Information

What phase of Action Potential (AP) exactly defines the Relative Refractory Period?

What phase of Action Potential (AP) exactly defines the Relative Refractory Period?


We are searching data for your request:

Forums and discussions:
Manuals and reference books:
Data from registers:
Wait the end of the search in all databases.
Upon completion, a link will appear to access the found materials.

I am posting below, word for word, two statements made on Relative Refractory period - the first from the text: Human Physiology for Medical Students by Magdi Sabry, and the second from a web page with the URL: https://content.byui.edu/file/a236934c-3c60-4fe9-90aa-d343b3e3a640/1/module5/readings/refractory_periods.html.

In addition, I've attached a photo from Google which appears to be in support of the second statement. But which of these is correct?

  1. "Relative refractory period (RRP)… corresponds to the remaining part of the descending limb of the AP till the start of after-depolarization (i.e. during the later 2/3 of RP)"

2."… there are two types of refractory periods; the absolute refractory period, which corresponds to depolarization and repolarization, and the relative refractory period, which corresponds to hyperpolarization. "


Neither is an accurate definition; both are correct and not conflicting if you interpret "corresponding" to mean "typically/approximately corresponding".

The absolute refractory period is any time in which you cannot evoke another action potential no matter the strength of stimulus, due to an action potential in progress/that has just occurred.

The relative refractory period is any time in which you can trigger an action potential but need a stronger stimulus than normal.

Neither of these definitions refers to specific phases of the action potential in terms of voltage or change in voltage. Yes, typically the absolute period includes the ascending and descending phases of the AP, but there's no reason it can't last longer depending on the gating properties of the sodium channels. Similarly, the relative refractory period starts with the end of the absolute refractory period and continues through the hyperpolarization phase, but there is no reason it cannot end sooner or later, again depending on gating properties.


The Action Potential in Cardiac Pacemaker Cells

In the heart, electrical impulses are generated by specialised pacemaker cells and spread across the myocardium in order to produce a coordinated contraction in systole.

The action potential generated is generated by a change in the potential difference between the inside and the outside of the cell. The particular action potential generated by cardiac pacemaker cells is very different from that of ventricular myocardial cells. In this article, we will discuss cardiac pacemaker cells and the action potential they generate in more detail.


Arrhytmias

2. Sinus bradycardia describes a slow heart rate (&amplt 60 to 40 beats per minute) that has the origin in the SA node. It may be normal in trained athletes who maintain a large stroke volume, during sleep in pathological condition after influenza or typhoid, intracranium pressure rise, irritation of the n. Vagus nucleases, may be an indicator of poor prognosis in patient with acute myocardial infarction that is associated with hypotension. ECG sings: all waves have normal configuration and priority, normal P wave and PR interval precedes each QRS complex (sinus rhythm), all R-R are lengthened. This arrhythmia may cause heart output decrease and leads to cerebral or coronary blood flow insufficiency, in that condition ectopic pacemaker could be activated.

3. Sinus (respiratory) arrhythmia is characterized by gradually lengthening (at expiration) and shortening (at inspiration) R-R intervals and is the result of intrathoracic pressure changes during respiration. It is the normal for the children and can occur in adult after influenza, at neurocirculative dystone, hypertension, congestive heart failure, diabetes mellitus. ECG sings: sinus rhythm, difference of all R-R is more than 0.15 second (at norm difference of all R-R is less than 0,15 sec).


Cardiovascular pathology stomatological faculty

2. Sinus bradycardia describes a slow heart rate (&amplt 60 to 40 beats per minute) that has the origin in the SA node. It may be normal in trained athletes who maintain a large stroke volume, during sleep in pathological condition after influenza or typhoid, intracranium pressure rise, irritation of the n. Vagus nucleases, may be an indicator of poor prognosis in patient with acute myocardial infarction that is associated with hypotension. ECG sings: all waves have normal configuration and priority, normal P wave and PR interval precedes each QRS complex (sinus rhythm), all R-R are lengthened. This arrhythmia may cause heart output decrease and leads to cerebral or coronary blood flow insufficiency, in that condition ectopic pacemaker could be activated.

3. Sinus (respiratory) arrhythmia is characterized by gradually lengthening (at expiration) and shortening (at inspiration) R-R intervals and is the result of intrathoracic pressure changes during respiration. It is the normal for the children and can occur in adult after influenza, at neurocirculative dystone, hypertension, congestive heart failure, diabetes mellitus. ECG sings: sinus rhythm, difference of all R-R is more than 0.15 second (at norm difference of all R-R is less than 0,15 sec).


Cardiac Action Potentials Made Easy: Summit, Plummet, Climb, Continue

Save yourself time and studying with the above video full of animations, visuals, and tricks to remember everything discussed below!

Don’t miss out on the other EZmed videos people are using to make medicine easy! Click below to check them out, and join to save time and help you study!

A male patient presents after a syncopal episode 30 minutes ago. He states he was at home cooking dinner when he began to feel lightheaded. The next thing he remembers is waking up on the kitchen floor.

