Spatial resolution of body surface potential maps and magnetic field maps: a simulation study applied to the identification of ventricular pre-excitation sites R. Hren I

G. Stroink 2"3

B.M.

Horb~ek 2

1Nora Eccles Harrison Cardiovascular Research & Training Institute, University of Utah, Salt Lake City, UT 84112, USA 2 Department of Physiology & Biophysics, Dalhousie University, Halifax, Canada B3H 4H7 3Department of Physics, Dalhousie University, Halifax, Canada B3H 3J5

Abstractm-l-he spatial resolution of body surface potential maps (BSPMs) and magnetic field maps (MFMs) is investigated by means of an anatomically accurate computer model of the human ventricular myocardium. BSPMs and MFMs are calculated for the simulated activation sequences initiated at 35 pre-excitation sites located along the atrioventricular (AV) ring of the epicardium. Changes in the BSPMs and MFMs corresponding to different pre-excitation sites are quantified in terms of the correlation coefficient r. The spatial resolution (selectivity) for a given pre-excitation site is defined as the half-distance between those neighbouring locations at which morphological features of maps, in terms of r, become distinct (r < 0.95). It is found that, at 28 ms after the onset of preexcitation and with no noise added, this distance JzSD, for all sites along the AV ring for the 117-lead BSPMs, is 0.834-0.32cm, and for the 64-lead and 128-lead MFMs it is 1.54 4- 0.84 cm and "1.15 4- 0.43 cm, respectively. The findings suggest that, when features of non-invasively recorded electrocardiographic and magnetocardiographic map patterns are used for identifying accessory pathways in patients suffering from W P W syndrome, BSPMs are likely to provide more detailed information for guiding the ablative treatment than MFMs. For some sites MFMs provide more information. Both modalities may provide additional assistance to the cardiologist in locating the site of the accessory pathway. Keywords--Body surface potential mapping, Electrocardiography, Magnetic field mapping, Biomagnetism, Spatial resolution, Pre-excitation syndrome Med. Biol. Eng. Comput., 1998, 36, 145-157

1 Introduction

THE PRECISE identification of the pre-excitation sites in patients suffering from Wolff-Parkinson-White (WPW) syndrome (GALLAGHER et al., 1978; YEE et al., 1995) is a prerequisite for successful radiofrequency (RF) catheter ablation (JACKMAN et al., 1991; LESH et al., 1992). Non-invasive methods for imaging electric cardiac sources, such as body surface potential mapping and magnetic field m~/pping, can provide guidance in such a treatment. As the noninvasiveness of these modalities makes them routinely applicable in the clinical setting, it is of practical interest to explore their efficacy in identifying target sites for RF ablation. Several investigators (BENSON et al., 1982; DE AMBROGGI et al., 1976; GIORG! et al., 1991; IWA and MAGARA, 1981;

Correspondence should be addressed to Dr, Hren; email: [email protected] First received 10 March 1997 and in final form 12 November 1997 9 IFMBE:1998 Medical & Biological Engineering & Computing

March 1998

KAMAKURA et al., 1986; YAMADA et al., 1975; LIEBMAN et al., 1991; GROGrN et aL, 1992) have correlated specific patterns of body surface potential maps (BSPMs), typically obtained at the anterior and posterior torso, with the particular location of any given pre-excitation site, using empirical criteria for interpretation. They noted that the potential maximum is relatively stationary during the early phase (up to 40 ms after the onset) of ventricular activation initiated by the pre-excitation and is positioned on the left anterior torso for all pre-excitation sites. It is the position of the potential minimum (and of the negative area) that identifies a specific pre-excitation site. In particular, it was observed that, first, a minimum on the fight anterior torso corresponds to pre-excitation sites located in the right ventricle (RV); secondly, a minimum on the back corresponds to pre-excitation sites in the left ventricle (LV); thirdly, a region of negative potentials over the entire lower torso corresponds to both RV and LV posterior pre-excitation sites; and, fourthly, a region of positive potentials over the entire lower torso corresponds to both RV and LV anterior pre-excitation sites. These criteria were later substantiated by 145

computer models (LORANGEand GULRAJANI,1986; WEI et aL, 1990; NENONEN et aL, 1991b) and used in clinical practice at some institutions to guide catheter ablation of accessory pathways (NADEAU et al., 1986; GROGIN et aL, 1992; DUBUC et al., 1993). However, the usefulness of BSPMs for clinical purposes largely depends on how precisely it is possible to discriminate between patterns of BSPMs for adjacent pre-excitation sites. DUBUC et al. (1993) recently reported that pacing at sites separated by only 5 mm gives rise to BSPMs that significantly differ in morphological features, such as the locations of the extrema, the distance between the extrema, and the configuration of the region of near-zero potentials, but their study explored the resolution of BSPMs only at a single segment of the atrioventricular (AV) ring of the epicardium. More recently, a canine experimental study was performed by GREEN et al. (1994), who concluded that quantitative comparison of BSPMs can be used to identify some LV endocardial pacing sites within a 4 mm range. The spatial resolution of magnetic field maps (MFMs), typically obtained near the anterior torso only, has been explored only indirectly using an inverse solution that attempted to localise the pre-excitation activity represented as a single current dipole embedded in a torso model (MOSHAGE et aL, 1989; NENONEN et aL, 1991d; WEISMOLLERet aL, 1992; Ms163 et al., 1993; STROINK, 1993; NOMURA et al., 1994). Accuracies in the 2cm range relative to the site determined from electrophysiological studies or to the site of successful ablation have been reported. Two studies (LAMOTHE et al., 1995; NAKAYA et al., 1995) indicated that having both BSPMs and MFMs available may enhance the accuracy of non-invasive localisation. The spatial resolution of BSPMs and MFMs in identifying the pre-excitation sites remains to be determined in a systematic manner under the same study conditions. Also, no attempt has yet been made to compare the spatial resolutions of BSPMs and MFMs. Accordingly, we used an anatomically accurate computer model of the human ventricular myocardium to calculate sequences of BSPMs and MFMs for a set of pre-excitation sites along the AV ring. Specifically, we assessed changes in patterns of BSPMs and MFMs against distance between the pre-excitation sites. The ultimate goal of this study was to improve the interpretation of BSPMs and MFMs as actually recorded in patients suffering from WPW syndrome.

