min(Rk).

The matched CDI and DTI image slices were registered through a sim-ple 2D cross-correlation of the image slices’ masks. Finally, following [26],Principal Component Analysis (PCA) using Singular Value Decomposition(SVD)[36] was used to reduce the dimension of the acquired compilation ofimages for CDI and DTI per state in preparation for fusion.

2.3. Feature-Based Data Fusion Techniques

2.3.1. Joint Independent Component Analysis

Pioneered by V.D. Calhoun and T. Adali [28], jICA has been extensivelyused to fuse neurological data, such as Electroencephalographs (EEG), fMRI,

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and sMRI, data to study disorders such as schizophrenia and bipolar disorder[28, 26, 27]. jICA focuses on the interaction of data sets and its application inidentifying components that are useful in quantitatively categorizing statesbased on the underlying cross-information between modalities [28]. The aimof jICA is to estimate a set of N × N vectors of weights or loadings, W,which can demix a given set of N ×M data, X, to its corresponding N ×Mcomponents, Y, such that Y = WX where N is the number of states andM is the number of variables within a state. Considering that the given dataset X is composed of concatenated data obtained from data modalities XA

and XB which can have different number of variables M1 and M2 in whichM = M1 + M2, such data sets must also be normalized for the modalitiesto have similar contributions. Group loadings that are statistically differentfrom one another are used for quantitative separation between a control anda patient group. The data organization for jICA is shown in Fig. 5B.

Originally, jICA uses a maximum-likelihood estimation method (MLEM)which requires an a priori knowledge or an idea of the nature of the distribu-tion the data sets at hand [28]. However, in the case of fusing CDI and DTIdata sets, such information is not available as there is no a priori knowledgeof current density maps and tensors for a certain state. In this work, Infor-mation Maximization (IM) [37] is instead utilized to perform jICA. Previousworks have proven that IM has the similar end result as MLEM when usedfor mixture decomposition [38]. Mathematically, IM estimates W such that

Wnew = [WTold]

−1 + η(1 − 2U)XT (1)

where η is the learning rate and U is defined as the sigmoid function

U = g(Y) =1

1 + e−Y(2)

Details of the implementation of the IM algorithm is explained elsewhere[37].

2.3.2. Canonical Correlation Analysis

CCA has also been used in the study of neurological disorders [29] and incombination with other data fusion techniques [30]. CCA is a multivariate,statistical method which is used to expose linear relationships that exist be-tween two given data sets [36], XA and XB, with dimensions N ×M1 andN ×M2, respectively. A linear relationship between the two data sets is un-raveled by calculating two N×N matrices, WA and WB, known as canonical

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variates (CV), columns of which are maximally correlated to each other, andestimating two component matrices, YA and YB, where Yi = WiXi for i =A,B, with the dimensions N ×M1 and N ×M2. Like the weights for jICA,the Wi weight matrix are called loadings and only those loadings and/orcomponents that are statistically different from the others are analyzed. Fig.5C shows how data sets are organized for performing CCA.

WA and WB are calculated through WTi = UiX

Ti for i = A,B. Ui are

the eigenvectors of the Lagrange Multipliers

(Σ−0.5A ΣA,BΣ−1

B ΣB,AΣ−0.5A − rI)UA = 0 (3a)

(Σ−0.5B ΣB,AΣ−1

A ΣA,BΣ−0.5B − rI)UB = 0 (3b)

where Σi and Σi,j, are the covariance and cross-covariance of data sets Xi fori = A,B, respectively. While r and I are the eigenvalue and identity matrices,respectively. Both equations in Eq. 3 are constrained in such a way that WA

and WB are column-wise maximally correlated by maximizing Eq. 4 below.

corr(UAXTA,UBXT

B) =UAΣA,BUT

B√(UAΣAUT

A)(UBΣBUTB)

(4)

Furthermore, WA and WB must exhibit qualities, such as column-wise or-thogonality within each matrix, which are described in detail elsewhere [36].

2.3.3. Combination of jICA and CCA

By performing CCA and jICA in succession, a more flexible link betweendata sets, through correlation, can be established: the constraints imposedby CCA and jICA are relatively relaxed such that both common and uniquesources can be extracted along with their respective loadings from estimatedmixing profile [32, 31]. Such a combination is applicable especially when theassociated source maps derived are not sufficiently differing from each other(CCA) and that the modalities are assumed to have a one-to-one correlation(jICA) since there is only one mixing matrix estimated for the two modalities.Following the works of J. Sui et. al [30, 32, 31], the technique from hereonin will be called CCA+jiCA, is performed as follows: CCA is first performedon given data sets, XA and XB, from two different modalities. WA andWB are estimated and are used to extract CA and CB, respectively, suchthat Ci = WiXi for i = A,B. Results are then concatenated side by side,creating the matrix C. D is then estimated using jICA to extract S, suchthat S = DC. Since S is a concatenation of two modalities, it can be divided

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in to two matrices SA and SB, from which sources can obtained throughYi = EiSi where Ei = DW−1

i for i = A,B. Fig. 5D summarizes the dataorganization for CCA+jICA.

