CLAIRE ELIZABETH BOURGEOIS ANDREW E. POLLARD, CHAIR XUN AI SILVIO H. LITOVSKY JACK M. ROGERS A THESIS

Transcription

1 THE INFLUENCE OF MICROSCALE HETEROGENEITY OF THE COLLAGEN NETWORK OF HEALTHY RABBIT VENTRICULAR SUBEPICARDIUM ON ACTION POTENTIAL PROPAGATION AND INTERSTITIAL POTENTIAL DISTRIBUTIONS by CLAIRE ELIZABETH BOURGEOIS ANDREW E. POLLARD, CHAIR XUN AI SILVIO H. LITOVSKY JACK M. ROGERS A THESIS Submitted to the graduate faculty of The University of Alabama at Birmingham, in partial fulfillment of the requirements for the degree of Master of Science BIRMINGHAM, ALABAMA 2012

2 THE INFLUENCE OF MICROSCALE HETEROGENEITY OF THE COLLAGEN NETWORK OF HEALTHY RABBIT VENTRICULAR SUBEPICARDIUM ON ACTION POTENTIAL PROPAGATION AND INTERSTITIAL POTENTIAL DISTRIBUTIONS CLAIRE ELIZABETH BOURGEOIS BIOMEDICAL ENGINEERING ABSTRACT The goal of the present study was to identify the microstructural variability in myocyte orientation and in the arrangement of the collagen network to explore the interstitial compartment s contribution to discontinuous propagation. Microstructural data was obtained from healthy rabbit ventricular subepicardium through a sequence of image processing steps. Collagen quantity was measured in successive serial sections using established histological techniques. Binary 2D maps of collagen quantity were obtained from each section as a difference of images acquired under (i) brightfield illumination with a rhodamine filter and (ii) polarized illumination. Images were then registered by x- y translation and rotation to align a set of tissue markers in each section. A realistic 250 x 500 x 260 µm 3 3D collagen map was obtained as a stack of the aligned images. To obtain collagen quantities for completion of 3D bidomain simulations, collagen quantity was measured for each 22.7 x 22.7 x 25 µm 3 block (n=3146) composing the collagen map. This block size was advantageous as it provided an opportunity to examine conduction with a fine spatial resolution. The principal angle of collagen orientation was calculated and collagen quantity and orientation values were converted to microimpedances for completion of bidomain simulations. Simulations were completed using microimpedances calculated in three ways: (i) assuming homogeneous collagen ii

3 distribution, (ii) using histologically validated collagen quantity and constant orientation, (iii) using histologically validated collagen quantity and orientation values. Reconstruction of the collagen matrix revealed two primary collagen arrangements: longitudinal strands and punctate architecture. In computer simulations, maximum upstroke velocity significantly increased in punctate regions (paired t-test, p<0.05), while upstroke velocity was maintained in longitudinal regions. This indicates that collagen architecture modulates impulse propagation. Further, reconstructed bipolar surface electrograms with 50 µm spacing revealed increases in interstitial potential amplitude, both in simulations with impedance distributions derived from collagen quantity data alone and derived from collagen quantity and orientation data. This reveals that microstructural heterogeneity is reflected in surface potential recordings even on this small scale. iii

4 DEDICATION To my husband, Robert Wild; my mother, Ann Lane; my brother, Elliot Bourgeois; and the rest of my family. Thank you all for your endless support, constant encouragement, and unlimited love. iv

5 ACKNOWLEDGMENTS I would like to offer my sincerest gratitude to my advisor, Dr. Andrew Pollard, for such a wonderful opportunity. I would also like to thank Dr. Jack Rogers and Dr. Elliot Bourgeois for their tremendously helpful centroid function. I would like to acknowledge support from the University of Alabama at Birmingham s Ireland Tuition Scholarship. v

6 TABLE OF CONTENTS Page ABSTRACT... ii DEDICATION... iv ACKNOWLEDGMENTS...v LIST OF TABLES... vii LIST OF FIGURES... viii INTRODUCTION...1 Intracellular influence on propagation...1 Interstitial influence on propagation...2 Experimental challenges...4 THE INFLUENCE OF MICROSCALE HETEROGENEITY OF THE COLLAGEN NETWORK OF HEALTHY RABBIT VENTRICULAR SUBEPICARDIUM ON ACTION POTENTIAL PROPAGATION AND INTERSTITIAL POTENTIAL DISTRIBUTIONS SUMMARY...40 REFERENCES vi

7 LIST OF TABLES Table Page THE INFLUENCE OF MICROSCALE HETEROGENEITY OF THE COLLAGEN NETWORK OF HEALTHY RABBIT VENTRICULAR SUBEPICARDIUM ON ACTION POTENTIAL PROPAGATION AND INTERSTITIAL POTENTIAL DISTRIBUTIONS 1 Directional interstitial and intracellular microimpedances Activation sequence correlation coefficients vii

8 LIST OF FIGURES Figures Page THE INFLUENCE OF MICROSCALE HETEROGENEITY OF THE COLLAGEN NETWORK OF HEALTHY RABBIT VENTRICULAR SUBEPICARDIUM ON ACTION POTENTIAL PROPAGATION AND INTERSTITIAL POTENTIAL DISTRIBUTIONS 1 Image processing method Model elements Reconstructed collagen network Collagen network quantity and orientation data Maps of transmembrane potentials Transmembrane potential in select building block groups Bipolar surface electrogram arrangement and resulting traces viii

9 1 INTRODUCTION Intracellular influence on propagation. Cardiac myocytes account for the bulk of the volume of the myocardium (Gaudesius et al. 2003; Baudino et al. 2006) and are connected to the intracellular space of neighboring myocytes by channels called gap junctions. A single gap junction is formed when two adjacent cells each form a membrane-spanning connexon (one connexon is a hexamer of the protein connexin) and the two connexons abut each other. Gap junctions form primarily at the transverse edges of cardiac myocytes and allow ion flow that drives action potential propagation. The nonuniform arrangement of gap junctions accounts for much of the anisotropy in the intracellular space. In experiments with partial gap junction uncoupling by treatment of cardiomyocytes with palmitoleic acid, conduction velocity decreased by ~98% (Rohr et al. 1998). The relationship between gap junction availability and conduction failure in the heart is complex. Reductions in channel conductance, which lower conduction velocities, also diminish the electrotonic load imposed by downstream myocytes, which enhances membrane source charge generation. Spach et al. suggested these interactions were responsible for the elevated transmembrane potential (V m ) upstroke velocities observed during propagation across myocyte axes (slower velocity) in comparison with upstroke velocities observed during propagation along myocyte axes (faster velocity) in canine atrial preparations, as well as to the unidirectional conduction block that established anisotropic reentry in response to premature stimuli delivered to their preparations (1992). Similarly, in a fiber model with discrete myoplasmic and gap

