• 21,241 words
• 171 pages
• 31 floats (images/tables

Today I incorporated another study, and at one point the page count nearly hit 200. However, I realized that my (long) figure captions were severely bloating the list of figures, so I cut them out and did some other editing. That eliminated between twenty and thirty (!) pages. There remains now only one more study to be incorporated, although I still have to do the writing for that study. I also have to write bits and pieces throughout the dissertation and do some massive editing, but it’s nice to feel like I’m picking up some positive momentum on this thing. It’s also much easier to cut and rearrange than it is to generate text, so that part should be easier.

Today’s status:

• 16,112 words
• 139 pages
• 20 floats (images/tables)

I added 17 of those floats today.

Today, while doing this, I noticed that there’s an “Export comments to Data File” option in the Comments menu. “Hmm,” I thought, “I wonder how easy it would be to read this data file?” It turns out that it’s just some ASCII text with a bunch of (to me) useless information, and the highlighted comments in parseable “Contents([highlighted text here])” containers.

I wrote a quick and dirty Perl script that pulls the comments into a text file. I can then just copy and paste that file into FreeMind, and it creates all of the leaves for me. This will save me hours carpal-tunnel-syndrome-inducing mousing and frustration. The perl script, for your perusal (improvements welcome) is available here: extract_comments.pl.

Kindly Let me know if you get any use out of this, and if you find any parsing bugs. It’s in the public domain.

Introduction

The occlusion of a coronary artery sets off a series of pathological changes in the heart. The first stage of these events is termed regional ischemia phase 1A, and it lasts 10-15 min following the initial block. Spontaneous arrhythmias begin to occur within 2.5 min (Scherlag et al., 1974). Akinesia begins within 3-5 min (Brooks et al., 1975), and ventricular tachycardia (Scherlag et al., 1974) and then fibrillation (Fleet et al., 1994) follow in the first 4-6 min. If fibrillation is not terminated by an electrical shock, the patient will suffer brain death within 5 additional minutes.

While there are three major coronary arteries, the left anterior descending (LAD) coronary artery is the most critical. It supplies a large portion of the left ventricular free wall via its branches (Lie et al., 1975; Brooks et al., 1975; Scherlag et al., 1974), one-half to one-third of the interventricular septum (Brooks et al., 1975; Scherlag et al., 1974) via the septal perforator arteries, and the septal third of the lower right ventricular free wall (Brooks et al., 1975), for a total of nearly 30% of the ventricular tissue by weight (Brooks et al., 1975; Li et al., 2005; Kuo et al., 1983). Largely because of its importance, it is commonly used in experimental animal models of regional ischemia and infarction. Because of the importance of the LAD, and because of the established base of literature available for comparison, occlusion of the LAD is also used in the research presented herein.

Over the past 40 years, a detailed account of the temporal progression of acute ischemia phase 1A has been assembled. While VT and VF begin to occur after four minutes, this is not always the case. The progression varies from species to species, but the general time course is as follows. After 5 min, action potential duration (APD), amplitude (APA), and maximum upstroke velocity are reduced (Downar et al., 1977). Activation delay – the difference between the time at which a point in the tissue is activated during disease conditions relative to the time at which it is activated during normal conditions – becomes noticeable. After 6 min, the action potential plateau disappears, the changes in APD and APA are accentuated, and conduction block occurs in the most ischemic areas (Downar et al., 1977; Fleet et al., 1994). By 9 min, APA alternans are manifested, sometimes leading to 2:1 (normal:ischemic tissue) capture (Downar et al., 1977). Activation delays lengthen, and APDs degenerate to around 100 ms (Downar et al., 1977). After 10 min, PVC occurrence reaches its peak frequency, and the ischemic zone becomes unresponsive (Kimura et al., 1986).

