Computational simulation of the heart Edmund Altman 2010/2011

Size: px
Start display at page:

Download "Computational simulation of the heart Edmund Altman 2010/2011"

Transcription

1 Computational simulation of the heart Edmund Altman 2010/2011 The candidate confirms that the work submitted is their own and the appropriate credit has been given where reference has been made to the work of others. I understand that failure to attribute material which is obtained from another source may be considered as plagiarism. (Signature of student)

2 Abstract In an ideal world there would be a complete computational simulation of the human body. There would be no need for medical testing as drugs could be trialled using the computational model instead of being tested on animals or humans. Although this ideal situation is a long way from reality, there are a lot of people working on creating models of particular parts or systems of the human body. One of the areas that has a lot of research put into it is simulations of the heart. In this project I will examine the biology behind how the heart works, examine existing heart models and attempt to recreate some of existing heart models.

3 Acknowledgements I would like to sincerely thank Matthew Hubbard for his help and guidance in writing of this project and with my code. I would also like to thank David Duke for his input and comments on my mid-project report.

4 Contents 1 Introduction Project Aim Objectives Minimum requirements Deliverables Schedule Proposed plan Final plan Background reading Anatomy of the heart Origins of heart modelling Current heart models Cell models Tissue models Anatomical models Implementation Single Cell One dimensional model Two dimensional model Evaluation Further work A Appendix A - Personal reflection 27 B Appendix B - Code 28 B.1 fitzhugh.m B.2 fitzplot.m

5 B.3 fhn1d.m B.4 fhn2d.m

6 Chapter 1 Introduction 1.1 Project Aim An ideal goal for biomedical research would be to produce a computational model of the entire human body, which modelled all of its different systems, organs and structures. If this idealistic model was accurate then it could mean the end of long, expensive medical trials which may cause harm to the participants. Unfortunately this goal is a very long way away, but research groups around the world have been working towards making computational models of smaller parts of the body such as the heart. The field of cardiac modelling has been around for around 60 years and in this project I intend to investigate other people s work in this field, and reproduce some of these models myself. Using these computational models I hope to study the heart dysfunctions such as types of Arrhythmia, and go on to produce these models on much larger domains to see if their behaviour changes. 1.2 Objectives The key objectives of this report are as follows: Investigate current cardiac models Gain an understanding of the biochemistry behind basic heart function Produce my own results from existing cardiac models 1.3 Minimum requirements The minimum requirements that I specified for this project are as follows: Simulate at least one single cell model 3

7 Simulate diffusion across cells in 2D Reproduce a spiral wave pattern 1.4 Deliverables The final project report Results from my reproductions of existing cardiac models, for a single cell and in one or two dimensions Any code written to produce these results 1.5 Schedule Proposed plan I constructed a Gantt chart in order to plan out a schedule for when I will complete each section of work. Figure 1.1: Project Schedule Final plan Due to certain problems that are mentioned in appendix A, my schedule ended up as this. 4

8 Figure 1.2: Project Schedule 5

9 Chapter 2 Background reading 2.1 Anatomy of the heart The heart is an integral part of the circulatory system that pumps blood around the body, providing muscles, other organs and the brain with oxygenated blood. The heart is a muscular organ that rhythmically contracts and relaxes to act as a pump for the circulatory system. The walls of the heart are made up of involuntary cardiac muscle, which is mainly constructed of myocytes [1]. These are the base cells of muscles that contract and relax on a cellular level to contract and relax the muscle as a whole. This is accomplished by the movement of ions across the cell membrane through ion channels. The movement of these ions causes a change in voltage of the cell membrane which creates an action potential. Ion channels are gates in the cell membrane present in all biological cells. They control the movement of ions in and out of the cell which controls all of the cells functions. The main ions that move across the cell membrane are Sodium (Na + ), Potassium (K + ) and Calcium (Ca ++ ) [2]. These ion channels are integral to cell function that many pharmaceuticals specifically focus on altering certain ion channels to give their desired effect. Current drugs that affect ion channels are local anaesthetics which selectively inhibit sodium channels, and anti-epileptic drugs focus on inhibiting sodium and calcium channels [3]. The combined effects of the movement of these ions changes the voltage of the cell membrane which directly affects whether a myocyte will contract [4]. Incorrect movement of ions can lead to heart dysfunction such as Ventricular fibrillation, which is a life-threatening condition where the hearts rhythm becomes disordered and the heart fails to pump blood correctly. When a myocyte enters an excited state through changes to it s action potential from ion channels it contracts by 20% in the direction of the muscle fibres [5]. Cardiac cells are not self-excitatory, they require an external stimulus to function at all. This external stimulus is provided in the sino-atrial node of the heart which functions as a pacemaker [6]. 6

10 2.2 Origins of heart modelling Cardiac modelling started in the 1950 s when Alan Hodgkin and Andrew Huxley published the Hodgkin-Huxley model that described the ionic mechanisms of giant squid axons [7]. Many cephalopods such as the squid have evolved especially large axons which it uses to control its muscles. An axon is the part of a neuron that transmits information to other cells, and it works using ion channels, similar to cardiac muscles. The axons in squids are of comparable length to those found in other animals, but have a far greater diameter. For example most axons in humans are between 2µm and 20µm in diameter, but the Squid giant axon is between 250µm and 750µm. For normal fibers, the thicker the axon, the higher the conduction rate as shown in figure 2.1. This thicker axon allows the Squid to make very rapid movements, possibly to escape potential predators [8]. Figure 2.1: Diameter of animal axons against conduction rate The additional advantage of the giant axon is that it was physically big enough for Hodgkin and Huxley to attach electrodes to the axon and measure the action potential across the cell membrane. This allowed them to gather detailed findings about the ion channels of cells. 2.3 Current heart models In this section I will discuss different cardiac models and their applications. 7

11 2.3.1 Cell models Cardiac cell models attempt to model each individual cell as a separate entity with their own interactions. Ideally these will model all the processes of the cardiac cell, mainly their action potential, but ideally including all ion channels. Simplified models In some cases we may not want to have a completely realistic model of cells, a simplified model would be sufficient and would make any computations far more efficient. The first model that I studied was the Fitzhugh Nagumo model which is a simplified twovariable model, based on the Hodgkin-Huxley model for Giant Squid Axons. It was constructed in 1961 by Richard Fitzhugh and J. Nagumo. V t = 2 V + (a V )(V 1)V v x2 (2.1) v = ɛ(βv αv δ) t (2.2) This model reduces the complexity of the ion channels and instead represents the cells functions through a voltage variable (2.1) and a recovery variable(2.2) [9]. The simplicity of the Fitzhugh-Nagumo model was the main reason for choosing this model to implement myself first. Complex models On the other end of the spectrum we have complex cell models which aim to not simplify at all, instead representing every ion channel and process within the cardiac cells. These models are far more computationally expensive but give a deeper understanding of cell dynamics. The Luo-Rudy model is an exceptionally complex model that models all of the ion channels plus many intercellular interactions. Figure 2.2 shows all of the separate ion channels and extra cell processes that it models Tissue models The behaviour of the individual cells working together over a large area of tissue has additional effects to the hearts behaviour. There are two models for cardiac tissue: Monodomain model The monodomain model is a simpler representation which ignores extracellular space and only represents the cells and their individual behaviours through ion channels. 8

12 Figure 2.2: Diagram of ion channels represented in the Luo-Rudy model [10] Bidomain model The bidomain model also considers the extracellular space which changes from the contraction and relaxation of the cells over an area. This has effects on diffusion of ions as cells are pushed closer together during contraction, and apart during relaxation Anatomical models Anatomical models consider cardiac modelling as a three-dimensional problem and attempt to fit cell models and tissue models onto a three-dimensional mesh. This includes modelling the orientation of muscles fibres, and ideally the position of the sinoatrial node. [9] 9