10 2 junction components that were predominantly localized at the ends of model myocytes, Shaw and Rudy found that decreases in conduction velocity when gap junction conductance was modestly reduced resulted in an increased safety factor of conduction (1997). Their observations suggested microscopic discontinuities established slow but safe conduction because upstream maintenance of membrane source charge was preserved after sodium channel inactivation. This theoretical prediction is consistent with routine findings in electronically coupled cell pair experiments (Huelsing et al 2000, Huelsing et al 2003) where long delays (>5 ms) between two weakly coupled pipetteattached myocytes shift the emphasis for conduction maintenance from the fast sodium current to the transient outward potassium current and the L-type calcium current (Joyner et al, 1996 ). Such delays were also observed in V m dependent fluorescence recordings from synthetic strands cultured from germline Cx43+/- mouse ventricular myocytes (Beauchamp, 2004), with marked differences in upstroke velocities apparent at locations where source-load relationships were altered. A simulation of gap junctional remodeling in epicardial border zone myocytes (surviving myocytes found at the edge of an infarct) found that inclusion of the interstitial space resulted in smaller changes in conduction velocity when gap junction resistance increased (Cabo and Boyden 2009). These findings indicate the importance of considering both intracellular and interstitial spaces for more complete analysis of action potential propagation in the myocardium. Interstitial influence on propagation. The extracellular matrix that resides within the interstitial space has long been considered of vital importance to the mechanical function of the heart. Collagen, comprising 80% of the extracellular matrix, is the most prevalent protein (McClain, 1973). The extracellular matrix of cardiac tissue is organized

11 3 in discrete laminae with collagenous sheaths separating bundles of myocytes (Peters and Wit, 1998) and fiber orientation rotating transmurally (Vetter, 2005; Nielsen, 1991). A recent Pope et al (2008) study described perimysial collagen organization across the heart wall in rats. That study found that while much of the heart is divided by collagenous interlaminar clefts, perimysial collagen of the subepicardium is arranged in longitudinal strands aligned with myocytes. The extracellular matrix is a dynamic structure that responds to pathological stress with alterations in architecture. Cardiac fibroblasts, the most numerous cell type in the myocardium, play a vital role in maintaining the balance between extracellular matrix protein synthesis and degradation in both healthy and pathological states in the myocardium (Camelliti et al, 2005). Changes in extracellular matrix architecture are controlled in part by matrix metalloproteinases (MMPs), a class of proteins synthesized by fibroblasts that degrade collagen (Spinale, 2002). In pathological states, there is a distinct three stage response in which the structure of the extracellular matrix changes over a ~20 week period (Janicki, 2004). During the initial stage, MMPs are upregulated, leading to degradation of collagen strands (Janicki, 2004). In a compensatory stage, MMP activity is greatly reduced and collagen content returns to normal (Janicki, 2004). Finally, during a decompensatory phase, MMP activity increases and is accompanied by marked fibrosis (Janicki, 2004). This degradation and remodeling of structural proteins alters the mechanical function and is believed to alter action potential propagation as well. While the extracellular matrix of the heart is known to be an important part of the mechanical function of the heart, relatively few cardiac electrophysiology studies have considered the role of the extracellular matrix in conduction. Although the role of the

12 4 interstitial space in conduction has been explored in greater depth recently, that role is still not fully understood. In a one dimensional model in which cardiac myocyte geometry and gap junctional resistance were varied, increases in interstitial resistance improved conduction in poorly coupled tissue (Hubbard and Henriquez, 2009). Further, as indicated by Kawara et al., the distribution of that interstitial resistance is a determining factor in conduction maintenance. In a study of intact human hearts in end stage heart failure, fibrotic architecture influenced conduction delays more than collagen content alone (Kawara, 2001). As many pathological states in the heart cause increased collagen deposition (fibrosis) and changes in extracellular matrix structure that ultimately lead to cardiac arrhythmia, elucidating the effects of cardiac microstructure on electrical propagation will improve the understanding of the link between structure and arrhythmia development. Experimental challenges. The interstitial and intracellular contributions to electrical propagation can each be described in three unique orthogonal components. The resistances that contribute to these components on a subcellular scale, cardiac microimpedances, are crucial in understanding microstructural influences of cardiac tissue on conduction. Traditional electrode arrays are not suitable for detecting changes in action potential propagation caused by tissue heterogeneity because electrodes are spaced wider than the microstructural features of interest. Recording potential differences on a size scale where the intracellular and interstitial resistances can be experimentally determined requires the use of very small, finely spaced electrodes. Electrode size and spacing present their own difficulties. Low electrode impedance is desirable to improve the signal to noise ratio, but electrode impedance increases as

13 5 electrode surface area decreases. Consequently, electrode size must be chosen to both minimize noise and maximize spatial resolution. Fabricating an electrode array that satisfies these constraints is a major challenge in microscale impedance measurement. Recently, Pollard et al. (2008) fabricated microelectrode arrays with impedances much smaller than electrodes produced by others, but edge-to-edge spacing of the electrodes to guide accurate reconstruction of potential distributions still needs to be determined. Electrode spacing controls the sampling region size and allows sampling of potentials in the interstitial domain or the interstitial and intracellular domains in parallel (Le Guyader et al., 2001). The resistive and capacitive components of the membrane form a frequency dependent membrane impedance (Le Guyader et al., 2001). With an increase in electrode spacing or decrease in stimulation frequency, current is distributed between both the interstitial and intracellular spaces (Plonsey and Barr, 1982; Le Guyader et al., 2001; Pollard et al., 2008). When electrode spacing is sufficiently decreased or stimulation frequency is sufficiently increased, an increase in membrane capacitance shunts current to the interstitial space (Plonsey and Barr, 1982; Pollard and Barr, 2004; Le Guyader et al., 2001; Pollard et al., 2008).

