The Hodgkin-Huxley Neuron Model
|
|
- Sharleen Hampton
- 7 years ago
- Views:
Transcription
1 The Hodgkin-Huxley Neuron Model Neuron Structure and Function Neurons are nerve cells with a cell body or soma which contains the nucleus and protein manufacturing apparatus, an axon which propagates action potentials and distributes them to other neurons, and a system of dendrites which collect signals from other neurons. The axon is essentially a coaxial conducting cable with an ionic conducting medium inside, surrounded by the cell membrane which is a leaky insulator, and immersed in the extrcellular ionic conducting fluid. It has similar electrical properties to an undersea communications cable. In a living neuron, energy from ATP molecules is continually used to power ion pumps which maintain a resting potential difference of approximately 70 mv across the cell membrane. When the axon is subjected to a small depolarizing excitation, it responds in a linear fashion to dissipate the signal and quickly revert to its resting state. When the axon is subjected to a large depolarizing excitation, it responds in a nonlinear fashion by generating a large voltage spike or action potential which propagates down the axon at constant speed without changing its shape. Neural computation in the brain is based largely on spike trains propagating through a neural network PHY Computational Physics 2 1 Monday, March 3
2 consisting of billions of neurons each connected to tens of thousands of other neurons. Ion Channels Living cells maintain a potential gradient across their membranes using Ion-channel pumps powered by energy stored in ATP molecules. The Na-K-Pump maintains a resting potential difference of approximately 70 mv across the membrane of a nerve axon. PHY Computational Physics 2 2 Monday, March 3
3 The figure shows the Crystal structure of the sodium-potassium pump which contains three polymer subunits. The trans-membrane potential is determined by the concentration gradient of ions, according to the Goldman-Hodgkin-Katz voltage equation. Hodgkin-Huxley Equations In the final paper of a series of 5 articles, A.L Hodgkin and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117(4), (1952) proposed a model to describe the generation and propagation of an action potential in a neuron. In this series of experimental, theoretical and computational studies, they measured the membrane properties of the giant axon of the common squid Loligo not to be confused with the Giant squid, deduced a set of theoretical equations, and showed numerically how they explained the propagation of action potentials. PHY Computational Physics 2 3 Monday, March 3
4 The I V characterisitics of a small patch of axon membrane are determined by the following equations: I = C M dv dt + ḡ K n4 ( V V K ) + ḡ Na m 3 h ( V V Na ) + ḡl (V V l ) PHY Computational Physics 2 4 Monday, March 3
5 dn dt = α n(1 n) β n n dm dt = α m(1 m) β m m dh dt = α h(1 h) β h h 0.01(V + 10) α n = exp [ ] V (V + 25) α m = exp [ ] V ( ) V α h = 0.07 exp 20 PHY Computational Physics 2 5 Monday, March 3
6 ( ) V β n = exp 80 ( ) V β m = 4 exp 18 1 β h = exp [ ] V The values of the physical parameters in these equations were determined by their experiments, and are summarized in Table 3 in their article: PHY Computational Physics 2 6 Monday, March 3
7 The Membrane Action Potential and Propagated Action Potential Hodgkin and Huxley solve these equations numerically under two different experimental conditions. 1. Constant Uniform Membrane Potential The potential is held constant and uniform over the whole length of the axon. This is done by inserting a wire axially through the length of the axon and holding it at a constant potential. There is no current along the cylinder axis. The net membrane current must therefore always be zero, except during a stimulus. The stimulus is taken to be a short shock at t = 0. The equation I = C M dv dt + ḡ K n4 ( V V K ) + ḡ Na m 3 h ( V V Na ) + ḡl (V V l ) is solved with I = 0 and the initial conditions that V = V 0 and m, n and h have their steady state resting values, at t = Propagated Action Potential An axon at rest in a living organism is excited at its junction with the cell body. The excitation generates a spike, which propagates down the length of the axon. To model this propagated action potential, the axon is represented by segments of Hodgkin-Huxley circuit elements connected in series by longitudinal resistors: PHY Computational Physics 2 7 Monday, March 3