Using the surface harmonic expansion enabled us to calculate analytically tangential and normal vectors to the epicardial and endocardial surfaces. From these vectors, we defined the tangential plane for each cell and constrained the vectors of the principal fibre direction to lie in these planes. By analogy with data for the canine heart (NIELSEN et al., 1991) (using the LV epicardial apex, the LV endocardial apex, the RV endocardial apex, the LV anterior papillary muscle, the pulmonary outflow tract and the anterior and posterior ventricular sulci as anatomical landmarks), we assigned the fibre angle in each tangential plane as a function of the distance from the epicardium to the endocardium. The fibre direction rotated counterclockwise and linearly in the compacta, then abruptly changed at the border between the compacta and trabeculata and was oriented predominantly in the apico-basal direction in the trabeculata (NIELSENe t al., 1991). Finally, we also included a rudimentary conduction system by constructing a cable-like network that connected the known sites of early activation (DURRErt et a t , 1970; VAN DAM, 1976) on the surfaces of the LV and RV endocardium. Propagation of electrical excitation in the model of anisotropic ventricular myocardium was based on the previously published algorithm (LEONand HORACEK,1991; NENONEN et al., 1991a). Both the previous and present versions of the model simulate the electrotonic interactions of cells by solving a non-linear parabolic partial differential equation derived from the bidomain model, but the model's behaviour is ruled by a cellular automaton when the transmembrane potential Vm exceeds the threshold value (LEON and HORAOEK, 1991; NENONEN et al., 1991a; I-'IREN, 1996). Each cell has a principal direction a~ and its own action-potential function. The chosen conductivity values characterising the anisotropic myocardium were a t = 2.75 mS c m - t along the fibres and O"t = 0.321 mScm -1 across the fibres. Table 1 gives details of simulated tissue parameters. The infinite medium electric potential at each torso node point and the infinite medium magnetic field at each point of the extracorporal measurement grid were calculated using the oblique dipole model of cardiac sources (LEONand HORACEK, 1991; NENONEN et al., 1991b; HREN, 1996): 47zal 1 { at~i Vv ~ 9 VR~I A V

(a~ --

+

(Gt --

O.t)E(Vv/. i

i i3 9VRi-IAV / a3)a

(1)

J

~o

2 Methods The construction of our ventricular model (HREN et al., 1995a, b; HREN, 1996; HREN and HOR~EK, 1997) is presented in detail in Appendix 1. Briefly, sections sliced through a human heart at 1 mm intervals were first accurately digitised to include papillary muscle and trabeculae (RITSEMA VAN ECK, 1972; EIFLER et al., 1981). Next, the ventricular myocardium was subdivided into two distinct anatomical regions: compacta and trabeculata (STREETER, 1979). The geometries of the relatively smooth surfaces that enclose the compacta were reconstructed by a globally parameterised model based on a surface harmonic expansion method (HREN and STROrNK, 1995).The shapes of more complex trabecular surfaces were reconstructed using bilinear interpolation. The space between surfaces was then filled with a cubic lattice of discrete points separated by d = 0.5 mm.The resulting solid structure represented the geometry of ventricular myocardium with nearly 1.7x106 cells (each of which has a volume AV = 0.125 mm3). 146

i

a3)a 3 -RF'IAV

(2) J

where a 1 is the conductivity o f the homogeneous monodomain, and R i is the distance from the source point (activated cell i) to a field point. The summation in Eqns. 1 and 2 was Table 1 Simulated tissue parameters

Spatial step d Time step ~t Resting potential vr Threshold potential vth Peak potential vp Membrane capacitance C,, Surface-to-volume ratio Z Transverse conductivity a t Longitudinal conductivity a t

Medical & Biological Engineering & Computing

0.5 mm 0.1 ms - 84 mV - 60 mV + 20 mV 1 laF cm -2 225 cm- t 0.321 mS cm-l 2.75 mS cm- J March 1998

performed over the entire region containing all cardiac sourccs.

To account for the influence of the torso's outer boundary and of its internal interfaces between regions of different conductivity on extracardiac electric potentials and magnetic field, we used a boundary element method (BEM) applied to three torso models. The model of the human ventricular myocardium was positioned in each torso model so best to best fit the heart's anatomical location documented by radiographic images. Our standard model of the male torso (shown in Fig. 1) (HORAI2EK,1974) uses 700 triangles (defined by 352 nodes) to represent the outer boundary, and 326 triangles (defined by 167 nodes) to represent the lungs. We also used individualised male and female torso models (HREN and STROn~K, 1995) to account for variations in the volume conductor's properties. The outer boundary of the male torso model was approximated by 782 triangles (defined by 393 nodes), and the outer boundary of the female torso model had 762 triangles (defined by 383 nodes). The male and female torso models included lung boundaries tessellated with 456 triangles (defined by 232 nodes) and 432 triangles (defined by 220 nodes), respectively. The conductivities assigned to torso tissues and the lungs were 2.0 mS c m - l and 0.5 mS c m - ~ in all three models. The discretisation of fundamental integral equations for electric potential (GESELOWITZ, 1967) and the component of the magnetic field normal to the chest (GESELOWITZ, 1970) was performed in a manner that produced a node-to-node relationship among variables (HRENe t al., 1995c; SCHLITT et al., 1995; HREN et al., 1996) r = r

(3)

