==============================BIO_ELECTRIC=====================

bioelectric potential         difference in potential between inside and outside cell;
                              potential across the cell wall or membrane. 
cell                          an ionic conductor 
                              separated from outside by semipermeable cell membrane. 
Human cells                   1 micron to 100 microns diameter, 1 millimeter to 1 meter length 
                              typical membrane thickness of 100 Angstrom units. 
internal resting potential    within a cell approximately Ñ90 millivolts reference to outside
                              changes to approximately +20 millivolts for short period during cell activity. 
HodgkinÑHuxley theory,        interior cell primarily contains concentrations of sodium and potassium ions. 
                              These concentrations differ from the concentrations outside the cells 
                              uneven distribution of ionic concentration result in a potential difference 
                              If solutions unequal concent ions separated by semipermeable membrane 
This potential                the gradient	chemical gradient, is given by the  Nernat  relation:
                              Potential (mV) =  61.6*Log( Conc one side membrane/Conc other side )
Nernst relation               for uniÑunivalent ionic solutions, the simplifies to:
                              Potential (mV)   = 61.6*(U Ñ V)/(	U + V)
                              U                = Mobility of negative ions(anions) through membrane
                              V                = Mobility of positive ions (cations) through  membrane
can be confirmed              with a voltmeter  
                              This potential will run down as diffusion proceeds, unlike t a living cell.
Potential (mV)                for a 10:1 activity (concentration) ratio at 370C, 
                              relative mobilities of chloride and sodium ions are 65.4 and 43.6
                              = 61.6*(65.4 Ñ 43.6)/(65.4 + 43.6)
                              = 12 mV
Potential ionic conc          difference between two solutions
                               +   12mV -
                             |~~~~~~M~~~~~~~~|
                             | conc M dilute |
                             | NaCl M NaCl   |
                             |______M________|
                                    -> Na+            Cl- mobilty is greater than Na+
                                    => Cl-       thus Cl- on left and Na+ on Right
sodium and potassium          Typical concentrations ions within a cell.
                              internal  external   permeability  Diffusion    
                              rel conc  rel conc
Sodium                        1         10         lower         into cell    Na+ ionic current\equal
Potassium                     30        1          medium        out of cell  K+  ionic current/
voltage                       gnd      -90mV     

                              relative external  conc Na 01 K 1
                              _____________________
cell concentations            | ___________________ |
                              || relative internal ||<- Na+ ions diffuss in
                              || conc Na 1 K 30    || ->K+  ions diffuse out 
                              ||___________________||
                              |_____________________|<= semiperameable membrane
                              resistance =1/permeability

Semipermeable mebrane         resistance to ionic flow    
                              the iverse of permeability of membrane  to that ion
relative mobilities           chloride and sodium ions are 65.4 and 43.6

inside polarized cell         ionic current     outside  polarized cell 
-90mV                         | cell |          outside is 90mV lower than inside
                              | memb |  
large net                     | <--  | sodium ionic current   produced by large Na+ gradient 
sodium gradient              _|_/\  _|_   low permeability    and low permeabilty
across membrane               |   \/ |
                              |      |
small net                     |  --> |  potassium ionic current   balance by smaller K+ gradient 
potassium gradi              _|_/\  _|_  med permeability         and higer permeabilty
across membrane               |   \/ |

Sodium ionic current          produced by large Na+ gradient and low permeabilty 
                              is balances by smaller K+ gradient and higher permeabity


inside depolarized cell       ionic current    outside depolarized cell
20mV                          | cell |         outside is 20mV higher than inside
                              | memb |
low net                       | <--  | sodium ionic current   produced by small Na+ gradient 
sodium gradient              _|_/\  _|_   high permeability   and high permeabilty
across membrane               |   \/ |
                              |      |
large net                     |  --> |  potassium ionic current   balance by large K+ gradient 
potassium gradi              _|_/\  _|_  med permeability         and medium permeabilty
across membrane               |   \/ |

                              R_d           Dep
electic model                 |___/\  ______o     +   |
                              |380  \/        __/\____|
                              |___/\  ______o/  \/    |
Inside  cell  E_c             |150k \/R_na  Pol   E_na|   Outside cell
                              |                62mV   |
                              |_/\  ________/\________|
                              |1K \/ R_k   +\/ E_k    |
                              |                91mV   |
                              |______||_______________|
                              |      || cell membrane |