14 6 THE INFLUENCE OF MICROSCALE HETEROGENEITY OF THE COLLAGEN NETWORK OF HEALTHY RABBIT VENTRICULAR SUBEPICARDIUM ON ACTION POTENTIAL PROPAGATION AND INTERSTITIAL POTENTIAL DISTRIBUTIONS by CLAIRE E. BOURGEOIS, ANDREW E. POLLARD In preparation for American Journal of Physiology- Heart and Circulatory Physiology Format adapted for thesis

15 7 Abstract The goal of the present study was to identify the microstructural variability in myocyte orientation and in the arrangement of the collagen network to explore the interstitial compartment s contribution to discontinuous propagation. Microstructural data was obtained from healthy rabbit ventricular subepicardium through a sequence of image processing steps. Collagen quantity was measured in successive serial sections using established histological techniques. Binary 2D maps of collagen quantity were obtained from each section as a difference of images acquired under (i) brightfield illumination with a rhodamine filter and (ii) polarized illumination. Images were then registered by x- y translation and rotation to align a set of tissue markers in each section. A realistic 250 x 500 x 260 µm 3 3D collagen map was obtained as a stack of the aligned images. To obtain collagen quantities for completion of 3D bidomain simulations, collagen quantity was measured for each 22.7 x 22.7 x 25 µm 3 block (n=3146) composing the collagen map. This block size was advantageous as it provided an opportunity to examine conduction with a fine spatial resolution. The principal angle of collagen orientation was calculated and collagen quantity and orientation values were converted to microimpedances for completion of bidomain simulations. Simulations were completed using microimpedances calculated in three ways: (i) assuming homogeneous collagen distribution, (ii) using histologically validated collagen quantity and constant orientation, (iii) using histologically validated collagen quantity and orientation values.

16 8 Reconstruction of the collagen matrix revealed two primary collagen arrangements: longitudinal strands and punctate architecture. In computer simulations, maximum upstroke velocity significantly increased in punctate regions (paired t-test, p<0.05), while upstroke velocity was maintained in longitudinal regions. This indicates that collagen architecture modulates impulse propagation. Further, reconstructed bipolar surface electrograms with 50 µm spacing revealed increases in interstitial potential amplitude, both in simulations with impedance distributions derived from collagen quantity data alone and derived from collagen quantity and orientation data. This reveals that microstructural heterogeneity is reflected in surface potential recordings even on this small scale.

17 9 Introduction Computational modeling of electrical activity in the heart has the potential to inform the next generation of antiarrhythmic therapies (Trayanova et al., 2006). While significant progress has been made toward this end, a critical knowledge gap exists in understanding how the microstructure of the heart modulates current flow through the organ. Many studies have focused on the role of gap junction heterogeneity and remodeling in disease to clarify the relationship between structure and propagation. Gap junctions are often expressed laterally in myocytes in disease states, and this has been implicated in slowed conduction. However, remodeling also occurs in the extracellular space of diseased hearts. The link between micro-scale structural alterations and conduction failure has not been fully explored. Conduction in the myocardium depends on the passive electrical properties of both the intracellular and interstitial spaces. Directional differences as well as local microstructural alterations have been proposed as mechanisms for discontinuous conduction that may promote conduction failure and arrhythmogenesis. Intracellular and interstitial compartments can be described using unique subcellular resistive components (microimpedances) in three orthogonal directions. The effects of variations in cardiac microstructure are poorly understood, specifically in the interstitial space. Because the downstream electrical load depends upon the electrical properties of both the intracellular and interstitial compartments, microimpedances likely modulate discontinuous conduction. Using perfused rabbit papillary muscles, Fleischauer et al. (1995) measured interstitial potentials with amplitudes approximately ½ those of action potential upstrokes and further documented the sensitivity of core-conductor impedances

18 10 to interventions that altered interstitial compartment size. Cabo and Boyden (2009) modeled canine epicardial border zone myocytes and demonstrated that inclusion of the interstitial space reduced sensitivity of conduction velocity to changes in gap junction conductance. Additionally, the geometry of the interstitial volume is believed to alter propagation. For example, Roberts et al (2008) used a multidomain model of an idealized cardiac fiber with nonuniform interstitial geometry, and showed that while conduction velocity was relatively insensitive to changes in interstitial geometry alone, narrowing of the interstitial space altered action potential morphology and interstitial potential. To extend earlier findings of Roberts et al., we considered the impact of variations in microimpedances resulting from heterogeneity of the interstitial compartment on microscopic conduction. Our focus therefore differs from that of traditional studies in that the macroscopic expansion and constriction of depolarization wavefronts are not considered in a detailed way. Simulations were performed in which microimpedance distributions were prescribed using detailed quantitative analyses of pixels from images of picrosirius red stained serial sections in which intracellular and interstitial tissue fractions were quantified. Those distributions were then refined to account for variation in collagen network orientation at different depths within the sampled volume. Collagen was observed in two primary arrangements: longitudinal strands and punctate structures. Our major finding is that maximum excitation upstroke velocity was increased in regions rich in punctate collagen. This suggests that regions of heterogeneous punctate collagen could serve as an arrhythmogenic source in poorly coupled tissue.

