A little note to say that a textbook chapter I wrote last year is now online and available as part of the Springer Reference work “Drug Discovery and Evaluation: Safety and Pharmacokinetic Assays“
The chapter is available here, and if you have trouble accessing it let me know via ResearchGate.
The chapter is about computational modelling of drug-induced pro-arrhythmic risk. So what does that mean?
Below are a couple of real electrocardiograms (ECGs). An ECG records the difference in electrical potential between two points on the outside of your body through time, and since the heart is the main source of electrical activity it dominates the signal (although you can also pick up signals from other muscles if you don’t stay still!). The top one is mine from a smartphone device and app measuring the electrical potential between my index fingers. When you think about it, there being any difference between electrical potential on opposite hands reflects the fact there’s asymmetry in heart chamber shapes and sizes (one side pumps to just lungs, other bigger one to all the rest of body), and/or heart orientation in the chest, and/or how waves of activity move through the heart.
(Incidentally, by putting 10 different electrodes in certain places on arms/legs/chest you – or at least an expert cardiologist – can read a surprising amount into what is going on in the full 3D electrical activity of the heart through time. Somewhat confusingly this is called a “12 lead ECG”. That’s because looking at 12 differences between combinations of the 10 electrodes is usually considered comprehensive enough to figure out what’s going on without causing cardiologists’ brains to explode. There’s research work with patients wearing jackets with hundreds of electrodes, and computers figuring out what’s going on, called “ECG imaging“.)
In the healthy top trace the 7 big spikes relate to the ventricles – the big main pumping chambers at the bottom of the heart – activating or depolarising. That is, going from low to high voltage and starting the chain of events that leads to contraction of the muscle. A large difference in electrical potential occurs across space as the activation wave travels up the ventricles, and so the time of maximum difference in potential between your left and right hands gives the peak of the big spike, and there’s one spike per heart beat, so we’re looking at 7 heartbeats here. When the ventricles are completely depolarised there’s no potential difference across the body, and the signal goes relatively flat again, before the lower and wider big bump relating to ventricles repolarising (going back from high to low voltage ready for the next beat and starting the relaxation of the muscle). Then there are longer flat bits where nothing happens until my next heartbeat. (Aside, the little bump before the big spike corresponds to the atria activating – the little chambers at the top of the heart that pump blood into the ventricles)
In the middle of the second ECG from wikipedia we see a kind of rhythm disturbance (arrhythmia) called Torsade de Pointes (TdP). Here there are no ‘flat bits’ at all, suggesting waves moving constantly around the heart, and the oscillatory nature with the spikes getting higher and lower over about 10 spikes suggests some sort of shifting axis of rotation or drifting spiral activity (“torsade” = French for “twist”) as symmetry is broken in different ways with different wave directions.
Looking at the timescale (the medium sized squares in the background are the same scale on both plots – 0.2 seconds wide each) we see how the TdP spikes occur at a rate of pretty much one every 0.2 seconds, this 0.2 seconds is not really long enough for each cell to recover from being activated, suggesting activation chasing repolarisation constantly, round and round the heart. So at all times throughout the TdP episode somewhere in the ventricles is recovered whilst other bits are activated. This is bad news, because the heart doesn’t pump efficiently, or at all, when waves of activity are going all over the place like this, as opposed to nicely coordinating muscle contraction and relaxation with the whole of the ventricles being activated at once. Blood pumping will almost stop completely when the ECG looks like this, giving you just a few minutes to survive unless you can snap out of this arrhythmia spontaneously, which does happen sometimes. Here a shock is applied, sending the voltage off the axis at the end which basically forces the whole heart to depolarise at once and gives the heart a chance to break the TdP cycle and get back into a healthy rhythm (this is what all defibrillators try and do).
We are particularly interested in TdP from a drug safety point of view, as quite a number of drugs introduced in the 1990s and early 2000s increased the risk of TdP happening. Even in the ‘riskier’ drugs TdP was very very rare (typically 1 TdP event in 10,000 patient-years of dosing or something like that) but when millions of people take a drug regularly, those TdP events do occur in a significant number of people. So for things like a hayfever drug it was not worth the risk* and they were pulled off the market. A lot of effort has gone into making sure this doesn’t happen with new drugs today, without being overcautious and ruling out potentially good drugs, which is what the textbook chapter discusses from a computational modelling standpoint.
So I hope the chapter provides a relatively accessible introduction to computational cardiac electrophysiology modelling for assessing pro-arrhythmic risk of new compounds, for both modellers and experimental safety pharmacologists.
For computational modellers, there are a couple of bits in the chapter that I hope you read in particular:
Firstly, it’s the first time I’ve put down in a publication the argument here from an earlier blog, about the usefulness of ever-increasing realism in simulations being limited by rarity of TdP that I mentioned above. In a nutshell, with enough realism the simulations will show TdP too rarely to be useful, so we need simplified models, and it’s not obvious what degree of simplification is best!
Secondly, and somewhat in tension with the previous point, it would still be very nice to understand more about tissue-level arrhythmia mechanisms. What is actually going on in the heart to start and sustain an episode of TdP? It would be nice to model the TdP ECG arising, see how the waves move around the heart, then have a look at what is going on at a cell and even ion channel level.