8 The continuum limit of an infinite number of circuit elements results in a partial differential equation a 2 V 2R 2 x = C V 2 M t + ḡ ( ) K n4 V V K + ḡ Na m 3 h ( ) V V Na + ḡl (V V l ) see Eq. (29) in Hodgkin-Huxley, where x measures longitudinal distance along the axon, and R 2 is the specific resistance of the axoplasm (cytosol). This form of partial differential equation is called the Telegrapher s equation. For a derivation and further information, see Wikipedia Cable theory and Scholarpedia Neuronal cable theory. Hodgkin and Huxley suggest solving this partial differential equation in the steady state approximation. Assuming the spike propagates like a soliton without changing its shape, V (x, t) as a function of x at any fixed time has the same functional form as V (x, t) as a function of t at any fixed position x. Thus 2 V x = 1 2 V 2 θ 2 t 2 PHY Computational Physics 2 8 Monday, March 3
9 where θ is the speed of the spike. Assuming the circuit constants and conductances do not depend on x results in an ordinary differential equation a d 2 V 2R 2 θ 2 dt 2 = C M dv dt + ḡ K n4 ( V V K ) + ḡ Na m 3 h ( V V Na ) + ḡl (V V l ) Because θ is not known in advance, they guess a value of θ and solve this equation starting from the resting state at the foot of the action potential. They then find that V tends to either + or if the guess is either too small or too large. The correct value of θ results in V tending to zero when the action potential is over. This value can be found using a root-finding algorithm. The partial differential equations can be solved without the assumption of soliton-like behavior, see Wikipedia Hodgkin-Huxley model: Mathematical properties and the existence of the stable propagating solutions can be proven rigorously. Solving the Hodgkin-Huxley Model Equations import math import sys from tools.odeint import RK4_adaptive_step hodgkin-huxley.py PHY Computational Physics 2 9 Monday, March 3
10 # Membrane constants from Table 3 C_M = 1.0 V_Na = -115 V_K = +12 V_l = g_na = 120 g_k = 36 g_l = 0.3 # membrane capacitance per unit area # sodium Nernst potential # potassium Nernst potential # leakage potential # sodium conductance # potassium conductance # leakage conductance # Voltage-dependent rate constants (constant in time) def alpha_n(v): return 0.01 * (V + 10) / (math.exp((v + 10) / 10) - 1) def beta_n(v): return * math.exp(v / 80) def alpha_m(v): return 0.1 * (V + 25) / (math.exp((v + 25) / 10) - 1) def beta_m(v): PHY Computational Physics 2 10 Monday, March 3
11 return 4 * math.exp(v / 18) def alpha_h(v): return 0.07 * math.exp(v / 20) def beta_h(v): return 1 / (math.exp((v + 30) / 10) + 1) # Membrane current as function of time def I(t): # In a voltage clamp experiment I = 0, see page 522 of H-H article return 0 # For propagated action potential see Eqs. (30,31) in the article # Hodgkin-Huxley equations def HH_equations(Vnmht): # returns flow vector given extended solution vector [V, n, m, h, t] V = Vnmht[0] n = Vnmht[1] m = Vnmht[2] PHY Computational Physics 2 11 Monday, March 3
12 h = Vnmht[3] t = Vnmht[4] flow = [0] * 5 flow[0] = ( I(t) - g_k * n**4 * (V - V_K) - g_na * m**3 * h * (V - V_Na) - g_l * (V - V_l) ) / C_M flow[1] = alpha_n(v) * (1 - n) - beta_n(v) * n flow[2] = alpha_m(v) * (1 - m) - beta_m(v) * m flow[3] = alpha_h(v) * (1 - h) - beta_h(v) * h flow[4] = 1 return flow print(" Hodgkin-Huxley Fig. 12") # resting state is defined by V = 0, dn/dt = dm/dt = dh/dt = 0 # calculate the resting conductances n_0 = alpha_n(0) / (alpha_n(0) + beta_n(0)) m_0 = alpha_m(0) / (alpha_m(0) + beta_m(0)) h_0 = alpha_h(0) / (alpha_h(0) + beta_h(0)) V_0 = -90 print(" Initial depolarization V(0) =", V_0, "mv") t = 0 Vnmht = [ V_0, n_0, m_0, h_0, t ] t_max = 6 PHY Computational Physics 2 12 Monday, March 3
13 dt = 0.01 dt_min, dt_max = [dt, dt] print(" Integrating using RK4 with adaptive step size dt =", dt) print(" t V(t) n(t) m(t) h(t)") print(" ") skip_steps = 10 step = 0 file = open("hodgkin-huxley.data", "w") while t < t_max + dt: if step % skip_steps == 0: print(" ", t, Vnmht[0], Vnmht[1], Vnmht[2], Vnmht[3]) data = str(t) for i in range(4): data += \t + str(vnmht[i]) file.write(data + \n ) dt = RK4_adaptive_step(Vnmht, dt, HH_equations) dt_min = min(dt_min, dt) dt_max = max(dt_max, dt) t = Vnmht[4] step += 1 file.close() print(" min, max adaptive dt =", dt_min, dt_max) PHY Computational Physics 2 13 Monday, March 3
14 print(" Data in file hodgkin-huxley.data") PHY Computational Physics 2 14 Monday, March 3
Simulating Spiking Neurons by Hodgkin Huxley Model
Simulating Spiking Neurons by Hodgkin Huxley Model Terje Kristensen 1 and Donald MacNearney 2 1 Department of Computing, Bergen University College, Bergen, Norway, tkr@hib.no 2 Electrical Systems Integration,
More informationModelling Hodgkin-Huxley
University of Heidelberg Molecular Biotechnology (Winter 2003/2004) Modelling in molecular biotechnology Dr. M. Diehl Modelling Hodgkin-Huxley Version 1.0 Wadel, K. (2170370) Contents 1 Introduction 1