Ionic and Metabolic Changes in Ischemia

The pathological effects of ischemia described above result from the combined effects of changes in ionic concentrations and metabolic state of ischemic tissue. Because no blood is delivered to or washed away from the tissue, the cells begin to deplete their energy stores, and waste products accumulate. This results in metabolic impairment, intra- and extracellular acidosis, and hyperkalemia in the ischemic tissue.

Without oxygen, mitochondrial production of ATP slows. Since the tissue is still dephosphorylating ATP for energy, ADP accumulates within the cytosol. A decreased ratio of ATP/ADP has been found to activate an ATP-sensitive potassium channel, referred to as K(ATP) (Furukawa et al., 1991; Kimura et al., 1986; Taniguchi et al., 1983), which significantly speeds repolarization and thereby shortens APD. While the fraction of K(ATP) channels opened by ischemic levels of ATP and ADP is small (approx. 0.5%), there are a large number of such channels in the sarcolemma, and the opening of even a small fraction of them can dramatically increase K⁺ efflux (Weiss et al., 1992; Taniguchi et al., 1983; Wilde and Aksnes, 1995).

Efflux of potassium across the sarcolemma secondary to acute ischemia begins shortly after occlusion of coronary flow (Coronel et al., 1991). While the mechanisms underlying this accumulation are not completely understood, efflux from K(ATP) channels, coupled with influx of Na⁺ (Weiss et al., 1992; Shivkumar et al., 1997) and lack of washout in the extracellular space are thought to overwhelm the Na⁺/K⁺ pump (Bollensdorff et al., 2004; Ferrero et al., 2002). As a result, K⁺ accumulates in the extracellular space. The change in [K⁺]_o /[K⁺]_i causes diastolic depolarization, eventually inactivating the fast sodium current. Extracellular potassium accumulation is the most pronounced effect of acute myocardial ischemia phase 1A, and causes conduction block after 6-10 min (Shaw and Rudy, 1997).

Without delivery of oxygen to the working myocardium, production of ATP becomes glycolytic, and acid production is increased. Acidosis inhibits contraction, I_Na and I_Ca(L) (Kimura et al., 1991; Yatani et al., 1984; Irisawa and Sato, 1986).

The Ischemic Border Zones

Between the ischemic and normal tissue lie transitional border zones (Coronel et al., 1988; Lie et al., 1975; Cox et al., 1968; Factor et al., 1981; Li et al., 2005; Pogwizd and Corr, 1987; Brooks et al., 1975; Cohn et al., 1973; Di Rocco et al., 1997). These include lateral border zones at the limits of the region perfused by the occluded coronary artery, endocardial border zones produced by perfusion from blood in the ventricles, and in some cases, an epicardial border zone.

Lateral border zones secondary to occlusion of the LAD extend as far as 1 cm from the border of LAD-perfused tissue in pigs (Coronel et al., 1988). They result from diffusion and from washout, even in the absence of LAD perfusion (Coronel et al., 1988), and possibly from the interdigitation of vascular beds (Factor et al., 1981). The borders between ischemic and normal tissue in the left-ventricular free wall, the septum, and the right-ventricular free wall are lateral border zones.

Endocardial border zones were suspected to exist by Pogwizd and Corr (Pogwizd and Corr, 1987) and first observed by Li et al. to cover the entire endocardial surface of the ischemic area in rabbits (Li et al., 2005). As the rabbit coronary vasculature is considered to be very similar to that of humans, endocardial border zones are thought to be clinically relevant (Li et al., 2005).

The presence or absence of an epicardial border zone seems unresolved in the existing literature. This perception is due to a large variability in collateral coronary vasculature among animal models. While dogs have been a popular experimental model for studies of ischemia and infarction, they have a large degree of collateral vascularization (Brooks et al., 1975; Cohn et al., 1973; Factor et al., 1981). Pigs, rabbits, and humans are known to have less extensive collateral vascularization (Brooks et al., 1975; Di Rocco et al., 1997), although this varies with age in rabbits (Igor Efimov, personal correspondence). The role of an epicardial border zone, and the importance of the inclusion of one in a model of acute ischemia, is therefore still unresolved. As will be shown in this document, the presence of an epicardial border zone has a significant effect on the nature of reentry in the ischemic heart.