3. Results

Only image slices 3 to 5 were chosen to be included in both fusion tech-niques; because of the conductive nature of the E/D electrodes, some Jimages had areas that have extremely high electrical current and were elim-inated through the process of masking. Some of the CDI slices were frag-mented especially those close to the E/D electrodes (i.e. 1st and 2nd slice).As for the 6th slice, for some states, fragmentation was observed because ofthe closeness of the bottom C electrode to the slice itself and therefore wasexcluded from fusion as well.

Loadings were selected for a binary classification, between VF and non-VF (i.e. NM and AS) subjects, through a two-sample t-test, to quantify thediscriminative ability of the information content for every cardiac state. ForjICA, the first component yielded the most significant difference between VFand non-VF subjects (p = 0.022). Furthermore, while using the same com-ponent, AS and NM subjects display some difference between them althoughnot statistically significant (p > 0.1). This may be attributed to the smallsample sizes within each group involved. Figs. 6A and B summarizes theresults obtained from jICA. Additionally, a separate jICA procedure was per-formed on individual modalities in order to provide evidence that by usingonly CDI and DTI data sets, the technique’s discriminative ability is poor,shown in Figs. 7A and B.

As with CCA, the eighth component for CDI and DTI loadings yieldedstatistically significant difference between VF and non-VF subjects (p =0.018), with a correlation(r) of 0.9. Using the same component, AS and NMsubjects, however, were found to share similarities (p > 0.1). Shown in Figs.6C and D the summary of the results obtained from CCA.

Finally, the third component from CCA+jICA showed to be statisti-cally different (p = 6.5e−3) with a r = 0.9 on the CCA stage. Moreover,CCA+jICA did not yield any better classification between AS and NM sub-jects, using the same component (p > 0.1). The results from CCA+jICA aresummarized on Fig. 6E and F.

To measure the accuracy of loadings as tools to contrast between car-diac states, a Linear Discriminant Analysis (LDA) was performed which was

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Figure 5: Overall data organization implemented for each technique data fusion technique:A) demonstrates the feature generation step from the calculated CDI (Mod A) and DTI(Mod B) slices for each state; B) shows the procedure in performing jICA through infor-mation maximization before which CDI and DTI vectors are concatenated; C) CCA, onthe other hand, requires the reduction of number of columns (SVD) before fusion can beaccomplished; finally, D) shows the intermediate steps in performing CCA+jICA by usingthe output of CCA as an input to jICA

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Figure 6: Loading distribution comparison representing difference in information contentbetween VF (A,C,E) and non-VF states and AS and NM (B,D,F) states for jICA, CCA,and CCA+jICA, respectively

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Figure 7: Loading distribution comparison showing results obtained by separately per-forming the ICA on CDI (A) and DTI (B) data. Based on the ICA loading distributions,using CDI or DTI alone could not be used differentiate cardiac states from each other.

validated through Leave-One-Out (LOO). First, with an overall accuracy of83.3%, jICA successfully identified 75.0% and 87.5% of VF and non-VF sub-jects, respectively. Secondly, CCA correctly distinguished 75.0% and 50.0%of the VF and non-VF groups with an overall accuracy of 58.3%. Lastly,with CCA+jICA, overall accuracy was marked at 75.0% with 50.0% samplesclassified as VF and 87.5% as non-VF. It is important to note, that the re-sults shown under CCA and CCA+jICA were scaled by 2 since the numberof loadings analyzed for these methods were double that of jICA. Summariesof LDA-LOO from jICA, CCA, and CCA+jICA are summarized on Table 1.

In evaluating the reconstructed images from all data fusion techniques, we

Table 1: Number of correctly identified and cross-validated subjects (categorized by car-diac states) in percent as a result of performing LDA-LOO on CDI and DTI jICA, CCA,and CCA+jICA Loadings on 4 VF and 8 Non-VF subjects

jICA CCA CCA+jICA

VF (n = 4) 75.0% 75.0% 50.0%

Non-VF (n = 8) 87.5% 50.0% 87.5%

Accuracy 83.3% 58.3% 75.0%

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Figure 8: Evaluation of fused reconstructed images. Panels and B show the averaged (fromall 12 datasets) correlations and mutual information between CDI and DTI componentspost-fusion compared with the original, unfused CDI and DTI images. In both cases,CDI and DTI components show the highest correlation and mutual information under theCCA+jICA method compared to other data fusion schemes.

used correlation and mutual information as metrics to measure how well CDIand DTI images were fused. Figs. 8 A and B show the correlation and mutualinformation between reconstructed images from all data fusion paradigmscompared to their original counterparts: there is an observed increase in themean correlation from all twelve subjects under jICA and CCA with 5.29%and 7.63%, respectively, while CCA+jICA provides 37.93%; on the otherhand, while there is a slight decrease in the mean mutual information ofthe reconstructed images under CCA (4.36%), both jICA and CCA+jICA’sincreased by approximately three-fold.