He admits he has been experiencing intermittent palpitations for the past 2 days. You are concerned his syncopal episode could be from a cardiac conduction abnormality. You begin to recall the conduction system along with the types of cardiac action potentials that occur in the myocardium.

Introduction

An action potential is a change in voltage across a cell membrane, specifically a rise in voltage followed by a fall.

Action potentials are used to send information throughout the body, and they are also necessary for some types of cells to function as they trigger intracellular processes (such as contraction of muscle cells).

Cells that use action potentials are also called excitable cells and include: neurons, muscle cells (skeletal, cardiac, and smooth), cardiac pacemaker cells (specialized cardiac muscle cells), and endocrine cells to name a few.

This post will focus on the action potentials of cardiac pacemaker cells and cardiac muscle cells (non-pacemaker cells).

Understanding cardiac action potentials becomes clinically relevant when using antiarrhythmic drugs or managing conduction disorders.

EZmed always provides an easy way to remember medical topics.

In this post you will learn a simple catchphrase that will help you understand everything you need to know about cardiac action potentials including the different phases and what ions are involved.

Cardiac Conduction System

Make sure to check out the EZmed blog that makes the conduction system easy! Conduction System of the Heart: The Electrical Pathway

There are 2 main processes that occur in the heart: cardiac conduction (pacemaker cells) and cardiac contraction (non-pacemaker cardiac muscle cells).

Of note: cardiac muscle cells are also called cardiac myocytes, cardiomyocytes, or myocardiocytes.

Pacemaker Cells

The pacemaker cells are specialized cardiac myocytes that are capable of generating spontaneous action potentials and are responsible for cardiac conduction.

Pacemaker cells are primarily located in the sinoatrial (SA) node and atrioventricular (AV) node.

However, they are also present in other parts of the conduction system including the bundle of His, right and left bundle branches, and Purkinje fibers.

The inherent pacemaker rate of the SA node is faster than the other pacemaker cells, and for that reason the SA node generates the initial action potential in a normal functioning heart.

If the SA node becomes suppressed, then the other pacemaker cells are capable of generating spontaneous action potentials but at a slower heart rate.

The SA node is located in the back of the right atrium near the superior vena cava entry.

The action potential generated by the SA node will travel through the right atrium and to the left atrium through Bachmann’s bundle, thereby depolarizing the atria and leading to atrial contraction.

The impulse then travels to the AV node, located at the base of the right atrium, via an internodal pathway.

Conduction velocity is slowed through the AV node long enough to allow for atrial contraction and movement of blood from the atria to the ventricles before ventricular contraction occurs.

From the AV node, the impulse will travel through the bundle of His and down the right and left bundle branches.

The right bundle branch is responsible for depolarizing the right ventricle, and the left bundle branch is responsible for depolarizing the left ventricle.

The bundle branches terminate into Purkinje fibers which also help stimulate the ventricular myocardium to contract.

In a normal functioning heart the SA node generates the action potential that will ultimately lead to cardiac contraction. The action potential travels to the AV node, through the bundle of His, into the right and left bundle branches, and lastly through the Purkinje fibers.

Non-Pacemaker Cardiac Myocytes

The non-pacemaker cardiac myocytes are the contractile cardiac muscle cells that are responsible for atrial and ventricular contraction, and they make up the bulk of the myocardium.

Since the contractile myocytes do not generate spontaneous action potentials like the pacemaker cells do, their action potentials are generated when neighboring cardiac myocytes are depolarized or when pacemaker cells stimulate them.

Cardiac Action Potentials

The action potentials between non-pacemaker cells (such as atrial and ventricular myocytes) and pacemaker cells (such as the SA node and AV node) are similar but slightly different.

Let’s discuss each one below while providing an easy way to remember the material.

Atrial and Ventricular Myocytes

“Summit, Plummet, Continue, Plummet”

Let’s first discuss the action potentials of non-pacemaker cardiac myocytes - the contractile cardiac muscle cells that contract the atria and ventricles.

All you need to memorize is the following phrase: “summit, plummet, continue, plummet”.

Through this simple catchphrase, you have just learned all of the action potential phases and the ion channels involved.

“Summit” = Sodium = Phase 0

When a cardiac myocyte becomes stimulated, the resting membrane potential (-90 mV) becomes more positive and an action potential is generated if the threshold (-70 mV) is met.

The action potential will first “summit” as the voltage across the cell membrane becomes more positive.

This is referred to as depolarization and it is phase 0 of the action potential.

What ion is going to be involved in depolarizing the cell?

Here’s where the catchphrase is helpful.

Summit starts with the letter “S”, and this will help you remember when the action potential summits it is sodium involved.

In order for the cell to become more positive and depolarize, will sodium ions enter the cell or exit it?

They will need to enter the cell.

And this is exactly what occurs during phase 0 of the cardiac myocyte action potential.

Sodium ion channels open when the threshold cell membrane voltage is met, and an influx of sodium ions into the cell leads to depolarization.