More informationSimulation of an Action Potential using the Hodgkin-Huxley Model in Python. Nathan Law 250560559. Medical Biophysics 3970
Simulation of an Action Potential using the Hodgkin-Huxley Model in Python Nathan Law 250560559 Medical Biophysics 3970 Instructor: Dr. Ian MacDonald TA: Nathaniel Hayward Project Supervisor: Dr. Andrea
More informationAction Potentials I Generation. Reading: BCP Chapter 4
Action Potentials I Generation Reading: BCP Chapter 4 Action Potentials Action potentials (AP s) aka Spikes (because of how they look in an electrical recording of Vm over time). Discharges (descriptive
More informationBIOPHYSICS OF NERVE CELLS & NETWORKS
UNIVERSITY OF LONDON MSci EXAMINATION May 2007 for Internal Students of Imperial College of Science, Technology and Medicine This paper is also taken for the relevant Examination for the Associateship
More informationEXCITABILITY & ACTION POTENTIALS page 1
page 1 INTRODUCTION A. Excitable Tissue: able to generate Action Potentials (APs) (e.g. neurons, muscle cells) B. Neurons (nerve cells) a. components 1) soma (cell body): metabolic center (vital, always
More informationNerves and Nerve Impulse
Nerves and Nerve Impulse Terms Absolute refractory period: Period following stimulation during which no additional action potential can be evoked. Acetylcholine: Chemical transmitter substance released
More informationPassive Conduction - Cable Theory
Passive Conduction - Cable Theory October 7, 2013 Biological Structure Theoretical models describing propagation of synaptic potentials have evolved significantly over the past century. Synaptic potentials
More informationBi 360: Midterm Review
Bi 360: Midterm Review Basic Neurobiology 1) Many axons are surrounded by a fatty insulating sheath called myelin, which is interrupted at regular intervals at the Nodes of Ranvier, where the action potential
More informationLab 1: Simulation of Resting Membrane Potential and Action Potential
Lab 1: Simulation of Resting Membrane Potential and Action Potential Overview The aim of the present laboratory exercise is to simulate how changes in the ion concentration or ionic conductance can change
More informationAn Introduction to Core-conductor Theory
An Introduction to Core-conductor Theory I often say when you can measure what you are speaking about and express it in numbers you know something about it; but when you cannot measure it, when you cannot
More information12. Nervous System: Nervous Tissue
12. Nervous System: Nervous Tissue I. Introduction to the Nervous System General functions of the nervous system The nervous system has three basic functions: 1. Gather sensory input from the environment
More informationThe mhr model is described by 30 ordinary differential equations (ODEs): one. ion concentrations and 23 equations describing channel gating.
On-line Supplement: Computer Modeling Chris Clausen, PhD and Ira S. Cohen, MD, PhD Computer models of canine ventricular action potentials The mhr model is described by 30 ordinary differential equations
More informationBiology Slide 1 of 38
Biology 1 of 38 2 of 38 35-2 The Nervous System What are the functions of the nervous system? 3 of 38 35-2 The Nervous System 1. Nervous system: a. controls and coordinates functions throughout the body
More informationSlide 1. Slide 2. Slide 3. Cable Properties. Passive flow of current. Voltage Decreases With Distance
Slide 1 Properties of the nerve, axon, cell body and dendrite affect the distance and speed of membrane potential Passive conduction properties = cable properties Signal becomes reduced over distance depending
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Chapter 2 The Neural Impulse Name Period Date MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The cell body is enclosed by the. A) cell membrane
More informationThe FitzHugh-Nagumo Model
Lecture 6 The FitzHugh-Nagumo Model 6.1 The Nature of Excitable Cell Models Classically, it as knon that the cell membrane carries a potential across the inner and outer surfaces, hence a basic model for
More informationPART I: Neurons and the Nerve Impulse
PART I: Neurons and the Nerve Impulse Identify each of the labeled structures of the neuron below. A. B. C. D. E. F. G. Identify each of the labeled structures of the neuron below. A. dendrites B. nucleus
More information580.439 Course Notes: Cable Theory
58.439 Course Notes: Cable Theory Reading: Koch and Segev, chapt, 3, and 5; Johnston and Wu, Chapt. 4. For a detailed treatment of older subjects, see Jack, Noble, and Tsien, 1975. A recent text with up
More informationPropagation of Cardiac Action Potentials: How does it Really work?