19 11 Methods Tissue Preparation. To obtain successive serial sections from rabbit subepicardium for histological measurements and assignment of microimpedance distributions, we completed one animal experiment. The animal protocol was approved by the Institutional Care and Use Committee at the University of Alabama at Birmingham. Following the approach documented in Wiley et al. (2005), a New Zealand white rabbit was anesthetized and the heart excised and perfused with hyperkalemic solution. To make fiducial marks in the tissue for image registration of histological sections, a customfabricated marking system was used to guide the parallel insertion of three syringe needles (30 gauge) into the epicardium. Two holes were aligned with the left anterior descending coronary artery because epicardial fibers typically emanate from that vessel. The heart was then perfused with 10% formalin solution, a tissue block containing the fiducials was excised and placed in a 10% formalin solution for 24 hours, and the block was placed in 80% ethyl alcohol for 2-4 days. The tissue was embedded in paraffin and sectioned (5 µm thick) in a plane parallel to the epicardium. Sections were treated with phosphomolybdic acid and stained with picrosirius red (PSR). PSR, an acidophilic stain routinely used in staining collagen, binds to collagen to produce red strands that are easily visible with brightfield illumination. Because collagen is birefringent, it may be viewed under polarized light to obtain an image with an enhanced collagen signal. Collagen Identification and Characterization. Each PSR-stained section (52 total) from the tissue block was imaged on an inverted microscope at 40x magnification (Nikon Eclipse TE2000-U) with a CCD camera (Roper Scientific Photometrics CoolSnap ES) and µmanager ( software. Collagen was quantified as

20 12 described by Whittaker et al (1991) using custom-written software in Matlab (ver. 2011b, The Mathworks, Natick, MA). A grayscale image was first collected from each section under brightfield illumination with a rhodamine filter. Figure 1A shows one such image in which the fiducials are evident in the upper left corner (i), the lower left corner (ii) and a separate location closer to the right edge (iii). The collagen pixels were much darker than the non-collagen pixels. Immediately after brightfield acquisition, the section was illuminated using polarized light. Figure 1B shows an image from the same field of view acquired with polarized light from section 1A. Collagen pixels were gold colored and much lighter than the non-collagen pixels. To enhance the collagen signal, the grayscale brightfield image was then subtracted from the grayscale polarized image, negative values were set to black, and positive values were set to white. This established a single black and white image with an amplified collagen signal. In this way, we were able to define each 2.84x2.84x5 µm 3 volume associated with a pixel as being either collagen or non-collagen. While an advantage to the use of PSR-stained sections was the straightforward identification of collagen and non-collagen pixels, transmural registration of serial sections required development of a procedure in which pixels from one image were carefully aligned with pixels from images in the sections above and below. That procedure is outlined in Figure 1C. Transmural alignment with the fiducial markers was achieved using an approach in which the centroid of fiducial i was positioned at the center of a large zero-filled matrix and the image was rotated by calculating the angle of rotation needed to align the centroids of fiducials i and ii with the vertical axis. Position and rotation for the section described in Figures 1A and 1B is shown in Figure 1C. As

21 13 seen, use of the zero-filled matrix insured individual images transformed in this way were not cropped. The large amount of unused space within each matrix had no impact on the overall measurement procedure, as we focused attention on a 500x250 µm 2 regions whose upper left corner was located 500 µm from the fiducial i centroid (black rectangle, Figure 1C). For this specific section, rotation to align fiducials i and ii was only 6. The end result of this procedure was that we identified collagen and non-collagen pixels from each section that could be stacked to assemble a sampled volume measuring 500x250x260 µm 3. Figure 1D shows the collagen (white) and non-collagen (black) pixels from the sampled region in Figure 1C. Consistent with all regions used to assemble the sampled volume, there was no evidence of tissue disruption associated with the preparation of serial sections, there were no large vessels that passed through the sampled volume, and separation from fiducials was sufficient to insure the displacement of myocytes and the collagen network associated with needle insertion did not influence the cellular architecture. Assembly of the sampled volume in this way allowed structural measurements based on local distributions of collagen and non-collagen pixels, as well as visual inspection to identify regions where collagen was arranged in longitudinal strands (L) as opposed to being primarily punctate (P). To determine collagen quantity, we grouped pixels into 8x8x4 building blocks (22.7x22.7x20 µm 3 ) as shown schematically in Figure 2A. Each pixel in this schematic was drawn white to represent non-collagen, which we presumed to be intracellular space. Grouping pixels in this way allowed a unique fraction of white pixels (f cq ) to be measured for each of the 3146 building blocks. To determine collagen orientation, we used the Fourier transform method developed by

22 14 Sander and Barocas (2009). Based on their approach, a discrete Fourier transform of the image resulting from the set of pixels that occupied the sampled volume from each serial section was taken and the magnitude spectrum was shifted to the zero frequency value. The resulting spatial orientation (γ c ) values were considered independently and also averaged through four serial sections to provide building block descriptions. For visual inspection to identify L and P regions of the sampled volume, building blocks were combined into 4x2x3 groups that measured 90.8x45.4x60 µm 3 and the collagen pixels from all blocks in each of the 100 groups were displayed. Figure 2B (left side) shows one such block group in which collagen pixels drawn in red clearly suggested an arrangement of collagen fibers with orientation on the long- or x-axis. For comparison, Figure 2B (right side) shows a different block group in which more sparse collagen was in punctate arrangements, with no clear demonstration of orientation on the long- or x-axis. Microimpedance assignment. Because the building blocks provided a sufficient number of pixels to quantify f cq variations throughout the sampled volume while also including subcellular dimensions, we derived microimpedances using f cq, γ c and literature-based values for specific intracellular and extracellular resistivities from the limited available reports. As shown in Figure 2C, each building block was assigned a set of intracellular (Rix, Riy, Riz) and interstitial (Rox, Roy, Roz) microimpedances, with the components themselves coupled to one another via membrane. Every component microimpedance was then derived from the general equation 1 1

23 15 where the subscript s denoted the compartment (intracellular or interstitial), subscript j denoted the direction (x, y, z), A was the cross-sectional area for the block in direction j, ρ was the specific resistivity associated with compartment s for direction j, and f s was the fraction of the building block occupied by intracellular (1- f cq ) or interstitial (f cq ) volume. The ρ term in Eqn. (1) was derived from γ γ 2 with set to 166 Ω-cm on the model s long axis for the intracellular compartment as identified by Kleber and Rieger (1987) in their perfused rabbit papillary muscle experiments, 63 Ω-cm on the model s long axis for the interstitial compartment as identified in that same report and set to 1560 Ω-cm on and 170 Ω-cm on the model s short axis for the intracellular and interstitial compartments, respectively, based on ratios from superfused calf trabeculae data identified by Clerc (1977). In Eqn. (2), γ c was the angle difference between the expected and measured orientation with the expectation being the model s long axis formed the lower resistance pathway for both compartments. Three microimpedance distributions were considered. As a reference case, we assumed a homogeneous f cq at 0.2, consistent with the value commonly prescribed in bidomain simulations that is based on the report of Polimeni et al. (1983). For the reference case, we further assumed no change in γ c with depth from the topmost surface of the sampled volume. This resulted in an (Rix, Riy, Riz) of 104 kω, 976 kω, and 758 kω, respectively, and (Rox, Roy, Roz) of 158 kω, 426 kω, and 330 kω, respectively, for each of 3146 building blocks. To assess the contribution of structural heterogeneity associated with variability in collagen quantity alone, we then prescribed (Rix, Riy, Riz) and (Rox, Roy,