E_c                           Intraceluar potential with respect to cout side of the cell
E_k                           Nernst potential due to potassium ionic differential across memebrane
E_Na                          Nernst potential due to sodium ionic differential across memebrane
R_k                           relative permeability of membrane to flow of potassium ions through it
R_Na                          relative permeability of membrane to flow of sodium ions through it
R_d                           relative permeability membrane to flow sodium ions when cell depolarized


values RK, RN5 and RD         are 1 kd, 150 kP and  0.35 k²Oi respectively. 
Potassium ion conc ratio      30:1 inside to outside.
Sodium ion conc ratio         10:1 outside to inside.
                              E_k=	61.6*Log(30/1) = 91 mV ÑÑ by Nernst relation.
                              E_Na = 61.6*Log(10/1) = 62 mV in opposite polarity to E_K ÑÑ Nernst.
For a polarized cell          net potassium current + net sodium current = 0
                              (net potassium gradient)/R_k +	(net sodium gradient)/R_Na  =0
                              
                              potassium   potassium     sodium    sodium
                              chemical  + electrical    chemical + electrical
                              gradient     gradient  +  gradient   gradient
                              _____________________     ____________________   	=0
                                 R_k                          R_Na
                              
                              (E_K + E_C)/R_K + (-E_Na + E_C)/R_na =0
                              (91e3 +	E_C)/(1e3) +(	Ñ62eÑ3 + E_c)/(150e3)	= 0
Solving:                      E_c = 90 x lOÑ3 = Ñ90 mV (polarized)
a depolarized cell            R_na is replaced by R_D.	a
                              E_c= 20 mV (depolarized)
                              
                              Bioeleccric currents due to positive and negative ion movement 
                              within a conductive fluid. 
ions possess finite mass      and encounter resistance to movement within fluid ,speeds are limited. 
                              cell action potential, finite ÒrisetimeÓ and Òfalltime.Ó
                              The ionic concentration gradient across the cell
                              membrane is maintained by virtue of metabolic
                              energy expended by the cell in ÒpumpingÓ ions
                              sodiumÑ	against the ionic gradient formed by the differing
                              potassium	ionic concentrations between the inside and
                              outside pump	of the cell. This action has been referred to as
                              the ÒsodiumÑpotassium pump.Ó

                             
                             
equivalent circuit electrodes                         _____||________
                                                     |     ||        |
                                              1K     |10uF     10K   |
                                                     |               |    ___
                                    _____/\  /\  /\__|__/\  /\  /\___|___|   |
                                   |       \/  \/         \/  \/         |___|
                                   /
                              100  \Bulk     Skin        Double Layer
                                   /Tissue   Resis       Impedance
                                   \                                      ___
                                   |_____/\  /\  /\_____/\  /\  /\_______|   |
                                           \/  \/    |    \/  \/     |   |___|
                                              1k     |           10K |
                                                     | 10uF          |
                                                     |_____||________|
                                                           ||
                            
                             
                             
                             
                             
                             
                                        depolar     repolar
                                    |
                                    |   <--1msec-><--1msec-->
                                    |
                                20mV|            |\
                                    |           |  \
                                 0mV|____________________________
                                    |          |    \
                                    |          |    \
                                    |         |      \
                                    |         |      \
                                    |        |        \
                                    |threshol|        \
                                60mV|......../         \
                                    |       /          \
                                    |      /            \
                                    |     /             \
                                -90m| ___/               \____
                             
                                           _______
                                     _____|       |_______ stimulus
                                                           current
                             
 

ECG  20mV/mV  
50mm/s             0.5mV  80mV   P TA Q S R T U U wave unknown orgin

                                                       R
       .^....^.........................................^...............
        |   | |                                       | |
       0.5mV| |  90ms                                 | |
        |   | | <->                                   | |
        V...| |.......................................| |..............
            | |                                       | |
            | |       ___                             | |       ___
            | |      /   \    __              _-_  TA | |      /   \    __              _-_
          _ | | ____/     \__/  \____________/   \___ | | ____/     \__/  \____________/   \
           \| |/                                     \| |/
                                               P      Q S         T     U        U wave unknown orgin
P wave -artial depolariztion                 <--->
TA wave -artial repolarization may occur          <--->
PR interval -artial-ventricular              <-------->
            conduction time  0.12-0.22
QRS segment -ventricular depolarization 0.1s max      <->   
T wave  ventricular repolarization                            <------>
ST segment -iso electric                                 <----------->
QT intrerval