Phase 0 = “Summit” phase of action potential = Sodium ion influx

Phase 0 is the “summit” phase in which the voltage across the cell membrane becomes more positive (depolarizes) due to the influx of sodium ions.

Plummet = Potassium = Phase 1

As the cell becomes more positive from the influx of sodium ions, these sodium channels begin to close thereby reducing the influx of sodium.

The action potential will then “plummet” as the voltage across the cell membrane becomes slightly more negative.

This causes the cell to slightly repolarize and is phase 1 of the action potential.

What ion is going to be involved in repolarizing the cell?

Again, here is where the catchphrase comes in hand.

Plummet starts with the letter “P”, and this will help you remember when the action potential plummets it is potassium involved.

In order for the cell to become more negative and repolarize, will potassium ions enter the cell or exit it?

They will need to exit the cell.

And this is exactly what occurs during phase 1 of the cardiac myocyte action potential.

The sodium channels from phase 0 have closed thereby reducing the influx of sodium ions, and the potassium channels are open leading to an efflux of potassium ions and a slight repolarization of the cell.

Phase 1 = “Plummet” phase of action potential = Potassium ion efflux

Phase 1 is a slight “plummet” phase in which the voltage across the cell membrane becomes slightly more negative (repolarizes) due to the efflux of potassium ions.

Continue = Calcium = Phase 2

After slight rerpolarization has occurred in phase 1, the action potential will then “continue” as the voltage across the cell membrane stays fairly constant.

This plateau in the voltage is phase 2 of the action potential.

If potassium is exiting the cell, then there needs to be another positive ion entering the cell to keep the action potential level and counteract the loss of positive charge.

Again, use the catchphrase.

Continue starts with the letter “C”, and this will help you remember when the action potential continues it is calcium involved.

We know that when calcium enters muscle cells it will lead to contraction.

And this is exactly what occurs during phase 2 of the cardiac myocyte action potential.

L-type calcium channels are open, and an influx of calcium ions into the cell leads to myocyte contraction. This contraction will lead to systole of the heart.

Phase 2 = “Continue” phase of action potential = Calcium ion influx

Phase 2 is the “continue” phase in which the voltage across the cell membrane remains constant (contraction) due to calcium influx that counteracts potassium efflux.

Plummet = Potassium = Phase 3

After myocyte contraction has occurred in phase 2, the action potential will then “plummet” again as the voltage across the cell membrane becomes negative.

This is referred to as repolarization and is phase 3 of the cardiac myocyte action potential.

We know from phase 1 that plummeting will involve the efflux of potassium ions.

And this is exactly what occurs during phase 3 of the cardiac myocyte action potential.

The calcium channels have now closed thereby reducing the influx of calcium, and the potassium channels are open leading to an efflux of potassium ions and repolarization of the cell.

Phase 3 = “Plummet” phase of action potential = Potassium ion efflux

Phase 3 is the major “plummet” phase in which the voltage across the cell membrane becomes more negative (repolarizes) due to the efflux of potassium ions.

Resting Phase = Phase 4

After the cell has repolarized, it is now back at its resting membrane potential.

This is phase 4 of the cardiac myocyte action potential in which the cell is at rest until the next stimulus occurs.

The heart is in diastole during phase 4 as there is no action potential being generated to lead to contraction.

Phase 4 is when the cell is at rest and the voltage remains at a fairly constant level (resting membrane potential) until the next stimulus generates an action potential.

Pacemaker Cells: SA and AV Node

“Climb and Plummet”

Now that we have a good understanding of the action potentials of the non-pacemaker cardiac myocytes, let’s discuss those of the pacemaker cells - the specialized cardiac muscle cells that lead to conduction.

These specialized pacemaker cells are primarily found in the SA and AV node, along with the rest of the conduction system (bundle of His, bundle branches, Purkinje fibers).

All you need to memorize is the following phrase: “climb and plummet”.

Through this simple catchphrase, you have just learned all of the action potential phases and the ion channels involved with pacemaker cells.

Climb = Calcium = Phase 0

Unlike the non-pacemaker cardiac myocytes, the pacemaker cells have the ability to spontaneously generate an action potential.

They do not require an external stimulus, and their cell membrane at “rest” slowly becomes more positive on its own (discussed below during phase 4).

Once the threshold cell membrane voltage is met, then an action potential is generated.

The action potential will first “climb” as the voltage across the cell membrane becomes more positive.

This is referred to as depolarization and it is phase 0 of the action potential (similar to non-pacemaker cardiac myocytes).

What ion is going to be involved in depolarizing pacemaker cells?

Climb starts with the letter “C”, and this will help you remember when the action potential climbs it is calcium involved.

In order for the cell to become more positive and depolarize, will calcium ions enter the cell or exit it?

They will need to enter the cell.

And this is exactly what occurs during phase 0 of the pacemaker cell action potential.

Calcium channels open and an influx of calcium ions into the cell leads to depolarization.