24 16 Roz) assuming γ c =0 in Eqn (2). We referred to this case as the CQ distribution. Finally, we prescribed (Rix, Riy, Riz) and (Rox, Roy, Roz) using the f cq data with γ c values determined from the average of all four serial sections that served as sources for the sampled volume in each building block. We referred to this last case as the CQCO distribution. Active membrane simulations. To assess the likely impact of the structural heterogeneity associated with the collagen network on action potential propagation, we used the three microimpedance distributions to assemble coefficient matrices for active membrane simulations performed in Matlab following our previous report (Pollard and Barr, 2010). In these simulations, each building block was treated as a node in a finite difference model at which a transmembrane (V m ) and interstitial (ϕ o ) potential was determined through successive solutions of the sparse linear system 3 where [G] was a coefficient matrix that accounted for connections between building blocks via the microimpedances based on total membrane current (I m ) 4 and 5 with Eqns (4) and (5) balanced by capacitive charging (and discharging) and sarcolemmal current flow

25 17 6 In Eqn. (6), C m was the membrane capacitance (46.72 pf) and I ion included the fast sodium current (I Na ), the L-type calcium current (I Ca, L ), the inward rectifying potassium current (I K1 ) and the transient outward potassium current (I to ) from the Puglisi-Bers membrane equations for rabbit ventricular myocytes (2001). Analyses were limited to this set because action potential propagation throughout the small sampled volume was completed rapidly in our simulations. Therefore, interactions between nodes undergoing depolarization and phase two repolarization were never established, and we limited our focus to the upstroke and early phase one repolarization. In this form, was a vector of unknown potentials whose lower half contained V m values and whose upper half contained ϕ o values, and was a source vector whose lower half depended upon Eqn. (3) and whose upper half was set to zero. In simulations, V m was set to a resting potential of -87 mv, ϕ o was set to 0 mv and all integrated variables in the Puglisi-Bers membrane equations were set to steady-state values associated with V rest. Because [G] was assembled using the Matlab (Mathworks, Natick) sparse matrix function, solutions for at time t were readily achieved using the GMRES function that implemented a generalized minimum residual scheme. Solver tolerance was set to 1E-12. Time steps were fixed at ms. Integrated potential and PB membrane equation variables were then used to advance simulations over 5000 time steps such that 5 ms of action potential propagation were considered. Stimulation of a 3x3 cluster of nodes was achieved by adding current to the I ion term for a 1.0 ms duration 0.5 ms after the simulation s outset. Stimulus current was relatively low, as all simulations used 1.2 times diastolic threshold identified with the reference case.

26 18 Assembly of surface electrograms. Resulting ϕ o values were used to derive surface potential electrograms similar to those one would record experimentally using small, closely spaced electrodes. Potential difference electrograms were constructed from the difference of ϕ o at every other surface building block on the long and short edges opposite the stimulus site. This method yielded ten recordings derived the long edge and five from the short. Statistical comparisons of activation sequence parameters. To parameterize activation sequences in a systematic way, effects of microimpedance distributions on action potential propagation in each building block were measured by calculating Pearson correlation coefficients (Matlab, corr()) to compare the following parameters: V m, maximum and minimum ϕ o, maximum upstroke velocity (dv m /dt) max, time of (dv m /dt) max, action potential amplitude (APA), peak I Na, and I Ca, L. Small building block size yielded a large number of samples for (n=3146) for these statistical analyses. Statistical comparisons of block groups. To consider the impact of the changes in collagen structure at different positions within the sampled volume, the reconstructed collagen network was visually inspected as 100 block groups, with each group classified as either L or P. Ten block groups identified as L and P were selected for comparison of (dv m /dt) max. L and P block groups were compared using t-tests and ANOVA in Matlab. Statistical comparison of surface electrograms. Finally, we compared bipolar surface electrograms from simulations with different microimpedance distributions of the type one might anticipate recording experimentally. Differences in ϕ o amplitudes on short and long edges of were analyzed using Microsoft Excel (2010).

27 19 Results Structural heterogeneity in the collagen network. Systematic image processing of the PSR-stained sections allowed inspection of the collagen network at the pixel, building block, and block group levels, and also allowed the impact of the structural heterogeneity in the sampled volume on the CQ and CQCO microimpedance distributions to be quantified. Figure 3 shows pixels identified as collagen in the sampled volume (drawn in red) surrounded by 20 selected block groups from that volume that were extracted from different regions The overall rendering shows gaps in the collagen network that allowed identification of the general orientation of collagen fibers in the volume. Fibers in the uppermost section of the sampled volume were aligned with the long axis. Closer inspection of the block groups revealed regions in which the collagen fibers collected into longitudinal strands (marked L) with sparsely distributed lateral connections or punctate collagen (marked P) with more limited collagen oriented along the short axis of the sample volume. We selected 10 L and 10 P block groups as examples. Visual identification of all block groups suggested 60% L and 40% P. In this specific volume, we found no instances in which collagen fibers appeared to orient with depth along the z- axis, suggesting serial sections were successfully collected parallel to the epicardial surface and imbrication angle had little impact on the structural heterogeneity. These findings are generally consistent with Weber (1989), who reported the arrangement of collagen in parallel strands between myocytes with perimysial collagen sparsely forming lateral connections to prevent myocyte slippage. While visual inspection allowed segmentation of block groups into longitudinal and primarily punctate regions, analyses of f cq and γ c provided quantitative details we