+ M~,

B. = B~,. + A ~

(4)

where ~ , B, and q ~ , B~., are vectors of the discretised potential and discretised normal component of the magnetic field associated with torso surfaces and infinite medium, respectively. The elements of matrices M and A are geometrical integrands that were calculated using analytical expressions (DEMUNCK, 1992; FERGUSON et al., 1994). Eqn. 3 was solved using the non-iterative fast forward method (PURCELL and STROINK, 1991). We simulated sets of BSPMs and MFMs for 35 pre-excitation sites positioned along the AV ring (Fig. 2). The average distance between the adjacent pre-excitation sites was 0.66 4-0.10cm. For each activation sequence, we calculated BSPMs (at 117 lead sites on the anterior and posterior torso)

a Fig. 1

and MFMs (at 64 lead sites near the anterior torso) at 4ms increments within the first 40ms after the onset of preexcitation.) BSPMs were displayed as isopotential lines on a flattened torso and MFMs were displayed as isofield lines in the plane 2 cm above the anterior chest (Figs. 3 and 4). For comparison, we also calculated 68-lead BSPMs that covered the same area as the 64-lead anterior MFMs, and 128-lead MFMs where the same 64-lead measuring grid (Fig. lb) was positioned near both the anterior and posterior torso. Using the simulated maps, we developed the protocol for quantitatively assessing changes in patterns of BSPMs and MFMs as a function of distance between the pre-excitation sites. We expressed these changes in terms of the correlation coefficient r, defined as the normalised dot product between pairs of n = 68 and n = 117 values for BSPMs and n = 64 and n = 128 values for MFMs: n

Ex~Y; i= 1

i=1

We performed a total of 2450 correlations between BSPMs and MFMs for a given pre-excitation site X~ and the maps for all the 35 sites along the AV ring Yi obtained at the same time step. The resulting 35 correlation coefficients for a given map belonging to a given site and time step were displayed by plotting the correlation coefficients as a function of their position along the AV ring. Such plots are shown in Fig. 5. Finally, we determined the correlation threshold that identified morphological features of maps as 'similar' when their correlation coefficient was above 0.95. The location of the threshold points (at a distance s I and s z from the given preexcitation site) is indicated by black dots in Fig. 5. We used the half-distance between these threshold points, i.e. (s t + s2)/2, as a measure of the spatial resolution of BSPMs and MFMs for the given pre-excitation site.

3 Results Figs. 3 and 4 show the l17-1ead BSPMs and 64-lead anterior MFMs calculated at 28 ms after the onset of activation for 18 pre-excitation sites. Table 2 contains a summary of these pre-excitation sites. In BSPMs, the potential maximum is relatively stationary and is positioned on the left anterior torso for all pre-excitation sites. For the initial site of ventricular activation being chosen

b

The anterior and posterior views of standard torso model with 117 lead positions displayed. Lungs and epicardial surface are also shown. Outer boundary of torso was tessellated with 700 triangles (352 nodes), and lungs were tessellated with 326 triangles (defined by 167 nodes). Anterior view of standard torso model with epicardiat surface. Magnetic field component normal to chest was simulated at 64 points on an 8 x 8 grid with 4 cm spacing and situated 2 cm in front of anterior chest

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147

Fig. 2

Basal view o f atrioventricular ring shown with 35 pre-excitation sites. Top 21 layers o f human ventricular model are shown; they are 1 mm apart, and each is represented by smoothed contour lines to achieve better rendering o f the shape. Average distance between adjacent pre-excitation sites is O.66 + O. 10 cm; farthest apart are pre-excitation sites 4 and 5 (0. 88 cm); nearest are sites 24 and 25 (0.50 cm). R V = right ventricle; L V = left ventricle; PA = pulmonary artery

at pre-excitation sites 1-35, the body-surface minimum migrates along the projection of the AV ring on the human torso (SPACH et al., 1978; IWA and MAGARA, 198l; KAMAKURA et al., 1986; GROGrN et al., 1992; NADEAUet al., 1993) from the upper sternal region to the lower right anterior chest (for sites 1-15) and from the lower right anterior chest (for 17 and 19) through the lower right posterior chest (for 21), cranially along the spine (for 23-33) and back to the upper sternal region. The simulated BSPMs were compared visually with the maps recorded in patients suffering from WPW syndrome by (BENSON et al. (1982), DE AMBROGGIet al. (1976), GIORGI et Table 2

(1991), IWA and MAGARA (1981), KAMAKURA et al. (1986), YAMADA et al. (1975), LIEBMAN et al. (1991), GROGIN et al. (1992) and NADEAU et al. (1986) (see Table 2). In general, the simulated dipolar patterns with the characteristic position of the extrema and the configuration of the region of near-zero values corresponded well to those measured for the same pre-excitation sites. A discrepancy between the simulated and measured data was found for the left posterior paraseptal pre-excitation site (site 17), where the potential minimum appears on the right posterior torso in the measured BSPMs, but on the right anterior torso in the simulated BSPMs; the configuration of the region of nearal.

Pre-excitation sites around A V ring

Number

Abbreviation

Anatomical description

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

RAP RAL RAL RL RPL RP RP RPP LPP LP LP LPL LPL LL LAL LAL LAP LAP

right anterior paraseptal fight anterolateral right anterolateral fight lateral right posterolateral fight posterior right posterior right posterior paraseptal left posterior paraseptal left posterior left posterior left posterolateral left posterolateral left lateral left anterolateral left anterolateral left anterior paraseptal left anterior paraseptal

Published BSPMs

Published MFMs

1-3 10, 11 2-5 1, 3, 5, 6 2-5, 7 1, 3, 6 2, 5, 6 1, 4, 5 5 3, 4, 6, 7 1 2, 3, 5, 6 1-4, 6, 8 3, 6, 9 3, 6 1, 3, 5, 6 7

12, 13 10 I0, 13 10, 12, 13 10, 11, 14 10 10-15

10, 15

1: IWA and MAGARA(1981); 2: LIEBMANet al. (1991); 3: NADEAUet al. (1986); 4: BENSONet al. (1982); 5: GROGINet al. (1992); 6: GIORGIet al. (1991); 7. DE AMBROGGIet al. (1976); 8: YAMADAet al. (1986); 9: KAMAKURAet al. (1986); 10: LAMOTHEet al. (1995); 11: NENONENet al. (1993); 12: NENONENet al. (199tc); 13: FENICIet al. (1990); 14: MAKiJ~.RVlet al. (1992); 15: NENONENet al. (1991d) 148