4. Discussion

In this work, we have shown the combined capability of CDI and DTIto capture unique characteristics of different cardiac states which were fur-ther enhanced by feature-based data fusion methods. By fusing structuraland functional information derived from MRI techniques, we also provideda quantitative metric for identification of such imaging datasets as physio-logically classified. Not only that MRI techniques could provide an alternateperspective to the exploration of cardiac arrhythmias, it could also offer anadded level of depth and span within which cardiac arrhythmias are studied.This is going to be particularly helpful in analyzing VF since the current

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tools used for its analysis has been limited only to electrograms from sur-face and regional mapping as well as mathematical models. With this workwe can potentially advance to provide information on electrical activity andstructure over entire cross sections of myocardial tissues through imagingdatasets.

As seen from the spread of the component loadings of jICA, the distinc-tion between the current distribution pathways of the three cardiac states wasimproved by data fusion. Even with a limited number, the information con-tent between VF and non-VF groups portrayed significant differences fromeach other. This is a valuable and yet expected finding as these variations inthe current pathways or specific patterns of current distribution might holdthe key to characterizing cardiac arrhythmias. With regards to VF loadings,we suspect that the variation of loadings for VF on all data fusion paradigmswas caused by CDI capturing VF at different cycles with current densitiesaveraged at different places within the image slice. In AS and NM groups,the contrast between their spreads is evident although only qualitatively.Distinction of current distribution pathways between the VF and non-VFgroups under the CCA data fusion paradigm has shown improvement as wellcompared to using their respective jICA loadings. Finally, by combiningCCA and jICA in succession, we noticed a significant improvement in thedifferentiation of all three cardiac states. Such results show that the load-ings derived from CCA+jICA provide improved statistical results comparedeither CCA or jICA only.

Under AS and NM states, J component of CDI and B component ofDTI are known to have high correlation with each other which implies thatcurrent propagation is directional within the tissue micro-structure. Afterfusion, consequently, it is expected that these CDI and DTI components willhave higher correlation with each other. Intuitively, since the idea of fusionbrings the two data sets together, the resultant mutual or shared informationmust be higher than their original counterparts. Hence, the results obtainedfrom correlation and mutual information strengthens our previous reportsthat CDI and DTI share correlated information [35]. The findings in thisstudy then extends to the idea that by methodically combining electricalcurrent pathways and fibre orientation within a tissue can better depict theelectrophysiological phenomena than using only one type of information.

Another interesting outcome from all data fusion paradigms is that thereis an observed linearity between the distributions of the loadings of each car-diac state: with the VF group having high-value loadings, NM group with

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mid-value loadings, and AS group with low-value loadings; an apparent trendwhich bode well for combining CDI and DTI. This means that the compli-mentary aspects of CDI and DTI might bolster their utility in characterizingcardiac states which could prove useful in the study of a wide variety ofcardiac arrhythmia.

5. Conclusions and Future Work

Overall, despite the limited number of cardiac states due to the resourceintensive nature of the experimental protocol and logistical constraints, thiswork presented evidence towards the potential use of CDI and DTI to studycardiac arrhythmias, such as VF, in an ex-vivo mobile Langendorff setup.Data fusion techniques can provide quantitative methods to enhance andquantify unique current distribution pathways in combination with struc-tural information of a cardiac state. This study presents a strong precursorfor medical imaging techniques as viable tools to study cardiac arrhythmia.The availability and viability of more advanced instruments to gain deeperinsights of the underlying mechanisms of VF could lead to better treatmentoptions for cardiac arrhythmia patients. Future works could include the de-sign of data-driven, three-dimensional model of the images as a result offusion that could prove useful in studying cardiac arrhythmia. These modelscan be used to study the myocardium from the macro- and microscopic lev-els. In addition, fusing information from surface mappings and other clinicaldata could result in the development of sophisticated tools and proceduresto improve treatment options for cardiac arrhythmia.

6. Limitations

CDI by nature of the MRI protocol provides time-averaged informationover the scan duration and hence may not reflect instantaneous dynamicsof cardiac arrhythmia. Image-to-Noise ratio and spatial resolution couldbe improved with a higher Tesla MR machine than the one used in thisstudy. We recognize that image matching and registration techniques usedin this work are rudimentary and more sophisticated techniques could beused in future studies. Despite of these limitations, CDI was able to capturedifferences in the average current distributions during cardiac states and wasfurther enhanced by fusing with DTI.

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Acknowledgment

In recognition of their technical expertise, the authors would like to thankMr. J. Koch of Ryerson University, who assisted our team in preparation andimprovement of our electronics and mechanical aspects of our experimentalset-up, and Dr. W. Foltz, Mr. N. Spiller, and Mr. E. Hlasny, for lending ustheir time and technical expertise on MR scanners and helped us optimize ourimaging experiments. Finally, the authors would like to thank the CanadianInstitutes of Health Research (CIHR) for providing us with resources to makethis study possible (CHIR grant no. 111253).

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