28 20 used to characterize structural heterogeneity. Figure 4A shows a histogram of all 3146 building blocks grouped by f cq at 0.05 steps. Most building blocks in the sampled volume had a limited number of collagen pixels. No building blocks had an f cq greater than Most of the sampled volume was therefore non-collagen pixels, which we assumed to be intracellular space in our assignment of microimpedance distributions. In fact, only 5% of pixels in the sampled volume were defined as collagen pixels, which was consistent with our finding that only 7% of pixels in the total volume were defined as collagen pixels. These fractions are lower than that reported by Polimeni and commonly used in simulations with a bidomain representation of tissue structure. Collagen orientation varied modestly with depth in the sampled volume. Figure 4B shows γ c measured for individual serial sections (filled circles) and averaged for building blocks (open triangles) as functions of depth from the uppermost layer. Overall γ c change gradually from 0 to ~70 with depth, with approximately 1/3 of the central portion of the volume (80 to 180 µm) being oriented at 27. Use of the derived f cq and γ c values for assignment on microimpedance distributions led to marked differences in (Rox, Roy, Roz) and (Rix, Riy, Riz) between the reference case and the CQ and CQCO distributions. Table 1 shows mean ± SD for all directional microimpedances. Mean intracellular microimpedances were lower and mean interstitial microimpedances were higher in the CQ distribution than in the reference distribution in all directions because f cq values were consistently below the commonly used 0.2 value. With primarily non-collagen pixels in the sampled volume, most tissue was assumed to be intracellular. Limiting interstitial volume increased (Rox, Roy, Roz) as shown. Directional differences between Rix and Riy and between Rox and Roy were

29 21 more limited in the CQCO distribution than in the CQ distribution. This occurred because γ c changed with depth such that resistance increased in the x-direction and decreased in the y-direction over the depth of the volume. Perhaps most strikingly, the SD values tabulated for both the CQ and CQCO distributions ranged from 8% to 139% of the mean values, highlighting a large impact of the structural heterogeneity identified visually on the prescribed microimpedances. Simulated activation sequences. To assess the impact of incorporating the measured structural heterogeneity on the electrical activation sequence, we next compared parameters derived from V m and the associated sarcolemmal currents in the PB membrane equations using the CQ and CQCO microimpedance distributions to parameters derived from a simulation using the reference distribution. Figure 5 shows the spatial distribution of V m throughout the sampled volume 2.1 ms after the onset of a stimulus applied in the upper left corner of that volume with reference (top), CQ (middle), and CQCO (bottom) microimpedance distributions prescribed to building blocks. Despite the large differences in prescribed microimpedances, general activation sequence characteristics were highly similar. Tissue oriented on the volume s long axis activated more rapidly than tissue oriented on the short axis or in the transmural direction, consistent with the resistive anisotropy (Rix<Riy, Riz; Rox< Roy, Roz) suggested by the structural arrangement of collagen fibers. Modest differences between sequences with the CQCO and reference distributions were evident in the portion of the sampled volume where γ c changed with depth from the uppermost layer (filled arrow) although no major differences between sequences with the CQ and reference distributions were found. Systematic comparison of derived parameters from each of the 3146

30 22 building blocks further supported a limited influence of the microimpedance distributions on overall activation sequence, as Pearson correlation coefficients shown in Table 2 were generally above 0.9 with most values being close to 1.0. Only the maximum interstitial potential and the action potential amplitudes using the CQCO microimpedance distribution had Pearson correlation coefficients below 0.9, consistent with the modest differences from the reference case highlighted in the V m distributions shown in Figure 5. While these overall characteristics were highly similar, we did find differences between L and P block regions that were more pronounced. Figure 6A shows V m from simulations using all three microimpedance distributions at the central building blocks from each of the 10 L blocks. V m traces are labeled i-x to correspond with block regions highlighted in Figure 3. For each V m trace, we identified (dv m /dt) max and included those values alongside the records themselves. Differences in this parameter with position highlighted the impact of location relative to the stimulus as the variability at different sites was more pronounced than the variability at any one site. For example, (dv m /dt) max ranged from 158 to 163 V/s at site ii and from 255 to 287 V/s at site ix. Paired t-tests between the reference and CQ distributions and between the reference and CQCO microimpedance distributions revealed no significant differences (p>0.05) in (dv m /dt) max. This suggested that microstructural heterogeneity had limited impact on action potential propagation in sampled volume regions where collagen fibers oriented along the sampled volume s long axis. Figure 6B shows V m records with (dv m /dt) max values at the central building blocks from the 10 P block groups (i-x). Paired t-tests using these block groups showed statistically significant differences in (dv m /dt) max between reference and CQ distributions (p<0.001) and between reference and CQCO distributions (p<0.05). This

31 23 suggested microstructural heterogeneity did have a more profound impact on action potential propagation through punctate regions of the sampled volume. Two-way ANOVA confirmed this finding as no synergistic effect between localized collagen arrangement (L, P) and microimpedance distribution (reference, CQ, and CQCO) was found. Surface electrograms. Figure 7A shows the building block arrangement used to derive potential difference electrograms. Short axis electrograms shown in Figure 7B had larger amplitude with the CQ and CQCO microimpedance distributions than with the reference distribution. Amplitudes for the reference distributions varied from 5.5 to 12.3 mv, while those from the CQ distribution varied from 11.6 to 25.3 mv and those from the CQCO distribution varied from 9.9 to 22.1 mv. Both differences were statistically significant (reference/cq, p<0.01; reference/cqco, p<0.01). Additionally, small differences in the time of maximum ϕ o were observed in both CQ and CQCO distributions. Long axis electrograms shown in Figure 7C were largely indistinguishable from one another. Amplitudes for the reference, CQ, and CQCO distributions varied from 0.2 to 1.1 mv, 0.2 to 1.4 mv, and 0.4 to 2.9 mv, respectively. Both differences were statistically significant (reference/cq, p<0.05; reference/cqco, p<0.001). This occurred, predominantly, because myocytes in the uppermost layer were oriented along this axis and the rapid activation associated with action potential propagation in this direction limited spatial differences in the source interstitial potentials, highlighting cellular coupling.