13 Chapter 3 Implementation This section contains the work I made towards studying existing heart models. I wrote all the code myself as to get a better understanding of the problem. I decided to write the code in matlab for easier prototyping and testing, and so I could focus more on the models and quickly get graphical results of them 3.1 Single Cell I constructed the Fitzhugh-Nagumo model (2.1)(2.2) for a single cell in Matlab. I used the forward Euler method to calculate the value of each variable at the following timestep, and used Dirichlet boundary conditions, where both boundaries were set to 0. In figure 3.1 a small stimulus is provided at 100 timesteps, which causes the voltage variable in red to spike and then rapidly fall. While the voltage variable is hitting its minimum point, the recovery variable peaks at 0.18, then the two variable converge back to zero. This process of spiking and then converging to zero represents a myocyte (cardiac cell) contracting and then relaxing. In figure 3.2 I experimented with introducing stimuli at different times. Here I introduced a stimulus at 300 timesteps and another at 500 timesteps before the system had converged back to zero. The gap between stimuli was sufficiently large in this case that although the second spike is slightly different in shape, the system still reacted in a similar way. In figure 3.3 I introduced a stimulus at 100 and then shortly after at 180 timesteps. This was too soon after the last stimulus and the system failed to react properly, and it did not produce a second spike from the second stimulus. 3.2 One dimensional model I then implemented the Fithugh-Nagumo model in 1 dimension with a computational mesh of 100 cells, and introduced a small stimulus at the centre cell in figure 3.4. I used dirichlet 10

14 Figure 3.1: Fitzhugh-Nagumo with a single stimulus at 100 timesteps Figure 3.2: Fitzhugh-Nagumo with two stimuli at 300 timesteps and 500 timesteps 11

15 Figure 3.3: Fitzhugh-Nagumo with two stimuli at 100 timesteps and 180 timesteps boundary conditions for simplicity, and I used central differences to discretise the diffusion term. The central stimulus affected the adjacent cells causing a ripple effect in both directions which continued with the same magnitude until it reached the boundary. The voltage for each cell behaves in the same way as the single cell demonstration as after spiking from stimulus, the voltage negative then slowly converges back to zero. This demonstrates the way that a cardiac cell being stimulated stimulates adjacent cells and propagates a wave outwards from the point of stimulus. 3.3 Two dimensional model Now that I have constructed my model in 1 dimension, I can take the model further and make it into a two dimensional model. The ripple effect that I observed in my one dimensional model doesn t apply in the same way though. As discussed in the background reading section, the Sino-Atrial node generates a stimulus in the heart that makes the heart beat. This impulse from the Sino-Atrial node causes a spiral wave effect on the heart tissue which I will attempt to recreate. For a spiral wave to form I had to change several aspects of my model. Dirichlet boundary conditions will make it impossible to create the spiral wave, so I had to implement homogeneous Neumann boundary conditions to prevent the boundaries of the domain affecting the spiral wave 12

16 Figure 3.4: Fitzhugh-Nagumo implemented in 1 dimension at 50 timesteps 13

17 Figure 3.5: Fitzhugh-Nagumo implemented in 1 dimension at 300 timesteps 14

18 negatively. One way to induce this spiral wave is to set the grid up so that the left half of the domain has the u, the voltage variable, set to 1. And in the lower half the of the domain v, the recovery variable should be set to 0.5. This setup is shown in figure 3.6. Figure 3.6: 2D model - initial setup This should be only left for a short amount of time, and then have both these sections wiped to zero. This will leave a single wave, as shown in figure 3.7. This wave propagates forward and through diffusion and the chain-reaction effect of the Fitzhugh-Nagumo model a spiral wave is created. This effect is shown in figures 3.8 to I have changed the visualisation to be displayed from the top down, so that is easier to observe the spiral wave form. 15

19 Figure 3.7: 2D model - initial wave 16

20 Figure 3.8: 2D model - Spiral wave 1 17

21 Figure 3.9: 2D model - Spiral wave 2 18

22 Figure 3.10: 2D model - Spiral wave 3 19

23 Figure 3.11: 2D model - Spiral wave 4 20

24 Figure 3.12: 2D model - Spiral wave 5 21

25 Chapter 4 Evaluation The goal of this project was to study heart simulation models to better understand them, and to possibly apply this knowledge to investigating heart dysfunction. I believe that I ve accomplished the first part of my aims, but I have fallen short on coming close to achieving the second part. I recreated the Fitzhugh-Nagumo model and gauged it s accuracy based on other recreations of the model that I have found. The best recreation of the Fitzhugh-Nagumo model that I found on Flavio Fenton, and Elizabeth cherry s website, thevirtualheart.org [11]. Figure 4.1 shows the results that they produced, and if you look back to my own recreation of Fitzhugh-Nagumo as a single cell model in figure 3.1 you can see the similarities. Figure 4.1: Fitzhugh-Nagumo model - Thevirtualheart.org Attempting to replicate these results I discovered some of the limitations of the model. Larger values of dt caused instability in the model and produced useless results. This was due to the way that the forward Euler method works, in that there is a maximum value of dt that 22

26 the model will take, and any more than that will cause instability and bad results. Once I had created the model in 1 dimension, I just expanded on the code on top of the model to first apply it across 100 cells in 1 dimension (figures 3.6 to 3.7). With a bit of special setup, I was able to recreate the spiral waves that I had deemed to be my final minimum requirement. The 2 dimensional model remains true to the original model, and the single cell behaviour is clearly visible if seen from an angle, such as in figure 4.2. Figure 4.2: 2 Dimensional Fitzhugh-Nagumo from an angle Changing the variables of the model can produce different spiral wave results. For example, increasing the diffusion rate by a factor of three results in a much thicker spiral wave, as shown in figure Further work If I had the chance to do this project again and have the time to take the work further than the minimum requirements there are several areas that I would have liked to study. I m personally interested in computer graphics, and I would ve liked to get a simulation of a very large domain, or one of very fine detail. This could produce some interesting results, 23

27 Figure 4.3: 2 Dimensional Fitzhugh-Nagumo with triple diffusion 24

28 but would involve a lot of extra work as realistically I would have to stop using matlab. I used matlab to start with because it s perfect for quickly trying ideas out and then visualising them with matlab s built in tools, but I would have to write the software in C for it s greater efficiency and speed. Another possible idea would be to write it up for GPGPU computing, perhaps using the CUDA (Compute Unified Device Architecture) by Nvidia, or another GPU computing framework. The massively parallel design of graphics processors would be perfect for a problem such as this and once the software is written could produce very fast simulations of high detail. I also would ve liked to have been able to move on from the Fitzhugh-Nagumo model and attempt to implement some of the more complex models. These complex models which represent more of the actual functions of myocytes rather than approximating them allow for much more experimentation. Implementing a model such as Fenton-Karma or even Luo-Rudy would have given me a deeper insight into heart function. But this would have meant that Ihad to spend more time on the computation side of the project as a more complex model would require far more efficient code to get results within a reasonable time frame. Implementing more complex models would also open up another area of study that I am interested in. When I was researching ion channels, I discovered that certain drugs work to specifically target individual ion channels which I think is very interesting. I would have liked to replicate the effects of a certain drug by suppressing a certain ion channel and viewing the results. And finally, I would have liked to take the model from 2 dimensional, to 3 dimensional. But as with more complex models, this would have required me to rewrite most of my code to make it efficient enough to get results in a timely manner. 25