We could then think about (or just simulate with brute force!) what drug properties make starting and sustaining TdP more or less likely, particularly looking at what drug properties are important for tissue-level relative to those that determine simpler cell-level properties like action potential duration or ‘qNet’ from the CiPA papers that we already know work quite well.
Here’s a couple of simulated ECGs from the earliest papers I found on this topic – “The Mechanism of Simulated Torsade de Pointes in a Computer Model of Propagated Excitation” by Abildskov & Lux in 1991 and “Mechanisms in Simulated Torsade de Pointes” by the same authors in 1993:
Those simulations are done on a 25×25 grid of 625 cells, and appear to capture a surprising amount of what might be going on in terms of wandering rotors that give rise to this characteristic oscillatory waveform in Torsade de Pointes.
Below is an example I pulled out of a much more recent paper on simulating TdP risk with whole ventricles models, with millions of nodes in the mesh that each have an action potential model attached. So here is a computational mesh and a simulated ECG underneath
We seem to have lost the ‘continual’ spiking activity in the ECG – lots of flat bits appear here which is a bit un-TdP like to me and suggesting 50% of the time there are no waves anywhere. So perhaps this is not quite such a good mechanistic representation of what’s going on in TdP?
In another example in this simulation below, the rapid spikes in the pseudo-ECG don’t appear to have the long slow ‘twisting’, and they turn out to relate to the red-arrow membrane voltage, at -30 to +30mV oscillations (not repolarizing down to the usual -80mV at all) which is an interesting prediction, but not what other simulations do as far as I know (or optical mapping of TdP-like arrhythmias suggests as far as I know – comments pointing to examples of cellular action potential recordings/optical mapping during TdP episodes are very welcome!).
I’m not trying to pick on these papers in particular, most of the whole-organ sims I’ve seen show these kinds of differences you might not want. So, alongside a few other slightly provocative comments (that I hope spice it up and make it worth a read) you’ll find this sentence in my textbook chapter:
“Strikingly, the ECG-like waveforms in [Abildskov & Lux] appear to be more realistic representations of Torsade-de-Pointes than those in some of the recent publications using whole ventricle three-dimensional simulations in realistic geometries that use millions of action potential models, suggesting that it is worth revisiting and examining the basic mechanisms that we need to observe Torsade-like electrocardiograms.”
There is a notable exception to this that I know about, very happy to learn about more in the comments, which is some work done by Jeremy Rice at IBM with their cardioid simulator which I first saw in 2013. The video below is hosted on that cardioid link:
So the good news is that quite realistic TdP ECGs are possible to simulate. The bad news is that sadly Jeremy is no longer with us, and I haven’t been able to find anyone with the code to run this simulation, and although Cardioid was introduced here, I don’t think the simulation above ever appeared in a publication or showed what the membrane voltages looked like underneath. I remember Jeremy mentioning in person using “M cell islands” when he showed this, which are controversial let’s say. But whatever the setup was, it evidently resulted in an arrhythmia in this video that captures a lot of what is going on in TdP.
Another honourable mention is “R-From-T as a Common Mechanism of Arrhythmia Initiation in Long QT Syndromes” by Michael Liu and co. who have one or two TdP-like ECGs, they also included a Purkinje system. Below is a screenshot from one of their supplementary movies in one of their most TdP like sims, where we see that voltage does seem to go back down to circa -80mV. Seems a closed source CUDA code was used for this so difficult to play more.
For example in the above we can see the Purkinje system on the right, normally this carries the activation from the atria to ventricles through these specialised conductive fibres. But you can get waves going back into the Purkinje system and popping out again to keep arrhythmic behaviour going – is that important/necessary here?
The Purkinje system probably isn’t needed (as pointed out to me on twitter, thanks Axel!) because Nele Vandersickel also has some promising Torsade simulations without one in “Perpetuation of torsade de pointes in heterogeneous hearts: competing foci or re-entry?” and “Spatial Patterns of Excitation at Tissue and Whole Organ Level Due to Early Afterdepolarizations” which explore how EADs and TdP are linked across 1D to 3D simulations:
So consider this a friendly challenge to big-tissue-simulation people. It would be nice to assemble a review of what sort of cell properties/geometries lead to what sort of TdP-like arrhythmias, what do we need to have in the simulations? And once we have established what mechanisms are necessary/sufficient, can we make sure open source codes are all published with the necessary meshes etc. so that people can reload, run and investigate them further…
*people have actually debated that: terfenadine was the first antihistamine that didn’t make you drowsy, so arguably taking it off the market could have led to a significant or even larger number of deaths (e.g.) from people falling asleep at the wheel when they reverted to the previous drugs. Drug safety and risk/benefit analysis is tough. Luckily, within a couple of years, drug developers figured out that a metabolite of terfenadine was also an effective antihistamine, kept its non-drowsy property, but had very low TdP risk, and that drug is still in use today (fexofenadine).
Mathematical Matters of the Heart 