The overall width of the ischemic border zone has been found to be between 250 µm and 15 mm. This wide range stems from the variety of species and preparations in which regional ischemia has been studied, as well as different resolutions of data acquisition, and focus on different aspects of ischemia. Studies that focused on the visible border of cyanosis found it to be sharp and jagged (Becker et al., 1973; Brooks et al., 1975; Di Rocco et al., 1997; Harken et al., 1978, 1981). Discrete vascular beds (Factor et al., 1981) and an all-or-nothing response from mitochondria (Harken et al., 1981) produce distinct normal and ischemic regions with limited interdigitation (Factor 1981). Predictably, the border zone of [ATP]_i coincides with that of oxygen supply (Hearse 1977). Extracellular potassium washes and diffuses out 6 to 15 mm from the ischemic border (Coronel1988Distribution, Coronel 1991, Harken 1978, Hearse 1977).

Transmural Electrophysiological Heterogeneities Within the Ischemic Region

Extracellular potassium accumulation is not homogeneous within the central ischemic zone. Rather, there is a gradual increase in [K⁺]_o into the ischemic zone (Coronel et al., 1988). This is possibly due to maximal flow reduction in the center of the ischemic area (Becker et al., 1973; Di Rocco et al., 1997; Pogwizd and Corr, 1987; Hearse et al., 1977), and occurs despite an opposite gradient of potassium efflux from K(ATP) channels.

While metabolic impairment in the central ischemic zone appears to be homogeneous, its effects on K(ATP) channels are not. Even in normoxia, APA, APD, and other aspects of AP morphology (Furukawa et al., 1991; Kimura et al., 1986) vary transmurally within the ventricular walls. With the onset of anoxia, these differences become more pronounced. I_K(ATP) activation is much greater in epicardial cells than in endocardial cells (Furukawa et al., 1991; Kimura et al., 1986, 1991). The time course of I_K(ATP) activation is also different in epicardial tissue than in endocardial tissue. Although APD (which is reduced by K(ATP) activation) progressively decreases in the endocardium over the first 30 min of ischemia, in the epicardium it shortens up to 10-20 min and then begins to lengthen again (Kimura et al., 1986). Refractory period (RP) progresses similarly, with post-repolarization refractoriness occurring after 5-10 min in epicardial cells, but not in endocardial cells (Kimura et al., 1986).

Arrhythmogenesis in Regional Ischemia Phase 1A

Because acute global ischemia inhibits tissue activation throughout the myocardium, it has been found to have an anti-arrhythmic effect (Rodríguez et al., 2004a,b). Regional ischemia phase 1A, on the other hand, produces a region of injured tissue surrounded by normal tissue with a border zone of varying ischemic degree. As a result, the normal tissue can sustain conduction while the ischemic tissue progresses through various stages of electrophysiological dysfunction, setting the stage for arrhythmogenic interactions between the two zones.

Given the variability in space and time of ischemic injury, along with the fact that phase 1A is completely reversible and leaves no lasting impression on the tissue, it is not surprising that the investigation of arrhythmogenic mechanisms in regional ischemia phase 1A has thus far been inconclusive. Initially, evidence for a reentrant mechanism of arrhythmia was lacking (Scherlag et al., 1974). However, subsequent studies using increased resolution were able to detect and track reentrant wavefronts, and implicated unidirectional block as the mechanism of initiation (Pogwizd and Corr, 1987; Downar et al., 1977). Occasional premature excitations from the RV subendocardium may have encountered unidirectional block from nonuniform recovery, and thereby initiated reentry (Kaplinsky et al., 1981; Pogwizd and Corr, 1987). The actual nature of the block was never discerned, but it was suspected to be from nonuniform recovery. This suspicion is supported by other studies, which found a critical level of dispersion of APD and extended refractory period for the initiation of reentry (Kuo et al., 1983; Behrens et al., 1997). Dispersion of APD and refractory period were found to correlate well with the width of the vulnerable window for arrhythmogenesis (Behrens et al., 1997). Triggered automaticity from ischemic effects including so-called injury current has been suspected as an arrhythmogenic mechanism, but not confirmed (Downar et al., 1977).