Propagation of Cardiac Action Potentials: How does it Really work? J. P. Keener and Joyce Lin Department of Mathematics University of Utah Math Biology Seminar Jan. 19, 2011 Introduction A major cause
More informationNeurophysiology. 2.1 Equilibrium Potential
2 Neurophysiology 2.1 Equilibrium Potential An understanding of the concepts of electrical and chemical forces that act on ions, electrochemical equilibrium, and equilibrium potential is a powerful tool
More informationOrigin of Electrical Membrane Potential
Origin of Electrical Membrane Potential parti This book is about the physiological characteristics of nerve and muscle cells. As we shall see, the ability of these cells to generate and conduct electricity
More informationThe Action Potential Graphics are used with permission of: adam.com (http://www.adam.com/) Benjamin Cummings Publishing Co (http://www.awl.
The Action Potential Graphics are used with permission of: adam.com (http://www.adam.com/) Benjamin Cummings Publishing Co (http://www.awl.com/bc) ** If this is not printed in color, it is suggested you
More informationBiological Neurons and Neural Networks, Artificial Neurons
Biological Neurons and Neural Networks, Artificial Neurons Neural Computation : Lecture 2 John A. Bullinaria, 2015 1. Organization of the Nervous System and Brain 2. Brains versus Computers: Some Numbers
More informationModel Neurons I: Neuroelectronics
Chapter 5 Model Neurons I: Neuroelectronics 5.1 Introduction A great deal is known about the biophysical mechanisms responsible for generating neuronal activity, and these provide a basis for constructing
More informationResting membrane potential ~ -70mV - Membrane is polarized
Resting membrane potential ~ -70mV - Membrane is polarized (ie) Electrical charge on the outside of the membrane is positive while the electrical charge on the inside of the membrane is negative Changes
More informationIon Channels. Graphics are used with permission of: Pearson Education Inc., publishing as Benjamin Cummings (http://www.aw-bc.com)
Ion Channels Graphics are used with permission of: Pearson Education Inc., publishing as Benjamin Cummings (http://www.aw-bc.com) ** There are a number of ion channels introducted in this topic which you
More informationHow To Solve The Cable Equation
Cable properties of neurons Eric D. Young Reading: Johnston and Wu, Chapt. 4 and Chapt. 13 pp. 400-411. Neurons are not a single compartment! The figures below show two snapshots of the membrane potential
More informationCHAPTER 5 SIGNALLING IN NEURONS
5.1. SYNAPTIC TRANSMISSION CHAPTER 5 SIGNALLING IN NEURONS One of the main functions of neurons is to communicate with other neurons. An individual neuron may receive information from many different sources.
More informationREVIEW SHEET EXERCISE 3 Neurophysiology of Nerve Impulses Name Lab Time/Date. The Resting Membrane Potential
REVIEW SHEET EXERCISE 3 Neurophysiology of Nerve Impulses Name Lab Time/Date ACTIVITY 1 The Resting Membrane Potential 1. Explain why increasing extracellular K + reduces the net diffusion of K + out of
More informationThe Membrane Equation
The Membrane Equation Professor David Heeger September 5, 2000 RC Circuits Figure 1A shows an RC (resistor, capacitor) equivalent circuit model for a patch of passive neural membrane. The capacitor represents
More informationBefore continuing try to answer the following questions. The answers can be found at the end of the article.
EXCITABLE TISSUE ELECTROPHYSIOLOGY ANAESTHESIA TUTORIAL OF THE WEEK 173 8 TH MARCH 2010 Dr John Whittle Specialist Registrar Anaesthetics Dr Gareth Ackland Consultant and Clinical Scientist Anaesthetics,
More informationSimulating a Neuron Soma
Simulating a Neuron Soma DAVID BEEMAN 13.1 Some GENESIS Script Language Conventions In the previous chapter, we modeled the simple passive compartment shown in Fig. 12.1. The membrane resistance R m is
More informationHow To Understand The Distributed Potential Of A Dendritic Tree
Systems Biology II: Neural Systems (580.422) Lecture 8, Linear cable theory Eric Young 5-3164 eyoung@jhu.edu Reading: D. Johnston and S.M. Wu Foundations of Cellular Neurophysiology (MIT Press, 1995).