29 Bibliography [1] R. Clayton, O. Bernus, E. Cherry, H. Dierckx, F. Fenton, L. Mirabella, A. Panfilov, F. Sachse, G. Seemann, and H. Zhang, Models of cardiac tissue electrophysiology: Progress, challenges and open questions, Progress in Biophysics and Molecular Biology, vol. 104, no. 1-3, pp , Cardiac Physiome project: Mathematical and Modelling Foundations. [2] B. Hille, Ionic channels in excitable membranes, Biophysical Journal, [3] D. J. Camerino DC, Tricarico D, Ion channel pharmacology, Neurotherapeutics, pp , April [4] C. E. Dangerfield, D. Kay, and K. Burrage, Stochastic models and simulation of ion channel dynamics, Procedia Computer Science, vol. 1, no. 1, pp , [5] M. Nash, Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias, Progress in Biophysics and Molecular Biology, vol. 85, pp , July [6] M. Boyett and H. Dobrzynski, The sinoatrial node is still setting the pace 100 years after its discovery, Circ Res, vol. 100, no. 11, pp , [7] D. Noble, From the hodgkin-huxley axon to the virtual heart, Oct [8] Robert.C.Eaton, Neural Mechanisms of Startle Behaviour. Springer, [9] R. H. Clayton and A. V. Panfilov, A guide to modelling cardiac electrical activity in anatomically detailed ventricles, Progress in Biophysics and Molecular Biology, vol. 96, pp , Jan [10] Y. Rudy, Single Cell Phenomena, [11] F. F. Elizabeth Cherry, Fitzhugh-Nagumo (FHN) model,

30 Appendix A Appendix A - Personal reflection I asked my supervisor, Matthew Hubbard on how I should approach this segment and he said Think of it as general advice to a second year who might be starting a similar type of project next year. With that in mind, I think that this project shows the importance of a proper work ethic and time management. Over the past 16 weeks I have struggled to find motivation to work on this project. I haven t shown what I believe to be my full academic potential by a long way, due to my own personal issues with time management and having any form of a work ethic. I m certain that sixteen weeks of a couple of contact hours per week helped a lot of people have the time to focus and work on their project without lectures or other educational deadlines to meet. But I think I found this made it easy to distance myself from the university and my work, and I found myself slowly slipping behind on work after the first month or so and failed to ever catch up to the point that I should have been. And from this a cycle of procrastination and guilt over said procrastination followed, and without seeking help at an early stage it s possible to fall very far behind and be a week from the deadline with nothing but your mid-project report to your name. That said, I completed my minimum requirements, but there is so much more I would ve like to add, and I ve mentioned them in the further work section of the evaluation. In some respects I really enjoyed this particular area of study, but the above issues stopped me from getting close to anything like my plans that I had for taking the project past my minimum requirements and I m really disappointed with myself for letting this happen. I would ve also liked to do a proper write-up of my work and be able to come to a proper conclusion over what I ve accomplished. 27

31 Appendix B Appendix B - Code B.1 fitzhugh.m f u n c t i o n [ du, dv ] = fitzhugh (u, v ) %FITZHUGH a = 0. 1 ; b = 0. 5 ; gam = 1 ; e p s i = ; d e l t a = 0 ; du = ( a u ) ( u 1) u v ; dv = e p s i ( b u gam v d e l t a ) ; end 28

32 B.2 fitzplot.m f u n c t i o n [ t, u, v ] = f i t z P l o t ( t0, u0, v0, t f i n a l ) % f i t z P l o t ( 0, 1, 0. 1, ) % timestep dt = ; %s e t up m a t r i c e s t = z e r o s ( t f i n a l /dt, 1 ) ; u = z e r o s ( t f i n a l /dt, 1 ) ; v = z e r o s ( t f i n a l /dt, 1 ) ; %i n i t i a l vars t ( 1 ) = t0 ; u ( 1 ) = u0 ; v ( 1 ) = v0 ; f o r i = 1 : t f i n a l / dt ct = i dt ; [ du, dv ] = fitzhugh ( u ( i ), v ( i ) ) ; u ( i +1) = u ( i ) + dt du ; v ( i +1) = v ( i ) + dt dv ; t ( i +1) = t ( i ) + dt ; i f ( ct > 100) && ( ct < 105) u ( i +1) = u ( i +1) ; end i f ( ct > 125) && ( ct < 130) u ( i +1) = u ( i +1) ; end end c l o s e a l l ; pu = p l o t ( t, u ) ; s e t ( pu, Color, red ) hold on ; pv = p l o t ( t, v ) ; 29

33 B.3 fhn1d.m f u n c t i o n [ u, v ] = fhn1d ( save, c e l l s, d i f f R a t e, stime, sduration, t F i n a l ) %fhn1d ( 0, 1 0 0, , , 0. 2, 6 ) %stime = Time o f s p i k e % This i s as a f r a c t i o n o f t F i n a l %sduration = Duration o f s p i k e s P o s i t i o n = c e l l s / 2 ; %S i z e o f problem : x l = 0 ; xr = 1 ; dx = ( xl xr )/ c e l l s ; %timestep dt = ; %s e t up m a t r i c e s u = z e r o s ( t F i n a l /dt, c e l l s +2); v = z e r o s ( t F i n a l /dt, c e l l s +2); %Boundary c o n d i t i o n s u ( 1 : t F i n a l /dt, 1 ) = 0 ; u ( 1 : t F i n a l /dt, c e l l s +2) = 1 ; %Set up animation c l o s e a l l s e t ( gca, nextplot, r e p l a c e c h i l d r e n ) a x i s ( [ 0 c e l l s ] ) x l a b e l ( C e l l s ) ; y l a b e l ( Voltage ) ; d2u = 0 ; %Loop through time f o r i = 1 : t F i n a l / dt %c t = Current time ct = i dt ; s e t ( gcf, Position, [ 2 4 0, 2 0 0, 6 0 0, ] ) s e t ( gca, PlotBoxAspectRatio, [ 1, 1, 1 ] ) 30

34 %Loop through space f o r j = 2 : c e l l s +1 %2nd D i f f e r e n t i a l d2u = d i f f R a t e ( u ( i, j +1) 2 u ( i, j ) + u ( i, j 1))/( dx ˆ 2 ) ; %Fitzhugh algorithm [ du, dv ] = fitzhugh ( u ( i, j ), v ( i, j ) ) ; du = 100 du + d2u ; dv = 100 dv ; %Update v a l u e s u ( i +1, j ) = u ( i, j ) + dt du ; v ( i +1, j ) = v ( i, j ) + dt dv ; end p l o t ( u ( i, : ) ) ; F( i ) = getframe ; f r a m e f i l e = [ frame i n t 2 s t r ( i 1)] i f ( ct >= stime t F i n a l ) && ( ct <= stime t F i n a l + sduration ) u ( 1 : t F i n a l /dt, s P o s i t i o n ) = u ( 1 : t F i n a l /dt, s P o s i t i o n ) ; s p i k e = 1 end end i f save == 1 end p r i n t ( djpeg, f r a m e f i l e ) i f save == 0 disp ( Playing the movie... ) movie (F) end 31

35 B.4 fhn2d.m f u n c t i o n [ u, v ] = fhn2d ( save, c e l l s, d i f f R a t e, stime, sduration, t F i n a l ) %fhn2d ( 0, 1 0 0, , , 2 0, ) %stime = Time o f s p i k e % This i s as a f r a c t i o n o f t F i n a l %sduration = Duration o f s p i k e %S i z e o f problem : x l = 0 ; xr = 1 ; dx = ( xl xr )/ c e l l s ; %timestep dt = 0. 5 ; %s e t up m a t r i c e s u = z e r o s ( c e l l s +2, c e l l s +2); v = z e r o s ( c e l l s +2, c e l l s +2); u D i f f = z e r o s ( c e l l s +2, c e l l s +2); v D i f f = z e r o s ( c e l l s +2, c e l l s +2); %Set up animation c l o s e a l l a x i s ( [ 0 c e l l s +1 0 c e l l s ] ) s e t ( gca, nextplot, r e p l a c e c h i l d r e n ) x l a b e l ( C e l l s x ) ; y l a b e l ( C e l l s y ) ; z l a b e l ( Voltage ) ; sa = s i z e ( u ) ; %Loop through time f o r t = 1 : t F i n a l / dt %c t = Current time ct = t dt ; %s e t ( gcf, Position, [ 2 4 0, 2 0 0, 6 0 0, ] ) s e t ( gca, PlotBoxAspectRatio, [ 1, 1, 1 ] ) %%% Neumann boundary c o n d i t i o n s 32