In an attempt to resolve some of the questions surrounding arrhythmogenesis in acute regional ischemia phase 1A, we assembled an ionic model incorporating the most relevant ischemic effects, realistic tissue geometry, and realistic geometry of the ischemic zone, with transitional border zones and transmural heterogeneities of electrophysiological properties. Using this synthesized model, the goal of this study is to characterize the arrhythmogenic substrate created by electrophysiological heterogeneities associated with regional myocardial ischemia phase 1A.

ATP Peeling

Progressive movement of collision location between two wave sources of different frequencies. Each horizontal line schematically represents the one-dimensional space between two wave sources. Curved lines represent wavefronts. Source B has a more rapid frequency than source A, so the location of collision moves progressively toward A with each iteration of the cycle (N).

In anti-tachycardia pacing, however, it is nearly impossible to target the core of re-entry in this fashion – pacing must be applied from a distant source. The core can therefore only be reached if stimulation is applied at a frequency more rapid than the intrinsic frequency of the re-entrant wave. This principle is illustrated schematically in the figure above. Each line between sources A and B represents the one-dimensional space in which wavefront collisions play out when the sources have different frequencies. In this example, conduction velocity is assumed to be constant, and both sources begin creating wavefronts at the same time for the sake of explanation. The concept holds even if they do not, but the position is shifted in one direction or the other depending on the difference in start time. The iterations (N) move from 1 through 6, indicating the first through sixth wavefront collisions. In this example, source B has a slightly higher frequency than source A. As such, wavefront collision proceeds as follows. On iteration 1, each source produces a wavefront at the same time. The waves travel with equal velocity toward each other, colliding in the middle of the space, and both are terminated. On iteration 2, B initiates a wave slightly before A, and so that wave has a longer period of time to travel before it encounters the wave from A. The region of collision is therefore shifted toward A a bit. On iteration 3, the head start of the wave from B in iteration 2 has been doubled, and so the region of collision is shifted twice as far toward A as it was in iteration 2. This continues in iterations 4 and 5, until in iteration 6, the wavefront reaches source A before it has an opportunity to initiate a wave. In cardiac tissue, this would result in overdrive stimulation of site A, and it would no longer initiate its own waves as long as B continued producing them and they continued to reach A.

Thus, if A is the re-entrant wave and B is the site of anti-tachycardia pacing, the core of the re-entry at A will be reached within 6 paced beats, and re-entry will be terminated. However, if the situation is reversed and B is the re-entrant wave, the site of anti-tachycardia pacing will quickly be overdriven and the therapy will be ineffective. Furthermore, if some region between A and B cannot support the higher frequency of activation produced by a sufficiently-fast anti-tachycardia pacing therapy, the therapy will be blocked from reaching the core of the re-entrant wave. These difficulties with anti-tachycardia pacing can, however, be circumvented while using an electrode distant from the site of re-entry, using the technique of far-field stimulation.

This example was inspired by a conversation with Dr.Valentin Krinsky

Resetting and termination in a ring

The classic model of re-entry is the one-dimensional system of a wave propagating within a ring composed of an excitable medium (see figure above). If the ring is longer than the wavelength of the wave of excitation, there will be an excitable gap between the tail of the wave and the head (white regions in figure). A stimulus applied in that gap can either reset or terminate re-entry. Resetting occurs when the stimulus results in an orthodromic wave (that is, moving in the same direction as the original wave) and an antidromic wave (that is, moving in the opposite direction from the original wave) in the excitable gap and the following happens: the antidromic wave collides with the original wavefront and terminates it, while the orthodromic wave follows the recovering tail of the original wave and becomes the starting point of a new re-entrant wave (figure panel A). If, however, the orthodromic wave collides with the recovering tail of the original wave and terminates, then re-entry will be terminated entirely (figure panel B). Thus, if a stimulus were applied at the appropriate time and position to consume the excitable gap, it would terminate re-entry.

