Novel Experimental Preparation to AssessElectrocardiographic Imaging Reconstruction Techniques

Jake A Bergquist1,2,3, Brian Zenger1,2,3,4, Wilson W Good1,2,3, Lindsay C Rupp1,2,3, Laura R Bear 5,Rob S MacLeod1,2,3,4

1 Scientific Computing and Imaging Institute, University of Utah, SLC, UT, USA2 Nora Eccles Cardiovascular Research and Training Institute, University of Utah, SLC, UT, USA

3 Department of Biomedical Engineering, University of Utah, SLC, UT, USA4 School of Medicine, University of Utah, SLC, UT, USA

5IHU LIRYC, Université de Bordeaux, CRCTB Inserm U1045, Bordeaux, France

Abstract

Electrocardiographic imaging (ECGI) systems are stillplagued by a myriad of controllable and uncontrollablesources of error, which makes studying and improvingthese systems difficult. To mitigate these errors, we de-veloped a novel experimental preparation using a rigidpericardiac cage suspended in a torso-shaped electrolytictank. The 256-electrode cage was designed to record sig-nals 0.5–1.0 cm above the entire epicardial surface ofan isolated heart. The cage and heart were fixed in a192-electrode torso tank filled with conductive fluid. Theresulting signals served as ground truth for ECGI per-formed using the boundary element method (BEM) andmethod of fundamental solutions (MFS) with three regular-ization techniques: Tikhonov zero-order (Tik0), Tikhonovsecond-order (Tik2), truncated singular value decompo-sition (TSVD). Each ECGI regularization technique re-constructed cage potentials from recorded torso potentialswell with spatial correlation above 0.7, temporal correla-tion above 0.8, and root mean squared error values below0.7 mV. The earliest site of activation was best identifiedby MFS using Tik0, which localized it to within a rangeof 1.9 and 4.8 cm. Our novel experimental preparationhas shown unprecedented agreement with simulations andrepresents a new standard for ECGI validation studies.

1. Introduction

ECGI is an established technique that uses subject-specific geometry and body-surface electrocardiograms toreconstruct cardiac source signals. ECGI has high clinicalapplicability and has several commercial companies asso-ciated with its development. However, experimental andclinical validation studies for ECGI techniques have con-sistently shown significant errors from controllable and un-

controllable sources, including geometric registration, sig-nal noise, conductivity, source modeling, and the inversecomputation method.[1, 2] These various sources of errormake it difficult to understand and interrogate ECGI ap-proaches thoroughly, therefore there is a need for robustand controlled validation platforms with minimal sourcesof error.

To address this need, we developed a novel experimen-tal preparation to limit sources of uncontrolled error. Thepreparation is similar to others used previously with a mod-ified Langendorff perfused heart suspended inside a humanshaped torso tank [3–5]. The torso tank allows us to con-trol for several sources of error by utilizing a homogeneousisotropic volume conductor, recording high SNR body sur-face signals using electrodes in direct contact with theconductive media, and attaining expansive sampling using192-electrodes spread across the tank surface. To furtherimprove this preparation, we recently created a novel 256-electrode pericardiac cage electrode array to record signalsimmediately adjacent to the heart surface. The pericardiaccage array was rigidly fixed relative to the tank surface andsampled evenly around the entire cardiac source, furtherreducing geometric and source sampling errors. Using thismodel, we have shown significant improvements in the up-per error bounds of the forward problem, and leveraged thesampling of the cardiac cage to investigate atrial signal re-construction.[6,7] However, we have not demonstrated theutility of the preparation for the inverse problem and ECGI.

In this report, we introduce our novel experimentalpreparation and demonstrate its value for validating the ac-curacy of ECGI-based reconstruction of ventricular-pacedbeats with a range of inverse techniques. Specifically, weexamined an ECGI formulation defined by the boundaryelement formulation (BEM) of the forward problem andthe method of fundemental solutions (MFS) with Tikhonovzero-order (Tik0), Tikhonov second-order (Tik2), and

truncated singular value decomposition (TSVD) regular-ization techniques. We reconstructed the cardiac potentialson the rigid pericardiac cage with ECGI and assessed eachformulation using standard global metrics, signal-basedcomparisons, and clinically relevant standards.

2. Methods

Experimental Preparation: The experimental prepa-ration was based on a modified Langendorff system usinga support animal to sustain the normal function of an iso-lated heart.[3,5] In brief, a heart was isolated from a donoranimal and connected via arterial and venous access to asupport animal. The isolated heart was perfused throughthe coronary vasculature via the aorta and blood was re-turned to the support animal via a suction pump in theright ventricle. The isolated heart was attached to a rigidgantry, which could be precisely lowered and fixed in thetorso tank. Registration points were recorded using a Mi-croscribe digitizer throughout the experiment to mark thelocation of the recording electrodes. All experiments wereperformed under deep anesthesia. The procedures were ap-proved by the Institutional Animal Care and Use Commit-tee of the University of Utah and conformed to the Guidefor the Care and Use of Laboratory Animals.