32 24 Discussion The absence of experimentally validated interstitial microimpedance data in the literature contributes to an incomplete understanding of structure and its influence on action potential propagation and potential sources for arrhythmias. In this study, we measured heterogeneity in collagen quantity on the size scale at which cardiac microimpedances likely impact conduction. We incorporated that heterogeneity into simulations to determine likely influences of a realistic collagen distribution on action potential propagation. The main new findings that arose from this study include: (1) collagen heterogeneity is pronounced even on this small scale, (2) activation sequences changes were modest with alterations in collagen arrangement, despite large differences in microimpedances distributions, (3) (dv m /dt) max, an indicator of membrane excitability, was significantly greater in building block groups that contained punctate collagen, and (4) bipolar surface electrograms showed marked increases in maximum interstitial potential in CQ and CQCO microimpedance distributions despite close spacing. Our finding regarding the heterogeneity in collagen quantity in healthy rabbit ventricular subepicardium on the size scale studied is important because the collagen matrix is the major structural component within the interstitium. The collagen distribution should therefore dictate the interstitial microimpedance distribution. The extracellular matrix of the myocardium is a dynamic structure that connects and supports myocytes. Most of this matrix, which consisted of ~5% of the sampled volume in our measurements in healthy myocardium, is made of collagen. The chief function of the matrix is to maintain the structural integrity of the heart under the load of cardiac contraction. The dynamic forces of cardiac contraction are variable, over the short term

33 25 with changing heart rate and over the longer term as pressure/volume loading changes with age. To respond to these variable mechanical demands, the collagen architecture is necessarily complex and undergoes constant remodeling. Fibroblasts, the most numerous cell type in the myocardium, produces much of the collagen found in the cardiac interstitium as well as the matrix metalloproteinases that control protein degradation (Camelliti, 2005). Our findings are consistent with those of others in that collagen is arranged in longitudinal strands in the subepicardium (Pope, 2008), with sparse lateral connections between stands that provide structural integrity and prevent slippage during myocyte contraction (Weber, 1989). On the building block size scale, collagen quantity varied widely, with individual building blocks containing as much as 52% collagen. Additionally, we found that collagen in building block groups could be visually classified as either longitudinal strands or punctate collagen. The presence of more punctate structure in groups farther from the subepicardial surface was unexpected and contributed to greater structural and electrical heterogeneity. Our approach differed from the work of others (Sands et al, 2005; Pope, 2008; Young, 1998; Vetter, 1998) in that we focused on a smaller sampled volume in an attempt to relate the heterogeneity to the microimpedance distribution. Because the myocardial architecture is complex and spatially variable, we used a small building block size in this study. Large samples size (>3000 building blocks) allowed us to obtain generalizable measures of collagen quantity and orientation. The large sample size allowed further analysis of propagation in block groups. Block group classification and

34 26 analysis allowed more detailed investigation of small scale structural changes and their impacts on propagation. Our finding that including the histological detail for microimpedance assignment had limited impact on activation sequence characteristics was initially surprising because that assignment caused such large changes and variability in (Rox, Roy, Roz) and (Rix, Riy, Riz) in the CQ and CQCO distributions compared to the reference case, with mean interstitial resistances increasing more than ten-fold in CQ and CQCO distributions. The subtlety of changes in activation sequences highlights the large impact of resistive coupling on microscopic conduction. Large sample size (3146 building blocks) allowed rigorous statistical analysis. While differences in action potential propagation were generally small, differences in conduction were apparent in the CQCO distribution where transmural fiber rotation was maximal. Mean collagen quantity in the CQ and CQCO distributions was reduced to approximately 20% of that found in the reference distribution. The difference in collagen quantity alone from the reference to the CQ distribution appeared to have little impact on propagation. Although the differences in activation sequences found in this study are slight, small regional changes in propagation caused by microstructural heterogeneities may be compounded over larger areas. Notably, the volume of tissue we studied is roughly the same size as a single simulated element in recent whole-heart modeling work (Trayanova, 2011). While subtle changes in activation sequence may accumulate over larger areas, the extent of coupling was sufficient to average out larger overall changes in (Rix, Riy, Riz) and (Rox, Roy, Roz) on this small scale.

35 27 While the overall activation sequences were minimally affected by inclusion of histologically validated collagen data in the microimpedance assignments, we did find marked differences in (dv m /dt) max in regions identified visually as containing punctate block groups. Our finding that (dv m /dt) max was most affected by nonuniform interstitial microimpedances is consistent with that of Spach and Barr, who found that structural discontinuities have more profound effects on (dv m /dt) max than on other measures of propagation (2000). Spatial variability of (dv m /dt) max, which increased by as much as 56 mv/ms and decreased by as much as 16 mv/ms in the CQCO distribution, produced regions of heterogeneous impulse propagation. Regions of heterogeneous membrane excitability, predicted by (dv m /dt) max as a nonlinear indicator of sodium channel availability, create vulnerability to conduction block. With a premature stimulus, regions with reduced sodium channel availability would not depolarize, while conduction would be maintained in other tissue regions. As a result, the nonuniform conduction produced by interstitial discontinuities found here could have arrythmogenic potential in larger tissue volumes (Kleber and Rudy, 2004). A transition in collagen arrangement from longitudinal strands to more punctate architecture has been observed in failing ferret hearts (Graham and Trafford, 2006). In the presence of gap junction lateralization (as is frequently observed in diseased tissue) (Jongsma, 2000), regions with increased punctate collagen are likely to have an even greater effect in promoting discontinuous conduction. In addition, although similar activation sequences were found, assignment of microimpedances based on structural parameters identified in our histologic analyses established much larger bipolar surface electrograms than in the reference distribution. While the changes in interstitial potential were pronounced in both CQ and CQCO

36 28 distributions, the inclusion of fiber orientation data resulted in smaller changes in surface potential electrograms. Intracellular and interstitial microimpedances can be obtained from analysis of experimentally derived interstitial potential recordings (Pollard et al, 2004), however empirical measures of microscopic conduction (e.g., ~50 µm spacing) (Hofer et al, 1994; Wiley et al, 2005) are scarce because of the technical challenges of such experiments. While electrodes with lower impedance are desirable for improved signal to noise ratio, electrode size and impedance are inversely related. Very small, finely spaced electrodes must be used to obtain interstitial potential recordings that reflect the influence of the microstructural features of interest.