More informationThe Action Potential
OpenStax-CNX module: m46526 1 The Action Potential OpenStax College This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 By the end of this section, you
More informationES250: Electrical Science. HW7: Energy Storage Elements
ES250: Electrical Science HW7: Energy Storage Elements Introduction This chapter introduces two more circuit elements, the capacitor and the inductor whose elements laws involve integration or differentiation;
More informationThe Electrical Activity of Cardiac Tissue via Finite Element Method
Adv. Studies Theor. Phys., Vol. 6, 212, no. 2, 99-13 The Electrical Activity of Cardiac Tissue via Finite Element Method Jairo Villegas G, Andrus Giraldo M Departamento de Ciencias Básicas Universidad
More informationCable and Compartmental Models of Dendritic Trees
Cable and Compartmental Models of Dendritic Trees IDAN SEGEV 5.1 Introduction In the previous chapter, we used a single compartment model to study the mechanisms for the activation of voltage-activated
More informationIons cannot cross membranes. Ions move through pores
Ions cannot cross membranes Membranes are lipid bilayers Nonpolar tails Polar head Fig 3-1 Because of the charged nature of ions, they cannot cross a lipid bilayer. The ion and its cloud of polarized water
More informationBiology/ANNB 261 Exam 1 Name Fall, 2006
Biology/ANNB 261 Exam 1 Name Fall, 2006 * = correct answer. 1. The Greek philosopher Aristotle hypothesized that the brain was a) A radiator for cooling the blood.* b) The seat of the soul. c) The organ
More informationBiology/ANNB 261 Exam 1 Spring, 2006
Biology/ANNB 261 Exam 1 Spring, 2006 Name * = correct answer Multiple Choice: 1. Axons and dendrites are two types of a) Neurites * b) Organelles c) Synapses d) Receptors e) Golgi cell components 2. The
More informationCELLS IN THE NERVOUS SYSTEM
NEURONS AND GLIA CELLS IN THE NERVOUS SYSTEM Glia Insulates, supports, and nourishes neurons Neurons Process information Sense environmental changes Communicate changes to other neurons Command body response
More informationParts of the Nerve Cell and Their Functions
Parts of the Nerve Cell and Their Functions Silvia Helena Cardoso, PhD [ 1. Cell body] [2. Neuronal membrane] [3. Dendrites] [4. Axon] [5. Nerve ending] 1. Cell body The cell body (soma) is the factory
More informationProblem Sets: Questions and Answers
BI 360: Neurobiology Fall 2014 Problem Sets: Questions and Answers These problems are provided to aid in your understanding of basic neurobiological concepts and to guide your focus for in-depth study.
More informationAP Biology I. Nervous System Notes
AP Biology I. Nervous System Notes 1. General information: passage of information occurs in two ways: Nerves - process and send information fast (eg. stepping on a tack) Hormones - process and send information
More informationElectrophysiological Recording Techniques
Electrophysiological Recording Techniques Wen-Jun Gao, PH.D. Drexel University College of Medicine Goal of Physiological Recording To detect the communication signals between neurons in real time (μs to
More informationCellular Calcium Dynamics. Jussi Koivumäki, Glenn Lines & Joakim Sundnes
Cellular Calcium Dynamics Jussi Koivumäki, Glenn Lines & Joakim Sundnes Cellular calcium dynamics A real cardiomyocyte is obviously not an empty cylinder, where Ca 2+ just diffuses freely......instead
More informationLab #6: Neurophysiology Simulation
Lab #6: Neurophysiology Simulation Background Neurons (Fig 6.1) are cells in the nervous system that are used conduct signals at high speed from one part of the body to another. This enables rapid, precise
More informationLab 6: Bifurcation diagram: stopping spiking neurons with a single pulse
Lab 6: Bifurcation diagram: stopping spiking neurons with a single pulse The qualitative behaviors of a dynamical system can change when parameters are changed. For example, a stable fixed-point can become
More informationActivity 5: The Action Potential: Measuring Its Absolute and Relative Refractory Periods. 250 20 Yes. 125 20 Yes. 60 20 No. 60 25 No.
3: Neurophysiology of Nerve Impulses (Part 2) Activity 5: The Action Potential: Measuring Its Absolute and Relative Refractory Periods Interval between stimuli Stimulus voltage (mv) Second action potential?
More informationCHAPTER 5.1 5.2: Plasma Membrane Structure
CHAPTER 5.1 5.2: Plasma Membrane Structure 1. Describe the structure of a phospholipid molecule. Be sure to describe their behavior in relationship to water. 2. What happens when a collection of phospholipids
More informationParameter Identification for State of Discharge Estimation of Li-ion Batteries
Parameter Identification for State of Discharge Estimation of Li-ion Batteries * Suchart Punpaisarn ) and Thanatchai Kulworawanichpong 2) ), 2) Power System Research Unit, School of Electrical Engineering
More information3.4 - BJT DIFFERENTIAL AMPLIFIERS
BJT Differential Amplifiers (6/4/00) Page 1 3.4 BJT DIFFERENTIAL AMPLIFIERS INTRODUCTION Objective The objective of this presentation is: 1.) Define and characterize the differential amplifier.) Show the
More information7. A selectively permeable membrane only allows certain molecules to pass through.