Phase 0 = “Climb” phase of action potential = Calcium ion influx

We can see how phase 0 of pacemaker cells differs from atrial/ventricular myocytes.

Depolarization of atrial/ventricular myocytes is a result of sodium ions entering the cell (“summit”), whereas depolarization of pacemaker cells is the result of calcium ions entering the cell (“climb”).

Phase 0 is the “climb” phase in which the voltage across the cell membrane becomes more positive (depolarizes) due to the influx of calcium ions.

Plummet = Potassium = Phase 3

There is no phase 1 or phase 2 of pacemaker cell action potentials as they are not muscle cells and do not need to contract.

They are conduction cells and only need to depolarize and repolarize over and over. This will lead to SA automaticity and AV conduction.

As the cell becomes more positive from the influx of calcium ions in phase 0, these calcium channels begin to close thereby reducing the influx of calcium.

The action potential will then “plummet” as the voltage across the cell membrane becomes more negative.

This causes the cell to repolarize and is phase 3 of the action potential.

We know from non-pacemaker myocytes that a plummet/repolarization phase is due to the efflux of potassium ions out of the cell.

This is the case for the plummet phase of pacemaker cells as well.

Calcium channels have closed and potassium channels are open leading to an efflux of potassium ions and repolarization.

Phase 3 = “Plummet” phase of action potential = Potassium ion efflux

Phase 3 is the “plummet” phase in which the voltage across the cell membrane becomes more negative (repolarizes) due to the efflux of potassium ions.

“Resting” Phase = Phase 4

Unlike the atrial/ventricular myocytes, pacemaker cells do not have a true “resting phase”.

During phase 4, the pacemaker cells continue to become more positive due to baseline influx of positive ions until a threshold voltage (-40 mV) is met thereby generating the next action potential.

Phase 4 occurs when the voltage across the cell membrane slowly becomes more positive until the next action potential is generated.

Practical Applications

Antiarrhythmics

The various phases of the action potentials of cardiac muscle cells and pacemaker cells provide opportunity for medications to act, and this is exactly how antiarrhythmics work.

There are 4 different classes of antiarrhythmics including: sodium channel blockers (Class I), beta blockers (Class II), potassium channel blockers (Class III), and calcium channel blockers (Class IV).

Each class of medication functions by blocking different phases of the cardiac myocyte and pacemaker cell action potentials.

Problems with the conduction system of the heart can lead to heart blocks or dysrhythmias.

Conduction disorders can affect the SA node (sick sinus syndrome), the AV node (1st, 2nd, and 3rd degree AV blocks), and the bundle branches (right or left bundle branch blocks).

There are also disorders of the ion channels that can lead to long QT syndrome and Brugada syndrome.

Increased sympathetic activity stimulates beta adrenergic receptors in the heart to increase heart rate and cardiac contractility by increasing the slope of phase 4 in pacemaker cells and augmenting phase 2 in non-pacemaker cells respectively.

Parasympathetic activity stimulates the muscarinic cholinergic receptors in the heart to normalize heart rate by slowing the rate of depolarization.

Conclusion

Hopefully this helped you better understand cardiac action potentials.

Remember “summit, plummet, continue, plummet” for non-pacemaker cardiac myocytes (such as atrial and ventricular myocytes).

Atrial and ventricular myocyte action potentials have a phase 0 (summit = sodium in), phase 1 (plummet = potassium out), phase 2 (continue = calcium in), phase 3 (plummet = potassium out), and phase 4 (resting phase).

Remember “climb and plummet” for pacemaker cells (such as SA node and AV node).

Pacemaker cell action potentials do not have a phase 1 or 2 as there is no need for contraction. Their action potentials have a phase 0 (climb = calcium in), phase 3 (plummet = potassium out), and phase 4 (“resting” phase).

Before You Go, Make Your Medical Experience Easier!

If you enjoyed the content in this post, don’t forget to join the EZmed community for free on the bottom of the page or in the navigation bar so you don’t miss out on future medical topics made easy.

Boost your medical knowledge, perform well on exams, and keep up with your medical education throughout your career using:

High yield EZmed content on Instagram: @ezmedlearning

EZmed animations and videos on YouTube: Ezmed

EZmed Illustrations and flashcards on Pinterest: ezmedlearning

Feel free to use the contact button to reach out with any feedback or suggestions you may have for future topics. Thank you for using EZmed!


Results

Distribution of the analyzed parameters

In the first step, the estimated parameters were analyzed using the normality Shapiro-Wilk test to verify their distribution to be normal or not normal. The normality of the distribution has been rejected for all analyzed parameters in subsequent age groups and registration conditions. The visual inspection into the distribution of the individual parameters shows their tendency to be rather log-normal than normal (see the exemplary distribution of VCoPM in "Fig 2"). Thus, the analysis has been repeated for the logarithms of the individual parameters analyzed. The exemplary distributions for the logarithms of the parameters are presented in "Figs 3 and 4". "Fig 3" shows the close to normal distribution of LVCoPM, and "Fig 4"–for LECoP. Similar tendencies have been observed for all of the analyzed parameters.

vCoPM ZC denotes the value of vCoPM in the given ZC point and VCoPM denotes the mean over all the ZC points in the given signal. Values for all patients and their registration conditions are presented. The distribution is log-normal rather than normal.