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Fig. 3 BSPMs calculated at 28 ms after onset of activation sequence initiated at 18 pre-excitation sites. Number of given pre-excitation site is shown above each map and corresponds with site numbering of Fig. 1. Top border of each map represents neck and shoulders, and lower border represents waist; anterior chest is depicted on left half of map, with left midaxillary line at centre of map. Precordial leads Vt-V 6 are shown as black squares. Extrema are denoted in #V, and isopotential lines are plotted in logarithmic increments

zero potentials was, however, similar in the simulated and measured BSPMs (GROGrN et al., 1992). In MFMs, the morphological features are rotated by about 90 ~ relative to those found in BSPMs on the anterior torso. The region of near-zero values of MFMs and the axis joining the extrema in corresponding BSPMs have approximately the same direction. However, MFMs for the left lateral preexcitation sites (sites 25-31 in Fig. 4) depart from this characterisation. These MFMs feature low-amplitude extrema, as the primary sources (and the corresponding electrocardiographic axis joining the extrema in BSPMs) point predominantly from the posterior to the anterior torso, i.e., perpendicularly to the MFM measuring plane. It is well known (STROINK et al., 1995; HREN et al., 1996) that the patterns of such primary sources are sensitive to alteration in the volume conductor properties. We found indeed that the MFMs for these sites were affected when lungs were excluded from the torso model. The simulated MFMs were more difficult to compare with their measured counterparts (FENICI et al., 1990; NEONEN et al., 1991c, d; 1993; MAKIJARVI et al., 1992; I.AMOTHE et al., 1995) than BSPMs, because the measured data were not consistent for at least a few pre-excitation sites: e.g. MFMs Medical & Biological Engineering & Computing

March 1998

for the left lateral pre-excitation sites of NENONEN et al. (1991c, d) and of the same group in (MAKIJARVI et al. (1992) and NENONEN et al. (1993); or MFMs for the right anterior paraseptal pre-excitation sites of LAMOTHE et al. (1995) and of NENONEN et al. (1993); or MFMs for .the left posteroparaseptal pre-excitation sites of NENONEN et ~l. (1991d) and of FENIC[ et al. (1990). The agreement was good for the fight anteroseptal, right lateral, left posteroparaseptal, left posterior, and left postero lateral pre-excitation sites. Complete disagreement between the simulated and some measured MFMs (MAKIJ.~R.VI et aL, 1992; NENONEN et al., 1993) (with reversed polarity of MFMs) was found for the left lateral pre-excitation sites. Figs. 5a and b show correlation diagrams for the 117-lead BSPMs and 64-1ead anterior MFMs calculated at 28 ms after the onset of activation for 18 pre-excitation sites. As expected, correlation diagrams reveal pattern similarity between the maps corresponding to adjacent pre-excitation sites. However, a marked pattern similarity was found between some MFMs (e.g. sites 15, 19, 21 and 23 in Fig. 5b) corresponding to distant sites. This phenomenon was also observed in some BSPMs (e.g., sites 13, 15 and 21 in Fig. 5a), but the correlation coefficients for BSPMs (in contrast to MFMs) corres149

ponding to these remote regions were lower than the correlation threshold and therefore did not affect the spatial resolution. In their clinical studies, SIPPENSGROENEWEGENet al. (1990; 1992) used a correlation threshold o f 0.95 to define distinct morphological features among maps corresponding to different locations of pacing sites. This threshold value is supported by the modelling study in Appendix 2, which indicates that variations in BSPMs and MFMs due to the measuring noise and individualised torso boundaries have on average correlation coeffi'cients higher than 0.95. Table 3 shows the spatial resolution defined as a half-span between the threshold points for each time step averaged over 35 pre-excitation sites. Thus, at 28ms after the onset of activation, pre-excitation sites 0.83 4-0.32cm apart could be distinguished in BSPMs, whereas, in MFMs, the spatial resolution was within 1.54 4- 0.84 cm. In some BSPMs (sites 31 and 33 in Fig. 5a), pre-excitation sites as far apart as 1.53 cm were similar; in some MFMs (site 15 in Fig. 5b), no distinct changes could be observed within up to 3.76 cm. BSPMs performed better than MFMs even when only 68 leads on the anterior torso were included, resulting in the average spatial resolution, at 28 ms after the onset of preexcitation, of 0.89 4-0.39 cm. Conversely, the spatial resolution of MFMs was markedly improved when 64 additional leads near the posterior torso were included in simulations. Fig. 6 shows posterior MFMs calculated at 28ms after the onset of pre-excitation for sites 19-35. Comparison with Fig. 4 reveals that patterns of MFMs near the posterior torso can provide additional information for locating sites 23-3 l. Fig. 7 shows correlation diagrams for 18 pre-excitation sites when 128-lead MFMs are used near both the anterior and posterior torso; the average spatial resolution at 28 ms after the onset o f pre-excitation was 1.15 4-0.43 cm, and sites separated by up to 2.36 cm could not be distinguished. Between 20 and 32 ms after the onset o f pre-excitation, the spatial resolution was, on average, 0.88 4- 0.41 cm, 1.56 4- 0.83 cm and 1.17 4- 0.48 cm for the 117-1ead BSPMs, 64-lead anterior MFMs and 128-lead MFMs, respectively. Table 4 shows results o f a Student's t-test applied to calculate significance levels for differences between the 117lead BSPMs and the 64-lead anterior MFMs and 128-lead MFMs, respectively. (We considered differences significant for levels p < 0.05.) During the early phases of the preexcitation sequence (< 20ms), the differences between the l l7-1ead BSPMs and 128-lead MFMs were not significant.