CHAPTER 2 GETTING IN & OUT OF CELLS PASSIVE TRANSPORT Cell membranes help organisms maintain homeostasis by controlling what substances may enter or leave cells. Some substances can cross the cell membrane
More information3. Diodes and Diode Circuits. 3. Diodes and Diode Circuits TLT-8016 Basic Analog Circuits 2005/2006 1
3. Diodes and Diode Circuits 3. Diodes and Diode Circuits TLT-8016 Basic Analog Circuits 2005/2006 1 3.1 Diode Characteristics Small-Signal Diodes Diode: a semiconductor device, which conduct the current
More informationControlling the brain
out this leads to a very exciting research field with many challenges which need to be solved; both in the medical as well as in the electrical domain. Controlling the brain In this article an introduction
More informationElectric Current and Cell Membranes
Electric Current and Cell Membranes 16 Thus far in our study of electricity, we have essentially confined our attention to electrostatics, or the study of stationary charges. Here and in the next three
More informationEXPERIMENT NUMBER 8 CAPACITOR CURRENT-VOLTAGE RELATIONSHIP
1 EXPERIMENT NUMBER 8 CAPACITOR CURRENT-VOLTAGE RELATIONSHIP Purpose: To demonstrate the relationship between the voltage and current of a capacitor. Theory: A capacitor is a linear circuit element whose
More information4. Biology of the Cell
4. Biology of the Cell Our primary focus in this chapter will be the plasma membrane and movement of materials across the plasma membrane. You should already be familiar with the basic structures and roles
More informationIntroduction to Cardiac Electrophysiology, the Electrocardiogram, and Cardiac Arrhythmias INTRODUCTION
Introduction to Cardiac Electrophysiology, the Electrocardiogram, and Cardiac Arrhythmias Alfred E. Buxton, M.D., Kristin E. Ellison, M.D., Malcolm M. Kirk, M.D., Gregory F. Michaud, M.D. INTRODUCTION
More informationApplication Note AN- 1095
Application Note AN- 1095 Design of the Inverter Output Filter for Motor Drives with IRAMS Power Modules Cesare Bocchiola Table of Contents Page Section 1: Introduction...2 Section 2 : Output Filter Design
More informationUSING LIPID BILAYERS IN AN ARTIFICIAL AXON SYSTEM. Zachary Thomas VanDerwerker. Master of Science In Mechanical Engineering
USING LIPID BILAYERS IN AN ARTIFICIAL AXON SYSTEM Zachary Thomas VanDerwerker Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements
More informationMeasurement of Capacitance
Measurement of Capacitance Pre-Lab Questions Page Name: Class: Roster Number: Instructor:. A capacitor is used to store. 2. What is the SI unit for capacitance? 3. A capacitor basically consists of two
More informationNeural Computation. Mark van Rossum. Lecture Notes for the MSc module. Version 2015/16 1
Neural Computation Mark van Rossum Lecture Notes for the MSc module. Version 2015/16 1 1 October 2, 2015 1 Introduction: Neural Computation The brain is a complex computing machine which has evolved to
More informationMuscle Tissue. Muscle Physiology. Skeletal Muscle. Types of Muscle. Skeletal Muscle Organization. Myofibril Structure
Muscle Tissue Muscle Physiology Chapter 12 Specially designed to contract Generates mechanical force Functions locomotion and external movements internal movement (circulation, digestion) heat generation
More informationCHAPTER XV PDL 101 HUMAN ANATOMY & PHYSIOLOGY. Ms. K. GOWRI. M.Pharm., Lecturer.
CHAPTER XV PDL 101 HUMAN ANATOMY & PHYSIOLOGY Ms. K. GOWRI. M.Pharm., Lecturer. Types of Muscle Tissue Classified by location, appearance, and by the type of nervous system control or innervation. Skeletal
More informationNodus 3.1. Manual. with Nodus 3.2 Appendix. Neuron and network simulation software for Macintosh computers
Nodus 3.1 Manual with Nodus 3.2 Appendix Neuron and network simulation software for Macintosh computers Copyright Erik De Schutter, 1995 Copyright This manual and the Nodus software described in it are
More informationStudent Academic Learning Services Page 1 of 8 Nervous System Quiz
Student Academic Learning Services Page 1 of 8 Nervous System Quiz 1. The term central nervous system refers to the: A) autonomic and peripheral nervous systems B) brain, spinal cord, and cranial nerves
More informationKIA7805AF/API~KIA7824AF/API SEMICONDUCTOR TECHNICAL DATA THREE TERMINAL POSITIVE VOLTAGE REGULATORS 5V, 6V, 7V, 8V, 9V, 10V, 12V, 15V, 18V, 20V, 24V.