Recording Arrays: We used two electrical recordingarrays in this study, as shown in Figure 1. The first was thenovel cage array, which was constructed from 256 silver-silver chloride electrodes evenly spaced around the cen-troid of the cage. Spacing between each electrode locationallowed electrical current to flow unimpeded to the torsotank surface. The cage was rigidly fixed around the entireheart 0.5–1.0 cm from the epicardial surface.

Figure 1. Schematic of experimental preparation with isolated heart,surrounded by the pericardiac cage and submerged in the torso tank.

The fixed cage and the Langendorff perfused heart were

then mounted in the torso tank, which has been used in pre-vious studies and was modeled after a 10-year-old boy’storso. The tank contains 192 embedded silver-silver chlo-ride electrodes evenly spaced around the torso surface. Thetank was filled with electrolytic fluid (500 Ω·cm), whichmimics the average conductivity of the human torso. Sig-nals were acquired using a custom analog-to-digital multi-plexer at 1 kHz with a bandpass filter at 0.3 to 500 Hz anda notch filter at 60 Hz. Signals were postprocessed, andannotated using methods described previously. [8]

Beat Morphologies: For this study, we selected beatsrecorded during anterior and posterior left ventricular freewall pacing using transmural plunge needle electrodes nearthe epicardial surface. For each site, 40 individual beatswere identified, processed, and used to compare recon-struction techniques.

Inverse Methods: We applied four common inverseformulations to calculate cage potentials: MFS with Tik0regularization and BEM with Tik0, Tik2, and TSVD reg-ularization. These inverse methods were implemented inthe SCIRun problem-solving environment using the For-ward/Inverse Toolkit and MATLAB.[9] For the BEM regu-larizations, the L-curve corner was used to select the regu-larization parameter λ (Tik0 and Tik2) or the level of trun-cation (TSVD). For the MFS regularization with Tik0, weused the CRESO method to determine λ. The result wasfour inverse pipelines: BEM with Tik0, BEM with Tik2,BEM with TSVD, and MFS with Tik0.

Evaluation Metrics: To assess the accuracy of the in-verse solutions, we calculated three standard statisticalmeasures: RMSE, spatial correlation (SC), and temporalcorrelation (TC) according to the equations below. HereΦ(k, n) is a K × N matrix of measured (Φm) or calcu-lated (Φc) potentials at K electrodes on the cage for Ntime instances. To calculate spatial or temporal correlation,we constructed zero mean vectors of either time signals oneach electrode (φt = Φ(k, :)−Φ(k, :)) or surface potentialdistributions at each time instance (φs = Φ(; , t)−Φ(:, t))respectively.

RMSE =

√∑Kk=1

∑Nn=1((Φc(k, n)− Φm(k, n))2

N ·K (1)

SC =1

N

N∑n=1

φsm(n)Tφsc(n)

||φsm(n)|| · ||φsc(n)|| (2)

TC =1

K

K∑k=1

φtm(k)Tφtc(k)

||φtm(k)|| · ||φtc(k)|| (3)

Previous studies have demonstrated that global statisticscan be misleading.[1] To address this shortcoming, we im-plemented additional metrics: 1) the average magnitude ofthe spatial potential gradient at the peak of the RMS sig-nal; 2) the activation localization error between the earliest

computed and measured activation sites, and 3) a spatialcorrelation of reconstructed and measured activation maps.

3. Results

Table 1 contains global statistics for all inverse ap-proaches; the overall performances of most were compa-rable. Mean RMSE values, spatial correlation, and tempo-ral correlation varied from 0.52–0.65 mV, 0.77–0.88, and0.80–0.95, respectively. Across most global metrics, MFSwith Tik0 performed consistently better with higher spatialand temporal correlations and slightly lower RMSE val-ues. Correlations for activation maps ranged from 0.50–0.84, with MFS Tik0 performing best. Figure 2 containssamples of the best and worst inverse reconstructions withrespect to spatial correlation.

The additional metrics also revealed differences in re-construction performance. For example, the mean magni-tudes of the measured gradient were 0.095±0.10 mV/mmand 0.073±0.065 mV/mm for the first and secondventricular-paced beat morphologies, respectively. BEMTik0 and TSVD preserved the magnitude of the gradientsbetter than BEM Tik2 or MFS Tik0. The localization errorwas slightly lower with BEM Tik0 and TSVD, both iden-tifying the earliest site of activation equally with an meanrange of 2.0–3.6 cm.