36 %Top boundary f o r i = 2 : c e l l s +1 u ( i, 1 ) = u ( i, 3 ) ; end %bottom boundary f o r i = 2 : c e l l s +1 u ( i, c e l l s +2) = u ( i, c e l l s ) ; end %l e f t boundary f o r i = 2 : c e l l s +1 u ( 1, i ) = u ( 3, i ) ; end %r i g h t boundary f o r i = 2 : c e l l s +1 u ( c e l l s +2, i ) = u ( c e l l s, i ) ; end %Loop through space ( x ) f o r i = 2 : c e l l s +1 %Loop through space ( y ) f o r j = 2 : c e l l s +1 %2nd D i f f e r e n t i a l d2u = d i f f R a t e ( ( u ( i, j +1) 2 u ( i, j ) + u ( i, j 1))/( dx ˆ2) + ( u ( i +1, j ) 2 u ( %Fitzhugh algorithm [ du, dv ] = fitzhugh ( u ( i, j ), v ( i, j ) ) ; du = du + d2u ; %C a l c u l a t e d i f f e r e n c e s u D i f f ( i, j ) = dt du ; v D i f f ( i, j ) = dt dv ; %Update c u r r e n t value u ( i, j ) = u ( i, j ) + u D i f f ( i, j ) ; v ( i, j ) = v ( i, j ) + v D i f f ( i, j ) ; end end mesh ( u ) ; view ( [ ] ) %Induce Stimulus f o r s p i r a l wave 33

37 i f ct < 35 u ( 2 : ( ( c e l l s + 1 ) / 2 ), 2 : ( c e l l s +1)) = 1 ; v ( 2 : ( c e l l s +1),(( c e l l s +1)/2):( c e l l s +1)) = 0. 5 ; end % Wipe 3/4 o f mesh to s t a r t s p i r a l wave i f ct >= 35 && ct < 50 u ( ( 2 : c e l l s +1),(( c e l l s +1)/2):( c e l l s +1)) = 0 ; v ( ( 2 : c e l l s +1),(( c e l l s +1)/2):( c e l l s +1)) = 0 ; u ( 2 : ( ( c e l l s + 1 ) / 2 ), 2 : ( c e l l s +1)) = 0 ; v ( 2 : ( ( c e l l s + 1 ) / 2 ), 2 : ( c e l l s +1)) = 0 ; end end 34

6.3.4 Action potential

6.3.4 Action potential I ion C m C m dφ dt Figure 6.8: Electrical circuit model of the cell membrane. Normally, cells are net negative inside the cell which results in a non-zero resting membrane potential. The membrane potential

More information

The Physics of the Heart. Sima Setayeshgar

The Physics of the Heart. Sima Setayeshgar The Physics of the Heart Sima Setayeshgar Department of Physics Indiana University Indiana Unversity Physics REU Seminar, July 27 2005 1 Stripes, Spots and Scrolls Indiana Unversity Physics REU Seminar,

More information

APPM 2360 Project 3 Mathematical Investigation of Cardiac Dynamics

APPM 2360 Project 3 Mathematical Investigation of Cardiac Dynamics APPM 2360 Project 3 Mathematical Investigation of Cardiac Dynamics Due: Thursday, December 6, 2018 by 4:59 p.m. Submit as a PDF to Assignments on Canvas 1 Introduction Cardiac Arrhythmia, or irregular

More information

A note on discontinuous rate functions for the gate variables in mathematical models of cardiac cells

A note on discontinuous rate functions for the gate variables in mathematical models of cardiac cells Procedia Computer Science (2) (22) 6 945 95 Procedia Computer Science www.elsevier.com/locate/procedia International Conference on Computational Science ICCS 2 A note on discontinuous rate functions for

More information

Lecture Notes 8C120 Inleiding Meten en Modelleren. Cellular electrophysiology: modeling and simulation. Nico Kuijpers

Lecture Notes 8C120 Inleiding Meten en Modelleren. Cellular electrophysiology: modeling and simulation. Nico Kuijpers Lecture Notes 8C2 Inleiding Meten en Modelleren Cellular electrophysiology: modeling and simulation Nico Kuijpers nico.kuijpers@bf.unimaas.nl February 9, 2 2 8C2 Inleiding Meten en Modelleren Extracellular

More information

2013 NSF-CMACS Workshop on Atrial Fibrillation

2013 NSF-CMACS Workshop on Atrial Fibrillation 2013 NSF-CMACS Workshop on A Atrial Fibrillation Flavio H. Fenton School of Physics Georgia Institute of Technology, Atlanta, GA and Max Planck Institute for Dynamics and Self-organization, Goettingen,

More information

Introduction to Physiology V - Coupling and Propagation

Introduction to Physiology V - Coupling and Propagation Introduction to Physiology V - Coupling and Propagation J. P. Keener Mathematics Department Coupling and Propagation p./33 Spatially Extended Excitable Media Neurons and axons Coupling and Propagation

More information

The Physics of the Heart. Sima Setayeshgar

The Physics of the Heart. Sima Setayeshgar The Physics of the Heart Sima Setayeshgar Department of Physics Indiana University Indiana Unversity Physics REU Seminar: August 1, 2007 1 Stripes, Spots and Scrolls Indiana Unversity Physics REU Seminar:

More information

Topics in Neurophysics

Topics in Neurophysics Topics in Neurophysics Alex Loebel, Martin Stemmler and Anderas Herz Exercise 2 Solution (1) The Hodgkin Huxley Model The goal of this exercise is to simulate the action potential according to the model

More information

Simulating Cardiac Electromechanics using Abaqus UEL

Simulating Cardiac Electromechanics using Abaqus UEL 1 Simulating Cardiac Electromechanics using Abaqus UEL Introduction From a finite elements point of view, modeling the complex beating of heart tissues involves solving strongly coupled electromechanical

More information

Electrophysiology of the neuron

Electrophysiology of the neuron School of Mathematical Sciences G4TNS Theoretical Neuroscience Electrophysiology of the neuron Electrophysiology is the study of ionic currents and electrical activity in cells and tissues. The work of

More information

Parameters for Minimal Model of Cardiac Cell from Two Different Methods: Voltage-Clamp and MSE Method

Parameters for Minimal Model of Cardiac Cell from Two Different Methods: Voltage-Clamp and MSE Method Parameters for Minimal Model of Cardiac Cell from Two Different Methods: oltage-clamp and MSE Method Soheila Esmaeili 1, * and Bahareh beheshti 1 Department of Biomedical engineering, ran University of

More information

The Department of Electrical Engineering. nkrol Mentors: Dr. Mohammad Imtiaz, Dr. Jing Wang & Dr. In Soo Ahn

The Department of Electrical Engineering. nkrol Mentors: Dr. Mohammad Imtiaz, Dr. Jing Wang & Dr. In Soo Ahn Bradley University The Department of Electrical Engineering nkrol Mentors: Dr. Mohammad Imtiaz, Dr. Jing Wang & Dr. In Soo Ahn AN ELECTRICAL ENGINEERING PERSPECTIVE OF THE HUMAN HEART This research project

More information

STUDENT PAPER. Santiago Santana University of Illinois, Urbana-Champaign Blue Waters Education Program 736 S. Lombard Oak Park IL, 60304

STUDENT PAPER. Santiago Santana University of Illinois, Urbana-Champaign Blue Waters Education Program 736 S. Lombard Oak Park IL, 60304 STUDENT PAPER Differences between Stochastic and Deterministic Modeling in Real World Systems using the Action Potential of Nerves. Santiago Santana University of Illinois, Urbana-Champaign Blue Waters