Fig. 4 MFMs calculated at 28 ms after onset of activation sequence initiated at 18 pre-excitation sites. Number of given preexcitation site is shown above each map and corresponds with site numbering of Fig. 1. Magnetic field component normal to chest was simulated at 64points on an 8 x 8 grid with 4 cm spacing and situated 2 cm in front of anterior chest. Extrema are denoted in pT, and isofield lines are plotted for equal intervals, with solid lines representing magnetic fieldfrom anterior to posterior torso

Table 3 Average spatial resolution 4- SD (cm) for correlation threshold 0.95, as function of time after onset of activation

Standard male torso t, ms

BSPM

BSPM*

MFM

MFM]"

4 8 12 16 20 24

1.04 4- 0.75 1.104-0.73 1.154-0.73 1.104-0.66 0.98 4- 0.55 0.86 4- 0.42

1.2 4- 0.9 1.44- 1.0 1.34-0.9 1.204-0.81 1.08 4- 0.67 1.14 4- 0.62

1.20 4- 0.70 1.604-0.84 1.384-0.61 1.534-0.71 1.58 4- 0.80 1.56 4- 0.84

0.98 + 0.35 1.154-0.48 1.104-0.38 1.154-0.40 1.17 4- 0.50 1.16 4- 0.45

28

0.83 4- 0.32

0.894- 0.39

1.54 4- 0.84

1.15 4- 0.43

32 36 40

0.86 4- 0.28 0.88 4- 0.24 0.924- 0.20

0.91 4- 0.33 0.96 4- 0.30 0.974- 0.25

1.55 4- 0.87 1.7 4- 1.0 2.1 4- 1.2

h 18 4- 0.50 1.22 + 0.43 1.394- 0.59

* Only 68 leads on the anterior torso were used t leads near both the anterior and posterior torso were used

150

Medical & Biological Engineering & Computing

March 1998

BSPM

MFM

1 (o.s2)

13 (0.651

(o..~)

3 (0.82)

15 10.361

5 (0.71)

1 (1.101

13 (1-311

25 (0.74)

27 (1.04)

3 IO.331

1513.761

2710.711

17 (0.85)

29 (e.5~

5 11.011

17 11.351

29 11.171

7 (0.86)

19 (0.56)

31 (1.52)

7 11.15)

19 (2.821

3111.311

9 10.511

21 10.751

33 11.531

9 10.851

11 10.551

23 10,811

35 (0.44)

11 11.041

21

/1

Y\

21 12.33)

33 11.161

23 (2.841

35 (12.21

(2.93)

1.00 0.95

~1( I

.~

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0.75

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0.50

1

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,

i

i

15

20

....

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pre-excitation site C

Fig. 5

Correlation diagrams ealculated for (a) 117-1ead BSPMs and (b) 64-lead anterior MFMs at 28 ms after onset of activation sequence initiated at 18 pre-excitation sites. (c) Details of layout." (.) location of threshold points along A V ring of epicardium; number of given pre-excitation site is shown above each map, with corresponding spatial resolution shown in brackets

Later in the pre-excitation sequence, the differences in the spatial resolution of the 117-1ead BSPMs and 64-lead anterior MFMs and 128-lead MFMs, respectively, were significant. The spatial resolution of the 64-lead anterior MFMs (and, to a lesser degree, that of the 128-lead MFMs) was, for the given pre-excitation site, markedly dependent on the specific segment of the AV ring (Fig. 5b). For the posteroseptal and left posterior pre-excitation sites (sites 15-24 for the 64-lead anterior MFMs and sites 15-21 for the 128-lead MFMs), patterns within 2.7 4-0.6 cm for the 64-lead anterior MFMs and within 1.8 4- 0.3 cm for the 128-lead MFMs were similar. On the other hand, the left lateral (sites 25-27) and left anterior (sites 31-33) pre-excitation sites 1.0 4- 0.2 cm (0.9 4- 0.2 cm for the 128-lead MFMs) apart, could be distinguished better by MFMs than by BSPMs. The spatial resolution of 117-lead BSPMs was relatively uniform along the AV ring (Fig. 5a) and showed a marked departure from the average value only in the left anterolateral segment (sites 30-34 with the average spatial resolution of 1.4 4- 0.2 cm). M e d i c a l & Biological Engineering & C o m p u t i n g

M a r c h 1998

The choice of the correlation threshold did not qualitatively affect the comparison between the 117-lead BSPMs and 64lead anterior MFMs. Fig. 8 shows the spatial resolution averaged over 35 pre-excitation sites as a function of the correlation threshold. For all correlation thresholds, the average spatial resolution of 117-lead BSPMs was less than that of 64-1ead MFMs. Standard deviations of average spatial resolutions were larger for 64-lead MFMs than for 117-1ead BSPMs which again indicates that the spatial resolution of 64-lead MFMs varied more than that of 117-lead BSPMs with respect to the specific segment of the AV ring. The individual differences in the size and shape of the torso and position of the heart also had a relatively small effect on the spatial resolution. Table 5 presents the spatial resolution of 117-1ead BSPMs and 64-lead anterior MFMs for each time step averaged over 35 pre-excitation sites when individualised male and female torso models were used in simulating activation sequences. Results show the same trend as those in Table 3. 151

19

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correlation threshold

Fig. 8 Spatial resolution as a function of correlation threshold (--) Fig. 6

MFMs near posterior torso calculated at 28 ms after onset of activation sequence initiated at nine pre-excitation sites (sites 19-35). The number of given pre-excitation site is shown above each map and corresponds with site numbering of Fig. 1. MFMs for sites 1-17 are not displayed as the extrema were too small. Magnetic field component normal to chest was simulated at 64 points on an 8 x 8 grid with 4cm spacing and situated 2 cm from the posterior chest. Posterior MFMs are displayed as viewed from anterior torso to make comparison with MFMs in Fig. 4 easier (see Fig. 4for other details of layou 0

t, ms

BSPM-MFM

BSPM-MFM*

0.359 0.033! 0.157 0.002! 5 x 10-4! 6 • 10-5! 3 x 10-5! 6 • 10-5! 4 x 10-5! 2 • 10-6! 7 x 10-5!