SEMICONDUCTOR TECHNICAL DATA KIA785AF/API~KIA7824AF/API BIPOLAR LINEAR INTEGRATED THREE TERMINAL POSITIVE VOLTAGE REGULATORS 5V, 6V, 7V, 8V, 9V, 1V, 12V, 15V, 18V, 2V, 24V. FEATURES Internal Thermal Overload
More informationAnatomy Review. Graphics are used with permission of: Pearson Education Inc., publishing as Benjamin Cummings (http://www.aw-bc.
Anatomy Review Graphics are used with permission of: Pearson Education Inc., publishing as Benjamin Cummings (http://www.aw-bc.com) Page 1. Introduction The structure of neurons reflects their function.
More informationStep response of an RLC series circuit
School of Engineering Department of Electrical and Computer Engineering 332:224 Principles of Electrical Engineering II Laboratory Experiment 5 Step response of an RLC series circuit 1 Introduction Objectives
More informationModes of Membrane Transport
Modes of Membrane Transport Transmembrane Transport movement of small substances through a cellular membrane (plasma, ER, mitochondrial..) ions, fatty acids, H 2 O, monosaccharides, steroids, amino acids
More informationNerves and Conduction of Nerve Impulses
A. Introduction 1. Innovation in Cnidaria - Nerve net a. We need to talk more about nerves b. Cnidaria have simple nerve net - 2 way conduction c. Basis for more complex system in Vertebrates B. Vertebrate
More information= (0.400 A) (4.80 V) = 1.92 W = (0.400 A) (7.20 V) = 2.88 W
Physics 2220 Module 06 Homework 0. What are the magnitude and direction of the current in the 8 Ω resister in the figure? Assume the current is moving clockwise. Then use Kirchhoff's second rule: 3.00
More informationSteady Heat Conduction
Steady Heat Conduction In thermodynamics, we considered the amount of heat transfer as a system undergoes a process from one equilibrium state to another. hermodynamics gives no indication of how long
More informationElectrical Fundamentals Module 3: Parallel Circuits
Electrical Fundamentals Module 3: Parallel Circuits PREPARED BY IAT Curriculum Unit August 2008 Institute of Applied Technology, 2008 ATE310- Electrical Fundamentals 2 Module 3 Parallel Circuits Module
More informationSubminiature Load Cell Model 8417
w Technical Product Information Subminiature Load Cell 1. Introduction... 2 2. Preparing for use... 2 2.1 Unpacking... 2 2.2 Using the instrument for the first time... 2 2.3 Grounding and potential connection...
More informationA METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS
A METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS Joseph J. Stupak Jr, Oersted Technology Tualatin, Oregon (reprinted from IMCSD 24th Annual Proceedings 1995) ABSTRACT The
More informationFUNCTIONS OF THE NERVOUS SYSTEM 1. Sensory input. Sensory receptors detects external and internal stimuli.
FUNCTIONS OF THE NERVOUS SYSTEM 1. Sensory input. Sensory receptors detects external and internal stimuli. 2. Integration. The brain and spinal cord process sensory input and produce responses. 3. Homeostasis.
More informationThe Neuron and the Synapse. The Neuron. Parts of the Neuron. Functions of the neuron:
The Neuron and the Synapse The Neuron Functions of the neuron: Transmit information from one point in the body to another. Process the information in various ways (that is, compute). The neuron has a specialized
More informationE. K. A. ADVANCED PHYSICS LABORATORY PHYSICS 3081, 4051 NUCLEAR MAGNETIC RESONANCE
E. K. A. ADVANCED PHYSICS LABORATORY PHYSICS 3081, 4051 NUCLEAR MAGNETIC RESONANCE References for Nuclear Magnetic Resonance 1. Slichter, Principles of Magnetic Resonance, Harper and Row, 1963. chapter
More informationAS COMPETITION PAPER 2007 SOLUTIONS
AS COMPETITION PAPER 2007 Total Mark/50 SOLUTIONS Section A: Multiple Choice 1. C 2. D 3. B 4. B 5. B 6. A 7. A 8. C 1 Section B: Written Answer Question 9. A mass M is attached to the end of a horizontal
More informationBiological Membranes. Impermeable lipid bilayer membrane. Protein Channels and Pores
Biological Membranes Impermeable lipid bilayer membrane Protein Channels and Pores 1 Biological Membranes Are Barriers for Ions and Large Polar Molecules The Cell. A Molecular Approach. G.M. Cooper, R.E.