Methods

Heart preparations

Littermate control (LMC) and transgenic rabbits were injected with buprenorphene (0.03 mg kg 𢄡 i.m. ), acepromazine (0.5 mg kg 𢄡 i.m. ), xylazene (15 mg kg 𢄡 i.m. ), ketamine (60 mg kg 𢄡 i.m. ), pentothal (35 mg kg 𢄡 i.v. ) and heparin (200 U kg 𢄡 ). After appropriate level of anaesthesia was obtained as determined by corneal reflex and response to painful stimuli, rabbits were killed via beating heart harvest. To preserve uniformity in our sample and to avoid the potential differences that sex hormones may generate, we chose only male LQT2 and LMC rabbits weighing 𢏃.5𠄵.5 kg. Due to shared resources with other investigations, rabbits were obtained and studied from three different litters over a 10 month period. This investigation conformed to the current Guide for Care and Use of Laboratory Animals published by the National Institutes of Health (NIH Publication No. 85-23, revised 1996), as well as the standards recently delineated in this journal (Drummond, 2009), and was approved by the Animal Welfare Committee at Rhode Island Hospital.

The heart was excised from the chest and retrogradely perfused through the aorta with (in mmol l 𢄡 ) 130 NaCl, 24 NaHCO3, 1.0 MgCl2, 4.0 KCl, 1.2 NaH2PO4, 5 dextrose, 25 mannitol, 1.25 CaCl2, at pH 7.4, gassed with 95% O2 and 5% CO2. In total, 10 rabbits were studied: littermate control (n= 5) and LQT2 (n= 5). Temperature was maintained at 37.0 ± 0.2ଌ and perfusion pressure was adjusted to � mmHg with a peristaltic pump (Radnoti Glass Technology, Monrovia, CA, USA). Hearts were placed in a chamber to maintain temperature, and to reduce movement artifact 5 μmol l 𢄡 blebbistatin was added to the perfusate (Fedorov et al. 2007).

Optical mapping

The optical apparatus has been previously described (Choi et al. 2007). Fluorescence images from the anterior surface and LV free wall of heart were focused on a CMOS camera (100 × 100 pixels, Ultima-L, Scimedia, Japan) with a 50 mm Nikon f/1.2 lens which results in the field of view of 1.5 cm × 1.5 cm Fig. 1A ) with a spatial resolution of 150 μm × 150 μm. Excitation light was illuminated through a dichroic box located between the camera lens and the camera. Sampling rate was set to 1000 frames s 𢄡 and data was analysed with a custom built software using Interactive Data Language (ITT Visual Information Solutions, Boulder, CO, USA). Hearts were stained with a voltage sensitive dye, di-4 ANEPPS (Invitrogen, Carlsbad, CA, USA), using 25 μl of stock solution (1 mg ml 𢄡 of dimethyl sulfoxide, DMSO) delivered through a bubble trap, above the aortic cannula. ECG and perfusion pressure were continuously monitored (Powerlab, ADInstruments, Colorado Springs, CO, USA). Hearts were monitored for adequate perfusion throughout the study by visual inspection for pink hue, homogeneous fluorescence and action potential shape (with prominent plateau phase). Typically, data sampling was begun 10 s post-change in pacing CL and was completed within 30 s of rate change (see protocol below).

A, typical heart field of view (1.5 cm × 1.5 cm, red square) is represented by the cartoon with the position of left anterior descending artery. B, sample fluorescence recording. a, APD at 350 ms CL in LQT2 was substantially longer than LMC (see text for further detail). b, the decrease of CLs triggered APD alternans in both LMC and LQT2 (CL = 160 for LMC and 190 for LQT2 in the examples provided). C and D, APD restitution in LMC and LQT2, respectively. APDs were averaged from all pixels in the field of view and plotted against CLs. At short CLs, APDs alternate between long (□) and short (▪). The slope of APD restitution was measured from even beats with short APDs.

Stimulation protocol

All hearts were initially challenged with our standard protocol (Banville & Gray, 2002 Hayashi et al. 2007 Brunner et al. 2008) of decrement in pacing CL consisting of 10 ms steps with progressively shorter cycle length (CL) until loss of 1: 1 capture or VF induction. Shortening of CLs induced alternans in both LMC and LQT2 (see Fig. 1B ). While this standard protocol consistently generated DA in the LQT2 rabbits, it usually failed to generate DA in LMC rabbits. Only 1 of 5 LMC hearts demonstrated DA with this standard protocol, in contrast to 5 of 5 LQT2 hearts (P= 0.024 compared to LMCs). Since we were interested in comparing the mechanism by which DA can occur in the arrhythmia prone LQT2 hearts and normal controls, we further refined our stimulation steps (𢏂𠄵 ms instead of 10 ms) to increase DA induction in LMC hearts as previously done in the rabbit heart (Hayashi et al. 2007). With this more gradual decrement in pacing CL, 3 of the 4 remaining LMCs demonstrated DA. Thus, combining both protocols a total of four LMC and five LQT2 hearts demonstrated DA. These nine hearts were used in analyses comparing mechanisms of DA.