4. Discussion

In this study, we highlighted a new experimental prepa-ration with a rigid pericardiac cage recording array andshowed its utility as a validation platform for ECGI tech-niques. The preparation successfully attenuated many fa-miliar sources of error, including geometric, signal noise,and torso conductivity. The recorded signals had both highresolution and coverage. We selected ventricular-pacedbeats for this initial assessment for their simplicity, wideuse for validating ECGI, and their clinical relevance. Wefound that most of the inverse methods performed simi-larly based on global metrics, corroborating previous stud-ies using simulated and experimental datasets. However,to our knowledge, the ECGI performance presented herewas the highest published with an experimental validationmodel. These results must be carefully interpreted becausethe signals were recorded just above the heart surface andnot directly on the epicardium. The cage possessed sub-stantial advantages, such as uniform coverage over the en-tire heart, and its robustness to cardiac motion artifacts.

We assessed the reconstruction results with specialized,clinically driven metrics, for example an assessment of theaverage spatial gradient at the peak of the RMS. Accurategradient reconstruction is essential to correctly identify thedirection of wave propagation and early activation devel-opment. BEM Tik0 performed well at reconstructing the

gradient of potentials, which is expected because the Tik0regularization smooths the signal based on amplitudes. Incontrast, Tik2 smooths based on the spatial derivative andlimits the gradients between neighboring sites. BEM Tik0performed the best at localizing the earliest site of acti-vation, even if this error was larger than that reported inother ECGI systems. We anticipated this result because ofthe spacing between the pericardiac cage and the epicar-dial surface. We did identify best case scenarios in whichseveral of the experimental vs. computed locations werea perfect match. Despite the superior spatial and temporalcorrelation values of the MFS Tik0 technique, it did notperform well on the other signal or clinically driven met-rics.

In summary, our experimental preparation has severalunique and compelling features that we have designed tocontrol various components of error related to the inverseproblem and ECGI. We can examine the inverse problemin unprecedented detail in an environment in which manyof the common errors plaguing ECGI are controlled. Therigid pericardiac cage geometry limits the amount of ge-ometric error, and the homogeneous torso tank and em-bedded electrode arrays give us adequate sampling andhigh-quality signal recordings while simplifying the vol-ume conductor models. We recognize that this prepara-tion fails to completely representations human anatomyor physiology; however, the resulting datasets can be im-mensely valuable in testing fundamental characteristics re-lated to ECGI and practical applications. Future studieswill further refine the experimental model to perfect thevalidation platform and use it in a variety of ECGI andclinically driven contexts.

Acknowledgments

Support for this research came from the NIH-NIGMS Center for Integrative Biomedical Computing(www.sci.utah.edu/cibc), NIH NIGMS grant no.P41GM103545and the Nora Eccles Treadwell Foundation for Cardiovas-cular Research.

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Table 1. Reconstruction accuracy statistics: RMSE (mV), spatial correlation (SC), temporal correlation (TC), localization error (LE) (cm), activationmap spatial correlation (SCact), mean gradient magnitude at RMS peak (Grad) (mV/mm)c. Btik0: BEM Tik0, Btik2: BEM Tik2, Btsvd: BEM TSVD, Mtik0:MFS Tik0. Statistics are shown as mean over all 40 beats per morphology ± one standard deviation. Two pacing locations, one on the anterior (VP1) andone on the posterior (VP2) left ventricular free wall.

RMSE (mV) SC TC LE (cm) SCact Grad (mV/mm)

Btik

0 VP 1 0.55 ±0.043 0.79 ±0.028 0.88 ±0.011 3.6 ±1.4 0.60 ±0.18 0.082±0.049VP 2 0.67 ±0.011 0.77 ±0.013 0.82 ±0.0043 2.0 ±0.55 0.55 ±0.10 0.082±0.061

Btik

2 VP 1 0.52 ±0.041 0.88 ±0.031 0.95 ±0.012 4.7 ±2.4 0.81±0.18 0.053±0.028VP 2 0.62 ±0.011 0.85 ±0.0089 0.86 ±0.00039 2.6 ±1.5 0.72 ±0.10 0.054±0.033

Bts

vd VP 1 0.56 ±0.043 0.77 ±0.029 0.87 ±0.0096 3.6 ±1.5 0.59 ±0.15 0.088±0.048VP 2 0.67 ±0.011 0.78 ±0.013 0.80 ±0.0050 2.0 ±0.55 0.50 ±0.12 0.085±0.055

Mtik

0 VP 1 0.49 ±0.041 0.90 ±0.012 0.95 ±0.0097 5.2 ±2.3 0.84 ±0.18 0.055±0.029VP 2 0.60 ±0.010 0.87 ±0.0083 0.86 ±0.0036 3.3 ±0.36 0.77 ±0.058 0.050±0.035

Figure 2. Identified best and worst case potential reconstructions on the pericardial surface. Best case construction (SC = 0.91) used MFS Tik0 andthe worst case (SC = 0.65) used BEM TSVD. The pink star corresponds to the measured earliest site of activation. The brown diamond corresponds tothe computed earliest site of activation

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Address for correspondence:

Jake Bergquist72 Central Campus Dr, Salt Lake City, UT 84112jbergquist@sci.utah.edu