Interesting aside. I was at first stumped on how to make ring gradients like what you see above. I used a combination of what I found here and going back and forth from GIMP to OmniGraffle Pro. They key appears to be the use of an asymmetrical conical gradient in GIMP.

I’m getting back on the horse.

Anyway, it’s a little tricky to apply the Martini Method when using LaTeX — as a markup language a bit like HTML, it’s full of special words, symbols, characters and whatnot that are not actually part of what you’re writing. A simple Emacs word count will not do the trick. Much as I’d love to count all of those extra words, the point here is to produce a certain volume of output and that would miss the point. Plus, it’s dishonest. There exists a PERL script that will parse LaTeX and count the non-special words. However, someone’s gone even a step further and made a nice web interface for it, with color coding and everything. That interface is here, apparently hosted by one Einar Andreas Rødland in Norway.

So far, it’s working quite well for me. Unfortunately, it just informed me that I’m not quite to my desired word count yet. More writing!

Now all that’s between me and the PhD are a few simulations and a lot of writing. I think I’m going to employ Anthony Burgess’ Martini Method. 1000 words per day, after which I can have a martini, relax, etc.

There’s also the small issue of my baby arriving soon, which will certainly complicate matters.

The fact is, writing in E-Prime would be extremely awkward as compared with the status quo. Not only that, my advisor would probably fire me if I attempted it. What can be done when writing a paper is to take a hard look at every use of “is”, and determine whether each one can be replaced by a better verb. For example, “This figure is a set of images from …” can be replaced with, “This figure contains a set of images from …”.

Also, I don’t know if I’ve mentioned this before, but I commit a few punctuation atrocities intentionally, and I don’t intend to change them. Foremost is my placement of final sentence punctuation outside of quotes. As a programmer, it just drives me crazy to place punctuation inside of a quote, where it doesn’t belong, simply because the rules say so. I have read that my placement is more accepted in British English writing, which is I guess some consolation. Here’s an example of breakage and how my use circumvents it:

Tom leaned forward, a glint in his eyes, and said, “You don’t really mean to imply that we should eat babies, do you?”

Tom’s sentence ends with a question mark, but the sentence overall is a statement! (Perhaps there’s already some convention about this that I’m unaware of. I really should read Strunk and White one of these days.) I would therefore write:

Tom leaned forward, a glint in his eyes, and said, “You don’t really mean to imply that we should eat babies, do you?”.

Now you know my dirty little secret, and it’s out in the open. Lest you be tempted to correct me.

This is one of those things that I know how to write property, but I can’t explain why.

Or couldn’t — for now I can. While waiting for the hopkins med campus shuttle today, I sat and wrote some sample “which” and “that” sentences and tried to discern what differentiates them. Here are the examples that I wrote. (Or, here are the examples, which I wrote.)

“This is the house that Jack built.”

“This is aspirin, which is used for headaches.”

“This is the aspirin that I took for my headache.”

The last sentence is when the answer snapped into focus for me: the difference was analogous to the difference between classes and their instantiations in object-oriented programming. “This is aspirin” describes the aspirin class — any and all aspirin. “Which is used for headaches” specifies more detail about the aspirin. On the other hand, “That I took for my headache” specifies a particular instance of the class “aspirin”, namely, the specific aspirin that I took for my headache. I wrote this note next:

“Look up whether ‘classes’ and ‘instances’ have analogous counterparts in language — they must.”

Sure enough, upon looking up the question, I found that I was almost exactly right. If you are uncertain about the proper usages of “that” and “which”, I suggest you read about the issue here.