Data analysis

The activation and repolarization time points at each site were determined from fluorescence (F) signals by calculating (dF/dt)max and (d 2 F/dt 2 )max, which has been shown to coincide with �% repolarization to baseline and recovery from refractoriness (Efimov et al. 1994). Data were filtered using a spatial Gaussian filter (3 × 3 pixel) and first/second derivatives (dF/dt, d 2 F/dt 2 ) were calculated using polynomial filter (3rd order, 13 points). Pixels with low signal-to-noise ratio determined by (dF/dt)max (lower than 3 ×σ of baseline) and outliers of pixels determined by Grubbs's test were removed from the analysis (typically less than 1% of total pixels). APD dispersion was defined as APD|max – min| across the field of view.

Figure 1B shows sample traces from LMC and LQT2 rabbits during baseline and APD alternans. Note that the degree of APD oscillation was greater in LQT2 compared to LMC. Furthermore, during alternans, the action potential rise in some traces occurs before full recovery of the previous action potential as shown in Fig. 2A . This phenomenon is likely to have been due to spatial and depth summation of the optical signals from a surface area of 150 μm × 150 μm and depth of � μm. In addition, light scattering and the spatial filter used (see above) may cause further signal summation (Bray & Wikswo, 2003 Mironov et al. 2006 Pertsov et al. 2006 Bishop et al. 2007a,b). In such a case, (d 2 F/dt 2 )max cannot be used to reliably detect repolarization time points, and instead 75% recovery time was used to measure repolarization and repolarization dynamics. The diastolic interval using 75% APD recovery can be overestimated at high CLs, thus affecting APD restitution plots. To avoid this issue, we generated plots of APD restitution by plotting APD as a function of activation interval (AI) at the site of recording, rather than diastolic interval (DI). During alternans, two y values exist for each x value at the same pacing CL. We defined the slope of APD restitution as the slope of the linear regression line generated using the shorter APD during alternans at the four shortest pacing CLs achieved ( Fig. 1C and D ). APD restitution dispersion was defined as |max – min| of this slope across the field of view. Although this slope is not the correct restitution slope, the slope of APD restitution as defined here is sufficient to represent spatial dispersion trends and heterogeneous APD restitution in the heart. Note that in Fig. 1D , LQT2 exhibits APD shortening in both even and odd beats during alternans. This is due to the occurrence of DA (see details in Result), where long and short APD across the field of view occur in both even and odd beats and are averaged together.

A, nodal line detection using 㥊PD. a, APD alternans in an LQT2 heart. b, phase of alternans at each pixel was represented as +1 when the following APD is longer, 𢄡 when the following APD is shorter, and zero when 㥊PD is within small variation (υ%) (black line). c, after filtering alternans phase maps with a 15 × 15 Gaussian filter, contour lines were drawn along the zero phase (black) to divide two regions alternating out of phase (red and green). B, nodal line detection using cross-correlation. a, signal from reference location (red) at top trace, overlapped with a trace from a nodal line region (black) and out-of-phase region (green). b, cross-correlation will give the maximum correlation when a time delay between two signals is introduced such that their overlap is optimized. When discordant alternans occurs, two locations that are out of phase will have maximum correlation at the delay of one cycle length, signifying APD oscillation is out of phase (see green lines in the trace and cross-correlation plots). When a region with APD alternans is cross-correlated with a nodal line region, maximum correlation remains constant at delay the one cycle length (black). c, contour lines are drawn separating out of phase regions. Both methods showed compatible patterns of nodal lines.

Local conduction velocity (CV) vectors were calculated for each pixel from the differences in activation time-points of that pixel (determined from (dF/dt)max) and its 7 × 7 nearest neighbours, as previously described (Efimov et al. 1994). Local conduction velocities were averaged and represented as means ± standard deviation. Local CV can be overestimated when two wave fronts collide, transmural conduction occurs, or near the stimulation site where a small area of tissue was stimulated simultaneously. To correct this error, CVs greater than 1.0 m s 𢄡 were removed from mean/standard deviation statistics. CV restitution as a function of pacing CL was also analysed. Nodal lines were detected automatically. This algorithm was previously used to construct nodal lines in computer modelling studies (Echebarria & Karma, 2007) and our high signal to noise ratio (100: 1) allows us to apply the same algorithm to detect small changes in APD during alternans correctly (see Results for details). The norm vector of each pixel on a nodal line was calculated and compared with the CV vector obtained from the activation map by generating the angle of incidence between the two vectors (Jammalamadaka & SenGupta, 2001).