More information

Math 345 Intro to Math Biology Lecture 20: Mathematical model of Neuron conduction

Math 345 Intro to Math Biology Lecture 20: Mathematical model of Neuron conduction Math 345 Intro to Math Biology Lecture 20: Mathematical model of Neuron conduction Junping Shi College of William and Mary November 8, 2018 Neuron Neurons Neurons are cells in the brain and other subsystems

More information

Mathematical Foundations of Neuroscience - Lecture 3. Electrophysiology of neurons - continued

Mathematical Foundations of Neuroscience - Lecture 3. Electrophysiology of neurons - continued Mathematical Foundations of Neuroscience - Lecture 3. Electrophysiology of neurons - continued Filip Piękniewski Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Poland

More information

Biomedical Instrumentation

Biomedical Instrumentation ELEC ENG 4BD4: Biomedical Instrumentation Lecture 5 Bioelectricity 1. INTRODUCTION TO BIOELECTRICITY AND EXCITABLE CELLS Historical perspective: Bioelectricity first discovered by Luigi Galvani in 1780s

More information

Lecture 10 : Neuronal Dynamics. Eileen Nugent

Lecture 10 : Neuronal Dynamics. Eileen Nugent Lecture 10 : Neuronal Dynamics Eileen Nugent Origin of the Cells Resting Membrane Potential: Nernst Equation, Donnan Equilbrium Action Potentials in the Nervous System Equivalent Electrical Circuits and

More information

CSD-TR R. Samade, B. Kogan

CSD-TR R. Samade, B. Kogan The properties of the cardiac cell mathematical model with a Markovian representation of potassium channel gating processes under high pacing rate (Computer simulation study) CSD-TR040007 R. Samade, B.

More information

Nonlinear Observer Design and Synchronization Analysis for Classical Models of Neural Oscillators

Nonlinear Observer Design and Synchronization Analysis for Classical Models of Neural Oscillators Nonlinear Observer Design and Synchronization Analysis for Classical Models of Neural Oscillators Ranjeetha Bharath and Jean-Jacques Slotine Massachusetts Institute of Technology ABSTRACT This work explores

More information

Bo Deng University of Nebraska-Lincoln UNL Math Biology Seminar

Bo Deng University of Nebraska-Lincoln UNL Math Biology Seminar Mathematical Model of Neuron Bo Deng University of Nebraska-Lincoln UNL Math Biology Seminar 09-10-2015 Review -- One Basic Circuit By Kirchhoff's Current Law 0 = I C + I R + I L I ext By Kirchhoff s Voltage

More information

ACTION POTENTIAL. Dr. Ayisha Qureshi Professor MBBS, MPhil

ACTION POTENTIAL. Dr. Ayisha Qureshi Professor MBBS, MPhil ACTION POTENTIAL Dr. Ayisha Qureshi Professor MBBS, MPhil DEFINITIONS: Stimulus: A stimulus is an external force or event which when applied to an excitable tissue produces a characteristic response. Subthreshold

More information

Membrane Potentials, Action Potentials, and Synaptic Transmission. Membrane Potential

Membrane Potentials, Action Potentials, and Synaptic Transmission. Membrane Potential Cl Cl - - + K + K+ K + K Cl - 2/2/15 Membrane Potentials, Action Potentials, and Synaptic Transmission Core Curriculum II Spring 2015 Membrane Potential Example 1: K +, Cl - equally permeant no charge

More information

Simulation of Cardiac Action Potentials Background Information

Simulation of Cardiac Action Potentials Background Information Simulation of Cardiac Action Potentials Background Information Rob MacLeod and Quan Ni February 7, 2 Introduction The goal of assignments related to this document is to experiment with a numerical simulation

More information

PCMI Project: Resetting Reentrant Excitation Oscillations in Different Geometries

PCMI Project: Resetting Reentrant Excitation Oscillations in Different Geometries PCMI Project: Resetting Reentrant Excitation Oscillations in Different Geometries Elizabeth Doman mentor: John Milton summer 2005 PCMI Project:Resetting Reentrant ExcitationOscillations in Different Geometries

More information

me239 mechanics of the cell - syllabus me239 mechanics of the cell me239 mechanics of the cell - grading me239 mechanics of the cell - overview

me239 mechanics of the cell - syllabus me239 mechanics of the cell me239 mechanics of the cell - grading me239 mechanics of the cell - overview 6 mechanotransduction wong, goktepe, kuhl [2010] me239 mechanics of the cell add l information http://biomechanics.stanford.edu and coursework 1 me239 mechanics of the cell - syllabus favorite topics in

More information

Neurons, Synapses, and Signaling

Neurons, Synapses, and Signaling Chapter 48 Neurons, Synapses, and Signaling PowerPoint Lecture Presentations for Biology Eighth Edition Neil Campbell and Jane Reece Lectures by Chris Romero, updated by Erin Barley with contributions

More information

Electrophysiological Modeling of Membranes and Cells

Electrophysiological Modeling of Membranes and Cells Bioeng 6460 Electrophysiology and Bioelectricity Electrophysiological Modeling of Membranes and Cells Frank B. Sachse fs@cvrti.utah.edu Overview Recapitulation Electrical Modeling of Membranes Cardiac

More information

Peripheral Nerve II. Amelyn Ramos Rafael, MD. Anatomical considerations

Peripheral Nerve II. Amelyn Ramos Rafael, MD. Anatomical considerations Peripheral Nerve II Amelyn Ramos Rafael, MD Anatomical considerations 1 Physiologic properties of the nerve Irritability of the nerve A stimulus applied on the nerve causes the production of a nerve impulse,

More information

Modeling Action Potentials in Cell Processes

Modeling Action Potentials in Cell Processes Modeling Action Potentials in Cell Processes Chelsi Pinkett, Jackie Chism, Kenneth Anderson, Paul Klockenkemper, Christopher Smith, Quarail Hale Tennessee State University Action Potential Models Chelsi

More information

Neurophysiology. Danil Hammoudi.MD

Neurophysiology. Danil Hammoudi.MD Neurophysiology Danil Hammoudi.MD ACTION POTENTIAL An action potential is a wave of electrical discharge that travels along the membrane of a cell. Action potentials are an essential feature of animal

More information

From neuronal oscillations to complexity

From neuronal oscillations to complexity 1/39 The Fourth International Workshop on Advanced Computation for Engineering Applications (ACEA 2008) MACIS 2 Al-Balqa Applied University, Salt, Jordan Corson Nathalie, Aziz Alaoui M.A. University of

More information

Scroll Waves in Anisotropic Excitable Media with Application to the Heart. Sima Setayeshgar Department of Physics Indiana University

Scroll Waves in Anisotropic Excitable Media with Application to the Heart. Sima Setayeshgar Department of Physics Indiana University Scroll Waves in Anisotropic Excitable Media with Application to the Heart Sima Setayeshgar Department of Physics Indiana University KITP Cardiac Dynamics Mini-Program 1 Stripes, Spots and Scrolls KITP

More information

Scroll Waves in Anisotropic Excitable Media with Application to the Heart. Sima Setayeshgar Department of Physics Indiana University

Scroll Waves in Anisotropic Excitable Media with Application to the Heart. Sima Setayeshgar Department of Physics Indiana University Scroll Waves in Anisotropic Excitable Media with Application to the Heart Sima Setayeshgar Department of Physics Indiana University KITP Cardiac Dynamics Mini-Program 1 Stripes, Spots and Scrolls KITP

More information

Final Project Descriptions Introduction to Mathematical Biology Professor: Paul J. Atzberger. Project I: Predator-Prey Equations

Final Project Descriptions Introduction to Mathematical Biology Professor: Paul J. Atzberger. Project I: Predator-Prey Equations Final Project Descriptions Introduction to Mathematical Biology Professor: Paul J. Atzberger Project I: Predator-Prey Equations The Lotka-Volterra Predator-Prey Model is given by: du dv = αu βuv = ρβuv