0.670 0.787 0.721 0.301 0.135 0.005! 8 x 10-4] 2 • 10-3! 2 • 10-4[ 6 x 10-5! 8 x 10-3[

1 0.72)

13 (1.111

25 0.77)

3 (0.63)

15 {2.18)

27 0.59)

s (t.os)

17 0.42)

29 (o.g7)

* 128 leads near both anterior and posterior torso were used; p-values marked for those cases where the difference between two modalities was significant (p < 0.05)

7 11.031

19 (2.361

31 11.07)

9 10.97)

21 11.261

33 (1.051

/l Yli\ / 23 (0.86)

35 (1.03)

Correlation diagrams calculated for 128-lead MFMs at 28 ms after onset of an activation sequence initiated at 18 preexcitation sites. Two 64-lead measurement grids were positioned above both anterior and posterior chest (for details of layout, see Fig. 5)

4 Discussion This study suggested that marked morphological changes in BSPMs occured even for pre-excitation sites separated by distances o f less than 1 cm. The exception was the left anterolateral segment of the AV ring (sites 30-34), where BSPMs were, on average, indistinguishable within 1.4cm. Mean dimensions o f the focal lesion of RF ablative procedure were reported to be 0.7 4- 0.3 cm long, 0.5 4- 0.2 cm wide and 0.4 4- 0.2cm deep (HUANG et al., 1988). The sub-centimetre

152

Table 4 Significant levels (p-values)for differences between 117lead BSPMs and 64-lead MFMs (BSPM-MFM) and 128-1cad MFMs (BSPM-MFM*), as a function of time after onset of activation

4 8 12 16 20 24 28 32 36 40 20-32

11 (1.10)

Fig. 7

for BSPMs and (---) MFMs at 28ms after onset of activation. Spatial resolutions were averaged over 35 pre-excitation sites; standard deviations are shown with vertical bars

spatial resolution o f BSPMs thus appears to be adequate for differentiating between the accessory pathways located along the AV ring. Our results suggest that morphological features of 128-lead MFMs are, on average, also useful in providing a precise guidance to ablative treatment, with the possible exception of the left posterior (sites 19-21) and posteroseptal (sites 15-17) pre-excitation sites. In general, our simulated BSPM patterns, with the characteristic position o f the extrema and the near-zero potential configuration for nearly all pre-excitation sites corresponded well with the measured ones. However, a discrepancy between the simulated and measured data was found for site 17, where GROGIN et al. reported maps with the potential minimum on the right posterior torso (GROGIN et al., 1992). In our simulations, the minimum was located on the right anterior torso, possibly because of a discrepancy in the position o f the heart between the model and the actual patients, or because the clinical left posterior paraseptal pre-excitation site is located more anteriorly (toward the septum) than in simulations presented here. In our recent study on BSPMs generated by the various septal pre-excitation sites (HREN et al., 1997), we positioned the left posterior paraseptal pre-excitation site approximately

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Table 5 Effect of individualised torso boundaries on average spatial resolution • SD (cm) for correlation threshold O.95, as a function of time after onset of activation

Male torso

Female torso

t, ms

BSPM

MFM

4 8 12 16 20 24

0.99• 1.13i0.72 1.20• 1.14• 1.01• 1.04•

2.2• 2.0• 2.0• 2.1• 2.1• 2.1•

0.84• 1.03• 1.03• 1.01• 0.96• 0.90•

1.9• 1.9• 2.2• 2.0• 1.9• 1.75•

28

0.92•

2.3•

0.85•

1.84•

32 36 40

0.94• 1.01• 1.04~0.31

2.4il.3 2.7• 3.0•

0.87• 0.95• 0.98•

2.0• 2.5• 2.8•

0.5 cm more anteriorly than site 17 and obtained BSPMs with the minimum on the posterior torso, which, 28 ms after the onset of pre-excitation, progressively migrated toward the torso's right midaxillary line. BSPMs corresponding to a pre-excitation site located midway between the right posterior paraseptal and left posterior paraseptal site had the minimum on the right anterior torso. It appears that, in this particular segment of the AV ring, qualitative features of BSPMs are very sensitive to changing locations of pre-excitation sites. We compared the simulated and measured MFMs for only a few pre-excitation sites and although we found a good agreement, a comprehensive validation that includes the measurement of more pre-excitation sites should be carried out. Disagreement between the simulated and some measured MFMs for the left lateral pre-excitation sites may be due to the fact that these MFMs feature low-amplitude extrema and are therefore susceptible to measurement noise and variations in the volume conductor properties. We are aware that our study has some limitations. First, we simulated 'pure' pre-excitation sequences, without interference from atrial repolarisation or fusion with the normal ventricular activation, which may depart from the actual measurements. Secondly, we simulated pre-excitation via accessory pathways located along the epicardial side of the AV ring; in some patients, accessory pathways can be located closer to the endocardium. Thirdly, we assumed that we can define the given instant in the cardiac cycle within the millisecond range. Fourthly, we calculated the value of magnetic field at a point, rather than averaged over a coil. Finally, we did not investigate the spatial resolution for the septal preexcitation sites. Such extensions of this study could be readily undertaken with our model of the human ventricular myocardium. Other areas o f future work could include simulating preexcitation sequences arising from multiple accessory pathways or investigating possible effects o f different types of measurement noise. The simulation studies in this paper present a systematic investigation o f the spatial resolution of BSPMs and MFMs. We used a computer model of the human ventricular myocardium that features an anatomically accurate geometry, an intramural rotating anisotropy and a computational implementation o f the excitation process based on electrotonic interactions among cells. No modelling studies have yet incorporated such a detailed representation of the ventricular myocardium. The findings of this study suggest that under ideal measuring conditions and using available technology, it is possible, on average, to identify the pre-excitation site more precisely with the l l7-1ead BSPM patterns than with the 64-lead anterior MFM patterns. The spatial resolution o f MFMs can, however, be improved when magnetic field leads are also

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BSPM

MFM

included near the posterior torso. These conclusions are reached for classification of pre-excitation sites based on morphological features of BSPMs and MFMs. As shown in our earlier study (HREN et al., 1996), classification based on an inverse solution using a current dipole in a torso model does not show any particular advantage of BSPMs over MFMs. Both BSPM and MFM identification of accessory pathways before RF catheter ablation have already proven useful in the clinical setting. In our institution, fewer repeated discharges have been required to ablate the given pathway, which, in turn, decreases the extent of tissue damage. Secondly, the duration of the ablative procedure has been shortened, which reduces the risks associated with the procedure, including radiation exposure of both patient and operator. The BSPMs and MFMs displayed here (Figs. 3 and 4) in a systematic manner might provide additional assistance to the cardiologist in locating the site of the accessory pathway. Acknowledgments--We wish to thank Dr. Jukka Nenonen and Dr. Robert S. Macleod for their helpful suggestions. This study was supported by the Richard A. and Nora Eccles Harrison Fund for Cardiovascular Research, the Nora Eccles Treadwell Foundation and, in part, by the Heart and Stroke Foundation of Nova Scotia.