Statistical analysis

Normally distributed continuous variables were compared using Student's unpaired t test. Angle of incidence between vectors in LMC and LQT2 rabbits was compared using a Mann–Whitney test. Categorical values were compared using a Fisher's exact test. Statistical significance was set at P < 0.05. Mean data in the manuscript are represented as ±S.D.


How do super-Avogadro dilutions in Homeopathy work?

Scientific plausible mechanism of biological action and pathways of 'potentised high dilutions'

How &lsquosuper-avogadro dilutions&rsquo in homeopathy stimulate the biological activity (immunological and inflammatory reactivity) and pathways (supra-cellular and sub-cellular), and restore the homeostatic mechanism?
Memory of Unique Water structure, Potentisation, Quantum Macro Entanglement Model, Corporeal Signifiers
Keywords: Quantum Coherance Domains, nanostructures, nanotechnology, Properties & Structure of Water, supramolecular
Key Persons: G.O. Barnard, Jacques Benveniste, G S Anagnostatos, Elia Vittorio, Rustom Roy, Harald Walach, Luc Montagnier, Prashant S Chikramane, Wolfgang Ludwig


RESULTS

This study represents experimental data recorded from November 2003 to May 2007. Throughout the study we recorded intracellularly 147 movement-sensitive neurons in the optic lobe of the crab, from which 98 could be well characterized physiologically and 36 were successfully stained. This report is based on those neurons that were successfully recorded for ≥1 h. As illustrated throughout this paper, all stained neurons showed a general pattern consisting of an extensive tangential arborization in the lobula, with the somata located in the cell body cluster between the lobula and the lateral protocerebrum, and the axon exiting the optic lobe through the protocerebral tract. Despite these commonalties, four distinguishable cell morphologies were repeatedly observed. An analysis of physiological characteristics of the stained cells revealed clear relationships between each morphological identity and certain intrinsic cell properties and response characteristics. Thus we were able to recognize any one of the four types based solely on its electrophysiological behavior. Before outlining the particular characteristics of each of the different cell types, we describe their common features.


Conclusions

This paper has highlighted a number of different kinds of evolutionary and adaptive techniques used to exploit dynamics in the creation of embodied behaviours.

The experiments on evolving FPTA controllers for a visually guided robot, described in Section 3 demonstrated three things. First, it is possible to evolve, directly in hardware, component level analog electronic circuits to generate non-trivial visually guided sensorimotor behaviour in a mobile robot. More generally, it was established that concise evolved transistor-based circuits could successfully coordinate sensory input and actuator output to produce robust behaviour even when the sensors and actuators were low-grade, noisy and unreliable. By integrating visual feature extraction and selection into the evolutionary approach, highly robust embodied sensorimotor dynamics emerged which were readily exploited by evolution.

Second, and perhaps most interesting, controller circuit analysis and comparative experiments established that the successful evolved circuits exploited the rich dynamics of the FPTA hardware medium. The evolved solutions to non-trivial visual navigation tasks can be viewed as dynamical systems with (behavioural) attractors that result in completion of the task regardless of start conditions [42, 53]. The continuous analog medium of the FPTA seems a particularly good substrate to enable the evolution of such attractors. This possibility of rich unconventional dynamics to be exploited is a large part of what makes the FPTA a highly evolvable medium for this kind of application. Naively it might be thought that the large search space defined by the FPTA genetic encoding used would make it much more difficult to find solutions than for the more constrained, smaller search space of the fixed-architecture CTRNN controllers, which were also rich with dynamics. Comparative experiments showed this was not the case, with the FPTA being significantly more evolvable. The unconventional, potentially complex, dynamics afforded by the physical properties of the hardware medium, increases the degeneracy of the FPTA as an evolvable substrate. We use degeneracy as it is applied to biological systems [34, 120]: multiple, often interacting, ways of achieving an outcome (in this case implying many different, easily accessible, routes through the fitness landscape towards high fitness areas). Degeneracy has been shown to greatly boost evolvability [54].

Third, with a carefully constructed, special kind of simulation, it was possible to evolve robot controllers that transferred seamlessly to the real world. Our methodology involved refining the simulation in light of problems with early transfers (making sure the visual latency matched that of the physical robot, and the severe limitations introduced by errors in the vision turret, and so on, were replicated in the simulation). The robustness and generality of evolved behaviours was such that the robot controllers could handle unseen variations in the environment and continued to perform well when used in completely different environments [40], thus exhibiting behavioural resilience.

The ant-inspired navigation algorithms described in Section 4 provide insights into the way insects navigate with low resolution vision and modest neural resources. Their successful demonstration on robots operating in dynamic outdoor environments also shows that they can form the basis of autonomous robot navigation systems in applications where processing is at a premium (e.g. planetary exploration), or GPS and mapping data is unavailable or infeasible (and hence makes SLAM approaches [119] difficult). In summary, this research shows that taking inspiration from insects and taking advantage of the embodied dynamics of innate behaviours allows a parsimonious approach and simple algorithm which does not require precise place recognition. By removing the need for localisation, we can use a simple ANN trained for familiarity and not image recognition, meaning that all computation can be performed on board a small autonomous robot. The next stages are to take further advantage of the bio-inspired embodied dynamics and to 1) embody the image search process using sinuous paths modulated by the visual input [111] 2) optimise the visual processing by copying insect eyes [83] and 3) add temporal dynamics into the ANN [60].