More information

Automatic Validation and Optimisation of Biological Models

Automatic Validation and Optimisation of Biological Models Automatic Validation and Optimisation of Biological Models Jonathan Cooper St John s College Computational Biology Research Group Computing Laboratory University of Oxford Trinity Term 2008 This thesis

More information

9 Generation of Action Potential Hodgkin-Huxley Model

9 Generation of Action Potential Hodgkin-Huxley Model 9 Generation of Action Potential Hodgkin-Huxley Model (based on chapter 12, W.W. Lytton, Hodgkin-Huxley Model) 9.1 Passive and active membrane models In the previous lecture we have considered a passive

More information

MEMBRANE POTENTIALS AND ACTION POTENTIALS:

MEMBRANE POTENTIALS AND ACTION POTENTIALS: University of Jordan Faculty of Medicine Department of Physiology & Biochemistry Medical students, 2017/2018 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Review: Membrane physiology

More information

ROLE OF BIDOMAIN MODEL OF CARDIAC TISSUE IN THE DYNAMICS OF PHASE SINGULARITIES

ROLE OF BIDOMAIN MODEL OF CARDIAC TISSUE IN THE DYNAMICS OF PHASE SINGULARITIES ROLE OF BIDOMAIN MODEL OF CARDIAC TISSUE IN THE DYNAMICS OF PHASE SINGULARITIES Jianfeng Lv Submitted to the faculty of the University Graduate School in partial fulfillment of the requirement for the

More information

Converting energy into nerve impulses, resting potentials and action potentials Sensory receptors

Converting energy into nerve impulses, resting potentials and action potentials Sensory receptors D 1.3 s Converting energy into nerve impulses, resting potentials and action potentials Sensory receptors A receptor converts an external or internal stimulus into an electrical signal. Sensory receptors

More information

FRTF01 L8 Electrophysiology

FRTF01 L8 Electrophysiology FRTF01 L8 Electrophysiology Lecture Electrophysiology in general Recap: Linear Time Invariant systems (LTI) Examples of 1 and 2-dimensional systems Stability analysis The need for non-linear descriptions

More information

Quantitative Electrophysiology

Quantitative Electrophysiology ECE 795: Quantitative Electrophysiology Notes for Lecture #1 Wednesday, September 13, 2006 1. INTRODUCTION TO EXCITABLE CELLS Historical perspective: Bioelectricity first discovered by Luigi Galvani in

More information

Transport of ions across plasma membranes

Transport of ions across plasma membranes Transport of ions across plasma membranes Plasma Membranes of Excitable tissues Ref: Guyton, 13 th ed: pp: 61-71. 12 th ed: pp: 57-69. 11th ed: p57-71, Electrical properties of plasma membranes Part A:

More information

Particles with opposite charges (positives and negatives) attract each other, while particles with the same charge repel each other.

Particles with opposite charges (positives and negatives) attract each other, while particles with the same charge repel each other. III. NEUROPHYSIOLOGY A) REVIEW - 3 basic ideas that the student must remember from chemistry and physics: (i) CONCENTRATION measure of relative amounts of solutes in a solution. * Measured in units called

More information

Quantitative Electrophysiology

Quantitative Electrophysiology ECE 795: Quantitative Electrophysiology Notes for Lecture #1 Tuesday, September 18, 2012 1. INTRODUCTION TO EXCITABLE CELLS Historical perspective: Bioelectricity first discovered by Luigi Galvani in 1780s

More information

Learning Cycle Linear Hybrid Automata for Excitable Cells

Learning Cycle Linear Hybrid Automata for Excitable Cells Learning Cycle Linear Hybrid Automata for Excitable Cells Sayan Mitra Joint work with Radu Grosu, Pei Ye, Emilia Entcheva, I V Ramakrishnan, and Scott Smolka HSCC 2007 Pisa, Italy Excitable Cells Outline

More information

All-or-None Principle and Weakness of Hodgkin-Huxley Mathematical Model

All-or-None Principle and Weakness of Hodgkin-Huxley Mathematical Model All-or-None Principle and Weakness of Hodgkin-Huxley Mathematical Model S. A. Sadegh Zadeh, C. Kambhampati International Science Index, Mathematical and Computational Sciences waset.org/publication/10008281

More information

9.01 Introduction to Neuroscience Fall 2007

9.01 Introduction to Neuroscience Fall 2007 MIT OpenCourseWare http://ocw.mit.edu 9.01 Introduction to Neuroscience Fall 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 9.01 Recitation (R02)

More information

BME 5742 Biosystems Modeling and Control

BME 5742 Biosystems Modeling and Control BME 5742 Biosystems Modeling and Control Hodgkin-Huxley Model for Nerve Cell Action Potential Part 1 Dr. Zvi Roth (FAU) 1 References Hoppensteadt-Peskin Ch. 3 for all the mathematics. Cooper s The Cell

More information

Reproducing Cardiac Restitution Properties Using the Fenton Karma Membrane Model

Reproducing Cardiac Restitution Properties Using the Fenton Karma Membrane Model Annals of Biomedical Engineering, Vol. 33, No. 7, July 2005 ( 2005) pp. 907 911 DOI: 10.1007/s10439-005-3948-3 Reproducing Cardiac Restitution Properties Using the Fenton Karma Membrane Model ROBERT A.

More information

Biological membranes and bioelectric phenomena

Biological membranes and bioelectric phenomena Lectures on Medical Biophysics Dept. Biophysics, Medical faculty, Masaryk University in Brno Biological membranes and bioelectric phenomena A part of this lecture was prepared on the basis of a presentation

More information

Overview Organization: Central Nervous System (CNS) Peripheral Nervous System (PNS) innervate Divisions: a. Afferent

Overview Organization: Central Nervous System (CNS) Peripheral Nervous System (PNS) innervate Divisions: a. Afferent Overview Organization: Central Nervous System (CNS) Brain and spinal cord receives and processes information. Peripheral Nervous System (PNS) Nerve cells that link CNS with organs throughout the body.

More information

Neurons and Nervous Systems

Neurons and Nervous Systems 34 Neurons and Nervous Systems Concept 34.1 Nervous Systems Consist of Neurons and Glia Nervous systems have two categories of cells: Neurons, or nerve cells, are excitable they generate and transmit electrical

More information

SUMMARY OF THE EVENTS WHICH TRIGGER AN ELECTRICAL IMPUSLE IN NERVE CELLS (see figures on the following page)

SUMMARY OF THE EVENTS WHICH TRIGGER AN ELECTRICAL IMPUSLE IN NERVE CELLS (see figures on the following page) Anatomy and Physiology/AP Biology ACTION POTENTIAL SIMULATION BACKGROUND: The plasma membrane of cells is a selectively permeable barrier, which separates the internal contents of the cell from the surrounding

More information

An Approach for Applying Data Assimilation Techniques for Studying Cardiac Arrhythmias

An Approach for Applying Data Assimilation Techniques for Studying Cardiac Arrhythmias Rochester Institute of Technology RIT Scholar Works Theses Thesis/Dissertation Collections 5-3-214 An Approach for Applying Data Assimilation Techniques for Studying Cardiac Arrhythmias Stephen T. Scorse

More information

Physiology Unit 2. MEMBRANE POTENTIALS and SYNAPSES

Physiology Unit 2. MEMBRANE POTENTIALS and SYNAPSES Physiology Unit 2 MEMBRANE POTENTIALS and SYNAPSES Neuron Communication Neurons are stimulated by receptors on dendrites and cell bodies (soma) Ligand gated ion channels GPCR s Neurons stimulate cells