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Appendix 1 Construction o f ventricular model The basic premise of our approach was that the myocardium can be subdivided into two distinct anatomical regions: compacta and trabeculata (STREETER, 1979). The volume occupied by compacta is bounded by four relatively smooth principal surfaces: an epicardial surface separating the excitable ventricular myocardium from the surrounding volume conductor; a surface separating the compacta from trabeculata or intracavitary blood masses in the LV; a surface separating the compacta from trabeculata or intracavitary blood masses in the RV; and a basal plane oriented perpendicularly to the long axis of the ventricles at the level o f the mitral valve. Our reconstruction o f the human ventricu[ar architecture can be described in several steps that were organised in such a fashion that every subsequent step incorporated more detail into the model without affecting the results of the preceding steps. Owing to the absence of accurate measurements of local fibre orientation in human ventricular myocardium, we have adopted for our purposes the canine model of ventricular myocardium constructed by NIELSEN et al. (1991). The first step was accurately to define and reconstruct the principal surfaces in which the fibres were constrained to lie. The second step, which concluded the construction of the geometrical frame for the assignment of local fibre rotation, was to identify the tangential planes in the volume bounded by these surfaces. The third step was to assign the angle of fibre rotation 7 over the reconstructed principal ventricular surfaces in the model of the human ventricular myocardium, according to the corresponding angle c~ on the principal surfaces in the canine ventricular model (NIELSEN et al., 1991). The fou~h step was to define the angle ct as the function of depth (wall thickness) in consecutive layers between the principal surfaces. The final step was to add the trabeculata to the model. Each of these steps will be discussed in more detail. Step 1: assignment o f principal surfaces: After the geometry of the principal ventricular surfaces had been digitised with an adequate number of data points, the sets of surface harmonic expansion parameters were evaluated separately for each principal ventricular surface. Next, the reconstruction of the surfaces was performed on a regular Cartesian grid. The grid position of each volume element (voxel) was identified by three integer indices (i,j, k). In this representation, the 3D principal surfaces were considered as shells in the voxel representation; each voxel was allocated a byte in the memory storage and was assigned a flag to identify which principal surface it was on. The normals to the principal

155

surfaces were analytically calculated at the centre of each voxel, thereby locally defining the tangential plane to the surface. To save memory, the normal to this plane at each voxel was identified by the spherical angles ( and q and stored in a byte format, with the angle ( mapped into a byte as 0-127, and the angle r/mapped as -127-127.

surfaces could be described by the mathematically smooth analytical function :t =fjk(#, e), where e corresponds to the wall thickness. The parameter e was evaluated as follows. The endocardial voxel identified by the indices (i,j, k) represented the origin of a piecewise-linear path # that was defined along the vectors normal to the local tangential planes lying between the endocardial and epicardial voxels; the distance e between these two voxels and measured along the path /.t represented the local wall thickness. As the epicardium and endocardium are irregularly shaped, the distance e varied through the ventricles and was a function of the starting endocardial voxel determined by the grid co-ordinates i,j, k. The function f of transmural rotation can vary for different regions of the ventricles, if required.

Step 2: assignment of tangential planes for intramural voxels: First, to establish the solid structure that represents the ventricular myocardium, we had to identify the intramural voxels between principal surfaces by means of a raster-filling algorithm. We assigned the spherical angles ~ and q of each voxel on the principal surface to the myocardial voxels intersected by the local normal to that surface. The drawback of this relatively simple approach was that the reconstructed epicardial and endocardial surfaces, although relatively smooth in general, change locally from a convex to a concave shape and vice versa. This can cause local variation in the principal surface shape to propagate into deeper layers of the myocardium, and the algorithm may not necessarily reconstruct the tangential planes within the myocardium realistically. Thus we calculated, specifically for this task, normals on the principal surfaces by using lower-order harmonics to attain globally smoother principal surfaces. Then we proceeded iteratively, with every subsequent iteration propagating deeper into the wall simultaneously from the endocardial and epicardial surfaces, along the normal direction derived from the progressively lower-order fit by the surface harmonic expansion to the principal surface. As the change in the normal direction specifying the given 'normal' path depended on the initial voxel of the given principal surface, all voxels processed along the given path were coded so that every myocardial voxel corresponded to only a single voxel on the principal surface. The algorithm described is analogous to a solution, known from graph theory (HADLOCK, 1977), to the problem of finding the shortest path between the given voxel on the endocardial surface and the epicardial surface.

Step 5: incorporation of trabeculata: As the bounding surfaces of the trabeculata on the interface with the intracavitary blood masses can have very complex shapes,we reconstructed these surfaces using the bilinear interpolation of data obtained by digitising anatomical sections. The tangential planes in the trabecular voxels were assigned by the algorithm propagating into the trabeculata along the directions determined by normals on the principal (LV endocardial, RV endocardial and RV septal) surfaces. The tangential planes thus defined may differ from the actual tangential planes of the voxels lining the RV and LV cavities. However, as the fibres in the trabeculata are oriented primarily in the apico-basal direction, the resulting imbrication angle should be small. The fibre rotation angle c~of the trabecular voxels of the LV cavity was assigned, as in step 3, by the axial matching of canine and human ventricular models. All trabecular voxels with the same axial co-ordinate were given the same value of ct. This matching of the canine and human ventricular models was an approximation, because the trabecular surface was much more detailed in the human than in the canine model. As the trabecular structures (e.g. the trabecula septomarginalis) were largely excluded from the reconstruction of the RV in the canine model, the fibre rotation angle ~ was assumed to be 90~ throughout the RV trabeculata.