The modular coupled oscillator control architecture described in Section 5 has been shown to be highly effective in a number of ways. First, adjustable chaos is generated at all levels of the embodied neuromechanical systems being controlled, and is exploited to power a performance-directed exploration of the space of possible motor behaviours. Second, this exploration and discovery of high performing behaviours does not require any prior or built-in knowledge of the robot body morphology or the properties of the environment. The control architecture automatically adjusts itself to whatever body-environment system it is connected to, as long as the basic setup is as illustrated in Figs. 8 and 9 homeostatic sensory adaptation being a crucial part of the system. Third, neuromechanical systems in this class are resilient: they are able to compensate in realtime to bodily damage, failures and changes to the environment, rapidly finding new control patterns that produce the desired behaviour.

Most other approaches to the development of resilient machines, for instance from the field of evolutionary robotics, make use of some form of self-model [16, 27]. Evaluations based on the model guide an explicit search process where possible new behaviours are tried out in an internal simulation. As the size of the system increases this approach can become computationally expensive and time consuming and requires significant amounts of a priori knowledge of the robot and its environment. In contrast, the chaotic exploration method is model-free, it requires no expensive internal self-simulations or a priori knowledge, and occurs in realtime.

The evolutionary robotics approach, as exemplified by the work described in Sections 3 and 6, can discover highly unconventional systems when it is unconstrained. For instance the evolved FPTA control circuits did not have to conform to some pre-specified architecture. When properties, including the morphology, of the sensors and/or the robot body are coevolved with the controller (as in Section 3.1), a powerful shaping and harmonising of all levels of dynamics underlying behaviour can be achieved. But this comes at a cost – very large numbers of robot evaluations must be undertaken. In contrast the chaotic exploration approach is much more efficient, occurring in realtime through the intrinsic dynamics of the control architecture, without the need for costly offline evaluations. In this case the architecture is constrained and pre-specified (if very general), but its potential applications are nonetheless widespread (any system that can conform to the scheme shown in Fig. 8).

Interestingly, there is a closer relationship between evolutionary search and chaotic exploration than may at first be obvious [106]. In fact the overall chaotic exploration process has a number of parallels with evolutionary dynamics. The whole system (literally) embodies a population of (motor behaviour) attractors which is sampled by chaotic exploration. The proprioceptor-driven homeostatic adaptation process warps (mutates) the state space such that a new landscape of attractors is created, but one that inherits the major properties of the previous (ancestor) landscape (replication with variation). The process repeats with the new population being sampled by chaotic exploration (Fig. 8). Since the population of attractors is effectively implicit – the intrinsic dynamics of the system drive it to sample the space of attractors – our embodied system can be thought of as a kind of generative search process. The overall brain-body-environment system (literally) embodies a population of motor pattern attractors through its dynamics it cannot help but sample them during the exploration phases. This is loosely analogous to the generative statistical models used by Estimation of Distribution Algorithms (EDAs) [72, 92], which are well established as part of the evolutionary computing canon. Instead of using an explicit population of solutions and the traditional machinery of evolutionary algorithms, EDAs employ a (often Bayesian) probabilistic model of the distribution of solutions which can be sampled by generating possible solutions from it. Search proceeds through a series of incremental updates of the probabilistic model guided by feedback from sampled fitness. In an analogous way our generative system (the overall system dynamics) is incrementally updated in relation to evaluation based feedback. The overall system dynamics is the generative model, the exploration phase is the sampling step, with the performance evaluation, E, controlling a selection pressure, and the homeostatic adaptation process provides a kind of mutation which facilitates the replication (with variation) of the whole phase space, now containing a slightly different population of attractors but with a bias towards preserving more stable and fitter areas. This work thus points towards the possibility of intrinsic mechanisms, based entirely on neuro-body-environment interaction dynamics, that might be involved in creating Darwinian processes that could continually run within the nervous systems of future robots [35].

To some extent morphology is important to all of the case studies used in this paper. Be it the way the sensor morphology co-evolves with the robot controllers in the FPTA study, or the behavioural strategy relies on morphological constraints in the ant-inspired navigation work, or the way in which continually changing wing and tail morphologies generate beneficial airflow patterns in the flapping wing flyer example. In common with the use of chaotic exploration for the development of locomotion behaviours, in all these cases information processing is not located solely in the nervous system of the machine it is spread out over the brain-body-environment system. Some strands of work in soft robotics seek to push this idea further, to blur the line between body and nervous system even more, with greater amounts of processing offloaded onto the body [15, 49, 58, 59].

The behaviours described in this paper, although robust and resilient, are still fairly simple. The dynamics exploited, although often complex, are limited when compared with those used in many animal behaviours. There is still much to explore in the two-way exchange between biology and robotics.