More information

Signal processing in nervous system - Hodgkin-Huxley model

Signal processing in nervous system - Hodgkin-Huxley model Signal processing in nervous system - Hodgkin-Huxley model Ulrike Haase 19.06.2007 Seminar "Gute Ideen in der theoretischen Biologie / Systembiologie" Signal processing in nervous system Nerve cell and

More information

3.3 Simulating action potentials

3.3 Simulating action potentials 6 THE HODGKIN HUXLEY MODEL OF THE ACTION POTENTIAL Fig. 3.1 Voltage dependence of rate coefficients and limiting values and time constants for the Hodgkin Huxley gating variables. (a) Graphs of forward

More information

Nervous Lecture Test Questions Set 2

Nervous Lecture Test Questions Set 2 Nervous Lecture Test Questions Set 2 1. The role of chloride in a resting membrane potential: a. creates resting potential b. indirectly causes repolarization c. stabilization of sodium d. it has none,

More information

Modelling biological oscillations

Modelling biological oscillations Modelling biological oscillations Shan He School for Computational Science University of Birmingham Module 06-23836: Computational Modelling with MATLAB Outline Outline of Topics Van der Pol equation Van

More information

PHYSIOLOGY CHAPTER 9 MUSCLE TISSUE Fall 2016

PHYSIOLOGY CHAPTER 9 MUSCLE TISSUE Fall 2016 PHYSIOLOGY CHAPTER 9 MUSCLE TISSUE Fall 2016 2 Chapter 9 Muscles and Muscle Tissue Overview of Muscle Tissue types of muscle: are all prefixes for muscle Contractility all muscles cells can Smooth & skeletal

More information

The Membrane Potential

The Membrane Potential The Membrane Potential Graphics are used with permission of: adam.com (http://www.adam.com/) Benjamin Cummings Publishing Co (http://www.aw.com/bc) ** It is suggested that you carefully label each ion

More information

General Physics. Nerve Conduction. Newton s laws of Motion Work, Energy and Power. Fluids. Direct Current (DC)

General Physics. Nerve Conduction. Newton s laws of Motion Work, Energy and Power. Fluids. Direct Current (DC) Newton s laws of Motion Work, Energy and Power Fluids Direct Current (DC) Nerve Conduction Wave properties of light Ionizing Radiation General Physics Prepared by: Sujood Alazzam 2017/2018 CHAPTER OUTLINE

More information

Physiology Coloring Book: Panels 29, 32, 33,

Physiology Coloring Book: Panels 29, 32, 33, ELEC4623/ELEC9734: Semester 2, 2009 Dr Stephen Redmond School of Electrical Engineering & Telecommunications Email: s.redmond@unsw.edu.au Ph: 9385 6101 Rm: 458, ELECENG (G17) Physiology Coloring Book:

More information

The Membrane Potential

The Membrane Potential The Membrane Potential Graphics are used with permission of: Pearson Education Inc., publishing as Benjamin Cummings (http://www.aw-bc.com) ** It is suggested that you carefully label each ion channel

More information

On Parameter Estimation for Neuron Models

On Parameter Estimation for Neuron Models On Parameter Estimation for Neuron Models Abhijit Biswas Department of Mathematics Temple University November 30th, 2017 Abhijit Biswas (Temple University) On Parameter Estimation for Neuron Models November

More information

Νευροφυσιολογία και Αισθήσεις

Νευροφυσιολογία και Αισθήσεις Biomedical Imaging & Applied Optics University of Cyprus Νευροφυσιολογία και Αισθήσεις Διάλεξη 5 Μοντέλο Hodgkin-Huxley (Hodgkin-Huxley Model) Response to Current Injection 2 Hodgin & Huxley Sir Alan Lloyd

More information

... Cardiac Gap Junctions Physiology, Regulation, Pathophysiology and Pharmacology

... Cardiac Gap Junctions Physiology, Regulation, Pathophysiology and Pharmacology ... Cardiac Gap Junctions Physiology, Regulation, Pathophysiology and Pharmacology S. Dhein, Cologne 23 figures and 3 tables, 1998 StefanDhein InstituteofPharmacology UniversityofCologne (Germany) All

More information

Fundamentals of the Nervous System and Nervous Tissue

Fundamentals of the Nervous System and Nervous Tissue Chapter 11 Part B Fundamentals of the Nervous System and Nervous Tissue Annie Leibovitz/Contact Press Images PowerPoint Lecture Slides prepared by Karen Dunbar Kareiva Ivy Tech Community College 11.4 Membrane

More information

Boundary-induced reentry in homogeneous excitable tissue

Boundary-induced reentry in homogeneous excitable tissue Boundary-induced reentry in homogeneous excitable tissue Fernando Siso-Nadal, 1 Niels F. Otani, 2 Robert F. Gilmour, Jr., 2 and Jeffrey J. Fox 1 1 Gene Network Sciences, Ithaca, New York 1485, USA 2 Department

More information

Channels can be activated by ligand-binding (chemical), voltage change, or mechanical changes such as stretch.

Channels can be activated by ligand-binding (chemical), voltage change, or mechanical changes such as stretch. 1. Describe the basic structure of an ion channel. Name 3 ways a channel can be "activated," and describe what occurs upon activation. What are some ways a channel can decide what is allowed to pass through?

More information

لجنة الطب البشري رؤية تنير دروب تميزكم

لجنة الطب البشري رؤية تنير دروب تميزكم 1) Hyperpolarization phase of the action potential: a. is due to the opening of voltage-gated Cl channels. b. is due to prolonged opening of voltage-gated K + channels. c. is due to closure of the Na +

More information

Simulating Hodgkin-Huxley-like Excitation using Comsol Multiphysics

Simulating Hodgkin-Huxley-like Excitation using Comsol Multiphysics Presented at the COMSOL Conference 2008 Hannover Simulating Hodgkin-Huxley-like Excitation using Comsol Multiphysics Martinek 1,2, Stickler 2, Reichel 1 and Rattay 2 1 Department of Biomedical Engineering

More information

Membrane Potentials and Bioelectricity

Membrane Potentials and Bioelectricity Membrane Potentials and Bioelectricity Hugh Purdy Honors University Physics II November 29, 2010 Most, if not all, cells in the human body have a net electric charge to some degree on either side of their

More information

Nervous System Organization

Nervous System Organization The Nervous System Nervous System Organization Receptors respond to stimuli Sensory receptors detect the stimulus Motor effectors respond to stimulus Nervous system divisions Central nervous system Command

More information

Naseem Demeri. Mohammad Alfarra. Mohammad Khatatbeh

Naseem Demeri. Mohammad Alfarra. Mohammad Khatatbeh 7 Naseem Demeri Mohammad Alfarra Mohammad Khatatbeh In the previous lectures, we have talked about how the difference in permeability for ions across the cell membrane can generate a potential. The potential

More information

Questions: Properties of excitable tissues Transport across cell membrane Resting potential Action potential Excitability change at excitation

Questions: Properties of excitable tissues Transport across cell membrane Resting potential Action potential Excitability change at excitation Questions: Properties of excitable tissues Transport across cell membrane Resting potential Action potential Excitability change at excitation EXCITABLE TISSUES The tissues can change the properties under

More information

Single-Compartment Neural Models

Single-Compartment Neural Models Single-Compartment Neural Models BENG/BGGN 260 Neurodynamics University of California, San Diego Week 2 BENG/BGGN 260 Neurodynamics (UCSD) Single-Compartment Neural Models Week 2 1 / 18 Reading Materials

More information

Introduction Principles of Signaling and Organization p. 3 Signaling in Simple Neuronal Circuits p. 4 Organization of the Retina p.

Introduction Principles of Signaling and Organization p. 3 Signaling in Simple Neuronal Circuits p. 4 Organization of the Retina p. Introduction Principles of Signaling and Organization p. 3 Signaling in Simple Neuronal Circuits p. 4 Organization of the Retina p. 5 Signaling in Nerve Cells p. 9 Cellular and Molecular Biology of Neurons

More information

Dendrites - receives information from other neuron cells - input receivers.