Step 3: assignment of fibre direction on the principal surfaces: In this step, we mapped the distribution of the fibre angles c~ over the principal surfaces of the canine ventricular model (NIELSEN e t aL, 1991) onto the principal surfaces of our human model. To make such a transformation between the irregularly shaped surfaces tractable, we selected seven anatomical reference points: the LV epicardial apex, the LV endocardial apex, the RV epicardial apex, the LV anterior papillary muscle, the pulmonary outflow tract, the anterior ventricular sulcus, and the posterior ventricular sulcus. The transformation between the principal surfaces of the two ventricular models was approximated by successively scaling the canine model, first along the long axis of the ventricles and then in each of the short-axis slices. Scaling along the long axis was performed piecewise: the two ventricular models were subdivided into four vertical sectors by the first five of the anatomical landmarks listed above, and then the height, of each sector in the canine model was scaled to match the height of the corresponding sector of the human model. Scaling in the short-axis slices was carried out by matching the axial (angular) positions in the two models of the ventricular sulci relative to the geometric centre of each slice of the given principal surface.

Step 4: assignment of intramural fibre direction: Once the fibre orientation had been completely specified (by (, q and ~) in the voxels on the principal surfaces, the angle ~ could be assigned to intramural voxels. To accomplish that, we assumed that the transmural fiber rotation between the principal ventricular

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Appendix 2

Effect of measuring noise and volume conductor boundaries on BSPMs and MFMs Before we identified the correlation threshold for BSPMs and MFMs, we estimated how sensitive the forward solution that used primary sources generated by a model of the human ventricular myocardium was to the measuring noise and variations in the volume conductor's properties. This Appendix summarises the results of our investigations. Firs,t, we quantitatively assessed changes in BSPMs and MFMs due to the measuring noise. Using the standard torso model with lungs, we also performed simulations with added

Table 6 Average correlation coefficient (with range of values) between maps with and without measuring noise, as a function of time after onset of activation t, ms

BSPM

MFM

4 8 12 16 20 24 28

0.302 (0.008-0.641) 0.768 (0.507-0.929) 0.937 (0.784--0.984) 0.980 (0.924-0.995) 0.992 (0.967-0.997) 0.996 (0.978-0.998) 0.997 (0.991-0.999)

0.516 (0.015---0.940) 0.870 (0.440--0.996) 0.966 (0.775-0.999) 0.990 (0.940-1.000) 0.996 (0.969-1.000) 0.998 (0.985-1.000) 0.999 (0.990-1.000)

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Table 7 Average correlation coefficient (with range o f values) between maps obtained with standard torso and maps obtained with male and female torso models, as a function o f time after onset o f activation

Male torso t, ms 4 8 12 16 20 24 28 32 36 40

Female torso

BSPM 0.980 0.981 0.979 0.980 0.980 0.980 0.980 0.982 0.982 0.984

(0.971-0.997) (0.972-0.996) (0.951-0.997) (0.969-4).997) (0.975-0.997) (0.972-0.996) (0.972-0.996) (0.975-0.997) (0.975-0.997) (0.9764).996)

MFM 0.973 0.973 0.977 0.980 0.982 0.984 0.985 0.986 0.986 0.987

(0.887-0.995) (0.890-0.993) (0.903-0.994) (0.923-0.996) (0.9264).996) (0.937-0.995) (0.944-0.995) (0.943-0.996) (0.942-0.996) (0.935-0.997)

Gaussian noise. The standard deviation of the Gaussian noise was kept constant for all times following the onset and all preexcitation sites and was 10% of the average peak-to-peak value, taken over all 35 simulated BSPMs and MFMs at 20 ms after the onset of pre-excitation. For each pre-excitation site, we calculated 10 noisy BSPMs and MFMs, and each of these simulations was correlated with the reference distributions obtained via the standard torso model with lungs under nonoise conditions. Table 6 shows the average correlation coefficients (with range of values shown in brackets) over 35 pre-excitation sites for the first 24ms after the onset. Inspection of the results reveals that the measuring noise markedly affects the morphological patterns of BSPMs and MFMs only within the first 12ms after the onset of preexcitation. Secondly, we investigated the effect of individualised torso boundaries on BSPMs and MFMs. We used the individualised male and female torso models presented in Section 2. The BSPMs and MFMs obtained by the standard torso model with lungs were again taken as the reference distributions. Table 7 summarises the average correlation coefficients (with range of values shown in brackets) over 35 pre-excitation sites for each time step. A comparison with Table 6 reveals that, following the first 16 ms after the onset of pre-excitation, the effect of tailored boundaries in both the male and female torso models is much more pronounced than that of measuring noise. Although the effect of noise and individualised torso bound-

Medical & Biological Engineering & Computing

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BSPM 0.959 0.96l 0.959 0.961 0.961 0.961 0.962 0.964 0.965 0.967

(0.899-0.991) (0.922-0.988) (0.899~).987) (0.930-0.987) (0.936-0.987) (0.925-0.988) (0.924--0.988) (0.935-0.991) (0.941-0.988) (0.948-0.987)

MFM 0.968 0.969 0.973 0.977 0.980 0.983 0.984 0.984 0.984 0.984

(0.882-0.997) (0.8794).995) (0.901-0.995) (0.920-0.995) (0,916-0.996) (0.937-0.997) (0.940--0.997) (0.941-0.996) (0.9364).997) (0.925-0.997)

aries is, on average, less pronounced for MFMs than for BSPMs, the difference between the two modalities is not statistically significant (p _> 0.05). In conclusion, the results in Tables 6 and 7 indicate that the correlation threshold 0.95 is, on average, below variations in the correlation coefficient due to the measuring noise and differences in torso geometries and thus can be used as an appropriate choice for defining distinct morphological features of maps.

Author's biography Rok Hren was born in Ljubljana, Slovenia. He received a Dipl. Ing. degree in Physics from the University o f Ljubljana in 1991. In 1993 and 1996, he received an MSc degree in Physics and a PhD degree in Physiology and Biophysics from Dalhousie University. Between 1993 and 1996, he held an Izaak Walton Killam Memorial Scholarship. Currently, he is a Postdoctoral Fellow in the Nora Eccles Harrison Cardiovascular Research and Training Institute at the University of Utah. His research interests include forward and inverse modelling in electrocardiography and magnetocardiography.

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