37 29 References Cabo C, Boyden PA. Extracellular space attenuates the effect of gap junctional remodeling on wave propagation: a computational study. Biophys J 96: , Camelliti P, Borg TK, Kohl P. Structural and functional characterisation of cardiac fibroblasts. Cardiovasc Res 65: 40-51, Clerc L. Directional differences of impulse spread in trabecular muscle from mammalian heart. J Physiol 255: , Fleischauer J, Lehmann L, Kléber AG. Electrical resistances of interstitial and microvascular space as determinants of the extracellular electrical field and velocity of propagation in ventricular myocardium. Circulation 92: , Graham HK, Trafford AW. Spatial disruption and enhanced degradation of collagen with the transition from compensated ventricular hypertrophy to symptomatic congestive heart failure. Am J Physiol Heart Circ Physiol 292: H1364 H1372, Hofer E, Urban G, Spach MS, Schafferhofer I, Mohr G, Platzer D. Measuring activation patterns of the heart at a microscopic size scale with thin-film sensors. Am J Physiol Heart Circ Physiol 266:H2136-H2145, Jongsma HJ, Wilders R. Gap junctions in cardiovascular disease. Circ Res 86: Kléber AG, Riegger CB. Electrical constants of arterially perfused rabbit papillary muscle. J Physiol 385: , Kléber AG, Rudy Y. Basic mechanisms of cardiac impulse propagation and associated arrhythmias. Physiol Rev 84: , Polimeni PI, Williams S, Weisman H. Application of an automatic electronic image analyzer to the measurement of myocardial extracellular space. Comp Biomed Res 16: , Pollard AE, Barr RC. A biophysical model for cardiac microimpedance measurements. Am J Physiol Heart Circ Physiol 298: H1699-H17091, Pollard AE, Barr RC. Feasibility of cardiac microimpedance measurement using multisite interstitial stimulation. Am J Physiol Heart Circ Physiol 287: H2402-H2411, Pope AJ, Sands GB, Smaill BH, LeGrice IJ. Three-dimensional transmural organization of perimysial collagen in the heart. Am J Physiol Heart Circ Physiol 295: H1243 H1252, Puglisi JL, Bers DM. LabHEART: an interactive computer model of rabbit ventricular myocyte ion channels and Ca transport. Am J Physiol Cell Physiol 281: C2049 C2060, 2001.

38 30 Roberts SF, Stinstra JG, Henriquez CS. Effect of Nonuniform Interstitial Space Properties on Impulse Propagation: A Discrete Multidomain Model. Biophys J 95: , Sander EA, Barocas VH. Comparison of 2D fiber network orientation measurement methods. J Biomed Mater Res A 88: , Sands GB, Gerneke DA, Hooks DA, Green CR, Smaill BH, LeGrice IJ. Automated imaging of extended tissue volumes using confocal microscopy. Microsc Res Tech 67: , Spach MS, Barr RC. Effects of cardiac microstructure on propagating electrical waveforms. Circ Res 86:e23 e28, Trayanova N, Plank G, Rodriguez B. Whole heart modeling: Application to cardiac electrophysiology and electromechanics. Circ Res 108: , Trayanova N, Plank G, Rodriguez B. What have we learned from mathematical models of defibrillations and postshock arrhythmogenesis? Application of bidomain simulations. Heart Rhythm 3: 1232, Vetter FJ, Simons SB, Mironov, Hyatt CJ, Pertsov AM. Epicardial fiber organization in swine right ventricle and its impact on propagation. Circ Res 96: , Weber KT. Cardiac interstitium in health and disease: the fibrillar collagen network. J Am Coll Cardiol 13: , Whittaker P, Boughner DR, Kloner RA. Role of collagen in acute myocardial infarct expansion. Circulation 84: , Wiley JJ, Ideker RE, Smith WM, Pollard AE. Measuring surface potential components necessary for transmembrane current computation using microfabricated arrays. Am J Physiol Heart Circ Physiol 289: H2468-H2477, Young AA, Legrice IJ, Young MA, Smaill BH. Extended confocal microscopy of myocardial laminae and collagen network. J Microsc 192: , 1998.

39 31 Table 1. Directional interstitial and intracellular microimpedances Reference CQ CQCO Rix kω ± ± 139 Riy kω ± ± 237 Riz kω ± ± 52 Rox kω ± ± 3327 Roy kω ± ± 4537 Roz kω ± ± 4687

40 32 Table 2. Activation sequence correlation coefficients CQ CQCO Min ϕo Max ϕo APA Peak INa I Peak ICaL I dvm/dt /dt Max Time at dvm/dt /dt Max

41 33 Figure 1. A. Example of one section viewed under brightfield illumination with a rhodamine filter. Collagen strands in this view appear black. Fiducials used in image registration are labeled i, ii, and iii. B. The same section viewed under polarized light. Birefringence of collagen causes it to appear gold. C. Full image of the section (shown here as a grayscale brightfield image) with center of fiducial i aligned with the center of the zero-filled (black) matrix. Fiducials i and ii are vertically aligned. The region selected for collagen analysis is outlined in black. D. Resulting image of the sampled region (500x250 µm2) obtained from the rotated image. Collagen is white.

42 Figure 2. A. Graphic representation of one building block obtained after stacking images of the sampled region. Each building block is 8x8x4 pixels. Collagen pixels are drawn in white and non-collagen pixels are drawn in black. B. Examples of building block groups visually classified as longitudinal or punctate. Each building block group is 4x3x2 building blocks. Collagen is shown in red. C. Circuit diagram of each building block used in simulations. (Rix, Riy, Riz) and (Rox, Roy, Roz) values were determined histologically and connect to resistances in neighboring building blocks in the intracellular and interstitial spaces, respectively. 34

43 Figure 3. Reconstructed collagen network. Collagen shown in red. Ten punctate block groups (P) are shown on the left; ten longitudinal block groups (L) are shown on the right. 35

44 36 Orientation ( ) Building Blocks Figure 4. A. Histogram of collagen quantity in all building blocks (n=3146). B. Transmural fiber orientation in each sampled region (squares). Building block fiber orientations incorporate fiber orientation measurements from four sampled regions. Building block fiber orientations are shown as triangles.

45 Figure 5. Maps of V m in each microimpedance distribution 2.1 ms after onset of stimulus. Volumes (composed of 3146 building blocks) were stimulated at the back left corner. Filled arrow indicates transmural depth of greatest fiber rotation. 37