More informationBistability in a Leaky Integrate-and-Fire Neuron with a Passive Dendrite
SIAM J. APPLIED DYNAMICAL SYSTEMS Vol. 11, No. 1, pp. 57 539 c 1 Society for Industrial and Applied Mathematics Bistability in a Leaky Integrate-and-Fire Neuron with a Passive Dendrite Michael A. Schwemmer
More informationCore conductor theory and cable properties of neurons
CHAPTER 3 Core conductor theory and cable properties of neurons I I A Mathematical Research Branch, National Institute of Arthritis, Metabolism, and Digestive Diseuses, National Institutes of Health, Bethesda,
More informationSee Horenstein 4.3 and 4.4
EE 462: Laboratory # 4 DC Power Supply Circuits Using Diodes by Drs. A.V. Radun and K.D. Donohue (2/14/07) Department of Electrical and Computer Engineering University of Kentucky Lexington, KY 40506 Updated
More informationName: Teacher: Olsen Hour:
Name: Teacher: Olsen Hour: The Nervous System: Part 1 Textbook p216-225 41 In all exercises, quizzes and tests in this class, always answer in your own words. That is the only way that you can show that
More informationAnatomy and Physiology Placement Exam 2 Practice with Answers at End!
Anatomy and Physiology Placement Exam 2 Practice with Answers at End! General Chemical Principles 1. bonds are characterized by the sharing of electrons between the participating atoms. a. hydrogen b.
More informationElectricity. Confirming Coulomb s law. LD Physics Leaflets P3.1.2.2. 0909-Wie. Electrostatics Coulomb s law
Electricity Electrostatics Coulomb s law LD Physics Leaflets Confirming Coulomb s law P3... Measuring with the force sensor and newton meter Objects of the experiments Measuring the force between two charged
More informationBasic Scientific Principles that All Students Should Know Upon Entering Medical and Dental School at McGill
Fundamentals of Medicine and Dentistry Basic Scientific Principles that All Students Should Know Upon Entering Medical and Dental School at McGill Students entering medical and dental training come from
More informationAndrew Rosen - Chapter 3: The Brain and Nervous System Intro:
Intro: Brain is made up of numerous, complex parts Frontal lobes by forehead are the brain s executive center Parietal lobes wave sensory information together (maps feeling on body) Temporal lobes interpret
More informationModule 1 : Conduction. Lecture 5 : 1D conduction example problems. 2D conduction
Module 1 : Conduction Lecture 5 : 1D conduction example problems. 2D conduction Objectives In this class: An example of optimization for insulation thickness is solved. The 1D conduction is considered
More informationChapter 8. Movement across the Cell Membrane. AP Biology
Chapter 8. Movement across the Cell Membrane More than just a barrier Expanding our view of cell membrane beyond just a phospholipid bilayer barrier phospholipids plus Fluid Mosaic Model In 1972, S.J.
More informationHomework #11 203-1-1721 Physics 2 for Students of Mechanical Engineering
Homework #11 203-1-1721 Physics 2 for Students of Mechanical Engineering 2. A circular coil has a 10.3 cm radius and consists of 34 closely wound turns of wire. An externally produced magnetic field of
More informationChapter 7: The Nervous System
Chapter 7: The Nervous System Objectives Discuss the general organization of the nervous system Describe the structure & function of a nerve Draw and label the pathways involved in a withdraw reflex Define
More informationChapter 7: Polarization
Chapter 7: Polarization Joaquín Bernal Méndez Group 4 1 Index Introduction Polarization Vector The Electric Displacement Vector Constitutive Laws: Linear Dielectrics Energy in Dielectric Systems Forces
More informationNonlinear Cable Properties of the Giant Axon of the Cockroach Periplaneta americana
Nonlinear Cable Properties of the Giant Axon of the Cockroach Periplaneta americana IDAN SEGEV and ITZCHAK PARNAS From the Neurobiology Department, Institute of Life Sciences, The Hebrew University, Jerusalem,
More informationExercises on Voltage, Capacitance and Circuits. A d = (8.85 10 12 ) π(0.05)2 = 6.95 10 11 F
Exercises on Voltage, Capacitance and Circuits Exercise 1.1 Instead of buying a capacitor, you decide to make one. Your capacitor consists of two circular metal plates, each with a radius of 5 cm. The
More informationAC Transport constant current vs. low impedance modes
Application Note 184-42 AC Transport constant current vs. low impedance modes The AC Transport option offers the user the ability to put the current source in a low output impedance mode. This mode is
More informationHow Brain Cells Work. Part II The Action Potential
How Brain Cells Work. Part II The Action Potential Silvia Helena Cardoso, PhD, Luciana Christante de Mello, MSc and Renato M.E. Sabbatini,PhD Animation and Art: André Malavazzi Electricity is a natural
More information