Dendrites - receives information from other neuron cells - input receivers. The Nerve Tissue Neuron - the nerve cell Dendrites - receives information from other neuron cells - input receivers. Cell body - includes usual parts of the organelles of a cell (nucleus, mitochondria)

More information

Instructor (Brad Osgood)

Instructor (Brad Osgood) TheFourierTransformAndItsApplications-Lecture26 Instructor (Brad Osgood): Relax, but no, no, no, the TV is on. It's time to hit the road. Time to rock and roll. We're going to now turn to our last topic

More information

3 Action Potentials - Brutal Approximations

3 Action Potentials - Brutal Approximations Physics 172/278 - David Kleinfeld - Fall 2004; Revised Winter 2015 3 Action Potentials - Brutal Approximations The Hodgkin-Huxley equations for the behavior of the action potential in squid, and similar

More information

Lecture 11 : Simple Neuron Models. Dr Eileen Nugent

Lecture 11 : Simple Neuron Models. Dr Eileen Nugent Lecture 11 : Simple Neuron Models Dr Eileen Nugent Reading List Nelson, Biological Physics, Chapter 12 Phillips, PBoC, Chapter 17 Gerstner, Neuronal Dynamics: from single neurons to networks and models

More information

Chapter 2 Basic Cardiac Electrophysiology: Excitable Membranes

Chapter 2 Basic Cardiac Electrophysiology: Excitable Membranes Chapter Basic Cardiac Electrophysiology: Excitable Membranes Deborah A. Jaye, Yong-Fu Xiao, and Daniel C. Sigg Abstract Cardiomyocytes are excitable cells that have the ability to contract after excitation;

More information

Nerve Signal Conduction. Resting Potential Action Potential Conduction of Action Potentials

Nerve Signal Conduction. Resting Potential Action Potential Conduction of Action Potentials Nerve Signal Conduction Resting Potential Action Potential Conduction of Action Potentials Resting Potential Resting neurons are always prepared to send a nerve signal. Neuron possesses potential energy

More information

me239 mechanics of the cell me239 mechanics of the cell - final projects 4 6 mechanotransduction downloadable layout file from coursework

me239 mechanics of the cell me239 mechanics of the cell - final projects 4 6 mechanotransduction downloadable layout file from coursework 6 mechanotransduction downloadable layout file from coursework wong, goktepe, kuhl [2010] me239 mechanics of the cell 1 me239 mechanics of the cell - final projects 2 downloadable sample project downloadable

More information

Membrane Physiology. Dr. Hiwa Shafiq Oct-18 1

Membrane Physiology. Dr. Hiwa Shafiq Oct-18 1 Membrane Physiology Dr. Hiwa Shafiq 22-10-2018 29-Oct-18 1 Chemical compositions of extracellular and intracellular fluids. 29-Oct-18 2 Transport through the cell membrane occurs by one of two basic processes:

More information

Neural Modeling and Computational Neuroscience. Claudio Gallicchio

Neural Modeling and Computational Neuroscience. Claudio Gallicchio Neural Modeling and Computational Neuroscience Claudio Gallicchio 1 Neuroscience modeling 2 Introduction to basic aspects of brain computation Introduction to neurophysiology Neural modeling: Elements

More information

80% of all excitatory synapses - at the dendritic spines.

80% of all excitatory synapses - at the dendritic spines. Dendritic Modelling Dendrites (from Greek dendron, tree ) are the branched projections of a neuron that act to conduct the electrical stimulation received from other cells to and from the cell body, or

More information

Deconstructing Actual Neurons

Deconstructing Actual Neurons 1 Deconstructing Actual Neurons Richard Bertram Department of Mathematics and Programs in Neuroscience and Molecular Biophysics Florida State University Tallahassee, Florida 32306 Reference: The many ionic

More information

Kirchhoff s Rules. Survey available this week. $ closed loop. Quiz on a simple DC circuit. Quiz on a simple DC circuit

Kirchhoff s Rules. Survey available this week. $ closed loop. Quiz on a simple DC circuit. Quiz on a simple DC circuit RC Circuits. Start Magnetic Fields Announcement on MTE 1 This Lecture: RC circuits Membrane electrical currents Magnetic Fields and Magnets Wednesday Oct. 4, slightly later start time:5:45 pm - 7:15 pm

More information

NEURONS, SENSE ORGANS, AND NERVOUS SYSTEMS CHAPTER 34

NEURONS, SENSE ORGANS, AND NERVOUS SYSTEMS CHAPTER 34 NEURONS, SENSE ORGANS, AND NERVOUS SYSTEMS CHAPTER 34 KEY CONCEPTS 34.1 Nervous Systems Are Composed of Neurons and Glial Cells 34.2 Neurons Generate Electric Signals by Controlling Ion Distributions 34.3

More information

Physiology Unit 2. MEMBRANE POTENTIALS and SYNAPSES

Physiology Unit 2. MEMBRANE POTENTIALS and SYNAPSES Physiology Unit 2 MEMBRANE POTENTIALS and SYNAPSES In Physiology Today Ohm s Law I = V/R Ohm s law: the current through a conductor between two points is directly proportional to the voltage across the

More information

Microsystems for Neuroscience and Medicine. Lecture 9

Microsystems for Neuroscience and Medicine. Lecture 9 1 Microsystems for Neuroscience and Medicine Lecture 9 2 Neural Microsystems Neurons - Structure and behaviour Measuring neural activity Interfacing with neurons Medical applications - DBS, Retinal Implants

More information

Discrete and Indiscrete Models of Biological Networks

Discrete and Indiscrete Models of Biological Networks Discrete and Indiscrete Models of Biological Networks Winfried Just Ohio University November 17, 2010 Who are we? What are we doing here? Who are we? What are we doing here? A population of interacting

More information

Basic mechanisms of arrhythmogenesis and antiarrhythmia

Basic mechanisms of arrhythmogenesis and antiarrhythmia EHRA EDUCATIONAL REVIEW AND PREPARATORY COURSE ON INVASIVE CARDIAC ELECTROPHYSIOLOGY EUROPEAN HEART HOUSE, February 2011 Basic mechanisms of arrhythmogenesis and antiarrhythmia Antonio Zaza Università

More information

Multiple Mechanisms of Spiral Wave Breakup in a Model of Cardiac Electrical Activity

Multiple Mechanisms of Spiral Wave Breakup in a Model of Cardiac Electrical Activity Multiple Mechanisms of Spiral Wave Breakup in a Model of Cardiac Electrical Activity Flavio H. Fenton and Elizabeth M. Cherry Center for Arrhythmia Research at Hofstra University and The Heart Institute,

More information

The Intersection of Chemistry and Biology: An Interview with Professor W. E. Moerner

The Intersection of Chemistry and Biology: An Interview with Professor W. E. Moerner The Intersection of Chemistry and Biology: An Interview with Professor W. E. Moerner Joseph Nicolls Stanford University Professor W.E Moerner earned two B.S. degrees, in Physics and Electrical Engineering,

More information

Electrical Signaling. Lecture Outline. Using Ions as Messengers. Potentials in Electrical Signaling

Electrical Signaling. Lecture Outline. Using Ions as Messengers. Potentials in Electrical Signaling Lecture Outline Electrical Signaling Using ions as messengers Potentials in electrical signaling Action Graded Other electrical signaling Gap junctions The neuron Using Ions as Messengers Important things

More information

7.013 Spring 2005 Problem Set 4

7.013 Spring 2005 Problem Set 4 MIT Department of Biology 7.013: Introductory Biology - Spring 2005 Instructors: Professor Hazel Sive, Professor Tyler Jacks, Dr. Claudette Gardel NAME TA 7.013 Spring 2005 Problem Set 4 FRIDAY April 8th,

More information